SECOND EDITION
ABSORPTION CHILLERS AND HEAT PUMPS
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SECOND EDITION
ABSORPTION CHILLERS AND HEAT PUMPS Keith E. Herold
University of Maryland, College Park, USA
Reinhard Radermacher
University of Maryland, College Park, USA
Sanford A. Klein
University of Wisconsin, Madison, USA
CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20160211 International Standard Book Number-13: 978-1-4987-1435-8 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
Contents List of Figures..................................................................................................................................xi List of Tables................................................................................................................................. xix List of Examples......................................................................................................................... xxiii List of EES Files........................................................................................................................... xxv Preface.......................................................................................................................................... xxix About the Authors...................................................................................................................xxxiii Nomenclature............................................................................................................................ xxxv 1. Introduction..............................................................................................................................1 1.1 Heat Pumps.....................................................................................................................1 1.2 Heat-Driven Heat Pumps..............................................................................................3 1.3 Description of Current Absorption Chiller Products...............................................4 1.3.1 Water/Lithium Bromide Chillers...................................................................4 1.3.2 Ammonia/Water Chillers...............................................................................5 1.3.3 Ammonia/Water/Hydrogen Refrigerators...................................................5 1.4 Overview of Absorption Technology Market Trends..............................................5 2. Absorption Cycle Fundamentals..........................................................................................7 2.1 Carnot Cycles..................................................................................................................7 2.2 Absorption Heat Pump, Type I....................................................................................9 2.3 Absorption Heat Pump, Type II................................................................................. 11 2.4 Absorption Heat Pump as Combination of Rankine Cycles................................. 12 2.5 Reversible Analysis with Variable Temperatures.................................................... 13 2.6 Irreversibilities in Absorption Cycle Processes....................................................... 14 2.7 Zero-Order Absorption Cycle Model........................................................................ 15 2.8 Absorption Cycle Design Optimization................................................................... 20 Homework Problems............................................................................................................. 21 References................................................................................................................................22 3. Properties of Working Fluids.............................................................................................. 23 3.1 Analytical Treatment of Thermodynamic Properties............................................ 24 3.1.1 Property Relations for Systems of Fixed Composition.............................. 25 3.1.2 Open-System Property Relations................................................................. 27 3.1.3 Equations of State........................................................................................... 31 3.1.3.1 Thermodynamic Consistency....................................................... 33 3.1.4 Mixture Volume..............................................................................................34 3.1.5 Mixture Energy Properties............................................................................ 36 3.1.5.1 Specific Heat..................................................................................... 38 3.1.5.2 Reference States............................................................................... 39 3.1.6 Mixture Entropy............................................................................................. 40 3.1.7 Phase Equilibrium..........................................................................................43 3.1.7.1 Heat of Vaporization.......................................................................43 3.1.8 Summary.......................................................................................................... 49 v
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3.2
Graphical Perspective on Thermodynamic Properties of Absorption Working Fluids............................................................................................................. 50 3.2.1 Temperature–Mass Fraction Diagram......................................................... 50 3.2.2 Pressure–Temperature Diagram................................................................... 55 3.2.3 The Enthalpy–Mass Fraction Diagram........................................................ 57 3.3 Transport Properties.................................................................................................... 59 Homework Problems.............................................................................................................61 References................................................................................................................................ 62 4. Thermodynamic Processes with Mixtures......................................................................65 4.1 Mixing of Fluids and the Heat of Mixing.................................................................65 4.2 Specific Heat of Mixtures............................................................................................ 68 4.3 Desorption.................................................................................................................... 69 4.4 Absorption.................................................................................................................... 75 4.5 Condensation and Evaporation..................................................................................80 4.6 Compression................................................................................................................. 81 4.7 Pumping........................................................................................................................ 82 4.8 Throttling......................................................................................................................83 4.9 Ammonia Purification................................................................................................. 86 4.9.1 Reflux Cooling or Partial Condensation...................................................... 86 4.9.2 Rectification.....................................................................................................90 4.10 Heat Exchangers......................................................................................................... 101 4.10.1 Heat Exchanger Diagrams........................................................................... 102 4.10.2 Heat Exchanger Models............................................................................... 103 4.10.3 UA-Type Heat Exchanger Models.............................................................. 103 4.10.4 Effectiveness Type Heat Exchanger Models............................................. 104 Homework Problems...........................................................................................................105 References.............................................................................................................................. 106 5. Overview of Water/Lithium Bromide Technology....................................................... 107 5.1 Fundamentals of Operation..................................................................................... 107 5.1.1 Solution Circuit............................................................................................. 107 5.1.2 Refrigerant Leg.............................................................................................. 109 5.2 Crystallization and Absorber Cooling Requirements.......................................... 110 5.3 Corrosion and Materials Compatibility.................................................................. 111 5.4 Vacuum Requirements.............................................................................................. 112 5.4.1 Component Size............................................................................................ 115 5.4.2 Effect of Nonabsorbable Gases................................................................... 116 5.4.3 Hydrostatic Head Effects in Evaporator Design...................................... 117 5.5 Octyl Alcohol.............................................................................................................. 117 5.6 Normal Maintenance and Expected Life............................................................... 119 5.7 Controls....................................................................................................................... 120 Homework Problems........................................................................................................... 120 References.............................................................................................................................. 121 6. Single-Effect Water/Lithium Bromide Systems............................................................ 123 6.1 Single-Effect Water/Lithium Bromide Chiller Operating Conditions............... 123 6.1.1 Mass Flow Analysis...................................................................................... 125 6.1.2 Thermodynamic States within the Cycle.................................................. 126
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6.1.3 6.1.4
Energy Balance Analysis............................................................................. 128 Discussion of the Operating Conditions................................................... 129 6.1.4.1 Dühring Plot Representation....................................................... 129 6.1.4.2 Temperatures................................................................................. 130 6.1.4.3 Mass Fractions............................................................................... 130 6.1.4.4 Solution Heat Exchanger.............................................................. 131 6.2 Single-Effect Cycle with Heat Transfer Models..................................................... 132 6.2.1 Heat Exchanger Models............................................................................... 134 6.2.2 Cycle Performance........................................................................................ 137 6.2.3 Desorber Inlet Temperature Variations..................................................... 137 6.2.4 Evaporator Temperature Variations........................................................... 140 6.2.5 Rejection Temperature Variations.............................................................. 141 6.2.6 Solution Flow Rate Variations..................................................................... 142 6.2.7 Heat Transfer Loop Flow Rate Variations................................................. 143 6.2.8 Evaporator–Absorber Pressure Drop Variations...................................... 144 6.2.9 Heat Exchanger Size Variations.................................................................. 144 6.2.10 Summary of Single-Effect Operating Conditions.................................... 148 6.3 Single-Effect Water/Lithium Bromide Heat Transformer (Type II Heat Pump).................................................................................................. 148 6.3.1 Solution Heat Exchanger Size Effects........................................................ 154 6.4 Discussion of Available Single-Effect Systems...................................................... 154 Homework Problems........................................................................................................... 155 References.............................................................................................................................. 156 7. Double-Effect Water/Lithium Bromide Technology.................................................... 157 7.1 Double-Effect Water/Lithium Bromide Cycles...................................................... 157 7.2 Solution Circuit Plumbing Options......................................................................... 160 7.3 Operating Conditions of Double-Effect Machines................................................ 162 7.3.1 Parallel Flow Double-Effect Machines...................................................... 162 7.3.2 Series Flow Double-Effect Machines......................................................... 167 7.4 Systems on the Market.............................................................................................. 169 Homework Problems........................................................................................................... 170 References.............................................................................................................................. 171 8. Advanced Water/Lithium Bromide Cycles..................................................................... 173 8.1 Half-Effect Cycle........................................................................................................ 173 8.2 Triple-Effect Cycle...................................................................................................... 177 8.3 Resorption Cycle........................................................................................................ 181 Homework Problems........................................................................................................... 184 References.............................................................................................................................. 185 9. Single-Stage Ammonia/Water Systems.......................................................................... 187 9.1 Properties of Ammonia and Safety Concerns....................................................... 187 9.2 Material Considerations............................................................................................ 188 9.3 Water Content of the Refrigerant Vapor................................................................. 188 9.4 Simple Single-Stage Ammonia/Water System...................................................... 192 9.5 Measures to Improve Single-Stage Performance................................................... 196 9.5.1 Condensate Precooler................................................................................... 196 9.5.2 Rectifier Heat Integration............................................................................ 202
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9.5.3 Solution Recirculation.................................................................................. 204 9.5.4 Solution-Cooled Absorber........................................................................... 208 9.6 Comparison of Ammonia/Water and Water/Lithium Bromide......................... 208 9.7 Examples of Ammonia/Water Absorption Systems in Operation..................... 210 Homework Problems........................................................................................................... 212 References.............................................................................................................................. 212 10. Two-Stage Ammonia/Water Systems.............................................................................. 215 10.1 Double-Effect Ammonia/Water Systems............................................................... 215 10.2 Double-Lift Ammonia/Water Systems................................................................... 224 10.3 Two-Stage, Triple-Effect Ammonia/Water System............................................... 226 Homework Problems........................................................................................................... 232 References.............................................................................................................................. 232 11. Generator/Absorber Heat Exchange Cycles................................................................... 235 11.1 Concepts, Configurations, and Design Considerations....................................... 235 11.2 Branched GAX Cycle................................................................................................. 245 11.3 GAX Cycle Hardware................................................................................................ 251 Homework Problems........................................................................................................... 252 References.............................................................................................................................. 252 12. Diffusion–Absorption Cycle............................................................................................. 255 12.1 Introduction................................................................................................................ 255 12.2 Cycle Physics............................................................................................................... 256 12.3 Choice of the Auxiliary Gas..................................................................................... 259 12.4 Total Pressure of the System..................................................................................... 260 12.5 Cycle Performance..................................................................................................... 261 References.............................................................................................................................. 262 13. Applications of Absorption Chillers and Heat Pumps............................................... 265 13.1 Industrial Waste Heat Utilization............................................................................ 265 13.2 Gas Turbine Inlet Air Cooling.................................................................................. 266 13.3 Solar Absorption Cooling......................................................................................... 268 References.............................................................................................................................. 269 Appendix A: Using EES (Engineering Equation Solver) to Solve Absorption Cycle Problems............................................................................................................................ 271 A.1 Overview..................................................................................................................... 271 A.2 Recommended Way to Use EES (Example Problem 2.2)...................................... 271 A.3 Property Data in EES................................................................................................. 276 A.4 Lithium Bromide/Water Property Libraries.......................................................... 277 A.5 Ammonia/Water Property Library......................................................................... 282 A.6 Coaxing a Set of Equations to Converge (Example 10.1)......................................284 A.7 Conclusion................................................................................................................... 287 References.............................................................................................................................. 287 Appendix B: Absorption Cycle Modeling............................................................................. 289 B.1 Introduction................................................................................................................ 289 B.2 Mass Balance Considerations................................................................................... 289 B.3 Energy Balances......................................................................................................... 296
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ix
B.4 Heat Transfer Processes............................................................................................ 296 B.5 Equation and Variable Counting............................................................................. 297 B.6 Convergence Issues and the Importance of Selecting an Initial Guess............. 302 B.7 Equation Solvers......................................................................................................... 303 References..............................................................................................................................304 Appendix C: Modeling a Water/Lithium Bromide Absorption Chiller..........................305 C.1 Mass Balances.............................................................................................................305 C.2 Temperature Inputs...................................................................................................305 C.3 Energy Balances.........................................................................................................308 C.4 UA Models..................................................................................................................309 C.5 Summary..................................................................................................................... 312 Appendix D: Modeling an Ammonia/Water Absorption Chiller.................................... 313 Appendix E: The ABSIM Software Package......................................................................... 323 E.1 Overview..................................................................................................................... 323 E.2 Introduction to ABSIM.............................................................................................. 324 E.3 ABSIM Program Structure....................................................................................... 325 E.4 Selected Examples of ABSIM Simulations............................................................. 328 E.4.1 LiBr–Water Cycles......................................................................................... 328 E.4.2 Water–Ammonia Cycles.............................................................................. 330 E.4.3 LiCl–H2O Open and Hybrid Cycles........................................................... 332 References.............................................................................................................................. 333 Appendix F: Vapor Surfactant Theory................................................................................... 335 F.1 Introduction................................................................................................................ 335 F.2 Background................................................................................................................. 335 F.3 Vapor Surfactant Theory........................................................................................... 336 F.4 Key Experimental Results.........................................................................................340 F.4.1 Drop Proximity Experiment.......................................................................340 F.4.2 Active Surface Experiment..........................................................................340 F.4.3 Surface Tension Measurements.................................................................. 341 F.4.4 Effect of Flux on Enhancement...................................................................342 F.5 Modeling Marangoni Flows with Vapor Surfactant Effects................................343 F.6 Summary.....................................................................................................................344 References..............................................................................................................................344 Index��������������������������������������������������������������������������������������������������������������������������������������������� 347
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List of Figures 1.1 Single-effect absorption cycle schematic.............................................................................2 1.2 Vapor compression heat pump.............................................................................................2 1.3 Type I heat pump....................................................................................................................3 1.4 Type II heat pump...................................................................................................................4 2.1 The Carnot cycle for power generation on a temperature–entropy diagram................8 2.2 The Carnot cycle for heat pumping on a temperature–entropy diagram......................9 2.3 I dealized representation of an absorption heat pump as the combination of a Carnot heat engine and a Carnot heat pump................................................................ 10 2.4 C arnot cycles for a combined power generation/heat-pumping facility such as an absorption heat transformer..................................................................................... 11 2.5 Illustration of the combination of two Rankine cycles to a combined system............ 12 2.6 Temperature versus cumulative heat transfer rate for condensation of steam at 100 kPa from 150°C to 50°C............................................................................................. 14 2.7 Zero-order model schematic............................................................................................... 16 2.8 Cooling COP for a single-effect absorption machine...................................................... 18 2.9 T emperatures associated with zero-order model of a single-effect Type I absorption heat pump.......................................................................................................... 18 3.1 Chemical potential for an ideal mixture........................................................................... 31 3.2 Volume versus mass fraction for ammonia/water.......................................................... 35 3.3 Enthalpy versus mass fraction............................................................................................ 37 3.4 Entropy of mixing for an ideal mixture............................................................................42 3.5 NH3/H2O bubble-point diagram with an example of the cooling of a superheated vapor mixture with initial dew formation..............................................44 3.6 Differential vaporization process....................................................................................... 45 3.7 Total evaporation process.................................................................................................... 46 3.8 Mass transfer in total evaporation process....................................................................... 48 3.9 Heat transfer and mass fractions in total evaporation process...................................... 48 3.10 Enthalpy–mass fraction diagram for water/lithium bromide..................................... 50 3.11 Enthalpy–mass fraction diagram for ammonia/water.................................................. 51 3.12 Schematic of temperature–concentration diagram (bubble-point diagram)............. 52 3.13 Evaporation process in temperature–concentration diagram...................................... 52 xi
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List of Figures
3.14 Size of temperature glide dependence on boiling point difference............................54 3.15 S chematic of the temperature–concentration diagrams for two variations of an azeotropic mixture....................................................................................................54 3.16 Pressure–temperature plots for pure ammonia and pure water................................. 55 3.17 Pressure–temperature diagram for water/lithium bromide........................................ 56 3.18 Pressure–temperature diagram for ammonia/water.................................................... 56 3.19 S chematic of an enthalpy–concentration diagram for a generic mixture showing a single isobar...................................................................................................... 57 3.20 S chematic for finding the saturated vapor mass fraction from a given saturated liquid mass fraction using the auxiliary line................................................ 58 3.21 Thermal conductivity of aqueous lithium bromide...................................................... 59 3.22 Dynamic viscosity of aqueous lithium bromide............................................................ 59 3.23 Thermal conductivity of ammonia/water...................................................................... 60 3.24 Dynamic viscosity of ammonia/water............................................................................ 60 4.1 Steady-state mixing of two fluid streams.......................................................................... 66 4.2 Constant pressure mixing process on an enthalpy–mass fraction diagram............... 66 4.3 Desorption process............................................................................................................... 69 4.4 D esorption process in an h–x diagram for a mixture such as NH3/H2O, where both components are volatile.................................................................................. 71 4.5 Graphical representation of the desorber heat requirement at constant pressure.........................................................................................................................72 4.6 Desorption process in h–x diagram with subcooled inlet stream................................. 72 4.7 Absorption process............................................................................................................... 76 4.8 A bsorption in h–x diagram with saturated inlet and outlet liquid streams and saturated vapor.............................................................................................................. 76 4.9 A bsorption process in h–x diagram with two-phase solution inlet, saturated liquid outlet, and saturated vapor inlet.............................................................................77 4.10 Adiabatic absorption.......................................................................................................... 78 4.11 Throttling process...............................................................................................................83 4.12 Reflux cooler........................................................................................................................ 87 4.13 Reflux cooling process in an enthalpy–mass fraction diagram................................... 88 4.14 Distillation column.............................................................................................................90 4.15 T he pole of rectification determined by extending the line that connects the vapor and liquid states at one cross section of the column till it intersects with the isostere of the purified vapor............................................................................ 93 4.16 Determination of the pole of rectification....................................................................... 94
List of Figures
xiii
4.17 D etermination of the number of theoretical plates. In this case, the rectification column has two theoretical plates.............................................................. 95 4.18 Counterflow desorber to minimize need for rectification............................................ 96 4.19 Rectifier column with zero plates..................................................................................... 97 ectifier column with one theoretical plate shown as a bubble cap........................... 97 4.20 R 4.21 R ectifier diagram for column with one theoretical plate.............................................. 99 4.22 Sensitivity of the pole position to the feed concentration.......................................... 101 4.23 Typical counterflow heat exchanger.............................................................................. 102 5.1 Single-effect absorption cycle schematic......................................................................... 108 5.2 Aqueous lithium bromide phase diagram...................................................................... 110 5.3 Vacuum terminology and units........................................................................................ 113 5.4 Cold trap design schematic............................................................................................... 114 5.5 Ejector purge system.......................................................................................................... 117 6.1 Cycle schematic of a single-effect water/lithium bromide absorption chiller........... 124 6.2 H ardware schematic of a single-effect water/lithium bromide absorption chiller........................................................................................................ 124 6.3 Dühring plot for cycle solution......................................................................................... 130 6.4 Cooling COP and solution heat exchanger heat transfer rate versus solution heat exchanger effectiveness for a single-effect chiller................................................. 131 6.5 S ingle-effect water/lithium bromide absorption chiller with external heat transfer models................................................................................................................... 132 6.6 Heat exchanger diagram for evaporator.......................................................................... 134 6.7 Heat exchanger diagram for condenser........................................................................... 135 6.8 Heat exchanger diagram for desorber............................................................................. 136 6.9 Heat exchanger diagram for absorber............................................................................. 137 6.10 E ffect of desorber inlet temperature on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 138 6.11 E ffect of desorber inlet temperature on heat transfer rates for a single-effect water/lithium bromide absorption chiller.......................................... 138 6.12 E ffect of desorber inlet temperature on temperature for a single-effect water/lithium bromide absorption chiller.......................................... 139 6.13 E ffect of chilled water inlet temperature on COP and capacity for a single-effect water/lithium bromide a bsorption chiller.......................................... 140 6.14 E ffect of cooling water inlet temperature on COP and capacity for a single-effect water/lithium bromide a bsorption chiller.......................................... 141
xiv
List of Figures
6.15 E ffect of solution pump flow rate on COP, capacity, and solution heat exchanger heat transfer rate for a single-effect water/lithium bromide absorption chiller.............................................................................................................. 142 6.16 E ffect of desorber heat transfer fluid flow rate on COP and capacity for a single-effect water/lithium bromide a bsorption chiller.......................................... 144 6.17 E ffect of pressure drop between evaporator and absorber on COP and capacity for a single-effect water/lithium bromide absorption chiller..................... 145 6.18 E ffect of desorber heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 145 6.19 E ffect of absorber heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 146 6.20 Effect of condenser heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 146 6.21 Effect of evaporator heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 147 6.22 E ffect of solution heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.......................................... 147 6.23 Single-effect water/lithium bromide temperature booster heat pump (Type II absorption cycle) with external heat transfer models.................................. 150 6.24 Dühring plot for the cycle solution................................................................................ 152 6.25 Adiabatic absorption temperature calculation schematic.......................................... 153 6.26 Effect of solution heat exchanger effectiveness on COP and capacity of the Type II cycle............................................................................................................ 154 7.1 D ouble-effect water/lithium bromide chiller Dühring chart schematic (parallel flow)....................................................................................................................... 158 7.2 D ouble-effect water/lithium bromide chiller piping chart schematic (parallel flow)....................................................................................................................... 161 7.3 S eries flow double-effect water/lithium bromide chiller Dühring chart schematic showing state points (solution to high desorber first)................................. 161 7.4 S eries flow double-effect water/lithium bromide chiller Dühring chart schematic (solution to low desorber first)........................................................................ 162 7.5 P arallel flow double-effect water/lithium bromide chiller Dühring chart schematic showing state points......................................................................................... 163 7.6 D ühring state plot for baseline double-effect water/lithium bromide example from Section 7.3.1 (parallel flow)....................................................................... 166 7.7 P arallel-flow double-effect absorption chiller performance as a function of the desorber inlet temperature..................................................................................... 167 8.1 Cycle schematic for the half-effect cycle.......................................................................... 174 8.2 Dühring plot for the half-effect cycle.............................................................................. 175
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xv
8.3 Cycle schematic for the triple-effect cycle....................................................................... 178 8.4 Dühring plot for the triple-effect cycle............................................................................ 180 8.5 Cycle schematic for the resorption cycle......................................................................... 182 8.6 Dühring plot for the resorption cycle.............................................................................. 184 9.1 Single-stage ammonia/water cycle.................................................................................. 189 ingle-stage ammonia/water cycle showing effect of water accumulation 9.2 S in evaporator........................................................................................................................ 189 9.3 Simple single-stage ammonia/water cycle with rectifier............................................. 193 9.4 Ammonia/water absorption cycle with a condensate precooler................................. 196 9.5 E vaporator temperature glide as a function of exit quality for an overall inlet mass fraction of 0.99 at 4 bar............................................................................................. 197 9.6 Single-stage ammonia/water cycle with integrated rectifier....................................... 202 9.7 Solution recirculation in desorber (thick lines)............................................................... 205 9.8 Solution recirculation in absorber (thick lines)............................................................... 206 9.9 Solution-cooled absorber.................................................................................................... 208 9.10 Residential ammonia/water air conditioner with solution-cooled absorber........... 209 9.11 Ammonia/water single-stage unit for refrigerated warehouse................................. 211 9.12 Ammonia/water single-stage unit used in dairy industry........................................ 211 wo-stage double-effect ammonia/water absorption system; R2 and R3 are 10.1 T the high- and low-temperature s ections of the second-stage rectifier...................... 216 10.2 Two-stage absorption cycle with bleed line (stream 28).............................................. 217 10.3 Necessity for double-lift system..................................................................................... 224 10.4 Double-lift configuration.................................................................................................225 10.5 Two-stage, triple-effect ammonia/water system.......................................................... 227 10.6 Triple-effect, two-stage absorption air conditioner..................................................... 228 11.1 GAX concept...................................................................................................................... 236 11.2 Generator/absorber heat exchange (GAX) cycle.......................................................... 236 11.3 Generator/absorber heat exchange (GAX) cycle origins............................................. 237 11.4 GAX cycle with absorber solution recirculation.......................................................... 238 11.5 Heat and mass transfer in the desorber/absorber heat exchanger............................ 241 11.6 GAX absorber and desorber as vertical components with heat transfer loop......... 242 11.7 GAX cycle cooling COP versus approach temperature difference............................ 243 11.8 GAX cycle heat transfer results....................................................................................... 243
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List of Figures
11.9 T ransition from GAX to single-stage cycle at constant heat rejection temperature........................................................................................................................ 244 11.10 G AX mismatch: amount of heat available and amount of heat required in GAX temperature overlap region................................................................................. 246 11.11 Branched GAX cycle....................................................................................................... 247 11.12 COP versus approach temperature for branched GAX cycle................................... 249 11.13 Branched GAX results.................................................................................................... 249 11.14 E nergy mismatch between the absorber and the desorber for an approach temperature difference of 5 K................................................................. 250 11.15 Cooling COP versus heat rejection temperature........................................................ 251 11.16 Heating COP versus evaporator temperature............................................................. 251 12.1 Three loops in diffusion absorption refrigerator......................................................... 257 12.2 Diffusion–absorption refrigerator hardware schematic............................................. 258 12.3 Schematic diagram of a bubble pump........................................................................... 259 12.4 Measured DAR performance versus input power....................................................... 262 Overview of industrial waste heat utilization options, including 13.1 absorption heat pumps.................................................................................................... 266 13.2 Two-stage 10 MW absorption cooling plant installed in Egypt................................ 267 Gas turbine power plant with absorption inlet air cooling........................................ 268 13.3 A.1 Plot of specific enthalpy versus mass fraction of lithium bromide at 10°C and 100°C............................................................................................................... 281 A.2 Schematic of a two-stage absorption system with condensate precooling............... 285 B.1 Schematic of single-effect cycle with external heat transfer processes...................... 290 B.2 Schematic of single-effect cycle without external heat transfer processes (internal model).................................................................................................................. 291 B.3 Mass flows in simple single-effect cycle......................................................................... 293 B.4 Mass flows in a double-effect cycle................................................................................. 293 B.5 Mass balance equation counting schematic with control volumes............................ 294 B.6 Mass balance schematic for resorption cycle................................................................. 295 B.7 Mass balance schematic for single-stage ammonia/water cycle................................. 295 C.1 Schematic of a water/lithium bromide absorption chiller.......................................... 306 C.2 S chematic of a water/lithium bromide absorption chiller including heat exchanger models at the four corner components in the cycle................................... 310 D.1 Schematic of an ammonia/water absorption chiller.................................................... 314 E.1 Screen view of the ABSIM program................................................................................ 327
List of Figures
xvii
E.2 Schematic description of a 4-effect LiBr–H2O absorption cycle.................................. 329 E.3 S chematic description of the GAX cycle according to the configuration proposed by Phillips (1990)............................................................................................... 331 E.4 S chematic description of a hybrid air-conditioning cycle comprising a vapor compression system for cooling and an LiCl–H2O liquid desiccant system for dehumidification.......................................................................................................... 333 F.1 S chematic of the surface tension measurement facility designed to control the surfactant vapor concentration................................................................................... 341 F.2 S urface tension data for 60% lithium bromide in water obtained from the apparatus in Figure F.1 showing the strong effects of vapor concentration and drop frequency............................................................................................................342 F.3 H eat transfer coefficient versus surfactant liquid concentration showing the effect of heat flux..........................................................................................................343
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List of Tables 2.1 Irreversible Effects in Absorption Technology................................................................. 15 2.2 COP Predictions from the Zero-Order Model Assuming a Balanced Conductance Design ........................................................................................................... 20 3.1 Absorption Working Fluid Properties............................................................................... 24 3.2 Property Routines Used in This Book............................................................................... 49 4.1 Properties of Ammonia/Water at the State Points Defined in Figure 4.3.................... 73 4.2 Properties of Ammonia/Water at the State Points According to Figure 4.7................ 78 4.3 Data for the Reflux Cooler................................................................................................... 89 4.4 Result for Rectifier with Zero Plates (Reflux Cooler Only)............................................. 98 4.5 Result for Rectifier with One Plate..................................................................................... 98 4.6 Result for Rectifier with Two Plates................................................................................... 98 4.7 Result for Rectifier with Three Plates.............................................................................. 100 6.1 Operating Conditions for a Single-Effect Water/Lithium Bromide Machine ........... 125 6.2 Thermodynamic State-Point Summary for the Simulation................................................127 6.3 Operating Conditions for a Single-Effect Water/Lithium Bromide Cycle with Heat Exchangers ................................................................................................................ 133 6.4 Baseline Inputs Defining Single-Effect Operating Conditions.................................... 134 6.5 C omparison of Condenser and Absorber Coolant Piping Configurations................ 142 6.6 S ingle-Effect Type II Operating Conditions.................................................................... 149 6.7 Thermodynamic State-Point Summary........................................................................... 150 6.8 Baseline Inputs Defining Type II Operating Conditions.............................................. 151 7.1 C omparison of Parallel and Series Solution Flow for Double-Effect Water/Lithium Bromide Cycles ....................................................................................... 162 7.2 State-Point Summary for Parallel Flow Double-Effect Cycle........................................ 164 7.3 Inputs for the Parallel Flow Double-Effect Cycle Model............................................... 164 7.4 B aseline Operating Conditions for a Parallel Flow Double-Effect Water/Lithium Bromide Machine......................................................................................................................165 7.5 O perating Conditions for a Series Flow Double-Effect Water/Lithium Bromide Machine................................................................................................................................ 168 8.1 Operating Conditions for the Half-Effect Cycle............................................................. 175 8.2 Input Summary for Half-Effect Model............................................................................ 176 xix
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List of Tables
8.3 Inputs for the Triple-Effect Cycle Model......................................................................... 178 8.4 Operating Conditions for the Triple-Effect Cycle.......................................................... 179 8.5 Inputs for the Resorption Cycle Model............................................................................ 182 8.6 Operating Conditions for the Resorption Cycle............................................................. 183 9.1 Data for Example 9.1 Showing Evaporator Temperature Glide.................................... 192 9.2 State Points for the Ammonia/Water System of Example 9.2 and Figure 9.3............ 195 9.3 S tate Points for the Ammonia/Water System of Example 9.3, Which Includes a Condensate Precooler...................................................................................................... 198 9.4 C ombined Effects of Condensate Precooler and Rectifier Using an Internal Model................................................................................................................ 200 9.5 Combined Effects of Condensate Precooler and Rectifier Using UA Model............. 201 9.6 S tate Points for the Ammonia/Water System of Example 9.5 Including Rectifier Heat Integration................................................................................................... 203 9.7 S tate Points for the Ammonia/Water System According to Figure 9.8 Using Rectifier Heat Integration and Solution Recirculation within the Absorber.............. 207 10.1 Summary of Inputs for Example 10.1............................................................................. 218 10.2 S tate Points for the Ammonia/Water System According to Figure 10.1 and Ex10_1.ees...................................................................................................................222 10.3 Summary Data from Example 10.1 Organized by Stage.............................................223 10.4 State Points for the Two-Stage Triple-Effect Ammonia/Water System..................... 229 10.5 Summary Data from Example 10.2 Organized by Stage............................................. 230 11.1 S tate Points for the Ammonia/Water GAX Cycle According to Example 11.1, Figure 11.4, and Ex11_1.ees.............................................................................................. 240 11.2 S tate Points for the Branched GAX Cycle According to Figure 11.11 (Approach Temperatures 0 K) and Ex11_3.ees............................................................. 248 13.1 Comparison of Three Solar Cooling Options............................................................... 269 A.1 Summary of LiBrSSC Routines........................................................................................ 278 A.2 Summary of LiBrSSC Helper Functions......................................................................... 278 A.3 Calling Ammonia/Water Property Routines in EES Using a Simplified Interface...................................................................................................................... 282 B.1 Model Inputs and Outputs............................................................................................... 290 B.2 Mass and Energy Balances for Cycle............................................................................... 292 B.3 Nonredundant Set of Mass Balances for System........................................................... 293 B.4 Variables, Equations, and Inputs in the Single-Effect Model....................................... 298 B.5 Variables, Equations, and Inputs in the Single-Effect Model of Figure B.2 (Internal Model).................................................................................................................. 301
List of Tables
xxi
C.1 Mass Balance Formulation................................................................................................306 C.2 M ass Balance Solution Based on Formulation............................................................... 307 C.3 Temperature Inputs........................................................................................................... 307 C.4 Results after Entering Temperature Inputs.................................................................... 307 C.5 Energy Balance Formulation............................................................................................308 C.6 Evaluation of Specific Enthalpies.....................................................................................308 C.7 Three Final Models to Complete the Cycle Model........................................................309 C.8 Complete Solution for the Internal Cycle Model.................................................................309 C.9 UA Model Calculations Used as Inputs.......................................................................... 310 C.10 Results from Initial UA Model....................................................................................... 311
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List of Examples 2.1 Determine Minimum Heat Input Temperature............................................................... 19 2.2 Absorption Cycle Optimization......................................................................................... 21 3.1 Relationship between Partial Molal and Partial Mass Properties................................. 28 3.2 Thermodynamic Consistency.............................................................................................34 3.3 Total Evaporation of Ammonia/Water Mixture.............................................................. 47 4.1 Adiabatic Mixing with Water/Lithium Bromide............................................................. 67 4.2 Desorption from NH3/H2O................................................................................................. 73 4.3 Desorption of Water from Aqueous Lithium Bromide................................................... 73 4.4 Absorber Using NH3/H2O................................................................................................... 78 4.5 Absorption of Water Vapor into Aqueous Lithium Bromide......................................... 79 4.6 Condensation and Evaporation of Water..........................................................................80 4.7 Throttling Process with Pure Fluid....................................................................................84 4.8 Throttling Aqueous Lithium Bromide..............................................................................84 4.9 Throttling of Liquid Ammonia/Water..............................................................................85 4.10 Reflux Cooler....................................................................................................................... 89 4.11 Rectifier................................................................................................................................. 96 5.1 Pressure Units...................................................................................................................... 114 7.1 Reversible COP of the Double-Effect Machine............................................................... 159 7.2 Zero-Order Model of a Double-Effect Machine............................................................. 159 9.1 Evaporator Temperature Glide.......................................................................................... 190 9.2 Simple Single-Stage Ammonia/Water System............................................................... 192 9.3 Condensate Precooler......................................................................................................... 198 9.4 Examine Effects of Condensate Precooler and Rectifier............................................... 199 9.5 Rectifier Heat Integration.................................................................................................. 203 9.6 Solution Recirculation in the Absorber............................................................................ 205 10.1 Two-Stage, Double-Effect Ammonia/Water System with Separate Rectifiers......... 217 10.2 Two-Stage, Triple-Effect Ammonia/Water System...................................................... 227 11.1 GAX Cycle.......................................................................................................................... 238
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List of Examples
11.2 Effect of Approach Temperature.................................................................................... 242 11.3 Branched GAX Cycle........................................................................................................ 247 B.1 Resorption Cycle................................................................................................................. 295 B.2 Mass Balances in Ammonia/Water Cycles.................................................................... 295 B.3 Resorption Cycle Equation Counting..............................................................................300
List of EES Files The EES files used in the Examples can be downloaded from F-Chart Software, LLC, http://fchart.com/ees/books.php. File Name
Related Object
Description
Ex2_2.ees Ex3_1.ees
Example 2.2 Example 3.1
Ex3_2.ees Ex3_3.ees Ex3_4a.ees Ex3_4b.ees Ex3_5.ees Sect3_1_4&5.ees Ex4_1_H2OLiBr.ees Ex4_1_NH3H2O.ees Ex4_2_NH3H2O.ees Ex4_3_H2OLiBr.ees Ex4_4.ees Ex4_5.ees Ex4_6_H2O.ees Ex4_6_NH3H2O.ees Ex4_7.ees Ex4_8.ees Ex4_9.ees Ex4_10.ees Ex4_11.ees Ex4_11_0plate.ees Ex4_11_1plate.ees Ex4_11_2 plates.ees Ex4_11_3 plates.ees Ex4_11_fig.ees
Example 3.2 Example 3.3 Example 3.4 Example 3.4 Example 3.5
Zero-order model optimization Relationship between partial molal and partial mass properties Thermodynamic consistency Isobaric total evaporation, Figures 3.8 and 3.9 Properties of aqueous LiBr using SSCLiBr.LIB Properties of aqueous LiBr using LiBrSSC.dll Properties of NH3/H2O, including chemical potential Volume and enthalpy calculations in text Adiabatic mixing with water/LiBr An ammonia/water example related to Example 4.1 Desorption from ammonia/water Desorption from water/LiBr Absorber using ammonia/water Absorber using water/LiBr Condenser and evaporator using water/LiBr An ammonia/water example related to Example 4.6 Throttling of pure water Throttling of water/LiBr solution Throttling of ammonia/water solution Reflux cooler example Works for all four cases by changing m Specific for zero plates, including diagram Specific for one plate, including diagram Specific for two plates, including diagram Specific for three plates, including diagram Generates enthalpy–mass fraction diagram useful for Example 4.11 h–x diagrams related to Example 4.11 Single-effect, Type I internal cycle model Single-effect, Type I cycle model with external heat exchangers Single-effect, Type II cycle model with external heat exchangers Generate Figure 6.4 Generate Figures 6.9 through 6.12 Generate Figures 6.13 through 6.15 Generate Figures 6.16 through 6.21
Example 4.1 Example 4.2 Example 4.3 Example 4.4 Example 4.5 Example 4.6 Example 4.7 Example 4.8 Example 4.9 Example 4.10 Example 4.11 Example 4.11 Example 4.11 Example 4.11 Example 4.11
Fig4_21.ees Ex6_1.ees Ex6_2.ees
Section 6.1 example Section 6.2 example
Ex6_3.ees
Section 6.3 example
Fig6_4.ees Fig6_10 to 6_13.ees Fig6_14 to 6_16.ees Fig6_17 to 6_22.ees
Continued
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File Name Fig6_26.ees Table6_5.ees Ex7_2.ees DBL_effect_P.ees
List of EES Files
Related Object
Example 7.2
DBL_effect_PUA.ees DBL_effect_S1.ees DBL_effect_S1UA.ees DBL_effect_S2.ees DBL_effect_S2UA.ees Fig7_7.ees HALF_effect.ees HALF_effect_UA.ees
Figure 7.7 Table 8.1
TRIPLE_effect.ees RESORPTION.ees Ex9_1.ees Ex9_2.ees Ex9_3.ees Ex9_3_UA.ees Ex9_5.ees Ex9_6.ees Fig9_4.ees Robur.ees Verona.ees Verona mass.ees Ex10_1.ees Ex10_1_mass.ees Ex10_2.ees Ex10_2_mass.ees Ex10_2_plus.ees
Table 8.4 Table 8.6 Example 9.1 Example 9.2 Example 9.3
Ex10_2_mixed.ees Fig10_2.ees Fig10_4.ees Fig10_4_mass.ees Ex11_1.ees Ex11_1_loop.ees Ex11_2.ees Ex11_3.ees Fig11_14.ees App A LiBr example.ees
Example 9.5 Example 9.6 Figure 9.4
Example 10.1 Example 10.2
Example 11.1 Example 11.2 Example 11.3 Figure 11.14
Description Generate Figure 6.25 Generate Table 6_5 Double-effect, zero-order model Parallel flow double-effect model, UA models for external, effectiveness models for SHX Parallel flow double-effect model, UA models for all heat exchangers Series flow double-effect model, high desorber first, UA models for external, effectiveness models for SHX Series flow double-effect model, high desorber first, UA models for all heat exchangers Series flow double-effect model, low desorber first, UA models for external, effectiveness models for SHX Series flow double-effect model, low desorber first, UA models for all heat exchangers Based on DBL_effect_PUA.ees Half-effect cycle model Modified half-effect cycle model to include UA heat exchanger models Triple-effect cycle model Resorption cycle model Temperature glide in evaporator Simple ammonia/water cycle with rectifier Add condensate precooler Example 9.3 modified as a UA model Add rectifier heat integration Add absorber solution recirculation Code to create Figure 9.4 Model of Robur system from Section 9.7 Model of Verona system from first edition Supporting file for Verona analysis (from first edition) Two-stage cycle Mass balances for Example 10.1 Two-stage triple effect Mass balances for Example 10.2 Example 10.2 with two added internal heat exchange options Mixed triple-effect cycle with LiBr/H2O lower stage Model of cycle shown in Figure 10.2 Model of cycle shown in Figure 10.4 Mass balances for cycle in Figure 10.4 GAX cycle performance GAX cycle with heat transfer loop GAX performance vs. heat transfer driving potential Branched GAX performance GAX energy plot Demonstrate how to use property routines for aqueous LiBr Continued
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List of EES Files
File Name
Related Object
App A NH3H2O example.ees AppB_1.ees ExB_1.ees ExB_2.ees ExC_1.ees
Example B.1 Example B.2 Example C.1
ExC_2.ees ExC_3.ees ExC_4.ees ExC_5.ees
Example C.2 Example C.3 Example C.4 Example C.5
Example for Appendix D.ees
Description Demonstrate how to use property routines for ammonia/water Mass balances for Figure B.5 Mass balances for Example B.1 Mass balances for Example B.2 Mass balance formulation, with specified mass fractions Add temperature inputs to ExC_1.ees Add energy balances to ExC_2.ees Convert ExC_3.ees to UA model Change inputs from ExC_4.ees to demonstrate versatility of model Modified version of Example 9.2
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Preface Since the publication of the first edition of this book in 1996, the field of absorption chillers and heat pumps has continued its slow evolution. The primary applications for aqueous LiBr technologies are in building air-conditioning systems, which is a field that is constrained by many forces, including economics, governmental regulations, and the industry knowledge base. The relative importance of these forces varies significantly by geographical regions, resulting in large geographical differences in absorption technology utilization and manufacturing. The US air-conditioning market has, for many years, been dominated by electric-driven systems. The existence of low-cost, dependable electricity in the United States means that there is less motivation to consider gas-fired cooling. However, the seasonal nature of cooling means that peak electric loads typically occur in summer when there is unused natural gas pipeline capacity. Variable electricity demand puts stress on electricity providers, and they charge accordingly, with lower rates for customers with steady consumption. Building cooling is a major factor in demand peaks and, thus, running an all-electric mechanical room often leads to high demand charges. Although electricity rates are generally low in the United States, demand charges do provide an economic motivation to consider gas-fired cooling. Absorption chillers have been used in the United States since the 1950s for these reasons: they provide cooling using an energy source that is generally in low demand in that season. Although the economics works in favor of absorption chillers in some US markets, most of the other forces are arrayed against the technology such that LiBr absorption chillers carry only a small fraction of the cooling market in the United States. One measure of the interest in such systems in the United States is the number of patents on the subject, as shown in the below figure, which shows a low but continuous interest in the subject. 14
US patents issued
12 10 8 6 4
2014
2010
2006
2002
1998
1994
1990
1986
1982
0
1978
2
Year
The major LiBr absorption chiller market today is the Far East (China, Japan, and South Korea). The common characteristic of these diverse markets is that they all have enjoyed regulatory incentives in favor of gas-fired cooling. As a result, they have large and thriving absorption chiller markets with a large domestic manufacturer base. Major fractions of the xxix
xxx
Preface
cooling market are covered by absorption cooling in some locations. The remarkable success of absorption cooling in the Far East markets makes clear that the US experience is a result of the market conditions unique to the United States. The other major absorption working fluid pair is ammonia/water, where ammonia is the refrigerant. Ammonia-based absorption chillers are widespread in the form of recreational vehicles and hotel-room refrigerators. These applications typically utilize the three-fluid system described in Chapter 12. The recreational vehicle market application typically runs on a fuel, such as propane, that is easily transported. The hotel room application typically runs off an electric heater, and the key feature is its silent operation. Ammonia/water chillers for residential cooling have been available for many years, but market penetration is minimal because they compete with low-cost electric drive systems. The performance of these systems has improved somewhat, but they can only compete in markets where low-cost electricity is not available. Ammonia/water provides a wider range of operating conditions than is possible with LiBr-based systems because ammonia does not freeze until –78°C. Thus, a wide range of low-temperature refrigeration applications are possible and have been considered. Ammonia/water heat pumps and chillers also have applications in heat integration in chemical plants and other large-scale process plants. These applications allow utilization of waste heat to provide cooling and/or heating at another location in the plant. The economics of such applications depends on a number of factors, including knowledge of the technology. A small number of ammonia/ water absorption experts can be found around the world who can provide consultations on such projects. Absorption and adsorption systems gained considerable attention in Europe over the last decade. A renewed push to solar energy utilization and the need for gas-fired heat pumps for heating purposes creates a new impetus for sorption technology, resulting in a number of new sorption concepts, products, and companies. The ultimate application for absorption cooling would be one where the machines are driven by waste heat. Applications such as gas turbine inlet air cooling and bottoming cycles for power plants (i.e., utilizing the waste heat from the power plant) come to mind. At current energy costs, waste heat has modest economic value with the result that such applications are not widespread. However, there will likely be a future where fossil fuels are more expensive, due to increased costs of extraction and tax penalties associated with carbon release. As the value of waste heat is expected to follow the value of the primary energy, it may be expected that the value of waste heat will rise in the future. When this occurs, the economic niche for heat-driven refrigeration technologies, such as absorption chillers, may grow as well. Other sources of heat, such as solar, may also play a role in this future. Process heat integration, on various scales, will become more economically viable when the energy costs rise in relation to the capital costs of the equipment. The reality is that the absorption community has been patiently waiting for this energy future, and it has not progressed very rapidly. The most recent developments on the fossil fuel supply side (fracking and directional drilling) seem to promise additional delays since they expand the economic availability of both oil and natural gas. These developments may mean that the status quo, where absorption cooling is a niche technology, is destined to continue for several more decades at least. Continuing patience may be needed for researchers who have invested their efforts, assuming that a different energy future was on the horizon. One of the many attractions of the absorption technology research community is the conference series summarized here. These conferences attract typically a few hundred participants, and they have a very intimate feel. The next conference is expected to take
Preface
xxxi
place in 2017 and will be hosted by Waseda University in Tokyo, Japan. We always enjoy these conferences and hope to meet many of you at the next one. Absorption Chiller Conference Series • • • • • • • • • • • • • •
1980–Stockholm 1982–Berlin 1985–Paris 1988–London 1991–Tokyo 1992–Paris 1994–New Orleans 1997–Montreal 1999–Munich 2002–Shanghai 2005–Denver 2008–Seoul 2011–Padua 2014–College Park
The primary motivation for writing this second edition was to update this book and improve it based on the feedback received from many readers over the years. The basic structure of this book remains the same, but there are extensive changes throughout. In editing the text, we followed the original philosophy, which combines a streamlined discussion of the concepts in the text with detailed examples in the computer files. This design is meant to facilitate a complete understanding while keeping the text readable. Major changes in this second edition of this book include the following: • Details on the vapor surfactant theory, developed after the publication of the first edition, which explains the surfactant enhancement mechanism • Revised computer examples for internal consistency, clarity, and consistency with the latest version of EES • New LiBr/H2O property routines that provide accuracy over a wider range of conditions • New NH3/H2O helper functions in EES that simplify access to the property routines in EES and provide enhanced utility, including integration with the unit system in EES • A new chapter on absorption technology applications, which provides more details than the previous treatment • Rearranged and revised appendices All of the examples were extensively revised with an emphasis on consistency and clarity. The new versions include more extensive internal documentation designed to make the approach used more understandable. For the examples based on LiBr/H2O, the
xxxii
Preface
property routines used in the original edition were replaced by a new set of routines that are accurate over a much wider range of both temperature and concentration. This change results in only minor differences in the predicted energy flows and performance measures coefficient of performance (COP) for most cycles, but it results in a much more versatile starting point for the consideration of cycles that utilize either high-temperature or lowconcentration conditions. The vapor surfactant theory was developed at the University of Maryland during several years following the publication of the first edition in 1996. This theory is a major advance in understanding of the mechanism of action of surfactant additives in absorption systems. The theory is summarized in Chapter 5 and covered in more detail in Appendix F. A new chapter (Chapter 13) is added that covers several absorption cycle applications that have gained traction since the publication of the first edition. These include industrial waste heat utilization, cogeneration, and solar cooling. This chapter is meant to tie this book in with these new developments in the field. Appendices A and B from the first edition have been eliminated because that information can now be found in EES. Thus, these property appendices were superfluous for the new edition. Four appendices are included with the objective of helping the reader better understand absorption cycle model creation in EES. Appendix A is an introduction to EES with an absorption modeling perspective. Appendix B is an updated version of Appendix C from the first edition, which summarizes some of the complexities of absorption cycle modeling. Appendices C and D (for LiBr/H2O and NH3/H2O, respectively) go through model development in more detail than is provided in the text. Appendix D from the first edition has been eliminated because these titration methods are viewed as historical. Appendix F from the first edition was a brief summary of ABSIM, an alternative modeling environment for absorption cycles. The ABSIM appendix is significantly expanded and included as Appendix E in the second edition. Lastly, the vapor surfactant theory forms the subject of Appendix F. Finally, we would like to thank our families for their support of this project. Yanli, Paula, and Jan have endured the effort and contributed through their patient support. Without their support, this would not have been possible. Additional material is available from the CRC Press Web site: https://www.crcpress. com/Absorption-Chillers-and-Heat-Pumps-Second-Edition/Herold-RadermacherKlein/9781498714341. Keith E. Herold University of Maryland Reinhard Radermacher University of Maryland Sanford A. Klein University of Wisconsin–Madison
About the Authors Keith E. Herold started working in absorption refrigeration during his PhD studies at The Ohio State University, Columbus, Ohio. This research focus was motivated by his work at Battelle Memorial Institute, Columbus, Ohio, where he was involved in building and running custom absorption refrigeration cycles under contract to the US Department of Energy, among others. Subsequent to those experiences, he joined the University of Maryland, College Park, Maryland, where he was the director of the Sorption Systems Consortium, which was funded by various companies, including the three largest absorption refrigeration manufacturers in the United States. Dr. Herold has authored approximately 50 publications on the subject of absorption refrigeration. The first edition of Absorption Chillers and Heat Pumps was published by CRC Press in 1996, which predated the development of the important vapor surfactant theory, which describes the mechanism of action of the surfactant additive used in many absorption chillers. One of the motivations for publishing the second edition is to include details of this theory. After publication of the first edition of Absorption Chillers and Heat Pumps, Dr. Herold shifted his research focus toward bioengineering and joined the new Department of Bioengineering at Maryland when it was formed in 2006. Reinhard Radermacher holds a diploma and PhD in physics from the Technical University of Munich, Munich, Germany, and conducts research in heat transfer and working fluids for energy conversion systems—in particular, heat pumps, air conditioners, refrigeration systems, and integrated cooling heating and power systems. His work resulted in nearly 400 publications, as well as numerous invention records and 12 patents. He has coauthored three books on absorption and vapor compression heat pumps. His research includes the development of software for the design and optimization of heat pumps and air conditioners, which is now in use at more than 60 companies worldwide. Dr. Radermacher is Minta Martin professor of Mechanical Engineering and Director and cofounder of the Center for Environmental Energy Engineering (CEEE) at the University of Maryland. He represents the United States at the International Energy Agency Annexes 13, 34, and 40 and is the former vice president of Commission B1 and former president of Commission B2 of the International Institute of Refrigeration (IIR). In February 2015, he was awarded the Institute of Refrigeration (IOR) J&E Hall Gold Medal for his contributions in the field of refrigeration. The IIR awarded Radermacher with the 2015 Gustav Lorentzen Medal for his innovation and development in the field of refrigeration. He received the award at the IIR International Congress of Refrigeration (ICR2015) held in August 2015 in Yokohama, Japan. He is a fellow of the American Society of Heating, Refrigeration, and Air-Conditioning Engineers (ASHRAE) and also holds memberships in the American Society of Mechanical Engineers (ASME), SAE International, formerly known as Society of Automotive Engineering, German Society of Refrigeration and Air Conditioning (DKV), and IIR and serves as the editor of the ASHRAE publication Science and Technology for the Built Environment. He is the cofounder and co-owner of Optimized Thermal Systems, providing custom simulation software services and innovative solutions to energy conversion challenges. xxxiii
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About the Authors
Sanford A. Klein is currently the Bascom Ouweneel Professor of Mechanical Engineering at the University of Wisconsin–Madison, Madison, Wisconsin, and the director of the Solar Energy Laboratory. He received his PhD in chemical engineering at the University of Wisconsin–Madison in 1976, and he has been on the faculty at Wisconsin since 1977, associated with the Solar Energy Laboratory. He is the author or coauthor of more than 160 publications relating to energy systems and the coauthor (with Professor Greg Nellis) of recent books in heat transfer and thermodynamics published by Cambridge University Press. Professor Klein’s current research interests are in thermodynamics, refrigeration, and solar energy applications. In addition, he has been actively involved in the development of engineering computer tools for both instruction and research. He is the primary author of the TRNSYS (TRaNsient SYSytem) simulation program that is widely used for solar energy system studies. He is also the author of a finite element heat transfer program, FEHT, and the general engineering equation solving program, EES. Professor Klein is a fellow of the American Society of Heating, Refrigeration, and Air-Conditioning Engineers (ASHRAE), the American Society of Mechanical Engineers (ASME), the International Building Performance Simulation Association (IBPSA), and the American Solar Energy Society (ASES).
Nomenclature Primary Symbols Δ difference ε effectiveness η efficiency μ chemical potential v specific volume, partial molal volume ρ density σ surface tension ψ Helmholtz free energy, ψ = u + pv A area AHP absorption heat pump AR absorption refrigeration system c molar concentration CFC chlorofluorocarbon refrigerant COP coefficient of performance c p specific heat at constant pressure c v specific heat at constant volume D diffusion coefficient EES Engineering Equation Solver F, f solution circulation ratio g specific Gibbs free energy; g = h + pv, acceleration of gravity G extensive Gibbs free energy GAX generator-absorber heat exchange h specific enthalpy, heat transfer coefficient H extensive enthalpy HT heat transformer k thermal conductivity l liquid L length mass flow rate m M molecular weight N number of moles Nu Nusselt number pi partial pressure P,p pressure xxxv
xxxvi
q Q Q r R RHX S SHX T U v V W x Subscripts 0 a A B c d e eff fg h ht hx l lm mix N R, r ref p q s S sa
Nomenclature
heat flux, heat transfer per unit mass heat transfer rate vapor quality latent heat universal gas constant, thermal resistance refrigerant heat exchanger entropy solution heat exchanger temperature overall heat transfer coefficient, internal energy Specific volume, partial molal volume volume, velocity mechanical work rate mass fraction
reference state absorber component A component B condenser, intermediate desorber evaporator, low effective vapor-liquid transition hot, heating, high heat transfer solution heat exchanger liquid log mean property of mixing mole fraction refrigeration reference state, reflux at constant pressure, pump specifc heat transfer specific entropy rate of entropy flowing with heat transfer entropic average
Nomenclature
shx T u v w
solution heat exchanger at constant temperature specific internal energy vapor specific work
Superscripts 0 pure component ‘, ‘’ designate phase
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1 Introduction
1.1 Heat Pumps The term “heat pump” refers to a group of technologies that transfer heat from a low temperature to a high temperature. Such technologies include refrigeration systems as well as heat pump heating systems. Such a transfer requires a thermodynamic input in the form of either work or heat. This is made clear in the Clausius statement of the Second Law of thermodynamics: It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body.
The thermodynamic implications of the Second Law for heat pump technology are the factors that complicate the application and understanding of this technology. Even when the Second Law is not explicitly applied in a heat pump analysis, its requirements are in force implicitly through the properties of the working fluids. In simplified terms, we can say that transferring heat from a low temperature to a high temperature requires an expenditure of energy. The type of energy input, whether heat or work, changes the details of the technology needed to provide the heat-pumping function. Absorption technology, which is the focus of this book, is an example of a heat-driven technology. A schematic diagram of a simple absorption cycle is shown in Figure 1.1. The details of the schematic are discussed fully, starting in Chapter 2. The main point here is to focus on the energy transfers between the cycle and its surroundings. It is possible to transfer heat from a low temperature to a high temperature while supplying only heat as the driving energy. By eliminating the need for a work input, an absorption cycle provides a unique solution for a range of technological problems from solar cooling to steam-driven refrigeration. Many other heat-driven heat pump technologies have been conceived, but absorption technology is by far the most widely applied. Other heat-driven technologies that have been demonstrated include adsorption (solid/vapor), Stirling cycle, ejector refrigeration, and magnetic refrigeration. Many other ideas have appeared in the literature. Heat pumps that require a work input provide solutions to a complementary range of technological problems. The vapor compression heat pump, the most widely used variant of this technology, is widely used for residential and commercial heating and cooling, food refrigeration, and automobile air conditioning, among other uses. This technology is illustrated in Figure 1.2. A mechanical compressor, typically driven by an electric motor, provides the work input that drives the heat transfer from the low temperature to the high temperature. 1
2
Absorption Chillers and Heat Pumps
· Qc
· Qd
Condenser
Desorber
Solution heat exchanger
Refrigerant expansion valve · W
Solution expansion valve
Pump
Pressure Evaporator
Absorber · Qe
· Qa
Temperature FIGURE 1.1 Single-effect absorption cycle schematic. Heat rejection
Condenser
Work input
Compressor Pressure Evaporator Heat in at the lowest temperature Temperature FIGURE 1.2 Vapor compression heat pump.
3
Introduction
The emphasis in this book is on absorption heat pumps that are heat driven. It should be kept in mind that the basic function, that is, transferring heat from a low temperature to a high temperature, can be implemented in a wide range of technologies of which absorption machines are just one family.
1.2 Heat-Driven Heat Pumps The simplest heat-driven heat pump is a device that transfers heat at three temperature levels. There are two variations of this arrangement that represent two fundamentally different heat-pumping types. The first, Type I, is illustrated in Figure 1.3. In this type of heat pump, the driving heat is the input at the highest temperature level and the product is either (1) refrigeration at the lowest temperature or (2) heating at the intermediate temperature. The second, Type II, is illustrated in Figure 1.4. In a Type II heat pump, the driving heat is the input at the intermediate temperature level, and the product is the heat provided at the highest temperature level. Type II heat pumps, which are also known as heat transformers, temperature boosters, or temperature amplifiers, are useful for upgrading the temperature of a waste heat stream to a useful level. A consequence of the Second Law is that this upgrade in temperature requires a portion of the input heat to be rejected at a lower temperature. The blocks with temperatures, indicated in Figures 1.3 and 1.4 as T h, Tc, and Te, represent the thermal boundary conditions with which the absorption machine must interact. The highest temperature is at the top and the lowest is at the bottom of both diagrams. Internal to the absorption machine, another set of temperatures is designated with the subscript i. The relationship between the internal temperatures (with subscript i) and the external temperatures that the machine interacts with is defined by a heat transfer process. For example, for Type I heat pump in Figure 1.3, we expect Th > Thi because that would drive heat transfer in the direction shown. At each temperature level, the heat transfer Heat input Thi Type I heat pump
Rh
Th
· Heat output Qc Tci
Tei
Tc
Rc
Heat input
FIGURE 1.3 Type I heat pump.
· Qh
Re
· Qe
Te
4
Absorption Chillers and Heat Pumps
Heat output Thi
· Qh
Rh
Type II heat pump
Heat input Tci
· Qc Tc
Rc
Heat output Tei
Re
Th
· Qe Te
FIGURE 1.4 Type II heat pump.
interaction between the absorption machine and the surroundings occurs through a heat exchanger represented by the sawtooth thermal resistance. These diagrams emphasize the key role of temperature in understanding absorption technology. Type I absorption heat pumps are commonly used in commercial buildings as water chillers for air-conditioning applications. They can be found in thousands of mechanical rooms across the world. Type II heat pumps have been demonstrated in laboratories, including facilities run by the authors, and have been demonstrated in a few industrial installations. The economics of Type II heat pumps with current technology and at current energy prices is not particularly compelling. There are installations where the economics look favorable but, because the capital cost and maintenance are significant, the payback period is often longer than the investment horizon, making Type II heat pumps a tough sell to industry. However, a full understanding of heat-driven heat pumping requires an understanding of both Type I and Type II heat pump variations.
1.3 Description of Current Absorption Chiller Products Three distinct absorption technologies are currently marketed in the United States: (1) water/lithium bromide chillers, (2) ammonia/water chillers, and (3) ammonia/water/ hydrogen refrigerators. Within each of the three categories, there is some differentiation among products, but it is useful to divide the technology in this way to facilitate the discussion. 1.3.1 Water/Lithium Bromide Chillers Water/lithium bromide technology is discussed in detail in Chapters 5 through 8. Water/lithium bromide is an absorption working fluid that has been used widely since the 1950s when the technology was pioneered by several manufacturers in the United States. This working fluid utilizes water as the refrigerant and is therefore limited to
Introduction
5
refrigeration temperatures above 0°C. Absorption machines based on water/lithium bromide are typically configured as water chillers for air-conditioning systems in large buildings. Machines are available in sizes ranging from 10 to 1500 Ton. (Note: Ton is a unit of refrigeration capacity, 1 Ton = 12,000 BTU/h = 3.517 kW.) The coefficient of performance (COP) of these machines, defined as the refrigeration capacity divided by the driving heat input, typically varies over the range 0.7 < COP < 1.2 depending on the particular cycle configuration. These machines have a mixed reputation among mechanical room operators. When operated according to manufacturer specifications, they exhibit consistent and dependable cooling service. However, they require specific maintenance procedures, and ignoring these procedures often leads to early failure. The main competing technology is vapor compression chillers, and the choice between the two depends strongly on economic factors. 1.3.2 Ammonia/Water Chillers Ammonia/water absorption technology is discussed in detail in Chapters 9 through 11. Ammonia/water is an absorption fluid that has been used since the late 1800s, at which time it was used for ice production prior to the introduction of vapor compression technology. This working fluid utilizes ammonia as the refrigerant. Thus, the role of water is distinctly different between ammonia/water and the water/lithium bromide (discussed in Section 1.3.1). One advantage of ammonia as refrigerant is that the allowable refrigeration temperature is much lower. (The freezing temperature of ammonia is –77.7°C). However, the toxicity of ammonia is a factor that has limited its use to well-ventilated areas. Ammonia/water absorption chillers are commonly sold as air-conditioning components, and this use is regulated in some densely populated urban areas. The ability to provide direct gas-fired and air-cooled air conditioning is the primary selling point of this technology. Machines are available in capacity ranging from 3 to 25 Ton (10–90 kW) with COP typically around 0.5. These units have a niche market because there are few competing gas-fired technologies suitable for many applications. Custom ammonia/water applications in industry for waste heat utilization are an interesting application of this technology. 1.3.3 Ammonia/Water/Hydrogen Refrigerators Ammonia/water/hydrogen refrigerators are discussed in detail in Chapter 12. This technology is a direct descendant of that patented by von Platen and Munters in 1921. Domestic refrigerators based on ammonia/water/hydrogen have been continuously available since that time. Machines based on this cycle are manufactured by numerous companies throughout the world. In the United States, refrigerators are used primarily for the recreational vehicle market, where the lack of need for any electric input is the selling point. Internationally, the technology has a significant niche market as hotel room refrigerators. The selling point here is the silent operation.
1.4 Overview of Absorption Technology Market Trends The absorption cooling market in the United States experienced a brief resurgence in the 1990s after a period of approximately 20 years of decline. This decline was driven by political decisions in the early 1970s to limit usage of natural gas due to expected
6
Absorption Chillers and Heat Pumps
supply shortfalls. Although the predicted supply shortfalls never materialized, the damage was done to the industry. The three manufacturers of absorption equipment saw their business dry up, and production of absorption machines was reduced to less than 10% of earlier production levels. Companies were forced to reassign staff and reallocate resources away from the absorption business center. In the meantime, the Japanese absorption industry boomed due to Japanese domestic demand and product innovation. The resurgence in the 1990s was driven by market forces that stimulated absorption demand, including peak electric power rate premiums, gas utility rebate programs, and the chlorofluorocarbon replacement issue. When demand for absorption machines began to rise in the early 1990s, the US manufacturers found themselves in the position of having to license the newer technology from Japanese manufacturers. The resurgence in the United States was relatively short lived, and today there is no absorption machine manufacturing in the United States. This is because the domestic US market is small, and it is not profitable for US companies to manufacture these machines domestically. This is in sharp contrast to the market conditions in East Asia (Japan, China, and Korea) and India where absorption cooling is a thriving business with greater than 50% market share in some regions. The differences between the market conditions in the United States and Asia are understood to be primarily due to regulatory forces and energy economics. In particular, absorption cooling is very attractive in markets where electricity supply is limited and other fuels are available. Absorption machine manufacturing is thriving in Asia with major manufacturers in every region. The largest manufacturers have introduced robotic welding that has enabled improved performance due to reduced air leakage. The building conditioning requirements in Europe lean more toward heating, and there has been considerable research and development effort in solar energy utilization and gas-fired heat pumps for heating purposes. This nascent market has promise but currently represents a tiny market share.
2 Absorption Cycle Fundamentals This chapter explains the concept of absorption cycles in terms of idealized energy conversion cycles. It provides a description of the operation of absorption cycles within the larger context of what is thermodynamically possible. In this chapter, many of the relationships require absolute temperatures. This point will be reiterated when we come to such relations.
2.1 Carnot Cycles The Carnot cycle is used as an idealized energy conversion cycle. It exhibits the highest possible performance because it is thermodynamically reversible (i.e., no losses). Figure 2.1 shows a Carnot cycle for power generation on a temperature-entropy diagram (T,s diagram). The process line AB represents the isothermal heat transfer rate Q 2 at the temperature T2 to a working fluid. Here we use the convention that an arrow pointing to a process line represents energy supplied to the cycle. BC represents the isentropic output. Process CD represents the isothermal heat rejection rate Q 1 at the power output, W input. When it is assumed temperature T1, and DA represents the isentropic input power, W that all processes are reversible, then the area enclosed by ABCD represents the net power =W output − W input, and the area CDEF is the rate of thermal energy Q 1 rejected produced, W by the cycle assuming E and F are at T = 0 K. All temperatures are measured in absolute units. For a work-producing process, as shown in Figure 2.1, the processes follow a clockwise direction in the T,s diagram. The sum of the two areas is the heat transfer rate Q 2 (thus, area ABFE) supplied to the cycle. The energy rates are related by the First Law of thermodynamics as (2.1) Q 2 = Q 1 + W The signs of the heat transfer rates in Equation 2.1 follow the arrow directions indicated is positive in Figure 2.1 (i.e., positive in the direction of the arrow). The net power out, W, for a power generation cycle. The efficiency η for power generation is defined as the net power produced divided by the rate of heat supplied at the high temperature.
W η = (2.2) Q2
The Second Law of thermodynamics for the Carnot cycle shown in Figure 2.1 requires that, for reversible operation, the net entropy production is zero. This implies that
Q 2 Q 1 = 0 (2.3) − T2 T1 7
8
Absorption Chillers and Heat Pumps
· Q2 T2
A
B
· Winput
· Woutput D
· Q1
Temperature
T1
E
C
F Entropy
FIGURE 2.1 The Carnot cycle for power generation on a temperature–entropy diagram.
where it is noted that the temperatures must be expressed in absolute temperature units in this equation (and all subsequent equations in Sections 2.1 through 2.3). Equation 2.2 can be modified to a form that contains only temperatures using Equations 2.1 and 2.3 by resulting in eliminating W,
η=
T2 − T1 T = 1 − 1 (2.4) T2 T2
The expression in Equation 2.4 is frequently termed the Carnot efficiency for power generation. Figure 2.2 shows a Carnot cycle that is operated as a heat pump cycle in a heating application. The directions of all processes are reversed as compared to the power generation cycle. Heat Q 0 is transferred to the working fluid at T0 along the process line GH; the fluid is compressed isentropically along HI; heat is rejected at rate Q 1 at T1, IJ; and the fluid is expanded isentropically along JG. Following the discussion of Figure 2.1, the areas represent energy transfer rates. The net power input required for this cycle is represented by the area GHIJ and the rate of heat absorbed, Q 0, by the area GHKL. The sum of both areas (area IJLK) represents the rate of heat rejected at T1, Q 1. The performance of a heat pump is described by the ratio of the benefit obtained, that is, the rate of heat available at the high temperature, divided by the expenditure, that is, the net power requirement. As this value is always greater than 1.0, the term “coefficient of performance” (COP) is used customarily. For the heat pump in Figure 2.2, we obtain
COPh =
T1 (2.5) T1 − T0
where the subscript h denotes heating. This equation is derived by using the First and Second Laws for the heat pump process shown in Figure 2.2 and by following the same procedure as for Equation 2.4. In addition to using it as a heating cycle, the Carnot cycle
9
Absorption Cycle Fundamentals
Temperature
· Q1 J
T1
I · Winput
· Woutput T0
G L
· Q0
H K
Entropy FIGURE 2.2 The Carnot cycle for heat pumping on a temperature–entropy diagram.
shown in Figure 2.2 can also be used for cooling or refrigeration applications. Although the cycle itself does not change, the way we view the application differs. For refrigeration, the heat removed at T0 is of primary interest, and the refrigeration COP is defined as the ratio of the cooling capacity Q 0 over the power input
COPr =
T0 (2.6) T1 − T0
where subscript r is used to designate that the COP is defined for refrigeration. Equation 2.6 is derived by applying the First and Second Laws to the cycle in Figure 2.2. For the COP of a heat pump cycle and a refrigeration cycle, the following relationship can be derived. COPr + 1 = COPh (2.7) This expression can be verified by substituting Equations 2.5 and 2.6 into Equation 2.7. The key thermodynamic concept that underpins the Carnot performance measures defined in Equations 2.4 through 2.6 is reversibility. In other words, the Carnot model assumes there are no thermodynamic losses. As real systems always involve losses (all transport processes contribute losses), the Carnot relations provide only an upper bound on cycle performance. In many cases, the real performance is much less than the Carnot upper bound. With these caveats in mind, the Carnot results are applied to absorption cycles next.
2.2 Absorption Heat Pump, Type I To describe an absorption heat pump with the help of Carnot cycles, both the power generation and the refrigeration cycles in Figures 2.1 and 2.2 are combined into one device. It is assumed that the net power produced by the first cycle (see Figure 2.1) is identical to the net power required by the second cycle (see Figure 2.2). The new device, pictured in
10
Absorption Chillers and Heat Pumps
· Q2
Temperature
T2
T1
A
B · W . Q˝1
J D
I
C
. Q´1
T0
G E
L
F
· Q0
H K
Entropy FIGURE 2.3 Idealized representation of an absorption heat pump as the combination of a Carnot heat engine and a Carnot heat pump.
Figure 2.3, provides refrigeration (Q 0) at T0. The cycle raises the temperature level of Q 0 from T0 to T1 by using the exergy (thermodynamic availability) of the high-temperature is rejected at T . The waste heat of the power heat supplied at T2. Waste heat Q 1′′= Q 0 + W 1 ) is also rejected at T . Thus, the generation portion of this combined cycle ( Q 1′ = Q 2 − W 1 total rate of heat rejected at T1 has two contributions, Q 1′ and Q 1′′. This combined cycle (Figure 2.3) represents a heat-pumping device that is driven by the input of heat only. It is an idealized representation applicable to any heat-driven, heatpumping concept. Examples include an engine-driven vapor compression heat pump, a combination of a steam power plant with an electrical vapor compression heat pump and an absorption heat pump. Based on the model of Figure 2.3, the heating COP is defined as
COPAHP =
Q 1′ + Q 1′′ (2.8) Q 2
and the cooling COP as
Q COPAR = 0 (2.9) Q2
where the subscript AHP stands for absorption heat pump and subscript AR stands for absorption refrigerator. By assuming thermodynamic reversibility and applying the First and Second Laws (and eliminating either Q 0 or Q 1 with Q 1 = Q 1′ + Q 1′′), Equations 2.8 and 2.9 can be converted into expressions that depend on temperature only. In the following equations, all temperatures are absolute temperatures.
COPAHP =
T2 − T0 T1 (2.10) T2 T1 − T0
COPAR =
T2 − T1 T0 (2.11) T2 T1 − T0
11
Absorption Cycle Fundamentals
As with vapor compression heat pumps and refrigerators, the distinction between a heat pump and a chiller is only a function of the application, not of the operating mode. The analogue to Equation 2.7 is also valid for absorption systems: COPAR + 1 = COPAHP (2.12) The system analyzed here is referred to in the literature at times as “Type I absorption heat pump.” The other variation, which is called a Type II absorption heat pump, is described in Section 2.3.
2.3 Absorption Heat Pump, Type II The combined cycle in Figure 2.3 can be operated in a reversed mode. For this purpose, the directions of all fluid streams and all energy streams are reversed and the combined cycle of Figure 2.4 is obtained. This cycle is sometimes referred to as a “heat transformer” or a “temperature booster.” In this case, the cycle operating between T1 and T2 is a heat pump cycle, while the cycle operating between T1 and T0 is a power generation cycle (note the circulation directions). In Figure 2.4, heat is supplied at T1 to both cycles. The purpose of this combined cycle is to utilize heat at an intermediate temperature level, for example, 80°C waste heat, to provide high-temperature heat, for example, 120°C. This transformation is accomplished by using a portion of the waste heat in a power generation cycle that rejects heat at T0 while it provides the power for the heat pump cycle. The performance of a heat transformer cycle is typically measured by a COP defined as Q COPHT = 2 (2.13) Q1′ + Q1′′
· Q2
Temperature
T2
T1
A
B · W . Q˝1
J D
. Q´1
T0
G E
I
C
F
L
· Q0
H K
Entropy FIGURE 2.4 Carnot cycles for a combined power generation/heat-pumping facility such as an absorption heat transformer.
12
Absorption Chillers and Heat Pumps
COPHT is the rate of high-temperature heat output divided by the total rate of waste heat required. Q 1′ and Q 1′′ represent the two contributions of waste heat, one to be pumped to T2 and the second to drive the power plant that enables the heat-pumping process. Performing First and Second Law analyses for the heat transformer and eliminating the heat Q 0, the following expression for the COP involving only the temperatures is obtained
COPHT =
T1 − T0 T2 (2.14) T1 T2 − T0
As was true for Equations 2.10 and 2.11, this result provides a performance prediction for a heat pump operating reversibly. Thus, we interpret this result as an upper bound on performance and note that it overpredicts the real COP by a considerable margin. Even so, it represents a useful idea of the ultimate potential of heat-driven, heat-pumping technologies.
2.4 Absorption Heat Pump as Combination of Rankine Cycles Figure 2.5a shows the components of a Rankine heat pump cycle, and Figure 2.5b shows a basic Rankine cycle that produces power. By studying the direction of the working fluid streams, it is apparent that the two cycles could potentially be combined into one. For example, when the following conditions are fulfilled, the compressor and turbine can be eliminated because they overlap and perform inverse functions:
1. The stream leaving the boiler of the power generation cycle must have the same high pressure level and flow rate as the stream entering the condenser of the heat pump cycle, and 2. The stream leaving the heat pump evaporator must have the same low pressure level and flow rate as the stream entering the power cycle condenser.
Condenser
Compressor
Expansion valve Evaporator (a)
Boiler
Work
Turbine Condenser (b)
Pump
FIGURE 2.5 Illustration of the combination of two Rankine cycles (a, heat pump; b, power generation) to a combined system.
13
Absorption Cycle Fundamentals
The result is a combined cycle that provides heat pumping with only a small power input required for the pump. This sounds very much like an absorption heat pump. Thus, an absorption heat pump cycle is a heat-driven refrigeration cycle that can be viewed as a combination of a power cycle and a power-driven heat pump all in one machine. In practice, this combination would not work with a pure working fluid because it would imply that the boiler and condenser would operate at the same temperature, which would defeat the thermodynamic objective. However, a higher boiler temperature can be achieved when the vapor in the boiler is evaporating out of a mixture with a fluid of a much higher boiling point. This higher boiling point fluid is usually termed the absorbent. Only with such a mixture of absorbent and refrigerant in the power generation portion is the absorption heat pump process possible. This requirement is explained in more detail in Chapter 3. The absorbent remaining in the boiler must be circulated in its own loop. For this purpose, a dashed line with a pressure-reducing valve is shown in Figure 2.5b. As we found for the Carnot cycle version, this conceptual derivation makes it plausible that the absorption cycle can be viewed as a combination of two Rankine cycles, one a power cycle and the other a heat pump cycle. The value of this Rankine cycle version of the “derivation” is that it brings us closer to a practical understanding of the absorption cycle, as compared with the Carnot cycle version, which is more abstract.
2.5 Reversible Analysis with Variable Temperatures The reversible analysis discussed in Sections 2.1 through 2.3 is based on the assumption that all heat transfers occur at a fixed temperature. This assumption makes the analysis simple, and the resulting models do provide some insight into the thermodynamics of absorption cycles. However, the heat transfer processes in an absorption system actually occur over a range of temperatures in all the components. The working fluid experiences temperature changes as it passes through the components due to a number of factors, including pressure changes, mass fraction changes, superheating, and subcooling. From the perspective of reversible analysis, it is desirable to determine an average temperature that can represent the variable-temperature heat transfer processes. The appropriate temperature is the entropic average temperature. Consider an arbitrary heat transfer process occurring over a range of temperatures. A simple example is the cooling of water flowing in a pipe. As energy is transferred out of the system, the temperature decreases. An energy balance on the system allows determination of the total energy transfer rate as a function of the flow rate and the end-state temperatures. A reversible analysis, of the type done in Sections 2.1 through 2.3, requires the Second Law analysis, which, in turn, requires knowledge of the temperature at which the heat transfer occurs. As the temperature of the system is a continuously changing variable, it is necessary to view the process on a differential basis. Consider a more complex but arbitrary heat transfer process shown on temperature versus cumulative heat transfer rate coordinates in Figure 2.6. The cumulative heat transfer rate is the integral of the heat flux over the heat exchanger area with the zero set arbitrarily at one end of the device. The total rate of entropy flowing with the heat transfer can be written as
S =
∫
dQ (2.15) T
14
Absorption Chillers and Heat Pumps
150
Water, P = 100 kPa, m = 1 kg/sec De-superheating
Temperature (ºC)
130
110 Condensation
90
70
50
Subcooling
0
500
1000 1500 2000 Cumulative heat transfer rate (kW)
2500
3000
FIGURE 2.6 Temperature versus cumulative heat transfer rate for condensation of steam at 100 kPa from 150°C to 50°C.
is transferred at temperature T (note that T must be meawhere the heat transfer rate, dQ, sured in absolute temperature units). Temperature T corresponds to the temperature of the system boundary selected by the analyst. An average temperature, Tsa, called the entropic average, can be defined such that the entropy transfer would be the same if the entire heat transfer occurred at the average temperature. The definition is
Q Tsa = = S
∫
Q (2.16) dQ T
The entropic average temperature, as defined in Equation 2.16, reflects the thermodynamic “quality” of a variable-temperature heat transfer. Thus, the entropic average temperature is the appropriate temperature to use whenever a variable-temperature process is to be analyzed thermodynamically as if it were a constant temperature process. This formulation retains the simplicity of the constant temperature model but makes it applicable to varying temperature processes.
2.6 Irreversibilities in Absorption Cycle Processes The reversible cycle analyses discussed in Sections 2.1 through 2.3 represent idealized performance limits for absorption cycles. In real cycles, performance falls below the idealized limits due to irreversible processes such as those listed in Table 2.1. Thermodynamic irreversibilities occur whenever transport occurs for momentum, mass, or heat. These transport processes are always accompanied by a finite difference in the driving potential (such as the temperature difference for heat transfer). The irreversibility of a given process
15
Absorption Cycle Fundamentals
TABLE 2.1 Irreversible Effects in Absorption Technology Phenomena Viscous friction Thermal mixing Mass mixing Heat transfer Unrestrained expansion
Example Vapor flow, liquid flow Liquid inlet to desorber Liquid inlet to desorber Every component Expansion valve
is related to both the quantity of transport and to the potential difference over which it is transported. An introduction to the analysis of irreversibilities in thermal systems can be found in Bejan (1982). Irreversibility can be defined as the entropy generation rate multiplied by a reference temperature, called the dead state temperature. Although this is helpful, in the sense that it allows a specific definition for this concept, it also introduces some confusion because the choice of dead state temperature is dependent on the application and the interpretation depends on the temperature used. An alternative that avoids the need for introduction of the dead state temperature is to simply concentrate on the entropy generation rate and to avoid introducing the concept of irreversibility. This method may be preferable for heat pump analysis because it avoids the confusion associated with the dead state temperature. This method has been applied to absorption heat pump analysis by Alefeld (1987). By analyzing the state at the inlet and outlet of each component, and, with several assumptions about the processes occurring in the components, it is possible to calculate the entropy generation in each component. By comparing the entropy generation in the various components, the analyst can develop an understanding of which components are causing performance degradation and where to invest design efforts to improve performance. The details of such analyses yield some very informative general results. For a welldesigned absorption machine, the major irreversibilities are those associated with the heat transfer processes. Those processes include the solution heat exchanger, which is an internal heat transfer, and the external heat transfers. In the case of the external heat transfer processes, the process on the solution side of the machine is a coupled heat and mass transfer process. The irreversibilities associated with the coupled processes are lumped together in this discussion and assigned to the heat transfer. In a typical machine, the other transport processes occurring within the machine are also irreversible, but fluxes and potential differences are low enough so that they are insignificant compared with the heat transfer processes. This result is important because it points toward potential performance improvements. It also points toward the type of models needed to predict the performance of absorption machines. As long as a model predicts the major irreversibilities, it should also predict performance.
2.7 Zero-Order Absorption Cycle Model The ability to predict the performance of a particular absorption cycle, utilizing a particular absorption working pair, is a fundamental skill for the engineer who needs to determine the applicability of an absorption cycle to a particular situation. The experienced heat pump engineer has rules of thumb and intuition on which to base a decision.
16
Absorption Chillers and Heat Pumps
A newcomer to the field must have modeling tools to enable the careful evaluation of a given design. In this book, a series of tools are presented that allow absorption cycle performance to be predicted with varying levels of accuracy. The factors that determine the performance of a thermodynamic cycle in a given application are the irreversibilities, which are losses of thermodynamic availability or exergy. The major irreversibilities in a typical absorption cycle application are associated with heat transfer between the cycle and the surroundings. The simplest singleeffect absorption cycle requires four heat transfer interactions with the surroundings (two of which occur typically at the same temperature level). Each of these heat transfer processes has an associated irreversibility or loss. The summation of losses, plus the losses internal to the cycle, determines the approach of the cycle performance to the reversible limit introduced in Sections 2.1 through 2.3. The zero-order model described here is based on the concept of modeling only those processes that contribute the largest irreversibilities, ignoring all other losses. Thus, the internal losses are ignored in the zero-order model. The method results in a model that is easy to solve and understand and produces excellent predictions of performance trends, but the one that provides only a rough approximation to absolute performance prediction. A detailed description of the zero-order model can be found in Herold and Radermacher (1990), Herold (1997), and Herold (1999). The zero-order model is based on the schematic shown in Figure 2.7. The AHP block represents the internal workings of the absorption cycle. The internal workings are modeled as thermodynamically reversible. The zero-order model emphasizes the heat exchanger losses between the AHP and the surroundings represented in Figure 2.7 by thermal resistances, denoted by R. There are three thermal resistances shown, corresponding to the three temperature levels. When interpreting the model, one must realize that the thermal conductance at the intermediate temperature level represents the sum of the condenser and the absorber heat transfer conductances. The zero-order model consists of the following equations. There is one heat transfer equation for each of the three thermal resistances shown in Figure 2.7.
Thi
· Qh Rh
Th
AHP
Tci
Tei
FIGURE 2.7 Zero-order model schematic.
· Qc Rc
· Qe Re
Tc
Te
Absorption Cycle Fundamentals
17
T − Thi (2.17) Q h = h Rh
T − Tc (2.18) Q c = ci Rc
T − Tei (2.19) Q e = e Re
An overall energy balance on the system requires that the sum of the three heat transfer rates must be zero. Note that the model assumes steady state and that the pump power and environmental heat losses are neglected.
Q h + Q e = Q c (2.20)
The performance of the AHP is assumed to be internally reversible and can be represented in terms of the internal temperatures (in absolute units) as (see Equation 2.11)
Q T T −T COP = e = ei hi ci (2.21) T Qh hi Tci − Tei
The system represented by Equations 2.17 through 2.21 includes five equations in the six unknowns, including the three unknown Q ′s and the three unknown internal temperatures. An additional equation is needed to close the system. One such equation that can be deduced from the working fluid characteristics is
Thi − Tci = Tci − Tei (2.22)
Assuming that the condenser and the absorber operate at the same temperature, Equation 2.22 indicates that the temperature difference between the evaporator and the condenser is the same as between the absorber and desorber. This characteristic is a reasonable approximation for a single-effect machine. For other cycles, Equation 2.22 must be replaced accordingly (Herold 1999). The six equations in six unknowns represented by Equations 2.17 through 2.22 can be solved numerically. The result is a very simple absorption cycle model that predicts performance trends remarkably well considering the minimal effort required to set up and execute the model. The model does an excellent job of clarifying and defining the physics underlying the shape of the COP curve for an absorption machine. A typical single-effect performance curve is plotted in Figure 2.8 that shows that the COP is relatively insensitive to changes in the heat input temperature. This result seems odd when compared to the Carnot performance, also plotted in Figure 2.8, which was obtained by plotting Equation 2.11. Based on the Carnot model, cycle performance is seen to increase significantly as the heat input temperature increases. However, experience in the field shows that the COP curve is relatively flat like that predicted by the zero-order model. This characteristic results from the fact that the irreversibilities in the external heat transfer processes increase significantly as the heat input temperature increases. The irreversibilities increase because both the fluxes and the potential differences increase. As in a real absorption machine, any change in the temperature inputs causes changes in the operating conditions throughout the cycle. These changes are realistically reflected in the result of the zero-order model and thus the shape of the COP curve is predicted realistically. The Carnot model, which is reversible, cannot capture these real-world effects.
18
Absorption Chillers and Heat Pumps
3
Cooling COP
2.5
Tc = 35°C Te = 5°C Carnot
2 1.5 1
Zero-order model
0.5 0 340
360
380 400 420 Heat input temperature (K)
440
460
FIGURE 2.8 Cooling COP for a single-effect absorption machine.
Th
∆Th Thi
These three temperatures represent the external temperatures of the application.
∆Tc
Tc
Te
These connected temperatures represent the relationship in Equation 2.22, which is for a single-effect absorption cycle. Tci
∆Te Tei
FIGURE 2.9 Temperatures associated with zero-order model of a single-effect Type I absorption heat pump.
Another quite useful aspect of the zero-order model is in determining the minimum ring temperature for a particular cycle design. The temperatures associated with the fi zero-order model are illustrated in Figure 2.9, which shows the temperatures internal to the absorption machine as a connected set which are linked by the relationship in Equation 2.22. The external temperatures are also shown. It is useful to define the temperature lift as the difference between the heat rejection temperature, Tc, and the refrigeration temperature, Te, as
∆Tlift = Tc − Te (2.23)
19
Absorption Cycle Fundamentals
It is noted that, in general, the temperature differences between the machine and its surroundings, which represent the heat transfer potential difference, will not be equal at the three levels. These differences will depend on the size of the heat exchangers at each of the three temperature levels. Although these differences are not necessarily equal, it is sometimes useful at the design stage to think in terms of a design temperature difference that would be equal at all three levels. This perspective is taken here, and the heat transfer temperature difference is referred to as ΔT ht, where subscript ht stands for heat transfer. It is assumed also that the heat rejection temperature and the refrigeration temperature are known for a given design and that the minimum heat input temperature is to be determined. By inspection of Figure 2.9, the following relationship is derived
(
)
Th = ∆Tlift + 2 ∆Tht + 2 ∆Tht + Tc = ∆Tlift + 4 ∆Tht + Tc
(2.24)
This relationship is used in the following example to determine the minimum heat input temperature. Example 2.1: Determine Minimum Heat Input Temperature Consider a single-effect absorption cycle. Determine the minimum heat input temperature assuming the rejection temperature is 35°C and the refrigeration temperature is 8°C. Solution: Direct application of Equation 2.24 requires a specification of the heat transfer driving potential difference. Assuming values of 0°C, 5°C, and 10°C yields Th values of 62°C, 82°C, and 102°C. Observations: The magnitude of the heat transfer driving potential difference has a major impact on the required heat input temperature.
The zero-order model can be solved analytically if the heat transfer coefficient (UA) distribution throughout the machine is balanced such that there is one unit of UA allocated to each heat exchanger (Herold 1999). This balanced design is not expected to be the optimum design (see Section 2.8), but it approximates the optimum design reasonably closely. The COP predictions that result from this model are remarkable in their simplicity and their utility. The COP prediction for a single-effect cycle is
COP =
Te (2.25) Th
This result says that the COP of a single-effect absorption refrigeration cycle is independent of the heat rejection temperature. As an example, consider a refrigeration temperature of 5°C and a heat input temperature of 100°C, which lead to COP = 0.745. This result provides a very realistic target COP for design purposes. The model on which it is based includes the major losses, and thus the performance predicted is much lower than the Carnot (reversible) prediction. Similar results can be obtained for other cycle configurations that are covered later in this book, and several of these are summarized in Table 2.2, including comparisons of the COP prediction with experimental results.
20
Absorption Chillers and Heat Pumps
TABLE 2.2 COP Predictions from the Zero-Order Model Assuming a Balanced Conductance Design T h (°C)
York singleeffect, steam-fired, YIA-ST-1A1 York doubleeffect, steam-fired, YPC-ST-14G Triple-effect
108
34
9.4
0.736
0.74
153.5
31.8
9.1
1.23
1.29
200
31.8
9.1
80
32
9.0
100
70
Battelle half-effect Battelle Type II
Tc (°C)
Te (°C)
Zero-Order Model COP
Machine
30
Actual COP
1.79
Zero-Order Model COP Expression Te Th
2
Te Th
3
Te Th
0.35
0.40
1 Te 2 Th
0.41
0.55
Th Te + Th
Note: Actual COP values obtained from York literature and from direct observation (Herold 1985).
In all cases shown, the zero-order model provides an upper bound on real performance that is much more realistic than the bound provided by the reversible model. The zeroorder model provides a remarkable combination of simplicity and utility.
2.8 Absorption Cycle Design Optimization Design optimization requires an understanding of the interactions between design variables to arrive at a final design. Thus, it is fundamental to consider the meaning of optimum design as it applies to absorption technology. It is tempting to consider maximization of COP as a design philosophy because this would result in the most efficient energy utilization and the least environmental damage due to machine operation. However, this is not a particularly practical approach because it ignores first-cost considerations. Another reason why COP is not an appropriate objective to maximize is that the machine capacity is usually inversely related to COP such that the maximum in COP occurs at zero capacity. A more meaningful optimization approach is to consider minimizing the life cycle cost of a particular machine in a given application. In this approach, two designs are compared by weighing the first costs, associated with building the machine, together with the operating costs to determine a single overall cost for each design. The design with the lowest cost is considered the best. Modifications to this method can take opportunity costs and environmental costs into account. A simplified alternative method of design, which works well for technology that has high first costs like absorption technology, is to choose a design that maximizes capacity for a given first cost. This approach is related to the power cycle capacity maximization efforts that have appeared in the literature. The approach has been applied to refrigeration
Absorption Cycle Fundamentals
21
cycles by Klein (1992). The concept is to allocate the heat exchanger area, based on a fixed total area (approximately fixed cost), so as to maximize heat pump capacity. The zeroorder model presented in Section 2.7 provides a particularly simple model on which to base such an optimization. Example 2.2: Absorption Cycle Optimization Using the zero-order model, determine the optimum distribution of heat exchanger surface area at the three temperature levels. Assume that the U value for all the heat exchangers is identical and equal to 0.5 kW/m2-K. Assume that the total area available is 10 m2. Further assume that the heat pump operates between the three temperatures: 200°C, 50°C, and –20°C. (See File Ex2_2.ees.) Solution: Using the zero-order model, search for the heat exchanger area distribution that maximizes the evaporator heat transfer. Do this by iteratively solving the model for a wide range of different cases until the best one is found. For the conditions given, the maximum capacity was found to be 17.49 kW at a cooling COP of 0.53. The area distribution at the maximum is 2.705 m2 at the high temperature, 2.286 m2 at the low temperature, and 5.009 m2 at the rejection temperature. Observations: The maximum capacity result is obtained at a COP below the maximum possible COP. It is left as an exercise to use COP as the objective function with the same constraints. It is quite possible to demonstrate COP values well above 0.6 for the given conditions. However, the capacity for the high COP cases is significantly reduced. The maximum COP occurs when the capacity is driven to zero. As zero capacity is of no value, the objective of maximizing COP comes into question.
Homework Problems 2.1 The reversible coefficient of performance (COP) of an absorption refrigeration cycle is a function of the three temperatures of the external heat transfer interactions as given in Equation 2.11. a. Determine the sensitivity of the reversible COP to each of the three temperatures by evaluating the partial derivative with respect to each temperature. b. Consider a baseline set of operating temperatures of 90°C, 30°C, and 5°C. Plot the derivatives determined in (a) by holding two of the baseline temperatures constant and varying the third around the baseline value (three plots required). c. Based on the results in (a) and (b), propose a design solution to improve the COP. 2.2 Repeat Problem 1 for an absorption heat pump. Compare the results of Problem 2 to those of Problem 1. 2.3 Repeat Problem 1 for a Type II absorption heat pump. For the baseline set of temperatures, use 120°C, 90°C, and 30°C. 2.4 Compute the entropic average temperature of the heat transfer process from a stream of liquid water as it is cooled from 50°C to 30°C. Assume the process is reversible.
22
Absorption Chillers and Heat Pumps
2.5 Compute the entropic average temperature of the heat transfer process as a stream of steam is cooled and condensed. The process is isobaric at 1 bar. The starting temperature is 150°C and the ending temperature is 50°C. Assume the process is reversible. 2.6 Use the zero-order model to predict the impact on COP and capacity of varying the size of the evaporator heat exchanger. Start from the baseline configuration obtained in Example 2.2 and plot COP and capacity versus heat exchanger UA. 2.7 Derive an expression similar to Equation 2.24 for a double-effect absorption cycle. 2.8 Repeat Example 2.2 for a more realistic set of U values in the desorber, absorber, condenser, and evaporator of 1.0, 0.25, 0.5, and 0.5 kW/m2-K, respectively. 2.9 It has been found from experience that the cooling COP of an absorption cycle is a strong function of the ratio between the high and low temperatures imposed on the cycle. Demonstrate this observation by running the zero-order model for a range of values for this ratio. In particular, include several cases that have the same ratio but which have different absolute temperatures. 2.10 Using the structure of Example 2.2, maximize the cooling COP under the same constraints and interpret the results in comparison to Example 2.2. 2.11 Using the result of Problem 2.7, determine the minimum heat input temperature for a double-effect cycle using the data from Example 2.1 (ignore the 90°C data).
References Alefeld, G. (1987). What Needs to be Known about Fluid Pairs to Determine Heat Ratios of Absorber Heat Pumps and Heat Transformers? Proceedings of the 1987 IEA Heat Pump Conference, Orlando, FL, Chapter 26, pp. 375–387. Bejan, A. (1982). Entropy Generation through Heat and Fluid Flow. New York: Wiley-Interscience. Herold, K. E. (1985). Projects at Battelle Memorial Institute, unpublished. Columbus, OH. Herold, K. E. (1997). An Analysis of the Major Variable Impacting Performance of Absorption Chillers and Heat Pumps. ASME Meeting, Proceedings of the Advanced Energy Systems Symposium, AESVol. 37, pp. 349–356. Herold, K. E. (1999). Performance Predictions of Absorption Cycles Using an Endo-Reversible Model. International Sorption Heat Pump Conference, Munich, pp. 465–470. Herold, K. E. and R. Radermacher. (1990). Optimum Allocation of Heat Transfer Surface in an Absorption Heat Pump. Proceedings of 25th IECEC (International Energy Conversion and Engineering Conference), Vol. 2, Reno, NV, pp. 217–221. Klein, S. A. (1992). Design Considerations for Refrigeration Cycles. Int. J. Refrig. 15(3): 181–185.
3 Properties of Working Fluids The performance and efficiency of the simple cycle models considered in Chapter 2 are independent of the properties of the working fluids in use. However, accurate p rediction of the capacity and efficiency of a real machine is dependent on the properties of the working fluids. Both the first cost and the operating cost of an absorption machine are strongly dependent on the working fluid properties. This chapter describes the properties of ammonia/water and water/lithium bromide mixtures, which are the conventional absorption working fluids. Typical diagrams of fluid properties are presented and discussed, and the methods of determination of the properties necessary for cycle calculations are explained in detail. Many other working fluids have been considered for absorption machines (Macriss et al. 1987; Macriss and Zawacki 1989; Sun et al. 2012). These include water/sodium hydroxide, water/sulfuric acid, ammonia/sodium thiocyanate, and hundreds of other mixtures. The literature contains numerous studies on properties of alternative working fluids. Some of these fluids are for specialized applications, such as high temperature, while others are proposed as possessing improved properties over the conventional fluids (i.e., water/ lithium bromide and ammonia/water). The reason why none of these alternative fluids have gained a market foothold is that the combination of properties exhibited by the conventional fluids is hard to compete against. In general, proposed alternatives may address one weakness of the conventional fluids while contributing several additional weaknesses of their own. The properties desirable in an absorption working fluid have been listed by other authors (Macriss and Zawacki 1989). A summary of these properties is given in Table 3.1. The desirable properties are sometimes mutually exclusive. An example is the need for (1) a high affinity between the absorbent and the refrigerant and (2) a low heat of mixing (needed for Type I cycles). It is apparently not possible to find a fluid mixture that meets all of the criteria. Thus, one must consider the compromises presented by existing fluids. The key tradeoffs that are available are illustrated in Table 3.1, where the conventional fluids are ranked according to the various desirable properties. Both conventional fluids utilize refrigerants that have high latent heat. This is advantageous in cycle design because it minimizes the refrigerant flow rate. However, neither fluid exhibits ideal vapor pressure characteristics. Ammonia pressures are inconveniently high, while water pressures are inconveniently low. Lithium bromide is advantageous as an absorbent because it is essentially nonvolatile, resulting in cycle designs that avoid the need for a rectifier. Water is advantageous as an absorbent because it does not crystallize (in the property ranges of interest). Numerous other properties are important in addition to the ones highlighted here. The preferred working fluid for a given application depends on the overall mix of properties. A key property is the freezing point of water, which restricts the use of water/ lithium bromide (and other systems utilizing water as refrigerant) to temperatures above 0°C. The restrictive nature of the requirements has resulted in very little success for fluids other than the conventional pairs.
23
24
Absorption Chillers and Heat Pumps
TABLE 3.1 Absorption Working Fluid Properties Property Refrigerant High latent heat Moderate vapor pressure Low freezing temperature Low viscosity Absorbent Low vapor pressure Low viscosity Mixture No solid phase Low toxicity High affinity between refrigerant and absorbent
Ammonia/Water
Water/Lithium Bromide
Good Too high Excellent Good
Excellent Too low Limited application Good
Poor Good
Excellent Good
Excellent Poor Good
Limited application Good Good
This chapter is divided into three major sections that deal with properties of the conventional absorption working fluids. Section 3.1 covers an analytical treatment of thermodynamic properties, Section 3.2 covers a graphical treatment of thermodynamic properties, and Section 3.3 covers transport properties.
3.1 Analytical Treatment of Thermodynamic Properties Thermodynamic property relations for mixtures is a subject that has been well known in chemical thermodynamics for many years going back to Gibbs (1876). More recent general treatments of chemical thermodynamics include Lewis and Randall (1961) and Rowlinson and Swinton (1982). In recent years, mixtures have become commonly used in energy conversion cycles and, hence, a broader range of engineers have become interested in the subject. The subject, as it applies to energy conversion cycles, is treated partially in a wide range of textbooks, but no single source exists that provides a treatment directed at engineers who understand pure fluid thermodynamics but who do not have a background in mixtures. This chapter is designed to fill that void. The objective is to review the subject of mixture thermodynamic property relations and to highlight state-of-the-art approaches to dealing with mixtures. The emphasis in Sections 3.1 and 3.2 is on thermodynamic properties and, specifically, on the relationships between the thermodynamic properties of a mixture. These relationships allow the practitioner to derive thermodynamic properties from measured experimental data, to check the consistency of data, and to apply the laws of thermodynamics to an engineering system. For the sake of simplicity, the explanation here focuses on two-component (binary) mixtures only. From a thermodynamic point of view, a two-component mixture possesses one additional degree of freedom as compared to a pure fluid: the composition.
25
Properties of Working Fluids
The composition may be defined in many different ways, including mass fraction, mole fraction, and concentration. In this text, the mass fraction is used throughout, defined as
x=
mass of one component kg total mass of both components kg
3.1.1 Property Relations for Systems of Fixed Composition The properties of a mixture are related through their definitions and through the concepts of classical thermodynamics, including the First and Second Laws. This discussion is focused on a general binary mixture so as to avoid the complexity associated with additional mixture components. Once the binary mixture analysis is understood, it could be extended to a mixture with an arbitrary number of components without excessive effort. The internal energy of a system (u), or more exactly changes in the internal energy (du), is defined by the First Law, which can be written for a closed system as
du = δq − δw (3.1)
where the heat is assumed positive into the system, and the work is assumed positive out of the system. This analysis is done on a per unit mass basis. To obtain information about the equilibrium properties of a system, one can consider a reversible process. For such a process, the definition of entropy changes can be written as
dq = Tds (3.2)
and the work for a reversible process can be written as
dw = pdv (3.3)
Equation 3.3 assumes that volume change work is the only relevant work mode. Substituting Equations 3.2 and 3.3 into Equation 3.1 yields a fundamental property relation:
du = Tds − pdv (3.4)
Based on the definitions of the enthalpy (h), Gibbs free energy (g), and Helmholtz free energy (ψ), three other forms of Equation 3.4 are obtained as
dh = Tds + vdp (3.5)
dg = vdp − sdT (3.6)
dψ = −pdv − sdT (3.7)
Equations 3.4 through 3.7 provide simple relationships between property changes for a closed system. Although a reversible process was used in the derivation of Equation 3.4, the final result is a relationship between the properties of a closed system that is independent of any process since the relationship only involves properties. Equations 3.4 through 3.7 are frequently used to determine changes in a property based on known changes in other properties. These equations apply to mixture systems and multiphase systems, as well as to single-phase pure fluids, as long as a system of fixed composition is under consideration.
26
Absorption Chillers and Heat Pumps
In all cases, the properties are considered where the system is assumed to be in equilibrium, and the properties represent the average property for the entire system. An additional series of useful property relations can be obtained by assuming functional forms, as indicated by the functions in Equations 3.4 through 3.7. For example, from Equation 3.6, the following functional form is implied:
g = g(T,p) (3.8)
From calculus, the differential of g can be written as
∂g ∂g dg = dT + dp (3.9) ∂T p ∂p T
Equating Equations 3.6 and 3.9 yields ∂g v = (3.10) ∂p T
and
∂g −s = (3.11) ∂T p
Since the properties of interest possess exact differentials, the mixed derivative of g, obtained by differentiating both of Equations 3.10 and 3.11, can be equated to yield
∂s ∂v = − (3.12) ∂T p ∂p T
This relation is one of the so-called Maxwell relations. An analysis similar to the one that resulted in Equations 3.10 through 3.12 can be applied to the other differentials in Equations 3.4, 3.5, and 3.7. The result yields nine more differential equations representing relationships between thermodynamic properties. Many other such relations can be developed. As an example, note that by interpreting Equation 3.5 with respect to changes in temperature at constant pressure, an expression for the specific heat, cp, in terms of the entropy is obtained
∂h ∂s cp ≡ = T (3.13) ∂T p ∂T p
Equation 3.13 is useful if one is interested in the differential of entropy in terms of the independent variables pressure and temperature. Starting from s = s(T,p)
∂s ∂s ds = dT + dp ∂T p ∂p T
=
cp ∂v dT − dp ∂T p T
(3.14)
27
Properties of Working Fluids
where Equations 3.12 and 3.13 have been utilized in the second line. Substituting Equation 3.14 into Equation 3.5 yields a very useful expression for changes in the enthalpy in terms of commonly measured properties.
∂v dh = c p dT + v − T dp (3.15) ∂T p
Equation 3.15 contains the same information as contained in Equation 3.5, but Equation 3.15 is often more useful because the independent variables are those that are typically controlled and measured in experiments. Many insights can be obtained from examination of Equation 3.15. For example, for liquids away from the critical point, the entire term in the brackets can often be neglected, resulting in a simplified approximation for changes in enthalpy (dh = cp dT). The validity of such approximations can be routinely evaluated by referring to the exact expression in Equation 3.15. 3.1.2 Open-System Property Relations In general, mixture thermodynamics implies changes in composition of the system. Such changes can result from chemical reactions or mass flow into or out from the system. In this treatment, chemical reactions are assumed to be unimportant. Thus, the focus in this section is on open systems where transfer of mass between the system and the surroundings is allowed. The composition of a system can be specified in many ways, and in this treatment mass fraction is used. For a binary mixture, a functional form for the Gibbs free energy can be assumed as
g = g(T,p,x1) (3.16)
where x1 is the mass fraction of component 1. By definition, mass fraction changes imply that one is considering an open system. The differential of the function in Equation 3.16 can be written as
∂g ∂g dg = dT + ∂T p , x1 ∂p
∂g dp + dx1 (3.17) ∂ x1 T, p T ,x 1
The first two derivatives on the right-hand side of Equation 3.17 are identical to those in Equations 3.10 and 3.11 with the exception that the constant composition specification is explicit in Equation 3.17. Thus, dg can be written as
∂g dg = − sdT + vdp + dx1 (3.18) ∂ x1 T , p
The remaining partial derivative in Equation 3.18 is related to the chemical potentials, μi, of the components in the mixture defined as the partial molal Gibbs free energy
∂G (3.19) µi = ∂ N i T , p , N j
28
Absorption Chillers and Heat Pumps
where Ni is the number of moles of component i and the constraint Nj implies that the number of moles of all other components is held constant. As it is more convenient to work in terms of the intensive Gibbs free energy (g) and the mass fraction, the following expressions (which can be derived directly from the definition) will be used as the defining expressions for the chemical potentials in a binary mixture.
∂g µ 1 = g + ( 1 − x1 ) (3.20) ∂ x1 T, p
∂g µ 2 = g − x1 (3.21) ∂ x1 T, p
In this form, it is convenient to interpret the chemical potential on a mass basis instead of a molar basis, and it is convenient to refer to these as the partial mass Gibbs free energies. Example 3.1: Relationship between Partial Molal and Partial Mass Properties Consider subcooled liquid ammonia/water at 20°C, 1000 kPa and x = 0.5 (mass fraction of ammonia). Determine (1) the partial mass Gibbs free energy for each of the components, (2) the corresponding partial molal Gibbs free energy, (3) the mole fraction as a function of mass fraction, and (4) the molar enthalpy of the mixture state. (See File: Ex3_1.ees.) Solution:
1. Using Equations 3.20 and 3.21 and the properties of ammonia/water, the following values are obtained. First, the mixture Gibbs free energy is obtained from the mixture enthalpy and entropy as
h = −149.82 J/g
s = 0.14114 J/g - K g = h − Ts = −191.20 J/g Then the partial derivative is approximated numerically by using a small increment in x of Δx = 0.0001. Based on this, the partial derivative is ∂g = 41.147 J/g ∂ x T, p
Finally, the chemical potentials are calculated directly from Equations 3.20 and 3.21 as μ1 = −170.62 J/g μ2 = −211.77 J/g
As the mass fraction used is the mass fraction of ammonia, the subscripts are interpreted as 1 for ammonia and 2 for water.
2. The relationship between partial mass properties and partial molal properties is a simple unit conversion. Partial properties are expressed on the basis of one unit of the material. Thus, they can be expressed as above on a unit mass basis, or they can be expressed on a molar basis as follows by introducing the molecular weight of the species (M1 = 17.031 g/mol (NH3) and M2 = 18.015 g/mol (H2O)).
29
Properties of Working Fluids
µ 1 = µ 1 M1 = −2905.8 J/mol µ 2 = µ 2 M2 = −3815.0 J/mol
where the overbar denotes molar quantities.
3. The mole fraction is directly related to the mass fraction as shown next. First, define the mole fraction of component 1 as xN ,1 =
N1 N1 + N 2
where Ni represents the number of moles of component i. Now, since the number of moles is related to the mass through the molecular weight as m = NM, we have xN ,1 = =
x1 = 0.514 M1 x1 + (1 − x1 ) M2
For ammonia/water, the mass and mole fractions have similar values due to the fact that the molecular weights of the two constituents are close in value.
4. The conversion to a molar basis of the mixture enthalpy, determined on a unit mass basis as a part of the solution of part 1 earlier, is more complicated than the conversion performed in part 2 because mixture properties are expressed on the basis of a unit of mixture. Thus, the mixture enthalpy, given as h = –149.82 J/g, is interpreted as the enthalpy per gram of mixture. The conversion to a molar basis requires the effective molecular weight of the mixture, Meff, which can be calculated as
Meff = xN, 1 M1 + (1−xN, 1) M2 = 17.509 g/mol
m1 M1 m1 M1 + m2 M2
where the units are interpreted as grams of mixture per mole of mixture. Once the effective molecular weight is determined, the conversion is straightforward as h = hMeff = −2623.2 J/mol
Observations: The entire treatment in this text is done on a mass basis. However, some developments in the literature are found on a molar basis. The connection between these two approaches is one to one, but it can be confusing. This example is meant to illustrate the main types of manipulations that are of interest.
The relationship between the chemical potential and the mixture properties can be found by equating g in Equations 3.20 and 3.21, solving for the derivative and substituting into Equation 3.18 yielding dg = −sdT + vdp + (μ1 − μ2)dx1 (3.22) Equation 3.22 represents a generalized version of Equation 3.6 applicable to binary mixtures. The last term involving the chemical potentials represents the energy changes associated with changes in composition.
30
Absorption Chillers and Heat Pumps
The chemical potential of a component in a mixture is a measure of the contribution to the Gibbs free energy associated with that component. It plays a similar role in defining the enthalpy and internal energy associated with each component. For example, the differential of the enthalpy can be written as
dh = Tds + vdp + (μ1 − μ2)dx1 (3.23)
where we see that the term involving the chemical potentials takes an identical form in both Equations 3.22 and 3.23. Although it is defined in terms of the Gibbs free energy, the chemical potential is seen to play an important role in understanding changes in enthalpy with concentration. The chemical potential is also a key variable in defining and understanding phase equilibrium in mixtures. In this context, the chemical potential is found to be a key variable that is as important as the temperature (thermal potential) or pressure (mechanical potential) in understanding mixture thermodynamics. Completely apart from any consideration of chemical reactions, the chemical potential accounts for the energy and entropy of interaction between molecules as they mix. Following from its fundamental role, some additional discussion of the chemical potential is appropriate to gain additional insight into its nature. Based on the definition of μ as the partial mass Gibbs free energy, g can be written as
g = x1μ1 + (1−x1)μ2 (3.24)
Equation 3.24 represents an important general property of partial mass properties. In other words, we can say that the mixture property (g in this case) can be determined by a mass fraction weighted sum of the partial mass properties. It generalizes to other properties, so we could, for example, write a similar expression for the mixture enthalpy in terms of the partial mass enthalpies. Returning to Equation 3.24, differentiating this expression, assuming constant temperature and pressure, yields
dg = x1dμ1 + μ1dx1 + (1−x1)dμ2 + μ2 d(1−x1) (3.25)
but from Equation 3.22, under these conditions, dg is
dg = (μ1 − μ2)dx1 (3.26)
Then, by equating Equations 3.25 and 3.26, one obtains what is often called the Gibbs– Duhem equation
0 = x1dμ1 + (1−x1)dμ2 (3.27)
This equation provides a relationship between changes in the chemical potentials of the components in a binary mixture at constant temperature and pressure. The utility of Equation 3.27 is in understanding the shape of the chemical potentials as a function of composition. It is also occasionally useful for calculating the chemical potential of one component when the chemical potential of the other component is known and for checking thermodynamic consistency. The chemical potential of a pure component is equal to the Gibbs free energy of that component, as can be deduced from Equation 3.20 by setting x1 to 1 (or by setting x1 = 0 in
31
Properties of Working Fluids
Equation 3.21). Thus, the chemical potential of a pure component has a well-defined, finite value. The chemical potential of a component goes to negative infinity as the mass fraction of that component goes to zero. This can be deduced from Equation 3.27 by considering the approach to the pure component 2 state (consider x1 → 0). It is required that μ2 is finite at x1 = 0, so one expects that dμ2 will be finite so as to allow finite values of μ2 for the mixture states. However, as x1 goes to zero, the only way Equation 3.27 can be satisfied is for dμ1 to get large. In fact, μ1 must go to negative infinity at x1 = 0 because, as discussed later in the section on phase equilibrium, mass always transfers in the direction of decreasing chemical potential. Thus, the absence of any molecules of component 1 represents a singularity in the chemical potential. Just like nature abhors a vacuum, a pure fluid condition in the presence of other mixture components creates large chemical potential gradients that cause transport to eliminate the potential difference. The shapes of the chemical potentials for an ideal mixture are plotted in Figure 3.1 to provide the reader with an idea of the nature of the chemical potential. For this plot, the molecular weights of ammonia and water have been used to provide a mass fraction scale. As can be seen, the chemical potential falls off toward negative infinity as the concentration of that component goes to zero. Although this plot is for an ideal mixture, the general shape of these curves holds true for the mixtures of interest here. The chemical potential concept is key to understanding mixture thermodynamics, mixture phase equilibrium, and mass transfer in multiphase systems. The introduction provided here provides a direct method of relating the chemical potential to other thermodynamic variables. The applications, to phase equilibrium and mass transfer are discussed in Section 3.1.7. 3.1.3 Equations of State The usual meaning of the term “equation of state” is a relationship between pressure, volume, and temperature of a substance. In the mixture context, this concept must be generalized to include composition as a variable. It is convenient to generalize it further to cover any equation containing complete thermodynamic information about the substance.
0
(µ−µo)/RT
–1
–2 Component 1
Component 2
0.2
0.8
–3
–4
0
FIGURE 3.1 Chemical potential for an ideal mixture.
0.4 0.6 Mass fraction of component 1
1
32
Absorption Chillers and Heat Pumps
This definition implies that all other thermodynamic properties can be calculated from the equation of state. The most useful of such equations allow thermodynamic properties to be calculated explicitly through the use of the property relations discussed in Sections 3.1.1 and 3.1.2. Such property calculations are simplified if the equation of state is constructed as a fundamental function (Moran et al. 2011), as shown next. The concept of a fundamental function is useful in doing the bookkeeping associated with property relations and in forming equations of state. Based on Equation 3.6, for example, the Gibbs free energy is defined as the fundamental function associated with the independent variables temperature and pressure. Similarly, if one were to choose the temperature and volume as independent variables, the Helmholtz free energy would be the fundamental function. This choice is made for convenience in keeping the analysis organized. Once the independent variables are chosen for a given analysis, the remainder of the analysis can frequently be simplified if it is done in terms of the fundamental function. If an equation of state is formed as an expression relating the fundamental function to the so-called natural variables associated with that function (for example, g = g(T,p)), then all other thermodynamic properties can be derived from the fundamental function with a minimum of effort, starting with Equations 3.10 and 3.11. This approach has been used for pure fluids (Harr and Gallagher 1978; Harr et al. 1984) as well as for mixtures (Ziegler and Trepp 1984; Herold and Moran 1987; Ibrahim and Klein 1993; Yuan and Herold 2005). For the mixture applications, an additional independent variable is needed to define the mixture composition. Once the fundamental function is known as a function of the independent variables, other properties can be computed from it. As a summary, the following relations hold (based on the choice of temperature, pressure, and mass fraction as independent variables and Gibbs free energy as the fundamental function).
∂g v= (3.28) ∂ p T , x1
∂g ∂g u= g −T − p (3.29) ∂T p , x1 ∂ p T , x1
∂g h= g −T (3.30) ∂T p, x1
∂g −s = (3.31) ∂T p , x1
∂2 g (3.32) c p = −T 2 δT p , x1
The chemical potential can also be computed from the Gibbs free energy according to Equations 3.20 and 3.21. All of these property expressions have in common that they do not require integration. This is one key advantage of the fundamental function approach since integration tends to be more cumbersome to implement when dealing with property relations.
Properties of Working Fluids
33
As an example of a pure fluid equation of state constructed using the fundamental function approach, consider a fluid that is incompressible and has a constant specific heat. The equation of state for such a fluid has the form
T g (T , p ) = h0 − T0 s0 + v p − p0 − s0 [T − T0 ] + c p T − T0 − T ln (3.33) T0
In Equation 3.33, h0 and s0 are reference values of specific enthalpy and entropy at the reference temperature, T0 and pressure, P0. This fundamental function reproduces all of the thermodynamic behavior of such a fluid in a single function. It is left to the reader to perform the operations represented by Equations 3.28 through 3.32 and to verify the expected behavior. In fact, the form of Equation 3.33 was determined by integrating from the assumed characteristics (i.e., constant specific volume and constant specific heat). This type of reverse engineering of the form of the equation of state is quite useful in choosing a functional form to fit experimental data. Of course, in most cases of interest the model will be more complicated than that given in Equation 3.33. The reason for including Equation 3.33 here is as a simple but concrete example of the fundamental function concept. Numerous more complicated examples appear in the literature cited. Harr and Gallagher (1978) give a very useful discussion of the method, including details about overfitting, underfitting, and multiproperty fitting, all of which are topics beyond the scope of the present treatment. 3.1.3.1 Thermodynamic Consistency One of the advantages of the equation-of-state approach is that it can lead to superior thermodynamic consistency between different properties for a particular fluid (or substance). If all properties are derived from a single function, then the only inconsistencies should be those resulting from finite precision arithmetic. In the past, thermodynamic data were often calculated and tabulated for future use. Due to the coarse tabulations, it is quite difficult to obtain accurate estimates of related properties from such tabulations. Both differentiation and integration of such data lead to significant errors that tend to propagate and multiply as one performs the calculation. If one then attempts to calculate the original property from derived properties, it frequently does not match the original data. This is thermodynamic inconsistency. The problem of thermodynamic inconsistency arises frequently when entropy data for a given fluid are computed from enthalpy data. Inconsistencies between the entropy and enthalpy data sets then tend to obscure any subsequent entropy analysis, which often involves small differences between large numbers and thus requires highly accurate data. By utilizing an analytical form for the fundamental function, derivatives can be expressed exactly, and all properties computed from the function are inherently consistent. This inherent consistency is quite useful in that it ensures that the properties satisfy the laws of thermodynamics. However, it must be realized that just because the properties resulting from a given equation of state are self-consistent does not imply that they are correct. It is still up to the analyst to formulate a meaningful equation of state. It should be noted that the equation-of-state approach is not necessary to achieve thermodynamic consistency. Careful work using other methods can also minimize error. However, the advantage of the equation-of-state approach is that the consistency comes automatically and the analyst can focus effort on formulating appropriate models.
34
Absorption Chillers and Heat Pumps
Example 3.2: Thermodynamic Consistency Determine the thermodynamic consistency of the IAPWS equation of state for water (IAPWS 2009) around the subcooled liquid state defined by the temperature of 20°C and the pressure of 100 kPa. (See file Ex3_2.ees.) Solution: There are many consistency tests that could be performed if more than one property is available. In this case, the properties predicted by the equation are cp = 4.184 J/g-K
h = 84.006 J/g u = 83.906 J/g
s = 0.29646 J/g-K
v = 0.001002 m /kg 3
Based on these data, a first check is to see whether the enthalpy and internal energy are consistent according to their definition. The definition of enthalpy is h = u + pv and the calculation yields exact agreement through eight digits. A second check is to see whether the enthalpy and the specific heat values are consistent. To do this, the derivative of the enthalpy with respect to temperature must be estimated from the equation of state. This was done with a temperature increment of 0.001 K and the result is ∂h = 4.184 J/g-K ∂T P
These data were found to be consistent up to five digits of accuracy. A third check can be done on the entropy. To facilitate this, the Gibbs free energy is needed. This can be calculated from the definition as g = h – Ts. The derivative of the Gibbs free energy is related to the entropy according to Equation 3.11. The derivative was evaluated numerically here with a temperature increment of 0.001 K. The result is ∂g ∂T = −0.29647 J/g-K P
This matches the entropy out to four digits with a 10% error in the fifth digit. Observation: The IAPWS equation of state for water is the best current data source for water. As it is based on a fundamental equation approach, it is expected to be highly consistent. The method used here to check consistency, involving numerical derivatives with a temperature increment of only 0.001 K, would be expected to introduce some inconsistency. Thus, the consistency tests must be performed very carefully to get meaningful results. If such tests as these were applied to typical data tabulations, much lower consistency would be expected.
3.1.4 Mixture Volume When two miscible species are mixed, the resulting volume is not generally equal to the mass weighted average of the volumes of the pure components. Mixtures where such a simple relationship does hold are termed ideal mixtures. When the molecules of a mixture do not interact significantly, that is, when there are not significant attractive or repulsive forces between the dissimilar molecules, then the mixture can approach ideal behavior. A low-pressure gas mixture is an example where such conditions can occur. However, for most liquid mixtures, the molecules interact significantly and real mixture effects must be considered.
35
Properties of Working Fluids
As an example, consider the volume versus mass fraction plot in Figure 3.2. The data for the plot are for liquid ammonia/water and were generated from a Gibbs free energy equation of state (Ibrahim and Klein 1993). The heavy line represents mixture volume at a pressure of 10 bar and a temperature of 20°C (subcooled liquid states over the entire concentration range). The pure component volumes are found at the limits of mass fraction. An ideal mixture would be represented by the straight line connecting the endpoints. The fact that the actual volume falls below the ideal mixture line indicates that the mixture exhibits a reduction in volume when mixing occurs. This reduction is quantified here in two ways: (1) using partial volume and (2) using the concept of the volume change of mixing. These perspectives are equivalent, and they both lead to some useful techniques for analyzing volume changes. First, consider the volume changes in terms of the partial molal volume. The partial molal volume is defined as ∂V (3.34) vi = ∂ N i T , p , N j
As was done for the partial Gibbs free energy in Equations 3.19 through 3.21, it is convenient to express the partial volumes in terms of the mixture specific volume and the mass fraction as
∂v v1 = v + ( 1 − x1 ) (3.35) ∂ x1 T , p
∂v (3.36) v2 = v − x1 ∂ x1 T , p
2
Specific volume (cm3/g)
Ammonia/water, T = 20°C, P = 1000 kPa 1.5 Ideal mixture ∆vmix = 0.1191 cm3/g
1 Mixture: x = 0.55 v = 1.232 cm3/g Pure component volumes:
0.5
vH O = 0.915 cm3/g
= 1.639 cm /g
vNH = 1.491 cm3/g
2 0 NH3
v 0
Partial mass volumes:
v0H O = 0.998 cm3/g
2
3
3
0.2
0.4
0.6
Ammonia mass fraction FIGURE 3.2 Volume versus mass fraction for ammonia/water.
0.8
1
36
Absorption Chillers and Heat Pumps
As it is convenient to interpret these volumes in mass units, a better term might be to call these partial mass volumes. Equations 3.35 and 3.36 are represented graphically in Figure 3.2 by the tangent line to the mixture volume curve. The intersections of the tangent line with the pure component axes are the partial mass volumes. Example numerical values are given based on a mass fraction of x = 0.55 in Figure 3.2. The partial mass volumes represent the contribution that each mixture component makes to the total volume. Thus, one can add up the mass fraction weighted sum of the partial mass volumes to obtain the total volume as follows
v = x1v1 + (1 − x1)v2 (3.37)
In the example in Figure 3.2, the partial mass volumes at the point x1 = 0.55 are both less than the corresponding pure component volumes. This is consistent with the volume reduction that occurs when ammonia and water are mixed. From this perspective, a portion of that reduction is attributed to each component according to the definition in Equation 3.34. An alternative perspective is to formulate the real mixture characteristics as an ideal mixture with a term added to account for the nonideal behavior. This term is called the volume change of mixing or the excess volume. From this perspective, the mixture volume is expressed as
v = x1v10 + ( 1 − x1 ) v20 + ∆vmix (3.38)
where the superscript 0 denotes the pure component volume. The volume change of mixing is shown in Figure 3.2. The negative value indicates the volume reduction that this mixture experiences. The volume characteristics of aqueous lithium bromide are somewhat different than that of ammonia/water. When in solution, the salt ionizes and occupies more volume than when in the solid phase. Thus, when solid lithium bromide is added to pure water, the volume of the mixture is greater than the volume of the individual components. This implies that the volume change of mixing, defined in Equation 3.38, is positive. However, the magnitude of the volume changes is quite small. This change can be quantified by computing the partial volumes. At a LiBr mass fraction of 0.6 and a temperature of 20°C, the computed volumes are v = 0.5814 cm3/g, vH2O = 1.0003 cm3/g, vLiBr = 0.30214 cm3/g. Values are computed using the SSC equation of state for aqueous lithium bromide (Yuan and Herold 2005). These can be compared against the pure component volumes vH0 2O = 1.002 cm3/g and 0 vLiBr = 0.2887 cm3/g (Weast 1994). The fact that the partial volume of LiBr is greater than the pure component volume is consistent with the volume expansion upon mixing. 3.1.5 Mixture Energy Properties The energy properties referred to here include the enthalpy and internal energy. The entire analysis applies to both properties. To make for a streamlined treatment, the discussion is in terms of enthalpy. Many of the concepts and details introduced in the previous section on mixture volume also apply to the enthalpy. For completeness, these concepts are repeated in terms of the enthalpy to allow the unique aspects of the energy properties to be efficiently introduced. When two miscible species are mixed, the resulting enthalpy is not generally equal to the mass weighted average of the enthalpies of the pure components. As an example, consider
37
Properties of Working Fluids
the enthalpy versus mass fraction plot in Figure 3.3. The heavy line represents mixture enthalpy of liquid ammonia/water (Ibrahim and Klein 1993) for a pressure of 10 bar and a temperature of 20°C (subcooled liquid states). The fact that the actual enthalpy falls below the ideal mixture line indicates that the mixture exhibits a reduction in enthalpy when mixing occurs. This reduction is quantified here in two ways: (1) using partial mass enthalpy and (2) using the concept of the enthalpy change of mixing. First, consider the enthalpy changes in terms of the partial molal enthalpy defined as ∂H hi = (3.39) ∂ N i T , p , N j
As was done for the partial Gibbs free energy in Equations 3.19 through 3.21 and the volume in Equations 3.34 through 3.36, it is convenient to express the partial enthalpies in terms of the mixture specific enthalpy and the mass fraction as
∂h (3.40) h1 = h + ( 1 − x1 ) ∂ x1 T, p
∂h h2 = h − x1 (3.41) ∂ x1 T, p
Equations 3.40 and 3.41 are represented graphically in Figure 3.3 by the tangent line to the mixture enthalpy curve. The intersections of the tangent line with the pure component axes are the partial mass enthalpies. Example values are given in Figure 3.3 for an arbitrary mass fraction of x = 0.55.
300
Mixture: x = 0.55 h = –146.55 J/g Pure component enthalpy: h0H O = 84.74 J/g 2 h0NH = 93.68 J/g 3 Partial mass enthalpy: hH O = –216.15 J/g
200
Enthalpy (J/g)
100
Ideal mixture ∆hmix = –236.2 J/g
2
hNH = –89.60 J/g
0
3
–100 –200 –300
Ammonia/water, T = 20°C, P = 1000 kPa 0
FIGURE 3.3 Enthalpy versus mass fraction.
0.2
0.4 0.6 Ammonia mass fraction
0.8
1
38
Absorption Chillers and Heat Pumps
The partial mass enthalpies represent the contribution that each component makes to the mixture enthalpy. Thus, one can add up the mass fraction weighted sum of the partial mass enthalpies to obtain the total enthalpy as follows
h = x1h1 + (1−x1)h2 (3.42)
In the example in Figure 3.3, the partial mass enthalpies at the point x1 = 0.55 are both less than the corresponding pure component enthalpies. This observation is consistent with the exothermic energy release that occurs when ammonia and water are mixed. From this perspective, a portion of that reduction is attributed to each component according to the definition in Equation 3.42. It should be noted that the fact that the ideal mixture line is almost parallel to the abscissa is a coincidence for this particular mixture and the chosen reference states. An alternative, but equivalent, perspective is to formulate the real mixture characteristics as an ideal mixture with a term added to account for the nonideal behavior. This term is called the enthalpy change of mixing or the excess enthalpy. From this perspective, the mixture enthalpy is expressed as h = x1h10 + ( 1 − x1 ) h20 + ∆hmix (3.43)
The enthalpy change of mixing is shown in Figure 3.3. The negative value indicates the enthalpy reduction that this mixture experiences. The enthalpy of aqueous lithium bromide follows a similar pattern as water/ammonia, with both mixtures exhibiting a large exothermic heat release upon mixing (i.e., a negative heat of mixing). For such mixtures, the partial mass enthalpy of each of the components is expected to be less than the pure component enthalpy. At a mass fraction of 0.6 LiBr and a temperature of 20°C, the partial mass enthalpies are hH2O = –278.0 J/g and hLiBr = 313.9 J/g. The pure water enthalpy at 20°C is hH2O , Pure = 83.93 J/g. The corresponding pure LiBr state is a solid, crystalline salt. To make a meaningful comparison, the reference state enthalpy for the salt must be c hosen consistent with the solution enthalpy reference state (i.e., h = 0 for a saturated liquid at T = 0°C and x = 0.5 mass fraction LiBr). An estimation of the consistent enthalpy for the solid salt is possible based on a solid specific heat of 0.598 J/g-K (Cyprus Foote Minera, n.d.) and a simple mixing experiment. The experiment involves mixing equal masses of anhydrous LiBr and pure water at room temperature and recording the temperature of the resulting m ixture (~93°C). The result is that the enthalpy of the solid is 322 J/g at 20°C. These values are all consistent with the exothermic mixing associated with aqueous lithium bromide. 3.1.5.1 Specific Heat A property related to the enthalpy is the constant pressure–specific heat defined as
∂h cp = (3.44) ∂T p , x1
The relationship of the mixture specific heat to the specific heats of the components can be found by applying the definition in Equation 3.44 to either Equation 3.42 or 3.43. Application to Equation 3.42 results in
∂h ∂h c p = x1 1 + ( 1 − x1 ) 2 = x1c p ,1 + ( 1 − x1 ) c p ,2 (3.45) ∂T p , x1 ∂T p , x1
Properties of Working Fluids
39
The terms in Equation 3.45 are partial mass specific heats of the two mixture components. From this perspective, the specific heat of the mixture is viewed as having contributions from each of the two mixture components. Alternatively, by applying the definition in Equation 3.44 to Equation 3.43, one obtains
∂ h0 ∂ h0 ∂∆hmix c p = x1 1 + ( 1 − x1 ) 2 + = x1c p0 ,1 + ( 1 − x1 ) c p0 ,2 + ∆c p ,mix (3.46) ∂T p , x1 ∂T p , x1 ∂T p , x1
From this perspective, the mixture specific heat is viewed as consisting of the ideal mixture specific heat plus a correction term to account for real mixture effects. Both of the perspectives represented in Equations 3.45 and 3.46 are equivalent and both are useful. 3.1.5.2 Reference States One aspect of the energy properties that is not relevant to the volumetric properties is the need for a reference state. Energy properties are defined only as differences, based on the First Law. Absolute energy values have no intrinsic meaning. However, because it is convenient in utilizing enthalpy values in analyzing engineering systems, common practice is to arbitrarily define a zero energy or enthalpy and to express all values relative to this reference. It should be noted that this applies to pure fluids as well as to mixtures. It is often possible to ignore the reference state when dealing with a pure fluid as long as a single data source is used for all calculations. However, if two or more data sources are used with different reference states, it is necessary to convert all the data to the same reference state before use. This problem is more frequently encountered in dealing with mixtures because each mixture component contributes its own reference state and the possibility of encountering a reference state mismatch increases with the number of choices available. To enable tabulation or specification of enthalpy values for a pure substance, a reference state must be chosen. For example, the reference state commonly chosen for water is the liquid phase at triple point conditions. The internal energy of this state is arbitrarily assigned the value zero. Note that any value could be assigned, but that zero is a convenient choice. Since the enthalpy is defined in terms of the internal energy, it is not possible to independently choose reference values for both. The pv term in the definition of the enthalpy contributes a small term to the enthalpy of liquid water at the reference state. As a conceptual alternative, one could choose to specify the enthalpy as zero at the reference state and to compute the internal energy. However, to enable simple communication with others in the field, we follow convention here. It is usually possible to deduce the reference state by examining a tabulation of energy data. For a pure fluid, the enthalpy can be expressed in terms of the reference state enthalpy as h(T, p; T0, p0) = href (T0, p0) + ∆h(T, p; T0, p0) (3.47) The functional notation used in Equation 3.47 is meant to emphasize the role of the reference state denoted with subscript 0. This result gives a simple recipe for reference state corrections for a pure fluid. In general, to force two data sets to the same reference state, a constant must be added to all the values in one of the sets so that href is the same for both sets. The procedure is slightly more complicated for a binary mixture because two reference states are involved.
40
Absorption Chillers and Heat Pumps
Each of the two pure component enthalpy values appearing in Equation 3.43 can be written as in Equation 3.47. With this substitution, Equation 3.43 becomes
h(T, p, x1; T0,1, p0,1, T0,2, p0,2) = x1 [href,1(T0,1, p0,1) + ∆h1(T, p; T0,1, p0,1)] + (1−x1) [href,2(T0,2, p0,2) + ∆h2(T, p; T0,2, p0,2)] + ∆hmix (T, p,x1) (3.48)
For a binary mixture, two reference states affect the mixture enthalpy, as can be seen in Equation 3.48. The reference state enthalpies contribute according to the relative amount of each component in the mixture. A similar result is obtained if the mixture enthalpy is viewed as in Equation 3.42. In that case, the values of each of the partial mass enthalpies depend on the reference state enthalpy for that component and the reference state enthalpies appear in the mixture enthalpy expression in identical form to that in Equation 3.48. The implication of Equation 3.48 is that the mixture enthalpy depends on the reference state enthalpies according to
href = x1href, 1 + (1−x1)href, 2 = href, 2 + x1(href, 1− href, 2) (3.49)
Equation 3.49 implies that to compare two mixture enthalpy data sets that use different reference state enthalpy values, it is necessary to add a linear function of mass fraction to one of the data sets so that the enthalpy values of both data sets match at both reference states. The linear function has two parameters that can be computed by matching the two states. One restriction is that the two states must be at different mass fractions. Once the reference state correction has been applied, then any remaining differences between the two data sets are substantive. For the mixture water/lithium bromide, the nature of pure lithium bromide is such that it exists as a solid at room temperature and pressure. However, when mixed with sufficient water, it goes into aqueous solution. This behavior complicates the analysis of mixture properties because one does not always wish to include the solid-to-liquid-phase transition in the analysis. For the water component, convention is to use the same r eference state as conventionally used for pure water. For the second enthalpy reference state, common practice is to choose a solution state as the reference state in place of the pure lithium bromide state. One common choice is saturated liquid at x = 0.5, T = 0°C. This highlights the fact that the enthalpy reference states chosen for a mixture are actually mixture states. The analyst must choose two different mixture states for binary systems and assign enthalpy values to those states to define the mixture enthalpy. However, with water/lithium bromide as an exception, in practice it is often convenient to choose the pure fluid states (i.e., x = 0 and x = 1.0) to maintain consistency with pure fluid data tabulations and pure fluid equations of state. It should be noted that the two reference states chosen must be at different mass fractions. 3.1.6 Mixture Entropy When two components mix, there is an entropy increase even if the molecules of the components do not interact (i.e., an ideal mixture). This entropy change of mixing is associated with the fact that two substances can mix spontaneously (e.g., by diffusion), but a mixture will not separate into pure components spontaneously. The entropy change of mixing for
41
Properties of Working Fluids
an ideal mixture is used as a model against which to measure the characteristics of a real mixture. Thus, the entropy changes in an ideal mixture are discussed first. An ideal gas mixture is one example of an ideal mixture. The entropy changes in an ideal gas can be derived directly from Equation 3.14 as
s = s0 + c p ln
p T (3.50) − R ln T0 p0
From an ideal gas mixture perspective, Equation 3.50 applies to each component in the mixture with the pressure interpreted as the partial pressure, pi. The mixture entropy is then s=
f ( x1 ) 0 p ( 1 − f ( x1 )) 0 p T T s0,1 + c p0 ,1 ln s0,2 + c p0 ,2 ln − R ln 1 + − R ln 2 Meff T0,1 p0,1 Meff T0,2 p0,2
=
f ( x1 ) 0 p ( 1 − f ( x1 )) 0 p T T 0 s0,1 + c p0 ,1 ln + − R ln s0,2 + c p ,2 ln T − R ln p Meff T0,1 p0,1 Meff 0,2 0,2
+ =
∆smix ,ideal Meff
(3.51)
1 f ( x1 ) s10 + {1 − f ( x1 )} s20 + ∆smix ,ideal Meff
= x1s10 + ( 1 − x1 ) s20 + ∆smix ,ideal where the entropy change of mixing for the ideal binary mixture is
∆smix ,ideal = −
R f ( x1 ) ln ( f ( x1 )) + ( 1 − f ( x1 )) ln ( 1 − f ( x1 )) (3.52) Meff
and the effective molecular weight was defined in Example 3.1. The composition function is
f ( x1 ) =
x1 (3.53) M1 x1 + ( 1 − x1 ) M2
The function f(x) is actually just the mole fraction, which can be expressed in terms of the mass fraction, as is done here, to maintain a consistency in use of mass fraction throughout the development. Although derived for an ideal gas mixture, the expression in Equation 3.52 applies to any ideal mixture. Figure 3.4 shows the plot of the entropy change of mixing, where the molecular weights of ammonia and water have been used to define the mass fraction coordinates. The characteristic shape shows a maximum entropy of mixing at a mass faction of 0.486 falling off to zero at both pure component limits. For the ideal mixture, the entropy change of mixing is independent of temperature and pressure.
42
Absorption Chillers and Heat Pumps
0
–∆Smix, ideal /R
–0.2
–0.4
–0.6
–0.8
0
0.2
0.4 0.6 Mole fraction
0.8
1
FIGURE 3.4 Entropy of mixing for an ideal mixture.
It is sometimes useful to express the entropy in terms of the partial mass entropies. The partial mass entropy of component 1 in the mixture can be derived from Equation 3.51 as
∂s s1 = s + ( 1 − x1 ) ∂ x1 T , p R ln ( f ( x1 )) =s − Meff
(3.54)
0 1
and the partial mass entropy of component 2 is
∂s s2 = s − x1 ∂ x1 T , p R ln ( 1 − f ( x1 )) =s − M eff
(3.55)
0 2
The mixture entropy can also be expressed as the sum of the mass fraction weighted partial mass entropies as
s = x1s1 + (1−x1)s2 (3.56)
It is left to the reader to substitute Equations 3.54 and 3.55 into Equation 3.56 and demonstrate that this approach is equivalent to that in Equation 3.51. For real mixtures, the mixture entropy can be represented as
s = x1 s10 + ( 1 − x1 ) s20 + ∆smix , ideal + ∆smix , real (3.57)
or equivalently as in Equation 3.56. For a real mixture, the partial mass entropies in Equation 3.56 will have additional terms beyond those of the ideal mixture given in Equations 3.54 and 3.55.
43
Properties of Working Fluids
Although the Third Law of thermodynamics defines absolute entropies, it is common in applications where chemical reactions are not significant to use relative entropy values. This approach involves selecting reference states and assigning reference state entropy values analogous to the method used for enthalpy. This approach works as long as the subsequent analysis using the entropy values involves only differences in entropy. Since the reference state analysis for entropy is identical to that for the enthalpy, no additional discussion of entropy reference states is needed. 3.1.7 Phase Equilibrium Phase equilibrium between liquid and vapor plays a key role in the understanding of absorption technology. A general requirement for phase equilibrium is that the thermodynamic potentials must be equal between the phases. The potentials of interest are thermal (temperature), mechanical (pressure), and mass transfer (chemical potential). If the two phases are represented by a single prime and a double prime, phase equilibrium requires that
T′ = T″ (3.58)
p′ = p″ (3.59)
µ i′ = µ i′′
i = 1, … , n (3.60)
where n is the number of mixture components. The chemical potential of component i, denoted μi, was defined previously in Equation 3.19. This property has been called the escaping potential (Lewis and Randall 1961) because an imbalance in chemical potential between two phases drives a transfer of that component from the phase with the higher chemical potential to the phase with the lower chemical potential. The transfer tends to equalize the potentials between the two phases until, at equilibrium, there is no net transfer between the phases. The composition of the equilibrium phases is, in general, not the same. This characteristic is a key aspect of mixture thermodynamics and is an important property in absorption cycle design. As an example, consider vapor–liquid equilibrium in ammonia/water as plotted in Figure 3.5. Such phase diagrams are sometimes called bubble-point or dewpoint diagrams and are used to visualize certain mixture-phase-change processes such as cooling of superheated vapor at constant pressure, as shown by the line labeled A to B in Figure 3.5. The intersection of line AB with the dew line indicates the temperature at which the first drop of liquid will form (146.1°C in this case). The composition of that liquid can be read from the diagram as well by determining the intersection of the temperature line with the bubble line and then reading the liquid mass fraction off the mass fraction axis (xl = 0.1266 in this case). This determination is indicated by the dashed lines in Figure 3.5. The energy transfers associated with two-phase processes in mixture systems can be calculated if mixture properties are known. The mass fraction variable must be accounted for, and it contributes some complication. The type of analysis required is outlined in the following discussion of the heat of vaporization. 3.1.7.1 Heat of Vaporization The concept of heat of vaporization requires some additional specification when d ealing with mixtures. In particular, it is necessary to fully define the vaporization process under consideration. A constant-pressure vaporization requires a different heat than
44
Absorption Chillers and Heat Pumps
200 Dew line
A
P = 1000 kPa
Temperature (ºC)
150 B 100
50 xl = 0.1266 0
0.2
Bubble line 0.4 0.6 Ammonia mass fraction
0.8
1
FIGURE 3.5 NH3/H2O bubble-point diagram with an example of the cooling of a superheated vapor mixture with initial dew formation.
a constant-temperature vaporization. There are an infinite number of such processes one could use to define the heat of vaporization of a mixture, making it necessary to specify the process being considered whenever the concept is utilized for a mixture. For a pure fluid, it is also necessary to specify the process, but it is generally implied by a specification of either the temperature or the pressure and both remain constant during the vaporization. Since this is not generally true for a mixture, the specification of the vaporization process becomes necessary for clarity. Furthermore, one can define (Bosnjakovic 1965) a total heat of vaporization, for complete evaporation of a liquid sample, or a differential heat of vaporization, for evaporation of an infinitesimal amount of mass from a finite sample of liquid. These two quantities are related, as is discussed next for the constant-pressure process. Consider the differential vaporization process illustrated in Figure 3.6. A balance on the ammonia mass yields
dm dx = (3.61) m x − xv
An energy balance on the same control volume yields
+ ( hv − h ) dm (3.62) dQ = mdh
Normalizing the heat based on the mass flow rate of the vapor yields
∂h q p = hv − h − ( xv − x ) (3.63) ∂x p
where Equation 3.61 has been used to eliminate the mass flow rates in terms of the mass f raction. Also, it should be noted that the constant-pressure specification given in Equation 3.63 is just one of the processes for which one can define such a heat of vaporization.
45
Properties of Working Fluids
Vapor
Liquid
Liquid Differential control volume (expanded view below)
x ,h dm, v v
x, h m,
x+dx, h+dh m–dm,
dQ FIGURE 3.6 Differential vaporization process.
The constant-pressure differential heat of vaporization is denoted by qp. This is interpreted as the rate of heat transfer, on a unit mass basis, required to evaporate an infinitesimal amount of liquid at constant pressure. Alternatively, one can view it as the amount of heat transfer required to evaporate 1 kg of vapor from an infinite amount of liquid. The energy required for complete vaporization of a binary mixture depends on the conditions of the process. The process implied in Figure 3.6 allows the vapor to escape from the system. If the vapor is kept with the liquid (i.e., in equilibrium with the liquid), some additional energy is needed to heat the vapor as the equilibrium temperature changes. For the complete evaporation process, or for a finite partial evaporation process, the heat requirement can be determined by a simple energy balance. For a complete evaporation process, the result is
qc = hv − hl (3.64)
where hv and hl are the vapor and liquid enthalpies, respectively, at the entrance and exit of the process. The heat required, qc, is slightly greater than that obtained from integrating Equation 3.63 over the same process because of the energy required to raise the temperature of the vapor. In the differential vaporization process illustrated in Figure 3.6, the vapor is ducted away from the surface as it is generated. The vapor leaving the liquid surface is assumed to be at the local equilibrium concentration. Furthermore, the liquid is assumed to be well mixed at every location so that the bulk liquid concentration equals the surface concentration. All of these idealizations are not strictly accurate in a real evaporator, but they allow some insight into the evaporation process. In particular, the heat of vaporization defined in Equation 3.63 is a property of the fluid that is related to the actual heat required to evaporate the mixture in a real device.
46
Absorption Chillers and Heat Pumps
˙v m
˙ NH dm
3
˙H O dm
Vapor
2
Liquid
˙l m
Nonuniform heat input FIGURE 3.7 Total evaporation process.
Another evaporation process of interest is total evaporation in a flowing duct with heat applied. This process involves vapor and liquid flowing co-current, as shown in Figure 3.7. As a first approximation, assume that the liquid and vapor are in equilibrium at every point along the tube and that the process is isobaric. In a real case of two-phase flow in a tube, a major flow mode is annular flow, where the liquid flows along the wall, moving slowly due to viscous forces, and the vapor flows, at higher velocity, in the core. This flow mode would not be expected to achieve vapor/liquid equilibrium conditions. Thus, this analysis is rather oversimplified for real-world applications. One difference between this tube-flow process and that illustrated in Figure 3.6 is that in tube-flow the vapor must be heated, along with the liquid, to maintain the equilibrium temperature. Another difference comes from mass balance considerations. For total evaporation, the exiting vapor composition must match the entering liquid composition. By inspection of a bubble-point diagram, such as in Figure 3.5, it is observed that the vapor bubbles that form in the device have much more of the volatile component, as compared to the liquid, at every temperature. For the problem discussed here, the vapor concentration drops continuously throughout the device. Thus, as the temperature rises through the device, it is concluded that the transfer of mass between the liquid and vapor cannot occur at the equilibrium concentration. What happens instead is that as the temperature rises and the equilibrium concentration shifts according to the bubble-point characteristics, the vapor that evolves is enriched in water such that the mass fraction of the equilibrium shifts toward lower mass fraction. The evaporation process is driven by the chemical potential differences between the vapor and the liquid. Thus, in practice, the chemical potential differences of the two components would adjust to drive the required transport of both components. An ammonia mass balance for a differential change in the mass fraction of the liquid can be derived by writing ammonia balances on both the liquid and vapor streams and then eliminating the transfer term between them to yield
N = dm
l + xl m v xv m xl − xv
∂ xv ∂ xl
dxl (3.65)
Similarly for the mass transfer of the water component
H = dm
( 1 − xv ) m l + ( 1 − xl ) m v xl − xv
∂ xv ∂ xl
dxl (3.66)
47
Properties of Working Fluids
The model is completed by enforcing overall mass balance considerations on the liquid and vapor, which amounts to v +m l = m in (3.67) m
in is the inlet mass flow rate. Finally, by definition, where m v = m N +m H (3.68) m
The mass balance details in Equations 3.65 through 3.68 are illustrated for a particular case in the following example. Example 3.3: Total Evaporation of Ammonia/Water Mixture Consider a system consisting of a heated pipe with a mixture of ammonia/water flowing isobarically at a pressure of 10 bar. Analyze the case where the inlet condition is saturated liquid with a mass fraction of ammonia of 0.5. Assuming the vapor and liquid are in equilibrium at every location within the pipe, trace the mass transfer process as the vapor quality goes from 0 to 1.0. In addition, determine the heat transfer rate needed to drive the evaporation process. (See file Ex3_3.ees.) Solution: The inventory of mass can be determined by integrating Equations 3.65 through 3.68 over the full range of concentrations. At 10 bar, the inlet and outlet states are Saturated Liquid (Inlet) T = 63.97°C xl = 0.5 xv = 0.9912
Saturated Vapor (Outlet) T = 153.6°C xl = 0.09813 xv = 0.5
Thus, if we consider the liquid mass fraction as the independent variable, the integration proceeds from 0.5 to 0.098. The derivative in Equations 3.65 and 3.66 was evaluated numerically by introducing an increment in mass fraction and approximating the derivative as
∂ xv ≈ ∂ xl
∆x ∆x xv xl + l − xv xl − l 2 2 (3.69) ∆xi
where the vapor mass fractions are the saturated values associated with the liquid mass fractions in parentheses. The appropriate size for the increment in liquid mass fraction depends on the accuracy required and was chosen as ∆xi = 10−5 for this calculation. The equations can then be integrated numerically. These equations represent a coupled set of first-order ordinary differential equations, and the boundary conditions define the problem as an initial value problem. This system was integrated using the semi-implicit scheme in Engineering Equation Solver (EES). The size of the integration step will influence the accuracy of the final result. The result obtained for an integration step of Δxl = 0.004 is shown in Figure 3.8. The total heat transfer rate needed for the total evaporation process can be obtained simply from an overall energy balance as
in ( hv − hl ) (3.70) Q = m
48
Absorption Chillers and Heat Pumps
1
P = 1000 kPa
Mass flow rate (kg/sec)
0.8
˙l m
˙v m 0.6 ˙n m
0.4 0.2
˙h m 0
0.1
0.2 0.3 Ammonia mass fraction
0.4
0.5
FIGURE 3.8 Mass transfer in total evaporation process.
1
2000
xv
0.8
xt
1500
0.6
1000
0.4
500
0.2
Q˙ 0
0.1
0.2
0.3
Mass fraction
Cumulative heat transfer rate (kW)
2500
0.4
0 0.5
Ammonia mass fraction in liquid FIGURE 3.9 Heat transfer and mass fractions in total evaporation process.
where the enthalpy values correspond to the inlet and outlet of the tube. The heat flux required to evaporate all of the liquid varies along the length of the tube. An energy balance on a differential section yields an expression for dQ as
v +m l dhl + m v dhv (3.71) dQ = ( hv − hl ) dm
By integrating Equation 3.71 over the entire process, the cumulative heat transfer rate profile given in Figure 3.9 is obtained. Also plotted in Figure 3.9 are the equilibrium vapor mass fraction (xv) and the mass fraction of vapor transferring (xt) from the liquid. Discussion: The shapes of the curves in Figures 3.8 and 3.9 are governed by the properties and equilibrium characteristics of ammonia/water. As the total mass flow rate is fixed, the sum of the mass flow rates of the liquid and vapor must equal the inlet value.
49
Properties of Working Fluids
Thus, the point where the two curves cross in Figure 3.8 is the point where each phase carries 50% of the mass. The process proceeds from a liquid mass fraction of 0.5 down to N ) and water about 0.1 (i.e., from right to left on the plots). The flow rates of ammonia ( m ( m H ) in the vapor are a function of the equilibrium concentrations at each location in the device. In a real device, deviations from equilibrium would be expected because p otential differences are required for transport to occur. This example is meant to provide an introduction to some of the complexity inherent in phase change processes in mixtures.
3.1.8 Summary The overview of mixture thermodynamics given here has concentrated on those issues of direct relevance to absorption cycle analysis. Not all of the issues will be addressed in a particular analysis. If the object is to simply calculate the performance of a cycle from a complete set of thermodynamic data, then much of this material will be superfluous. However, if a new working fluid is being used, if the cycle conditions extend beyond the range of available data, or if a detailed component analysis is needed, then many of the topics treated will be found useful. An alternative analysis procedure, useful when limited thermodynamic data are available, is given in Alefeld and Radermacher (1994). The absorption working fluid pairs that are considered in this book are water/lithium bromide and ammonia/water. With few exceptions, all of the calculations in this book, including the generation of the property figures, are done using property routines included in EES program. The water/lithium bromide routines were developed by Yuan and Herold (2005), and the ammonia/water routines were developed by Ibrahim and Klein (1993). A summary of the function calls available for water/lithium bromide are included in two files, as shown in Table 3.2. One file demonstrates the syntax from the original dynamic link library (DLL) implementation. A second file demonstrates a repackaging of the same routines but with more flexible unit capabilities using EES built-in unit conversions. The original DLL formulation provides some additional capabilities, as described in the file. The repackaged version is preferred for general use because of the unit flexibility. For ammonia/water, an original DLL formulation is also available and was used in the first edition of this book. However, it is rather cumbersome to use and its direct use is not r ecommended because all of its functionalities are available in a repackaged version that is built in to EES and uses the familiar syntax from pure fluid property routines. The example file, shown in Table 3.2, demonstrates all of the basic function calls available for ammonia/water. TABLE 3.2 Property Routines Used in This Book Working Fluid Pair
EES Implementation
Features
Ammonia/water
DLL called NH3H2O.dlp
Ammonia/water
EES library
Water/lithium bromide Water/lithium bromide
DLL called LiBrSSC.dll
Original implementation; cumbersome to use due to multiple arguments; fixed units Very flexible, easy to use, syntax similar to other EES property routines, gets properties from original DLL, extended to include transport properties Original implementation, fixed units, more function options Uses EES built-in unit conversions
EES library called SSCLiBr.LIB
Example File
Ex3_5.ees
Ex3_4b.ees Ex3_4a.ees
50
Absorption Chillers and Heat Pumps
3.2 Graphical Perspective on Thermodynamic Properties of Absorption Working Fluids The treatment of absorption working fluids presented in Section 3.1 was analytical in nature. In this section, the focus shifts to a graphical view of absorption working fluid properties and absorption cycle analysis. Both of these approaches have significant value and should be used in parallel by an absorption system designer or analyst. When designing an absorption system, the most important thermodynamic variables to be considered are pressure, temperature, mass fraction, enthalpy, specific volume, and entropy. To display all variables, a multidimensional diagram would be required, but this is not very practical. Several two-dimensional diagrams are in common use. These diagrams show any two variables on their axes and display other variables as sets of curves of constant properties such as isobars and isotherms. Usually, T–s, ln(P)–h, or h–s diagrams are used for design calculations of cycles with pure fluids. However, in absorption processes, the additional variable, composition, must be considered. Historically, enthalpy‑mass fraction diagrams (h–x diagrams) were preferred with temperature and pressure as parameters. Figures 3.10 and 3.11 are examples. They will be discussed later in full detail. 3.2.1 Temperature–Mass Fraction Diagram When the liquid and vapor phases of a mixture coexist in equilibrium, the saturation temperature varies with the mass fraction, even though the pressure is constant. This is in contrast to a pure fluid. Figure 3.12 shows a schematic of a temperature–mass fraction diagram (T–x diagram) for a mixture of two components, A and B, at constant pressure. This is a generic form of the ammonia/water diagram in Figure 3.5. The mass fraction axis ranges from 0 (only component A is present) to 1.0 (only component B is present). 500
Enthalpy (J/g)
400
300
200
180 160 140 120 100 80 60
100
40 20°C
0 0.4
0.45
0.5
0.55 Mass fraction LiBr
FIGURE 3.10 Enthalpy–mass fraction diagram for water/lithium bromide.
0.6
0.65
0.7
51
Properties of Working Fluids
3000 20
2500
10
6 2
1
0.6
60 40
2000
20
0.4 0.2 bar
80 100 bar
Enthalpy (kJ/kg)
10 6 2 1 0.6 0.4 0.2 bar
1500
1000
500
0
–500
0 H2O
260 °C 240 220
100 bar
200 180
60
80
160 140 120 100 80 60 40
40 20 10 6 2 1 0.6 0.4 0.2 bar
0.2
0.4 0.6 Ammonia mass fraction
140 120 100 80 60 40 20 10 0 –10 –20 –30 –40 °C
0.8
1 NH3
FIGURE 3.11 Enthalpy–mass fraction diagram for ammonia/water.
The area below the boiling line (alternatively called the bubble line) represents subcooled liquid. The area above the dew line represents superheated vapor. The area enclosed by the boiling and dew lines is the two-phase region. The boiling point temperature for a mixture of mass fraction x is located (by horizontal projection to the temperature axis) at the intersection of the boiling line and a vertical line through the specified mass fraction. The boiling line indicates the temperature at which the first vapor bubble is formed for the specified pressure and mass fraction. The boiling points of the pure components, TA and TB, are found on the respective ordinates. In Figure 3.12, the boiling point of component A is higher than that of component B. In a similar manner, the dew line indicates the temperature at which the first liquid droplet is formed when a gas mixture of a given mass fraction is cooled and begins to condense. To demonstrate the use of a bubble-point diagram, a slow (quasi-equilibrium) evaporation process at constant pressure in a closed system is illustrated as an example in Figure 3.13. The process begins with subcooled liquid at point 1′. Points with a single prime denote the liquid phase; points with a double prime denote the vapor phase. As the liquid mixture is heated, the temperature increases and eventually the boiling line is reached.
52
Absorption Chillers and Heat Pumps
Pressure = constant
Dew line
Superheated vapor
Temperature
TA
Two
-pha
se r
ang
e
Boiling
TB
line
Subcooled liquid 0 A
Mass fraction of component B
1 B
FIGURE 3.12 Schematic of temperature–concentration diagram (bubble-point diagram).
Pressure = constant
Superheated vapor
4´
T4 Temperature
5´´
Dew line
TA
4´´ 3
3´
T3
Two-phase range 3´´
2´
T2
2´´ TB
Boiling line
1´
Subcooled liquid x2´ – x3´
x3´´ – x3´ 0 A
x3´´
x1,2 Mass fraction of B
x3´´
1 B
FIGURE 3.13 Evaporation process in temperature–concentration diagram.
This is point 2′. Here the first vapor bubble forms. The mass fraction of the first vapor formed is in thermal equilibrium with the liquid found at point 2′ (i.e., T2′ = T2″). The vapor (2″) is enriched in component B as compared to the liquid. Its mass fraction is x2″ > x2′. This is a consequence of the fact that, at the same temperature, component B has a higher vapor pressure than component A.
53
Properties of Working Fluids
As the heating process continues, the evaporation process proceeds to point 3, where the mass fraction of the vapor in equilibrium with the remaining liquid is represented by point 3″ and the mass fraction of the liquid is 3′. At this point, the amount of component B in the remaining liquid has been reduced as compared to point 2′ while the vapor is enriched in component B. However, the vapor contains a lower fraction of component B than at point 2″ and more of component A. As the evaporation process proceeds, the state points of the saturated liquid and vapor phases continue to follow the boiling and dew point lines. When point 4″ is reached, the evaporation process is completed (all the liquid is gone). The vapor has the same mass fraction as the original subcooled liquid at 1′ and the mass fraction of the last liquid droplet is indicated by point 4′. Further heating produces superheated vapor at point 5′′. During the constant-pressure evaporation process, the saturation temperature changed from T2 to T4. The temperature difference (T4 – T2) is termed “temperature glide.” Vapor quality Q (defined as the ratio of mass of vapor over total mass) at point 3 can be calculated based on mass balances for the mixture and one pure component between points 2 and 3.
m3′′+ m3′ = m2′ (3.72)
m3′′x3′′+ m3′ x3′ = m2′ x2′ (3.73)
After elimination of m3′ , the vapor quality is obtained as
Q=
m3′′ x2′ − x3′ = (3.74) m2′ x3′′− x3′
The vapor quality at state 3 is seen to be a ratio of two mass fraction differences. These differences are shown graphically in Figure 3.13. It is worth observing that the vapor quality can be expressed as a function of mass fractions only. Thus, if one has an accurate bubblepoint diagram for the fluid pair of interest, one can determine the vapor quality graphically. The temperature glide can also be determined graphically, as shown for the evaporation process in Figure 3.13. The temperature glide depends strongly on the particular fluid pair under consideration. It can be shown that the temperature glide increases with increasing difference between the boiling points of the two pure components. Figure 3.14a shows a bubble-point diagram for a mixture where the difference in boiling points is relatively small; thus, the temperature glide ∆T is small as well. Figure 3.14b shows a bubble-point diagram of a mixture where the difference of the boiling points is larger. Accordingly, the temperature glide is large as well. The size of the temperature glide is also a function of the mass fraction. For small and large mass fraction, the glide is generally smaller than for intermediate values of mass fraction because the bubble and dew lines converge at both extremes in mass fraction. The mixtures in Figures 3.12 through 3.14 were traditionally termed “non-azeotropic mixtures” or, in more recent literature, “zeotropic mixtures.” The name implies that in phase equilibrium the mass fractions of the vapor and liquid phases are always different. Some fluids form more complicated azeotropic mixtures; for example, a mixture of R12 and R152a or a mixture of water and ethanol. For an azeotropic mixture, the mass fractions of the liquid and vapor phases are identical at a certain pressure and temperature, as shown in Figure 3.15. This state where the vapor and liquid mass fractions are equal is called the azeotropic point. The temperature glide is zero at this point. At all other mass fractions, an azeotropic mixture exhibits zeotropic behavior. The difference in mass
54
Absorption Chillers and Heat Pumps
P = constant
P = constant
De
wl
ine
ΔT Boi
ling
line
ΔT
line Temperature
Temperature
Dew
Boil
ing
line
ΔX
ΔX Mass fraction
Mass fraction
(a)
(b)
FIGURE 3.14 Size of temperature glide dependence on boiling point difference. (a) small difference, (b) large difference.
Pressure = constant
Pressure = constant Vapor Temperature
Temperature
Vapor
Azeotropic point
Liquid Liquid A
Mass fraction
Azeotropic point B
A
Mass fraction
B
FIGURE 3.15 Schematic of the temperature–concentration diagrams for two variations of an azeotropic mixture.
fraction between the liquid and vapor phases changes its sign when the overall mass fraction varies from a value less than the azeotropic mass fraction to a value larger than the azeotropic mass fraction. There are two types of azeotropes. These are distinguished from one another by the location of the boiling point at the azeotropic mass fraction relative to the boiling points of the pure fluids. The boiling point can either be higher than the boiling point of either of the two constituents of the mixture or lower than the boiling point of either of the two constituents as illustrated in Figure 3.15. Azeotropic mixtures can complicate certain mixture processes such as purification. The mixtures of primary interest in this book are zeotropic and thus the complexity of azeotropic mixtures can generally be avoided in absorption cycle analysis. This brief mention of azeotropic mixtures is included only to provide context to the mixture discussion.
55
Properties of Working Fluids
For water/lithium bromide, the T–x diagram has less utility because the vapor phase is essentially pure water. The main purpose of the T–x diagram is to allow the user to understand the relationship between the vapor and liquid mass fractions. But for water/ lithium bromide this relationship is known: the vapor is pure water independent of the liquid concentration. 3.2.2 Pressure–Temperature Diagram For preliminary investigations and comparisons of working fluids, the pressure– temperature diagram (or vapor pressure diagram as it is often referred to) turns out to be very helpful. In one common form, the logarithm of the pressure is plotted versus the negative reciprocal of the temperature. This diagram is referred to at times as the ln(P), (–1)/T diagram. The advantage of this representation is the fact that plots of saturation temperature versus saturation pressure are almost straight lines for most fluids and fluid mixtures when the mass fraction is constant. These plots are referred to as vapor pressure curves. Figure 3.16 shows vapor pressure curves for water and ammonia. The following statements in this paragraph are valid for pure fluids only. The area to the left of the vapor pressure curve of one particular fluid represents higher pressures and/or lower temperatures than saturation values and represents subcooled liquid. In contrast, the area to the right represents higher temperatures and/or lower pressures and represents superheated vapor. The two-phase range is represented by the vapor pressure line itself. In some representations, the vapor pressure curves are drawn exactly as straight lines. In those cases, the scale of the pressure axis is adjusted accordingly. These diagrams were originally developed by Dühring and are referred to as Dühring plots. For mixtures of fluids, curves similar to vapor pressure curves can be created by plotting the vapor pressure versus –1/T for isosteres (lines of constant mass fraction)
Pressure (kPa)
10,000
1000
100
Ammonia Water
10 –0.005
–0.004
–0.003
–0.002
–1/T (K–1) 200
300 T (K)
FIGURE 3.16 Pressure–temperature plots for pure ammonia and pure water.
400
500
56
Absorption Chillers and Heat Pumps
of the saturated liquid phase. As for pure fluids, this format has the advantage that the resulting curves tend to be very linear over a wide range of temperature. Alternatively, the logarithm of vapor pressure can be plotted against temperature (without the –1/T transformation) and the result is generally less linear but more convenient. Figure 3.17 shows such a P–T diagram for water/lithium bromide and Figure 3.18 for ammonia/water. The space between the vapor pressure curves of the pure constituents Pure water
Vapor pressure (kPa)
1000
5 0.4 5 0.5
100
0
0.5
0
0.6
5
0.6
0.70 mass fraction LiBr
10 Crystallization line
1 0.1 0.01 50
0
150
100
200
Temperature (°C)
FIGURE 3.17 Pressure–temperature diagram for water/lithium bromide.
10 –0.0045
–50
–0.004
0
FIGURE 3.18 Pressure–temperature diagram for ammonia/water.
1
2
H2O
0.
3
–0.0035
0.
NH3
0.
100
0. 4
1000
0. 7 0. 6 0. 5
Pressure (kPa)
10,000
–0.003 –1/T (1/K) 50 T (°C)
–0.0025
100
150
–0.002
–0.0015
200 250 300
57
Properties of Working Fluids
of the mixture is termed the “solution field.” These pressure–temperature diagrams of the most common absorption working fluids are used extensively for the representation of cycle configurations. 3.2.3 The Enthalpy–Mass Fraction Diagram The enthalpy–mass fraction diagram (h–x diagram) was originally introduced by Merkel and Bosnjakovic (Niebergall 1959). It found wide applications for the design of absorption heat pumps and distillation equipment. It provides information about enthalpies, composition of the liquid and vapor phases, temperature, and pressure. All lines on this diagram represent saturation properties. Enthalpy–mass fraction diagrams for water/lithium bromide and ammonia/water are given in Figures 3.10 and 3.11, respectively. Figure 3.19 shows a schematic of a constant pressure h–x diagram indicating three regions. The lower region displays properties of the liquid phase. Figure 3.11 shows sets of isotherms and isobars in this region. In Figure 3.10, only isotherms are shown for the sake of simplicity. Although the isobars and isotherms represent saturated liquid, they are also approximately valid for subcooled liquid, assuming that the enthalpy of the liquid phase is independent of the pressure. This assumption is usually fulfilled quite well when the temperature is below 90% of the critical temperature.
P = constant
Dew line
Superheated vapor
Two-phase range Enthalpy
Isotherm T1
Isotherm T2
Boiling line Subcooled liquid A
Mass fraction
B
FIGURE 3.19 Schematic of an enthalpy–concentration diagram for a generic mixture showing a single isobar.
58
Absorption Chillers and Heat Pumps
The middle region of the h–x diagram, as shown in Figure 3.19, represents the twophase region. This area is bordered by the boiling and dew lines, which are isobars in this case. The enthalpy difference at the endpoints (x = 0 and x = 1.0), between the boiling and dew lines, represents the latent heat of evaporation of the pure fluids. Within the two-phase region, the equilibrium vapor and liquid states can be connected by a tie line. Tie lines are both isotherms and isobars (all the lines in Figure 3.19 are for a single value of pressure). Two examples of typical tie lines are shown in Figure 3.19. The more complicated form in Figures 3.10 and 3.11 results when multiple pressure traces are included on a single diagram (requiring an alert user). The tie lines shown in Figure 3.19 can be generated in Figure 3.11 using the auxiliary lines by projection. For a particular saturated vapor state on a dew line for a particular pressure, project horizontally until an intersection with the auxiliary line for that pressure is reached. That yields the equilibrium liquid mass fraction paired with the original vapor mass fraction. Then project vertically down to the bubble line for that pressure. The tie line can then be drawn with a ruler between the two (vapor and liquid) end states. This construction is shown in Figure 3.20. The upper region of the diagram is the superheated vapor area. In this area, the isotherms approximate straight lines since the heat of mixing of gases is negligible at low pressure. The isotherms are usually not displayed in the vapor region to avoid complexity in the diagram.
P = constant Superheated vapor
Dew line
Au
xil
iar
yl
Enthalpy
ine
m
er
th
Iso
Boilin
g line
Subcooled liquid A
x0´
x0´´
B
Mass fraction FIGURE 3.20 Schematic for finding the saturated vapor mass fraction from a given saturated liquid mass fraction using the auxiliary line.
59
Properties of Working Fluids
3.3 Transport Properties In addition to the thermodynamic properties, transport properties are important for the design of absorption systems. The impact of temperature and composition on these properties is significant; thus, it is useful to plot the properties to obtain an understanding. The thermal conductivity and dynamic viscosity of water/lithium bromide are plotted in Figures 3.21 and 3.22. Similar plots for ammonia/water are provided in Figures 3.23 and 3.24. One dramatic difference between these pairs is the significant effect of LiBr concentration 0.8
Thermal conductivity (W/m-K)
0.7 0.6 0.5 0.4
50˚C
T = 0˚C
100˚C
0.3 0.2 0.1 0
0.1
0.2
0.4 0.5 0.3 Mass fraction LiBr
0.6
0.7
0.8
FIGURE 3.21 Thermal conductivity of aqueous lithium bromide.
Dynamic viscosity (N-s/m2)
0.02
0.015
0.01 T = 0˚C
50˚C
0.005
100˚C 150˚C 0
0.1
0.2
FIGURE 3.22 Dynamic viscosity of aqueous lithium bromide.
0.3 0.4 0.5 Mass fraction LiBr
0.6
0.7
0.8
60
Absorption Chillers and Heat Pumps
Thermal conductivity (W/m-K)
2
1.5
150˚C
1 100˚C 0˚C
0.5
0
50˚C
0
0.2
0.4 0.6 Mass fraction NH3
0.8
1
FIGURE 3.23 Thermal conductivity of ammonia/water.
Dynamic viscosity (N-s/m2)
0.0025
0.002
0.0015 0°C 0.001
50°C
0.0005
100°C
150°C 0
0.2
0.4
0.6
0.8
1
Mass fraction NH3 FIGURE 3.24 Dynamic viscosity of ammonia/water.
on viscosity. At high mass fraction, the viscosity rises by a factor of 5 over the value of pure water. The viscosity of the liquid has significant impact on the design of solution components such as pump, absorber, desorber, and solution heat exchanger. For ammonia/water, the viscosity is relatively low over the full concentration range except when the temperature is very low. These plots are not meant to be comprehensive but only to represent the importance and the accessibility of transport property information. Both of these properties are
61
Properties of Working Fluids
included in the property routines available in EES (files used to create the figures in this section are Fig3_21_and_3_22.ees and Fig3_23_and_3_24.ees). These files demonstrate the syntax of calls to the transport property functions in EES. At typical solution loop temperatures and concentrations, the viscosity of water/lithium bromide is on the order of 10 times larger than the ammonia/water viscosity, while the thermal conductivity is about the same. The large viscosity of water/lithium bromide has significant impact on the design of all the components in the solution loop.
Homework Problems 3.1 Derive Equations 3.20 and 3.21 from Equation 3.19. 3.2 Consider a mixture of ammonia and water. Evaluate the chemical potential of NH3 in both the liquid and vapor phases at equilibrium for the state at T = 100°C and P = 10 bar. 3.3 Repeat Problem 3.2 for the chemical potential of H2O. 3.4 Perform the analysis in Section 3.1.6 in terms of mole fraction. 3.5 The mixture molecular weight, Meff, is defined by
NMeff = m
where m is the mass of the mixture and N is the number of moles in the mixture. a. Find an expression for the mixture molecular weight in terms of the component molecular weights and the mole fraction. b. Repeat for the mass fraction. 3.6 Consider NH3/H2O liquid at P = 10 bar, T = 50°C, and x = 0.5 mass fraction. a. Determine the mixture specific enthalpy. b. Convert the mixture specific enthalpy to molar units (kJ/kmole). c. Determine the partial mass enthalpy of each of the components. d. Determine the enthalpy of mixing. e. Convert the partial mass enthalpy values to molar units. f. Convert the enthalpy of mixing to molar units. 3.7 Consider the properties of aqueous lithium bromide along a 50°C saturated isotherm. Since the states are all saturated, the state of the equilibrium vapor is fully known. Since it is essentially pure water vapor, the chemical potential is known. Thus, the chemical potential of the water in the liquid is also known. From this information, determine the chemical potential variation of the lithium bromide in the liquid. Hint: Use the Gibbs–Duhem equation (Equation 3.27). 3.8 Write a function to compute the specific heat at constant pressure for ammonia/ water and water/lithium bromide from the enthalpy. 3.9 Evaluate the chemical potential of LiBr in both the liquid and vapor phases at equilibrium for the state at T = 50°C and P = 4 kPa. Note that this problem is a natural follow-on problem to Problem 3.7.
62
Absorption Chillers and Heat Pumps
3.10 Repeat Problem 3.9 for H2O. 3.11 Check the thermodynamic consistency of the data for both ammonia/water and water/lithium bromide by integrating Equation 3.15 and comparing the result with the enthalpy differences obtained directly. It is of interest to perform this check at several points throughout the domain. To make the problem more specific, consider the following specifications: a. Ammonia/water from (T,p,x) = 100°C, 25 bar and 0.5 mass fraction ammonia to 80°C, 27 bar and 0.5 mass fraction ammonia. b. Ammonia/water from (T,p,x) = 100°C, 1 bar and 0.5 mass fraction ammonia to 120°C, 1.2 bar and 0.5 mass fraction ammonia. c. Water/lithium bromide from (T,p,x) = 100°C, 30 kPa and 0.6 mass fraction lithium bromide to 120°C, 40 kPa and 0.6 mass fraction lithium bromide. 3.12 Generate an enthalpy–mass fraction diagram for water/lithium bromide. 3.13 Generate a pressure–temperature–mass fraction diagram for water/lithium bromide. 3.14 Generate an enthalpy–mass fraction diagram for ammonia/water. 3.15 Generate a pressure–temperature–mass fraction diagram for ammonia/water.
References Alefeld, G. and R. Radermacher. (1994). Heat Conversion Systems. Boca Raton, FL: CRC Press. Bosnjakovic, F., translated by Blackshear, P.L., Jr. (1965). Technical Thermodynamics. New York: Holt, Rinehart and Winston. Cyprus Foote Mineral. (n.d.). Technical Data—Lithium Bromide. Cyprus Foote Mineral, Engelwood, CO. Gibbs, J. W. (1876). On the Equilibrium of Heterogeneous Substances. Transaction of the Connecticut Academy of Arts and Sciences 3: 108–520. Harr, L. and J. S. Gallagher. (1978). Thermodynamic Properties of Ammonia. Journal of Physical and Chemical Reference Data 7(3): 635–792. Harr, L., J. S. Gallagher, and G. S. Kell. (1984). NBS/NRC Steam Tables. New York: Hemisphere. Herold, K. E. and M. J. Moran. (1987). A Gibbs Free Energy Expression for Calculating Thermodynamic Properties of Lithium Bromide/Water Solutions. ASHRAE Transactions-American Society of Heating Refrigerating and Air-Conditioning Engineers 93(Pt. 1): 35–48. IAPWS. (2009). Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. IAPWS, at http://www.iapws.org/ relguide/IAPWS95-Rev.pdf. Ibrahim, O. M. and S. A. Klein. (1993). Thermodynamic Properties of Ammonia-Water Mixtures. ASHRAE Transactions 99: 1495–1502. Lewis, G. N. and M. Randall. (1961). Thermodynamics. Revised by Pitzer, K.S., and Brewer, L. 2nd ed. New York: McGraw-Hill. Macriss, R. A., J. M. Gutraj, and T. S. Zawacki. (1987). Absorption Fluid Data Survey: Final Report on Foreign Data. ORNL Report, Oak Ridge, TN, ORNL/Sub84-47989/2. Macriss, R. A. and T. S. Zawacki. (1989). Absorption Fluid Data Survey: 1989 Update. ORNL Report, Oak Ridge, TN, ORNL/Sub84-47989/4. Moran, M. J., H. N. Shapiro, D. D. Boettner, and M. B. Bailey. (2011). Fundamentals of Engineering Thermodynamics, 7th ed. New York: Wiley.
Properties of Working Fluids
63
Niebergall, W. (1959). Sorptions-Kaltemaschinen, Handbuch der Kaltetechnik, Vol. 7. Berlin: Springer-Verlag. Rowlinson, J. S. and F. L. Swinton. (1982). Liquids and Liquid Mixtures, 3rd ed. Butterworths, London. Sun, J., L. Fu, and S. G. Zhang. (2012). A Review of Working Fluids of Absorption Cycles. Renewable & Sustainable Energy Reviews 16(4): 1899–1906. Weast, R. C. (1994). Handbook of Chemistry and Physics, 75th ed. Boca Raton, FL: CRC Press. Yuan, Z. and K. E. Herold. (2005). Thermodynamic Properties of Aqueous Lithium Bromide Using a Multiproperty Free Energy Correlation. HVAC&R Research 11(3): 377–393. Ziegler, B. and C. Trepp. (1984). Equation of State for Ammonia-Water Mixtures. International Journal of Refrigeration 7(2): 101–106.
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4 Thermodynamic Processes with Mixtures In this chapter, thermodynamic processes involving mixtures are discussed with emphasis on how mixtures change the operation of equipment as compared to pure fluids. As shown in Section 3.2.1, one of the important changes is the introduction of a temperature glide, that is, nonisothermal evaporation, even though the pressure is constant.
4.1 Mixing of Fluids and the Heat of Mixing To explain the phenomenon of the heat of mixing, the following steady-state experiment is discussed. As shown in Figure 4.1, two fluid streams, labeled 1 and 2, are entering a mixing chamber. The mass flow rate of each stream, its temperature, and enthalpy are assumed to be known. It is further assumed that the pressure of both fluid streams is the same. The product of this mixing process leaves the mixing chamber as stream 3 at the same pressure as the two incoming streams. For the sake of simplicity, it is assumed that the two entering streams are pure fluids, for example, ammonia and water (but the analysis is unchanged when this is relaxed). The mixing chamber is adiabatic. The following mass balances must apply:
1 + m 2 = m 3 (4.1) m
1 x1 + m 2 x2 = m 3 x3 (4.2) m
Now we define f as a mass flow rate ratio
f=
1 m (4.3) m3
Then the other flow rate ratio can be expressed in terms of f using Equation 4.1 as
2 m −m 1 m = 3 = 1 − f (4.4) 3 3 m m
Combining Equations 4.1 through 4.3 yields
x3 = fx1 + (1 − f)x2 (4.5)
which can be rearranged to yield
f=
x3 − x2 (4.6) x1 − x2 65
66
Absorption Chillers and Heat Pumps
x1,h1,m· 1,T1,P1 · x3,h3,m3,T3,P3
· x2,h2,m2,T2,P2 · Q
FIGURE 4.1 Steady-state mixing of two fluid streams. P = constant Vapor Dew line
Tie
Enthalpy h1
2
h2
e
lin
3
h3
1
Bubble line Liquid x3
Pure absorbent
Mass fraction
Pure refrigerant
FIGURE 4.2 Constant pressure mixing process on an enthalpy–mass fraction diagram.
Now consider an energy balance on the adiabatic mixing process
1 h1 + m 2 h2 = m 3 h3 (4.7) m
3 and introduce the definition of f in Equation 4.3 to get Divide through by m
h3 = fh1 + (1 − f )h2 (4.8)
which can be rearranged as
f=
h3 − h2 (4.9) h1 − h2
When the properties (enthalpy and mass fraction) and flow rates of streams 1 and 2 are known, then the enthalpy, mass fraction, and flow rate of the mixed state (point 3) can be found quite readily from Equations 4.1 and 4.2 and the enthalpy–mass fraction diagram, Figure 4.2. According to Equations 4.6, 4.8, and 4.9, h3 is located on a straight line (tie line) on h–x coordinates that connects the state points of the two incoming
67
Thermodynamic Processes with Mixtures
streams, 1 and 2. Point 3 is located where the vertical line representing x3 intersects the tie line between points 1 and 2. The construction shown in Figure 4.2 for the mixing of two pure fluid streams works identically when one or both of the inlet streams are mixed states themselves. The steps are the same: (1) compute the outlet mass fraction by invoking Equations 4.1 and 4.2, (2) locate the inlet states on the h–x diagram, and (3) draw the tie line to determine the outlet enthalpy. The example shown in Figure 4.2 mixes a subcooled liquid state (state 1) with a superheated vapor state (state 2), resulting in a twophase state (state 3). The method works equally well independent of the phase as long as the points can be located on the h–x diagram. It should be noted that the enthalpy, mass fraction, and flow rate associated with the two-phase state are the average values (averaged over both phases). One interesting mixing case is if both inlet states are saturated liquid, one pure water and one pure ammonia at the same pressure. You can visualize this in Figure 4.2 as the endpoints of the bubble line. If the flow rates are the same, then the mass fraction of the outlet state will be 0.5. Due to the curvature of the bubble line, it is evident that the mixing of these two liquids will generate a two-phase state. In this case, the heat of mixing contributes to vapor generation. Another interesting case to consider is mixing of pure liquid water and pure liquid ammonia at the same temperature (and pressure). Assume both streams have the same mass flow rates. Now because the vapor pressure of ammonia is much higher than that of water, the water state must be subcooled. Solving this case on an h–x diagram is routine if you have both isotherms and isobars, as in Figure 3.11. If we consider a pressure of 20 bar and inlet temperatures of 20°C, the mixed outlet state is subcooled liquid at 72°C. The temperature rises considerably due to the heat of mixing between ammonia and water. A computer model of a related problem is included as Ex4_1_ NH3H2O.ees. For typical absorption fluid pairs, the heat of mixing is negative and there is an energy release upon mixing. Nevertheless, for an adiabatic process, the construction using the tie line to find h3 is still valid. The energy balance of Equation 4.8 is independent of the heat of mixing (i.e., the tie line construction is independent of the fluid properties). Once point 3 is located on the enthalpy–mass fraction diagram, the temperature of point 3 can be determined from the isotherm passing through that point. Similar graphical constructions can be done for water/lithium bromide using an h–x diagram. For this fluid pair, the vapor is essentially pure water. The role of graphical solutions of such mixture energy balance problems is as a complement to detailed computer solutions. The ability to visualize the solution on a graph remains a powerful tool even when most calculations involve computerized determination of the properties. Example 4.1: Adiabatic Mixing with Water/Lithium Bromide Consider an adiabatic mixing process where two water/lithium bromide solution streams, at the same temperature, are mixed. Assume that the mixing process occurs isobarically at a pressure of 1 bar. The data for the two streams are given. The object is to determine the outlet state. (See file Ex4_1_H2OLiBr.ees.)
Stream 1 Stream 2
T (°C)
x (Mass Fraction LiBr)
Mass Flow Rate (kg/sec)
50 50
0.5 0.6
1.5 7.5
68
Absorption Chillers and Heat Pumps
Schematic: 1 Adiabatic mixing chamber
3
2
Analysis: An overall mass balance yields 3 = m 1 +m 2 m = 9.0 kg/sec
A mass balance on the LiBr yields x3 =
1 x1 + m 2 x2 m 3 m
= 0.58333 mass fraction LiBr
Based on the known data for the input streams, the enthalpy values can be obtained from an enthalpy-concentration chart or from software that provides the specific enthalpy for the mixture. The results obtained from Engineering Equation Solver (EES) are h1 = 107.30 J/g, h2 = 137.27 J/g. An energy balance on the chamber then yields the enthalpy of the exiting stream as h3 =
1h1 + m 2 h2 m 3 m
= 132.28 J/g
Technically, the state is now fully determined since three properties are known. However, it is of interest to determine the temperature. This is done by a reverse process to the one used to find the inlet enthalpy values. The result is T3 = 51.4°C. Observations: Due to the high pressure specified, all three solution states are subcooled liquid. Although the pressure is well above the saturation pressure for these states, the effect of pressure on enthalpy is still negligible. The mass fraction of the outlet state lies between the mass fractions of the two inlet streams. This is also true of the enthalpy. The temperature of the outlet stream is higher than the temperature of either of the inlet streams because of the exothermic nature of the mixing process. Some of the internal energy associated with the LiBr–H2O interactions in the inlet streams is liberated and shows up as an increase in the thermal energy (i.e., as a temperature increase). A similar problem is solved for ammonia/water in file Ex4_1_NH3H2O.ees.
4.2 Specific Heat of Mixtures The specific heat of a mixture was considered in Section 3.1.5 in terms of partial enthalpy but is treated here in terms of the mixture enthalpy. Assume the experiment of Figure 4.1 is now conducted as an isothermal process. Then qmix is the amount of energy (the heat of
69
Thermodynamic Processes with Mixtures
mixing per kilogram of solution) that has to be removed to maintain a constant temperature. The energy balance yields
fh1 + (1 − f)h2 − h3=qmix (4.10)
1/m 3. By taking the derivative of Equation 4.10 with respect to temperature at where f = m constant pressure, all specific enthalpies result in specific heats at constant pressure
fc p 1 + ( 1 − f ) c p 2 − c p 3 =
dqmix dT
(4.11) P,x
Solving for the specific heat of the mixture, cp3, the following expression is obtained.
c p 3 = fc p 1 + ( 1 − f ) c p 2 −
dqmix dT
(4.12) P,x
Thus, the specific heat of the mixture is equal to the mass fraction-weighted average of the specific heats of the constituents plus a so-called mixing term that accounts for the change of the heat of mixing with temperature. Equation 4.12 is very important for the construction of the single-phase regions of enthalpy–mass fraction diagrams.
4.3 Desorption The term “desorption” describes the generation of vapor from the condensed phase (liquid or solid) of a mixture of two or more components. The term generally implies that the vapor contains predominantly one component, in contrast to evaporation where all components are assumed to vaporize. A typical example is the desorption of water out of a water/lithium bromide mixture or of ammonia/water vapor out of an ammonia/water mixture. Figure 4.3 shows a desorption process in a steady-state, steady flow configuration. By adding thermal energy to the entering stream 1, a vapor stream 2 is generated while any remaining liquid leaves as stream 3. It is assumed that the properties of all three streams are known. The mass balance for the overall mass flow is written as 2 +m 3 = m 1 (4.13) m
Vapor · x2,h2,m2,T2,P2
· x1,h1,m1,T1,P1 Liquid · · qd=Q/m2 FIGURE 4.3 Desorption process.
x3,h3,m· 3,T3,P3 Liquid
70
Absorption Chillers and Heat Pumps
and for one component as
2 x2 + m 3 x3 = m 1 x1 (4.14) m
2), the solution circulation ratio, f, can be After dividing by the vapor mass flow rate (m introduced
f=
1 m (4.15) 2 m
By introducing f, the following equations are all based on one unit of mass of refrigerant vapor produced in the desorption process. As will be shown later, this greatly simplifies the understanding of the interdependence of the variables involved. Rewriting the mass balance, Equation 4.14, using f yields
fx1 − (f − 1)x3 = x2 (4.16)
which can be arranged as
f=
x2 − x3 (4.17) x1 − x3
It should be noted that f depends only on the mass fractions of the entering and leaving streams. The energy balance on the system in Figure 4.3 yields
qd + fh1 = h2 + (f − 1)h3 (4.18)
2 is the desorption energy required per unit mass of vapor generated. The where qd = Q /m energy balance can be rearranged by solving for qd to obtain
qd = h2 − h3 + f(h3 − h1) (4.19)
This equation can be understood in the following way. The heat supplied for the desorption process, qd, consists of two terms (h2 − h3) and f(h3 − h1). The first term is an enthalpy difference between the liquid and vapor at the outlet. This term can be seen as the energy required for the actual phase change process. The second term is the enthalpy difference between the liquid streams entering and leaving the desorber multiplied by the solution circulation ratio. This term accounts for the temperature change of the remaining liquid. Referring to Figure 3.13, it can be seen that the temperature of the remaining liquid is increasing as such an evaporation process progresses. Figure 4.4 shows the desorption process in an h–x diagram. It is assumed here that all entering and leaving fluid streams are saturated and that the desorption process occurs at constant pressure. As it is assumed that three properties of each stream are known, the state points can be plotted. For Figure 4.4, it is also assumed that the vapor leaving the desorber is in equilibrium with the incoming liquid stream. However, the correctness of this assumption for a real design depends strongly on the design of the actual heat exchanger. In Figure 4.4, the isotherms Ta and Tb are shown. The isotherm Tb continues through the two-phase area to the vapor state 2, which is assumed to be in equilibrium with the incoming liquid stream. At the bottom of the h–x diagram in Figure 4.4, the relationship between the solution circulation ratio f and the mass fractions is shown by
71
Thermodynamic Processes with Mixtures
P = constant 2
Enthalpy
Tb 3
1
Ta
Tb
P = constant f–1
1
f x3 Pure absorbent
x1
x2
Mass fraction
Pure refrigerant
FIGURE 4.4 Desorption process in an h–x diagram for a mixture such as NH3/H2O, where both components are volatile.
applying the lever rule as follows. When, according to Equation 4.17, f is proportional to the difference x2 – x3, then f – 1 is proportional to the difference x2 – x1. This result can be shown by subtracting 1.0 from both sides of Equation 4.17 and doing some minor algebra. This graphical representation is an application of the lever rule defined by Equation 4.17. The amount of energy per unit mass of vapor required for the desorption process can be determined by a graphical procedure. For this purpose, Equation 4.19 is rewritten as qd = h2 − hd (4.20)
with
hd = h3 − f(h3 − h1) (4.21) Equation 4.21 can be rearranged to yield
f=
hd − h3 (4.22) h1 − h3
By using Equations 4.17 and 4.20 through 4.22 and applying the lever rule, the heat of desorption can be determined graphically on the h–x diagram, as shown in Figure 4.5. The desorber heat is the difference between the enthalpy of the leaving vapor stream, h2, and hd. hd is found graphically by using the relationship between the differences in concentration and enthalpy, as shown in Equations 4.21 and 4.17. This construction locates hd at the intersection of the extension of the tie line between points 1 and 3 with the isostere of the vapor (point 2). Thus, if we know the locations of all three points on the h–x diagram, we can determine the desorption heat with a ruler. Although such graphical methods have been largely supplanted by computer calculations, there is still significant complementary value in visualizing the process on a property graph.
72
Absorption Chillers and Heat Pumps
P = constant 2
h2
Enthalpy
Tb qd
3
1
Ta
P = constant Tb
hd f–1
1
f x3
x1
Pure absorbent
x2
Mass fraction
Pure refrigerant
FIGURE 4.5 Graphical representation of the desorber heat requirement at constant pressure. P = constant 2
h2
Enthalpy
Tb 3
qd
1
Ta Tb
P = constant
1s
1
hd
f–1 f
x3 Pure absorbent
x1 Mass fraction
x2 Pure refrigerant
FIGURE 4.6 Desorption process in h–x diagram with subcooled inlet stream.
The same method yields correct results independent of the state of the streams. For example, the entering solution may be subcooled or the leaving vapor may be superheated. As long as the respective state points are known, qd can be found either by Equation 4.19 or via the graphical method. Figure 4.6 shows an example where the incoming liquid is subcooled, state point 1s. The value of the resulting specific enthalpy, hd, decreases considerably as compared to Figure 4.5, increasing the desorber heat requirement. This is
73
Thermodynamic Processes with Mixtures
TABLE 4.1 Properties of Ammonia/Water at the State Points Defined in Figure 4.3 1 2 3
h (kJ/kg)
P (Bar)
Quality
T (K)
x
245.9 1575.4 396.5
9.2 9.2 9.2
0.000 1.000 0.000
100 100 123.6
0.300 0.922 0.200
particularly important for absorption systems because a subcooled desorber inlet is a common occurrence, and the desorber heat increases considerably due to the need to heat the solution stream to saturation before desorption begins. Example 4.2: Desorption from NH3/H2O The heat of desorption is calculated for the process in Figure 4.3. The inlet conditions of the rich liquid stream 1 are given as follows: T1 = 100°C, x1 = 0.30 and the fluid is saturated. The outlet conditions for the poor solution are given as x3 = 0.20 and the solution is saturated. It is assumed that the vapor is in equilibrium with the incoming liquid. (See file Ex4_2_NH3H2O.ees.) Solution: Using the enthalpy–mass fraction diagram or suitable software, the conditions of all state points can be determined, as shown in Table 4.1. With these properties and Equations 4.17 and 4.19, the mass flow rate of the rich solution per unit mass of vapor generated (f) as well as the amount of heat required can be calculated. f amounts to 7.216. This means further that the flow rate of the weak solution is f – 1 = 6.216. The heat requirement is 2265 kJ/(kg of vapor). The code is written so that the user can easily enter a subcooled inlet state (by entering a nonzero value for dTs) to see the effect on desorber heat, as illustrated in Figure 4.6. A similar problem is solved in Example 4.3 using water/lithium bromide as the working fluid.
Example 4.3: Desorption of Water from Aqueous Lithium Bromide Consider a desorber operating at steady state with the following operating data. Determine the heat input needed. Assume pressure losses are negligible and that the pressure is 10 kPa throughout. (See file: Ex4_3_H2OLiBr.ees.)
Point 1 Point 3
T (°C)
x (Mass Fraction LiBr)
Mass Flow Rate (kg/sec)
50 Saturated
0.55 0.60
1.0
Schematic: 2
Desorber 1
3 . Qd
74
Absorption Chillers and Heat Pumps
Assumptions: The exiting solution stream at 3 is saturated. The vapor exits the desorber at the saturation temperature of the entering solution stream. Isobaric process. Analysis: The vapor mass flow rate is obtained from mass balance considerations as 2 = m 1 −m 3 m x 1 1 − 1 =m x3
= 0.0833 kg/sec Similarly, the solution outlet flow can be written as
3 = m 1 m
x1 x3
1 =m
x1 x3
= 0.9167 kg/sec The enthalpy of the solution streams can be obtained from property charts, correlations, or computer programs. An h–x diagram such as Figure 3.10 enables the user to read the enthalpy values for points 1 and 3 from the respective isotherms. Point 1 is a subcooled state. Using the subcooled liquid approximation, the enthalpy is read from the chart at the same temperature and mass fraction. The water vapor (point 2) is superheated and the properties are taken from a pure water data source. The results using EES are h1 = 117.5 J/g, h3 = 216.9 J/g, and h2 = 2650 J/g. Based on these enthalpy values, the energy balance on the desorber yields 2 h2 + m 3 h3 − m 1h1 Q d = m
= 302.1 kW The energy required to raise the inlet stream temperature up to the saturation temperature can also be calculated. Designate the saturation state corresponding to the mass fraction of stream 3 as 3s. The saturation temperature can be obtained from a Dühring plot or an appropriate correlations as T1s = 80.4°C. The enthalpy is then h1s = 180.6 J/g. The sensible heat required is obtained from an energy balance on the inlet stream as 1 ( h1s − h1 ) Q sen = m
= 63.0 kW Then the remainder is the heat of vaporization of the working fluid Q vap = Q d − Q sen
= 239.1 kW For comparison, consider the heat that would be required to vaporize stream 2 at the same pressure (hfg = 2392 J/g) 2 h fg Q fg = m
= 199.3 kW
75
Thermodynamic Processes with Mixtures
Observations: The heat requirement can be broken down into two categories: sensible heat and heat of vaporization of the working fluid. The sensible heat requirement for this case is approximately 20% of the total heat requirement. This is fairly typical in practice. The heat of vaporization can be viewed as consisting of the heat of vaporization of pure water and the heat of mixing of the liquid solution. A rough comparison can be made with the heat of vaporization of water at the same pressure. This indicates that the heat of mixing is approximately 20% of the heat of vaporization. This is fairly typical for water/lithium bromide in absorption chiller practice. Normalization of the inlet mass flow rate using the vapor flow rate gives f=
1 m x3 = 2 x3 − x1 m
It is noted that this expression takes a different form for water/lithium bromide compared to that in Equation 4.17 for ammonia/water. The difference comes about because of two factors: (1) the vapor is pure water so the LiBr mass fraction of the vapor is zero, and (2) the mass fraction used for water/lithium bromide is the mass fraction of the absorbent while for ammonia/water the mass fraction of the refrigerant is used. The energy balance calculations follow directly from Equations 4.19 through 4.21. It is a good exercise to check the result against the definition qd =
Q d 2 m
A similar model for an ammonia/water desorber is included in Example 4.2.
4.4 Absorption The term “absorption” describes the transfer of a binary vapor into an absorbent mixture in a liquid or solid state. It is similar to “condensation” in the sense that a phase change occurs from a vapor to liquid. However, “absorption” implies that there is already a condensed phase present at the absorber inlet. Absorption is a complex coupled heat and mass transfer process that has been treated extensively in the literature (Haselden and Malaty 1959; Grossman 1983, 1991a, 1991b; Vliet and Cosenza 1991; Merrill et al. 1994; Miller and Perez Blanco 1994; Kyung et al. 2007). Figure 4.7 shows a schematic of an absorber. The vapor stream 2 is entering the absorber together with the liquid stream 1. After the vapor is absorbed into the condensed phase within the absorber and the heat of absorption released, the liquid product stream 3 is produced. Again, mass and energy balances can be applied to determine the heat transfer rate required by the absorption process. The analysis procedure is analogous to that done for the desorber. As a final result, we obtain for the absorber
qa = h2 − h1 + f(h1 − h3) (4.23)
with qa representing the amount of heat released per unit of mass of vapor absorbed and 3/m 2. As found for the desorber, there are f the solution circulation ratio defined as f = m
76
Absorption Chillers and Heat Pumps
Vapor · x2,h2,m2,T2,P2 · x3,h3,m3,T3,P3
· x1,h1,m1,T1,P1
Liquid
Liquid
· Qa
FIGURE 4.7 Absorption process. P = constant 2
h2
Enthalpy
Tb qa
1
3
Ta
P = constant Tb
x1 H2O
ha
x3
x2
Mass fraction
NH3
FIGURE 4.8 Absorption in h–x diagram with saturated inlet and outlet liquid streams and saturated vapor.
two terms in Equation 4.23, one for the phase change of the vapor and a second one that represents the cooling of the solution. The absorption process is shown in an h–x diagram in Figure 4.8. It is assumed that the liquid streams 1 and 3 are saturated. The vapor state point 2 represents vapor of the same pressure as the liquid streams; however, this vapor is not necessarily in thermodynamic equilibrium since it is supplied from some unknown source. In fact, the vapor could be superheated (2 would be located above the isobar), contain liquid droplets (2 would be located in the two-phase region), and can have any mass fraction, different from the one indicated in Figure 4.8. The graphical analysis shown in Figure 4.8 works for all of these cases. The absorber heat qa is the difference between the enthalpy of the vapor and the intersection of a line projected from the two liquid states to the vapor concentration. The graphical analysis follows directly from Equation 4.23, which can be rearranged, introducing ha, as
qa = h2 − ha (4.24)
77
Thermodynamic Processes with Mixtures
with ha = h1 − f(h1 − h3) (4.25)
Solving Equation 4.25 for f yields an expression that contains only differences in enthalpy. By expressing f also in terms of mass fraction, the lever rule can be applied, as shown in Figure 4.8. In this case, ha is found at the intersection of the line defined by points 1 and 3 with the isostere of point 2. This graphical construction to determine the absorber heat qa is quite similar to the analysis done for the desorber. A second absorber case is illustrated in Figure 4.9. In this case, the solution inlet is of two phases with a small amount of vapor, as one might expect coming from the desorber. This inlet condition shifts the tie line (defined by points 1 and 3) such that the absorber heat increases. Clearly, to minimize the absorber heat, the absorber inlet must have as low an enthalpy as possible. It is worth noting again that the graphical method on an h–x diagram works independently of the phase of the various state points. Thus, during component design, engineers are often seen drawing alternative designs on h–x diagrams while they think about the energy impacts. It is sometimes argued that the advent of computerized analysis tools, such as those emphasized in this book, makes the graphical approaches obsolete. The reality seems to be that absorption systems are sufficiently complicated that graphical insight is very powerful as a complement to computer calculations. In some absorption heat pumps, a so-called adiabatic absorber is employed. In this type of design, the incoming liquid stream is subcooled significantly. During the absorption process, the temperature of the liquid stream increases until saturation is reached, at that point the absorption process ceases. There is no heat released to the outside, qa = 0. An h–x diagram for an adiabatic absorber is shown in Figure 4.10. In this case, all three points are on the same line and ha becomes equal to h2. P = constant 2 h2
Ta
Enthalpy
Tb 1
qa
3
P = constant
Ta Tb
ha
x1 H2O
x3 Mass fraction
x2 NH3
FIGURE 4.9 Absorption process in h–x diagram with two-phase solution inlet, saturated liquid outlet, and saturated vapor inlet.
78
Absorption Chillers and Heat Pumps
P = constant 2 h2 = ha
Enthalpy
qa = 0
3 P = constant 1
x1
x3
x2 Mass fraction
H2O
NH3
FIGURE 4.10 Adiabatic absorption.
TABLE 4.2 Properties of Ammonia/Water at the State Points According to Figure 4.7 h (kJ/kg) 1 2 3
14.1 1278 –119.8
P (Bar)
Quality
T (°C)
x
0.585 0.585 0.585
0.000 1.000 0.000
35.0 –11.5 16.3
0.200 0.999 0.300
Example 4.4: Absorber Using NH3/H2O The heat of absorption is calculated for the absorption process in Figure 4.7. The inlet conditions of the liquid stream 1 are given as follows: T1 = 35°C, x 1 = 0.20, and the fluid is saturated. The outlet conditions for the rich solution are given as x 3 = 0.30, and the solution is saturated. It is assumed that the vapor originates from an e vaporator of the same pressure and has a mass fraction of 0.999. (See file Ex4_4.ees.) Solution: Using the enthalpy–mass fraction diagram or suitable software, the conditions of all state points can be determined, as shown in Table 4.2. With these properties and Equations 4.17 and 4.23, the mass flow rate of the rich solution per unit mass of vapor generated (f) as well as the amount of heat required can be calculated. f is found to be 7.99. The heat requirement is 2334 J/(g of vapor).
79
Thermodynamic Processes with Mixtures
Example 4.5: Absorption of Water Vapor into Aqueous Lithium Bromide Consider a water/lithium bromide absorber operating at steady state with the following operating data. Determine the cooling needed. Assume pressure losses are negligible and that the absorber pressure is 1 kPa throughout. (See file Ex4_5.ees.)
Point 1 2 3 4
x (Mass Fraction LiBr)
T (°C)
0.60a 0 0.55 0.6
b
10 Saturated, Q = 0 50
Mass Flow Rate (kg/sec)
1.0
The overall composition of the two-phase state is 0.6. Temperature determined by flashing calculation.
a
b
Assumptions: The solution exiting the valve as stream at 1 is saturated. Isobaric process. Analysis: The vapor mass flow rate is obtained from an overall mass balance 2 = m 3 −m 1 m x 3 1 − 3 =m x1 = 0.0833 kg/sec
1 = m 3 m
x3 x1
= 0.9167 kg/sec
The enthalpy of the solution stream at 3 is obtained from property charts or correlations as h3 = 89.6 J/g. Point 1 is a two-phase state arising from the solution partially flashing as it passes through the expansion valve. It was assumed that the temperature of the solution entering the valve is 50°C. Schematic: 2
Absorber 4
3
1 . Qa qa = . m2
This results in an enthalpy of h4 = 137.3 J/g. The process in the valve is assumed to be adiabatic so that h1 = h4. Based on the assumed temperature of the vapor stream,
80
Absorption Chillers and Heat Pumps
the enthalpy of water vapor is h2 = 2519 J/g. Based on these enthalpy values, the energy balance on the absorber yields 1h1 + m 2 h2 − m 3 h3 Q a = m
= 246.2 kW
Based on the given conditions at 1, the vapor quality is 0.26% and the temperature is 46.3°C. Because a portion of the water in the solution flashes, the liquid mass fraction entering the absorber is 0.6016. Observations: Frequently, the heat requirement in the absorber is approximately equal to the heat requirement in the desorber (of course, the direction is opposite). The heat requirement is larger than one would estimate from pure water considerations due to the heat of mixing in the solution. The heat of mixing increases the heat requirement in both the desorber and the absorber.
4.5 Condensation and Evaporation The terms “condensation” and “evaporation” refer to the phase change of a pure fluid or a mixture where the process is complete; that is, there is only vapor entering the condenser (no liquid stream as in an absorber) and there is only vapor leaving the evaporator. The details of condensation heat transfer can be complicated by a number of factors such as noncondensable gases (Minkowycz and Sparrow 1966; Sparrow et al. 1967). In an enthalpy–mass fraction diagram, the state points describing the beginning and end of the process are located on the same line of constant mass fraction. The energy released or absorbed in this phase-change process per unit mass of vapor is calculated as
q = hout − hin (4.26)
where hout and hin represent the enthalpies of the leaving and entering fluid streams. In the case of condensation, the entering vapor may be superheated, in which case hin is the enthalpy of superheated vapor. Furthermore, the leaving condensate may be subcooled liquid. In the case of the evaporator, the vapor at the exit may be saturated, superheated, or contain liquid droplets, depending on the design of the system. Example 4.6: Condensation and Evaporation of Water Consider a condenser and an evaporator connected by an expansion valve. Based on the given pressures and flow rate, determine heat transfer rates in the components. The high pressure is 10 kPa and the low pressure is 1 kPa. The mass flow rate of water into the condenser is 0.15 kg/sec and the inlet temperature is 50°C. (See file Ex4_6_H2O.ees.) Assumptions: Outlet from the condenser is a saturated liquid. Outlet from the evaporator is a saturated vapor. Throttling valve is adiabatic.
81
Thermodynamic Processes with Mixtures
Schematic: . Qc Condenser
7
8 Refrigerant expansion valve 9 Evaporator . Qe
10
Analysis: Incoming vapor (point 7) is superheated and the enthalpy can be obtained from the steam tables as h7 = 2591.8 J/g. The condenser exit is saturated liquid yielding h8 = 191.8 J/g. An energy balance on the condenser yields 7 ( h7 − h8 ) Q c = m
= 360.0 kW
Based on an adiabatic throttling model, we get h9 = h8. The enthalpy of the saturated vapor at point 10 is h10 = 2513.3 J/g. An energy balance on the evaporator yields 7 ( h10 − h9 ) Q e = m
= 348.2 kW
Observations: The load in the condenser is slightly higher than that in the evaporator due primarily to the superheating of the inlet vapor to the condenser. In a typical absorption cycle, the condenser and evaporator loads are approximately 10%–20% less than the corresponding generator and absorber loads (this rule of thumb is violated in many advanced cycles). This difference is largely due to the heat of mixing effects in the solution that are not present in the pure fluid. A similar model based on ammonia/water is included as file Ex4_6.NH3H2O.ees.
4.6 Compression Although not encountered often in the analysis of absorption cycles, a brief description of vapor compression is included here. An ideal compression process would be thermodynamically reversible and adiabatic. Together these specifications imply an isentropic process. Thus, as a starting point in the analysis of compression, we assume an isentropic process. Enforcing a process to occur along a line of constant entropy is a simple matter in
82
Absorption Chillers and Heat Pumps
a computerized analysis. Entropy is one of the properties available for both of our absorption working fluid pairs. Although the process occurs along a line of constant entropy, the work associated with the process is obtained from an enthalpy difference. The compression work per unit mass of working fluid is calculated using an energy balance, as shown next. w = hout − hin (4.27)
hout and hin represent the enthalpies of the entering and leaving fluid streams. A pumping process is compression of a liquid and is discussed next.
4.7 Pumping In absorption systems, liquid pumps are used for two purposes. The first is for circulating liquid streams through heat exchangers for increased heat and mass transfer, and the second is to convey liquid from the low-pressure side to the high-pressure side. As shown in Equation 3.15 for a pure fluid, the enthalpy difference can be expressed as
∂v dh = c p dT + v − T dP (4.28) ∂T P For incompressible flow (dv = 0), this equation simplifies to
dh = cpdT + vdP (4.29)
Also the following equation holds for the entropy change of a pure fluid (Klein and Nellis, 2012).
ds =
cp ∂v dT − dP (4.30) ∂T P T
Assuming that the compression process is isentropic, ds = 0. Then, since the fluid is incompressible (dv = 0), it is concluded that it is also isothermal, dT = 0, based on Equation 4.30. For an isothermal and incompressible process, Equation 4.29 shows that the enthalpy change is just the volume multiplied by the pressure change. When this result is integrated over a finite process and inserted into an energy balance on the pump, the pump work is calculated as
= Phigh − Plow v m W (4.31) ηp
(
)
Phigh – Plow represents the pressure difference across the pump, v is the specific volume of the mass flow rate, and ηp the pump efficiency. This type of pump model is the liquid, m used for all of the cycle models in all chapters except Chapters 12 and 13. It is noted that the specific volume of a liquid is generally quite low. Thus, even for a substantial pressure
83
Thermodynamic Processes with Mixtures
difference, the pump work is generally low. Furthermore, liquids do not experience much volume change (i.e., they come close to being incompressible), and this is particularly true for small molecule polar liquids like water and ammonia. Thus, as you raise the pressure on such a liquid, there is very little energy storage (unlike compression of a gas). It is not uncommon for a pump to operate with an efficiency of greater than 0.75 for large-capacity systems. Thus, for most absorption cycle applications, it is found that pump work is a minor component in the energy balance.
4.8 Throttling In absorption systems, throttling devices such as expansion valves, orifice plates, and capillary tubes are used to reduce the pressure of a liquid stream passing from the high-pressure side to the low-pressure side. The throttling process is assumed to be adiabatic, with negligible kinetic energy changes resulting in a constant enthalpy process. Since the enthalpy and the overall mass fraction of the stream do not change while passing a throttle under these conditions, the state point on the enthalpy–mass fraction diagram does not change either (Figure 4.11). When 1 represents the entering stream and 2 the leaving stream, then they occupy the same position. However, what does change are the other variables like temperature and pressure. Referring to Figure 4.11, before the throttle process, point 1 is subcooled liquid at pressure P1 and temperature T1. After the throttling process, the pressure has dropped to P2 and the fluid is now in the two-phase range. The new temperature, T2, is indicated by the respective isotherm in Figure 4.11. P = P1
Enthalpy
P = P2
P = P1 1,2
T1
P = P2
T2 x1,2 H2O FIGURE 4.11 Throttling process.
Mass fraction
NH3
84
Absorption Chillers and Heat Pumps
When a liquid is throttled, the outlet state can be subcooled or a portion of the liquid can flash (vaporize) as it passes through the throttle. The end result depends on the particular conditions. In general, when the inlet stream is more highly subcooled, the outlet stream will have less flash vapor. Assuming that the process is adiabatic, the amount of flash gas and the vapor quality of the outlet stream can be readily calculated, as shown in the following three examples. Example 4.7: Throttling Process with Pure Fluid Determine the outlet state from a throttling valve where water is throttled from a condenser to an evaporator. Assume the pressures are fixed at 10 and 1 kPa and that the inlet temperature ranges from the saturation temperature down to sufficient subcooling to ensure that the outlet state is still subcooled. (See file Ex4_7.ees.) Solution: The inlet state is completely specified once the pressure and temperature are specified. For a pressure of 10 kPa, the saturation temperature is 45.82°C. At the saturated liquid state, the enthalpy of the water is 191.8 J/g. For an adiabatic throttle (with no significant changes in velocities), the energy balance simplifies to Δh = 0. This implies that the enthalpy at the outlet equals the enthalpy at the inlet. Thus, for the outlet state, the enthalpy and the pressure are known. Since two properties completely define state for a pure fluid, the other properties of interest, including the temperature and vapor quality, can be determined. This determination typically requires an iterative process using the property routines (which is transparent in EES). This calculation was done for a series of temperatures, and the result is given in the following table. Tin (°C) 45.817 45.0 35.0 25.0 15.0 5.0
Tout (°C)
Q (Fraction)
6.970 6.970 6.970 6.970 6.970 5.002
0.065 0.064 0.047 0.030 0.014 —
h (J/g) 191.8 188.4 146.6 104.8 62.9 21.0
Observations: The last run, at an inlet temperature of 5°C, results in a subcooled state at the outlet because the inlet enthalpy is sufficiently low that there is not enough energy in the stream to cause vaporization. For that case, the temperature actually rises slightly as the liquid passes through the throttle. The temperature rise is due to viscous friction effects. In all other cases, a portion of the mass flashes as it passes through the throttle with a maximum of 6.5% when the liquid enters in a saturated state. For all the cases where the outlet is of two phases, the temperature is the same as determined by the given outlet pressure. Example 4.8: Throttling Aqueous Lithium Bromide Determine the outlet state from a throttling valve where aqueous lithium bromide is throttled. Assume the pressures are fixed at 10 and 1 kPa, the solution mass fraction is 0.6, and the inlet temperature ranges from the saturation temperature down to sufficient subcooling to ensure that the outlet state is still subcooled. (See file Ex4_8.ees.) Solution: This example is similar to Example 4.7 with the additional complexity that the fluid is a binary mixture. It is a special case of a binary mixture for which the vapor composition is known (i.e., vapor is pure water). The basic energy balance on the throttle
85
Thermodynamic Processes with Mixtures
remains the same. The iterative solution process is also quite similar (again transparent in EES). At the conditions specified for the inlet, the saturation temperature of aqueous lithium bromide is 91.02°C and the enthalpy is 216.9 J/g. The outlet conditions for a range of inlet temperature are indicated in the following table.
Tin (°C) 91.0 90.0 80.0 70.0 60.0 50.0 45.0
Tout (°C)
Q (Fraction)
49.8 49.7 48.8 47.9 47.1 46.3 45.0
0.0288 0.0281 0.0217 0.0154 0.0090 0.0026
xl,out (Mass h (J/g) Fraction LiBr) 216.9 214.9 195.4 175.9 156.5 137.3 127.7
0.6178 0.6174 0.6133 0.6094 0.6054 0.6016 0.6000
Observations: The last run, with an inlet temperature of 45°C, resulted in no flashing across the throttle. In this case, there is no temperature increase predicted for the throttling of the essentially incompressible liquid because the property model assumes the liquid volume is independent of pressure. For a binary mixture, as considered here, the vapor that flashes causes the mass fraction of the remaining liquid to change as it passes through the throttle. This can be seen in the last column, where the liquid mass fraction at the outlet is tabulated. It can also be seen in the fact that the temperature at the outlet changes according to how much vapor flashes. A useful relationship applicable to water/lithium bromide flashing can be derived from mass balance considerations only, resulting in
Q=
xl , out − xin xl , out
where Q is the vapor fraction (i.e., the vapor quality), xin is the inlet mass fraction, and xl,out is the outlet liquid mass fraction. It is interesting to compare the amount of flashing that occurs for pure water versus water/lithium bromide. In Examples 4.7 and 4.8, it was found that the temperature drops about 40°C in both cases, but the amount of flashing that occurs with water/ lithium bromide is less than half as much. This can be traced to the specific heat of the liquid, which is more than twice as high for water as it is for the water/lithium bromide solution considered here. The energy that causes flashing comes from the liquid and that is why the temperature drops during flashing. Liquid water can store more than twice as much energy per unit temperature change as compared to the mixture. The specific heat of water/lithium bromide is always less than that of water, over the entire mass fraction range. Example 4.9: Throttling of Liquid Ammonia/Water Determine the outlet state from a throttling valve where liquid ammonia/water is throttled. Assume the pressures are fixed at 1000 and 500 kPa, the solution inlet mass fraction is 0.3, and the inlet temperature ranges from the saturation temperature down to sufficient subcooling to ensure that the outlet state is still subcooled. (See file Ex4_9.ees.) Solution: The solution here is identical in concept to the preceding two examples. One difference here is that the vapor mass fraction is not known and must be included in the
86
Absorption Chillers and Heat Pumps
iterative calculation. It is assumed that the vapor and liquid at the outlet are in equilibrium. The results are indicated in the below table. Tin (°C) 103.5 100.0 90.0 80.0 70.0
Tout (°C)
Q (Fraction)
h (J/g)
xl,out
x v,out
84.24 83.25 80.45 77.70 70.08
0.052580 0.045700 0.026060 0.006414
261.8 246.0 201.1 156.8 113.0
0.2657 0.2702 0.2831 0.2959 0.3000
0.9179 0.9219 0.9323 0.9415
Observations: The overall observations are similar to those in the preceding two examples. The ammonia/water property routines used here do include a pressure term in the enthalpy determination; thus, the throttling of a liquid shows a temperature increase, as shown in the last case tabulated. For ammonia/water, the ammonia mass fraction decreases as vapor flashes because the mass fraction is defined in terms of the more volatile component. The opposite trend was seen for aqueous lithium bromide in Example 4.8 because the mass fraction is defined in terms of the less volatile component (i.e., the LiBr). Once again, a useful relationship can be derived from mass balance considerations only to yield
Q=
xin − xl , out xv , out − xl , out
where Q is the vapor fraction (i.e., the vapor quality), xin is the inlet mass fraction, xl,out is the outlet liquid mass fraction, and xv,out is the outlet vapor mass fraction. The specific heat of ammonia/water liquid at the inlet conditions is about 4.5 J/g·K. Thus, we see even more flashing in this case than was seen for pure water.
4.9 Ammonia Purification There are two standard ways to remove water vapor from an ammonia/water vapor mixture. The first is partial condensation and the second involves a counterflow purification column (Bogart 1981) that also includes a partial condensation step. In partial condensation, the vapor is cooled so that a small fraction condenses. The condensate, also called the reflux, has a low ammonia mass fraction compared to the vapor (i.e., it contains a larger fraction of water), as can be seen in a bubble-point diagram, which implies that the remaining vapor has a higher ammonia concentration. A counterflow purification column requires partial condensation at the top of a column, resulting in liquid reflux falling through the column collecting water from the upflowing vapor in counterflow contact. Thus, a purification column uses partial condensation as one component of the column to achieve a higher level of purification. 4.9.1 Reflux Cooling or Partial Condensation Partial condensation is performed in a component called reflux cooler. To enrich the ammonia in the vapor, it is brought into contact with a cooled surface in the reflux cooler.
87
Thermodynamic Processes with Mixtures
v2 (3) Enriched vapor
qref
Weak absorbent
Reflux cooler
l2 (5)
v1 (4)
l1 (1)
Strong absorbent (2)
qdes FIGURE 4.12 Reflux cooler. Numbers in parentheses are point numbers in Ex4_10.ees. lx and vx notations, also used in Example 4.11, help clarify which points are assumed to be in equilibrium (e.g., v1 and l1 are assumed to be in equilibrium).
The surface temperature is kept below the dew point of the vapor stream and a portion of the vapor condenses. This condensed portion is enriched in water and returns as reflux to the desorber. Figure 4.12 shows a reflux cooler mounted on top of a desorber. Here we assume that the vapor and liquid streams leaving the reflux cooler are in equilibrium (l2 and v2). Because the reflux liquid (l2) is enriched in water, the exiting vapor stream (v2) is enriched in ammonia. The control volume is shown as a dotted line. Equilibrium is assumed between the liquid stream entering the desorber and the vapor stream leaving the desorber (l1 and v1). In a real device, these equilibrium assumptions will be approached closely only with some design efforts. An overall mass balance yields
v1 − m l2 = m v 2 (4.32) m
A mass balance for the ammonia yields
v 1 xv 1 − m l 2 xl 2 = m v 2 xv 2 (4.33) m
l 2 can be calculated as The mass flow rate of the reflux m
l2 = m v2 m
xv 2 − xv 1 (4.34) xv 1 − xl 2
Thus, when the flow rate of vapor leaving the reflux cooler at the top as product is set to v 2 = 1 then the flow rate of reflux depends only on the mass fractions of the streams enterm ing and leaving the reflux cooler. An energy balance for the control volume yields
v 1 hv 1 = m v 2 hv 2 + m l 2 hl 2 + Q ref (4.35) m
which can be rearranged using Equation 4.32 as
v 2 ( hv 1 − hv 2 ) + m l 2 ( hv 1 − hl 2 ) (4.36) Q ref = m
88
Absorption Chillers and Heat Pumps
Then on a per unit mass of rectified vapor (at point v2) basis, Equation 4.36 becomes qref = hv 1 − hv 2 +
xv 2 − xv 1 ( hv1 − hl 2 ) (4.37) xv 1 − xl 2
where Equation 4.34 has been introduced. This equation reveals that the rate of heat removed per unit mass is composed of two terms. The first accounts for the vapor stream being cooled and the second for a portion of the vapor to be condensed. It is assumed that the entire process occurs at constant pressure and that the temperature of the vapor leaving at v2 is known. Figure 4.13 shows an enthalpy–mass fraction diagram that reveals the state points. It can further be observed that Equation 4.37 can be rewritten to introduce the “pole” for reflux cooling. The enthalpy of this pole is defined as qref = hpole − hv2 (4.38)
A more useful form is
hpole = hv 1 +
xv 2 − xv 1 ( hv1 − hl 2 ) (4.39) xv 1 − xl 2
Equation 4.39 can be rewritten as hpole − hv 1 xv 2 − xv 1 = (4.40) hv 1 − hl 2 xv 1 − xl 2
This expression can be interpreted graphically, as shown in Figure 4.13, by using the lever rule. The differences in h and x are shown in Figure 4.13, and the pole is found at the intersection of the extension of the operating line (dashed) with the isostere of the vapor P = constant hpole – hV1
Pole
hpole
v2
th Iso
l1
qref
er m
gl tin era
(2)
hv2
ine
hV1 – hl2
Op
Enthalpy
v1
l2
xv2 – xv1
xv1 – xl2 x(2) H2O
xl1
xl2
Mass fraction
FIGURE 4.13 Reflux cooling process in an enthalpy–mass fraction diagram.
xv1
xv2 NH3
89
Thermodynamic Processes with Mixtures
leaving the reflux cooler. The operating line is defined by an energy balance and must pass through both the v1 and l2 points. Thus, if the v1 and l2 points are marked on an enthalpy– mass fraction diagram, then the pole can be located using a ruler. The enthalpy difference (hpole – hv2) represents the heat removed by the reflux cooler per unit mass of vapor leaving at point v2. Example 4.10: Reflux Cooler Consider a reflux cooler, as given in Figure 4.12, designed to purify an ammonia/water vapor stream. It is assumed that the vapor outlet stream is saturated and cooled to a temperature of 60°C and that the vapor leaving the desorber is in equilibrium with the incoming saturated liquid solution of x3 = 0.50 and T3 = 100°C. Assume the mass flow rate of the rectified vapor (v2) is 1 kg/sec and the inlet liquid flow rate at 3 is 8 kg/sec. The process is isobaric. Determine the cooling required in the reflux cooler and the heat required in the desorber. (See File: Ex4_10.ees.) Solution: Using appropriate software or the enthalpy–mass fraction diagrams in Chapter 3, the state points of the fluid streams at the solution inlet into the desorber, point l1; the purified vapor leaving the reflux cooler, point v2; the vapor leaving the desorber (v1); and the liquid returning from the reflux cooler to the desorber (l2) can be determined, as shown next. For point l1, the temperature and concentration are known as well as the fact that the solution is saturated. Thus, the pressure can be read off a chart such as the enthalpy–mass fraction diagram or computed from an equation of state. Furthermore, the composition of the vapor in equilibrium with this solution can be determined using the same data source. Thus, point (v1) is found. Point v2 is assumed to be saturated vapor at the same pressure (no pressure loss in the reflux cooler) as l1, but at a temperature of 60°C. The saturated liquid at (l2) must be in equilibrium with the vapor at v2 and at the same pressure. The results of these calculations are shown in Table 4.3. Based on the data in Table 4.3, the desorber and reflux cooler heat transfer rates can be calculated from Equation 4.37 and a similar energy balance on the desorber. The results are qdes = 1949.7 J/g and qref = 396.4 J/g. In each case, these heat transfer rates are normalized to the mass flow rate of the vapor leaving at point v2. This reflux cooling process is illustrated in Figure 4.13. The “pole” that shows up in Figure 4.13 is defined in Equation 4.39. It is simply an algebraic point as opposed to a physical state point in the device. However, it is quite useful when solving such problems graphically. Once you know points v1 and l2, the pole is located by linear projection to the mass fraction of the vapor at point v2. This line, which is related to the energy balance, is called the operating line of the reflux cooler. The heat required is then just the difference between the enthalpy of the pole and the enthalpy at point v2. It is observed that the mass flow rate of vapor leaving the desorber (v1) is larger than the mass flow rate of vapor leaving the reflux cooler (v2). This difference is just the liquid TABLE 4.3 Data for the Reflux Cooler in Example 4.10 Point
h (J/g)
P (Bar)
Vapor Quality
1 2 v2 v1 l2
218.9 284.8 1310.7 1461.8 196.4
22.95 22.95 22.95 22.95 22.95
0.0 0.0 1.0 1.0 0.0
T (°C) 100 113.98 60 100 60
x 0.5 0.4287 0.9993 0.9788 0.8733
(kg/sec) m 8 7 1 1.194 0.194
90
Absorption Chillers and Heat Pumps
reflux (l2) that must drain back to the desorber. The liquid reflux is enriched in water as compared to the vapor stream leaving the desorber. This explains how the reflux cooler can provide a purification step where the ammonia fraction in stream v2 is higher than that in stream v1. Unfortunately, it is commonly found that the enrichment provided by a reflux cooler is insufficient, thus leading to the subject of rectification that provides the ability to purify the vapor to an arbitrary extent for this mixture.
4.9.2 Rectification Whenever reflux cooling does not provide vapor of the desired purity or the amount of energy released becomes large compared to the desorber heat, it is better to employ rectification using a rectification column (Haselden and Sutherland 1960; Bogart 1981). Figure 4.14 shows a rectification column (top portion) combined with a desorber (bottom portion). State point 1 represents the liquid feed of ammonia/water mixture entering the desorber. The feed enters the analyzer section first in counterflow to vapor rising from the reboiler and then falls into the reboiler where heat is added to produce a vapor stream. The remaining solution leaves the desorber at 2. The vapor rises from the reboiler in counterflow to the falling liquid solution. In this way, heat and mass exchange between vapor and liquid streams are enabled. The vapor rises further through the column in counterflow to a liquid stream that is the reflux which is condensed at the top of the column in the reflux cooler. This condensate has a relatively high concentration of water as compared to the vapor. Nevertheless, its ammonia content is much higher than that of the solution at 1, which means that it can attract water from the rising vapor. The rising vapor is in heat and mass exchange with the reflux. This process is enhanced by using a packing material or set of plates that enhance the heat and mass transfer between the vapor and liquid. The horizontal baffles in the column in Figure 4.14 symbolize the heat and mass transfer contact. Thus, as the vapor rises, its temperature is reduced, which for a constant pressure
Reflux cooler
a b 1
· Qdes
· · mla mva
m· lb m· vb Control surface c Liquid feed, from solution heat exchanger
Reboiler 2
FIGURE 4.14 Distillation column.
Rectified vapor out
· Qrec
Analyzer
Desorber
Rectification column
7
Liquid out, to solution heat exchanger
Thermodynamic Processes with Mixtures
91
equilibrium process requires that the amount of water is reduced as well. A portion of the water content of the vapor is transferred to the reflux, releasing heat of condensation. This heat is used to evaporate a certain amount of reflux that is almost pure ammonia. The temperature of the reflux liquid stream and its flow rate gradually increase as it flows toward the bottom of the column. Figure 4.14 shows a control volume within the column at an arbitrary cross section above the feed point. Applying a mass balance yields
la + m vb = m lb + m va (4.41) m
The subscripts a and b stand for the upper or lower surface of the control volume and the subscripts l and v for the liquid and vapor flow rates, respectively. Equation 4.41 can be rearranged as
va − m la = m vb − m lb (4.42) m
Such a mass balance must hold for all control volumes within the column that do not straddle the feed point. Applying the mass balance to the top of the column, around the reflux cooling coil, reveals that the mass flow rate difference between the vapor and liquid streams is the mass flow rate of vapor leaving the column as rectified vapor
v −m l = constant = m 7 (4.43) m
This relationship is true for any cross section of the column above the feed point. Applying the mass balance for one component of the mixture, for example, the ammonia, yields
la xla + m vb xvb = m lb xlb + m va xva (4.44) m
When this analysis is applied around the reflux cooler, it is found that the difference in the ammonia flow rates at any point in the column (above the feed point) is equal to the ammonia leaving the column with the rectified vapor
v xv − m l xl = m 7 x7 (4.45) m
Applying an energy balance to the control volume of Figure 4.14 yields the following equation, assuming that the control volume is adiabatic.
la hla + m vb hvb = m lb hlb + m va hva (4.46) m
This equation holds for all adiabatic control volumes that do not straddle the feed point and can be generalized to
v hv − m l hl = constant (4.47) m
Applying the energy balance to the top of the column around the reflux cooler, the following expression is obtained:
vc hvc = m lc hlc + m 7 h7 + Q rec (4.48) m
92
Absorption Chillers and Heat Pumps
The subscript c denotes an arbitrary cross section in the column above the feed point. The term Q rec denotes the rate of energy that has to be removed from the reflux cooler. It is termed the heat of rectification. Note that this heat was called Q ref in the previous section where focus was on the reflux cooler. In order to determine the flow rate of reflux at an arbitrary position in the column above the feed point, denoted by point c, a mass balance for the total mass flow rate and for the ammonia are employed for the entire rectification column above the point of interest. The total mass balance is
lc + m 7 = m vc (4.49) m
and the mass balance for the ammonia is
lc xlc + m 7 x7 = m vc xvc (4.50) m
vc yields Combining Equations 4.49 and 4.50 and eliminating m
lc = m
x7 − xvc 7 (4.51) m xvc − xlc
7 = qrec can be written as With Equation 4.51, the heat of rectification Q rec/m
qrec = hvc − h7 +
x7 − xvc ( hvc − hlc ) (4.52) xvc − xlc
The difference in the first two terms on the right-hand side of this equation represents the difference in the enthalpies of the vapor streams entering and leaving the column. The remaining term represents the heat of condensation that has to be removed to generate the liquid reflux. The challenge is now to determine the properties of the reflux state point at control surface c. For this purpose, an enthalpy–mass fraction diagram is considered, as in Figure 4.15. The operating line at a particular cross section in the column (defined as a line that connects two state points that exist at one cross section during the operation of the column) connects the state points of the reflux liquid at c with the state point of the rising vapor at c. This operating line can, at best, have the same slope as the local isotherm, meaning that the vapor and liquid are in thermodynamic equilibrium. In other words, the slope of the operating line cannot be smaller than the slope of the isotherm. In a real column, the vapor will contain less ammonia than under equilibrium conditions. Thus, the operating line for any cross section in an actual rectification column will be steeper than the isotherm (having a shallower slope would be a violation of the second law). This analysis holds for each cross section of the column. The vapor leaving each column cross section cannot be enriched beyond the equilibrium state. In Figure 4.15, only one operating line is shown corresponding to the control surface c of Figure 4.14. Since the location of control surface c is arbitrary, there is a similar operating line corresponding to any column cross section. All operating lines have to have a slope that is at least as steep or steeper than that of the local isotherms. One important characteristic of operating lines is that they all intersect at the pole of rectification.
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Thermodynamic Processes with Mixtures
P = constant Pole
Iso th erm s
Enthalpy
vc
Operating line
lc, reflux at point c
x7 H2O
Mass fraction
NH3
FIGURE 4.15 The pole of rectification determined by extending the line that connects the vapor and liquid states at one cross section of the column till it intersects with the isostere of the purified vapor.
To better understand the heat of rectification, define the pole of rectification such that
qrec = hpole − h7 (4.53)
which implies hpole = hvc +
lc m ( h − hlc ) 7 vc m
(4.54)
x − xvc = hvc + 7 ( hvc − hlc ) xvc − xlc Equation 4.54 can be rewritten as follows to clarify the graphical interpretation
hpole − hvc x7 − xvc = (4.55) hvc − hlc xvc − xlc
The distances are indicated in Figure 4.16. According to Equation 4.53, the heat of rectification is represented by the enthalpy difference between the pole and the state point of the rectified vapor leaving the column. Thus, the pole of rectification determines the amount of energy that has to be removed in order to achieve the desired vapor purity. The location of the pole is determined by the intersection of the operating lines with the isostere of the purified vapor. The slope of the operating lines cannot be smaller than that of the respective isotherm in a given column cross section in the two-phase range between xlc and x7. Thus, the minimum or theoretical heat of rectification is determined by the slope of the isotherm that provides the highest point of intersection. It is not known
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Absorption Chillers and Heat Pumps
hpole – hvc
Pole
hpole
vc
Iso
Op
er ati
ng l th erm ine s
h7
hvc – hlc
Enthalpy
qrec
lc
xvc – xlc x2 H2O
xlc Mass fraction
x7 – xvc xvc
x7 NH3
FIGURE 4.16 Determination of the pole of rectification.
a priori where this isotherm occurs. It could be at either end of the column or at an intermediate cross section. Procedures for locating the pole are described next. A rectification column is designed to provide heat and mass transfer between the counterflowing reflux liquid (flowing down) and the rising vapor, with the main goal of enriching the vapor stream in ammonia. Maximization of this coupled transport requires maximization of the vapor–liquid surface area, mixing of the liquid and vapor streams, and sufficient contact time. Ideally, it would be desirable if the liquid and vapor steams would reach equilibrium at every cross section. In real column design, transport potential differences are required to drive the transport so equilibrium is not realistic in a finite size column. It is useful, however, to think about the thermodynamic equilibrium limit so as to provide a realistic design limit. One variation on column design is to assume there are discrete locations (called theoretical plates) within the column where equilibrium between the liquid and vapor is achieved. This approach is common in column design, and it is discussed next. Several methods are available to determine the rectification heat requirement with a certain number of theoretical plates and a given vapor purity. For fluid mixtures with a small difference in boiling points, the McCabe and Thiele diagram (Bogart 1981) is employed, the use of which requires simplifying assumptions that are not very well fulfilled with ammonia/water. Another procedure involves the enthalpy–mass fraction diagram and a graphical method that entails plotting all operating lines and respective isotherms. Computer simulation of this graphical approach is the method of choice today. The procedure is summarized here. Figure 4.17 shows the isotherms and respective operating lines. All the operating lines have to terminate at the pole in order to satisfy the energy and mass balances. In this construction, working from left to right, the intersection of each operating line with the saturated liquid isobar determines the liquid concentration of the next higher plate in the column. When the isotherm reaches (or surpasses) the design vapor purity, then the process terminates and you can count the number of theoretical plates. The last operating line represents the balance around the reflux cooler. Each of the remaining
95
Thermodynamic Processes with Mixtures
P = constant
Enthalpy
Pole
Represents reflux cooler
Operating line Isotherm x1 H2O
Mass fraction
x7 NH3
FIGURE 4.17 Determination of the number of theoretical plates. In this case, the rectification column has two theoretical plates.
operating lines represents one theoretical plate. Proceeding in this way from operating line to isotherm to operating line across the entire two-phase range between x1 and x7, the total number of plates can be determined. The ability to draw the operating lines assumes that the location of the pole is known, but this is not the case at the beginning of the analysis. You can choose the location of the pole (this is equivalent to choosing the rectification heat) at the beginning of the analysis and then determine the number of theoretical plates required to achieve that heat. In general, this approach will lead to a noninteger number of theoretical plates. Alternatively, you can choose an integral number of plates and then determine the rectification heat that is consistent with that choice. This requires an iterative approach where you adjust the location of the pole until the properties line up. This iterative approach is suited to a computer solution, and it is the approach taken in Example 4.11. The location of the pole defines the rectification heat. If the pole is moved higher, rectification heat increases and the operating lines become steeper. The vapor- and liquid-phase mass fractions at each plate depart further from equilibrium. At the same time, fewer operating lines (and therefore fewer plates) are required to achieve the same purification. When more heat is removed, the amount of reflux is increased, which in turn provides more liquid that can participate in the heat and mass exchange process of the rectification column. Finally, the amount of heat that is required to operate the desorber (qdes) in tandem with the rectifier is calculated. Based on mass balances for the total flow rates and that of a mmonia only and the energy balance for the entire column, the following equation is obtained.
qdes = h7 − h2 + f(h2 − h1) + qrec (4.56)
7. qrec is calculated according to 1/m 7 and qdes = Q des /m The terms are defined as f = m Equation 4.52.
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Absorption Chillers and Heat Pumps
Vapor
Vapor out Liquid Rich solution from solution heat exchanger
Poor solution to solution heat exchanger
FIGURE 4.18 Counterflow desorber to minimize need for rectification.
Equation 4.56 shows that the heat of rectification and, therefore, the need to rectify is a penalty because it increases the heat requirement of the desorber. Thus, careful desorber design that limits the water content of the vapor by bringing the leaving vapor into contact with the entering rich solution is quite important. This is related to the analyzer section shown in Figure 4.14. Figure 4.18 is a schematic of a simplified design for the analyzer/ desorber. The boiling solution is flowing from left to right, while the vapor, in contact with the solution, flows in counterflow from right to left. Thus, an opportunity is provided for heat and mass exchange between vapor and solution, which is similar to the process occurring in the rectification column. In the absorption cycle computer models provided in this text, it is always assumed that the vapor leaving the desorber is in equilibrium with the incoming solution. Although only approached in practice, this is a worthy design goal that provides several performance benefits (reduced desorber heat and reduced rectification heat). Furthermore, it is very important that the rich solution entering the desorber be as rich as possible (i.e., have a high ammonia mass fraction). If the liquid supplied to the desorber has a high water content, then the respective two-phase isotherm at the entrance to the rectifier is quite steep, forcing the pole to a high point, which implies a high rectification heat. Column design based on theoretical plates provides a very useful design target, but it ignores transport and focuses primarily on thermodynamics. In the limit of infinite theoretical plates, the design becomes fully reversible. Although a finite number of plates provide a more realistic heat prediction as compared to a reversible model, they do not address the critical issues of how to accomplish the complex transport. In an actual system, the heat and mass transfer coefficients and contact time play important roles in the effectiveness of the column. Therefore, there is frequently an efficiency included in the design procedure that either increases the number of plates without lowering the pole or increases the heat. Thus, the rectification heat calculated for a fixed number of theoretical plates should be interpreted as a minimum value. The actual rectification cooling required will always be larger than the theoretical value. Example 4.11: Rectifier Analyze a rectifier for the following operating conditions. Assume the device operates at constant pressure. The vapor entering the column from the desorber section (labeled v1 in Figures 4.19 and 4.20) is in equilibrium with the incoming liquid (l1), which is assumed to be a saturated solution of ammonia mass fraction 0.20 at a temperature of 130°C. The rectified vapor (v2 in Figure 4.19 or v3 in Figure 4.20) is assumed saturated at a mass fraction 0.994. Calculate the minimum values for the reflux flow rate, rectifier heat, and desorber heat, assuming that zero (reflux cooler only), one, two, and three plates are used. For the desorber heat, assume that the incoming liquid flow rate at l1 is 8 times the rectified vapor flow rate (f = 8). (See file Ex4_11.ees.)
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Thermodynamic Processes with Mixtures
v2
Rectified vapor out
qrec
Reflux cooler
l2 v1
l1
Liquid feed, from solution heat exchanger
qdes
Out
Liquid out, to solution heat exchanger
FIGURE 4.19 Rectifier column with zero plates.
v3
Rectified vapor out Reflux cooler
qrec
Bubble cap configuration Vapor rising
l3 v2 Liquid falling
l2 v1 Liquid feed, from l1 solution heat exchanger
Vapor bubble Liquid droplet
qdes
Out
Liquid out, to solution heat exchanger
FIGURE 4.20 Rectifier column with one theoretical plate shown as a bubble cap. See Table 4.5 and Figure 4.21.
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Absorption Chillers and Heat Pumps
Solution and Assumptions: No pressure drop; the vapor and liquid leaving each plate and the reflux cooler are in thermodynamic equilibrium. Based on the information given, the states of the inlet vapor to the column, the outlet vapor, and the reflux leaving the reflux coil can be evaluated. Then the equations for the equilibrium at each plate have to be solved. The latter involves an iterative process best conducted with appropriate software or a graphical construction using the enthalpy– mass fraction diagram. The results for zero, one, two, and three plates are summarized in Tables 4.4 through 4.6. State point 2 represents the liquid and vapor stream leaving the reflux cooler (i.e., it represents the equilibrium isotherm for the reflux cooler). The liquid and vapor are assumed to be in thermodynamic equilibrium and have the same pressure and temperature. The vapor flows upward driven by the heat input and the reflux liquid falls downward due to gravity. The vapor and liquid flow rates in the earlier table r epresent the mass flow rate divided by the rectified vapor flow rate leaving the column. The model used here gives the same results as were found in Example 4.10 but with a different notation. The notation used here is more suitable as we add plates to the column. TABLE 4.4 Result for Rectifier with Zero Plates (Reflux Cooler Only) (see Figure 4.19)
1 2
hl (J/g)
h v (J/g)
Liquid Flow Rate (g/g)
T l (°C)
Tv (°C)
425.6 35.4
1798 1390
0.875
130.0 60.3
130.0 60.3
Vapor Flow Rate (g/g) 1.875
xl
xv
0.200 0.538
0.781 0.994
Note: Heat of rectification = 1951 J/g of rectified vapor, P = 10.64 bar, hpole = 3340 J/g, Desorber heat qdes = 4281 J/g of rectified vapor.
TABLE 4.5 Result for Rectifier with One Plate (see Figures 4.20 and 4.21)
1 2 3
hl (J/g)
h v (J/g)
Liquid Flow Rate (g/g)
T l (°C)
Tv (°C)
425.6 349.3 35.4
1798 1683 1390
0.400 0.421
130.0 118.2 60.3
130.0 118.2 60.3
Vapor Flow Rate (g/g) 1.400 1.421
xl
xv
0.200 0.248 0.538
0.781 0.859 0.994
Note: Heat of rectification = 986.7 J/g of rectified vapor, P = 10.6 bar, hpole = 2377 J/g, Desorber heat qdes = 3317 J/g of rectified vapor.
TABLE 4.6 Result for Rectifier with Two Plates (see file: Ex4_11_2plates.ees for a Figure Showing Each State Point)
1 2 3 4
hl (J/g)
h v (J/g)
Liquid Flow Rate (g/g)
T l (°C)
Tv (°C)
425.6 414.3 341.1 35.4
1798 1779 1673 1390
0.371 0.370 0.390
130.0 128.3 116.9 60.3
130.0 128.3 116.9 60.3
Vapor Flow Rate (g/g) 1.371 1.370 1.390
xl
xv
0.200 0.207 0.254 0.538
0.781 0.794 0.866 0.994
Note: Heat of rectification= 921.0 J/g of rectified vapor, P = 10.6 bar, hpole = 2311 J/g, Desorber heat qdes = 3252 J/g of rectified vapor.
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Thermodynamic Processes with Mixtures
The case involving one theoretical plate was calculated, and the data are given in Table 4.5. A theoretical plate implies a location in the column where the rising vapor is in equilibrium with the falling liquid. An approach to such an equilibrium would require favorable transport, including both heat and mass. The alternating baffles shown in Figure 4.14 are meant to indicate mixing between the two phases. However, in practice a number of more aggressive mixing/contacting designs are in use, including packed media (Strigle 1993) and bubble cap. A bubble-cap design is pictured in Figure 4.20 for this case of one plate. The main thing that this design implies is that the rising vapor and falling liquid approach equilibrium. In the limit, a theoretical plate implies that they reach equilibrium. In this case of a single theoretical plate, state point 3 represents the liquid and vapor streams leaving the reflux cooler. State point 2 represents the liquid and vapor streams leaving the plate. The temperatures Tl2 and Tv2 are identical, the thermal equilibrium condition assumed for each plate (only one plate in this case). State point 1 represents the liquid feed to the column and the vapor entering the bottom of the column. Compared to the case with no plate (Table 4.4), the reflux flow rate, rectification heat, and desorber heat are all reduced significantly. Thus, a single theoretical plate provides a large benefit. The solution in Table 4.5 is plotted in Figure 4.21 on enthalpy–mass fraction coordinates. This type of plot is a good way to visualize the rectification process. There are three isotherms corresponding to equilibrium conditions assumed at the liquid inlet, at the plate, and at the reflux cooler. The two operating lines represent energy balances at two elevations in the column (one for the reflux cooler and one for the plate). As required by the overall energy balance, all operating lines intersect at the “pole of rectification.” Significant insight about the rectification process results if you integrate the computer modeling and graphical approaches. The enthalpy–mass fraction diagram can be easily computed for a particular operating pressure, as in file Ex4_11_fig.ees. You can print the figure generated by that program and then use a ruler to scribe in the isotherms and operating lines for the design of interest. Table 4.6 describes the case with two theoretical plates for the same liquid in and vapor out conditions. State points 2 and 3 represent the liquid and vapor streams, 4000 3500
Operating line
P = 1064 kPa
Isotherm
Enthalpy (J/g)
3000 2500
Pole v1
2000 1500
v2
v3
1000 500
l1
0 –500
l2 l3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ammonia mass fraction FIGURE 4.21 Rectifier diagram for column with one theoretical plate. See Table 4.5 and Figure 4.20.
0.9
1
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Absorption Chillers and Heat Pumps
TABLE 4.7 Result for Rectifier with Three Plates (see file Ex4_11_3plates.ees for a Figure Showing Each State Point)
1 2 3 4 5
hl (J/g)
h v (J/g)
425.6 423.9 412.7 339.9 35.4
1798 1795 1777 1671 1390
Liquid Flow Rate (g/g)
T l (°C)
Tv (°C)
0.367 0.367 0.366 0.386
130.0 129.7 128.0 116.7 60.3
130.0 129.7 128.0 116.7 60.3
Vapor Flow Rate (g/g) 1.367 1.367 1.366 1.386
xl
xv
0.200 0.201 0.208 0.255 0.538
0.781 0.783 0.796 0.867 0.994
Note: Heat of rectification qrec = 912.2 J/g of rectified vapor, P = 10.6 bar, hpole = 2302 J/g, Desorber heat qdes = 3243 J/g of rectified vapor.
leaving the two plates. State point 4 is the rectified vapor out, and point 1 is the liquid inlet. Again, heat transfer and reflux flow rate are reduced, but the reduction obtained in going from one plate to two is much smaller than that obtained by adding the first plate. It can be observed that the amount of water in the reflux increases with each plate as we proceed from the top of the column (reflux cooler) to the bottom. This increase represents the amount of water (and some ammonia) that is being extracted from the vapor as the rectification process proceeds. The vapor gets enriched in ammonia at the expense of creating a liquid reflux stream enriched in water. Table 4.7 is for the case with three theoretical plates. An additional plate further reduces reflux and heat, but the effect is small. It becomes clear that the return for this additional complexity is diminishing rapidly. An inspection of Table 4.7 reveals that the effect of the lowest plates is very minimal (i.e., not much change in mass fraction is observed). Thus, it is found that under these conditions, an increase in the number of plates beyond the effective number is a wasted investment. This behavior results from the characteristics of the mixture. The only way to reduce the rectifier heat further is to change the feed conditions or the mass fraction of the incoming vapor. Such topics are of interest for advanced cycle design. A more advanced treatment of distillation analysis can be found in Bogart (1981).
As the example shows, rectification does purify the vapor and it reduces but does not eliminate the heat transfer required in the reflux cooler. It should be noted that the rectification heat increases quite dramatically as the concentration of the solution entering the desorber/rectifier decreases (point 1 in Figure 4.14). Figure 4.22 shows that as the solution concentration decreases (i.e., the water content increases), the pole rises rapidly because of the increasing slope of the isotherms in the two-phase range. However, there is a second purification method that is quite effective in absorption systems and is called an analyzer. The analyzer section of the purification column (see Figure 4.14) sits below the rectifier section and has the function of reducing the water content in the vapor stream entering the bottom of the rectifier. The analyzer works in a very similar manner as the rectifier, but it typically has a higher liquid flow rate because the reflux from the rectifier is added to the incoming liquid feed to the desorber. The analysis of an analyzer is very similar to that of a rectifier. The reasoning and derivation of all the equations are essentially the same. There exists a pole that is now located on the line of constant concentration for the strong absorbent leaving the generator (Bogart 1981).
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Thermodynamic Processes with Mixtures
P = constant Pole
Enthalpy
qrec
Operating line Isotherm x1 H2O
Mass fraction
x0 NH3
FIGURE 4.22 Sensitivity of the pole position to the feed concentration.
4.10 Heat Exchangers Heat exchange processes occur throughout absorption machines. The processes are complicated by coupled mass transfer and by the properties of the binary mixture working fluids. The purpose of this section is to introduce the terminology that is used in this text to describe the heat exchange processes and to introduce simple heat exchanger models. Coupled heat and mass transfer occurs in all of the major heat exchangers in an absorption machine except the solution heat exchanger. In the coupled heat/mass transfer processes, both heat and mass transfers occur simultaneously, and the two processes are coupled by the internal energy flowing with the working fluid. In particular, the latent heat couples the processes since all the coupled processes involve phase change. It may be argued that a pure fluid evaporator or condenser, such as those that exist in water/lithium bromide systems, does not experience mass transfer since there are no concentration gradients in the system. However, a more general definition of mass transfer is a transfer of mass due to a chemical potential gradient. From this perspective, all the phase-change devices experience both heat and mass transfer. Although these components undergo both heat and mass transfer, it is often convenient to analyze them based on heat transfer alone. This is convenient because it allows the engineer to concentrate on a single set of variables, which are temperature and heat transfer rate. Once these variables are specified for a given design, the mass transfer aspects can be deduced from appropriate models. This heat transfer perspective works because both processes are coupled together so that if you know one then you know the other. However, a full appreciation of the design perspective must give full acknowledgment to the role of both heat and mass transfer processes because either of these processes can control the overall transfer process.
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Absorption Chillers and Heat Pumps
As an example of this, consider the absorption process. It has been found from numerous modeling and experimental studies that the absorption process, in both water/lithium bromide and ammonia/water, is controlled by the mass transfer resistance on the liquid side. This is because the refrigerant vapor, which absorbs at the liquid interface, does not effectively transfer to the bulk of the liquid. Instead, it tends to stay near the interface and to slow down the absorption of additional refrigerant. The energy released at the liquid interface causes the interface temperature to rise, and this energy must also transfer through the liquid film to the heat transfer surface. However, the overall process is controlled by the mass transfer characteristics in the sense that augmentation of the mass transfer mechanisms has a larger effect on the overall transfer process than augmentation of the heat transfer mechanisms. In this section, a heat transfer perspective is taken to simplify the discussion. However, it must be kept in mind that this perspective is only appropriate for design purposes if the overall heat and mass transfer characteristics of the device are already known in terms of the heat transfer characteristics. In the more general case, it is necessary to account for both of the transfer processes to determine the overall transfer characteristics. 4.10.1 Heat Exchanger Diagrams A convenient format for visualizing the operating point of a heat exchanger is to plot the temperature versus cumulative heat transfer rate characteristics. Such diagrams are termed heat exchanger diagrams in this text. An example of such a diagram is provided as Figure 4.23. The temperature coordinate is simply the bulk temperature measured along the fluid stream as it passes through the heat exchanger. For a single-pass device, this is a well-defined quantity. The cumulative heat transfer rate coordinate represents the rate of energy transferred between any two temperatures. Thus, the difference between the end points of the heat exchanger, as measured on the cumulative heat transfer rate coordinate, Tc1
Tc2
Th1
Th2
Temperature (°C)
Th1 Hot side Th2 Tc1
Cold side Tc2 Cumulative heat transfer rate (kW)
FIGURE 4.23 Typical counterflow heat exchanger.
Thermodynamic Processes with Mixtures
103
represents the total heat transfer rate in the heat exchanger. The zero point for the cumulative heat transfer rate scale is arbitrary, but it is convenient to set it to zero at one end of the heat exchanger. When a heat exchanger operating point is plotted on these coordinates, it is immediately clear whether the heat exchanger is well designed. A primary objective in heat exchanger design is to achieve a uniform temperature difference throughout the device. What this implies is that the vertical difference (i.e., the temperature difference) between the hot and cold sides of the heat exchanger should be uniform for the entire energy transfer. Such a uniform design yields the lowest entropy production (i.e., the lowest irreversibility) of any possible design for the same heat transfer resistance. This is why a uniform temperature difference design is referred to as a well-matched design. When temperature matching can be achieved in a heat exchanger design, it pays off in increased system performance. Commonly, it is difficult to achieve a well-matched design in absorption components. This is true primarily because of sensible heat effects and nonlinear properties. One characteristic that can be identified for most real heat exchanger designs is a temperature pinch point. The temperature pinch is the point at which the hot and cold side temperatures have their closest approach. The pinch can usually be readily identified from a heat exchanger diagram. Frequently, but not always, the pinch point occurs at either the inlet or the outlet of the heat exchanger. The existence of a pinch point indicates the possibility of improvement of the heat exchanger design. If the two traces on the heat exchanger diagram are far from parallel, the pinch point acts as a bottleneck to the energy transfer. Examples of heat exchanger diagrams for absorption components are included in Chapter 6 for each of the five major heat exchangers in a single-effect water/lithium bromide machine. 4.10.2 Heat Exchanger Models Various heat exchanger models are useful when modeling absorption machines. These include (1) pinch point specification, (2) UA models, and (3) effectiveness models. The specification of the pinch point is a simple approach that does not require much discussion. However, it should be noted that such a simple model is an excellent place to start when modeling a new cycle because the complexity of the more realistic models can cause problems in the convergence of the overall cycle model. When analyzing heat exchangers with phase change on one side, it is often convenient to employ simplifying assumptions to deal with superheated and subcooled streams. The first-order assumption commonly made is to ignore the temperature effects associated with sensible heat. This implies that the solution side of the heat exchanger is represented by the saturation temperatures associated with the local streams. The results of such assumptions for each of the components in a typical cycle are discussed in Section 6.2. 4.10.3 UA-Type Heat Exchanger Models The product of the overall heat transfer coefficient, U, and the heat exchanger area, A, is a convenient way to specify the size and performance of a heat exchanger in a single parameter (i.e., the UA value). It is common to use the UA formulation along with the log-mean temperature difference as follows.
Q = UA∆Tlm (4.57)
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Absorption Chillers and Heat Pumps
with
∆Tlm =
(Th,1 − Tc ,1 ) − (Th,2 − Tc ,2 ) (4.58) ln
Th ,1 − Tc ,1 Th ,2 − Tc ,2
where h and c refer to the hot and cold sides, respectively. The subscripts 1 and 2 refer to either end of the device, as shown in the heat exchanger diagram in Figure 4.23. The difficulty in using a UA-type formulation comes from the logarithmic term, which exhibits singular behavior if the temperatures are not in the correct ranges. This causes problems for iterative solution schemes that sometimes search over wide ranges of the variables to find a final solution. The UA formulation can cause such an iteration to fail before it reaches the answer. Another difficulty with this formulation is that the overall heat transfer coefficient may be a function of other variables, such as flow rates, temperature, and pressures. Thus, although it is convenient to view the UA product as a constant for modeling purposes, reality is more complex. 4.10.4 Effectiveness Type Heat Exchanger Models The heat exchanger effectiveness is a useful way to define the performance of a heat exchanger. The effectiveness is defined as the ratio of the actual heat transfer to the maximum possible heat transfer for the given inlet conditions. Q ε = act (4.59) Qmax
Consider the heat exchanger shown schematically in Figure 4.23. The maximum possible heat transfer is taken to be the product of the minimum heat capacity rate multiplied by the temperature difference between the two inlet streams or
(
)
min
(
)
min
p Q max = mc p = mc
∆Tinlet
(Th1 − Tc 2 )
(4.60)
In general, the minimum heat capacity can occur on either the hot or cold sides of the heat exchanger. Consider a case where the minimum heat capacity side is known to occur on the cold side of the heat exchanger. Then the effectiveness would be ε=
) ( mc ) ( mc p
p
(Tc 1 − Tc 2 ) (Th1 − Tc 2 ) cold cold
(4.61)
T − Tc 2 = c1 Th1 − Tc 2 The definition of the effectiveness in terms of only the temperatures makes it a very convenient heat exchanger performance parameter. The definition of the effectiveness can be generalized to include heat exchangers that undergo a phase change on one side. For pure fluids, isobaric phase-change processes
Thermodynamic Processes with Mixtures
105
imply no temperature changes on the phase-change side, and thus the effective specific heat is infinite and the minimum heat capacity must occur on the non-phase-change side of the heat exchanger. For absorption components that involve a phase change and a temperature glide, it is not obvious how to proceed because the heat capacity is undefined in the two-phase region. In this text, the values of effectiveness are calculated for such components based on the assumption that the non-phase-change side has the minimum heat capacity. When defined in this manner, the interpretation of the effectiveness loses rigor, but it is still convenient and useful as a modeling scheme. As long as it is interpreted in the way it is defined, everything works smoothly.
Homework Problems 4.1 Determine the outlet state when two saturated vapor streams of ammonia/water are mixed in equal amounts adiabatically and isobarically at 10 bar. The two streams are at mass fractions of 0.7 and 0.9. 4.2 Consider a water/lithium bromide single-effect cycle operating between pressures of 0.8 and 8 kPa. Assume the solution circuit mass fractions are 0.55 and 0.60 and that the solution heat exchanger has an effectiveness of 50%. Assume that the streams leaving each of the components are saturated. Hint: Problems of this type are covered in some detail in Chapter 6. However, with the simplified inputs specified here, the calculations are direct if the property routines are available. a. Determine the heat transfer rate in each of the components. b. Determine the solution circulation ratio. c. Determine the cooling COP. d. Determine the ideal pump work. e. Determine the vapor quality at the outlet of the refrigerant expansion valve. f. Determine the vapor quality at the outlet of the solution expansion valve. 4.3 Utilize the properties of ammonia/water directly to determine the error introduced in the pump work prediction using the incompressible assumption. Use an isentropic process but evaluate the properties directly and compare the result against the approximation in Equation 4.31. Note: In reality, the liquid volume changes slightly as the pressure changes. Base it on an ammonia mass fraction of 0.2 and a pressure rise from 4 to 25 bar. 4.4 Evaluate the losses in the expansion valve by replacing it by a work-producing machine, such as a turbine. Model the turbine as isentropic and determine the specific work output. Compare this against the latent heat of the refrigerant to obtain a rough estimate of the magnitude of the losses in the expansion valve. a. Consider pure ammonia over the pressure range from 25 to 4 bar. Assume the expansion valve inlet is saturated liquid. b. Consider ammonia/water at a mass fraction of 0.99 under the same conditions as in (a). c. Consider pure water over the pressure range from 10 to 1 kPa. Assume the expansion valve inlet is saturated liquid.
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4.5 Compute the reversible rectifier solution for the conditions of Example 4.11. The results should include the rectifier heat transfer and the flow rate of the reflux liquid out of the column. Hint: The pole for this case can be found by extending the first isotherm to the outlet isostere. 4.6 Perform a parametric study, using the rectifier model of Example 4.11, to determine the influence of the key variables on the rectification heat and the reflux flow rate. For each of the following variables, consider a range and prepare a plot of rectification heat and reflux flow rate versus that variable. a. Number of plates b. Mass fraction of rectified vapor c. Mass fraction of inlet vapor 4.7 Plot the h–x diagram for each of the four cases contained in Tables 4.4 through 4.7.
References Bogart, M. (1981). Ammonia Absorption Refrigeration in Industrial Processes. Houston, TX: Gulf Publishing. Grossman, G. (1983). Simultaneous Heat and Mass Transfer in Film Absorption Under Laminar Flow. Int. J. Heat Mass Transfer. 26(3): 357–371. Grossman, G. (1991a). Film Absorption Heat and Mass Transfer in the Presence of Non Absorbable Gases. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 389–394. Grossman, G. (1991b). The Combined Heat and Mass Transfer Process in Film Absorption. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 43–52. Haselden, G. G. and S. A. Malaty. (1959). Heat and Mass Transfer Accompanying the Absorption of Ammonia in Water. Trans. Inst. Chem. Eng. 37: 137–146. Haselden, G. G. and J. P. Sutherland. (1960). A Study of Plate-Efficiency in the Separation of AmmoniaWater Solutions. International Symposium on Distillation, pp. 27–32. Klein, S. and G. Nellis. (2012). Thermodynamics. Cambridge University Press, ISBN 978-0-521-19570-6. Kyung, I., K. E. Herold, and Y. T. Kang. (2007). Model for Absorption of Water Vapor into Aqueous LiBr Flowing Over a Horizontal Smooth Tube. Int. J. Refrig. [Revue Internationale Du Froid] 30(4): 591–600. Merrill, T., T. Setoguchi, and H. Perez-Blanco. (1994). Compact Bubble Absorber Design and Analysis. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 217–224. Miller, W. A. and H. Perez Blanco. (1994). Vertical-Tube Aqueous LiBr Falling Film Absorption Using Advanced Surfaces. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 185–202. Minkowycz, W. J. and E. M. Sparrow. (1966). Condensation Heat Transfer in the Presence of Noncondensables, Interfacial Resistance, Superheating, Variable Properties and Diffusion. Int. J. Heat Mass Transfer. 9: 1125–1144. Sparrow, E. M., W. J. Minkowycz, and M. Saddy. (1967). Forced Convection Condensation in the Presence of Noncondensables and Interfacial Resistance. Int. J. Heat Mass Transfer. 10: 1829–1845. Strigle, R. F. (1993). Understand Flow Phenomena in Packed Columns. Chem. Eng. Prog. 89(8): 79–83. Vliet, G. C. and F. B. Cosenza. (1991). Absorption Phenomenon in Water-Lithium Bromide Films. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 53–61.
5 Overview of Water/Lithium Bromide Technology Aqueous lithium bromide is used as an absorption working fluid because it is one of the best choices found among hundreds of working fluid pairs that have been considered. Although aqueous lithium bromide is the preferred choice for many applications, there are numerous limitations associated with this choice that need to be understood. The thermodynamic and transport properties of working fluids are discussed in some detail in Chapter 3, and that material will not be repeated here. However, there are additional properties of aqueous lithium bromide, beyond the thermodynamic and transport properties discussed previously, that impact the design and operation of a machine based on this working fluid. These properties and the limitations that they impose form the focus of this chapter.
5.1 Fundamentals of Operation The fundamentals of operation of an absorption cycle using aqueous lithium bromide as the working fluid are discussed in this section. To keep the discussion simple, only the most basic cycle is considered. Advanced cycle design features are introduced in Chapters 6 through 8. This discussion is meant as an overview and as an introduction to many design aspects that must be considered to successfully use the technology. A block diagram of a single-effect machine is provided in Figure 5.1. The diagram is formatted as if it were superimposed on a Dühring plot of the working fluid. Thus, the positions of the components indicate the relative temperature, pressure, and mass fraction. The machine consists of four components that exchange energy with the surroundings, one internal heat exchanger, two flow restrictors that are termed valves on the diagram for brevity, and a pump. The connecting piping between these devices is also important for design. 5.1.1 Solution Circuit The solution circuit circulates between the desorber and absorber. This liquid loop is pumped from the low pressure in the absorber to the high pressure in the desorber. As a first approximation, the entire machine can be considered to operate between two pressure levels. Of course, in actual operation, there will be pressure losses associated with (1) flow through the components and (2) changes in elevation. These losses must be minimized by design. In its simplest form, an absorption machine is a two-pressure device with significant pressure changes occurring only in the flow restrictors and the pump. The liquid solution is pumped into the desorber, where heat is supplied by external means such as a combustion source or any other source with a sufficiently high temperature.
107
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. Qc
. Qd
Condenser
Refrigerant expansion valve Pressure
Desorber
Solution heat exchanger ˙ W
Solution expansion valve
Pump
Evaporator Absorber . Qe
. Qa
Temperature FIGURE 5.1 Single-effect absorption cycle schematic.
The required temperature level is governed by the properties of the working fluid and the operation of the other components in the machine. For a typical single-effect aqueous lithium bromide machine, the desorber heat must be supplied above a temperature of approximately 90°C. (This value is a rule of thumb, with actual requirements depending on the details of the application.) When heat is applied to the solution, the volatile component (i.e., the refrigerant) is boiled off. In the case of aqueous lithium bromide, water is the refrigerant. In dealing with mixtures, the relative volatility of the components is a property of major interest. In the case of aqueous lithium bromide, the salt (lithium bromide) is essentially nonvolatile and the relative volatility is effectively infinite. From a molecular viewpoint, we expect that some salt molecules (or ions) may escape from the liquid surface and be present in the vapor. However, the escaping tendency is so small under the conditions encountered in an absorption machine that the vapor above the liquid solution is essentially pure water vapor (steam). This fact can be appreciated more fully by realizing that the normal boiling point of solid lithium bromide salt is 1282°C (Cyprus Foote Minera n.d.). Thus, the vapor pressure of the salt at typical absorption machine conditions is exceedingly low. From a thermodynamic standpoint, we will assume that there is no salt content in the vapor and that the properties of the vapor are those of pure water (i.e., steam). At high vapor velocities, liquid entrainment can also carry salt throughout the machine. Trace salt quantities are important from a corrosion perspective. The p resence of trace amounts of salt contributes to accelerated corrosion throughout the vapor space. When heat is applied to the solution in the desorber, vapor is “generated” or “desorbed,” and the vapor flows to the condenser. The remaining liquid solution exits the desorber and flows back to the absorber. The process in the desorber is a partial evaporation. As the vapor leaving the desorber is essentially free of salt, the liquid solution becomes concentrated during the partial evaporation process. Thus, the solution flowing back
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to the absorber is a relatively concentrated salt solution (compared to that exiting the absorber). A number of terms are in common use to describe the concentrations in absorption systems. In general, the mass fraction is used as a concentration measure in this text. However, it may be of use to the reader to define the commonly used terms. The terms “rich” and “poor” are sometimes used, but care must be taken to know to which mixture component these terms refer. When using these terms, one must say, for example, that the solution is “rich in refrigerant.” A similar set of terms is “strong” and ”weak.” Once again, one can refer to a solution as “strong in refrigerant,” meaning a low mass fraction of lithium bromide in this case. The reader is referred to ASHRAE (1993) for suggestions on how to standardize this type of terminology. For our purposes in this book, it was decided to minimize the ambiguity by primarily using mass fraction of salt to describe the solution concentration. The concentrated salt solution leaving the desorber passes through a solution heat exchanger and exchanges energy with the solution leaving the absorber. This heat exchange process occurs between two liquid streams and involves primarily sensible heat (no phase change occurs in this device under normal conditions). The purpose of this internal heat exchange device is to reduce the external heat input requirement by utilizing the energy available within the machine that would otherwise be wasted. By including a solution heat exchanger, the rate of rejected heat in the absorber is also reduced. Thus, the solution heat exchanger is a key component; the performance of this component has a major impact on the design of an absorption machine. The solution stream leaving the desorber returns to the absorber. The stream gives up energy in the solution heat exchanger and typically arrives subcooled at the flow restrictor. As the liquid is throttled through the restrictor, some vapor may evolve from the liquid. The two-phase stream then enters the absorber. In the absorber, the concentrated salt solution is brought into contact with the vapor supplied by the evaporator. The absorption process occurs if the absorber is cooled by an external sink (e.g., a flow from a cooling tower). As the vapor is absorbed, the liquid mass fraction is reduced to the level of the desorber input. As vapor is absorbed into the solution, the mass flow rate of liquid leaving the absorber is greater than that of the liquid entering the absorber. The reverse is true for the desorber. 5.1.2 Refrigerant Leg The refrigerant leg of an absorption machine is identical in function to the corresponding components in a vapor compression machine. The refrigerant leg takes the refrigerant vapor from the desorber and directs it to the condenser, where it is liquefied by rejecting heat to a sink. In a typical installation, the absorber and the condenser would reject heat to the same sink (i.e., approximately the same temperature level). The subcooled liquid leaving the condenser is throttled through the restrictor to the low pressure. This throttling process is typically accompanied by some vapor flashing. However, due to the high latent heat of water, the vapor quality leaving the restrictor is relatively low as compared to common refrigerants used in vapor compression systems. The two-phase refrigerant then enters the evaporator. Evaporation takes place, accompanied by heat transfer from the evaporator environment to the evaporator, due to the low pressure created by the absorber. Complete evaporation then implies that all of the refrigerant flow arrives at the absorber as vapor. In a real evaporator, some liquid droplet entrainment can occur due to high vapor velocities. Entrainment needs to be minimized because liquid leaving the evaporator represents a loss in cooling capacity.
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5.2 Crystallization and Absorber Cooling Requirements The nature of salt solutions, such as aqueous LiBr, is that the salt component precipitates when the mass fraction of salt exceeds the solubility limit. The solubility limit is a strong function of mass fraction and temperature, and a weak function of pressure. Furthermore, crystal nucleation is a process sensitive to the presence of nucleation sites. If no suitable nucleation sites are present, supersaturation can occur where the salt content of the liquid is greater than the solubility limit. Once crystals begin to form, the crystals themselves provide favorable nucleation sites and the crystals grow on themselves. The phenomenon of precipitation of salt from an aqueous solution can be readily observed by preparing a solution of 0.70 mass fraction LiBr. Precipitation of LiBr crystals can be observed by mixing the solution at 100°C and then cooling it to room temperature. At 100°C, the solution consists of a single-phase liquid. As the solution is slowly cooled, wispy white flakes can be seen that appear to be only slightly more dense than the liquid. In the case of LiBr, the precipitate observed is a solid hydrate phase. The phase diagram for aqueous LiBr is shown in Figure 5.2. This phase diagram is a plot of temperature as a function of mass fraction and shows the various phase boundaries present in the system. It should be mentioned that the diagram was constructed based on the data taken at atmospheric pressure. However, because pressure has only a weak effect in the pressure range of 150
Sol. + LiBr·H2O
100
Sol. + LiBr·2H2O
50
Ice + LiBr·5H2O –100
0
0.2
FIGURE 5.2 Aqueous lithium bromide phase diagram.
0.4 0.6 LiBr mass fraction
0.8
LiBr + LiBr·H2O
–50
LiBr·H2O + LiBr·2H2O
Ice + solution
LiBr·2H2O + LiBr·3H2O
0 LiBr·3H2O + Sol. + LiBr·5H2O LiBr·3H2O
Temperature (°C)
Liquid solution
1
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111
interest, these data are directly applicable. The two-phase regions adjacent to the liquid region consist of solid hydrate along with liquid solution. This is typical of the wet solid (slush) that can form in the absorption machine piping if machine conditions wander from design conditions. The solid precipitate tends to cling to piping components and, if conditions are allowed to persist, the precipitate can completely clog the flowing system and stop the flow. When the flow stops, additional cooling of the piping occurs due to heat loss to the surroundings, and the wet solid slush in the pipes becomes even more solid. Visualization of the flowing solution prior to a crystallization shutdown typically shows floating solid. If filters are used in the system, the observation of floating solid is an indication of an imminent shutdown. When such a flow stoppage occurs in an operating absorption machine, it tends to occur at the outlet of the solution heat exchanger where temperatures are relatively low and mass fractions are high. The phase boundaries are usually included on enthalpy and Dühring plots to remind the designer of the proximity of this characteristic of the fluid (see Figures 3.10 and 3.18). Various methods can be used by the designer to minimize the possibility of crossing the phase boundary. The simplest method used is to ensure a sufficiently low-temperature sink for cooling the absorber. Based on the properties of aqueous lithium bromide, low temperatures in the absorber require lower absorber solution concentration and thus tend to avoid the phase boundary. The crystallization characteristic of the fluid is the main obstacle to producing an air-cooled absorption machine based on LiBr. Air-cooled absorbers tend to run hotter than water-cooled units due to the relative heat transfer characteristics of the coolants. Particularly in hot climates, air-cooling presents a difficult design problem. The result is that there are very few air-cooled absorption machines based on aqueous lithium bromide. Water-cooled absorption machines generally can operate year-round without crystallization problems if the machines are well maintained and carefully monitored. Crystallization events require considerable time and effort to correct. Although the slushy solid that forms is wet, it is quite viscous. Thus, the preferred recovery procedure is to raise the temperature of the piping/machine components that are crystallized to a point where the viscosity is reduced sufficiently so that the pumps can circulate the solution. Once the solution is circulating, it can be easily diluted using water from the evaporator. It is highly desirable to avoid crystallization events. Thus, manufacturers generally include controls that sense the possibility of crystallization and take appropriate action to avoid the condition, by reducing heat input to the desorber or by diverting liquid water from the evaporator to the absorber and thus diluting the solution. However, it is still possible to crystallize a machine under certain conditions (e.g., sudden loss of cooling), and thus it is important for the operator to be aware of the machine operating conditions at all times. Crystallization will generally not damage the absorption machine, but the downtime and extra work involved in getting the machine back online is an incentive to avoid such events.
5.3 Corrosion and Materials Compatibility In the presence of dissolved oxygen, aqueous LiBr is highly aggressive to many metals, including carbon steel and copper. However, in the hermetic environment inside a welldesigned and carefully operated absorption machine, very little oxygen is present and corrosion rates are much slower. For the temperature range of a typical single-effect
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application, carbon steel and copper are the preferred materials of construction. Over the extended life of a machine, significant corrosion can still occur, and care must be taken to minimize the effects. The primary measures available are (1) pH control and (2) corrosion inhibitors. Corrosion of steel (or copper) in the presence of an electrolyte, such as aqueous lithium bromide, is a multistep oxidation–reduction reaction involving iron (or copper) ions leaving the solid surface and combining with oxygen at a distance from the surface. This leaves the solid surface of the base metal available for more attack. The oxidation potential of the solution is a strong function of the pH level in the acidic range. By controlling the solution to be only slightly basic, the hydroxyl radicals are in excess, and this tends to cause oxide formation directly on the solid surface (passivation). Over time, alkalinity tends to increase as hydrogen gas is formed, and it is preferable to keep pH close to neutral. pH control in a LiBr absorption machine can be achieved by adding small amounts of HBr (typically in aqueous form as hydrobromic acid) to achieve the desired pH. As these components are already present within the solution, the addition of HBr does not significantly alter the solution properties. Corrosion inhibitors provide a complementary reduction in corrosion rates. Various corrosion inhibitors have been proposed and tested over the years, including lithium chromate, lithium molybdate, and lithium nitrate. These salts are added to the LiBr solution in amounts on the order of 1% by weight. Krueger et al. (1964) recommend 0.3% Li2CrO4 and 0.005% LiOH as the preferred inhibitor concentration. For molybdate, they recommend 0.1% Li2MoO4 and 0.2% LiOH. These inhibitors reduce corrosion rates, apparently by reacting with the metal surface and forming a relatively stable oxide coating (i.e., passivation). Lithium chromate was the corrosion inhibitor of choice for many years, but its toxicity to plant and fish life in event of spillage has reduced its usage. Lithium molybdate, although somewhat less effective, has been found to provide adequate machine life in many applications. High-temperature applications, including some components in double-effect machines, require special materials to maintain long life. Copper–nickel alloys resist corrosion at high temperature better than copper. Tubes made from copper–nickel can be substituted for copper tubes without significant changes in design other than introducing a heat transfer penalty. However, copper–nickel is relatively expensive and is only used when copper does not provide adequate service life. Copper–nickel tubes are also used when the external environment is corrosive, such as when ocean water is used as a coolant. A major design issue is to minimize the electrochemical potential between the tubes and the tube sheet. Stainless steels often exhibit pitting and corrosion cracking in the presence of high-temperature LiBr. Good compatibility is found with most rubber and polymer compounds. Seals in LiBr systems are not a particular problem because common rubber products are compatible. Leather is strongly attacked by LiBr solution. Use of leather garments (including shoes) is not recommended around LiBr systems because any splashing of the solution will destroy the leather rapidly.
5.4 Vacuum Requirements Typical pressures in a single-effect LiBr absorption machine are subatmospheric. The pressures are determined by the vapor pressure characteristics of the working fluids. As essentially pure water exists in the condenser and evaporator, the temperature of operation
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of these components defines the pressure. For an evaporator temperature of 5°C, the corresponding vapor pressure of water is 0.872 kPa or approximately 0.009 atm. This low pressure introduces several challenges to the designer, including (1) large components due to the large specific volume of the vapor, (2) requirement for hermetically sealed outer vessel, (3) sensitivity to trace amounts of internally generated gases, and (4) hydrostatic head effects in evaporator design. These design issues are interrelated and are discussed in this section. The pressure levels associated with LiBr absorption are not particularly low as compared to high-vacuum applications such as space simulation or metal deposition; however, the sensitivity of the technology to leaks is very high such that leakage control requirements are comparable to high-vacuum applications. Absorption machines are sensitive to leaks for two primary reasons: (1) air in the machine hurts transport performance, and (2) air in the machine causes corrosion. The pressure terminology used in the vacuum technique is often confusing because practitioners sometimes measure the difference between the pressure in their system and the pressure of the atmosphere. The alternative method is to simply specify the absolute pressure. These two methods are compared in Figure 5.3, where a number of common pressure units are also shown. In this book, absolute pressure units are used throughout. But even when absolute pressure units are used, the different unit systems in common use can still be confusing. For example, practitioners in the field commonly use “mm Hg” (millimeters of mercury) and “in Hg” (inches of mercury) for vacuum gauges. These are, of course, really measures of head and must be converted to a pressure by multiplying the head by the density of mercury and the acceleration of gravity. The low pressures in an absorption system are initially attained by pumping out the air and other gases from the vapor space. Gases dissolved in the liquids in the machine must also be removed. This removal occurs naturally if enough time is allowed for the gases to diffuse out of the liquid into the evacuated vapor space. The process is significantly accelerated if the liquid is agitated while the vapor space is being evacuated. The agitation can be done mechanically, for example, by circulating the liquid with the pump, or thermally by boiling the fluids.
0.0 in Hg
Atmospheric pressure (101.325 kPa) 7.501 mm Hg
Vacuum gauge readings (in Hg)
7.501 torr (same as mm Hg) 1 kPa =
0.01 bar 0.00987 atm 0.145 psi
29.9 in Hg FIGURE 5.3 Vacuum terminology and units.
Zero pressure (0 kPa)
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Absorption Chillers and Heat Pumps
Vacuum pump
From system
Ice/water or dry ice/alcohol bath FIGURE 5.4 Cold trap design schematic.
As the vacuum pump extracts from the vapor space, both unwanted gases and some water vapor are removed. The mass of the water removed is usually not significant from the standpoint of the absorption cycle operation because the specific volume of the vapor is so large. However, this vapor removal has some secondary effects. As the water vapor evaporates from the surface of the liquid pools within the machine, it sweeps the vapor space and assists in removing unwanted gases from the system. Although the system pressure never falls below the vapor pressure of the liquids in the system, the purging effect of the evaporating vapor is highly effective in reducing the partial pressure of the gases in the system to the necessary levels. Another secondary issue associated with water vapor removal is the effect of this vapor on the vacuum pump. For the pressure levels of interest in absorption technology, modern mechanical vacuum pumps designed for refrigeration practice are completely adequate. The main requirement is the ability to remove vapor at the vapor pressure of water. For oil-lubricated pumps, the water vapor tends to condense in the exhaust stages of the pump and to end up in the oil sump. The water tends to reduce the lubrication effectiveness and will harm the pump if the condition is allowed to persist. Careful observation of the oil is necessary, and when discoloration occurs, the oil must be replaced. To reduce or eliminate water condensation in the pump oil, a cold trap can be employed to trap the water before it gets to the pump. The cold trap can have a simple design, such as that shown in Figure 5.4, with the key feature being sufficient low-temperature surface area on which to “trap” the water. The water must condense in such a way that it does not block the gas flow path. To trap the water, the sump must be maintained at a temperature below the dew point of the gas mixture. Example 5.1: Pressure Units Consider an absorption machine operating at the pressure levels 10 and 1 kPa. Convert these to all the other commonly used units indicated in Figure 5.3. Known: Pressure levels Find: Representation in other unit systems
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Overview of Water/Lithium Bromide Technology
Assumptions: Unit conversions given in Figure 5.3. The following equation converts a head reading (1 in Hg) into a pressure reading. 1 in Hg = hρg = 1 in ×
kg 0.0254 m m × 13595 3 × 9.807 sec 2 m in
= 3.3865 kPa
Analysis: The conversion to vacuum gauge units requires the following analysis. One inch of mercury can be converted to the kPa equivalent as shown, noting that the density of mercury is 13,595 kg/m3. This conversion is applied to the difference between the actual pressure and the standard atmospheric pressure (101.325 kPa). The unit conversions result in the following table.
mm Hg torr bar atm psi in Hg (vacuum)
P = 1 kPa
P = 10 kPa
7.501 7.501 0.01 0.00987 0.145 29.63
75.01 75.01 0.1 0.0987 1.45 26.97
Observations: In practice, vacuum gauges often measure the difference between the system pressure and the local barometric pressure. The largest reading possible on such a vacuum gauge is 29.921 in Hg corresponding to zero pressure. A standard atmosphere was assumed in these calculations.
5.4.1 Component Size The lowest pressure in an absorption machine is in the evaporator and absorber. Typical pressures are on the order of 1 kPa. At this pressure, the specific volume of saturated steam is 129.2 m3/kg. This large volume leads to high velocities for vapor transfer between components. Large velocities generally imply large pressure drops. However, LiBr absorption machines are quite sensitive to pressure drop between the evaporator and the absorber. At a pressure of 1 kPa, the slope of the vapor pressure curve of water is 14°C/kPa, indicating that small pressure drops can have a large influence on temperature. Furthermore, due to the logarithmic nature of the vapor pressure curve, the sensitivity of temperature to pressure drop increases with each increment of pressure drop. In addition, pressure drop between the evaporator and absorber aggravates the design problems associated with crystallization because it forces the solution to achieve a higher concentration in order to maintain a lower pressure at the same temperature. Thus, the designer must balance these conflicting design requirements. The design solution is to provide a very large vapor transport cross section between the evaporator and the absorber. To achieve this in practice, these two components are usually housed in a single shell providing a minimum of viscous losses. A pressure difference is still required to drive the vapor from the surface of the evaporating liquid to the surface of the absorbing liquid. By minimizing tube bundle and wall viscous effects, this pressure drop can be minimized.
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Absorption Chillers and Heat Pumps
The high vapor velocities also provide design challenges within each of the components. The vapor velocity between tubes must be small enough so that viscous losses within the tube bundle are kept to acceptable values. This is a common problem in tube bundle design, but it is more significant in LiBr absorption technology because of the sensitivity of the cycle operation to the pressure drop. For both the evaporator and the absorber, the designer has very little pressure drop to spend in getting the vapor out of (or into) the tube bundle. In this case, another design aspect normally drives the bundle design away from pressure drop problems. The need for small temperature differences, for example, between the evaporating refrigerant and the chilled water flowing in the tubes, requires a large heat exchanger area and low heat fluxes. Low heat flux leads to lower vapor velocities but also leads to large component size. The evaporator and absorber vessel of a typical LiBr absorption machine is quite large due to these various ramifications associated with the low vapor pressure of water. 5.4.2 Effect of Nonabsorbable Gases Air leaks into an absorption machine cause unacceptable corrosion problems due to the oxygen as well as performance effects due to vapor side mass transfer resistance. Therefore, a LiBr absorption machine must be essentially hermetic in design. Nonabsorbable gases other than air can also cause poor performance. The corrosion chemistry at work in an absorption machine causes a low-level, continuous production of hydrogen gas. The rate of production depends on several factors, including the condition of the machine, usage profile, and solution chemistry. Hydrogen is essentially inert and has a very low solubility in both liquid water and aqueous LiBr solution in the temperature range of interest. Thus, the hydrogen produced accumulates in the vapor space of an absorption machine. The hydrogen has a tendency to migrate from the high-pressure side to the low-pressure side due to the influence of pressure on solubility (i.e., the solubility of hydrogen in both liquid water and liquid H2O/LiBr solution is slightly higher at higher pressure). The primary effect of inert gases in such a machine is to reduce the performance of both the condenser and the absorber. Since the absorber represents the most critical component design because it operates at low pressure and because of liquid mass transfer effects, the discussion is based on the absorber. Nonabsorbable gases in an absorbable vapor tend to get swept toward the vaporliquid interface by the bulk motion of the vapor. However, because the gas does not absorb appreciably into the liquid, the gas tends to accumulate on the vapor side of the interface. At steady state, the gas has a relatively high concentration at the interface, and it diffuses back into the bulk vapor due to the concentration gradient. This diffusion process implies that the refrigerant must diffuse toward the interface. As such, the gas tends to blanket the surface and significantly reduces the rate of absorption. The effect of nonabsorbable gas is most pronounced when the gas flow is laminar and not sweeping the absorbing surface. In a typical absorption machine, the vapor flows are turbulent. However, the effect of nonabsorbables can still be significant (Minkowycz and Sparrow 1966; Sparrow et al. 1967). Reductions in the performance of the absorber due to hydrogen buildup show up as reductions in capacity, coefficient of performance (COP), and more difficulty avoiding crystallization. Thus, the designer must provide a mechanism to purge the hydrogen from the system (Murray 1993). A direct method is to simply evacuate the vapor space periodically with a vacuum pump. Various other methods have been proposed to continuously purge a machine. These include palladium cells, which form a semipermeable membrane
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Gas receiver
Gas purge
Liquid outlet
Vapor inlet
High pressure liquid inlet FIGURE 5.5 Ejector purge system.
in the system, and ejector pumps, which use the existing solution pump to collect the gas. A schematic of an ejector pump system is given in Figure 5.5. In most designs, the machine operator must periodically purge the gas collection vessel with a vacuum pump. This is preferred over pumping on the entire vapor space of the machine since the gas is concentrated and removed quickly and easily. 5.4.3 Hydrostatic Head Effects in Evaporator Design Due to the low operating pressure of the evaporator in a LiBr absorption machine, hydrostatic effects can be quite important in evaporator design. At a liquid surface temperature of 5°C, the vapor pressure of pure water is 0.873 kPa. For a nominal 1 g gravitational field, a column of water exerts a pressure of 0.09807 kPa/cm of height. Based on the vapor pressure curve for water, this implies that a 1-cm head of liquid water above the boiling surface would cause the saturation temperature at the boiling surface to increase to 6.5°C. A 10-cm head would cause the saturation temperature at the boiling surface to reach 16.3°C. These effects make a pool boiler design impractical for the evaporator in a LiBr absorption machine because the evaporator temperature is highly sensitive to hydrostatic head. Instead, a sprayed design is usually used where a film of refrigerant is sprayed onto horizontal tubes. The maximum thickness of the film on the tubes is determined by the viscosity of the liquid and generally is on the order of 1 to 2 mm.
5.5 Octyl Alcohol The design of the absorber component in a LiBr absorption machine drives the design of the entire machine because it is the largest component. It is large for two reasons: (1) the large specific volume of water vapor at the absorber pressure requires large flow areas
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Absorption Chillers and Heat Pumps
to maintain acceptable pressure drops, and (2) the heat and mass transfer coefficients in the absorber are lower than the corresponding coefficients in the other components. The absorber transfer coefficients are low due to the relatively ineffective mass transfer process in the liquid on the solution side. Various techniques can be used to augment the mass transfer by inducing mixing in the liquid. One effective technique involves the addition of a surfactant additive, called octyl alcohol (2-ethyl-1-hexanol), which acts to induce Marangoni convection in the liquid. Use of octyl alcohol can increase transfer performance in absorber design by as much as two times (i.e., 200% performance improvement), but system effects (e.g., pressure drop and nonuniform flux effects) usually limit the effectiveness of the additive in bundles to much more modest gains. Marangoni convection is the name given to free surface flows driven by differences in surface tension. Surface tension–driven flows can be easily observed in the kitchen by adding a drop of detergent to dirty dishwater. Prior to adding the detergent drop, the oil is distributed fairly uniformly over the surface and the surface is static. When the detergent drop is added, the surface tension is reduced locally. Careful observation of the surface shows a radial flow away from the drop. The surface tension forces at a distance from the drop are no longer in balance and cause the flow. The surface flow must be accompanied by a convection cell within the liquid to satisfy mass continuity. Thus, Marangoni convection mixes the surface liquid into the bulk liquid. The processes in a LiBr absorber component are coupled heat and mass transfer processes. As the water vapor is absorbed into the liquid, the latent heat associated with the phase change is released along with the heat of mixing. This energy release occurs at the vapor–liquid interface and causes the interface to be the location of highest temperature in the system. To allow the process to continue, the energy must be transported through the liquid toward the cooling medium, and the excess water at the surface must be transported into the bulk of the liquid. These two transport processes are coupled in the sense that stopping either process causes the system variables to adjust in such a way as to stop the other process. For the overall transfer to take place, both processes have to proceed in tandem. The value of octyl alcohol in LiBr/water absorption machines was apparently discovered serendipitously when the alcohol was added to the system for some other purpose (possibly to control foam formation). However, the effect on absorption rate was found to be very significant. This led to a number of theories as to the mechanism of action. This discussion was resolved by the introduction of the vapor surfactant theory (Kulankara and Herold 2000; Herold 2005), which ties together all known observations on octyl alcohol effects. (See Appendix F for more detail.) The primary tenet of this theory is that the mechanism of action is Marangoni convection in the liquid, but the novel aspect of the theory is that the alcohol arrives at the absorbing surface from the vapor phase. A corollary of this is that the alcohol undergoes a cycle passing through all of the components and finally evaporates in the evaporator and arrives at the absorption surface along with the water vapor. The importance of the octyl alcohol for machine performance was very clear before the introduction of this theory. The advantage of a clear understanding of how the alcohol works is that now the user can better understand a number of observations. But the biggest impact of the theory is on design where the alcohol is no longer a mystery. For example, it had been known previously that the evaporator recirculation pump suction design could have a big impact on system performance. The vapor surfactant theory explains this very clearly since it is important to recirculate the alcohol as well as the water, but the alcohol tends to float on the surface in the evaporator sump. Thus, the recirculation pump suction design must entrain the
Overview of Water/Lithium Bromide Technology
119
liquid surface to avoid accumulation of alcohol and to keep the surfactant cycle flowing. Additional detail on the vapor surfactant theory is included in Appendix F. As octyl alcohol is present in the vapor phase as well as in the liquid phase, it comes into contact with all of the surfaces in the machine. Experience shows that it coats these surfaces with a layer of condensed alcohol. The alcohol is also frequently observed floating on liquid surfaces as a separate phase. These surface layers complicate many experiments using octyl alcohol because they make it difficult to clean the alcohol out of a system. The low solubility of the alcohol in water means that simply flushing the system with water does not clean the surfaces very rapidly. Through experience, it was found that effective cleaning requires mechanical brushing of all of the inner surfaces, followed by flushing with water. If this is not done, then the alcohol on the surfaces redistributes into the working fluids when a new solution charge is introduced into the machine. If the objective is to have an alcohol-free data point, it is necessary to clean the alcohol from all of the inner surfaces. This characteristic of the alcohol to distribute itself throughout a system significantly complicates the specification of the concentration of the alcohol in a system. It is easy to load a system with a known amount of working fluid charge and a known amount of alcohol, and many researchers specify the concentration on that basis (a system concentration). However, when the solubility in the liquid is very low and the amount of alcohol on the surfaces is significant, the specification of a liquid concentration is misleading at best. Although no good alternative definition of the alcohol concentration comes to mind, it is important to be aware of the character of the alcohol and to avoid attributing too much physical significance to the system concentration.
5.6 Normal Maintenance and Expected Life Normal maintenance for LiBr/water technology includes (1) periodically purging nonabsorbable gases, (2) periodic addition of octyl alcohol, (3) periodic addition of corrosion inhibitor, and (4) periodic addition of pH buffer. The appropriate period for performing these tasks depends on a number of variables, including size of the machine and the purging system, and is generally specified by the manufacturer of the machine. The basic procedures are quite simple and can be performed by trained technicians. The necessary chemicals are relatively inexpensive and readily available from suppliers. Along with the maintenance procedures described earlier, an assessment of cycle performance against norms should be made on a regular basis to help diagnose any potential problems. The ultimate failure mode of a LiBr absorption machine is usually corrosion induced. For long life, attention must be paid to avoid introduction of air into the machine and to ensure that the corrosion inhibition regime is strictly followed. Based on many years of experience, well-maintained LiBr absorption machines have been proven to have a life expectancy of approximately 20 years. After 20 years, significant corrosion can be observed on the steel surfaces and leakage may occur, particularly around the tubes in the tube sheets. At some point, a decision must be made to replace the machine instead of fighting a losing battle. The life of the machine is limited by corrosion. Thus, for long life, great attention must be paid to corrosion avoidance. Once a machine begins to leak, the presence of oxygen can greatly accelerate the degradation; thus, leaks must be avoided. Introduction of oxygen during special maintenance procedures
120
Absorption Chillers and Heat Pumps
is another destructive event that must be avoided or minimized. If the vacuum must be broken for any reason, it is important to fill the vapor space with nitrogen or another inert gas to avoid introduction of oxygen. Long-term shutdown of charged machines should involve pressurizing the vapor space with nitrogen to a pressure above atmospheric so that any leakage that may occur does not introduce oxygen.
5.7 Controls Considerable work has been done by absorption machine manufacturers to perfect controls that can provide trouble-free operation for the user. With the exception of crystallization issues, absorption machines are inherently stable and self-starting. The user must turn on the pumps, including the solution pump and possibly an evaporator recirculation pump, and the cycle will run. The solution concentration will adjust to the imposed temperatures according to its thermodynamic properties. Thus, in general, no active controls are necessary. However, because of the problems associated with crystallization, a number of controls are generally provided to deal with this issue. A major cause of crystallization is sudden loss of absorber and condenser cooling. This can occur due to various problems such as pump power loss or cooling tower failure. If the heat input to the machine continues with no cooling, the solution will concentrate until crystallization occurs. Each manufacturer takes a slightly different approach to sensing and heading off such events. One simple approach to avoiding crystallization is to ensure that the solution mass fraction never goes above some limiting value (e.g., 0.65 mass fraction LiBr). As long as the machine stays in the expected temperature range of operation, this restriction is enough to guarantee no crystals. The mass fraction of LiBr can be measured by sampling and performing a density measurement or by titration, but an automatic method is sought that does not rely on sampling. A method of inferring the concentration is used by some manufacturers based on a known initial charge of solution with a known LiBr mass fraction. The refrigerant level in the evaporator is monitored and when it is too high, it is inferred that the solution is too highly concentrated. This scheme is relatively simple to automate and can be implemented using widely available level-sensing transducers.
Homework Problems 5.1 Determine the mass fraction at which solid precipitate will form (i.e., crystallization) at a temperature of 50°C. 5.2 Determine the composition of the precipitate from Problem 5.1. 5.3 Determine the mass fraction of each of the hydrates of lithium bromide. 5.4 Determine the hydrostatic pressure exerted by a column of 0.25 m of pure water and aqueous lithium bromide of 0.5 mass fraction LiBr.
Overview of Water/Lithium Bromide Technology
121
References ASHRAE. (1993). ASHRAE Handbook of Fundamentals. New York: ASHRAE. Cyprus Foote Mineral. (n.d.). Technical Data—Lithium Bromide. Cyprus Foote Mineral, Engelwood, CO. Herold, K. E. (2005). Surfactant Vapor Experiments. Proceedings of the International Sorption Heat Pump Conference, Denver. Krueger, R. H., K. F. Dockus, and W. F. Rush. (1964). Lithium Chromate: Corrosion Inhibitor for Lithium Bromide Absorption Refrigeration Systems. ASHRAE J. 6: 40–44. Kulankara, S. and K. E. Herold. (2000). Theory of Heat/Mass Transfer Additives in Absorption Chillers. HVAC&R Res. 6(4): 369–380. Minkowycz, W. J. and E. M. Sparrow. (1966). Condensation Heat Transfer in the Presence of Noncondensables, Interfacial Resistance, Superheating, Variable Properties and Diffusion. Int. J. Heat Mass Transfer. 9: 1125–1144. Murray, J. G. (1993). Purge Systems for Absorption Chillers. ASHRAE Trans. 99(Pt. 1): 1485–1494. Sparrow, E. M., W. J. Minkowycz, and M. Saddy. (1967). Forced Convection Condensation in the Presence of Noncondensables and Interfacial Resistance. Int. J. Heat Mass Transfer. 10: 1829–1845.
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6 Single-Effect Water/Lithium Bromide Systems The objective of this chapter is to describe the operating characteristics of single-effect water/lithium bromide absorption chiller/heat pump systems (Herold and Radermacher 1989; Kühn et al. 2005; Herold 2007; ASHRAE 2010). That objective is addressed by examination of several examples with alternative design features and characteristics. The examples are presented as solutions of computer models of the respective cycle configurations. The computer models associated with the examples are provided on this book’s website (http://www.fchart.com/ees/books.php). The software Engineering Equation Solver (EES) is introduced in Appendix A, an overview of cycle modeling is provided in Appendix B, and more details about the cycle models used in this chapter is provided in Appendix C.
6.1 Single-Effect Water/Lithium Bromide Chiller Operating Conditions A single-effect absorption cycle using water/lithium bromide as the working fluid is perhaps the simplest manifestation of absorption heat pump technology. A cycle schematic of this configuration is provided in Figure 6.1, and a hardware schematic is provided in Figure 6.2. The major components are labeled, and the state points in the connecting lines are assigned state point numbers. The cycle schematic shows the energy transfers external to the cycle as arrows in the direction of transfer with variable names representing the four heat transfer rates and one pump power term. The cycle schematic is drawn as if it were superimposed on a Dühring chart of the working fluid properties, as indicated by the coordinates shown in the lower left-hand corner. The relative position on the schematic of the components with phase change indicates the relative temperature and pressure of the working fluid inside those components. The exception to this convention is the subcooled and superheated states, which cannot be accurately represented on a Dühring chart that displays only saturated states. The hardware schematic in Figure 6.2 provides additional details on some of the key assumptions used in modeling this cycle. The hardware consists of two cylindrical shells, each of which houses two components that operate at about the same pressure. For example, the evaporator and absorber are in the same shell. Although a flow from the evaporator to the absorber does require a pressure difference, the open nature of the geometry minimizes this difference. A set of operating conditions for the cycle in Figures 6.1 and 6.2 is listed in Table 6.1. This set of conditions was generated by imposing mass and energy balances on the components and the entire cycle as discussed in Chapter 4. The model used to generate the data in Table 6.1 is included in file Ex6_1.ees. As an introduction to the technology, these mass and energy balances are reviewed next.
123
124
Absorption Chillers and Heat Pumps
. Qc
. Qd 7
Condenser
Desorber 3
8
Solution heat exchanger
Refrigerant expansion valve Pressure
4
2
˙ W
5
Pump
Solution expansion valve
9 1
Evaporator
Absorber
10
. Qe
6
. Qa
Temperature
FIGURE 6.1 Cycle schematic of a single-effect water/lithium bromide absorption chiller.
Condenser 7
8 Desorber Steam or hot water
3
4
9 Chilled water Evaporator 10
Evaporator recirculation pump
6 Absorber Cooling water
5 Solution heat exchanger 2
Solution 1 pump
FIGURE 6.2 Hardware schematic of a single-effect water/lithium bromide absorption chiller.
125
Single-Effect Water/Lithium Bromide Systems
TABLE 6.1 Operating Conditions for a Single-Effect Water/Lithium Bromide Machine State Points
h (J/g)
(kg/sec) m
P (kPa)
Vapor Quality
1
87.76386
0.05000
0.676
0.000
32.72
0.5648
2
87.76796
0.05000
7.406
32.72
0.5648
3
149.9
0.05000
7.406
63.61
0.5648
4
223.3
0.04543
7.406
89.36
0.6216
5
155.0
0.04543
7.406
53.11
0.6216
6
155.0
0.04543
0.676
44.96
0.6216
7
2643.1
0.00457
7.406
76.76
0.0000
8
167.8
0.00457
7.406
0.000
40.06
0.0000
9
167.8
0.00457
0.676
0.065
1.39
0.0000
10
2503.1
0.00457
0.676
1.000
1.39
0.0000
0.000 0.005
T (°C)
x (kg/kg)
Summary of Energy Quantities W Q
Pump power
0.205 W
Heat transfer rate in absorber
14.09 kW
Q d
Heat transfer rate in desorber
14.73 kW
Q e
Heat transfer rate in evaporator
10.67 kW
Q c
Heat transfer rate in condenser
11.31 kW
Q hx
Heat transfer rate in solution heat exchanger
3.105 kW
COP
Coefficient of performance
a
0.724
Source: Based on Figures 6.1 and 6.2, and the computer file Ex6_1.ees.
6.1.1 Mass Flow Analysis At steady state, the net mass flow rate into each of the components must be zero. Furthermore, since it is assumed that no chemical reactions occur between water and lithium bromide, the net mass flow rate of each of the species into any component must also be zero. As there are two species (i.e., water and lithium bromide), there are only two independent mass balances (as discussed in Chapter 4). As an example, consider the mass balance on the desorber, which can be written on an overall mass basis as
3 = m 4 +m 7 (6.1) m
A balance on the lithium bromide species, assuming that the vapor leaving the desorber has zero salt content, yields
3 x3 = m 4 x4 (6.2) m
The water mass balance can be obtained by subtracting Equation 6.2 from Equation 6.1 to obtain
3 ( 1 − x3 ) = m 4 ( 1 − x4 ) + m 7 (6.3) m
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Absorption Chillers and Heat Pumps
The fact that only two of the three mass balances are independent is emphasized by the fact that the third was obtained algebraically from the first two. However, it is also possible to write the water mass balance directly from the schematic, as was done for the overall and lithium bromide mass balances. It is left as an exercise for the reader to prove that both procedures yield the same equation. Similar analyses can be performed on the other components using the data presented in Table 6.1. The conclusion is that mass conservation is satisfied for all components. It should be noted that the absolute values of the mass flow rates appearing in Table 6.1 were selected for illustration purposes only. In general, the mass flow rates scale with the capacity of the machine and will differ for each application. Another mass flow parameter that is sometimes useful is the solution circulation ratio, f, defined in Equation 4.15. For the state points in Figure 6.1, f can be expressed as
f=
3 m x4 = = 10.94 (6.4) 7 x 4 − x3 m
which shows that the liquid flow rate through the solution pump is 10.94 times the vapor flow rate leaving the desorber. This is a typical value and is useful to remember when dealing with design issues. The structure of the solution loop in an absorption machine leads to redundant mass balances. A rule of thumb is that there is one redundant overall mass balance and one redundant LiBr balance for each cycle. If you erroneously attempt to include the redundant balances in a cycle simulation, it will confound the solver and generate an error message, which may be cryptic. Thus, it is important to be aware of the issue of redundant mass balances and to avoid entering these redundancies at the beginning. One simple way to avoid the problem is to use one of the cycle models supplied with this book as a template for a modified cycle model. In the simulations provided here, the redundant mass balances are checked by defining an error term for each of the omitted mass balances. When the error terms evaluate very close to zero, this is a good indication that these mass balances were truly redundant and that the remaining mass balances are properly formulated. 6.1.2 Thermodynamic States within the Cycle The thermodynamic state of each of the points within the cycle must be defined to properly understand the cycle. A summary of the state-point descriptions is provided in Table 6.2. As listed in the table, three of the points are saturated liquid (1, 4, and 8), one is saturated vapor (10), three are subcooled liquid (2, 3, and 5), one is superheated vapor (7), and two are two-phase vapor-liquid states for a total of 10 state points. The vapor quality is assumed for four state points. Those are the three saturated liquid states (1, 4, and 8) and the saturated vapor state (10). These assumptions are made for convenience in modeling. In a real machine, the conditions at these points would not be exactly saturated. In general, the transfer processes within the components require a finite driving potential between the vapor and liquid phases. A saturated outlet condition would imply a zero potential difference at the outlet, which does not occur in practice. However, this assumption provides a worthy design goal, and it is typical of a first-order model of an absorption cycle. In a real machine, the liquid streams would be expected to be subcooled and the vapor stream would be superheated. These states could also be modeled, but as additional data would then be needed, their inclusion would introduce more complication. Experience shows that for typical design calculations, these assumptions provide adequate accuracy.
127
Single-Effect Water/Lithium Bromide Systems
TABLE 6.2 Thermodynamic State-Point Summary for the Simulation Detailed in Table 6.1 Point
State
Notes
1 2 3 4 5 6
Saturated liquid solution Subcooled liquid solution Subcooled liquid solution Saturated liquid solution Subcooled liquid solution Vapor–liquid solution state
7 8 9
Superheated water vapor Saturated liquid water Vapor–liquid water state
10
Saturated water vapor
Vapor quality set to 0 as assumption State calculated from isentropic pump model State calculated from solution heat exchanger model Vapor quality set to 0 as assumption State calculated from solution heat exchanger model Vapor flashes as liquid passes through expansion valve. Note: If the solution heat exchanger effectiveness is set higher than about 80%, state 6 will be subcooled liquid Assumed to have zero salt content Vapor quality set to 0 as assumption Vapor flashes as liquid passes through expansion valve Vapor quality set to 1.0 as assumption
The state at the vapor outlet from the desorber (point 7) is specified as superheated water vapor (steam) based on the perspective that the stream is pure water at a temperature above its saturation temperature at the desorber pressure. However, it is also possible to view this state as the vapor component of a two-phase system, where the solution in the desorber is the liquid phase. From this binary mixture perspective, the vapor is saturated. These two perspectives are both correct and they are both useful, depending on the type of analysis being performed. This point is emphasized here because it is possible to generalize the assumption about the outlet state of the working fluid from each of the components. Typical for the cycle models described in this book, saturated solution conditions are assumed at the outlet of each of the four major components (desorber, absorber, condenser, and evaporator). The outlet states from the expansion valves are determined by applying an energy balance to the valve, assuming an adiabatic expansion, as discussed in Section 4.8. It should be noted that the state-point data for these states (points 6 and 9) listed in Table 6.1 represent the overall two-phase state. Thus, the enthalpy, mass fraction, and mass flow rate values listed are for the overall two-phase flow at that point. A better understanding of the state at these points is obtained by computing the vapor quality to determine the amount of vapor that flashes as the expansion occurs. For the conditions listed and using the methods discussed in Section 4.8, the quality values obtained are listed in the table. At point 9, approximately 6.5% of the mass flow flashes into steam. Due to the substantial changes in volume that occur at such a low pressure, the flash gas significantly impacts the design of a refrigerant expansion device for this application. The amount of vapor that flashes at point 6 is much smaller for this example (only 0.5%) as a result of the significant subcooling that occurs in the solution heat exchanger at point 5. A change in the performance of the solution heat exchanger can cause more or less flash gas at point 6. As at point 9, the flash gas has a very high specific volume and causes the velocity of the two-phase stream at 6 to be significantly greater than the velocity at point 5. Note that kinetic energy effects are not included in these expansion valve models. The temperature drop that occurs across each of the expansion valves occurs because the vapor has a higher internal energy than the liquid. Thus, some energy must be extracted
128
Absorption Chillers and Heat Pumps
from the liquid to drive the phase change. The process attains its own equilibrium at a temperature below the starting temperature. The magnitude of the temperature drop correlates with the amount of vapor that flashes. 6.1.3 Energy Balance Analysis Mass and energy balances were imposed on each of the system components to obtain the solution listed in Table 6.1. In this section, the heat transfer values are manually reproduced by invoking the energy balances on each of the components. This process of checking the model output is an extremely important step in ensuring that the model output is correct and meaningful. An energy balance on the evaporator can be written as 10 h10 − m 9 h9 = 10.67 kW (6.5) Q e = m
Similarly for the condenser
7 h7 − m 8 h8 = 11.31 kW (6.6) Q c = m
Equations 6.5 and 6.6 could be simplified slightly by using the fact that the mass flow rate 10 = m 9). In fact, the mass flow rate is identical is the same at the inlet and outlet (e.g., m throughout the entire refrigerant circuit, as can be seen by examining the mass flow rate values in Table 6.1. An energy balance on the desorber can be written as
7 h7 + m 4 h4 − m 3 h3 = 14.73 kW (6.7) Q d = m
and similarly for the absorber as
10 h10 + m 6 h6 − m 1 h1 = 14.09 kW (6.8) Q a = m
An energy balance on the hot side of the solution heat exchanger can be written as
4 h4 − m 5 h5 = 3.11 kW (6.9) Q hx− h = m
Alternatively, one can write the cold side balance as
3 h3 − m 2 h2 = 3.11 kW (6.10) Q hx−c = m
The overall energy balance on the solution heat exchanger is satisfied if Q hx − h = Q hx − c, which is seen to be the case here. An energy balance on the pump can be written similarly as
=m 2 h2 − m 1 h1 = 0.000205 kW (6.11) W
The values listed for the enthalpy at points 1 and 2 in Table 6.1 have increased precision to display the small difference in enthalpy that occurs in the pumping process from points 1 to 2. This difference in enthalpy was obtained by assuming an isentropic pump model, as discussed in Section 4.7. The pump work is quite small as compared with the heat
Single-Effect Water/Lithium Bromide Systems
129
transfer rates associated with the other components. Thus, it can be concluded that from a thermodynamic standpoint, the pump work is negligible for a single-effect water/lithium bromide cycle. Based on this thought, the coefficient of performance (COP) is calculated without including the pump work term. Even if the pump were only 10% efficient, the pump work would still be only about 0.01% of the heat input in the desorber. One could also note that the availability (or exergy) of a work input is greater than that of a heat input. However, the pump work still appears negligible even when compared on an exergy basis. Although the t hermodynamic conclusion is that the pump can be ignored, practical experience shows that the pump is a critical component that must be carefully engineered. Major solution pump design issues include: (1) pump seals to avoid air leakage, (2) pump cost, (3) corrosion/materials, and (4) sufficient net positive suction head to avoid cavitation (i.e., two-phase flow) in the suction line. Once the heat transfer in each of the components has been determined, the COP for cooling can be calculated as Q COP = e = 0.724 (6.12) Qd
This value is fairly typical of single-effect water/lithium bromide chillers. In a commercial machine, the solution heat exchanger would have a higher effectiveness than was used here, but there are internal irreversibilities that this model ignores. Another view of the cycle performance is obtained by calculating the ratio of the rejected heat to the heat input. This ratio is the COP for heating defined as
COPh =
Q a + Q c Q d + Q e = = 1 + COP = 1.724 (6.13) Q d Q d
6.1.4 Discussion of the Operating Conditions The highest pressure in a single-effect water/lithium bromide machine is typically less than 10 kPa absolute pressure. Thus, the entire machine operates well below atmospheric pressure. This characteristic requires hermetic design to avoid air in-leakage. The low pressures also constrain component design because viscous pressure drops must be minimized in all components and hydrostatic effects can cause problems. 6.1.4.1 Dühring Plot Representation The cycle solution represented by the data in Table 6.1 is plotted on a water/lithium bromide Dühring plot in Figure 6.3. The saturated states are plotted at their state-point locations (points 1, 4, 6–9, and 10). The subcooled states are plotted at their respective temperatures and mass fractions. The pressure coordinate is not meaningful in this representation for subcooled states. The Dühring plot representation of a cycle solution is a very important step in visualizing the data. It is strongly recommended that such a plot be made as a tool to support understanding of any and all cycle solutions. This is particularly important for more complicated cycles but it applies to single-effect cycles as well. A number of pitfalls can be avoided by checking a solution instead of assuming that it is correct. One such pitfall is the approach of the operating envelope to the crystallization line. Others include maximum and minimum temperatures, reasonable heat rejection temperatures, reasonable pressures
130
Absorption Chillers and Heat Pumps
Pure water
Vapor pressure (kPa)
1000
0.45 0.55
100
0.1
0.60
0.65
7 3
8
10 1
0.50
9,10
1
2
5
6
0.70 mass fraction LiBr
4 Crystallization line
0.01 0
50
100 Temperature (°C)
150
200
FIGURE 6.3 Dühring plot for cycle solution in Table 6.1.
and reasonable mass fractions. The values that are reasonable depend on the particular application. The ability to view all of the data in one plot allows the designer to rapidly perform a number of reasonableness checks on the data. If the operating conditions violate design limits, the model inputs must be changed, the cycle model run again, and the plot recreated. 6.1.4.2 Temperatures The desorber temperature glide covers the range 76.8°C–89.4°C. (Note that this range does not include the temperature changes associated with heating stream 3 up to saturation because the energy associated with sensible heating is relatively small in this case.) This is the temperature range over which the heat input must occur. The heat source temperature must be higher than these internal temperatures. The evaporator temperature is 1.39°C, which is quite close to the freezing point of water. Thus, one observation on this operating condition is that the evaporator may be in danger of freezing if the operating condition wanders. Heat rejection occurs in both the absorber and condenser. The condenser saturation temperature is 40.1°C and the absorber temperature glide is 45.0°C–32.7°C. For a typical cooling tower design temperature of 30°C, the pinch point (i.e., the smallest driving temperature difference in the heat exchanger) in the absorber looks quite small. A heat transfer analysis is needed to determine if this design is workable. Such an analysis is performed in Section 6.2. 6.1.4.3 Mass Fractions The lithium bromide mass fraction in the solution circuit changes from 0.565 in the pumped leg to 0.622 in the return leg to the absorber. As is typically the case, the outlet state from the solution heat exchanger into the absorber is the closest approach to the crystallization line. This is clearly seen in Figure 6.3, where the calculated operating conditions avoid crystallization but without much margin of safety.
131
Single-Effect Water/Lithium Bromide Systems
6.1.4.4 Solution Heat Exchanger The effectiveness of the solution heat exchanger is defined as the ratio of the actual to the maximum possible heat transfer rates. The maximum possible heat transfer rate is the product of the minimum capacitance rate (i.e., mass flow rate – specific heat product) and the temperature difference between the entering streams. As the minimum capacitance rate occurs for the hot stream, the effectiveness for the solution heat exchanger can be expressed, as in Equation 4.61, as εSHX =
T4 − T5 = 0.64 (6.14) T4 − T2
1
5
0.8
4 COP 3
0.4
2
COP
0.6
. Qhx
0.2
0
0.2
0.4 0.6 Solution heat exchanger effectiveness
Solution heat exchanger heat transfer (kW)
The value of the effectiveness was an input to the model in this case. It is informative to examine the influence of the solution heat exchanger on cycle performance by running the model for a range of effectiveness values. This was done and the result is plotted in Figure 6.4. All of the other input parameters were held constant at the same values used to generate Table 6.1. As the effectiveness is varied, the outlet states on both sides of the solution heat exchanger change, which then influences the heat transfer requirements in the absorber and the desorber. The COP is influenced through the effect on the desorber heat transfer rate. The solution heat exchanger effectiveness can be viewed as an indirect measure of the heat exchanger size (larger effectiveness generally means a larger heat exchanger). As the effectiveness is increased, the COP increases. The sensitivity of COP to the heat exchanger effectiveness is quite high. With no solution heat exchanger, the cycle produces a COP of only 0.6 because the desorber heat requirement is significantly higher in the absence of the internal heat exchange between the legs of the solution circuit. With a very effective solution heat exchanger, the COP exceeds 0.8. The load (i.e., the heat transfer rate) on the solution heat exchanger is also plotted in Figure 6.4, and it is seen to vary linearly with
1
0.8
1
0
FIGURE 6.4 Cooling COP and solution heat exchanger heat transfer rate versus solution heat exchanger effectiveness for a single-effect chiller.
132
Absorption Chillers and Heat Pumps
the effectiveness. The absorber load is also substantially impacted by the effectiveness of the solution heat exchanger with the pleasant result that the absorber load decreases as the COP goes up (not shown). The conclusions here regarding the solution heat exchanger are generally valid but represent only a partial analysis. The performance of the solution heat exchanger is strongly tied to the heat exchanger design and the cycle operating conditions. This subject is returned to in the following section, where heat transfer models, with the external streams that transfer heat to and from the cycle, are added to the model.
6.2 Single-Effect Cycle with Heat Transfer Models In this section, the cycle introduced in Section 6.1 is viewed from a larger perspective so as to directly include the effects of the heat exchange processes between the cycle and the external streams that provide heat exchange. A schematic of the cycle including fluid loops at all four corners is provided in Figure 6.5. All of the internal state-point designations are identical to those introduced in Figure 6.1. Eight additional state points are added to represent the inlet and outlet state of each of the external heat exchange fluid streams. A heat transfer effectiveness model for the solution heat exchanger was used in Section 6.1 and that model is carried forward here to maintain consistency, but it can be simply replaced with a UA model if desired (see discussion around Figures 6.15 and 6.22).
15 . Qc
16
12 7
Condenser
3
4 Solution heat exchanger
Refrigerant expansion valve
2
˙ W
5
Pump
Solution expansion valve
9 6
1
Evaporator
18
Absorber
10 17
. Qd Desorber
8
. Qe
11
13
14
. Qa
FIGURE 6.5 Single-effect water/lithium bromide absorption chiller with external heat transfer models.
133
Single-Effect Water/Lithium Bromide Systems
A set of operating conditions for the cycle in Figure 6.5, generated by the model in file Ex6_2.ees, is listed in Table 6.3. It should be noted that the operating conditions internal to the absorption machine are identical to those listed in Table 6.1. This was arranged by running the more complete model first to determine pressures, temperatures, and mass fractions and then inserting those values as inputs to the more limited model to avoid the additional complexity of the heat exchangers in the introductory discussion. For a more complete understanding, realistic heat exchanger models need to be included in an absorption cycle model (as done here) because they represent the most important irreversibilities in a practical machine. Furthermore, the inclusion of the heat exchanger models allows for a more realistic set of inputs to a simulation model. The insight obtained from running the simulation models with a range of variables for these realistic inputs is much greater than the insight obtained from the approach in Section 6.1 (although somewhat more computation is required), as is brought out in the following discussion. TABLE 6.3 Operating Conditions for a Single-Effect Water/Lithium Bromide Cycle with Heat Exchangers State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
h (J/g)
(kg/sec) m
P (kPa)
87.76386 87.76796 149.9 223.3 155.0 155.0 2643.1 167.8 167.8 2503.1 419.1 404.3 104.8 155.1 104.8 145.1 42.0 15.3
0.05000 0.05000 0.05000 0.04543 0.04543 0.04543 0.00457 0.00457 0.00457 0.00457 1
0.676 7.406 7.406 7.406 7.406 0.676 7.406 7.406 0.676 0.676
Vapor Quality 0.000
0.000 0.005 0.000 0.065 1.000
0.28 0.28 0.4
T (°C)
x (kg/kg)
32.72 32.72 63.61 89.36 53.11 44.96 76.76 40.06 1.39 1.39 100.00 96.51 25.00 37.03 25.00 34.65 10.00 3.64
0.5648 0.5648 0.5648 0.6216 0.6216 0.6216 0.0000 0.0000 0.0000 0.0000
Summary of Energy Quantities W COP
Component Desorber Absorber Condenser Evaporator Solution HX
Pump power
0.205 W
Coefficient of performance
0.724
Heat Transfer Rate (kW) 14.73 14.09 11.31 10.67 3.105
Source: Based on Figure 6.5 and file Ex6_2.ees.
Log Mean Temperature Difference ∆T lm (K) 14.73 7.83 9.42 4.74 22.96
134
Absorption Chillers and Heat Pumps
6.2.1 Heat Exchanger Models The coupled heat and mass transfer processes on the four corners of the cycle are modeled using an overall heat transfer coefficient-area product (UA) formulation, as discussed in Section 4.10. The model inputs, including the UA values, are summarized in Table 6.4. Consider the evaporator first. The UA formulation is written as Q e = UAe ∆Tlm ,e = 10.67 kW (6.15)
where
∆Tlm ,e =
(T17 − T10 ) − (T18 − T9 ) = 4.74 K (T − T ) ln 17 10 (T18 − T9 )
(6.16)
This formulation is best visualized on a heat exchanger diagram such as that provided in Figure 6.6. The log mean temperature difference represents the average transfer potential TABLE 6.4 Baseline Inputs Defining Single-Effect Operating Conditions in Table 6.3 Input Name
Value
Input Name
Value
εSHX 1 (kg/sec) m UAa (kW/K) UAc (kW/K) UAd (kW/K) UAe (kW/K)
0.64 0.05 1.8 1.2 1.0 2.25
T13 (°C) 13 (kg/sec) m T15 (°C) 15 (kg/sec) m T11 (°C) 11 (kg/sec) m T17 (°C) 17 (kg/sec) m
25 0.28 25 0.28 100 1 10 0.4
12 17
Temperature (°C)
10 8 6
18
4 2
9
10
0
2
FIGURE 6.6 Heat exchanger diagram for evaporator.
4 6 8 Cumulative heat transfer rate (kW)
10
12
135
Single-Effect Water/Lithium Bromide Systems
between the hot and cold sides of the evaporator. As an aside, it can be seen by reviewing Figure 6.6 that the heat exchanger is not particularly well matched because the heat transfer loop experiences a glide of 6.3 K, while the evaporating fluid experiences zero glide. The design could achieve a better temperature match by increasing the flow rate of the heat transfer fluid with the penalty of higher pumping power in the external loop. A similar analysis on the condenser yields Q c = UAc ∆Tlm ,c = 11.31 kW (6.17)
with
∆Tlm ,c =
(T15 − T8 ) − (T16 − T8 ) = 9.42 K ln
T15 − T8 T16 − T8
(6.18)
The condenser heat exchanger diagram is shown in Figure 6.7. The condenser log mean temperature difference defined in Equation 6.18 ignores the temperature effect of the desuperheating section (T7 – T8) that shows up as a vertical leg on the right side of Figure 6.7. The energy involved in the desuperheating process is only 2.8% of the total energy transferred in the condenser. This model has been found to work very effectively, and it has the advantage of simplicity for the current discussion. The condenser exhibits a better match than the evaporator, as seen by the fact that the two sides of the heat exchanger are more closely parallel on this coordinate system, at least in the condensing section. A similar analysis for the desorber yields Q d = UAd ∆Tlm ,d = 14.73 kW (6.19)
80
7
Temperature (°C)
70 60 50 8
40 30 20
16
15 0
2
FIGURE 6.7 Heat exchanger diagram for condenser.
4 6 8 Cumulative heat transfer rate (kW)
10
12
136
Absorption Chillers and Heat Pumps
where ∆Tlm ,d =
(T11 − T4 ) − (T12 − T7 ) = 14.73 K (T − T ) ln 11 4 (T12 − T7 )
(6.20)
The heat transfer rate and log mean temperature difference are identical in this case because UAd = 1 kW/K. The heat exchanger diagram for the desorber is plotted in Figure 6.8. In generating Figure 6.8, the temperature effects of the subcooled inlet (point 3) were ignored. In place of the subcooled state, the low-temperature end of the cold side of the heat exchanger was plotted at the saturation temperature corresponding to the known pressure and the mass fraction at point 3. That temperature is the same as at point 7 under the assumptions used in the model. The desorber is not particularly well matched, showing a pinch at the high-temperature end of 10.6 K. The quality of the match can be seen by comparing the pinch against the log mean temperature difference. The closer they are, the better the match. In the solution components (desorber and absorber) that e xperience a t emperature glide on the solution side, there is a natural opportunity to obtain a t hermodynamic benefit from temperature matching. That opportunity is much more difficult to exploit in the condenser and evaporator components because they do not experience a glide on the refrigerant side. For the absorber, the heat transfer analysis yields Q a = UAa ∆Tlm , a = 14.09 kW (6.21)
with
∆Tlm , a =
(T6 − T14 ) − (T1 − T13 ) = 7.83 K (T − T ) ln 6 14 (T1 − T13 )
(6.22)
The absorber heat exchanger diagram is plotted in Figure 6.9. The temperature match exhibited by the absorber is the best among all the components examined here. 105
Temperature (°C)
100
11 12
95 4
90 85 80 75 7 0
2
4
6
8
10
Cumulative heat transfer rate (kW) FIGURE 6.8 Heat exchanger diagram for desorber.
12
14
16
137
Single-Effect Water/Lithium Bromide Systems
50 6
Temperature (°C)
45 40
14
35
1
30 13
25 20
0
2
4
6
8
10
12
14
16
Cumulative heat transfer rate (kW) FIGURE 6.9 Heat exchanger diagram for absorber.
6.2.2 Cycle Performance In operating an absorption machine, a change in any input variable will cause changes in all the other dependent variables. When an input changes, the entire cycle reacts to reach a new equilibrium operating condition. The coupled nature of this type of cycle model must be taken into account when interpreting operating data, since every variable is impacted whenever an input is changed. The model presented in Section 6.1 does not exhibit this type of complex coupled behavior, but the heat transfer model presented in this section (Section 6.2) does more closely reflect the actual cycle behavior with additional complexity and computational effort. 6.2.3 Desorber Inlet Temperature Variations A simple example of the interdependence of all operating variables can be obtained by varying the desorber water loop inlet temperature from 50°C to 120°C while holding all other inputs constant at the baseline values listed in Table 6.4. The cycle performance under these conditions is summarized in Figure 6.10, where COP and cooling capacity are plotted versus the desorber heat transfer fluid inlet temperature. The COP varies from a low value of 0.616 at 50°C and exhibits a maximum of about 0.74 around 75°C. The capacity varies approximately linearly starting from a low value of 1.5 kW up to 13.8 kW. The temperature range shown here was chosen because it spans the practical range for a single-effect application. The fact that the COP exhibits a maximum indicates that there are several competing changes occurring as the temperature increases. The capacity plot helps to explain one of the primary effects. As the temperature increases, the capacity also increases. This increased duty appears in all of the heat exchangers in the system, as shown in Figure 6.11. The increased duty results in increased heat transfer irreversibility in the heat exchangers. The interesting question then is why is the COP curve relatively flat? This question was already addressed in Section 2.7 based on the results of the zero-order model. The answer
138
15
COP
0.75
10
0.5
0.25
T17 = 10°C
5
Evaporator heat transfer (kW)
Absorption Chillers and Heat Pumps
T13 = 25°C
0 50
T15 = 25°C 60
70 80 90 100 Desorber inlet temperature, T11 (°C)
0 120
110
FIGURE 6.10 Effect of desorber inlet temperature on COP and capacity for a single-effect water/lithium bromide absorption chiller. 20
Heat transfer (kW)
15
Desorber Absorber Condenser Evaporator Solution heat exchanger
10
5
0 50
60
70
80
90
100
110
120
Desorber inlet temperature, T11 (°C) FIGURE 6.11 Effect of desorber inlet temperature on heat transfer rates for a single-effect water/lithium bromide absorption chiller.
comes from the fact that an absorption machine is fundamentally a three-temperature device. The performance of such a device can be largely determined by examining how the temperatures internal to the cycle change at each of the three temperature levels. The relevance of the three-temperature model is obscured somewhat by the fact that a real machine experiences a range of temperatures at each of the three temperature levels.
139
Single-Effect Water/Lithium Bromide Systems
Thus, the appropriate temperature to choose to make a meaningful comparison is not immediately obvious. However, some insight can be obtained by examining the trends exhibited by any of the temperatures. For example, Figure 6.12 shows a plot of T1, T4, and T10 versus the changes in the inlet temperature of the heating stream (T11). It is observed that the internal cycle temperatures follow a peculiar trend. The heat rejection temperature stays approximately constant, the desorber outlet temperature increases with the source temperature, and the evaporator temperature actually decreases. These effects can also be reproduced using the zero-order model of Section 2.7. The trends result from the constraints imposed by the working fluid properties. In particular, the slope of the vapor pressure curve for water on the Dühring plot is approximately the same as the slope of the vapor pressure curves for the lithium bromide solution. This observation indicates that the temperature difference between the evaporator and the absorber is approximately the same as that between the absorber and desorber. In the zero-order model formulation, this characteristic is represented by Equation 2.22. The performance of the cycle is strongly influenced by changes in the temperatures at all three levels. Since both the high temperature and the low temperature in the cycle are changing significantly, the net effect on COP is not obvious. The COP would be expected to increase with increasing desorber temperature but to decrease with decreasing evaporator temperature. In this particular example, the temperature trends are strong enough to cause an overall increase in COP at low values of heat input temperature, but as the heat exchanger duties increase, the heat transfer irreversibilities eventually overwhelm the effect and cause COP to decrease slightly. Although not shown here, the pressures and mass fractions within the cycle change significantly as the heat source temperature changes. From a thermodynamic standpoint, the performance is influenced most directly by the temperatures. Thus, the discussion 120 T4
100
Temperature (°C)
80 60 T1
40 20
T10
0 –20 50
60
70
80
90
100
110
120
Desorber inlet temperature, T11 (°C) FIGURE 6.12 Effect of desorber inlet temperature on temperature for a single-effect water/lithium bromide absorption chiller.
140
Absorption Chillers and Heat Pumps
here focuses on the temperatures. However, for a complete understanding of the changes, plots of all the variables should be produced to fully understand a particular trend. From the perspective of a user of the technology, the shape of the COP curve exhibited in Figure 6.10 is very important. Unlike what one might expect from intuition, there is no COP benefit to be obtained by firing a single-effect machine at a higher temperature. This conclusion must be made carefully. It applies to the single-effect technology. Double effect (see Chapter 7) and other cycle variations can provide higher performance when higher temperature heat sources are available. In fact, double-effect technology exhibits a similar flat trend in COP as a function of heat input temperature, but the heat input temperature and COP values are higher. Thus, this characteristic shape to the COP curve can be viewed as a fundamental characteristic of absorption technology. There is a step change in COP in going from single- to double-effect technology, but within each technology, the COP is nearly constant as any of the imposed temperatures are changed. It should be noted that some advanced cycles incorporate designs that overcome this limitation by essentially becoming variable effect cycles. An example is the GAX cycle, which exhibits variable effect characteristics and thus does not have this limitation, discussed in Chapter 11. 6.2.4 Evaporator Temperature Variations The effect of the variation of the inlet chilled water temperature (T17) is shown in Figure 6.13. In this case, the COP varies very little over the range of inlet temperature considered, but the capacity increases by about 30% over the indicated range. A full understanding of these trends again requires a detailed examination of the other variables in the cycle. As the inlet temperature is increased, the pressure in the evaporator increases in such a way that the heat transfer driving potential increases only slightly. The effect of the pressure on the absorber is to decrease the mass fractions slightly. Overall, the evaporator inlet
T15 = 25°C T11 = 100°C
COP
0.75
15
COP . Qe
0.5
10
0.25
0
5
8
10
12 14 16 Chilled water inlet temperature, T17 (°C)
18
Evaporator heat transfer (kW)
T13 = 25°C
0 20
FIGURE 6.13 Effect of chilled water inlet temperature on COP and capacity for a single-effect water/lithium bromide absorption chiller.
141
Single-Effect Water/Lithium Bromide Systems
temperature variation causes temperature effects that balance the increased capacity in such a way that the COP actually increases. The sensitivity of capacity to changes in the chilled water temperature is a function of the design of the machine. Different values for the heat exchanger sizes (the UA values) yield some variation in that sensitivity. 6.2.5 Rejection Temperature Variations The cooling streams to the condenser and absorber can be connected in parallel or series flow arrangements. The cases discussed earlier involved parallel flow where the inlet temperatures of both components are identical (25°C in the earlier discussion). To complete the examination of the effect of inlet temperature variations, the inlet coolant temperature was varied and the results are plotted in Figure 6.14. The COP is seen to drop about 13% over the range considered while the capacity drops by 55%. These changes are due to the combined effects of temperature and heat transfer irreversibility. The cycle capacity is seen to be more sensitive to coolant temperature than it is to chilled water temperature. Once again, these sensitivities depend somewhat on the design conditions. Series flow piping of the condenser and absorber is preferred by operators because a single pump can be utilized and control problems inherent in a parallel design are avoided. Two different series flow arrangements are possible depending on which component is first in the flow path. The cases are compared in Table 6.5, including parallel flow and both series flow arrangements. For the same total cooling water flow rate, the series flow with condenser first has higher COP and capacity than the other series flow case or the parallel flow case. However, if the same flow rate per component is provided, as in the second parallel flow case, then parallel flow looks preferable. This is intuitive since the effective rejection temperature is lower for the parallel flow case with the higher total cooling water flow rate. The trade-offs between series and parallel flow are indicated in Table 6.5. Other factors may influence 1
20
T11 = 100°C
0.75
15
COP
COP 10
0.5 . Qe
5
0.25
0 15
20 25 30 Heat rejection temperature, T15 and T13 (°C)
Evaporator heat transfer (kW)
T17 = 10°C
0 35
FIGURE 6.14 Effect of cooling water inlet temperature on COP and capacity for a single-effect water/lithium bromide absorption chiller.
142
Absorption Chillers and Heat Pumps
TABLE 6.5 Comparison of Condenser and Absorber Coolant Piping Configurations Based on Inputs in Table 6.4 COP
Capacity (kW)
Parallel, with mass flow rate in each component equal to 50% of series flow value Parallel, with mass flow rate in each component equal to 100% of series flow value 13 = 0.28 kg/sec) Series, condenser first (m
0.699
8.243
0.724
10.670
0.711
8.991
13 = 0.28 kg/sec) Series, absorber first ( m
0.696
8.488
1
Fixed SHX UA = 0.2 kW/K Fixed SHX effectiveness, εSHX = 0.64
COP
0.75
COP
0.5
Evaporator heat transfer
0.25
20
15
10
Heat transfer (kW)
Configuration
5 Solution heat exchanger heat transfer
0 0.02
0.04
0.06 Solution pump flow rate (kg/sec)
0.08
0 0.1
FIGURE 6.15 Effect of solution pump flow rate on COP, capacity, and solution heat exchanger heat transfer rate for a singleeffect water/lithium bromide absorption chiller.
the design and operating decisions. For example, the series flow arrangement, where the absorber is first, is the better of the two series designs as far as avoiding crystallization. 6.2.6 Solution Flow Rate Variations The effect of solution flow rate on cycle operating conditions is plotted in Figure 6.15 for the second parallel coolant flow case defined in Table 6.4. The COP varies from 0.79 to 0.65 over the range of solution flow rates considered. The key to understanding this effect is to examine the load on the solution heat exchanger, which is also plotted in Figure 6.15. As the solution flow rate increases, the load on the solution heat exchanger increases considerably because more energy is available in the solution stream leaving the desorber and more energy is needed in the stream leaving the absorber. It should be noted that an effectiveness model is in use for the solution heat exchanger for most of the plots in Chapter 6.
Single-Effect Water/Lithium Bromide Systems
143
For a fixed effectiveness, the size (i.e., the UA value) of the heat exchanger would increase along with the increased heat transfer rate (i.e., load). To get additional insight, Figure 6.15 includes data for fixed heat exchanger effectiveness (solid lines) as well as fixed solution heat exchanger UA (dashed lines). These two models yield similar results with some divergence at high solution flow rate where the solution heat exchanger load is largest. This increased load also implies increased losses (irreversibility) and explains why the COP decreases with increasing solution flow rate. The explanation for the capacity maximum exhibited in Figure 6.15 is more subtle. As was found before, changes in the solution flow rate cause changes throughout the entire cycle. The capacity is directly related to the refrigerant flow rate, and it can be shown (from mass balances) that the refrigerant flow rate can be expressed in terms of the solution pump flow rate as
7 = m
1 m x − x3 1 4 =m (6.23) f x4
Thus, the explanation for the capacity maximum can be traced to changes in the LiBr mass fractions in the solution loop. These mass fractions are not simple functions of any single variable but instead are impacted in a coupled manner by all of the model inputs. The maximum can be traced to temperature changes that occur in the absorber. At maximum capacity, the temperature profiles in the absorber are well matched in the sense that the temperature difference throughout the device is approximately constant (i.e., the temperature differences at both ends of the absorber are equal). For flow rates that are greater than or less than the optimum value, the temperature profiles become skewed so that there is a temperature pinch at one end of the heat exchanger. The well-matched design yields lower thermodynamic losses, resulting in a maximum refrigerant flow rate at the point where the lowest losses occur. Matching temperature profiles on both sides of a heat exchanger is an important consideration in optimum design of thermal systems, including absorption systems. The pronounced temperature glides occurring in the absorber and desorber in water/lithium bromide technology provide an opportunity or a design constraint, depending on your perspective. Clever system design should incorporate temperature matching in all system components to enable an appropriate balance between high performance (i.e., COP) and high refrigeration capacity. 6.2.7 Heat Transfer Loop Flow Rate Variations An example of the influence of the heat transfer loop flow rates on performance can be seen in Figure 6.16, where the COP and capacity are plotted versus desorber heat transfer fluid flow rate. The curves show very little COP sensitivity and only moderate capacity sensitivity. Similar trends were exhibited by the other three heat transfer loop flow rates. As the curves are all similar, they are not included here. It should be noted that the current cycle model does not include the influence of flow rate on heat transfer coefficient in the heat exchangers. In many cases, the controlling side of the heat exchanger may be the heat transfer fluid and, in such cases, changes in heat transfer coefficient with flow rate may be important. Such a feature could be simply added to the present models to compute the heat transfer coefficient from correlations.
144
Absorption Chillers and Heat Pumps
20
COP
0.75
15
COP
0.5
10
. Qe
0.25
5
0
0.2
0.4 0.6 0.8 Desorber heat transfer fluid flow rate (kg/sec)
1
Evaporator heat transfer (kW)
1
0
FIGURE 6.16 Effect of desorber heat transfer fluid flow rate on COP and capacity for a single-effect water/lithium bromide absorption chiller.
6.2.8 Evaporator–Absorber Pressure Drop Variations All of the results discussed so far were based on zero pressure drop between the evaporator and absorber (and between the desorber and condenser). In reality, there will be pressure drops in the system and those drops will affect performance. As an example of the magnitude of the effect, an analysis was done on the effect of pressure drop between the evaporator and absorber. Even if pressure drop is minimized by design, a pressure difference must exist between the surface of the evaporating liquid and the surface of the absorbent to drive the flow. The influence of pressure drop on system performance was calculated and is plotted in Figure 6.17. The biggest effect is a reduction in capacity, which is primarily due to the increase in the evaporator temperature as the pressure drop increases. This analysis was done by simply specifying a pressure drop between the two components and then calculating the performance. A more difficult task would be to predict the pressure drop for a particular heat exchanger design configuration. That task could be attempted using computational fluid dynamics. Alternatively, the pressure drop could be measured for an existing machine. 6.2.9 Heat Exchanger Size Variations The influence of heat exchanger size on performance is summarized in Figures 6.18 through 6.22. In each figure, the COP and capacity are plotted versus the UA of that particular heat exchanger. The abscissa scales were chosen to span the UA values used in the baseline case. In all cases, the same general trends are observed. That is, the COP is relatively insensitive to changes in UA except for the vicinity of very small values of UA for which the COP decreases significantly as UA decreases. Capacity is more sensitive to UA with the exception of the solution heat exchanger UA, which does not have much influence on capacity.
145
Single-Effect Water/Lithium Bromide Systems
20
0.75
15
COP
COP 0.5
10
. Qe
0.25
5
0
0.1 0.2 0.3 0.4 Pressure drop between evaporator and absorber (kPa)
Evaporator heat transfer (kW)
1
0 0.5
FIGURE 6.17 Effect of pressure drop between evaporator and absorber on COP and capacity for a single-effect water/lithium bromide absorption chiller. 20
COP
0.75
15
COP
0.5
10
. Qe
0.25
5
0
0.5
1 UAd (kW/K)
1.5
1
Evaporator heat transfer (kW)
1
0
FIGURE 6.18 Effect of desorber heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.
The baseline values of UA shown in Table 6.4 are somewhat arbitrary. It can be seen from these plots (Figures 6.18 through 6.22) that the baseline values are well beyond the knee of the capacity curve, with the desorber UA exhibiting the greatest effect on capacity. Based on these curves, it appears that the largest influence on capacity of adding one additional unit of heat exchange area would be in the desorber. This gives a clue as to the likelihood that the baseline distribution of heat exchange area is not optimum (Herold and Radermacher 1990).
146
Absorption Chillers and Heat Pumps
20
0.75
15
COP
COP
0.5
10 . Qe
0.25
5
0
0.5
1 UAa (kW/K)
1.5
2
Evaporator heat transfer (kW)
1
0
FIGURE 6.19 Effect of absorber heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.
20
0.75
15
COP
COP
0.5
10
. Qe
0.25
5
0
0.5
1 UAc (kW/K)
1.5
2
Evaporator heat transfer (kW)
1
0
FIGURE 6.20 Effect of condenser heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.
147
1
20
0.75
15
COP
COP 0.5
10 . Qe
0.25
5
0
0.5
1
2
1.5 UAe (kW/K)
2.5
3
Evaporator heat transfer (kW)
Single-Effect Water/Lithium Bromide Systems
0
FIGURE 6.21 Effect of evaporator heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.
20
COP
0.75
15
COP
0.5
10
. Qe
0.25
5
0
0.1
0.2
UAs (kW/K)
0.3
0.4
Evaporator heat transfer (kW)
1
0 0.5
FIGURE 6.22 Effect of solution heat exchanger UA on COP and capacity for a single-effect water/lithium bromide absorption chiller.
148
Absorption Chillers and Heat Pumps
6.2.10 Summary of Single-Effect Operating Conditions In this section, a single-effect water/lithium bromide cycle was examined from several angles. The interpretation and understanding of the technology is complicated by the cyclic nature of the device, which means that changes in any input influence all the dependent variables in the system. The approach taken here is to use a computer model to examine the effect of changes in various parameters. The results presented are a cross section of the many variables in the system. This presentation has been designed to bring out the key aspects without plotting each variable. However, as part of the learning process, it is recommended that the reader should exercise the models provided to reproduce the presented results as well as to examine other variables in the system to get a complete understanding of the interdependence of the absorption system variables.
6.3 Single-Effect Water/Lithium Bromide Heat Transformer (Type II Heat Pump) A Type II heat pump, sometimes called a temperature booster or heat transformer, is the second basic variation of a three-temperature device, as described in Sections 1.2 and 2.3. A typical application for which a Type II heat pump is considered is a case where waste heat is available and where heat is needed at a somewhat higher temperature than that of the waste heat. These heat pumps are primarily of interest in chemical plants with significant heat integration (Ma et al. 2002). The Type II cycle can convert a portion of the waste heat energy into a heat transfer out of the cycle at the highest temperature. Type II cycles based on water/lithium bromide have been built and tested at numerous research facilities and at a limited number of demonstration sites around the world. The cycle works well, and it is a proven energy-saving technology appropriate for industrial facilities with substantial thermal energy flows. Applications have been limited, apparently due to a combination of factors, including a limited number of potential customers that match the description given earlier and a lack of economic incentive to save energy (i.e., an environment of relatively cheap fuel). Application challenges have been experienced at some of the demonstration sites. The primary challenge seems to be corrosion. A Type II cycle naturally operates at a higher temperature than a single-effect Type I cycle due to the fact that the Type II cycle transfers heat out at the high-temperature end. Thus, assuming a nominal heat transfer driving potential of 20 K in the high-temperature device, the Type II cycle will operate 40 K above the highest temperature in the Type I cycle. However, the design temperatures for a Type II cycle are well within the typical range of temperatures routinely experienced in a double-effect machine. Double-effect technology, which is the focus of Chapter 7, is a proven long-life technology where corrosion challenges have been met effectively. Thus, Type II technology should be viewed as an available technology. The design of a Type II machine is a straightforward extension of chiller technology for an experienced water/ lithium bromide engineering team. The operating characteristics of a Type II cycle are best understood in terms of an example. A baseline set of operating conditions, generated by the model in file Ex6_3.ees, is given in Table 6.6 based on the cycle schematic in Figure 6.23. There are major differences and major similarities between the cycles shown in Figures 6.4 and 6.23. The presentation
149
Single-Effect Water/Lithium Bromide Systems
TABLE 6.6 Single-Effect Type II Operating Conditions Referring to Figure 6.23 and file Ex6_3.ees State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Vapor Quality
h (J/g)
(kg/sec) m
P (kPa)
274.1 274.1 339.8 345.3 274.5 274.4 2690.9 230.3 230.4 2677.4
1.077 1.077 1.077 1.000 1.000 1.000 0.077 0.077 0.077 0.077 4.000
15.766 105.328 105.328 105.328 105.328 15.766 15.766 15.766 105.328 105.328
1.000
105.328 105.328
1.000 0.000
0.014 0.000
0.000 0.000
4.000 4.000 4.000 2677.4 369.7
0.011 1.011
T (°C)
x (kg/kg)
102.41 120.93 153.90 149.67 111.63 111.60 102.41 55.02 55.02 101.09 135.00 146.02 120.00 108.92 120.00 108.80 30.00 41.26 101.09 164.01
0.5944 0.5944 0.5944 0.6399 0.6399 0.6399 0.0000 0.0000 0.0000 0.0000
0.6332
Summary of Energy Quantities /W W R S COP
Pump power
7.0/51.3 W
Coefficient of performance
0.495
Component
Heat Transfer Rate (kW)
Log Mean Temperature Difference ∆T lm (K)
Desorber Absorber Condenser Evaporator Solution HX
185.4 184.4 188.3 187.3 70.8
7.41 18.44 18.83 12.49 6.43
here is designed to highlight both for a complete understanding of the cycle. A major difference is that all the internal mass flows are in the opposite direction between the Type I and Type II cycles. In the Type II cycle, the solution is pumped up through the right-most leg of the solution circuit, and it flows down through the left leg. The flow in the refrigerant loop is from bottom to top, and a pump is required in the line to drive the flow from low pressure to high pressure. The direction of all of the external heat transfers is also reversed (e.g., the heat transfer is out of the Type II heat pump in the lower left-hand corner). A summary of the internal state points is provided in Table 6.7 to clarify a number of key assumptions used in the model. In particular, the condition of the fluid exiting each of the components is assumed to be saturated and thus the quality is set to either 0 or 1 for saturated
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Absorption Chillers and Heat Pumps
. 15 Qe
11
16
12 . Qa
10
Evaporator
Absorber 3
4
9 . Wr Pump
Solution heat exchanger
2
8
5 Pump . Ws
1
6
Condenser
18
Desorber
7
. Qc 17
14
13
. Qd
FIGURE 6.23 Single-effect water/lithium bromide temperature booster heat pump (Type II absorption cycle) with external heat transfer models.
TABLE 6.7 Thermodynamic State-Point Summary Point 1 2 3 4 5 6 7 8 9 10
State Vapor–liquid solution state Subcooled liquid solution Saturated liquid solution Subcooled liquid solution Subcooled liquid solution Saturated liquid solution Superheated water vapor Saturated liquid water Subcooled liquid water Saturated water vapor
Notes Vapor flashes as liquid passes through expansion valve State calculated from solution heat exchanger model Vapor quality set to 0 as assumption State calculated from solution heat exchanger model (Note: T4 < T3) State calculated from solution pump model Vapor quality set to 0 as assumption Assumed to have zero salt content Vapor quality set to 0 as assumption State calculated from refrigerant pump model Vapor quality set to 1 as assumption
liquid and vapor, respectively. To further clarify the model, the input variables are specified in Table 6.8. The inputs were chosen only to illustrate one potential operating condition and are emphasized here only to help the reader understand the model results presented. In the Type II cycle, the absorber and evaporator are assumed to operate at the ressure, but now the pressure is high in the system. This fact is emphasized same p
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Single-Effect Water/Lithium Bromide Systems
TABLE 6.8 Baseline Inputs Defining Type II Operating Conditions in Table 6.6 Input Name
Value
Input Name
Value
εSHX 6 (kg/sec) m UAa (kW/K) UAc (kW/K)
0.9 1.0
120 4.0
10.0 10.0
T13 (°C) 13 (kg/sec) m T15 (°C) 15 (kg/sec) m
UAd (kW/K) UAe (kW/K)
25.0 15.0
T11 (°C) 11 (kg/sec) m T17 (°C) 17 (kg/sec) m
135 4.0 30 4.0
120 4.0
in Figure 6.23, which is a Dühring-type schematic such that components at the top of Figure 6.23 operate at higher pressure. The desorber and condenser operate at low pressure in the system. The pressure levels for the Type II cycle are considerably different than the Type I. For the Type II cycle operating conditions in Table 6.6, the high pressure is 105.3 kPa and the low pressure is 15.8 kPa. Thus, the high-pressure end can operate close to atmospheric pressure (slightly above in this case) while the low pressure end is still in vacuum. The basic operation of the components of the Type II cycle is familiar from earlier discussion of these devices. For example, the solution circulation ratio can be calculated as
f=
6 m = 13.06 (6.24) 7 m
The value obtained here is slightly higher than that obtained for the Type I cycle because the definition is now in terms of the low flow rate side of the solution circuit. Although much of the technology is similar to Type I considerations, it may still be useful to briefly describe the operation of the cycle. A Dühring plot of the cycle state points is provided in Figure 6.24. This plot and the schematic should be referred regularly during study of the cycle. At low pressure in the cycle, water vapor is driven out of the solution in the desorber by heat transfer into the desorber. For a Type II application, this heat transfer would typically be waste heat. The desorbed vapor flows to the condenser, where it changes phase and heat rejection occurs. One of the requirements of the Second Law of thermodynamics is that this type of cycle must reject some of the input heat at the lowest temperature. The liquid refrigerant leaving the condenser is pumped up to the high pressure and sent to the evaporator. Waste heat is applied to the evaporator to effect a liquid-to-vapor phase change. The vapor then flows to the absorber, where it recombines with the LiBr solution to complete the cycle. The absorption process is accompanied by an energy release that is the product of the cycle. By transferring energy out at the high temperature of the cycle, the Type II cycle has a role in upgrading the temperature of a waste heat stream to a temperature level that is more useful. This functional description of the cycle has glossed over several additional differences between the Type I and II cycles. These differences include the operation of the solution heat exchanger and the absorber. These differences are best described with reference to the operating conditions in Table 6.6.
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Absorption Chillers and Heat Pumps
Pure water
Vapor pressure (kPa)
1000
3
10
100
2 7,8,9
10
1
0.45 0.55
0.50 0.60
0.65
4 0.70 mass fraction LiBr
6,5 Crystallization line
1 0.1 0.01 0
50
100 Temperature (°C)
150
200
FIGURE 6.24 Dühring plot for the cycle solution in Table 6.6.
The solution heat exchanger transfers heat from the hot leg to the cold leg in both Type I and Type II cycles. However, in the Type II cycle, the hot leg is the left leg of the solution circuit, as drawn in Figure 6.23. This observation implies that state point 4 must have a temperature less than or equal to the temperature of point 3. This situation is emphasized on the schematic by drawing the solution heat exchanger box in a different manner than that drawn for the Type I solution circuit. The basic methods of modeling and designing the solution heat exchanger are not different, but the fact that the solution enters the absorber subcooled at state 4 has a major impact on cycle performance because that solution must be heated to the saturation temperature in the absorber before any energy can be transferred out as the end product. The solution heat exchanger has a more critical impact on cycle performance in a Type II cycle than it does in a Type I cycle because it impacts both the energy available and the maximum temperature attained in the absorber. In steady-state operation, the highest temperature in the absorber is much higher than the temperature at point 4. The exothermic nature of the absorption of water in lithium bromide solution plays a key role in obtaining this high temperature in the absorber. As high-temperature heat is the product of the cycle, it is very important to understand and to be able to predict this temperature. The actual highest temperature achieved in a real Type II absorber will depend on both heat/mass transfer and thermodynamic design details. A limiting thermodynamic value is the adiabatic saturation temperature defined as the equilibrium temperature obtained by mixing the solution stream at state 4 with the vapor at state 10. The resulting temperature depends primarily on the level of subcooling in stream 4 as follows. The adiabatic saturation analysis is based on the absorber schematic in Figure 6.25, but the focus is only on the adiabatic section for now. The solution flow rate and state at point 4 are assumed known. The vapor inlet state is assumed to be identical to state 10 in Figure 6.23. The inlet vapor flow rate (state 19), outlet solution flow rate (state 20), and outlet solution mass fraction (state 20) are all unknowns determined from mass and energy balances.
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Single-Effect Water/Lithium Bromide Systems
11
12
10
21
Cooled section
20
19 Adiabatic section 4
3
FIGURE 6.25 Adiabatic absorption temperature calculation schematic.
The overall mass balance is 4 +m 19 = m 20 (6.25) m
The lithium bromide mass balance is
4 x4 = m 20 x20 (6.26) m
The energy balance on the adiabatic saturation process is
4 h4 + m 19 h19 = m 20 h20 (6.27) m
19, m 20, and x20. As the outlet These three equations are solved for the three unknowns, m state is assumed saturated, the pressure (which is assumed to be known) and the mass fraction are sufficient to define the state, and the enthalpy and temperature can be determined from these two. Due to the substantial subcooling of the inlet solution stream, considerable vapor must be absorbed to reach saturation and the mass fraction of the saturated stream (state 20) is lower than the mass fraction at state 4. Thus, the saturation temperature corresponding to the concentration at point 4 would overestimate the highest temperature in the absorber. Numerical results of this calculation are provided in Table 6.6 as a part of the cycle solution. The adiabatic saturation process requires approximately 14% of the total vapor flowing into the absorber, which reduces the heat transfer out by about the same amount. The latent heat of this vapor, added to the heat of mixing released d uring the absorption, raises the temperature of the solution to a saturation temperature of 164.0°C from an inlet temperature of 149.7°C. Due to the fact that the pressure differences are greater in the Type II cycle, the pump work requirements are larger than that found for the Type I cycle. In this case, the sum of the pump work for both the solution and the refrigerant pumps is approximately 0.016% of the total thermal input required in the evaporator and desorber. Thus, the pump work requirement is seen to be still quite small in relation to the thermal energy input requirements. In contrast to the Type I cycle, the Type II analysis shows that the heat transfer rates in the evaporator and condenser are larger than the rates in the desorber and absorber. This change seems counterintuitive because we expect that the solution components will also
154
Absorption Chillers and Heat Pumps
1
200
0.75
150
0.5
100 COP
0.25
50
0
0.2
0.4 0.6 Solution heat exchanger effectiveness
0.8
1
Absorber heat transfer (kW)
COP
. Qabs
0
FIGURE 6.26 Effect of solution heat exchanger effectiveness on COP and capacity of the Type II cycle.
have to account for the heat of mixing effects. This difference comes about because of changes in the input streams to the absorber and desorber. In the case of the absorber, the heat output is reduced due to the subcooling of state 4. In the case of the desorber, the heat input is reduced due to the fact that a significant fraction (~20%) of the vapor required at 1). 7 flashes as the solution passes through the expansion valve (vapor at state 1 is 1.4% of m Thus, this fraction of the vapor does not require external heat in the desorber. 6.3.1 Solution Heat Exchanger Size Effects A key choice in the design of a Type II cycle is the size of the solution heat exchanger. The influence of the solution heat exchanger on performance is plotted in Figure 6.26 in which COP and capacity are plotted versus solution heat exchanger effectiveness. The effectiveness is varied over the full range of possible values. It is observed that the COP increases significantly as effectiveness increases. With no solution heat exchanger the COP is 0.41, and with a very large solution heat exchanger the COP is 0.51, a 24% increase. The capacity increase is approximately 32% over the same range. The UA of the solution heat exchanger for an effectiveness of 0.9 was calculated as a part of the solution given in Table 6.6, and the value is UAs = 11.0 kW/K. In this case, the UA value required is comparable to the other heat exchangers.
6.4 Discussion of Available Single-Effect Systems Single-effect, Type I, water/lithium bromide systems are manufactured and sold throughout the world, primarily for air-conditioning applications. The technology is widespread as evidenced by manufacturing plants in Japan, South Korea, Mexico, India, and China.
Single-Effect Water/Lithium Bromide Systems
155
The technology was pioneered in the United States in the 1940s and has been widely available since the 1950s. Japanese manufacturing started in the 1960s with at least eight major manufacturers in the market. Due to economics unique to East Asia, absorption machines (including single and double effect) reportedly supply close to 50% of the space-cooling load in various parts of the region. The primary factors that have led to this robust market for absorption chillers in East Asia are regulatory stemming from energy economics. The US market for absorption chillers is currently weak due to the availability of lowcost electricity in most regions. Three companies manufactured single-effect machines in the United States in 1995 (AGCC 1995), but the US market has declined since that time and very few absorption chillers are sold in the United States today. All absorption chiller manufacturing has moved abroad. Single-effect, Type II, water/lithium bromide systems are manufactured by Thermax in India. The market for these systems is significantly smaller than the market for Type I systems.
Homework Problems 6.1 Using the internal model that was used to generate Table 6.1, vary the solution mass flow rate through the solution pump to generate plots of COP and capacity versus solution flow rate. 6.2 Using the heat transfer cycle model that was used to generate Table 6.3, vary the solution mass flow rate through the solution pump to generate plots of COP and capacity versus solution flow rate similar to Figure 6.15. 6.3 Compare the results of Problems 6.1 and 6.2. Note that the approach taken in Section 6.1 is quite limited and often results in confusing predictions if care is not taken in the interpretation. The approach taken in Section 6.2 is more realistic because all the internal variables adjust to changes in the operating conditions. 6.4 Using the model that generated Table 6.3, perform the following experiment. Reset the initial guesses to the default values provided by EES. Then, rerun the model to see what will happen. Do the same with the model used to generate Table 6.1. Hint: Before trying this, save the file under a new name to avoid overwriting the working file with one that will not converge. 6.5 Convert the model used to generate Table 6.3 such that the solution heat exchangers are modeled using a UA approach instead of the effectiveness approach used. Using a fixed UA value, reproduce the results found in Figures 6.9 through 6.22 to determine whether the solution heat exchanger modeling approach changes the nature of the results. 6.6 Convert the model used to generate Table 6.3 into a model for a machine with double the capacity of the existing version. Note: It should be possible to obtain a solution with identical state points, but double the capacity by carefully choosing the appropriate parameters to change. 6.7 Using the model that generated Table 6.3, change the absorber UA value to 20% of its nominal value and rerun the model. Be sure to check the approach of the solution to the crystallization line.
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Absorption Chillers and Heat Pumps
6.8 Repeat Problem 6.4 for the Type II (heat transformer) model used to generate Table 6.6. 6.9 Using the model that generated Table 6.6, vary the parameters to determine the effects of the following variables on performance. a. Absorber heat transfer fluid inlet temperature from 100°C to 145°C b. Desorber and evaporator inlet temperatures from 100°C to 140°C c. Condenser inlet temperature from 20°C to 40°C d. Solution circuit flow rate from 0.5 to 2 kg/sec e. Heat transfer fluid flow rates in each of the four heat transfer loops. Vary over the range of 50%–150% of existing flow rate. f. UA values for each of the heat exchangers in the machine. Vary over the range of 50%–150% of existing values. 6.10 Determine and plot the effect of solution heat exchanger effectiveness on the highest temperature obtainable in the absorber of a Type II machine.
References AGCC. (1995). Natural Gas Cooling Equipment Guide, 2nd ed. Arlington, VA: American Gas Cooling Center. ASHRAE. (2010). Absorption Equipment. ASHRAE Handbook, Refrigeration. ASHRAE, Atlanta, GA, pp. 18.1–18.11. Herold, K. E. (2007). Absorption Heat Pumps for Waste Heat Recovery Applications. In Encyclopedia of Energy Engineering and Technology, Vol. 3, ed. B. Capehart, Taylor and Francis, Philadelphia, PA, pp. 1541–1547. Herold, K. E., and R. Radermacher. (1989). Absorption Heat Pumps. Mechanical Engineering 111(8): 68–73. Herold, K. E., and R. Radermacher. (1990). Optimum Allocation of Heat Transfer Surface in an Absorption Heat Pump. Proceedings of the IECEC—Intersociety Energy Conversion Engineering Conference, Reno, pp. 217–221. Kühn, A., S. Petersen, F. Ziegler, P. Kohlenbach, M. Harm, and C. Schweigler. (2005). Operational Results of A 10 Kw Absorption Chiller for Low-Grade Driving Heat. International Sorption Heat Pump Conference, Denver, Paper #51, pp. 1–6. Ma, X., J. Chen, S. Li, Q. Sha, A. Liang, W. Li, J. Zhang, G. Zheng, and Z. Feng. (2002). Industrial Application of Absorption Heat Transformer for Waste Heat Recovery in Synthetic Rubber Plant. Proceedings of the International Sorption Heat Pump Conference, Shanghai, pp. 141–145.
7 Double-Effect Water/Lithium Bromide Technology As discussed in Chapter 6, one of the limitations of single-effect absorption cycles is that they cannot take advantage of the higher availability (exergy) of high-temperature heat sources to achieve higher coefficient of performance (COP). Although the COP of a reversible cycle is quite sensitive to heat input temperature, the COP of a real absorption machine is essentially constant due to the irreversible effects associated with heat transfer. Thus, the cooling COP of a single-effect water/lithium bromide machine is around 0.7, essentially independent of the heat input temperature. To achieve higher cycle performance, it is necessary to design a cycle that can take advantage of the higher availability (or exergy) associated with a higher temperature heat input. Double-effect technology represents one such cycle variation (Alefeld 1983; Alefeld and Ziegler 1985a, 1985b; Alefeld and Radermacher 1994; Wagner et al. 2005). This chapter is devoted to describing the operating characteristics and the performance potential of double-effect, water/lithium bromide technology. Other high-performance cycles are also possible, and an overview of some of these is presented in Chapter 8.
7.1 Double-Effect Water/Lithium Bromide Cycles Due to the relatively low COP associated with single-effect technology, it is difficult for single-effect machines to compete economically with conventional vapor compression systems except in low-temperature waste heat applications where the input energy is free. Double-effect technology, with COP in the range of 1.0–1.4, is much more competitive (Kurosawa and Yoshikawa 1982; Wilkinson 1987). The high end of this COP range is the cycle COP, which one would potentially attain if firing the machine with waste heat. A more realistic gas-fired COP would introduce a gas burner efficiency of about 85% for a well-designed burner, where the remaining 15% is lost in the high-temperature exhaust gas. Then the actual COP would be 1.4(0.85) = 1.19. Gas-fired double-effect water/lithium bromide technology is a mature technology that competes for the gas cooling market segment (DeVuono et al. 1990). Competing gas-fired technologies include gas engine-driven vapor compression systems and desiccant systems. Double-effect machines, using water/lithium bromide as working fluid, are produced by a large number of manufacturers worldwide. Each manufacturer uses a different design depending on its view of the market economics. Instead of focusing on the design details of one machine, the discussion here of design tradeoffs is based on generic double-effect machines. A schematic of a double-effect machine is provided in Figure 7.1 in the Dühring plot format. In Figure 7.1, the external heat transfer interactions are represented by arrows. Heat is transferred into the cycle in both the high desorber and the evaporator. Heat is transferred
157
158
Absorption Chillers and Heat Pumps
˙ Q d2
High condenser – c2
SHX – Solution heat exchanger
High desorber
– Solution pump – Expansion valve
SHX2
– Internal heat exchange ˙ = Q˙ Q c2 d1
Q˙ c1 Low desorber – d1
Low condenser
Pressure
SHX1
Evaporator Absorber Q˙ e
Temperature
˙ Q a
FIGURE 7.1 Double-effect water/lithium bromide chiller Dühring chart schematic (parallel flow).
out from the cycle in the absorber and low condenser. The double-effect cycle includes two solution heat exchangers that have a similar role in the solution circuits as was described for the single-effect cycle. A new feature of the double-effect machine is the internal heat exchange between the high condenser and the low desorber. This internal heat exchange is achieved in practice by incorporating these two components into a single transfer device. One side of the exchanger is the high condenser, and the other side is the low desorber. This combined component is represented by the dotted border in Figure 7.1. The low desorber and low condenser of the double-effect machine operate at approximately the same conditions as the desorber and condenser of a single-effect machine. The operating temperatures and pressures of the high-pressure end of the double-effect machine can be inferred from Figure 7.1. The heat input in the double-effect machine occurs at a much higher temperature than in the single-effect machine. The COP of the double-effect technology is greater than that of single-effect technology because it is able to utilize the increased availability (exergy) of the higher temperature input heat. As compared with a single-effect machine, the double-effect machine takes heat in at a higher temperature, but it rejects heat at about the same temperature and provides refrigeration at about the same temperature. Thus, the double-effect machine can still be viewed as a three-temperature device, as introduced in Section 2.2. However, because the cascade of energy through the machine is accompanied by irreversible effects, the actual COP falls short of the reversible value obtained in Section 2.2. The reversible analysis is still useful as the relative COP changes associated with increasing the heat input temperature for a real cycle roughly f ollow the reversible analysis.
Double-Effect Water/Lithium Bromide Technology
159
Example 7.1: Reversible COP of the Double-Effect Machine Determine the reversible performance of a three-temperature chiller operating between the temperatures 150°C, 30°C, and 12°C, which represent a typical double-effect operating condition. Solution: Direct application of Equation 2.11 yields COPrev =
T0 (T2 − T1 ) = 4.49 T2 (T1 − T0 )
Observations: The reversible analysis requires the use of absolute temperatures. This calculation indicates that the thermodynamic limit of COP for this set of temperatures is quite high. Actual double-effect machines that operate over this temperature range achieve a COP of approximately 1.0 to 1.4. Thus, great care must be taken in using the reversible COP since it is far from realistic. Example 7.2: Zero-Order Model of a Double-Effect Machine Using a zero-order model, determine the capacity and COP of a double-effect machine operating between the temperatures given in Example 7.1 and with UA values at the high, heat rejection and evaporator temperatures given as UAh = 1 kW/K, UAc = 3 kW/K, and UAe = 2 kW/K. Solution: The details of this model are provided in file Ex7_2.ees. The zero-order model for the double-effect machine uses Equations 2.17 through 2.21 as written. Equation 2.22 must be modified to better model the double-effect machine. One possibility is
Thi − Tci = 2(Tci − Tei)
Based on these conditions and equations, the model yields a COP of 1.35 and a capacity of 24.1 kW. The calculated internal temperatures are T hi = 405.3 K, Tci = 317.2 K, and Tei = 273.1 K. Observations: The difference between the reversible COP calculated in Example 7.1 and the more realistic COP calculated from the zero-order model is heat transfer irreversibility at all three temperature levels. The thermal resistance causes the internal temperatures to be different than the external ones, and this difference is characteristic of a real cycle. The model also gives a zero-order prediction of the capacity. This capacity prediction is quite idealized, but it is still useful. In Section 7.3, a more realistic model (UA model) is described. When that model is used to calculate the performance of a similarly specified cycle (i.e., with the same UA distribution), it yields a capacity of only 15 kW and a COP of 1.1 (demonstration of this is left to the reader). Thus, both the COP and capacity predictions from the zero-order model are too high, but it has the advantage of the ease with which it can be set up and solved and it correctly predicts the trends in COP and capacity as source and sink temperatures are changed.
A simplified but quite accurate view of a double-effect machine can be obtained by viewing it as a three-pressure device. As was done in modeling the single-effect machines in Chapter 6, it is assumed here that pressure drops occur only in the throttling valves and pressure increases occur only in pumps. This approximation is quite accurate because other design constraints require that the machine be designed to minimize pressure drops. The key design constraint here is identical to what was found for single-effect technology. There it was found that the pressure drops in the machine must be minimized due to the low absolute pressure that is associated with water/lithium bromide, and pressure drop
160
Absorption Chillers and Heat Pumps
tends to aggravate many other design issues, including crystallization. With reference to Figure 7.1, the three pressure levels are represented by the pairs of components connected by horizontal lines. The high condenser and high desorber operate at the high pressure, the low condenser and low desorber operate at the intermediate pressure, and the evaporator and absorber operate at the lowest pressure in the cycle. The model discussed in Section 7.3 is based on such a three-pressure model of the double-effect machine. The pressure levels are quantified in that section. The term “double effect” refers to the fact that the heat input at the high temperature is used twice within the cycle to generate vapor. Vapor is generated in the high desorber because heat is the input. This vapor then flows to the high condenser, where it changes phase by rejecting heat. This heat is at a sufficiently high temperature that it can be used to drive vapor out of the solution in the low desorber. Thus, the heat is used twice and the term “double effect” reflects this. Another term that is useful in describing the cycle pictured in Figure 7.1 is “two stage.” An absorption machine can always be decomposed into a series of basic stages, which are just single-effect machines. Such a building block approach is quite useful when designing new cycles (Alefeld and Radermacher 1994). By inspection, the double-effect cycle in Figure 7.1 can be seen to consist of two single-effect stages stacked one on top of the other. Thus, the cycle in Figure 7.1 can also be described as a two-stage system. It is noted that these two terms are not interchangeable since they have different meanings. It is possible to have a two-stage cycle that is triple effect (such as the cycle discussed in Chapter 10). Thus, the term “stage” is reserved for describing the physical configuration of the cycle, and “effect” is reserved for describing the performance level of the resulting cycle. The number of effects is an approximation to the increase in COP that can be expected. In reality, a double-effect machine typically shows an increase in COP of less than two times that of a single-effect machine due to heat transfer losses associated with the cascade of energy through the system. A superposition method for predicting the COP of multistage cycles can be found in Alefeld and Radermacher (1994).
7.2 Solution Circuit Plumbing Options One of the major design choices in double-effect technology is the choice of how to connect the solution circuits. The basic options are parallel or series flow (Fallek 1985; Gommed and Grossman 1990). The cycle in Figure 7.1 was drawn assuming parallel flow and assuming that the solution mass fraction change across each of the desorbers is identical. The actual piping configuration used depends on the manufacturer. One possible parallel flow piping diagram is provided in Figure 7.2. Parallel flow offers thermodynamic and heat transfer benefits over series flow, but achieving these relatively small benefits requires more control complexity. Series flow schematics are included in Figures 7.3 and 7.4. The two cases are differentiated by the plumbing of the solution leaving the absorber. In the configuration in Figure 7.3, the solution is sent first to the high desorber and then to the low desorber. In the configuration in Figure 7.4, these are reversed. In both cases, the internal heat exchange process between the high condenser and the low desorber constrains the temperatures. The high condenser must have a high enough temperature so as to provide a heat transfer driving potential to drive heat into the low desorber. Thus, the different series flow arrangements lead to different temperatures in various components, and, as expected,
161
Double-Effect Water/Lithium Bromide Technology
Heat source loop High desorber High Condenser heating the Low Desorber Cooling water loop Low condenser
Chilled water loop Evaporator
Cooling water loop—Absorber FIGURE 7.2 Double-effect water/lithium bromide chiller piping chart schematic (parallel flow).
21
22 c2
17
d2 14
13 Internal heat exchange ˙ Q˙ = Q c2
s2
d1
15
18
25
26
c1
9
s1 2
5
p1
1 e 28
10 27
6
a 23
d1
3
8 ˙ W p1
16
19 7
4
Component labels Desorbers Condensers Absorber Evaporator Solution heat exchangers Pump
d1 & d2 c1 & c2 a e s1 & s2 p1
24
FIGURE 7.3 Series flow double-effect water/lithium bromide chiller Dühring chart schematic showing state points (solution to high desorber first).
162
Absorption Chillers and Heat Pumps
21
22 17
c2 Internal heat exchange Q˙ c2 = Q˙d1
25
e 28
10 27
2
5
p1 6
a 23
15
p2
d1 s1
1
12
11
3
8
9
19
14
s2 ˙ W p2
7
c1
˙ W p1
18
26
d2 13
24
Component labels Desorbers Condensers Absorber Evaporator Solution heat exchangers Pump
d1 & d2 c1 & c2 a e s1 & s2 p1 & p2
FIGURE 7.4 Series flow double-effect water/lithium bromide chiller Dühring chart schematic (solution to low desorber first).
TABLE 7.1 Comparison of Parallel and Series Solution Flow for Double-Effect Water/Lithium Bromide Cycles Configuration
COP
Capacity (kW)
Parallel Series, high desorber first Series, low desorber first
1.3596 1.2420 1.1430
360.6 372.5 273.5
Note: All configurations use the same UA values throughout the cycle.
the performance of the various configurations differs. A summary of the performance of the three configurations is presented in Table 7.1. It can be seen that the difference in COP favors the parallel flow configuration. However, the capacity favors the first series flow configuration. The results in Table 7.1 are all based on the same heat exchanger sizes and the same external fluid loop inlet conditions as discussed in detail in Section 7.3.
7.3 Operating Conditions of Double-Effect Machines 7.3.1 Parallel Flow Double-Effect Machines The parallel flow configuration of Figure 7.1 is redrawn in Figure 7.5 showing the state points between components and showing the external heat transfers as heat transfer loops.
163
Double-Effect Water/Lithium Bromide Technology
22 17
c2 Internal heat exchange Q˙ c2 = Q˙ d1 26
25
11
7
c1 8
20
3 s1 ˙ W p1
9
2 p1
5
1 e 28
10 27
6
a 23
24
14 s2
˙ W p2 19
d2 13
18
21
12
15
p2 16
d1 4 Component labels Desorbers Condensers Absorber Evaporator Solution heat exchangers Pump
d1 & d2 c1 & c2 a e s1 & s2 p1 & p2
FIGURE 7.5 Parallel flow double-effect water/lithium bromide chiller Dühring chart schematic showing state points.
The plumbing of the solution loop in the vicinity of the low desorber is more detailed to clarify the assumptions used in the model. The assumptions about the internal state points are quite similar to those discussed in Chapter 6 with reference to the single-effect technology. However, it may still be useful to summarize them here. This is done in Table 7.2. The cycle was modeled by imposing mass and energy balances on all components and by requiring the heat exchangers to follow UA models. The methods used are quite similar to those described in Chapter 6. A better idea of the type of model can be obtained by examining the model inputs, which are summarized in Table 7.3. 1). In general, one would expect The solution flow rate leaving the absorber is specified (m to also specify the flow rate in the upper solution circuit (Pump 2). However, in this case the energy balance between the high condenser and the low desorber is used to calculate the upper circuit flow rate. There is only one upper circuit solution flow rate that exactly balances the heat requirements of these two components (assuming zero jacket losses). The mass flow rates of heat transfer fluids in the four external heat transfer loops are specified as well as the inlet temperature to each loop. The UA values are input to represent the size of each of the heat exchangers. A UA model was also used for the internal heat exchange between the high condenser and the low desorber (designated UAcd). The operating conditions calculated for the baseline case defined by the inputs in Table 7.3 are listed in Table 7.4. It is noted that the COP and capacity match the values reported in Table 7.1. All the results in Table 7.1 were made with the same baseline inputs as listed in Table 7.3. It is also noted that the heat transfer fluid was assumed to be water with a fixed cp = 4.2 J/g-K for all four of the external loops. The double-effect machine can be visualized by displaying the operating conditions in a graphical format such as the Dühring chart in Figure 7.6. The machine operates at three
164
Absorption Chillers and Heat Pumps
TABLE 7.2 State-Point Summary for Parallel Flow Double-Effect Cycle Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
State
Notes
Saturated liquid solution Subcooled liquid solution Subcooled liquid solution (typically) Saturated liquid solution Subcooled liquid solution Two-phase solution state (typically) Superheated water vapor Saturated liquid water Vapor–liquid water state Saturated water vapor Saturated liquid solution Subcooled liquid solution Subcooled liquid solution (typically) Saturated liquid solution Subcooled liquid solution Two-phase solution state (typically) Superheated water vapor Saturated liquid water Vapor–liquid water state
Vapor quality set to 0 as assumption State determined from pump model State determined from solution heat exchanger model Vapor quality set to 0 as assumption State determined from solution heat exchanger model Vapor quality determined from valve model Assumed to have zero salt content Vapor quality set to 0 as assumption Vapor quality determined from valve node 1 Vapor quality set to 1.0 as assumption Vapor quality set to 0 as assumption State determined from pump model State determined from solution heat exchanger model Vapor quality set to 0 as assumption State determined from solution heat exchanger model Vapor quality determined from valve model Assumed to have zero salt content Vapor quality set to 0 as assumption Vapor quality determined from valve node 1
TABLE 7.3 Inputs for the Parallel Flow Double-Effect Cycle Model Parameter 1 (kg/sec) m 21 (kg/sec) m 23 (kg/sec) m m25 (kg/sec) 27 (kg/sec) m T21 (°C) T23 (°C) T25 (°C)
Value 1.0 8.0 12.0 14.0 20.0 150 25 25
Parameter T27 (°C) UAd (kW/K) UAc (kW/K) UAe (kW/K) UAa (kW/K) UAcd (kW/K) UAhx1 (kW/K) UAhx2 (kW/K)
Value 12 25 65 85 50 10 1.25 2.0
pressure levels, which are 0.9, 4.2, and 65.5 kPa for this baseline case. Of course, these pressures depend on the other operating conditions. A change in any of the inputs will affect all three pressures. The pressures shown here are typical. The high-end pressure approaches atmospheric pressure but remains subatmospheric (depending on the operating conditions). A key aspect of the operating conditions is that the temperature of the high condenser must be greater than that of the low desorber, as required by heat transfer considerations. This is seen to be the case here. The high-end temperature in the machine is approximately 145°C. This is considerably greater than that encountered in single-effect machines. The high temperature has consequent corrosion implications.
165
Double-Effect Water/Lithium Bromide Technology
TABLE 7.4 Baseline Operating Conditions for a Parallel Flow Double-Effect Water/ Lithium Bromide Machine in Figure 7.5 Generated by File: DBL_effect_ PUA.ees State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
h (J/g)
(kg/sec) m
68.7303 68.7324 102.8 195.4 155.3 155.3 2606.8 124.3 124.3 2510.2 102.8 102.8 221.7 327.3 187.3 187.3 2726.6 369.5 369.5 102.8
1.000 1.000 1.000 0.849 0.849 0.849 0.066 0.151 0.151 0.151 0.567 0.567 0.567 0.481 0.481 0.481 0.086 0.086 0.086 0.433 8.000
P (kPa) 0.888 4.167 4.167 4.167 4.167 0.888 4.167 4.167 0.888 0.888 4.167 65.540 65.540 65.540 65.540 4.167 65.540 65.540 4.167 4.167
Vapor Quality 0.000
T (°C) 29.98 29.98 46.13 75.98 54.79 48.16 57.25 29.68 5.24 5.24 46.13 46.15 101.32 144.67 71.71 71.71 123.48 88.23 29.68 46.13 150.00 142.07 25.00 33.82 25.00 28.13 12.00 7.69
0.000 0.004 0.000 0.041 1.000 0.000
0.000 0.012 0.000 0.101
12.000 14.000 20.000
X (–) 0.52343 0.52343 0.52343 0.61663 0.61663 0.61663 0 0 0 0 0.52343 0.52343 0.52343 0.61663 0.61663 0.61663 0 0 0 0.52343
Summary of Energy Quantities /W W p1 p2 COP Component Evaporator Absorber Condenser 1 Cond. 2/ Des. 1 Desorber 2 Sol. HX 1 Sol. HX 2
Pump power (kW)
0.0021/0.022
Coefficient of performance
1.359
Heat Transfer Rate (kW)
UA (kW/K)
ΔT lm(K)
360.6 442.5 183.6 201.9 265.4 34.1 67.4
85 50 65 10 25 1.25 2.0
4.243 8.849 2.824 20.19 10.62 27.25 33.67
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Absorption Chillers and Heat Pumps
Pure water
Vapor pressure (kPa)
1000
.50 0.45 0 .60 0.55 0
100
17
18 13
10
8
1
9,10
2 1
19
12 7 11
3 6
5
15 4
16
0.65
14
0.70 mass fraction LiBr
Crystallization line
0.1 0.01 0
50
100 Temperature (°C)
150
200
FIGURE 7.6 Dühring state plot for baseline double-effect water/lithium bromide example from Section 7.3.1 (parallel flow).
Corrosion problems are more severe in double-effect technology than they are in single-effect technology due to the higher temperatures. The high mass fraction in the machine must be maintained below the point at which crystallization will occur. The margin shown by this case is typical of that encountered in practice. The mass fraction change in each of the solution circuits is the same for this model. This requirement was imposed as an assumption for convenience in modeling. In a real machine, the mass fraction change across a given component will be a complex function of the operating characteristics and conditions. Thus, in general, it is not possible to design such that the mass fraction difference is exactly the same in both solution loops. As a result, some additional mixing irreversibility would be expected if these two streams have different mass fractions when the solution returning from the high desorber is mixed with the solution returning from the low desorber before being sent on to the absorber. Another observation about the mass fraction is that the change across the solution circuits displayed here is quite large (approximately 0.093 change in mass fraction) compared to standard practice. A more typical design would use a larger mass flow rate for a machine of this capacity so that the mass fraction change is around 0.05. This case was also run by changing the solution flow rate input from 1.0 to 2.0 kg/sec. The result is quite informative about the technology. When the solution flow rate is increased to 2.0 kg/sec, the capacity decreases only slightly to 354.0 kW (1.8% decrease). However, the COP decreases to 1.09, which is a 19.4% reduction. The explanation for this is complex because many things are changing. The temperature matching in the external heat exchangers actually improves slightly, so that is not the source of the COP decrease. The COP decrease can be traced, finally, to (1) substantially increased heat transfer duty and temperature difference in the upper solution heat exchanger associated with the increased flow rate, and (2) increased heat transfer duty in the upper desorber associated with subcooling of the incoming solution stream. Such effects were also found in single-effect technology. The cycle performance is quite sensitive to the solution flow rate due to multiple effects, and an overall design process would need to balance heat exchanger sizes with flow rate choices. In practice, such a wide
167
2
500
1.8
400 Evaporator heat transfer
1.6 1.4
300 200
COP 1.2 1 120
Heat transfer (kW)
COP
Double-Effect Water/Lithium Bromide Technology
100
130
140 150 Desorber inlet temperature (°C)
160
0 170
FIGURE 7.7 Parallel-flow double-effect absorption chiller performance as a function of the desorber inlet temperature.
mass fraction change (as indicated in Table 7.4) is not usually practical due to the limited space between the available cooling temperature and the crystallization line (i.e., the solution field). In the baseline case shown in Table 7.4, a low cooling temperature was used, which allowed the cycle solution to work. If this design were put in operation, a hot ambient condition would be expected to cause operational problems due to crystallization. These operating characteristics indicate one possible control scheme to optimize performance. If a variable-speed solution pump were provided, it would be possible to allow a wider solution band when the cooling water temperature is lower. The performance advantage that this option would provide depends somewhat on the size of the solution heat exchangers. The benefit is generally less when the solution heat exchangers are more effective. An example of the utility of the model discussed here is shown in Figure 7.7, where the COP and evaporator capacity are plotted versus the desorber water inlet temperature over a range of values that straddles the nominal value used in the baseline case in Table 7.4. It can be seen that the COP goes down slightly as the capacity increases. The reasons for this were discussed previously in the discussion of single-effect cycles in Chapter 6. In summary, the irreversibilities due to increased heat exchanger loading overwhelm the benefit of higher temperature input heat. As for the single-effect technology, the COP of a double-effect machine does not vary much as the imposed temperatures change. Results similar to those in Figure 7.7 for other input variables can be obtained by small modifications in the model. 7.3.2 Series Flow Double-Effect Machines The series flow option is preferred in some cases because the solution path is simpler. Maintaining the correct flow split in parallel flow is problematic without active controls. Thus, particularly for small systems, series flow is attractive as a design compromise. The best series flow option seems to be the one shown in Figure 7.3, where the solution is sent first to the high desorber. A model of this cycle, using the same inputs and same basic assumptions as were used to model the parallel flow configuration, was written for the series flow case, and the operating conditions for this case are given in Table 7.5.
168
Absorption Chillers and Heat Pumps
TABLE 7.5 Operating Conditions for a Series Flow Double-Effect Water/Lithium Bromide Machine as in Figure 7.3 Generated Using File: DBL_effect_ S1UA.ees State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
h (J/g)
(kg/sec) m
P (kPa)
69.4 69.4 105.0 203.0 160.8 160.8 2624.9 127.5 127.5 2509.7
1.000 1.000 1.000 0.844 0.844 0.844 0.077 0.156 0.156 0.156
0.874 4.355 4.355 4.355 4.355 0.874 4.355 4.355 0.874 0.874
196.5 304.4 205.0 205.0 2735.8 387.5 387.5
1.000 0.921 0.921 0.921 0.079 0.079 0.079
77.046 77.046 77.046 4.355 77.046 77.046 4.355
Vapor Quality 0.000
0.000 0.004 0.000 0.043 1.000
0.000 0.016 0.000 0.107
8.000
T(°C)
X (–)
30.04 30.06 46.98 78.32 55.87 49.27 66.84 30.45 5.02 5.02
0.52537 0.52537 0.52537 0.62276 0.62276 0.62276 0 0 0 0
89.67 138.35 89.92 68.76 128.68 92.50 30.45
0.52537 0.57044 0.57044 0.57044 0 0 0
150.00 141.03 25.00 34.14 25.00 28.65 12.00 7.55
12.000 14.000 20.000 Summary of Energy Quantities
W p COP Component Evaporator Absorber Condenser 1 Cond. 2/Des. 1 Desorber 2 Sol. HX 1 Sol. HX 2
Pump power (W)
0.048
Coefficient of performance
1.242
Heat Transfer Rate (kW)
UA (kW/K)
ΔT lm(K)
372.5 458.8 213.8 185.5 300.0 35.6 91.5
85 50 65 10 25 1.25 2.0
4.383 9.176 3.289 18.55 12.00 28.48 45.75
Double-Effect Water/Lithium Bromide Technology
169
The state-point numbers in Table 7.5 refer to Figure 7.3. Point numbers 11, 12, and 20 were omitted intentionally in an attempt to maintain some consistency with the solution to the parallel flow example. As was already noted in the discussion of Table 7.1, the COP of the series flow configuration is lower than the parallel flow, but the capacity is slightly higher. A number of things change between the two cycle solutions, obscuring the cause of the COP difference. A careful study of the solutions reveals, however, that the key differences are (1) the increased heat transfer load and log mean temperature difference on the high solution heat exchanger and (2) the increased subcooling of the solution stream at point 13. The relatively larger solution flow rate in the upper solution circuit causes a small mass fraction difference but also implies more heat transfer load on the solution heat exchanger. This higher load implies higher irreversibility and lower thermodynamic performance. The larger subcooling at the desorber inlet increases the desorber heat requirement directly. The cause of the increased capacity of the series flow configuration is more complex since the vapor flow rate from both the high and low desorbers changes. In general, such changes can be traced to the performance of the heat exchangers, but, in this case, all of the heat exchangers change, some performing better and some worse, with the net result being a small increase in capacity. The point of this is that the comparisons between the two design choices are not very straightforward. Design optimization for each plumbing option would lead to different choices for the relative sizes of the components and for the optimum choice of heat transfer loop flow rates and all other inputs. Thus, it is somewhat simplistic to compare the configurations on the basis of an arbitrary set of design parameters. When the optimization is done, it would be expected that the differences between the two technologies would narrow somewhat but that the overall conclusions about the preferred choice would not change. In other words, the parallel flow configuration is still expected to yield the highest performance, while the series flow is still expected to be easier to operate (i.e., easier to control).
7.4 Systems on the Market In 1995, five manufacturers actively marketed double-effect water/lithium bromide machines in the United States. A summary of the systems offered can be found in AGCC (1995), which includes system schematics and overall performance levels and operating conditions. Differences between the operating conditions claimed by the manufacturers and the performance predictions presented in this chapter are the result of design choices in the sizing of the machine components. The primary trade-off here is economic. The main obstacle to market penetration of double-effect absorption systems is still the first cost. Alternative technologies with lower first cost are readily available in most cases (i.e., electric-powered vapor compression chillers). Thus, to make their absorption products as attractive as possible, manufacturers naturally reduce the heat exchanger sizes to reduce cost. This has the effect of reducing COP. The absorption chiller market has evolved considerably since the first edition of this book was published in 1996. The US market for double-effect absorption chillers has contracted with very few new units installed per year (one estimate for the year ending October 2014 is 30 units; panjiva.com). Although the technology has advanced due to manufacturing methods and improved controls, it remains a niche technology in
170
Absorption Chillers and Heat Pumps
the United States, being used only in markets where fossil fuels are much cheaper than electricity. The largest international market is China, where the domestic manufacturers have progressed dramatically, with current products competing well against the top manufacturers worldwide. We have visited several Chinese absorption chiller manufacturers and observed impressive operations, including state-of-the-art robotic welding, in-house materials testing, and advanced designs that improve performance. A starting point for understanding the Chinese domestic market is the long list of manufacturers provided by Alibaba at http://www.alibaba.com/lithium-bromide- absorption-chiller-manufacturers. html. A major difference between the US and Chinese markets, which helps explain the deep market penetration of absorption chillers in China, is government regulation that has limited the specification of electric chillers in large building applications. This appears to be an attempt to balance energy flows and avoid overtaxing the rapidly expanding electric supply system.
Homework Problems 7.1 Use the zero-order model of Example 7.2 and maximize the capacity of the double-effect machine under the conditions of fixed total UA to find the optimum distribution of UA around the machine. Use a total UA value of 6 kW/K and the temperatures in Example 7.2. 7.2 Use the model that generated Table 7.4 to investigate changes in operating conditions for a parallel flow double-effect machine. For the following subproblems, hold all inputs constant except for the one being varied in that particular subproblem. In each case, determine the COP and capacity as a function of that particular variable. a. Vary solution circuit flow rate. b. Vary solution heat exchanger UA in each circuit. c. Vary the UA in each of the five heat exchangers (absorber, evaporator, low condenser, high desorber, and the high condenser/low desorber). d. Vary the heat transfer fluid inlet temperature in each of the four external heat exchangers. e. Vary the heat transfer fluid flow rate in each of the four external heat exchangers. 7.3 Using the model of Table 7.4 as a starting point, convert the solution heat exchanger models to an effectiveness formulation where the effectiveness values are input. Run the model to determine the effect of this change by repeating some of the studies in Problem 7.2 and comparing the results. Appropriate effectiveness values can be obtained by running the UA model first and allowing it to calculate the effectiveness values for those components. 7.4 Experiment with the parallel flow model to determine whether series piping of the external fluid loops for the absorber and condenser is feasible. The model run in Table 7.4 is for a parallel flow arrangement where the inlet temperatures to each component are identical (and the flow rates are different). In the series flow arrangement, the flow rate to each is the same and the outlet temperature from
Double-Effect Water/Lithium Bromide Technology
171
one component is the inlet to the next. Calculate performance for both cases, differentiated by which component comes first. Note that by adding an additional constraining equation to the model set, one less input is required. 7.5 Examine the effect on performance of the temperature difference between the high- and low-temperature stages. This can be done by varying the UA between the high-temperature condenser and the low-temperature desorber. Note the effects on COP, capacity, and the highest temperature in the cycle. 7.6 Estimate the thermodynamic losses in the refrigerant expansion valves by performing a calculation to determine the work that could be obtained by expanding the vapor through a reversible, adiabatic turbine. Is the isentropic work that would be produced sufficient to drive the solution pumps? 7.7 Prepare heat exchanger plots (similar to those in Figures 6.5 through 6.8) for each of the two solution heat exchangers. By inspection, determine whether these components exhibit temperature matching. 7.8 Replace the heat transfer fluid in the high-temperature desorber with steam input at constant temperature. Describe the changes needed in the model to make this work.
References AGCC. (1995). Natural Gas Cooling Equipment Guide, 2nd ed. Arlington, VA: American Gas Cooling Center. Alefeld, G. (1983). Double-Effect, Triple-Effect and Quadruple-Effect Absorption Machines. Proceedings 16th International Congress of Refrigeration, Vol. 2, Paris, pp. 951–956. Alefeld, G. and R. Radermacher. (1994). Heat Conversion Systems. Boca Raton, FL: CRC Press. Alefeld, G. and F. Ziegler. (1985a). Advanced Heat Pump and Air Conditioning Cycles for the Working Pair H2O/LiBr: Domestic and Commercial Applications. ASHRAE Trans. 91(2B): 2062–2071. Alefeld, G. and F. Ziegler. (1985b). Advanced Heat Pump and Air-Conditioning Cycles for the Working Pair H2O/LiBr: Industrial Applications. ASHRAE Trans. 91(Pt. 2B): 2072–2080. DeVuono, A. C., R. N. Christensen, D. K. Landstrom, W. H. Wilkinson, and W. A. Ryan. (1990). Development of a Residential Gas Fired Double Effect Air Conditioner Heater Using Water and Lithium Bromide. ASHRAE Trans. 96(Pt. 1): 1494–1498. Fallek, M. (1985). Parallel Flow Chiller Heater. ASHRAE Trans. 91(Pt. 2B): 2095–2102. Gommed, K. and G. Grossman. (1990). Performance Analysis of Staged Absorption Heat Pumps: Water Lithium Bromide Systems. ASHRAE Trans. 96(Pt. 1): 1590–1598. Kurosawa, S. and M. Yoshikawa. (1982). The Highest Efficiency Gas Direct-Fired Absorption Water Heater-Chiller. ASHRAE Trans. 88(Pt. 1): 401–415. Wagner, T. C., S. Jung, and M. E. Marler. (2005). Development of A Waste-Heat-Driven Double-Effect Absorption Chiller. International Sorption Heat Pump Conference, Denver, Paper #100, pp. 1–8. Wilkinson, W. H. (1987). What Are the Performance Limits for Double Effect Absorption Cycles? ASHRAE Trans. 93(Pt. 2): 2429–2441.
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8 Advanced Water/Lithium Bromide Cycles The cycles discussed in Chapters 6 and 7 represent absorption chillers that are currently on the market as commercial products from various manufacturers. The focus of this chapter is on advanced cycles that have been conceived as the solution to some particular thermal management challenge. The cycles covered include the half-effect cycle, tripleeffect cycle, and resorption cycle. Each technology has a particular niche application that makes it desirable. However, in all cases, some barrier exists that limits the usage of the technology and that differentiates these technologies as experimental or developmentstage concepts. In the treatment that follows, these barriers are discussed along with the potential applications to give an overview of the potential of each concept. It is noted that the cycles described here do not exhaust all of the possible variations of advanced cycles (Alefeld and Radermacher 1994).
8.1 Half-Effect Cycle The half-effect cycle is considered for use when the temperature of the available heat source is less than the minimum necessary to fire a single-effect cycle. The determination of the minimum temperature is not completely straightforward since it depends on the other two temperatures in the system. An idea of the minimum temperature needed to fire a single effect was obtained in Chapter 2 by examining the zero-order model (Example 2.1). If the chilled water temperature is 10°C and the heat rejection temperature is 32°C, a 5 K heat transfer driving potential at each level yields a minimum heat input temperature of 74°C. A similar analysis with zero heat transfer driving potential yields a minimum heat input temperature of 54°C. When the heat source temperature is low, there is a practical limit below which single-effect design becomes overconstrained by the characteristics of the working fluid, as represented in Equation 2.22. For such low-temperature heat sources, the utilization options are limited. One option is the half-effect cycle discussed here. A Dühring schematic of the half-effect machine is provided in Figure 8.1. This figure shows the general relationship between the operating pressures and temperatures of the primary components. The half-effect machine is a three-pressure-level machine. The high- and low-pressure levels function in ways familiar from single-effect practice. The intermediate-pressure level is the new feature. At the intermediate-pressure level, the low desorber delivers refrigerant vapor to the high absorber. The high solution circuit transports the refrigerant up to the high desorber, where it is boiled out of solution a second time. The refrigerant then traverses the condenser, evaporator, and low absorber as usual. The unique feature of the half-effect machine is that the required heat input temperature is lower than that for a single effect with the same chilled water and heat rejection temperatures. Unfortunately, there is a thermodynamic penalty that must be paid to allow the cycle to be fired at a lower temperature. The cooling coefficient of performance (COP) 173
174
Absorption Chillers and Heat Pumps
˙ Q c Component codes
9
14
hd – high desorber ld – low desorber ha – high absorber la – low absorber c – condenser e – evaporator
˙ Q hd
13
˙ W p2
8
7
12
11
15 Pressure
16
4
3 2
1 ˙ Q e
˙ Q ld
17
˙ Q ha ˙ W p1
10
5 6
˙ Q la
Temperature FIGURE 8.1 Cycle schematic for the half-effect cycle.
of a half-effect machine is typically around half of that for a single-effect machine. Thus, for water/lithium bromide the half-effect machine would be expected to have a COP of approximately 0.4. This level of performance has been verified in our laboratory (CAC 1985). The half-effect cycle is similar to the double-effect cycle (discussed in Chapter 7) in that both have three pressure levels. However, they differ in that the half-effect cycle has a lower heat input temperature as compared to a single-effect cycle, whereas the doubleeffect cycle has a higher heat input temperature. The COP follows the temperatures with the COP of the half effect being lower than the single effect, which is lower than the double effect. In the “double effect,” a single unit of heat input boils off refrigerant twice (two units of refrigerant). In the “half effect,” two units of heat are required for one unit of refrigerant. The choice of which of these cycles to use comes down to the heat input temperature; it is advantageous to use the highest effect that can operate under the available heat input temperature. The niche for the half-effect cycle is situations where low-temperature waste heat is available and where the temperature is too low to fire a single-effect cycle. A model of the half-effect cycle was written to predict the performance and the details of the internal operating conditions. The results for a typical operating condition are given in Table 8.1. A plot of these conditions on a Dühring chart is included in Figure 8.2. The cycle is arranged such that the heat rejection at all three pressure levels occurs over approximately the same temperature range. Also, the heat input in the two desorbers occurs over approximately the same temperature range. The dotted line in Figure 8.2 represents the extension of the lower solution circuit as if the cycle were a single-effect cycle. This shows the significant difference in heat input temperature of the two cycles. By incorporating the intermediate-pressure level, the halfeffect cycle can realistically accept heat at 70°C–80°C, while the single-effect cycle requires more like 100°C–110°C. And this is while both cycles provide refrigeration at the same temperature.
175
Advanced Water/Lithium Bromide Cycles
TABLE 8.1 Operating Conditions for the Half-Effect Cycle. See file HALF_ effect.ees State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
77.5 77.5 105.6 184.0 151.7 151.7 57.9 57.9 90.6 140.4 101.8 101.8 2601.4 167.5 167.5 2502.4 2589.9
3.000 3.000 3.000 2.617 2.617 2.617 2.500 2.500 2.500 2.117 2.117 2.117 0.383 0.383 0.383 0.383 0.383
0.657 1.943 1.943 1.943 1.943 0.657 1.943 7.381 7.381 7.381 7.381 1.943 7.381 7.381 0.657 0.657 1.943
Vapor Quality 0.000
0.000 0.001 0.000
0.000 0.006 0.000 0.065 1.000
T (°C)
x (−)
30.00 30.00 43.88 65.00 47.50 46.41 30.00 30.00 43.54 65.00 47.50 39.93 54.75 40.00 1.00 1.00 48.01
0.55203 0.55203 0.55203 0.63294 0.63294 0.63294 0.42334 0.42334 0.42334 0.50004 0.50004 0.50004 0.0 0.0 0.0 0.0 0.0
Summary of Energy Quantities /W W p1 p2 COP Q e
Pump power (W) Coefficient of performance Evaporator load (kW)
2.38/9.61 0.402 895.4
Q c Q /Q
Condenser load (kW)
933.4
Absorber loads (kW)
1124/1064
Q ld/Q hd Q /Q
Desorber loads (kW)
1158/1068
Solution heat exchanger loads (kW)
84.4/81.6
la
ha
hxl
hxu
100
Vapor pressure (kPa)
Pure water
0
0
.45
0.5 0
.55
0
0.6 5
0.6
0
0.7
10 Crystallization line
1 0.1 0.01 0
FIGURE 8.2 Dühring plot for the half-effect cycle.
50
Temperature (°C)
100
150
176
Absorption Chillers and Heat Pumps
Model results are provided in Table 8.1 for an internal model, written without external heat exchanger models to maintain simplicity, using the input values in Table 8.2. Heat exchanger models can be added to this model with minimum effort by using the existing internal state point solution as a building block, as described in Appendix C. A UA version of the half-effect model is provided in file Half_effect_UA.ees. By examination of the solution in Table 8.1, it is noted that the solution mass fraction values in the upper circuit are somewhat low as compared to traditional single-effect design practice. This requires property routines that span a wide range of mass fraction. The SSC water/LiBr property relations used throughout this book are valid over the full concentration range, from pure water to crystallization. It is noted that the half-effect cycle rejects approximately 50% more heat than the single effect for the same evaporator capacity. This is consistent with the fact that the COP of the half effect is 0.402 for the operating conditions in Table 8.1 as compared with a typical single-effect COP of 0.7. This increased heat rejection is the thermodynamic penalty associated with using low-grade input energy and requires large heat exchangers. Various versions of the half-effect cycle have been built and tested in laboratory or one-of-a-kind installations. A water/lithium bromide machine with a nominal size of 175 kW was built at Battelle Memorial Institute in 1982. This machine was funded by the US Department of Energy for use in low-temperature heat recovery from g overnment facilities (CAC 1985). The machine was thoroughly tested and found to perform with a nominal COP of 0.35 as designed. More recently, an ammonia/water half-effect cycle was built and operated in Alaska for several seasons (Erickson 1995). These machines run well, but they have not captured any market share due to the poor economics. Although they can capture and use low-temperature waste heat, the first cost is s ufficiently high as to be prohibitive to many users. The costs are high primarily due to the large heat exchangers they require. A secondary cost multiplier is the fact that little design experience exists for such machines. The extrapolation of the designs from well-known absorption technology is reasonably straightforward, but it still requires additional design effort. An interesting operational detail is that the vapor transfer from desorber to absorber at the intermediate-pressure level often carries liquid droplets that have a much different concentration than the vapor. This liquid carryover tends to cause the concentrations of the two solution loops to move toward each other. Steady-state operation requires either (1) a design that eliminates “carryover,” or (2) a mechanism for returning the absorbent to the lower solution loop. For the machine built at Battelle, a return line that diverted
TABLE 8.2 Input Summary for Half-Effect Model. Refer to Figure 8.1 and Table 8.1 Parameter
Value
1 (kg/sec) m 7 (kg/sec) m
3.0 2.5
Solution flow rate, lower loop Solution flow rate, upper loop
Comment
ε shx
0.5
T4 = T10 (°C) T1 = T7 (°C) T16 (°C) T14 (°C)
65 30 1 40
Solution heat exchanger effectiveness, both solution heat exchangers Desorber high temperature, both desorbers Absorber low temperature, both absorbers Evaporator temperature Condenser temperature
Advanced Water/Lithium Bromide Cycles
177
a small flow rate of solution from the upper loop to the lower loop was utilized. This return line flow rate had to be adjusted if the average concentration in the loops began to drift. This return line approach has a performance penalty but it was found to be small (and it can be easily modeled). A corollary to this is that to maintain steady-state operation, the vapor flow rates at points 13, 16, and 17 all have to be identical. In the model, this is easy to specify. In actual operation, the mass fractions of the solution loops and the pressures will adjust to try and find a balance, but the heat inputs in the two desorbers and the heat rejection from the two absorbers are ultimately the inputs that drive the cycle. To maintain stable operation, this cycle requires, at a minimum, a control system that can modulate the relative heat inputs in the two desorbers.
8.2 Triple-Effect Cycle Triple-effect technology underwent an active development cycle by several of the leading absorption equipment manufacturers from 1996 to 2005 (Kujak and Schultz 2000; Yabase et al. 2005; Yabase 2012). Kawasaki announced a triple-effect product in 2005 which can be found on their website (http://www.khi.co.jp) by searching for the keyword “triple”. The promise of the triple-effect cycle is to raise the gas-fired cooling COP to the range of 1.4–1.6 with only a modest increase in first cost. The discussion in this section focuses on a version of triple-effect technology that appears to be a simple extension of double effect. The main challenges associated with this concept, and with triple-effect concepts in general, are corrosion and materials. Triple-effect inherently implies higher temperatures. The thermodynamic basis of the higher COP values comes from the increased availability (exergy) of the high-temperature heat input. The higher temperatures cause significant increases in the corrosion rates for traditional materials of construction. Thus, most triple-effect concepts revolve around the solution of the high-temperature corrosion challenge (Shu et al. 1999; Jiangzhou and Wang 2001). A simple extension of the double-effect concept can be made to arrive at the four-pressure triple-effect machine shown schematically in Figure 8.3. This cycle includes two internal heat exchange processes between a condenser and a desorber, as shown by the dashed lines in Figure 8.3. Thus, each unit of heat is used in three different desorbers to generate vapor and hence the name triple-effect. This particular cycle is a three-stage machine. A number of other three-stage, triple-effect configurations are also possible in theory. However, for water/lithium bromide, the cycle shown in Figure 8.3 shows the greatest promise. By examination of Figure 8.3 and in comparison with double-effect design, it can be seen that the triple-effect concept requires an additional desorber and solution heat exchanger at the highest temperature level. Also, the high-temperature condenser must be integrated into the highest temperature desorber of the double-effect components. The relative size of the heat exchangers changes somewhat because the heat transfer rates change. As expected with additional components, the number of design choices is increased, and this brings along increased difficulty in arriving at an optimized design. The approach in this section is to present modeling results for the cycle pictured in Figure 8.3, using water/lithium bromide, under the assumption that the corrosion challenges are solvable. The cycle pictured uses a parallel-flow solution circuit. An internal model is used that does not include heat exchanger models for the four external heat transfer interactions. Instead, a set of nominal temperatures were input in those four components to set the
178
Absorption Chillers and Heat Pumps
C3
Component codes
E – Evaporator C – Condenser A – Absorber D – Desorber p – Pump SHX – Solution heat exchanger 18
19
˙ Q c1 C1 8
9 E ˙
Qe
10
SHX1 5
2
25
p3 26
D2 31 14
p2 16
Internal heat exchange (dashed line) Q˙ c3 =Q˙ d2 Q˙ c2 =Q˙ d1
6
A
13 SHX2 12 15
22
D1 30 4
3
˙ W p1 1
11
7
21
D3 23 24 SHX3
28 29 17 C2
˙ Q d3
27
˙
Qa
FIGURE 8.3 Cycle schematic for the triple-effect cycle.
TABLE 8.3 Inputs for the Triple-Effect Cycle Model. See file TRIPLE_effect.ees Parameter
Value
1 (kg/sec) m T24 (°C) T8 (°C)
1.0
T1 (°C)
Parameter
Value 30
180 30
T10 (°C) εSHX ΔT (K)
5 0.5 5
operating conditions. This approach has the benefit of eliminating some complexity from the model, which was not needed for this discussion. A UA formulation for the heat exchange processes could be simply added to the model based on the known internal solution. The inputs for the triple-effect model are summarized in Table 8.3. Only a single pump flow rate is input because the other two solution pump flow rates are calculated from energy balances on the condenser–desorber internal heat exchange processes. For this modeling approach, internal temperatures at four locations are imposed to eliminate the needed heat exchanger models for the external heat exchange processes. Effectiveness models were used for the solution heat exchangers, and all three utilized the same value of effectiveness. For the condenser–desorber internal heat exchange processes, a pinch point model was imposed with a pinch temperature difference as indicated in Table 8.3. This set of inputs results in the cycle solution in Table 8.4 and the Dühring plot in Figure 8.4. Note that point 20 is omitted from the cycle schematic to obtain a more orderly numbering scheme.
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Advanced Water/Lithium Bromide Cycles
TABLE 8.4 Operating Conditions for the Triple-Effect Cycle. See file TRIPLE_ effect.ees State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
69.3 69.3 104.1 168.3 129.5 129.5 2608.1 125.7 125.7 2509.7 104.1 104.1 170.9 271.1 196.8 196.8 2699.4 311.1 311.1
1.000 1.000 1.000 0.898 0.898 0.898 0.031 0.102 0.102 0.102 0.692 0.692 0.692 0.621 0.621 0.621 0.029 0.071 0.071
0.87 4.25 4.25 4.25 4.25 0.87 4.25 4.25 0.87 0.87 4.25 37.47 37.47 37.47 37.47 4.25 37.47 37.47 4.25
170.9 171.0 264.1 391.3 287.7 287.7 2799.2 528.1 528.1 104.1 170.9
0.405 0.405 0.405 0.364 0.364 0.364 0.041 0.041 0.041 0.308 0.287
37.47 237.14 237.14 237.14 237.14 37.47 237.14 237.14 37.47
Vapor Quality 0.0
0.0 0.0060 1.0 0.0420 1.0
0.0 0.0097 1.0 0.0763
0.0 0.0401 1.0 0.0934
T (°C)
x (−)
30.00 30.00 46.55 69.31 49.66 41.33 57.92 30.00 5.00 5.00 46.55 46.56 77.79 120.71 83.63 70.53 108.10 74.31 30.00
0.52527 0.52527 0.52527 0.58491 0.58491 0.58491 0.00000 0.00000 0.00000 0.00000 0.52527 0.52527 0.52527 0.58491 0.58491 0.58491 0.00000 0.00000 0.00000
77.79 77.85 120.75 180.00 128.92 74.68 166.15 125.71 74.31 46.55 77.79
0.52527 0.52527 0.52527 0.58491 0.58491 0.58491 0.00000 0.00000 0.00000 0.52527 0.52527
Summary of Energy Quantities /W /W W p1 p2 p3
Pump power (W)
COP Q
Coefficient of performance Evaporator load (kW)
1.61 243.1
Q c1 Q
Condenser (C1) load (kW)
91.1
Absorber load (kW)
302.9
Q d3 Q /Q
Desorber (D3) load (kW)
150.9
Internal HX from C3–D2 (kW)
93.8
Q c 2/Q d 1 Q hx 1/Q hx 2/Q hx 3
Internal HX from C2–D1 (kW)
78.8
e
a
c3
d2
Solution heat exchanger loads (kW)
2.1/14.7/52.3
34.8/46.2/37.7
180
Absorption Chillers and Heat Pumps
Pure water
1000
Vapor pressure (kPa)
0.4
100
5 0.50 .55 0 0 0.6 5 0.6
0.70 mass fraction LiBr
10 Crystallization line
1 0.1 0.01 0
50
100
150
200
Temperature (°C) FIGURE 8.4 Dühring plot for the triple-effect cycle.
Several observations can be made regarding the cycle solution. The pinch temperature difference used in the internal heat exchange processes is quite tight at 5 K. To achieve this small temperature difference, large heat exchange areas would be needed. It is noted that the highest temperature in the cycle is sensitive to the pinch temperature difference used. An increase of 1 K in pinch temperature difference increases the heat input temperature by 2 K (with everything else held constant). The high end pressure is also of note in triple-effect cycles. From Figure 8.4, it is seen that the highest pressure in the cycle (238 kPa) is above atmospheric pressure. The relatively high pressure results in somewhat different design conditions for the high-pressure components as compared to the next lower pressure level. In particular, the lower specific volume of the vapor at higher pressures lowers boiling heat transfer coefficients, but it also results in some size reductions in the condenser geometry. The vapor fractions listed include eight points for which the vapor fraction was specified as an assumption. In general, these represent the assumption that the fluid leaving the component is saturated. These entries can be identified in Table 8.4 as the entries in the vapor fraction column that have only two digits shown (either 0.0 or 1.0). For the same heat input, the capacity of the triple-effect is greater than double-effect. This is because more vapor is generated for each unit of heat input. That vapor then finds its way to the evaporator to provide refrigeration capacity. The solution mass flow rate that was input essentially defines the capacities, and the input value was arbitrarily set to 1 kg/sec; the capacities shown in Table 8.4 are based on this arbitrary specification. The cooling COP calculated for this cycle is 1.610. This is a cycle COP that does not account for additional losses that would be expected in a gas burner. Assuming a burner efficiency of 90%, the gas-fired cooling COP for this cycle would be 1.48, which represents the practical upper limit of performance potential of gas-fired triple-effect configurations. Design optimization may be able to improve that value slightly, but it is unlikely that triple-effect will do significantly better in practice. Practical design tradeoffs may result in reductions
Advanced Water/Lithium Bromide Cycles
181
in that value. The percentage improvement in cooling COP obtained in going from double to triple-effect is less than that obtained in going from single to double-effect. Using the superposition principles of Alefeld and Radermacher (1994), the double-effect machine should achieve a COP of 1.24 and the triple-effect machine should achieve 1.61. In practice, double-effect machines are often built with design compromises that result in a COP of 1.0. If triple-effect machines are built with similar compromises, a realistic performance projection for gas-fired triple effect is a cooling COP of 1.3. Thus, the actual gas-fired cooling COP for triple-effect is expected to be in the range between 1.3 and 1.48. The design tradeoffs that result in reduced performance are typically due to economics. First cost of such machines is an important issue in the market, and first cost can be reduced by reducing the size of heat exchangers and giving up a few points on COP. Compactness is also an economic issue. If the machine is made small, it will sell better, but the smaller equipment results in higher velocities that tend to cause entrainment and carryover between components. Liquid carryover can be a major source of COP reduction in a real machine. Mist eliminators can minimize this problem, but the ultimate solution is to increase the flow areas so that the vapor velocities are low enough to avoid the problem altogether. Such issues need to be addressed in triple-effect design if the highest performance is to be obtained.
8.3 Resorption Cycle Another cycle variation, which has the potential of expanding the design options of water/ lithium bromide technology, is the resorption cycle. A simple single-effect resorption cycle is shown schematically in Figure 8.5. The cycle employs two solution circuits instead of only one. The condenser/expansion valve/evaporator section of a conventional singleeffect cycle is replaced in the resorption cycle by a solution circuit consisting of an absorber, solution heat exchanger, pump, and desorber. The absorber takes the role of the condenser and rejects heat, whereas the desorber takes the role of the evaporator. It should be noted that the new solution circuit flows counterclockwise similar to the solution circuit in a Type II cycle. The overall result of this arrangement is a cycle that is no longer tied to the thermodynamic properties of the pure refrigerant. By allowing the average mass fraction of the new solution circuit to be a design variable, the resorption cycle provides an additional degree of freedom in cycle design. This additional design flexibility is needed in certain advanced cycles where the resorption cycle can be used as a building block. The cycle solution provided here is an example of how to analyze such a configuration. The new solution circuit operates at a LiBr mass fraction much lower than found in the typical solution loop in a single-effect cycle. Thus, modeling this cycle requires property routines that span a wide range of concentration. The SSC water/LiBr routines used in this book work well for this application. The model that was created is an external model that utilizes UA models for all of the heat exchangers. The inputs to the model are summarized in Table 8.5. The mass flow rates in both solution pumps are input as well as the mass flow rates in all four external heat transfer loops. The UA values in each of the four major heat/mass exchangers are input as well as the UA values for the two solution heat exchangers. The inlet temperature to each of the heat transfer loops is also input. The remaining input is the mass fraction of the steam at state 1 leaving the lower absorber. The resorption cycle is unusual in requiring this type of input because it incorporates two solution circuits in the same stage.
182
Absorption Chillers and Heat Pumps
Q˙a2
25
26
22 7
Absorber 2 11 Solution heat exchanger 2
Desorber 1 4
3
Solution heat exchanger 1
10
5
2 12
9 Pump 2 8
13 Desorber 2
Q˙d2
Pump 1 ˙ W p1
Solution expansion valve
˙ W p2 6
1
Absorber 1
14 28
21 Q˙d1
27
23
Q˙a1 24
FIGURE 8.5 Cycle schematic for the resorption cycle.
TABLE 8.5 Inputs for the Resorption Cycle Model (See file RESORPTION.ees) Parameter
Value
1 (kg/sec) m 8 (kg/sec) m
0.05 0.05 0.50 1.50
UAd1 (kW/K) UAd2 (kW/K) UAa1 (kW/K) UAa2 (kW/K) x1 T21 (°C)
0.75 0.25 0.55 120
Parameter T23 (°C) T25 (°C) T27 (°C) 21 (kg/sec) m 23 (kg/sec) m 25 (kg/sec) m 27 (kg/sec) m
Value 25 25 20 1.0 1.0 1.0 1.0
Specifying the mass fraction at state 1 provides another constraint on the system of e quations. The need for this constraint to close the system stems from a fundamental difference between the conventional single-effect cycle and the resorption cycle. In the conventional cycle, the refrigerant can accumulate in the evaporator sump and allow the average concentration of the solution loop to adjust to the imposed conditions. In a resorption cycle, the solution loop concentrations adjust to operating conditions, but there is no sump of pure water; thus, when water is transferred from one solution loop to the other, the average concentration in both loops changes. In a real resorption machine, such a constraint
183
Advanced Water/Lithium Bromide Cycles
is imposed by the initial charge of aqueous lithium bromide. The initial charge in a conventional single-effect absorption chiller does not represent a constraint because the pure refrigerant can accumulate in the evaporator. The model used here does not account for such dynamics, hence the need for a somewhat artificial input. From a modeling perspective, it would be equally valid to choose the value of the mass fraction in any leg of either solution circuit. A discussion of the inputs needed for the resorption cycle can be found in Appendix B in the context of equation counting. A cycle solution for the inputs in Table 8.5 is given as Table 8.6. A Dühring plot of the cycle solution is given as Figure 8.6. Several features are worthy of note. The heat transfer TABLE 8.6 Operating Conditions for the Resorption Cycle (See file RESORPTION.ees) State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 21 22 23 24 25 26 27 28
93.9 93.9 169.9 229.4 146.5 146.5 2660.9 24.5 24.5 95.7 147.2 81.4 81.4 2527.6 503.8 490.6 104.8 117.4 104.8 112.7 83.8 76.4
0.0500 0.0500 0.0500 0.0458 0.0458 0.0458 0.0042 0.0500 0.0500 0.0500 0.0542 0.0542 0.0542 0.0042 1.0000
1.137 13.071 13.071 13.071 13.071 1.137 13.071 1.137 13.071 13.071 13.071 13.071 1.137 1.137
Vapor Quality 0.000
0.000 0.004 0.000
0.000 0.023
1.0000 1.0000 1.0000
T (°C)
x (−)
38.44 38.44 75.29 97.33 54.69 48.73 86.52 14.62 14.62 40.87 57.24 33.97 13.71 14.62 120.00 116.90 25.00 28.01 25.00 26.90 20.00 18.23
0.55000 0.55000 0.55000 0.60033 0.60033 0.60033 0.00000 0.33284 0.33284 0.33284 0.30710 0.30710 0.30710 0.00000
Summary of Energy Quantities /W W p1 p2
Pump power (W)
COP
Coefficient of performance
0.37/0.46 0.562
Component
Heat Transfer Rate (kW)
UA (kW/K)
∆T lm (K)
Desorber 1 Desorber 2 Absorber 1 Absorber 2 Sol. HX 1 Sol. HX 2
13.17 7.40 12.61 7.96 3.8 3.56
0.50 1.50 0.75 0.25 0.20 0.20
26.34 4.94 16.81 31.86 19.00 17.82
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Absorption Chillers and Heat Pumps
100
Vapor pressure (kPa)
Pure water
5 0.4
0
0.5 5 0.5
10
0
0.6 5
0.6
0
0.7
Crystallization line
1 0.1 0.01 0
50
Temperature (°C)
100
150
FIGURE 8.6 Dühring plot for the resorption cycle.
loop connected to the low-temperature desorber operates over the temperature range 18.2°C–20°C. Thus, although the cycle provides refrigeration, it does not appear to be very practical for conventional applications. The low temperature could be lowered by allowing the low pressure in the cycle to drop, but then the absorber crystallization problem would be aggravated. The cycle solution used in this illustration demonstrates the concept. In practice, the resorption cycle would probably be utilized as a component of a more complex, multistage cycle. The cooling COP of the resorption cycle is 0.562. This value is lower than that found for the conventional single-effect cycle due primarily to increased irreversibilities in the new solution circuit. In particular, streams 7 and 10 are far from equilibrium when they are brought together in the absorber. Another factor is the increased flow losses in the expansion valve. In the new solution circuit, the amount of vapor that flashes is considerably greater, and this is indicative of higher irreversibility. This irreversibility results from the fundamental difference in the thermal configuration of a solution heat exchanger in a counterclockwise-flowing solution circuit. Even though the effectiveness values of the two solution heat exchangers are identical, the amount of subcooling in stream 12 is much less than the amount of subcooling in stream 5. This behavior is typical of the difference between such oppositely flowing solution circuits.
Homework Problems 8.1 Check the mass and energy balances on each of the components in the half-effect cycle described in Table 8.1. 8.2 Run the half-effect model for a series of cases where the solution heat exchanger effectiveness is varied from 0 to 1.0 and plot the COP and capacity.
Advanced Water/Lithium Bromide Cycles
185
8.3 Using the half-effect model, compute the solution heat exchanger UA values corresponding to effectiveness values of 0.5. Convert the half-effect model such that the solution heat exchangers are modeled using a UA approach. Input the UA values already computed and compare the performance predicted using the two approaches. 8.4 Convert the half-effect model into a UA model by adding heat transfer loops at each of the heat exchangers transferring heat external to the cycle. Run the model to examine the effects on performance and capacity. a. Vary solution circuit flow rate in both solution circuits. b. Vary solution heat exchanger effectiveness in each circuit. c. Vary the UA in each of the heat exchangers where UA models are used. d. Vary the heat transfer fluid inlet temperature in each of the six external heat exchangers. e. Vary the heat transfer fluid flow rate in each of the six external heat exchangers. 8.5 Check the mass and energy balances for each of the components in the tripleeffect cycle described in Table 8.4. 8.6 Vary the inputs to the triple-effect model to examine the effect on COP and capacity. The inputs are listed in Table 8.3. 8.7 Check the mass and energy balances for each of the components in the resorption cycle described in Table 8.6. 8.8 Vary the inputs m · 1, m · 8 and x_1 to the resorption cycle model to examine the effect on COP and capacity. The inputs are listed in Table 8.5.
References Alefeld, G. and R. Radermacher. (1994). Heat Conversion Systems. Boca Raton, FL: CRC Press. CAC. (1985). Compound Absorption Chiller Project Performed for DOE. Columbus, OH: Battelle Memorial Institute. Erickson, D. C. (1995). Waste-Heat-Powered Icemaker for Isolated Fishing Villages. ASHRAE Trans. 101(Part 1): 1185–1188. Jiangzhou, S. and R. Z. Wang. (2001). Experimental Research on Characteristics of CorrosionResisting Nickel Alloy Tube Used in Triple-Effect LiBr/H2O Absorption Chiller. Appl. Therm. Eng. 21(11): 1161–1173. Kujak, S. and K. Schultz. (2000). Demonstration of a Direct-Fired Triple-Effect Absorption Chiller. Energy Eng. 97(3): 49–56. Shu, J. Z., Y. C. Hu, H. M. Chen, and C. J. Tu. (1999). Experimental Research on Heat Transfer Characteristics for Nickel Alloy Corrosion-Resisting Spiral Tube Bundle Used in Triple-Effect LiBr/H2O Absorption Chiller. 4th International Symposium on Multiphase Flow and Heat Transfer, Xian, China, 696–701. Yabase, H., K. Kawabata, F. Yakushiji, and T. Takigawa. (2005). Development of Triple-Effect Absorption Chiller-Heater. International Sorption Heat Pump Conference, Denver, Paper #48, pp. 1–8. Yabase, H., and K. Makita. (2012). Steam Driven Triple Effect Absorption Solar Cooling System. Purdue ePubs, Purdue University, West Lafayette, IN.
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9 Single-Stage Ammonia/Water Systems Single-stage, single-effect ammonia/water systems have been in use since the mid-1800s. They come in many different variations and implementations (Bogart 1981; Howe et al. 1989; Erickson 1991; Erickson 1995). Originally, the applications were refrigeration. Since the 1960s, a considerable number of these units were built for residential air conditioning, and since the 1970s they are also under consideration for residential and commercial heating. The basic single-stage absorption cycle for ammonia/water mixtures is, on first glance, very similar to that for water/lithium bromide. However, there are several important details that are significantly different, all of which are consequences of the fluid properties. Performance calculations for single-stage ammonia/water systems are discussed in this chapter. More advanced ammonia/water cycles are discussed in Chapters 10 and 11. The models discussed here are similar to, but more complex than, those discussed in Chapters 6 through 8. Thus, it may be that this chapter will be easier to understand once the chapters on water/lithium bromide systems (Chapters 6 through 8) are mastered.
9.1 Properties of Ammonia and Safety Concerns Ammonia is a naturally occurring substance that is produced and used in large quantities. In the United States alone, 20 million tons are used per year, according to the Ammonia Health and Safety Guide (IPCS 1990), for agriculture, as fertilizer, and as the source material for fibers, plastics, and explosives. Consequently, it is shipped in large quantities by rail and ship. Ammonia is also used as a cleaning and descaling agent and in food additives. Ammonia is a colorless gas of low density at room temperature with a pungent smell. It has a molecular mass of 17.03 g/mol and is thus lighter than air. It can be stored and transported as a liquid under a pressure of 1 MPa at 25°C. The critical point of ammonia is at 132.3°C and 11.3 MPa. The critical density is 235 kg/m3. Ammonia is highly soluble in water, generating NH +4 and OH– ions resulting in a basic solution (pH ~11) that reacts in a damaging way with mucus membranes. However, it is not absorbed through the skin. It can be smelled by humans in concentrations of very few parts per million. At about 50 ppm, the odor is almost unbearable. This is also the concentration range (25 ppm) to which the long-term exposure is limited from an occupational health point of view (IPCS 1990). At high dosages, ammonia exposure can be lethal. Ammonia is flammable and explosive in the range of 16%–25% by volume (IPCS 1990) in air. Safe use depends on an understanding of all these issues (Pentz et al. 1983; Bojanowski 1985). The strong odor of ammonia can be seen as a safety asset since it is self-alarming. Even very small leaks in systems are easily noticed, and the irritating smell provides a significant incentive for early repairs and consistent maintenance. One method of leak detection is to use wet indicator paper, which will quickly change color once it is exposed to air with a few parts per million of ammonia. However, traditional leak detection approaches such 187
188
Absorption Chillers and Heat Pumps
as soap (or bubble) solutions do not work since the ammonia can dissolve in the water without creating bubbles.
9.2 Material Considerations Ammonia is a very good solvent for copper. Thus, the use of any copper or copper- containing material is problematic. Experience in the laboratory indicates that even chromium-plated brass parts are susceptible to ammonia corrosion. The most common material for the c onstruction of ammonia/water systems is steel (carbon steel) or stainless steel. When carbon steel is used, corrosion inhibitors are required for most applications (Minato et al. 1991). These are salts that are added in small quantities (on the order of 1% by weight). They form a protective oxide layer on the metal surface so that there is no direct contact with the working fluid. The influence of these salts on the thermodynamic properties of the working fluid is usually neglected. Traditionally, the corrosion inhibitors are salts that contain heavy metals. These are being banned by the US Environmental Protection Agency, and manufacturers find themselves needing to develop new, environmentally acceptable replacements. The thermal conductivity of steel is about one-tenth that of copper. As a result, the heat transfer resistance of the wall material plays a larger role in heat exchanger design when compared to copper. As ammonia/water has a relatively high vapor pressure, chillers and heat pumps based on ammonia/water are not as susceptible to performance degradation due to the presence of noncondensable gases as water/lithium bromide systems. However, it is nevertheless good practice to keep all noncondensables out of the system. In particular, the presence of oxygen, even in small amounts, is an indicator of accelerated corrosion.
9.3 Water Content of the Refrigerant Vapor In comparing the conventional absorption working fluids, a key difference is the high vapor pressure of ammonia/water mixtures compared to that of water/lithium bromide. Here, ammonia is the refrigerant. The normal boiling point of ammonia is –33.35°C, and the vapor pressure at room temperature is 8.5 bar. Therefore, the pressure in the desorber component at the temperatures normally encountered in air-conditioning and refrigeration applications is relatively high (typically in the range of 5–25 bar). This pressure level is comparable to vapor compression systems that utilize R22 as the refrigerant. The high vapor pressure leads to rather small pipe diameters and relatively compact heat exchangers as compared to water/LiBr. A second important difference is that the absorbent (water) has a vapor pressure that is not negligible relative to that of ammonia. As a consequence, the vapor generated in the desorber contains a certain amount of water (typically on the order of 5% water). The mass fraction in the vapor depends on the mass fraction of the liquid mixture in the desorber, the temperature, and the desorber design. Any water contained in the desorber vapor is detrimental to the performance of the system. As can be seen in Figure 9.1, which depicts a basic single-stage cycle, the water will pass with the vapor into the condenser and then
189
Single-Stage Ammonia/Water Systems
Condenser
Desorber
˙ Q cond
Expansion device
Solution heat exchanger
Pump Expansion device Absorber
Evaporator ˙ Q evap
˙ Q des
˙ Q abs
FIGURE 9.1 Single-stage ammonia/water cycle. Desorber
Pressure
Condenser
Absorber
Pu
re
am
m
on
ia
Evaporator
Temperature FIGURE 9.2 Single-stage ammonia/water cycle showing effect of water accumulation in evaporator.
into the evaporator, where the water would tend to accumulate if a pool boiler design was used because the evaporating vapor is rich in ammonia. Although the evaporating vapor still contains some water, the ammonia mass fraction of this vapor is typically higher than that of the vapor leaving the desorber (which is what enters the evaporator). Thus, water would tend to accumulate in the evaporator, which is unworkable for a cycle. This issue is demonstrated in Example 9.1. The effect of accumulating water in a pool boiler-type evaporator can be looked at from several angles. If it is assumed that the evaporator temperature remains constant, an accumulation of water will lead to a decrease in evaporator pressure, which in turn will affect the absorber conditions. Figure 9.2 shows a single-stage cycle superimposed on the
190
Absorption Chillers and Heat Pumps
pressure–temperature diagram. The lines of constant mass fraction (isosteres) are shown for pure ammonia and the mixtures within the solution circuit. As the water accumulates in the evaporator, the pressure drops for a constant evaporator outlet temperature that is fixed by the application. The new location for the evaporator on this diagram is indicated by the dotted lines. The absorber has either to be cooled to a lower temperature, or the mass fraction of the solution has to change to a lower ammonia content. The latter is shown in Figure 9.2. Assuming that the desorber temperatures do not change, the condenser temperature must drop, which is usually prohibited by the cooling water temperature available to the condenser. As a consequence, the high-pressure level has to be raised and the desorber temperature will increase as well. As the water continues to accumulate in the evaporator, the operating conditions of the entire system drift and operation at design conditions is not possible. The main way to deal with water accumulation is to drain it periodically (or continuously) into the absorber. However, this method represents a loss of efficiency in two ways. First, the water was evaporated in the desorber, requiring desorber heat input, but it does not evaporate in the evaporator; thus, it does not provide cooling capacity. Second, it contains a considerable amount of ammonia that is drained as liquid, amplifying this effect. Several methods to deal with water volatility and its effect on performance are discussed in this chapter. Example 9.1: Evaporator Temperature Glide In the desorber of an NH3/H2O absorption system, the rich solution enters at a temperature of 150°C and a mass fraction of 0.3. The vapor produced in this desorber is assumed to be in equilibrium with the incoming rich solution (liquid).
1. Determine the ammonia mass fraction of the vapor produced by the desorber. 2. Assume that saturated liquid of the same ammonia mass fraction as the vapor leaving the desorber enters the evaporator and that the lowest temperature in the evaporator is Tevap = 0°C. What is the mass fraction of vapor in equilibrium with this liquid? 3. Assume that the evaporator outlet is a saturated two-phase mixture with a liquid mass fraction of 0.25. What is the temperature glide in the evaporator and the outlet vapor quality? 250
Pd = 25.9 bar
200 Temperature (°C)
150
d
100
e2 50 Pe = 3.7 bar 0 –50
e1 0
0.2
0.4
0.6
Mass fraction NH3
0.8
1
Single-Stage Ammonia/Water Systems
Solution: In this book, the properties of ammonia/water are evaluated using the ammonia/water routines in EES. Use of these routines is introduced in Appendix A (Section A.5). Numerous examples of their use are also provided in Chapter 3 and Appendix D as well as the extensive examples provided in Chapters 9 through 11 in the form of worked examples in the text accompanied by EES code for those examples. The solution is illustrated in the figure generated by the EES program, which shows bubble-point/dew-point curves for two pressure levels representing the desorber and evaporator. The upper set of curves, labeled Pd = 25.9 bar, is the pair for the desorber pressure. The specific conditions in this problem are illustrated by the horizontal tie line beginning at the specified condition of T = 150°C (labeled “d” in the right-hand margin). Let x and y indicate the mass fraction in the liquid and vapor, respectively.
1. From the specified conditions (Td = 150°C and xd = 0.3), we can determine the desorber pressure and the equilibrium vapor mass fraction from ammonia/ water property routines as
Pd = P (Td, xd, saturated liquid) yd = y (Td, Pd, saturated vapor)
The equilibrium vapor concentration is shown in the figure generated by the EES program, as the intersection of the horizontal tie line labeled “d” with the dew line. 2. It is assumed that the vapor leaving the desorber is completely condensed such that the liquid entering the evaporator is at the concentration xe1 = y d(note that the possible flashing process is ignored here). If the lowest temperature in the evaporator is Te1 = 0°C, then the evaporator pressure can be determined as
Pe = P (Te1 , xe1, saturated liquid)
The corresponding equilibrium vapor concentration is
y e1 = y (Te1 , Pe, saturated vapor)
3. As the evaporation process progresses at constant pressure starting from 0°C, the evaporation temperature increases as the ammonia fraction decreases. If we assume that the process in the evaporator is in equilibrium throughout and that the process ends when the liquid mass fraction reaches 0.25, then the process runs from the temperature level e1 to e2 on the diagram. The temperature at e1 is given. We can determine the temperature at e2 as
Te2 = T (Pe, x = 0.25, saturated liquid) and
Tglide = Te2 − Te1
With the known mass fractions of all streams entering and leaving the evaporator, the vapor quality at the outlet can be determined from a mass balance. The results are summarized in Table 9.1, and the solution is provided in file Ex9_1.ees.
For this mixture (ammonia/water) where both components have significant volatility, the evaporator normally will have a liquid outlet (as in this example) to minimize the temperature glide. This is sometimes called blow down. You can experiment with this issue by re-solving this problem with a range of liquid outlet mass fractions. Note that
191
192
Absorption Chillers and Heat Pumps
TABLE 9.1 Data for Example 9.1 Showing Evaporator Temperature Glide Desorber (d) Evaporator inlet (e1) Evaporator outlet (e2)
T (°C)
P (bar)
x, Liquid
y, Vapor
Vapor Quality
150 0 77.5
25.9 3.7 3.7
0.3 0.853 0.25
0.853 1.0 0.915
1 0 0.907
the mass fraction must be greater than approximately x = 0.2 to allow a mass balance to be possible. The value x = 0.2 is the saturated liquid mass fraction corresponding to the entering vapor mass fraction (y = 0.853) at 0°C. The maximum temperature glide occurs when the liquid outlet mass fraction is x = 0.2 and the vapor quality is 1 (no liquid out). A key assumption in this analysis is that the two-phase outlet is in vapor/liquid equilibrium. This is an idealization, but it is possible to approach it through thoughtful component design. In particular, it would be necessary to bring the liquid and vapor streams into mass transfer contact to encourage equilibration. Another important note is that the vapor produced at each position along the evaporator is at a different mass fraction due to the changes in temperature and liquid mass fraction. Thus, when a single value is specified for the outlet vapor state, a well-mixed condition is assumed. This is also an idealization that can only be approached in practice.
One way of reducing the water content of the vapor is to use rectification or dephlegmation (Bosnjakovic 1965). In concert with the rectifier, the condensate precooler presents an opportunity to utilize the large temperature glide that exists in the evaporator when water is present. These measures are addressed in Sections 9.4 and 9.5.
9.4 Simple Single-Stage Ammonia/Water System As a starting point for the analysis of ammonia/water absorption cycle design options, the cycle shown in Figure 9.3 is considered. This cycle is similar to the single-stage water/ lithium bromide cycle, with the important difference that a rectifier is added to deal with the water in the vapor leaving the desorber. The performance calculation for this cycle is shown in the following example. Example 9.2: Simple Single-Stage Ammonia/Water System The objective is to calculate the performance of the simple single-stage ammonia/water absorption system shown in Figure 9.3. The evaporator outlet saturation temperature is –10°C with two-phase fluid leaving at a vapor quality of 0.975 (a small liquid fraction at the outlet reduces the evaporator temperature glide). The mass flow rate of solution through the solution pump is 1 kg/sec. The temperature of the saturated liquid streams leaving both the absorber and the condenser is 40°C. The difference in ammonia mass fraction of the two solution streams (i.e., x1 – x4) is 0.10. Assume an ideal rectifier that produces vapor with an ammonia mass fraction of 0.9996. Assume that the pump efficiency is 100% (isentropic pump) and that the effectiveness of the solution heat exchanger is 80%. Assume that the only components that have pressure losses are the two valves. The solution to this example is provided in file Ex9_2.ees.
193
Single-Stage Ammonia/Water Systems
Rectifier
Condenser
7
9
˙ Q cond
˙ Q rect
8
Desorber
4
3 ˙ Q des
10 2 Expansion device 12
Pump 1 13
˙ Q evap
Evaporator
5
6
˙ Q abs
Solution heat exchanger
Expansion device
Absorber
FIGURE 9.3 Simple single-stage ammonia/water cycle with rectifier.
Find: The cooling coefficient of performance (COP), all heat transfer rates, and the pump power. Solution: The solution begins by processing all of the information provided in the problem statement. Referring to Figure 9.3 for the location of states, the temperature at state 13 is –10°C, and the temperatures at states 1 and 10 are both 40°C. The ammonia mass fraction at state 9 is 0.9996. The quality of state 13 is 0.975. The quality at states 1, 4, 8, and 10 are all 0 (saturated liquid), and the quality at states 7 and 9 are both 1.0 (saturated vapor). Since pressure losses are neglected in this analysis, there are only two pressure levels in this cycle and pressure changes occur only across the valves and the pump. The low pressure is fixed by the saturation conditions at the evaporator exit (state 13), which is known through property relations since the temperature, overall mass fraction, and quality at state 13 are specified. Plow = Psat(T13, x13, Q13) The high pressure is fixed by the saturation conditions at the condenser exit (state 10). Phigh = Psat(T10, x10, liq) In practice, the ammonia mass fractions throughout an absorption cycle are determined by the operating conditions and the component designs. In this example, the vapor mass fraction leaving the rectifier (state 9) is specified. The mass fraction of the ammonia-rich stream (states 1, 2, and 3) is determined by the given absorber temperature and the evaporator pressure. xrich = xsat(T1, Plow, Q1) The mass fraction of the ammonia-poor stream (states 4, 5, and 6) is determined by the specified difference between the rich and poor streams. xpoor = xrich − ∆x where ∆x = 0.1 is given. Thus, in the following, it is assumed that the pressures and the mass fractions are known throughout the cycle.
194
Absorption Chillers and Heat Pumps
The next step is to write an overall mass balance, an ammonia mass balance, and an energy balance on each component. As there are loops in this cycle, these balances are coupled and the equations will need to be solved simultaneously. These balances are described at some length in Appendices B and D and the EES code (Ex9_2.ees) lists all of the equations in the model. A major difference between the water/lithium bromide cycles discussed in Chapters 6 through 8 and the ammonia/water cycle discussed here is the inclusion of a rectifier. For the models discussed in Chapter 9, an ideal rectifier is assumed. An ideal rectifier is one that is thermodynamically reversible. One requirement for an ideal rectifier is that the counterflowing vapor and liquid at the desorber end (states 7 and 8) must be in equilibrium. This is imposed on the model by requiring that T8 = T7 and that both states are saturated. Another set of constraints that the model imposes is specification of the vapor outlet temperature and mass fraction from the desorber (state 7). It is assumed that the vapor outlet is in equilibrium with the mass fraction of liquid solution entering the desorber (state 3). Taken together with the ideal rectifier model, this can be simply written as x8 = x3. As is true for absorption cycle mass balances in general (see Appendix B), this cycle has redundant mass balances if you include the mass balances on all of the components. In this cycle, there are two redundant mass balances. To account for this, the absorber mass balances are not included as model equations. Instead, the absorber mass balances are written as follows with an error term (∆m, ∆a)
13 + m 6 = m 1 + ∆m m
13 x13 + m 6 x6 = m 1x1 + ∆a m The values of ∆m and ∆a will be zero if the absorber mass balances are exactly satisfied. This formulation omits the redundant equations but allows verification that the balances are satisfied. A summary of the model solution is provided in Table 9.2, which shows the statepoint properties, the energy rates, and the COP. Discussion:
1. The rectifier outlet vapor mass fraction (point 9) specified in the problem statement would ideally be pure ammonia to eliminate temperature glide in the evaporator. However, practical systems typically reduce the rectifier size and allow a small fraction of water in the vapor. The specified value used here is an arbitrary value, and the model allows the cycle performance to be calculated over a range of values to see the effect on performance. 2. The evaporator outlet is a two-phase state with a vapor quality of 0.975. The need for liquid at the outlet (blow down) from the evaporator was discussed in Example 9.1. Even with this liquid outlet, there still exists a small temperature glide of 0.4 K between points 12 and 13. 3. Based on experience with flashing, the temperature might be expected to drop slightly as the solution is expanded in the expansion valve from points 5 to 6. However, in this case, the temperature is seen to increase as a consequence of the fact that the liquid enters the valve with sufficient subcooling so that no flashing occurs. The mechanical energy dissipated in the valve is converted to thermal energy, causing a small temperature increase. This type of effect is more pronounced in ammonia/water compared to lithium bromide/water due to the large pressure change.
195
Single-Stage Ammonia/Water Systems
TABLE 9.2 State Points for the Ammonia/Water System of Example 9.2 and Figure 9.3 (Ex9_2.ees) State Points 1 2 3 4 5 6 7 8 9 10 11a 12 13
h (J/g)
(kg/sec) m
P (kPa)
–49.8 –48.3 209.6 358.9 58.3 58.3 1516.9 230.1 1310.3 190.7
1.000 1.000 1.000 0.8578 0.8578 0.8578 0.1526 0.01047 0.1422 0.1422
286.4 1556 1556 1556 1556 286.4 1556 1556 1556 1556
190.7 1224.3
0.1422 0.1422
286.4 286.4
Vapor Quality
T (°C)
x (kg/kg)
1.0 0.0 1.0 0.0
40.0 40.1 97.5 124.2 56.9 57.2 101.9 101.9 45.1 40.0
0.3962 0.3962 0.3962 0.2962 0.2962 0.2962 0.9582 0.3962 0.9996 0.9996
0.1828 0.975
–10.4 –10.0
0.9996 0.9996
0.0
0.0
Summary of Energy Quantities W p Q
Pump power Solution HX heat transfer rate
257.9 kW
Q abs Q
Absorber heat transfer rate
273.9 kW
Rectifier heat transfer rate
42.8 kW
Q des Q
Desorber heat transfer rate
327.5 kW
shx
rect
Condenser heat transfer rate
159.2 kW
Q evap
Evaporator heat transfer rate
146.9 kW
COP
Cycle coefficient of performance
cond
a
1.5 kW
0.447
State point 11 is left blank to maintain numbering consistency with sub sequent examples.
4. The calculated COP is 0.447, which is somewhat lower than the typical water/ LiBr value of 0.7. This lower COP can be traced to several factors including (1) low evaporator temperature, (2) rectifier heat loss, (3) increased flashing losses in the valve, and (4) increased losses in the solution heat exchanger. These factors can be minimized by some of the design options discussed in this chapter.
The performance of an actual absorption chiller with the components in Figure 9.3 may not be as good as calculated in Example 9.2. The effectiveness of the solution heat exchanger may not be as high as 0.8; there are also pressure drops in the heat exchangers, losses in rectification, and a less efficient pump. Problem 9.2 at the end of this chapter is an exercise to compute the effect of these losses on performance. Another source of performance degradation is the fact that the solution in the absorber has to be subcooled to a certain degree to provide a temperature-driving potential for the absorption process. Similarly, the vapor in the desorber may be superheated. Both effects degrade the heat exchange process. On the other hand, there are a number of ways of increasing the performance of a singlestage absorption system that are explored next.
196
Absorption Chillers and Heat Pumps
9.5 Measures to Improve Single-Stage Performance There are several opportunities to considerably improve the performance of the absorption system of Section 9.4. All measures that are discussed here apply in principle to all absorption systems, single stage or multistage, and independent of the fluids used. However, depending on the application and the challenges involved in introducing additional heat exchangers, only some of these features are practical for any given design application. All measures that lead to performance improvements have an important feature in common. They all are based on minimizing thermodynamic losses within the cycle, and the simplest way to accomplish this is to reuse heat within the cycle. This is often referred to as “internal heat exchange.” One important example of internal heat exchange that has already been introduced is the solution heat exchanger, which uses hot solution leaving the desorber to preheat the cold solution on its way to the desorber. Through this “heat integration” the external heat required to run the desorber is reduced and thus the performance of the cycle is increased (in addition, the absorber heat is reduced). The solution heat exchanger is the biggest opportunity for internal heat exchange in most cycles. However, there are several other interesting opportunities for internal heat exchange, which are discussed next. The following set of examples shows the influence of the various options. First, the effect of the condensate precooler on cycle performance is examined in Example 9.3 by extending Example 9.2. That is followed by Example 9.4, which looks at the combined effects of the rectifier and condensate precooler. Example 9.5 employs rectifier heat integration, and Example 9.6 adds absorber solution recirculation. 9.5.1 Condensate Precooler The condensate precooler (sometimes called a refrigerant heat exchanger), shown in Figure 9.4, subcools the refrigerant that leaves the condenser using the cooler stream Condenser Expansion device 10
Rectifier
9
˙ Q cond
˙ Q rect
2
11
Pump 13
Evaporator ˙ Qevap
8
Desorber
4
3 ˙ Q des
Condensate precooler
12
7
5
1 14
6
˙ Q abs
Absorber
FIGURE 9.4 Ammonia/water absorption cycle with a condensate precooler.
Solution heat exchanger
197
Single-Stage Ammonia/Water Systems
exiting the evaporator, thereby heating the stream entering the absorber. It can be useful in two distinct ways, as modeled in Examples 9.3 and 9.4. The less complex benefit is modeled in Example 9.3, where it can be seen that the condensate precooler reduces the enthalpy of the condensate, thus reducing the enthalpy at the evaporator inlet. Since the enthalpy at the evaporator outlet is unchanged, the cooling capacity per unit mass of working fluid is increased, yielding a performance benefit. Possible disadvantages of the condensate precooler include the following. The fact that the vapor entering the absorber has more energy leads to increased absorber heat transfer, meaning that the absorber must increase in size to maintain the same performance. Also, the condensate precooler causes an additional pressure drop requiring either (1) a higher evaporator pressure, (2) a lower heat rejection temperature in the absorber, or (3) lower ammonia mass fractions of the solution streams, which in turn will lead to higher desorber temperatures. Nevertheless, in ammonia/water systems, a condensate precooler usually provides a net performance benefit. A second benefit that comes from the condensate precooler has to do with water management in the evaporator. When the ammonia vapor purity leaving the rectifier is not very high, then the evaporator temperature glide (defined as the difference in temperature between the outlet and inlet of the evaporator) can be considerable, as shown in Figure 9.5. In the figure, the evaporator inlet ammonia mass fraction is assumed to be 0.99. Even with a water content of only 1%, the temperature glide associated with the evaporation process is greater than 10 K for vapor qualities greater than 0.96. This shows that the glide can be minimized by allowing some liquid at the evaporator exit, but the presence of the liquid degrades cycle performance because the liquid has to be boiled out of the desorber while it provides no refrigeration. The best option for dealing with the water is to evaporate the liquid at the evaporator exit in a condensate precooler. The condensate precooler provides both water management and a performance benefit due to increased cooling load in the evaporator. By providing a method for water management, the condensate precooler can reduce the requirement for a high-performance rectifier and thus increase cycle performance in several ways. The flow 50
Fluid pair: Ammonia/water Pressure = 4 bar Ammonia mass fraction = 0.99
Temperature glide (K)
40 30 20 10
0
0.2
0.4 0.6 Evaporator exit quality
0.8
1
FIGURE 9.5 Evaporator temperature glide as a function of exit quality for an overall inlet mass fraction of 0.99 at 4 bar.
198
Absorption Chillers and Heat Pumps
path in the condensate precooler can be traced in Figure 9.4. The liquid leaving the condenser is being subcooled, while the vapor leaving the evaporator is heated. Any liquid droplets contained in the vapor stream at state 13 are evaporated in the condensate precooler such that state 14 is superheated vapor. Example 9.3: Condensate Precooler Reevaluate the performance of the absorption system of Example 9.2. All operating conditions remain the same, except that the cycle now includes a condensate precooler, as shown in Figure 9.4, with an effectiveness of 0.8. The solution to this example is provided in Table 9.3 and in file Ex9_3.ees. Find: The cooling COP, all heat transfer rates, and the pump power. Solution: The solution to this problem is very similar to that for Example 9.2. The main difference is the condensate precooler, which is modeled with a specified effectiveness. The addition of the condensate precooler requires the addition of TABLE 9.3 State Points for the Ammonia/Water System of Example 9.3, Which Includes a Condensate Precooler (Ex9_3.ees) State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
–49.8 –48.3 209.6 358.9 58.3 58.3 1516.9 230.1 1310.3 190.7 63.2 63.2 1224.3 1351.8
1.000 1.000 1.000 0.858 0.858 0.858 0.153 0.010 0.142 0.142 0.142 0.142 0.142 0.142
286.4 1555.7 1555.7 1555.7 1555.7 286.4 1555.7 1555.7 1555.7 1555.7 1555.7 286.4 286.4 286.4
Vapor Quality 0.0
0.0
1.0 0.0 1.0 0.0 0.085 0.975 1.0
T (°C)
x (kg/kg)
40.0 40.1 97.5 124.2 56.9 57.2 101.9 101.9 45.1 40.0 13.6 –10.4 –10.0 30.0
0.3962 0.3962 0.3962 0.2962 0.2962 0.2962 0.9582 0.3962 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996
Summary of Energy Quantities W p
Pump power
Q shx
Heat transfer rate in solution HX
257.9 kW
Q abs
Heat transfer rate in absorber
292.0 kW
Q rect
Heat transfer rate in rectifier
42.8 kW
Q des
Heat transfer rate in desorber
327.5 kW
Q cond
Condenser heat transfer rate
159.2 kW
Q evap
Evaporator heat transfer rate
165.1 kW
Q pc
Heat transfer rate in precooler
18.1 kW
COP
Cycle coefficient of performance
1.5 kW
0.502
Single-Stage Ammonia/Water Systems
199
states 11 and 14, as shown in Figure 9.4. The properties at each state and a summary of the energy quantities are shown in Table 9.3. Discussion: An inspection of Table 9.3 and comparison to Table 9.2 reveals the following observations:
1. The enthalpy of the condensate drops by approximately 127.5 J/g, while the evaporator outlet stream picks up the same amount of energy. The temperature of the condensate is reduced by 26 K, while the temperature of the vapor increases by 40 K. Thus, most of the transferred energy contributes to raising the temperature of the vapor since there was only a small amount of liquid left at the evaporator outlet that requires evaporation. If the state at 13 were all vapor, then the vapor temperature would increase by approximately twice the amount by which the condensate temperature drops because the specific heat of the vapor is about half that of the liquid. 2. The only changes in the cycle state points occur around the condensate precooler (all others are not affected and are the same as in Example 9.2). 3. The COP increases from 0.447 to 0.502 (12%) due to an increase in the evaporator capacity of 18.2 kW. That energy must be rejected in the absorber where the heat transfer rate increases by 6.6%. This is because the cold vapor entering from the evaporator is no longer available to contribute to absorber cooling and thus more external cooling must be supplied. 4. The internal models discussed in this chapter can be expanded to include heat transfer models for the external components. A modified version of Example 9.3 is modeled in file Ex9_3_UA.ees, where each of the four main components is modeled with a UA model for the heat exchange process.
An ideal condensate precooler always improves the COP in an absorption system, while in vapor compression systems its benefits are often overwhelmed by performance penalties in the compressor resulting from the higher temperature inlet. In water/lithium bromide systems, the condensate precooler is seldom employed because it is a major design challenge to develop such a heat exchanger without incurring significant pressure drop penalties on the vapor side. Ammonia/water is more amenable to a condensate precooler because the pressures are much higher and the sensitivity to pressure drops is much lower. Under certain operating conditions, the advantage provided by the condensate precooler increases when a less effective rectifier is used. An introduction to these issues is presented in Example 9.4. Example 9.4: Examine Effects of Condensate Precooler and Rectifier Reevaluate the performance of the two cycles modeled in Examples 9.2 and 9.3, holding all operating conditions the same except that the mass fraction of the ammonia vapor leaving the rectifier is set to 0.99 (point 9) and the vapor quality at the evaporator exit is 0.95 (point 13). This example demonstrates the importance of both the condensate precooler and the rectifier in the ammonia/water absorption cycle and demonstrates some synergy between these components. Only two changes are required to Examples 9.2 and 9.3 to do the calculations and that is to change the ammonia mass fraction at state 9, x9, from 0.9996 to 0.99 and to change the vapor quality at state 13, Q13, from 0.975 to 0.95. To preserve the original files, it is recommended that the two EES files be renamed before changing the input values. A summary of key parameters is provided in Table 9.4. The first two columns of data are taken directly from Examples 9.2 and 9.3. The remaining columns are from new simulations.
200
Absorption Chillers and Heat Pumps
TABLE 9.4 Combined Effects of Condensate Precooler and Rectifier Using an Internal Model Q 13 = 0.975 x 9 = 0.9996
Q 13 = 0.95
x 9 = 0.99
x 9 = 0.9996
x 9 = 0.99
Precooler
w/o
w/
w/o
w/
w/o
w/
w/o
w/
Plow (kPa) Phigh (kPa) Tglide (K) T12 (°C) xpoor xrich T4 (°C) T7 (°C) x7 Q12 Tvalve inlet (°C) 12 (kg/sec) m
286 1556 0.4 –10.4 0.296 0.396 124.2 101.9 0.958 0.183 40 0.142
286 1556 0.4 –10.4 0.296 0.396 124.2 101.9 0.958 0.085 13.6 0.142
132 1540 17.7 –27.7 0.180 0.280 152.6 127.6 0.873 0.233 40 0.123
132 1540 17.7 –27.7 0.180 0.280 152.6 127.6 0.873 0.132 11.3 0.123
288 1556 0.2 –10.2 0.297 0.397 124.0 101.7 0.959 0.182 40 0.142
289 1556 0.2 –10.2 0.297 0.397 124.0 101.7 0.959 0.059 6.6 0.142
234 1540 4.9 –14.9 0.264 0.364 131.5 108.4 0.942 0.196 40 0.138
234 1540 4.9 –15.0 0.264 0.364 131.5 108.4 0.942 0.071 5.4 0.138
Q evap (kW)
146.9
165.1
129.7
146.8
142.5
165.3
138.6
161.3
Q rect (kW) Q (kW)
42.8
42.8
63.8
63.8
42.6
42.6
33.2
33.2
327.5
327.5
371.5
371.5
327.1
327.1
336.3
336.3
des
Q pc (kW) COP
—
18.1
—
17.0
—
22.8
—
22.7
0.447
0.502
0.348
0.393
0.433
0.503
0.410
0.478
Note: w/o, without precooler; w/, with precooler.
Discussion:
1. When the mass fraction at point 9 is decreased from 0.9996 to 0.99 (i.e., when the water content at point 9 increases), it is equivalent to using a less effective rectifier. The presence of the additional water in the evaporator has a major impact on the evaporator/absorber pressure, which impacts the solution loop and changes conditions throughout the cycle. 2. For an evaporator exit quality of 0.975, the temperature glide in the evaporator increases from 0.4 to 17.7 K when the water fraction increases. Correspondingly, the lowest temperature in the evaporator decreases from –10.4°C to –27.7°C. The temperature glide is considerably reduced when more liquid is in the evaporator exit stream, and the lowest temperature is considerably increased. 3. For an evaporator exit quality of 0.975, the rectifier heat increases; this appears counterintuitive but can be traced to the changed conditions in the desorber such that the water content in the vapor exiting the desorber is much higher when the water content at point 9 is higher. The temperature at the desorber outlet is also higher, which impacts both the desorber and rectifier heats. However, for the case where the exit quality is 0.95, the rectifier heat decreases when the vapor purity decreases. These differences ultimately trace to the properties of the working fluids. They indicate the importance of parametric studies over multiple variables for a complete understanding of design variable interactions.
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Single-Stage Ammonia/Water Systems
4. For an evaporator exit quality of 0.975, the performance benefit of the condensate precooler is ~12.5% with slightly larger benefit for the case with more water in the evaporator. When the vapor fraction at the outlet decreases to 0.95, the benefit due to the condensate precooler increases to ~16%. 5. For an evaporator exit quality of 0.975, the COP decreases significantly when the water content at point 9 is higher due to the combined effects of increased desorber heat and decreased evaporator heat. The decreased evaporator heat is traced to two primary factors: (1) reduced flow rate in the evaporator (13% reduction) and (2) increased flashing across the valve so that less liquid arrives at the evaporator (~5% reduction). The increased load in the desorber is traced to (1) an increased subcooling of the incoming liquid stream at point 3 (7.5% increase) and (2) an increase in the energy of the vapor stream leaving the desorber (6.5% increase). For an evaporator exit quality of 0.95, the same trends exist but the effects are all reduced in magnitude. 6. A similar analysis done using a UA model (file Ex9_3UA.ees) found very similar conclusions, although with many differences in the details. The results are summarized in Table 9.5. The UA values and water loop flow rates used can be found in the EES file. The largest difference between the two analyses is that with the UA analysis, changes in x9 have a smaller effect on performance. Instead of fixed internal temperatures and mass fraction difference in the solution loop, the UA model distributes the changes throughout the cycle. One interesting difference is that the rectifier and desorber heat transfer rates decrease for the case with x9 = 0.99 for both values of evaporator exit quality. The differences between the
TABLE 9.5 Combined Effects of Condensate Precooler and Rectifier Using UA Model Q 13 = 0.975 x 9 = 0.9996
Q 13 = 0.95
x 9 = 0.99
x 9 = 0.9996
x 9 = 0.99
Precooler
w/o
w/
w/o
w/
w/o
w/
w/o
w/
Plow (kPa) Phigh (kPa) Tglide (K) T12 (°C) xpoor xrich T4 (°C) T7 (°C) x7 Q12 Tvalve inlet (°C) 12 (kg/sec) m
288 1573 2.4 –10.2 0.298 0.400 124.4 101.7 0.959 0.184 40.4 0.145
278 1562 0.4 –11.1 0.294 0.392 125.0 103.0 0.956 0.087 13.4 0.139
192.9 1440 18.0 –19.4 0.262 0.342 128.6 110.1 0.932 0.201 37.6 0.109
190 1437 18.0 –19.8 0.260 0.338 129.0 110.9 0.929 0.113 12.8 0.106
291 1577 0.2 –10.0 0.299 0.402 124.2 101.3 0.960 0.184 39.4 0.157
279 1562 0.2 –11.0 0.294 0.392 125.0 102.9 0.956 0.061 6.3 0.140
263 1474 5.1 –12.2 0.284 0.386 124.5 101.7 0.955 0.182 38.4 0.152
253 1467 5.0 –13.1 0.280 0.377 125.3 103.2 0.952 0.068 6.2 0.146
Q evap (kW)
149.5
161.8
117.8
127.1
146.5
162.0
146.3
160.5
Q rect (kW)
43.1
43.2
30.9
31.1
43.0
43.2
26.6
27.6
Q des (kW) Q (kW)
332.1
325.0
289.2
284.7
334.2
325.2
331.2
322.7
pc
—
18.0
—
12.6
—
22.6
—
21.0
COP
0.448
0.495
0.405
0.444
0.436
0.496
0.440
0.495
Note: w/o, without precooler; w/, with precooler.
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Absorption Chillers and Heat Pumps
internal and UA models is traced to changes in the mass fractions in the solution loop, and the UA model results are expected to be closer to reality than those from the internal model. However, it should be noted that the UA values and water loop flow rates that were used were not optimized and thus the results presented are just one somewhat arbitrary design point.
The presence of the condensate precooler provides a substantial boost in performance (10%–16% in the cases shown in Tables 9.4 and 9.5). The benefit from the condensate precooler is a strong function of the evaporator outlet quality. Thus, it is observed that an optimized condensate precooler can compensate for the presence of water in the stream leaving the rectifier. The large temperature glide can be avoided by allowing a liquid fraction at the evaporator exit, and the energy penalty that this would otherwise impose can be largely canceled by internal heat transfer in the condensate precooler. A well-designed ammonia/water absorption system requires a careful analysis of the tradeoffs between the use of the rectifier and that of the condensate precooler. The examples covered so far do not discuss all of the possibilities for performance improvement. There are several more opportunities for heat integration that are considered next. 9.5.2 Rectifier Heat Integration When designing the solution heat exchanger, it can be observed that the heat capacity rates of the two streams do not match perfectly. Typically, the stream leaving the absorber has the higher mass flow rate and therefore a higher capacitance rate than the stream leaving the desorber. This imbalance can be compensated by having the rich solution leaving the absorber circulate through the rectifier as coolant before entering the solution heat exchanger, as shown in Figure 9.6. In this way, the rectifier heat is utilized within the system instead of being rejected to a heat sink outside of the absorption system. This internal heat exchange can be an important means of performance improvement. The following example demonstrates this alternative. Condenser Expansion device 10
Pump 13
Evaporator ˙ Qevap
5
1 14
6 ˙ Q abs
Absorber
FIGURE 9.6 Single-stage ammonia/water cycle with integrated rectifier.
Desorber
4
3 ˙ Q des
16
2
11
7 8
˙ Q cond
Condensate precooler
12
Rectifier
9
Solution heat exchanger
203
Single-Stage Ammonia/Water Systems
The solution of this example requires the addition of one new state point (16). Point 15 is skipped here but will show up in a subsequent example. The rectifier heat is calculated as before according to the ideal rectifier model. The rectifier heat exchange process is not modeled explicitly here; for simplicity, it is assumed that all of the rectifier heat is added to the solution stream. The remainder of the cycle model is identical to that of Example 9.3. The potential advantage of rectifier heat integration comes about when the solution leaving the solution heat exchanger at point 3 is subcooled. If there is a need for energy to bring stream 3 up to the saturation temperature, then rectifier heat integration makes sense. The solution to this example is provided in file Ex9_5.ees, and the properties at each state and a summary of the energy quantities are shown in Table 9.6. Example 9.5: Rectifier Heat Integration Consider the absorption system of Example 9.3 but use a value of x9 = 0.99. Now use the rectifier heat to preheat the rich solution before it enters the solution heat exchanger, as in Figure 9.6. The solution to this example is provided in file Ex9_5.ees. TABLE 9.6 State Points for the Ammonia/Water System of Example 9.5 Including Rectifier Heat Integration (Ex9_5.ees) State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 16
–8.3 –6.7 359.5 539.4 194.4 194.4 1675.6 380.2 1415.5 183.6 45.7 45.7 1234.4 1372.3 57.1
1.000 1.000 1.000 0.877 0.877 0.877 0.148 0.024 0.123 0.123 0.123 0.123 0.123 0.123 1.000
131.9 1540 1540 1540 1540 131.9 1540 1540 1540 1540 1540 131.9 131.9 131.9 1540
Vapor Quality 0.000
0.000 0.024 1.000 0.000 1.000 0.000 0.132 0.975
T (°C)
x (kg/kg)
40.0 40.1 123.2 152.6 74.5 64.1 127.6 127.6 76.6 40.0 11.3 –27.7 –10.0 30.0 55.0
0.2801 0.2801 0.2801 0.1801 0.1801 0.1801 0.8726 0.2801 0.9900 0.9900 0.9900 0.9900 0.9900 0.9900 0.2801
Summary of Energy Quantities W p
Pump Power
Q shx
Heat transfer rate in solution HX
302.4 kW
Q abs
Heat transfer rate in absorber
348.1 kW
Q des
Heat transfer rate in desorber
351.9 kW
Q cond
Condenser heat transfer rate
152.1 kW
Q evap
Evaporator heat transfer rate
146.8 kW
Q pc
Heat transfer rate in precooler
17.0 kW
COP
Cycle coefficient of performance
1.58 kW
0.415
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Absorption Chillers and Heat Pumps
Discussion: An inspection of Table 9.6 and a comparison of the summary results to those in the last data column in Table 9.4 reveal the following observations:
1. The COP is increased from 0.393 to 0.415 (5.6%) by rectifier heat integration. By using the rectifier heat internally, the heat load of both the solution heat exchanger and desorber are decreased, and the absorber heat rejection rate is increased. The desorber heat transfer rate is reduced because the rich solution stream enters with more energy. The heat rate in the solution heat exchanger decreases because the driving temperature difference decreases as the rectifier heat raises the temperatures in the rich solution stream. The absorber heat transfer rate increases because the solution heat exchanger transfers less energy out of the poor solution stream. Thus, the heat from the rectifier ultimately gets rejected from the cycle, but now this occurs at a lower temperature in the absorber. In the case selected here, the improvement is modest. There are other operating conditions under which rectifier integration can lead to more dramatic effects. 2. The potential for rectifier heat integration is generally limited by the amount of subcooling at state 3. If the rectifier heat transfer rate exceeds the heat transfer rate needed to achieve a saturated inlet solution, then that extra heat cannot be utilized effectively in this manner. 3. It is a useful exercise to compute the log mean temperature difference of the rectifier heat exchange process to confirm that it is practical. In this case, the result is ∆Tlm = 52.5 K, which is promising. It can be observed that the temperature match is not perfect with a temperature difference of 72.6 K at the hot end and only 36.5 K at the cold end. This issue can be partially addressed, as discussed in the next section. 4. As a check on the model assumptions, the saturation temperature associated with the desorber pressure and the mass fraction of the rich solution stream was calculated from the property routines as 127.6°C. The actual calculated temperature at point 3 is 123.2°C. Thus, in this case, all of the rectifier heat can be utilized to heat the rich solution.
9.5.3 Solution Recirculation In some instances, it is desirable to allow a large concentration change in the solution loop, which implies a large temperature glide in both the absorber and the desorber. This change has several consequences. The pump flow rate and pump power requirements are reduced. In addition, the absorber can operate with a smaller cooling water flow rate and heat the cooling water to higher temperatures, which may be important in certain heat pump applications. It also can lead to a reduction in the size of the cooling tower if such a device is used. Furthermore, the desorber outlet temperature of the poor solution increases. Thus, the benefit in the absorber is paid for by an increased temperature of the heat supplied to the desorber. The imbalance in the solution heat exchanger is increased. As a result of the reduced pump flow rate and assuming that the vapor flow rate through the condenser and evaporator remains constant, the difference between the two solution flow rates in the solution heat exchanger increases, which increases not only the differences in the heat capacities of the two streams but also the temperature mismatch. A key observation in this case is that the liquid leaving the desorber is considerably warmer than that required for preheating the incoming rich solution. One way of taking advantage of this situation is to use the heat content of the poor solution that exits the desorber to further generate refrigerant vapor. For this purpose, the liquid line containing the poor solution can be recirculated in counterflow through the desorber, as shown in Figure 9.7, which shows the schematic of the solution loop of
205
Single-Stage Ammonia/Water Systems
Rectifier
Desorber
. Qdes
Solution heat exchanger Pump Expansion device . Qabs
Absorber
FIGURE 9.7 Solution recirculation in desorber (thick lines).
an absorption system with the new feature displayed in thicker lines. With this arrangement, the poor solution can approach the lowest desorber temperature before it enters the solution heat exchanger. In this way, the availability (exergy) in that solution stream can be utilized in the most efficient way. However, this method used by itself will not generally be beneficial because the internal heat exchange in the solution heat exchanger is usually limited by the heat capacity of the poor solution. Thus, reducing the heat content of the poor solution further will not help unless special operating conditions exist. One cycle where desorber solution recirculation is used is the Robur cycle described in Section 9.7. On the other hand, a similar type of solution recirculation can be used in the absorber, where the rich solution is preheated in the absorber before entering the solution heat exchanger or the rectifier, as shown in Figure 9.8. Solution recirculation in the absorber can be quite advantageous. Here the rich solution, after passing through the pump, reenters the absorber in a separate pipe and flows in countercurrent heat exchange with the absorbing solution. In this way, the solution is preheated by utilizing absorber heat. The next example shows the effect of solution recirculation on a single-stage system when it is applied in the absorber only. Example 9.6: Solution Recirculation in the Absorber Example 9.5 is used as the baseline, and solution recirculation is added in the absorber (with point 15 defined in Figure 9.8 and all remaining points identical to Figure 9.6). To demonstrate the effect most clearly, it is assumed that the solution leaving the absorber solution recirculation heat exchanger, after it has picked up additional heat, has reached the saturation temperature occurring in the absorber (i.e., the solution recirculation heat exchanger effectiveness is 100%). Minor changes to Example 9.5 are needed for this example. Examination of the properties for state 6 shows that it is a saturated state. The temperature at state 15 is set equal to the temperature at state 6, assuming a perfect heat exchanger. The energy added to the rich solution in the absorber solution recirculation heat exchanger will show up as a temperature increase from points 2 to 15. When the rectifier
206
Absorption Chillers and Heat Pumps
Rectifier
9
Desorber
7 8 3
4 ˙ Q des
16
15
Solution heat exchanger
5
2 Pump
Expansion device 6
1 14 ˙ Q abs
Absorber
FIGURE 9.8 Solution recirculation in absorber (thick lines).
heat is also added, the temperature at point 16 is substantially increased, which has the potential to significantly improve cycle COP under certain conditions. The solution to this example is provided in file Ex9_6.ees. The properties at each state and a summary of the energy quantities are shown in Table 9.7. Discussion:
1. The COP is increased from 0.415 to 0.467 (12.5% increase as compared to Example 9.5). 2. The heat load of the solution heat exchanger is decreased by about 30%, and the absorber heat rejection and the desorber heat requirement are each reduced by about 11%. The desorber heat load is reduced because the solution entering the desorber has more energy at the exit of the solution heat exchanger. The absorber heat load is reduced because a portion of the cooling is provided by the solution recirculation, but it is not quite that simple because stream at 6 enters with more energy due to changes in the solution heat exchanger. The load in the solution heat exchanger decreases because the solution temperature at point 16 is significantly higher when solution recirculation is used, causing a lower driving potential difference in the solution heat exchanger. 3. The absorber heat duty is reduced by 39.3 kW. This reduction is less than the amount of cooling provided by the solution stream (127.9 kW) because the incoming poor solution now has higher energy due to changes in the solution heat exchanger. While the total heat exchange area needed for the absorber (including area needed for both the external and internal heat exchanges) increases, that of the solution heat exchanger decreases by a similar amount.
207
Single-Stage Ammonia/Water Systems
TABLE 9.7 State Points for the Ammonia/Water System According to Figure 9.8 Using Rectifier Heat Integration and Solution Recirculation within the Absorber (Example 9.6) State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
–8.3 –6.7 398.8 539.4 295.5 295.5 1675.6 380.2 1415.5 183.6 45.7 45.7 1234.4 1372.3 121.2 185.0
1.000 1.000 1.000 0.877 0.877 0.877 0.148 0.024 0.123 0.123 0.123 0.123 0.123 0.123 1.000 1.000
131.9 1540 1540 1540 1540 131.9 1540 1540 1540 1540 1540 131.9 131.9 131.9 1540 1540
Vapor Quality 0.000 0.009 0.000 0.064 1.000 0.000 1.000 0.000 0.132 0.975
T (°C)
x (kg/kg)
40.0 40.1 128.8 152.6 98.1 69.8 127.6 127.6 76.6 40.0 11.3 –27.7 –10.0 30.0 69.8 84.5
0.2801 0.2801 0.2801 0.1801 0.1801 0.1801 0.8726 0.2801 0.9900 0.9900 0.9900 0.9900 0.9900 0.9900 0.2801 0.2801
Summary of Energy Quantities
W p
Pump power
Q shx
Heat transfer rate in solution HX
213.8 kW
Q abs
Heat transfer rate in absorber
308.8 kW
Q des
Heat transfer rate in desorber
312.5 kW
Q cond
Condenser heat transfer rate
152.1 kW
Q evap
Evaporator heat transfer rate
146.8 kW
Q pc
Heat transfer rate in precooler
17.0 kW
COP
Cycle coefficient of performance
1.58 kW
0.467
4. In this simulation, which is done without a heat exchanger model for the rectifier, the rectifier performance is not affected by the fact that the coolant, the rich solution, enters at a higher temperature. In practice, the rectifier performance would be expected to shift when the temperature of the coolant shifts. Thus, a more complete analysis of these effects would require a more detailed rectifier model.
Several options for reusing heat internally within the system were discussed in Chapter 9 examples. This internal heat exchange can be important for efficiency improvements, but the significance depends on the specific operating conditions. Not all of the measures discussed show benefits under all operating conditions. Solution recirculation, for example, is more effective with larger temperature glides. It would not be very beneficial in a typical LiBr/water system. Also, attempting to utilize both rectifier heat integration and absorber solution recirculation in the same design (as was done in Example 9.6) is not always feasible
208
Absorption Chillers and Heat Pumps
Absorber, externally cooled
Absorber, cooled by rich solution
FIGURE 9.9 Solution-cooled absorber.
because the rich solution has a limited need for energy. In most circumstances, only one of these two measures can be employed in a given cycle design. Solution recirculation, as shown in Figures 9.7 and 9.8, implies that three-path heat exchangers are employed. These devices are difficult to manufacture. An alternative is to utilize two separate two-path heat exchangers in parallel to replace, for example, the absorber. While this alternative is easier to implement from a hardware point of view, it poses considerable control challenges. The two-phase flow entering the absorber, as well as the incoming vapor stream, have to be split and supplied to both heat exchangers in parallel at the proper flow rates, which is an engineering challenge. An alternative that avoids both three-path heat exchangers and the problems of parallel flow is discussed next. 9.5.4 Solution-Cooled Absorber A simplified heat exchanger design that achieves many of the benefits of absorber solution recirculation is to utilize a so-called solution-cooled absorber. Here the absorber is split into two two-path heat exchangers, but they are arranged in series, as shown in Figure 9.9. The original externally cooled absorber is essentially unmodified. It rejects heat to an external sink not shown in Figure 9.9. However, the high-temperature end of the temperature glide is now accommodated within a second absorber that is exclusively cooled by the solution. This concept is utilized in the residential ammonia/water chiller that is described in Section 9.7 and Figure 9.10.
9.6 Comparison of Ammonia/Water and Water/Lithium Bromide When the performance of a single-stage ammonia/water system is compared to that of a water/lithium bromide system, it is found that for the same application (i.e., the same external temperatures), the water/lithium bromide system is more efficient (i.e., it has a higher COP). The reasons are hidden in the working fluid properties. Ammonia/water systems usually require a rectifier that is not needed in water/salt systems. Furthermore, the specific heat of the ammonia/water solution is about double that for water/salt systems. Thus, any inefficiency of the solution heat exchanger causes a larger penalty in ammonia/
209
Single-Stage Ammonia/Water Systems
Gas chiller and chiller-heater Air cooled cycle of operation—Solution pump type: 3-ton chiller models; chiller side of 3-ton chiller–heater models Refrigerant heat exchanger
Restrictor
Evaporator Restrictor
Chilled water
Water pump Restrictor
Leveling chamber and rectifier
Solution cooled absorber
Generator analyzer
Burner
Strong solution
Weak solution
Vapor refrigerant
Liquid refrigerant
Chilled water
Solution pump
FIGURE 9.10 Residential ammonia/water air conditioner with solution-cooled absorber. (Courtesy of Robur, Evansville, IN.)
water systems. This is also a disadvantage in the desorber, where sensible heat effects can be significant. Last, the latent heat of ammonia is about half as large as that of water. For the same cooling capacity, the ammonia/water system requires higher solution flow rates than water/salt systems. It can be shown that the term fr = cpT/∆hfg is a good measure for the relative efficiency of the absorption working fluids (Alefeld and Radermacher 1994), where a low value is a better fluid. cp is the specific heat of the liquid phase and ∆hfg is the latent heat of vaporization. The reason that fr is a useful index is that one of the most significant losses within an absorption system is the expansion process that the refrigerant undergoes before entering the evaporator. A lower liquid specific heat implies that less vapor has to evaporate to cool the liquid from the condenser temperature to the evaporator temperature. When less liquid is lost to subcooling effects, more liquid (refrigerant) is available to provide cooling capacity. In terms of fr, water/lithium bromide is the better working fluid pair compared to ammonia/water. For pure water and ammonia at 10°C, fr,amm = 1.076 and fr,wat = 0.478. This analysis does not address the water management issues that formed the bulk of the discussion in this chapter.
210
Absorption Chillers and Heat Pumps
9.7 Examples of Ammonia/Water Absorption Systems in Operation In this section, a short overview is presented of ammonia/water absorption systems that are actually built and in service today. In the range of small-capacity units for residential to small commercial air-conditioning applications, 5- and 30-ton (17 to 105 kW) units are manufactured and sold in the United States by Robur Corporation. Figure 9.10 shows a schematic of this absorption system. To describe it, let us start in the lower right-hand corner. This device is the solution pump. The membrane in the middle of the pump acts as a piston that moves the ammonia/water solution from the receiver through the inlet valve to the high-pressure side. The membrane itself is moved by applying pressure via oil (lower half of pump) from an oil pump (not shown) that is cycled from low- to high-pressure levels about once a second. From there, the rich solution flows through the rectifier (horizontal device above the solution pump) and then into the solution-cooled absorber. After being preheated in the solution-cooled absorber, the rich solution enters the desorber. This system does not employ a solution heat exchanger. As discussed later, the change of mass fraction is so large that the temperature glide in the absorber is capable of preheating the solution close to the desorber inlet temperature. The desorber in this figure is direct-fired. The burner is arranged vertically on the side of the desorber, and the flue gases flow across the finned surface of the desorber tank. The poor solution is picked up by a tube at the bottom of the desorber and recirculated through the desorber to the solution-cooled absorber. Instead of a solution heat exchanger, just solution recirculation in the desorber is employed. In the solution-cooled absorber, the poor solution drips over the tube coil of the rich solution while absorbing vapor and is collected at the bottom of the tank. It continues to flow together with the vapor that was not yet absorbed through two parallel passes into a coil, the aircooled absorber. Here the absorption process is completed and the heat rejected to the surroundings. The outlet of the air-cooled absorber is connected to the solution pump receiver. The ammonia vapor leaves the desorber and is forced across the rectifier where the heat of rectification is rejected to the rich solution and proceeds to the condenser. The condenser, housed within the same set of fins utilized by the air-cooled absorber, rejects the heat of condensation to the surroundings. The condensate emerges at the same location where the rich solution leaves the air-cooled absorber and circulates through the refrigerant precooler into the evaporator. The refrigerant evaporates inside the coil while the water to be chilled flows across the outside of the coil. The refrigerant vapor returns via the condensate precooler to the solution-cooled absorber. This design appears to be quite complex, but it has proven successful since the 1960s. A model of this cycle is included as file Robur.ees. Larger capacity single-stage ammonia/water systems are used in various industries, typically for waste heat recovery. Examples include the system in Figure 9.11, which is a 280 kW ersion, unit produced by Energy Concepts Co. (http://www.energy-concepts.com). In one v the unit produces refrigeration at –30°C and is fired by steam produced from burning biomass, with a COP of 0.45. Another example of a single-stage ammonia/water system is the 320 kW unit shown in Figure 9.12 produced by Colibri bv (http://www.colibri-bv.com). This unit is used in the dairy industry to provide refrigeration at –9°C using a hot water source in the range of 93°C–82°C.
Single-Stage Ammonia/Water Systems
211
FIGURE 9.11 Ammonia/water single-stage unit for refrigerated warehouse. (Courtesy of Energy Concepts, Annapolis, MD.)
FIGURE 9.12 Ammonia/water single-stage unit used in dairy industry. (Courtesy of Colibri, Vaals, The Netherlands.)
212
Absorption Chillers and Heat Pumps
Homework Problems 9.1 For the evaporator data given in Example 9.1, calculate and plot the temperature glide, as temperature versus enthalpy, to obtain a smooth curve for the temperature ranging from 0°C to 88°C. Discuss the shape of the curve. Based on the enthalpy values, estimate what fraction of the total heat of evaporation is available in the first 10 K of the temperature glide. 9.2 Reanalyze the absorption system of Example 9.3 with the following modifications. Account for the following nonidealities, at first individually, and then all of them combined, to obtain a more realistic performance prediction. a. The effectiveness of the solution heat exchanger is 0.7. b. The effectiveness of the condensate precooler is 0.7. c. The pump efficiency is 0.5. d. To provide a driving potential for the absorption process, assume that the temperature of the solution in the absorber is actually 2 K higher than assumed in the problem statement. e. Combine all of the aforementioned features into one model and find the COP, all heat exchange rates, and the pump work. 9.3 Based on Example 9.2, evaluate and plot the COP versus the effectiveness of the solution heat exchanger over the full range from 0.0 and 1.0. What is the difference in the heat capacities of the poor and rich solution streams? 9.4 Based on Example 9.3, evaluate and plot the COP versus the effectiveness of the condensate precooler. Then vary the purity of the vapor leaving the rectifier and discuss the influence the condensate precooler has on the overall system. 9.5 Expand Example 9.6 to include solution recirculation in both the desorber and the absorber, using heat exchanger approach temperatures as the parameter that describes the heat exchange process. Then vary the approach temperature for both independently and discuss the effects on COP and solution heat exchanger heat transfer rate. 9.6 Using Example 9.6 as the basis, analyze the change in COP when the difference in mass fraction between the poor and rich solution is varied from 0.01 to 0.25. Discuss and explain the system changes that this introduces and relate these changes to the COP changes. 9.7 Open-ended project: Write a program for the best possible single-stage ammonia/water system that includes all means to improve efficiency and plot the COP, desorber heat requirement, rectification heat, and cooling capacity as the evaporator temperature is changed from –10°C to 10°C.
References Alefeld, G. and R. Radermacher. (1994). Heat Conversion Systems. Boca Raton, FL: CRC Press. Bogart, M. (1981). Ammonia Absorption Refrigeration in Industrial Processes. Houston, TX: Gulf Publishing. Bojanowski, W. (1985). Some Serious Safety Problems Using Ammonia-Operational Experience and Recommendations. Int. J. Refrig. 8(1): 56–57.
Single-Stage Ammonia/Water Systems
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Bosnjakovic, F., translated by Blackshear, P. L., Jr. (1965). Technical Thermodynamics. New York: Holt, Rinehart and Winston. Erickson, D. C. (1991). Isaac Solar Refrigerator. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 237–242. Erickson, D. C. (1995). Waste-Heat-Powered Icemaker for Isolated Fishing Villages. ASHRAE Trans. 101(Part 1): 1185–1188. Howe, L. A., R. Radermacher, and K. E. Herold. (1989). Combined Cycles for Engine-Driven Heat Pumps. Int. J. Refrig. 12(1): 21–28. IPCS. (1990). Ammonia, Health and Safety Guide #37. World Health Organization. http://www.inchem. org/documents/hsg/hsg/hsg037.htm, accessed on 11/29/2015. Minato, K., S. Takagi, and K. Matsuki. (1991). Anticorrosive Method for Ammonia Absorption Refrigerating Cycle. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 249–254. Pentz, N. E., J. F. Metzger, H. Bonar, II, L. Molsbee, and J. Polhemus. (1983). A Guide to Good Practices for the Operation of an Ammonia Refrigeration System. International Institute of Ammonia Refrigeration, Paris.
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10 Two-Stage Ammonia/Water Systems As with water/lithium bromide systems, two-stage ammonia/water absorption systems offer the potential for increased efficiency (coefficient of performance) or increased temperature lift (difference between lowest temperature and the heat rejection temperature) compared to single-stage cycles. There are at least 26 different classes of two-stage absorption systems (Richter 1962; Alefeld and Radermacher 1994; Inoue et al. 1994), but only a relatively small number of these classes have been investigated in detail. In this chapter, three of the most common two-stage cycles are discussed to illustrate the challenges and the potential of multistage absorption systems using ammonia/water. For the sake of consistency, the definitions for “effect” and “stage” are stated once more. The term “two-stage” refers to the inclusion of two solution circuits in the system. The term “double effect” refers to a configuration in which a certain quantity of heat is used twice to generate refrigerant vapor. In general, two-stage systems can be thought of as being composed of two single-stage absorption systems. The staging allows for increased efficiency (double-effect) or for increased temperature lift (double-lift). Examples of staging for both of these objectives are discussed in this chapter.
10.1 Double-Effect Ammonia/Water Systems Figure 10.1 shows an example of a two-stage double-effect ammonia/water system. The left stage of Figure 10.1 is largely identical to the conventional single-stage system discussed in Chapter 9 (see Figure 9.4). It consists of a solution circuit with absorber, desorber, solution heat exchanger, rectifier, and pump, all labeled with a suffix “1.” In addition, it includes the condenser, refrigerant heat exchanger, and evaporator, which are shared by both stages. The second-stage solution circuit is labeled with suffix “2.” The two stages are coupled by internal heat exchange such that the heat required by Desorber 1 is supplied by the combined heat rejected by Rectifier 2 and Absorber 2. The vapor to both absorbers is supplied from the evaporator, and the combined rectified vapor produced by both desorbers is sent to the condenser. Thus, both the condenser and evaporator do double duty in the sense that they both serve two stages. In this cycle, each unit of heat supplied to Desorber 2 produces refrigerant vapor that then produces a certain amount of cooling in the evaporator. When the vapor from Desorber 2 is absorbed in Absorber 2, the resulting heat of absorption is utilized, along with the rectifier heat from R2, to generate a second quantity of refrigerant vapor, this time in Desorber 1. The vapor stream from Desorber 1 is also condensed and evaporated, producing additional refrigeration capacity. In this way, the amount of heat supplied to Desorber 2 cascades through the cycle and is used twice to generate refrigerant vapor. From a thermodynamic viewpoint, this increased performance is made possible by the fact that the temperature of the heat input (and thus its exergy) in Desorber 2 is higher as compared to a typical single-stage system. 215
216
Absorption Chillers and Heat Pumps
SHX – Solution heat exchanger RHX – Refrigerant heat exchanger E – Evaporator C – Condenser
˙ Q cond C
˙ Q rect,1
25 9
R1
8
10
Desorber 1 4
3
SHX 1
RHX 11
W˙ p1
24
Q˙ rect,3
Q˙ des,1 = Q˙abs,2 + Q˙rect,2 ˙ W p2
R2
23
28
Desorber 2 18
19
SHX 2 17
26 14 15
16
6
1
Q˙evap
R3
Q˙ des,2
22
20
13
12 E
5
2
Q˙ rect,2
˙ 27 Q des,1
7
Absorber 1 ˙ Q abs,1
21
Absorber 2 29
Q˙abs,2
FIGURE 10.1 Two-stage double-effect ammonia/water absorption system; R2 and R3 are the high- and low-temperature s ections of the second-stage rectifier.
Compared to the double-effect water/lithium bromide system shown in Figure 7.1, the cycle in Figure 10.1 has a significantly different appearance. While the water/lithium bromide system has three pressure levels, the ammonia/water system shown here has only two. An ammonia/water two-stage system could be arranged in a three-pressure configuration, in the same manner as the water/lithium bromide system, but the highest pressure level would be very high. For a typical air-conditioning application, it would reach about 7 MPa, which represents a considerable design challenge. The two-stage arrangement in Figure 10.1 avoids the high pressure by installing the second stage to the side, maintaining two pressure levels. In contrast to water/lithium bromide, the solution field of ammonia/water is much wider and thus provides the space to allow this configuration (although the space can get tight, depending on the application). The crystallization region of water/lithium bromide seriously inhibits side-by-side cycle designs (in other words, water/lithium bromide has a narrow solution field). Furthermore, as can be seen from the examples in Chapters 6–9, the heat of absorption or desorption is always higher than that of condensation and evaporation because of the effects of the heat of mixing of the working fluid mixture. In the ammonia/water system of Figure 10.1, the heat from Absorber 2, along with the heat from rectifier R2, is used to fire Desorber 1. This modification produces more refrigerant vapor from the internal heat exchange as compared to the water/lithium bromide double-effect system in which condenser heat is used internally. However, the volatility of water at the low ammonia mass fractions present in Desorber 2 means that there is a relatively large water content in the vapor at state 22. This water is then largely stripped out by the rectifiers, leaving a relatively small flow rate of refrigerant at state 27. The lower stage works well in this configuration, but the upper stage contributes only a modest increment in performance.
217
Two-Stage Ammonia/Water Systems
SHX – Solution heat exchanger RHX – Refrigerant heat exchanger E – Evaporator C – Condenser
˙ Q cond
˙ Q rect,1 C
R1
8
10
24
Desorber 1 3
W˙ p1
5
2
R2
4 30
28
Q˙ des,1 = Q˙abs,2 + Q˙ rect,2 ˙ Q abs,2
˙ W p2
22 23
˙ Q des,2 Desorber 2 18
19
SHX 2 17
27
20
26 14 15
Absorber 1 Q˙ abs,1
21
16
6
1
˙ Q evap
˙ Q rect,2
13
12 E
˙ Q des,1
SHX 1 RHX
11
9
7
29
Absorber 2 Q˙ abs,2
FIGURE 10.2 Two-stage absorption cycle with bleed line (stream 28).
It should be kept in mind that the ammonia vapor streams emerging from the two desorbers have different mass fractions. The system, as shown in Figure 10.1, will only operate in a steady-state mode when both rectifiers produce vapor of the same mass fraction since each loop needs to maintain total mass, water, and ammonia inventories. In Example 10.1, this requirement is imposed by the steady-state mass balances on all of the components. However, in practice it is difficult to maintain such a condition, and an alternate scheme is discussed in Example 10.2, which considers a similar cycle with mass management between the two stages, as shown in Figure 10.2. This side-by-side cycle shows only a modest improvement in performance over a singlestage cycle, but this observation is not the only important point. Modifications that can be viewed as derivative from this cycle form the basis of a very important cycle, called the GAX cycle, which is the subject of Chapter 11. The GAX cycle is only possible with ammonia/water due to the width of the solution field. It is observed then that each working fluid combination has advantages for particular applications. Example 10.1: Two-Stage, Double-Effect Ammonia/Water System with Separate Rectifiers Evaluate the two-stage absorption heat pump cycle shown in Figure 10.1. The heat rejected by Absorber 2 and Rectifier 2 (R2) are completely and solely used to drive the first-stage desorber (Desorber 1). The working fluid pair is ammonia/water. The input data for the solution of this problem are summarized in Table 10.1. The rectifier of the high-temperature stage is subdivided into two rectifiers that operate at different temperature levels (R2 and R3, Figure 10.1). Rectifier R2 produces vapor at the temperature of the solution leaving Desorber 1 (i.e., T24 = T4). This is the lowest temperature where it is feasible to transfer heat from R2 to Desorber 1. The vapor leaving R2 is further rectified in R3 to a mass fraction of 0.99, the same as that of the vapor leaving the first-stage rectifier (R1). The isentropic efficiency of the solution pumps is assumed to be 100%, while the effectiveness values of both the solution heat exchangers and the condensate precooler (RHX) are 80%.
218
Absorption Chillers and Heat Pumps
TABLE 10.1 Summary of Inputs for Example 10.1 Mass flow rate Pump efficiency Heat exchanger effectiveness Temperatures Vapor quality
Concentration
1 = 1.0 kg/sec m ηp1 = ηp2 = 1.0 εshx1 = εshx2 = εrhx = 0.8 T1 = T10 = 40°C T13 = –10°C Q1 = Q4 = Q8 = Q10 = Q16 = Q19 = Q23 = Q28 = 0 Saturated liquid Q7 = Q9 = Q22 = Q24 = Q27 = 1 Saturated vapor Q13 = 0.88 Two phase to minimize temperature glide x9 = 0.99 Rectifier design goal Δx4−1 = Δx19−16 = 0.04 Solution loop design goal
Find the key properties for all state points. Furthermore, calculate the rate of heat exchange in all heat exchangers and the power needed to drive the pumps. Check the energy balance for consistency and calculate the COP. Solution: The solution to this example is provided in file Ex10_1.ees. The solution follows the basic outline of the examples presented in Chapter 9. This discussion focuses on the unique aspects of this example. The basis of the model is mass and energy balances on all of the components. As before, it is necessary to account for all of the interactions at the boundary of each component. Input Discussion: The mass flow rate is given for the flow through Pump 1. The flow rate through Pump 2 is a dependent variable. One way to think about this is to view the mass flow rate in the second stage as the variable that allows the energy balance associated with the internal heat exchange driving Desorber 1 to be satisfied. It is not really that simple because all of the equations in the model are coupled, but the variable that has the most direct effect on the output of the higher stage is the solution flow rate. The pump efficiency is set to an ideal value, but this specification has little effect on the other components in the absorption cycle. However, in practice the solution pump design for an ammonia/water system is nontrivial due to the high-pressure difference and the possibility of vapor bubbles at the inlet. In reality, the solution pump does not come close to ideal operation. Particularly for small-scale systems, the solution pump is a design bottleneck, and there are few off-the-shelf pumps that can handle the unique design requirements mentioned here. The heat transfer effectiveness values of the refrigerant heat exchanger and the two solution heat exchangers are all set to 0.8. This choice correlates with the size of the heat exchanger (amount of heat transfer area) provided, which is a complex engineering and economic decision in reality. In general, the heat exchanger design impacts pressure drop and thus impacts other components in the cycle. That level of complexity is not included in this model, but such detail would be necessary for an optimization study to determine the best choice of the relative sizes of the components in the cycle. In this case, the effectiveness values are just set arbitrarily. Specification of the three temperatures can be thought of as setting the two pressure levels and the ammonia mass fraction through Pump 1. This view also depends on other specifications such as the assumptions about the saturation conditions of these streams. These assumptions are discussed next. The vapor quality is specified at 14 states within the system. Eight states are assumed to be saturated liquid, five are saturated vapor, and one is a two-phase state.
219
Two-Stage Ammonia/Water Systems
In reality, none of the saturated conditions would be expected to be met exactly. For example, the condition at the outlet of the condenser would, in general, be expected to be somewhat subcooled. The amount of subcooling would depend on the details of the condenser design. Making the assumption of saturated liquid at that point has the advantage of simplifying the model while still providing a realistic view since the majority of the energy is transferred at the saturation temperature. It would be possible to expand the condenser model to include more detailed heat transfer with the ability to predict the subcooled outlet temperature at the expense of considerable complexity. This same viewpoint applies generally to all of the saturated state specifications. They represent a meaningful starting point to understand cycle operation. The ammonia mass fraction specifications can be viewed as cycle design goals. The vapor concentration at the rectifier outlet would ideally be pure ammonia, but that would require a large and complex rectifier with a corresponding energy penalty. The specified value (x9 = 0.99) represents a compromise typical of actual ammonia/ water cycle design, which works very well when a condensate precooler is included in the design. The vapor mass fraction is specified at the outlet of only one of the rectifiers. The other rectifier vapor outlet mass fraction is dependent; note that they have to be equal for a steady-state solution to this cycle. The concentration differences specified for the two solution loops are convenient ways to specify loop performance. In an actual cycle, the concentration difference would vary, along with all of the other cycle variables, as external conditions fluctuate. The concentration differences would, in general, depend strongly on the sizes and designs of the various heat exchangers and the pump flow rate. Redundant Mass Balances: As is always true for absorption cycles, simply writing mass balances for each component results in a set of equations that has some redundancy (see Appendix B). In general, the rule is that there are two redundant mass balance equations in each cycle. In the solution provided, the mass balances in Desorber 1 are considered redundant and eliminated from the solution by equating the balance, in residual form, to an error variable. When the solution is working correctly, we expect the error variables to be close to zero for each of the redundant balances. The choice of Desorber 1 is arbitrary—we could have picked any of the other nontrivial components (i.e., components with more than two connections). It is recommended that the reader run the solution and verify that the mass balances on all the components are satisfied, even though the redundant mass balances are not included in the solution. Mixer Before Condenser: Just before the Condenser, streams 27 and 9 mix, resulting in stream 25. This process is assumed to be adiabatic. Thus, the equations for this component are
25 = m 27 + m 9 m
Overall mass balance
25 x25 = m 27 x27 + m 9 x9 m
Ammonia mass balance
25 h25 = m 27 h27 + m 9 h9 m
Energy balance
One of the results of the mass balances for the entire cycle is that x9 = x27, which is required for a steady-state solution. As x9 is set to a value (0.99), we can conclude that x25 is also equal to that same value. As a result of the fact that the other state conditions are the same for both mixing streams, the enthalpy of the outlet is also equal to the (identical) inlet enthalpy values.
220
Absorption Chillers and Heat Pumps
Splitter Before Absorber 1: Just before Absorber 1, stream 14 splits into streams 26 and 15. This process is assumed to be adiabatic and well mixed. Thus, the equations for this component are
14 = m 26 + m 15 m
x26 = x14
Overall mass balance Ammonia mass balances
x15 = x14 h26 = h14
Energy balances
h15 = h14 These equations require that the state of both outlet streams equals the state of the inlet stream. Note that these specifications satisfy both the ammonia mass balance and the energy balance. Absorber 1 Internal Heat Exchange: The sawtooth line in Absorber 1 (Figure 10.1) represents an internal heat exchange process where the cold vapor stream from the evaporator, which ultimately ends up in Absorber 2, is used to partially cool Absorber 1. It is assumed that there is no mass exchange in this process. The cooling supplied by the vapor stream is not enough to completely satisfy the cooling needs of Absorber 1, so there is still a requirement for supplemental external cooling Q abs ,1 . The heat exchange model used here is optimistic because it assumes that the vapor stream is heated all the way to the highest possible temperature in Absorber 1 (T29 = T6). This assumption introduces only a small error in the overall cycle performance, since this heat exchange process is less than 2% of the total cooling requirement of absorber 1. The mass balance equations for the absorber side are
(
)
26 + m 6 = m 1 m
26 x26 + m 6 x6 = m 1 x1 m
The mass balance equations for the vapor side are 15 = m 29 m
x15 = x29 The energy balance equation is
26 h26 + m 6 h6 + m 15 h15 = m 1h1 + m 29 h29 + Q abs ,1 m
Internal Heat Exchange Firing Desorber 1: The energy required by Desorber 1 is supplied completely and solely by the combined output of Absorber 2 and Rectifier 2 (R2). That cascade of energy within the cycle is the key to the increased performance of this cycle as compared to a single-stage cycle. This requirement is implemented by the energy balance
Q des ,1 = Q abs ,2 + Q rect ,2
The heat exchange approach temperatures implemented in this model are optimistic at T16 = T4 and T24 = T4. Both of these specifications represent the limiting case of
Two-Stage Ammonia/Water Systems
221
zero approach temperature for these internal heat transfers. With this temperature specification for the outlet state of Rectifier 2 (along with the high pressure and the assumption of saturated vapor), the vapor mass fraction is determined to be 0.932. Thus, another rectifier (R3) is needed to further purify the ammonia up to the desired value of x27 = 0.99. The cooling required for R3 is at a temperature that is too low to be useful in Desorber 1. The formulation of the model includes mass and energy balances on all components (except the redundant mass balances described earlier). In addition, the model includes simplified heat transfer models for the internal heat transfer processes. The complete set of equations can be found in the accompanying solution file (Ex10_1.ees). The solution resulting from this model is summarized in Table 10.2. A subset of the data from Table 10.2 is included in Table 10.3, where the data are organized by stage, which allows an analysis of what each stage contributes to cycle performance. The first row of Table 10.3 shows the mass flow rate of the vapor leaving each of the stages. The second row expresses the flow from each stage as a percentage of the total. It is observed that the low-temperature stage contributes 75% of the total with only 25% coming from the high-temperature stage. The third row shows the desorber heat transfer rate in each stage, where it is observed that they are comparable. The fourth row computes the ratio of refrigerant flow rate to desorber heat rate, and the same pattern is seen where the amount of refrigerant obtained for each unit of energy input in the desorber is three times higher in the low-temperature stage. The basis for this imbalance is the mass fraction of the vapor leaving the desorber, where the high-temperature stage shows a very low fraction of 0.310 compared to 0.954 in the lowtemperature stage. This means that the rectifier of the high-temperature stage has a much bigger job to purify this stream up to the required level (0.99 in this case). This is reflected in the rectifier heat, which is much larger for the high-temperature stage. It is also reflected in the absorber heat that is much lower for the high-temperature stage. The mass fraction of the rich solution in each stage and the liquid reflux flow rate from each stage round out the picture. The most important factor here is that the high-temperature stage produces vapor with a higher water content, as compared to the low-temperature stage. The difference in performance of the two stages traces directly to that point. Table 10.3 also includes data on the absorber heat transfer rate and the solution heat exchanger heat transfer rate. For the low-temperature stage, the desorber and absorber heat transfer rates have similar magnitudes. However, for the high-temperature stage, the absorber rate is only 36% of the desorber rate. This difference can also be traced to the water content of the vapor leaving the desorber. The water must be evaporated in the desorber, but it is then stripped out in the rectifier. The vapor absorbed in the absorber is only the purified fraction; thus, the heat transfer rate is much less than the desorber heat transfer rate. To enable the energy balance, the mass flow rate of the rich solution in the high-temperature stage is about half of that in the low-temperature stage. Consistent with that, the heat transfer rate in the solution heat exchanger of the high-temperature stage is on the order of half of that in the low-temperature stage. The performance of the double-effect system of Example 10.1 is not encouraging because the COP is only about 26% higher than that of a single-effect system (see Example 9.3, where the single-stage COP was found to be about 0.393 for similar conditions) with considerable increase in complexity. Although this cycle does not yield much performance improvement, it was included because it can be seen as the starting point for the introduction of the socalled GAX cycles that are discussed in Chapter 11. An interesting variation on the same theme is discussed next.
One alternative two-stage concept that may be of interest is to use a bleed line to manage the water balance. A version of this is shown in Figure 10.2. In this case, the vapor from
222
Absorption Chillers and Heat Pumps
TABLE 10.2 State Points for the Ammonia/Water System According to Figure 10.1 and Ex10_1.ees State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
–47.5 –46.0 195.7 288.0 30.4 30.4 1525.8 239.0 1415.5 183.6 –5.0 –5.0 1095.0 1283.6 1283.6 430.6 431.9 704.7 814.3 529.7 529.7 2421.6 744.1 1572.5 1415.5 1283.6 1415.5 288.0 1407.6
1.000 1.000 1.000 0.938 0.938 0.938 0.066 0.004 0.062 0.082 0.082 0.082 0.082 0.082 0.020 0.479 0.479 0.479 0.459 0.459 0.459 0.076 0.054 0.022 0.082 0.062 0.020 0.002 0.020
269.9 1539.9 1539.9 1539.9 1539.9 269.9 1539.9 1539.9 1539.9 1539.9 1539.9 269.9 269.9 269.9 269.9 269.9 1539.9 1539.9 1539.9 1539.9 269.9 1539.9 1539.9 1539.9 1539.9 269.9 1539.9 1539.9 269.9
Vapor Quality 0.000
0.000 0.015 1.000 0.000 1.000 0.000 0.042 0.880 0.979 0.979 0.000
0.000 0.010 1.000 0.000 1.000 1.000 0.979 1.000 0.000 1.001
T (°C)
x (kg/kg)
40.0 40.1 94.2 112.2 54.9 49.3 103.5 103.5 76.6 40.0 0.3 –11.6 –10.0 13.0 13.0 112.2 112.3 174.8 194.1 129.1 124.2 183.4 183.4 112.2 76.6 13.0 76.6 112.2 49.3
0.386516 0.386516 0.386516 0.346516 0.346516 0.346516 0.954238 0.386515 0.990000 0.990000 0.990000 0.990000 0.990000 0.990000 0.990000 0.060811 0.060811 0.060811 0.020811 0.020811 0.020811 0.309686 0.060811 0.931803 0.990000 0.990000 0.990000 0.346515 0.990000
Summary of Energy Quantities /W W p ,1 p ,2 Q /Q
Pump powers
Q abs ,1/Q abs ,2 Q /Q /Q
Heat transfer rate in absorbers
153.3/64.8 kW
Heat transfer rate in rectifiers
11.9/109.5/5.6 kW
Q des ,1/Q des ,2 Q
Heat transfer rate in desorbers
174.4/179.5 kW
Condenser heat transfer rate
100.9 kW
Q evap Q
Evaporator heat transfer rate
90.1 kW
Refrigerant heat exchanger Cycle coefficient of performance
15.4 kW 0.502
shx ,1
rect ,1
cond
rhx
COP
Heat transfer rate in solution HXs
shx ,2
rect ,2
rect ,3
1.5/0.66 kW 241.7/130.6 kW
223
Two-Stage Ammonia/Water Systems
TABLE 10.3 Summary Data from Example 10.1 Organized by Stage Low-Temperature Stage Vapor out of rectifier (kg/sec) Fraction of total refrigerant Desorber heat (kW)
9 m 9/m 25 m Q des ,1
0.062 0.756 174.4
High-Temperature Stage 27 m 27/m 25 m Q des ,2
0.020 0.244 179.5
9/Q des ,1 m
3.56 × 10–4
27/Q des ,2 m
1.11 × 10–4
Mass fraction of vapor out of desorber
x7
0.954
x22
0.310
Mass fraction of rich solution
x3 1 m
0.386
0.061
23 + m 28 m Q
0.056
x18 16 m 8 m Q
Q abs ,1 Q
153.3
Vapor generation per unit of heat input (g/J)
Mass flow rate of rich solution (kg/sec) Liquid reflux (kg/sec) Rectifier heat (kW) Absorber heat (kW) Sol. HX heat (kW)
rect ,1
shx ,1
1.0 11.9 241.7
0.48 0.004
rect ,2
115.1
shx ,2
130.6
Q abs ,2 Q
64.8
the high-temperature desorber passes through the lower temperature desorber, where it is partially rectified. As the vapor returning to the high-temperature stage (state 29) contains less water than the vapor leaving the stage (state 24), there tends to be a net carryover of water from the high-temperature stage into the low-temperature stage. To compensate for this, a so-called bleed line is introduced (stream 28) that connects the right leg of the lowtemperature solution circuit to the left leg of the high-temperature solution circuit. With only a relatively small flow rate (on the order of 0.2% of the Pump 1 flow rate, depending on conditions) through this connection, the net water transferred via the vapor streams can be returned. The practicality of this measure was demonstrated experimentally in a combined absorption–vapor compression system (Rane et al. 1993). A model of the cycle shown in Figure 10.2 is provided in file Fig10_2.ees and, for somewhat comparable conditions, it yields a COP = 0.508, which is 1.2% greater than the two-stage system of Example 10.1. It is always a pleasant surprise when a simpler configuration gives higher performance, even if only 1%. The bleed line is a practical solution any time you have multiple solution circuits in the same cycle. The required flow rate is computed by the model from mass balances. In a hardware implementation, the flow rate could be controlled using a variable valve to maintain a constant liquid level in one of the major components. The presence of the bleed line makes the rectifier R3 in Figure 10.1 unnecessary because now it is no longer required that the vapor mass fractions coming from the two circuits be equal. Instead, stream 24 is introduced into Desorber 1, and it is partially rectified within the desorber. This change would likely require some design effort to bring that vapor into intimate contact with the desorber liquid, but it is pretty standard in ammonia/water component design. The biggest performance penalty that these two double-stage systems face is the increased water content of the vapor leaving the high-temperature desorber. For each unit of heat input to the desorbers, the high-temperature desorber produces only about 30% of the ammonia vapor flow that leads to refrigeration in the evaporator. Much of the heat supplied to the high-temperature desorber goes toward evaporation of water, which then must be stripped back out in a rectifier with an energy penalty.
224
Absorption Chillers and Heat Pumps
Careful optimization of the rectifier heat integration might yield small improvements, but the big issue here is the volatility of the water, which is inherent for this working fluid pair.
10.2 Double-Lift Ammonia/Water Systems
Pressure
Condenser
Evaporator
Absorber
Temperature FIGURE 10.3 Necessity for double-lift system.
Desorber
W at er
Am m on ia
Especially for low-temperature applications, it can happen that the solution field is too narrow to accommodate a single-stage ammonia/water system for the required temperatures, as shown in Figure 10.3. The single-stage system with the solid lines can be accommodated by the solution field. All major components, such as desorber, absorber, condenser, and evaporator, fit into the space limited by the vapor pressure lines of pure ammonia and pure water. The single-stage configuration works for evaporator temperatures down to about –50°C (for minimum absorber temperatures of about 40°C). However, when the evaporator is required to operate at a lower temperature (for example, –70°C) while the absorber temperature is fixed at 40°C, then the lower pressure level decreases and the absorber operating conditions fall outside the available solution field (Figure 10.3); that is, the cycle cannot work with ammonia/water at these conditions. Thus, another cycle configuration must be found to service this application. One option is a two-stage, doublelift cycle, as shown in Figure 10.4. In Figure 10.4, key differences compared to the two-stage systems discussed in Section 10.1 are that the lower solution loop is reversed (now a Type II loop) so that now Desorber 1 is at the low pressure, Absorber 1 is at the high pressure, and the condenser rejects heat to Desorber 1 such that there are no external heat interactions at
225
Two-Stage Ammonia/Water Systems
˙ Q rect,1
˙ Q abs,1
Absorber 1
Condenser
˙ Q rect,2
˙ Q des,2
Desorber 2
˙ =Q ˙ Q cond des1
Condensate precooler
Evaporator ˙ Q evap
SHX 2
SHX 1
Desorber 1
Absorber 2 Q˙ abs,2
FIGURE 10.4 Double-lift configuration.
that temperature. This arrangement allows a low evaporator temperature while still fitting within the solution field. This cycle also has a relatively low maximum pressure as compared to a single-stage system at the same operating conditions (assuming it could fit in the solution field). In this double-lift cycle, the low-temperature solution loop boosts the temperature of the condenser heat to a temperature where it can be rejected to the environment. In this cycle, the heat is rejected by two absorbers, Absorbers 1 and 2 in Figure 10.4. The function of Desorber 2 remains unchanged as the heat input component. From a big-picture viewpoint, there are two significant changes between Figures 10.1 and 10.4. First, the direction of flows in the low-temperature solution circuit, consisting of Desorber 1 and Absorber 1, are reversed, which also reverses the function of these two components and those of the pump and expansion valve. Second, the location of the internal heat exchange is modified. In Figure 10.4, the internal heat exchange occurs between the Condenser and Desorber 1 rather than having an absorber heat a desorber, as was the case in Figure 10.1. Although the configurations in Figures 10.1 and 10.4 have superficial similarities, they are actually very different and used for different applications. The configuration of Figure 10.1 is a double-effect system in which the concept of staging is used to increase the COP. For the configuration of Figure 10.4, the concept of staging is applied in order to obtain a high-temperature lift (i.e., a low evaporator temperature for a fixed heat rejection temperature). When the evaporator temperature is much lower, as in this cycle, the COP is expected to be lower (the thermodynamic penalty of double-lift). A model of the configuration in Figure 10.4 is provided in file Fig10_4.ees. For a refrigeration temperature of –50°C with other conditions similar to the single-stage model of Example 9.3, the COP was found to be 0.125 with a relatively low heat input temperature (highest temperature in Desorber 2 is 119°C). This can be increased to COP = 0.14 using rectifier heat integration into the high-stage solution loop. This double-lift configuration is presented as an example of staging. It is noted that a single-stage ammonia/water cycle could provide refrigeration under the same basic operating conditions (i.e., –50°C in evaporator and heat rejection at 40°C), but it would require heat input at a much higher temperature (190°C as compared to 119°C for the double-lift) and a much higher top end pressure.
226
Absorption Chillers and Heat Pumps
The COP would be higher (~0.19), but this is not surprising because the heat input temperature is much higher. If the available heat source temperature is less than that required for the single stage, then the double-lift system is an attractive option. One of the inputs to the double-lift model is the mass fraction of the stream leaving the rectifier and going to the condenser. A nominal value of 0.998 was used for the simulation results stated in the previous paragraph (the other inputs that were used can be found in file Fig10_4.ees). In experimenting with this input, it was found that the model will not converge for values below 0.9915. A mass balance model of the cycle was generated and is provided as file Fig10_4_mass.ees. The mass balance model highlights several key points about the cycle model (which has an embedded version of the mass balance model). In the mass balance model, the flow rate through both solution pumps is specified, but in the cycle model the flow rate in the second solution pump is dependent, essentially specified by the energy balance between the Condenser and Desorber 1. Also, it is found that this cycle has only six independent mass fractions that need to be specified (see the mass balance model). Although they are independent, not all sets will be physically realistic. Some sets of inputs are found to lead to negative flow rates. In the cycle model, the mass fractions are tightly constrained by the properties of the working fluids. Thus, the problem with nonconvergence for condenser inlet mass fractions below 0.9915 is understood to be an overconstrained mass balance problem (mass flow rates are restricted to positive values in the cycle model). To make the cycle operate, it has to employ a rectifier that strips out enough water before sending it to the condenser. It is observed that staging of absorption cycles can be used for two, mutually exclusive purposes. Staging can be used to increase efficiency (i.e., COP) or to increase temperature lift. Examples of staging to increase COP include the double- and triple-effect systems in Chapters 7 and 8 as well as the cycles discussed in Section 10.1. Examples of staging to increase temperature lift include the half-effect cycle discussed in Chapter 8 and the double-lift cycle discussed here (actually the half-effect is also a double-lift cycle). Clever use of staging leads to a large family of interesting cycles, as discussed in more detail in Ziegler et al. (1993), Alefeld and Radermacher (1994), and Kahn et al. (1994).
10.3 Two-Stage, Triple-Effect Ammonia/Water System As a result of the fact that the solution field of ammonia/water is relatively wide, it can accommodate an unusual cycle that has a high COP. It is a two-stage, triple-effect system, as shown in Figure 10.5, and sometimes called the Kangaroo cycle. In this figure, two singlestage absorption cycles can be recognized, one inside a second, larger one. The smaller of the two (the inner stage) operates at the conditions of a conventional single-stage cycle. However, its driving heat transfer is supplied by the condenser and absorber of the second, larger single-stage cycle. Both stages utilize the same evaporator. The absorber and condenser of the outer stage operate at sufficiently high temperatures so that the heat they reject can be used entirely to drive the desorber of the first cycle. Consequently, one unit of thermal energy supplied to the outer (components numbered 2 in Figure 10.5) stage produces a certain quantity of refrigerant that produces cooling in the evaporator. The heat of condensation and absorption of this refrigerant is also used to provide additional refrigerant, and capacity, by firing the inner stage. Thus, one unit of input energy is used three times to produce cooling capacity, which is the definition of a triple-effect system. This concept was
227
Two-Stage Ammonia/Water Systems
Internal heat exchange SHX – Solution heat exchanger
C2
˙ Q rect,2
˙ Q des,2
R2
Desorber 2
E – Evaporator C – Condenser R – Rectifier ˙ ˙ ˙ Q =Q +Q des,1 cond,2 abs,2
SHX
˙ Q rect,1 C1
R1
˙ Q cond,1
Desorber 1 SHX
˙ W p1 E
˙ Q evap
Absorber 1
˙ W p2 Absorber 2
˙ Q abs,1
FIGURE 10.5 Two-stage, triple-effect ammonia/water system.
described first by Alefeld (1983) and reduced to practice using a water/LiBr system as the inner stage and a water/zeolite system as the outer stage (Ziegler et al. 1985). A similar system was later patented by DeVault (DeVault and Marsala 1990; DeVault and Biermann 1993). Further work (Ivester and Shelton 1994) demonstrated that the configuration of Figure 10.5 can be operated using ammonia/water as the working fluid in both stages for air-conditioning applications. However, the solution field is very tight. All approach temperatures in the internal heat exchangers have to be very small (less than 5 K), and the system needs to be water cooled to reduce the absorber and condenser temperatures (and, with that, the desorber temperature) of the inner stage as much as possible. Similarly, the evaporator temperature should be as high as possible. Furthermore, in order to achieve good overall performance, it is important that all major options of internal heat exchange are exploited, as shown in the next example. Example 10.2: Two-Stage, Triple-Effect Ammonia/Water System Evaluate the performance of a triple-effect, two-stage absorption air conditioner according to Figure 10.6 (which is a variation of Figure 10.5). The heats rejected by both the hightemperature absorber (Absorber 2) and condenser (Condenser 2) are used entirely and solely to drive the low-temperature desorber (Desorber 1), thus generating additional vapor. For this purpose, the lowest temperatures of the high-temperature condenser and absorber (state points 12 and 20, respectively) are set 3 K higher than the lowest temperature of the low-temperature desorber. The lowest temperatures in the low-temperature condenser and absorber (state points 2 and 10) are 35°C. The mass fraction of the vapor leaving both rectifiers is 0.995. The mass fraction difference in both the low- and hightemperature solution circuits is 0.06. The mass flow rate of refrigerant in the solution pump of the inner stage is 1.0 kg/sec. The quality of vapor leaving the evaporator is 0.98. The isentropic efficiency of both the solution pumps is 100%. The effectiveness of both
228
Absorption Chillers and Heat Pumps
Internal heat exchange
19
C2
SHX – Solution heat exchanger
Q˙rect,1 R2
23
20
E – Evaporator C – Condenser
Desorber 2
14
Q˙cond,2
R – Rectifier
Q˙des,2
18
15
SHX 2 24
11 Q˙cond,1 C1
Q˙rect,1 9
R1
10
˙ W p1
E
26 1
Q˙evap
27
21 22
6 2
7
Absorber 1 ˙ Q
16
Desorber 1 4 5 SHX 1
3 25
8
13
˙ Q abs,2
˙ W p2 12 Absorber 2
17
abs,1
FIGURE 10.6 Triple-effect, two-stage absorption air conditioner.
solution heat exchangers is 0.8. It is assumed that liquid leaving the absorbers, condensers, and the desorbers is saturated. Similarly, vapor leaving the desorbers and rectifiers is saturated. The model for Example 10.2 is implemented in file Ex10_2.ees. Find the pressure, temperature, mass fraction, vapor quality, and enthalpy of all relevant state points. Calculate the heat transfer rate in all heat exchangers and the rectifiers and the work input to the pumps. Check the overall energy balance for the cycle and calculate the COP. Solution: With the information given earlier and the usual assumptions that the outlet conditions for all heat exchangers with phase change are saturated, the state-point properties and energy rates in Table 10.4 are found. A summary version of the data with selected parameters organized by stage is included in Table 10.5. The refrigerant contributions from the inner and outer stages are 69% and 31%, respectively. This is about as expected since the outer stage generates refrigerant with one unit of heat (i.e., the desorber heat input) while the inner stage generates vapor with two units of heat (from the condenser and absorber of the outer stage). The outer-stage solution loop mass fractions are not as high as the mass fractions in the high-temperature solution loop in Example 10.1 and, therefore, there is a much smaller impact from the volatility of water, which is not much of an issue in this cycle. Note that the heat transfer rates in the desorber and absorber of the outer stage are approximately equal. The mass fraction of the vapor generated in the desorber of the inner stage (0.991) is quite close to the required value (0.995), resulting in a small rectification heat requirement of 3.9 kW, relative to the cooling capacity of 182.6 kW. As a result of the fact that the outer solution loop operates at lower ammonia mass fractions, the rectification heat
229
Two-Stage Ammonia/Water Systems
TABLE 10.4 State Points for the Two-Stage Triple-Effect Ammonia/Water System (Figure 10.6 and Ex10_2.ees) State Points
h (J/g)
(kg/sec) m
P (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1265.8 –81.4 –80.4 68.6 127.3 –36.5 –36.5 1407.3 1383.7 162.6 346.0 105.4 108.8 469.9 604.8 271.0 271.0 1717.0 1357.7 346.0 83.4 –76.5 519.1 163.6 162.6 1265.8 1265.8
0.166 1.000 1.000 1.000 0.886 0.886 0.886 0.115 0.114 0.166 0.051 0.622 0.622 0.622 0.571 0.571 0.571 0.064 0.051 0.051 0.001 1.000 0.013 0.622 0.166 0.114 0.051
494.8 494.8 1344.1 1344.1 1344.1 1344.1 494.8 1344.1 1344.1 1344.1 1344.1 494.8 3365.4 3365.4 3365.4 3365.4 494.8 3365.4 3365.4 3365.4 1344.1 1344.1 3365.4 3365.4 494.8 494.8 494.8
Vapor Quality 0.980 0.000
0.000 0.002 1.000 1.000 0.000 0.163 0.000
0.000 0.037 1.000 1.000 0.000 0.000 0.000 0.118 0.980 0.980
T (°C)
x (kg/kg)
12.1 35.0 35.1 67.7 81.1 45.1 44.5 70.9 63.7 35.0 35.0 70.7 71.0 148.9 172.9 102.4 88.8 158.7 88.8 70.7 70.9 35.9 158.7 83.5 4.0 12.1 12.1
0.995000 0.529544 0.529544 0.529544 0.469544 0.469544 0.469544 0.991437 0.995000 0.995000 0.995000 0.327378 0.327378 0.327378 0.267378 0.267378 0.267378 0.859297 0.995000 0.995000 0.529543 0.529544 0.327377 0.327378 0.995000 0.995000 0.995000
Summary of Energy Quantities /W W p ,1 p ,2 Q /Q
Pump powers Heat transfer rate in solution HXs
145.1/190.7 kW
Q abs ,1/Q abs ,2 Q /Q
Heat transfer rate in absorbers
193.6/154.1 kW
Heat transfer rate in rectifiers
3.9/34.1 kW
Q des ,1/Q des ,2 Q /Q
Heat transfer rate in desorbers
206.0/156.7 kW
Condenser heat transfer rate
148.9/51.9 kW
Q evap COP
Evaporator heat transfer rate Cycle coefficient of performance
shx ,1
rect ,1
cond ,1
shx ,2
rect ,2
cond ,2
1.05/2.10 kW
182.6 kW 1.165
for the outer stage is almost 10 times larger than that for the inner stage. Even so, the outer-stage rectifier heat is only 22% of the desorber heat for these operating conditions. The flow rate of rich solution in the inner-stage solution circuit is arbitrarily set to 1.0 kg/sec. In the outer-stage solution circuit, the flow rate is 0.622 kg/sec. The heat duties in the respective solution heat exchangers are 145.1 kW for the inner-stage and
230
Absorption Chillers and Heat Pumps
TABLE 10.5 Summary Data from Example 10.2 Organized by Stage Inner Stage Vapor out of rectifier (kg/sec) Desorber heat (kW) Vapor generation per unit of heat input (g/J) Fraction of total refrigerant Mass fraction of vapor out of desorber Mass fraction of rich solution Mass flow rate of rich solution (kg/sec) Liquid reflux (kg/sec) Rectifier heat (kW) Absorber heat (kW) Sol. HX heat (kW)
9 m Q des ,1 /Q m
0.114
Outer Stage 19 m Q des ,2 /Q m
0.051
9/m 1 m
206.0 5.53 × 10–4 0.687
19/m 1 m
156.7 3.25 × 10–4 0.313
x8
0.991
x18
0.859
x2 2 m 21 m Q rect ,1 Q abs ,1 Q
0.530
x12 12 m 23 m Q rect ,2 Q abs ,2 Q
0.327
9
des ,1
shx ,1
1.0 0.001 3.9 193.6 145.1
27
des ,2
shx ,2
0.622 0.013 34.1 154.1 190.7
190.7 kW for the outer-stage circuit. The latter is expected to be larger because of the considerably larger temperature difference between the absorber and desorber. This cycle involves several complexities regarding the mass balances. Note that the input that defines the capacity of the cycle is the specification of the solution pump flow rate of the inner stage. Once that is specified, all other flow rates, including the mass flow rates through the other solution pump, are dependent because the mass fractions are determined by other constraints. It would be a good exercise to replace the specification of the solution pump flow rate with any other flow rate in the system. In this case, we can specify a single flow rate anywhere within the cycle instead of the solution pump flow rate, and the model should still be well posed and convergent, assuming that you input a value close to the values shown in Table 10.4. These cycle models are often sensitive to the initial guess values, so entering a value much different from the converged solution can cause a lack of convergence. The two stages of this cycle are coupled by the energy balance represented by
Q des ,1 = Q cond ,2 + Q abs ,2
This internal heat exchange between the two stages means that there is no external heat rejection at a high temperature; the heat rejection from the outer stage is recycled into the inner stage. The external heat rejections from Condenser 1 and Absorber 1 occur at temperatures typical of a single-stage cycle. The evaporator also operates at a typical temperature. The difference here is that the external heat input to the cycle in Desorber 2 is at a much higher temperature than was found for the single-stage cycle. Due to the increased availability (exergy) of the high-temperature heat, the COP of this cycle is much higher than that found for the single-stage cycle. The energy coupling between the two stages also imposes mass coupling such that the flow rates in the two stages are dependent; that is, it is not possible to independently specify mass flow rates in both stages unless you relax some other constraints. This cycle will only operate at steady state if the ammonia mass fraction leaving both rectifiers is the same (x29 = x9). Furthermore, it is required that the mass leaving each stage is returned to it as in 19 = m 27 m
9 = m 26 m
Two-Stage Ammonia/Water Systems
A hardware implementation of this cycle would probably require some sort of mass inventory control to maintain these balances. However, in the model these balances occur naturally once mass balances are written on all components except the single redundant set. A separate implementation of the mass balance aspects of the model is provided in file Ex10_2_mass.ees. This mass balance model helps clarify the redundant mass balances, and the fact that the two vapor mass fractions leaving the two stages are dependent. In this model, the balances for Desorber 2 are chosen as redundant and an error term is introduced for each. When the error terms evaluate close to zero (as is found here), it means that these mass balances are satisfied, even though they are not explicitly included in the equation set. The cycle schematic shows that the rectifier heat is added to the ammonia-rich leg of each solution loop. This is often a good way to recycle the rectifier heat in an ammonia/ water cycle. When this is done, it is always a good idea to check the state of the liquid leaving the solution heat exchanger to make sure it is not a two-phase flow. A two-phase flow through the solution heat exchanger would likely create pressure drop issues and is undesirable (although such two-phase flows often have higher heat transfer coefficients). In this case, both states 14 and 4 are subcooled, so the issue is avoided. The model used for recycling the rectifier heat is a simple energy balance model, where all of the energy available from the rectifier is transferred to the solution stream. It is worth checking that the temperatures are favorable to allow such a heat transfer to take place (it is confirmed that T22 < T8 and T24 < T18). Another observation is that the low-stage rectifier heat is so small in magnitude that it may not be cost effective to provide a heat exchanger for this small benefit. If you modify the cycle to eliminate the integration of the heat from Rectifier 1, the COP changes from 1.165 to 1.163. On the other hand, if you leave out the Rectifier 2 integration, the COP drops to 1.008, which is a much more significant change. The two-stage, triple-effect system has promising performance, as compared to the single-stage system, but the overall cycle design is quite complex. The solution heat exchanger effectiveness used for this example is 0.8. If this is increased to 1.0, the COP increases to 1.54. Thus, we can conclude that the performance is a strong function of the internal heat exchange processes. It is noted that the main internal heat exchange process that fires Desorber 1 is modeled in a simpler way using a fixed approach temperature, but it can easily be shown that the performance depends strongly on that approach temperature as well. There are two additional options for internal heat exchange that are not employed in this example and left to the reader to explore. The liquid leaving the high-temperature condenser can be subcooled by preheating the vapor entering the high-temperature absorber (just a condensate precooler for the outer stage). This measure increases the absorber capacity and thus contributes directly to a higher heat input for the low-temperature desorber with a resulting COP increase. The other option is to employ the condensate precooler for the condensate leaving the low-temperature condenser. The combination of these two options was modeled and is included in file Ex10_2_plus.ees. For the conditions in Example 10.2, the COP rises from 1.165 to 1.267 when these two additional internal heat exchange options are included. A key detail to emphasize is that good internal heat exchange is very important. A variation on the theme of the two-stage, triple-effect system is to use different working fluids in the two stages. Using the same working fluid pair for both stages is simpler in some ways because each fluid pair brings its own individual complexities. When you have two fluid pairs, the complexity increases. Furthermore, one evaporator can serve both stages when you use the same fluid pair. However, there may be both performance and practical advantages that can be expected when a cascade is used. For example, when the lower stage employs water/lithium bromide, then the efficiency of the triple-effect cycle is generally higher than that found when a mmonia/water is used for the lower stage. For the ammonia/water, a COP of about
231
232
Absorption Chillers and Heat Pumps
0.5 is expected for the lower stage (Chapter 9), while that of water/lithium bromide typically reaches 0.7, as discussed previously in Chapter 6. The higher temperature stage would still employ ammonia/water, as the temperatures are rather high for water/lithium bromide. A model of such a “mixed” triple-effect cycle is provided in file Ex10_2_mixed.ees. It is found that the COP = 1.246 without including the refrigerant heat exchanger in the ammonia/water cycle. Thus, the mixed triple-effect cycle may be able to achieve a higher performance for some applications. However, LiBr/ H2O cycles are only appropriate for cooling applications where the evaporator temperature is above 0°C.
Homework Problems 10.1 Using the pressure–temperature diagram of Figure 3.18, lay out the operating temperatures and pressures for double-effect cycle similar to that shown in Figure 7.6, but using ammonia/water as the working fluid. What are the pressure levels you expect for the high-temperature desorber? Estimate by what factor the pump power is increased as compared to water/LiBr. 10.2 Develop a model of the ammonia/water double-effect cycle of Problem 10.1 and compare the results with the results in Table 7.4. 10.3 Based on Example 10.1, vary the mass fraction difference for both solution circuits with the goal to find the optimum COP. 10.4 Consider the one-half effect cycle of Figure 8.1. This cycle can also be operated with an ammonia/water mixture. It is advantageous when low-temperature waste heat is available and refrigeration is needed. Assuming that waste heat will allow for a highest temperature in the desorber of 105°C and that a lowest heat rejection temperature of 35°C in the absorber and condenser is available, then: a. Write an EES program for this cycle. Assume typical values for rectifier vapor outlet mass fractions and other heat exchanger outlet conditions. b. What is the lowest temperature that can be achieved in the evaporator? c. What is the COP for this operating condition? 10.5 Using the computer model for Example 10.2, investigate the performance of the triple-effect system and determine the dependence of COP on the concentration difference in the solution circuits.
References Alefeld, G. (1983). Double-Effect, Triple-Effect and Quadruple-Effect Absorption Machines. Proceedings of the 16th International Congress of Refrigeration, Vol. 2, Paris, pp. 951–956. Alefeld, G. and R. Radermacher. (1994). Heat Conversion Systems. Boca Raton, FL: CRC Press. DeVault, R. C., and W. J. Biermann. (1993). Triple-Effect Absorption Refrigeration System with Double-Condenser Coupling. Martin Marietta Energy Systems, Inc., Oak Ridge, TN. US Patent 5,205,136.
Two-Stage Ammonia/Water Systems
233
DeVault, R. C. and J. Marsala. (1990). Ammonia-Water Triple-Effect Absorption Cycle. ASHRAE Trans. 96(Pt. 1): 676–682. Inoue, N., H. Iizuka, Y. Ninomiya, and K. Watanabe. (1994). COP Evaluation for Advanced Ammonia Based Absorption Cycles. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 1–6. Ivester, D. N., and S. V. Shelton. (1994). Varying Heat Exchanger Parameters in a Triple-Effect Absorption Cycle. Proceedings of the International Absorption Heat Pump Conference, New Orleans, pp. 243–250. Kahn, R., G. Alefeld, S. Hammerer, R. Pfeifer, and M. Tomasek. (1994). An Ammonia-Water Absorption Cycle with High Temperature Lift. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 93–100. Rane, M. V., K. Amrane, and R. Radermacher. (1993). Performance Enhancement of a Two-Stage Vapor Compression Heat Pump with Solution Circuits by Eliminating the Rectifier. Int. J. Refrig. 16(4): 247–257. Richter, K. H. (1962). Multi-Stage Absorption Refrigeration Systems. J. Refrig. 5(5): 105–111. Ziegler, F., F. Brandl, J. Völkl, and G. Alefeld. (1985). A Cascading Two-Stage Sorption Chiller System Consisting of a Water-Zeolite High Temperature Stage and a Water-LiBr Low-Temperature Stage. Absorption Heat Pumps Congress, Paris. Ziegler, F., R. Kahn, F. Summerer, and G. Alefeld. (1993). Multi-Effect Absorption Chillers. Int. J. Refrig. 16(5): 301–311.
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11 Generator/Absorber Heat Exchange Cycles
11.1 Concepts, Configurations, and Design Considerations The generator/absorber heat exchange (GAX) cycle is a very elegant way of achieving higher effect performance with a cycle configuration that essentially appears to be a single-stage configuration. The elegance comes from the conceptual simplicity, and this simplicity makes it attractive as a candidate commercial product. In the absorption community, the term “generator” is frequently used in place of “desorber,” and therefore the abbreviation GAX is widely found in the literature. To explain the GAX cycle, begin with Figure 11.1. It shows one possible configuration of a two-stage ammonia/water system that is similar to the cycles discussed in Section 10.1. Two of the design variables are the flow rates in the solution loops established by the solution pumps. Consider now that a designer reduces the flow rates for both solution pumps while all other parameters are adjusted such that the system capacity remains unchanged. Thus, the desorbers have to still produce the same amount of ammonia vapor, although there is less solution supplied to the desorbers. Similarly, the absorbers have to absorb the same amount of vapor as before but with less solution available. The mass balances for both the absorbers and the desorbers can only be satisfied when the change in ammonia mass fraction increases. This requires that the temperature glide in these heat exchangers must increase as well, as shown schematically in Figure 11.1. The solid lines symbolize the original two-stage cycle, while the dashed lines symbolize the cycle with reduced solution pump flow rates. The dashed lines are approaching each other, and when we further reduce the pump flow rates, the two dashed lines will eventually coincide. When the dashed lines coincide, the mass fractions in both lines are identical. Furthermore, it is observed that for the coincident lines, the directions of mass flows are opposite. If the flow rate is the same in both lines, then they cancel each other and they can be omitted altogether. This configuration is shown in Figure 11.2. All major components of the two original solution circuits are still present with some important changes. The original two desorbers are merged into one, as are the absorbers. One pump and one expansion valve cancel each other and are omitted. The solution heat exchangers, which were components of each solution circuit, are not required for the GAX cycle. Although there are still rich- and poor-solution streams circulating between the desorber and the absorber, the temperature differences between the two solution streams are very large and the respective energy flows are accommodated better by other means instead of a solution heat exchanger, as discussed later in this section. A condensate precooler has been added to the cycle in Figure 11.2. Actually it should have been there in Figure 11.1 but was omitted to provide focus on the solution loops. The configuration of Figure 11.2 is termed the generator/absorber heat exchange (GAX) cycle. It was first described by Altenkirch and patented in 1914 (Altenkirch and Tenckhoff 1914). 235
236
Absorption Chillers and Heat Pumps
Condenser
Desorber
at e r W
Pressure
Am
m
on ia
Desorber
Evaporator Absorber
Absorber
Temperature FIGURE 11.1 GAX concept. This figure shows a schematic of a two-stage cycle; the GAX cycle is obtained when the flow rates of both solution pumps are reduced; the solution circuits approach each other as shown by the dashed lines; when they coincide, they cancel each other. · Qcond
RHX–Condensate precooler C –Condenser E –Evaporator R –Rectifier
C
RHX
E
· Qrect
· Qdes Desorber
R
· Qgax · Wp
· Qevap
· Qabs
Absorber
FIGURE 11.2 Generator/absorber heat exchange (GAX) cycle.
The GAX cycle has a number of very interesting characteristics. For example, it can be considered a single-stage cycle (compare it with Figure 9.4). After all, there is only one solution pump and all major components that occur in a single-stage cycle, such as absorber, desorber, evaporator, and condenser, are present only once. The main difference is that the solution heat exchanger is now replaced by the GAX heat exchanger represented by the wavy line. An important implication of this similarity is that the first cost of the GAX cycle should be comparable to that of a single-stage system. On the other hand, the GAX cycle can be considered a two-stage or double-effect system because there is definitely an absorber heating a desorber. A certain quantity of the driving heat is reused to generate additional cooling capacity with potentially significant increases in efficiency. This thought can be taken a step further. The GAX cycle could be imagined as originating from a three-stage system, as shown in Figure 11.3. In this
237
Generator/Absorber Heat Exchange Cycles
Desorbers
W ate r
A
m
m
on
ia
Condenser
Evaporator
Absorbers FIGURE 11.3 Generator/absorber heat exchange (GAX) cycle origins.
three-stage system, the existing high-temperature desorber would then be heated by the new, even higher temperature absorber. Correspondingly, the new desorber would receive heat from the outside source. After undergoing a merging process similar to that described in the discussion of Figure 11.1, the resulting cycle would be the GAX cycle of Figure 11.2. The point is that the GAX cycle is a hybrid cycle that can exhibit multistage features. Since the classification of the GAX cycle is not clear and will probably be debated forever, it may be appropriate to suggest that the GAX cycle is a higher effect configuration (because of its potential for high COPs) with single-stage features (because of the apparent simplicity). Inspired by the simplicity and high performance, several development projects were attempted with the goal to develop a commercial, mass-produced version of the GAX system (Fiskum et al. 1996). Unfortunately, these projects never resulted in commercial success and are dormant today. A recent review of the GAX field gives a more detailed view of the literature (Jawahar and Saravanan 2010). It was mentioned earlier that the GAX cycle does not use a solution heat exchanger. Instead, the GAX cycle can utilize the thermal availability of the solution streams in other ways. First, the poor-solution stream is considered. The outlet of the poor solution from the desorber is at the highest temperature that occurs in the entire cycle. From a thermodynamic point of view, the energy contained in the poor solution should be used at as high a temperature level as possible. Thus, this solution should reject its heat in a solution recirculation configuration, as shown in Figure 9.7, where the poor solution is used to heat the high-temperature portion of the desorber. As an alternative, the energy can be carried into the high-temperature end of the absorber, as shown in Figure 11.2, where it is then transferred into the desorber at the lower desorber temperature range via the GAX heat exchanger. A detailed analysis of the GAX system reveals that both methods are largely equivalent from an energy point of view. This means the external desorber heat requirement does not change whether or not desorber solution recirculation is employed. Solution recirculation can also be employed in the absorber, as shown in Figure 11.4. Here, the cold, rich solution at point 17 is recirculated through the absorber and preheated to the desired desorber inlet temperature. The resulting absorber cooling causes the rate of heat rejected by the absorber to the outside to be reduced. At the same time, the preheating of the solution at the desorber inlet reduces the external desorber heat requirement. Due to these multiple performance benefits, absorber solution recirculation is typically included in GAX cycle design.
238
Absorption Chillers and Heat Pumps
10 E
7
C
R
8
· Qdes
5 6
Desorber
14 3
2 · Qgax
RHX 9
· Qrect
· Qcond
RHX –Condensate precooler C –Condenser E–Evaporator R –Rectifier
· Wp
11 12
17 4
1
· Qevap
· Qabs
13
Absorber
FIGURE 11.4 GAX cycle with absorber solution recirculation.
The GAX heat exchange, represented by the wavy line in Figure 11.4, is the main internal heat exchange feature of the GAX cycle. It is made possible when the high-temperature end of the absorber operates at a temperature that overlaps with the low-temperature end of the desorber. This overlap occurs under the condition of low-temperature lift, which is typical of air-conditioning applications (building cooling) and which sometimes occurs for heat pump applications (building heating) depending on the outside air temperature. The GAX cycle requires a wide solution field and is thus not practical with water/ lithium bromide due to crystallization concerns. The GAX cycle has the potential to achieve high COP due to the fact that it has a relatively high heat input temperature and very effective internal heat exchange. However, there are a number of challenges in realization of GAX technology that are discussed in this chapter along with the promising performance potential. Example 11.1: GAX Cycle Evaluate the conventional GAX cycle illustrated in Figure 11.4. The working fluid pair is ammonia–water. The highest evaporator temperature is 5°C, whereas the lowest absorber and condenser temperature is 40°C. The vapor quality of the solution leaving the evaporator is 0.94. Saturated liquid is assumed to leave the absorber (point 1), the generator (point 3), and the condenser (point 8). Saturated vapor leaves the generator (point 5) and the rectifier (point 7). The rectifier is analyzed as a reversible device that produces a vapor mass fraction of 0.995. The mass fraction difference between the rich and the poor solutions in the solution circuit is 0.35. The mass flow rate through the 1) is 1.0 kg/sec. The pump efficiency is 50%, and the condensate presolution pump (m cooler has an effectiveness of 0.8. Before entering the desorber, the rich solution is preheated (absorber solution recirculation) in the low-temperature part of the absorber (i.e., that part of the absorber that does not heat the desorber) with an approach temperature of 0 K. The approach temperature at either end of the GAX heat exchanger is set to 0 K as well. As a result, the rich solution enters the desorber saturated.
1. Find the pressure, temperature, enthalpy, vapor quality, and the mass fraction for each relevant state point.
Generator/Absorber Heat Exchange Cycles
239
2. What are the rates of heat exchange in the evaporator, condenser, absorber, generator, rectifier, condensate precooler, absorber solution recirculation, and between the absorber and the generator (GAX heat exchanger)? 3. Check the overall system energy balance and calculate the cooling COP of the system.
Solution: The solution to this example is provided in file Ex11_1.ees. Using mass and energy balances on the GAX cycle of Figure 11.4 and the given input values, the results in Table 11.1 are obtained for the individual state points. Point 14 in Figure 11.4 represents the two-phase state in the desorber at which the temperature is equal to the highest absorber temperature (which is the highest temperature that could receive absorber heat). Thus, between states 2 and 14, the desorber can accept heat from the absorber. State point 13 represents the two-phase point in the absorber where the temperature is equal to the low-temperature end of the desorber, which is the point below which energy cannot be transferred to the desorber by heat transfer. Thus, between points 13 and 4, the absorber can supply heat to the desorber. When all approach temperatures are zero (ideal heat transfer model), as assumed in this example, the temperatures are related as T13 = T2 and T14 = T4. The blank entries for points 13 and 14 are due to the fact that these are two-phase states so that there are two values for specific enthalpy, mass flow rate, quality, and mass fraction. More detail on these states can be obtained by running the model. It should be noted that the GAX cycle has only 15 state points. This is an indication of the apparent simplicity of the concept. State points 15 and 16 in Table 11.1 are omitted but will be used for another cycle configuration in Example 11.3. The total heat transfer rate from the absorber amounts to Q abstot = 768 kW with Q abs = 369 kW being rejected externally as waste heat. The remainder (399 kW) is transferred to the desorber in the GAX heat exchanger. Note that Q abstot already accounts for the cooling supplied by the absorber solution recirculation. The total desorber heat requirement is Q gentot = 821 kW with 399 kW supplied by the absorber. The remaining 422 kW for the desorber has to be supplied from an outside heat source. It is observed that about 48% of the desorber heat requirement is contributed by the absorber. The GAX temperature overlap between the absorber and desorber for this case is 40.0 K. The maximum heat transfer rate that the desorber could accept in this temperature range is calculated to be 468 kW. It is about 69 kW higher than what the absorber actually supplies. This mismatch is an opportunity for further performance improvement that is explored in Section 11.2. The evaporator capacity is Q evap = 468 kW, resulting in a COP of 1.11. This performance is optimistic for actual machinery due to a number of idealizations in the model that may be difficult to approach in an actual machine. Idealizations include ideal heat exchange models for GAX and solution recirculation, ideal rectifier model, zero pressure drops, and ideal desorber model. These idealizations reduce the model complexity and allow the basic idea of GAX to be more easily understood. The next example (Example 11.2) addresses the effect of nonideal heat transfer in the GAX heat exchanger.
The COP of a GAX cycle decreases with increased temperature lift (the difference between the condenser and evaporator temperatures) more strongly than in a singlestage cycle. The GAX overlap tends to be larger when the temperature lift is smaller. This is a very important point in understanding why GAX cycles are designed specifically for low-lift applications. This point is discussed further in Section 11.2. The heat and mass exchange processes in the desorber/absorber heat exchange (GAX) process are quite complex. This is exemplified in Figure 11.5, which shows, enlarged
240
Absorption Chillers and Heat Pumps
TABLE 11.1 State Points for the Ammonia/Water GAX Cycle According to Example 11.1, Figure 11.4, and Ex11_1.ees State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15a 16a 17
Vapor Quality
h (J/g)
(kg/sec) m
P (kPa)
–60.6 139.7 609.3 609.3 1440.4 139.7 1383.3 187.3 52.6 52.6 1198.0 1332.7
1.000 1.000 0.591 0.591 0.418 0.009 0.409 0.409 0.409 0.409 0.409 0.409
478.4 1548.0 1548.0 478.4 1548.0 1548.0 1548.0 1548.0 1548.0 478.4 478.4 478.4 478.4 1548.0
0.000 0.000 0.000 0.095 1.000 0.000 1.000 0.000
1.000
1548.0
–0.001
–58.0
0.033 0.940 0.993
T (°C)
x (kg/kg)
40.0 83.7 163.3 123.7 83.7 83.7 67.3 40.0 12.0 3.1 5.0 30.4 83.7 123.7
0.4893 0.4893 0.1393 0.1393 0.9845 0.4893 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950
40.4
0.4893
Summary of Energy Quantities W p Q
Pump power
2.6 kW
Generator/absorber heat transfer
399 kW
Q abs
Heat transfer rate in absorber
369 kW
Q rect
Heat transfer rate in rectifier
35 kW
Q des
Heat transfer rate in desorber
422 kW
Q cond
Condenser heat transfer rate
489 kW
Q evap
Evaporator heat transfer rate
468 kW
Q CE
Condensate precooler heat transfer
55 kW
Q recirc
Absorber recirculation heat transfer
198 kW
COP
Cycle coefficient of performance
gax
a
1.11
State points 15 and 16 is left blank to maintain numbering consistency with subsequent examples.
from Figure 11.4, the GAX sections of the desorber and absorber. The wavy lines in Figure 11.5 symbolize the liquid/vapor interface in each of the heat/mass exchangers. The temperature increases for each from left to right, as indicated by the arrow. This type of heat exchanger configuration is called a counterflow arrangement, which generally provides the most effective heat transfer because the heat transfer temperature differences within the device can be minimized. In each component (absorber and desorber), the liquid flows in the opposite direction to the vapor. This configuration is countercurrent from a mass transfer perspective (the high mass fraction in the vapor is at the same end as the high mass fraction in the liquid) and is thus the optimum
241
Generator/Absorber Heat Exchange Cycles
· m14,v
Desorber Vapor Liquid · Qgax
· m13,v
· m14,l
Point 14
Vapor
Point 13
· m13,l
Liquid Absorber Temperature
Assumptions: 1. Vapor and liquid are in equilibrium at each point. 2. Possible GAX heat transfer is governed by temperature overlap. 3. Point 13 represents the lowest temperature point in the absorber that can still supply heat to the desorber. 4. Point 14 represents the highest temperature point in the desorber that can be supplied by the absorber. FIGURE 11.5 Heat and mass transfer in the desorber/absorber heat exchanger.
configuration to minimize losses in the mass transfer process in each component. Thus, if the components could be arranged as shown in Figure 11.5, both the heat transfer process and the mass transfer processes (in both components) would be in counterflow. This arrangement is the best at minimizing entropy generation in the coupled heat and mass transfer processes. These issues are discussed in Bassols (1988) and Kang et al. (1996). Fulfilling these requirements in a piece of hardware represents a considerable challenge. For both the absorption and desorption processes, a vertical falling film heat/mass exchanger design tends to be the best option because it can maintain the vapor/liquid counterflow relationship and provide the required contact area. However, because the solution flow direction in the absorber and desorber is opposite, it is not possible to achieve the simple counterflow relationships in Figure 11.5 if both components employ a vertical falling film design, at least not directly. It is possible to run both the absorber and desorber in vertical components in parallel flow heat exchange, but this design compromises key benefits of the GAX concept. One possible design solution that maintains counterflow heat transfer is to employ a heat transfer loop (i.e., a water circulation loop) between the absorber and desorber, as is indicated in Figure 11.6. In both components (absorber and desorber), the liquid flows downward and the vapor flows upward. An effective design needs to provide large surface area between the two phases for mass transfer, and this is indicated schematically by the alternating baffles in each device. This design allows both components to have a vertical falling film design because the water loop can be plumbed in a cross-over arrangement so that the heat transfer is in counterflow. The disadvantage of such a loop is that two temperature differences are introduced for heat transfer (one for each component) and the water loop pump requires additional pump power. Example 11.2 investigates the effect of heat transfer losses and demonstrates that the additional temperature differences represent a considerable penalty.
242
Absorption Chillers and Heat Pumps
2
4
5 GAX heat exchanger
6
External cooling
External heat
Desorber
17
1
Absorber
3
FIGURE 11.6 GAX absorber and desorber as vertical components with heat transfer loop. Point numbers are referenced to Figure 11.4.
Example 11.2: Effect of Approach Temperature Modify Example 11.1 to investigate the effect of heat transfer limitations in the GAX heat exchanger using an approach temperature difference model. Vary the approach temperature differences on both sides of the GAX heat exchanger from 0 to 14 K. Plot the cooling COP as a function of the approach temperature difference. Solution: Using the computer model that describes the GAX cycle of Example 11.1, the approach temperatures are varied and the program is executed for approach temperature differences over the specified range. See EES file Ex11_2.ees. The results are summarized in Figures 11.7 and 11.8. Figure 11.7 shows the cooling COP of the GAX cycle versus the approach temperature difference. As this difference increases, the COP decreases quite dramatically. Depending on the heat exchanger design, an approach temperature difference of as much as 14 K may be realistic. However, for this value, the COP has dropped from 1.11 to about 0.85. Of course, the approach temperature differences may not be the same at both ends of the GAX heat exchanger in an actual machine, but this example gives an indication of how sensitive the GAX cycle performance is with regard to the effectiveness of the internal heat transfer. Figure 11.8 shows various heat transfer rates in the GAX cycle and how they change as the approach temperature difference increases. First, observe that the evaporator capacity, total heat transfer in the desorber, and total heat transfer in the absorber are all constant as controlled by the inputs selected for this model. Changes in the GAX heat
243
Generator/Absorber Heat Exchange Cycles
1.2 Evaporator temperature = 5°C Heat rejection temperature = 40°C Mass fraction difference in solution loop = 0.35
1.15
Cooling COP
1.1 1.05 1 0.95 0.9 0.85 0.8
0
2
4 6 8 10 Heat transfer approach temperature (K)
12
14
12
14
FIGURE 11.7 GAX cycle cooling COP versus approach temperature difference for Example 11.2. 1000
· Qgentot
Heat transfer rate (kW)
800
· Qabstot
600
· Qevap · Qreq
400 Evaporator temperature = 5C Heat rejection temperature = 40C Mass fraction difference in solution loop = 0.35
200
0
2
· Qavail
4 6 8 10 Heat transfer approach temperature (K)
FIGURE 11.8 GAX cycle heat transfer results for Example 11.2.
exchanger affect the external desorber heat, but they do not affect the vapor generation rate. The total heat transfer rate in the desorber is made up of the externally supplied heat transfer and the GAX heat transfer. The GAX heat transfer is constrained by the heat transfer feasible temperature overlap region of the absorber and desorber, which is reduced, at each end of the nominal overlap, by the heat transfer approach temperature difference. In the heat transfer feasible overlap region, the available absorber heat is denoted by Q avail, whereas the heat required by the desorber is denoted by Q req. Both of these heat transfer rates appear in Figure 11.8, and it can be observed that Q avail < Q req. The difference between these two varies with operating conditions, but the sign of the difference is typically as shown. This is a rule of thumb for the GAX cycle and represents an opportunity for increased performance, as discussed in the following section
244
Absorption Chillers and Heat Pumps
where a variation on GAX cycle design is introduced. The GAX heat transfer rate is equal to the heat transfer rate available in the absorber in this case. The heat transfer rate required by the desorber in the heat transfer feasible temperature overlap region (Q req) decreases with increasing approach temperature. This behavior is a consequence of the temperature differences required to drive the heat transfer process. Similarly, the heat transfer rate available from the absorber (Q avail) decreases. As the rate of heat exchanged internally between the absorber and desorber (Q gax = Q avail) is decreasing at constant total desorber heat as the approach temperature difference increases, the heat transfer rate to the desorber (Q des) must increase. The absorber heat rejection rate (Q abs) to an external sink must increase as well. These considerations explain the decrease in COP with increasing approach temperature difference. For the GAX cycle to work as designed, it is necessary that the temperature of the hot end of the absorber be warmer than the lowest desorber temperature (i.e., that there must be a temperature overlap). For a typical air-conditioning application, this condition is fulfilled with considerable overlap and essentially fixed-temperature lift if a cooling tower is used. However, when the same cycle is meant to operate as a heat pump that heats a building, the evaporator temperature varies as dictated by the outdoor temperature and the overlap depends on the temperature lift, which depends on the outdoor temperature. The effect of temperature lift on GAX overlap (and thus on GAX cycle performance) is illustrated in Figure 11.9, which shows a GAX cycle, in solid lines that exhibits a significant overlap. When the evaporator temperature decreases at fixed heat rejection temperature, the low pressure decreases, affecting both the evaporator and the absorber, as shown by the dotted lines. This is the case with a larger temperature lift. To maintain the same heat rejection temperature, the mass fraction change in the solution loop must decrease, which causes the operating temperature region represented by the lengths of both the desorber and absorber to shrink in Figure 11.9. The dotted case shown is the case where the GAX overlap is reduced to zero. At temperature lifts larger than this value, the GAX feature does not contribute and the cycle effectively reverts to a single stage, although good single-stage performance would require a solution heat exchanger.
In summary, the GAX cycle can attain higher COP than a single-stage cycle but has many of the characteristics of a single-stage cycle, so it is considered low complexity (hence
Condenser
Absorber
Temperature lift
Temperature FIGURE 11.9 Transition from GAX to single-stage cycle at constant heat rejection temperature.
ate
r
Evaporator
W
Pressure
Am
m
on
ia
Desorber
Generator/Absorber Heat Exchange Cycles
245
low cost). It attains the higher COP by a higher temperature heat input and effective integration of internal heat transfer opportunities such that heat rejection occurs at a relatively low temperature. The GAX cycle is a unique absorption cycle in that the COP is more sensitive to imposed temperatures as compared to all other absorption cycles. The GAX advantage is only present for low-lift applications, which lead to overlap of the temperature ranges of the desorber and absorber. The GAX cycle requires a wide solution field, which points away from water/lithium bromide and toward ammonia/water.
11.2 Branched GAX Cycle In Section 11.1, it was mentioned that, under most operating conditions, the heat transfer rate provided by the high-temperature end of the absorber is less than the heat requirement of the low-temperature end of the desorber. Details of this mismatch are described in Scharfe et al. (1986). The degree to which this happens varies considerably with the actual operating conditions. The causes of this mismatch between heat requirement and heat supply are the focus of the following discussion. Considering the pressure–temperature diagram in Figure 3.18, it can be observed that the lines of constant mass fraction lie more closely together at high mass fractions and are more widely spaced at low mass fractions. Furthermore, the mass fraction variable is highly nonlinear in the following sense: when adding 1 kg of ammonia to 9 kg of pure water, the mass fraction of the resulting solution is 0.10, a change from 0.00 to 0.10. However, when 1 kg of pure ammonia is added to 9 kg of ammonia/water solution with an initial mass fraction of 0.90, the mass fraction changes by only 0.01 from 0.90 to 0.91. In the first case, the saturation temperature (at constant pressure) changes quite considerably, while in the second the changes are minimal. Consequently, the resulting temperature glide (e.g., in the absorber) is considerable in the first case and close to zero in the second. However, in both cases, assuming that the added ammonia is absorbed from the vapor phase into the solution, approximately the same quantity of latent heat is released. It can be observed from Figures 11.1 and 11.2 that the GAX section of the absorber that supplies heat to the desorber operates with an average mass fraction that is lower than the average mass fraction present in the GAX section of the desorber (that receives the heat from the absorber). Thus, for the same heat transfer rate, the temperature glide in the absorber tends to be larger than the temperature glide in the desorber. In addition to these energy considerations, the potential for heat transfer from absorber to desorber is constrained by the temperature overlap of these components, as shown in Figure 11.10, since heat transfer requires a temperature d ifference. Within the heat transfer feasible overlap region, there is a mismatch between the energy available in the absorber and the energy needed by the desorber. This mismatch is illustrated in Figure 11.10. In this schematic of the GAX cycle, the amount of heat per unit temperature interval is superimposed above the absorber (sections a and b) and above the desorber (sections a, b, and c). The two curves have approximately the same shape for both components, but the curve for the desorber is shifted to higher temperatures as required by the solution field. The area between the absorber and the curved line marked a and b represents the amount of heat the absorber is able to deliver to the desorber. The absorber line is also plotted above the desorber for reference as a dotted line. Now consider the solid line above the desorber. The equivalent sections to a and b in the absorber are moved to higher temperatures for the desorber. The heat transfer required
246
(Amount of heat)/dt
Absorption Chillers and Heat Pumps
c b
a
Required Generator b
a
Available Absorber Overlap
Temperature FIGURE 11.10 GAX mismatch: amount of heat available and amount of heat required in GAX temperature overlap region.
by the desorber is represented by sections b and c. Due to the curvature of the heat transfer curve, the heat transfer rate the absorber is able to supply (dotted line) is always lower than the heat transfer rate the desorber needs (solid line). The mismatch between the available heat in the absorber and the required heat in the desorber for the GAX is primarily due to the difference in the average mass fraction in those components. Other variables play secondary roles, such as variations in the heat of mixing and variations in the specific heat of the solution due to temperature and pressure differences. But, as introduced in the previous two paragraphs, the effect of the average mass fraction can be significant. In this case, the two components see identical average mass fraction, but the mismatch is controlled by the average mass fraction in the region of temperature overlap. Once the mechanism of this mismatch is understood, a design modification can be proposed to increase the performance over the basic GAX design by eliminating the mismatch, as proposed next. The heat transfer rate provided by the absorber to the desorber (GAX heat exchange) can be increased by increasing the mass flow rate of solution in the overlap portion of the absorber. This is accomplished with the so-called branched GAX cycle (Herold 1991; Rane and Erickson 1994), as shown in Figure 11.11, where a second solution pump is added. This pump can be seen as leftover from the transition in Figure 11.1 that led to the GAX cycle. In the branched GAX cycle, the two solution streams that were assumed to cancel each other in Figure 11.1 do not cancel entirely because the flow rate in the pumped leg is larger than the flow rate in the expansion valve leg. In this design modification, the solution flow rates in the high-temperature ends of both the desorber and absorber are increased, and the high-temperature end of the absorber can now supply more heat to the low-temperature end of the desorber. At the same time, the heat requirement of the high-temperature section of the desorber is increased, but less external heat needs to be supplied to the low-temperature end of the desorber, so there is a net benefit. This concept could be generalized further to add more pumps, but there are diminishing returns.
247
Generator/Absorber Heat Exchange Cycles
RHX–Condensate precooler C –Condenser E–Evaporator R –Rectifier
10 E
7
C
R
8
RHX 9
· Qrect
· Qcond
· Wp
11 12
· Qdes
5 6
14
· Wp1
17
· Qgax
4
15
1
· Qevap
· Qabs
3
16
2
13
Desorber
Absorber
FIGURE 11.11 Branched GAX cycle.
Example 11.3: Branched GAX Cycle Evaluate the branched GAX cycle shown in Figure 11.11. This cycle differs from the GAX cycle in that it has an additional pump that transfers working fluid from the absorber to the desorber. This pump serves the function of balancing the GAX energy mismatch between the absorber and the desorber. The assumptions made in analyzing this cycle are the same as those used for the GAX cycle (Example 11.1). The additional pump draws liquid from the absorber, point 15, at a temperature equal to the saturation temperature of the rich solution entering the desorber, point 2 (heat transfer approach temperature difference is zero). The branch flow rate is determined by the requirement that the heat needed by the desorber and the heat available from the absorber must match exactly in the overlap region. The input parameters are as follows:
1. The pump isentropic efficiency is 50%, and the condensate precooler effectiveness is 80%. 2. T11 = 5°C; T8 = T1 = 40°C. 3. The mass fraction of vapor leaving the rectifier (x7) is 0.995. 4. The difference between the rich- and the poor-solution mass fractions in the solution circuit is 0.35. 1 ) is 1.0 kg/sec. 5. The mass flow rate through the main solution pump (m 6. The vapor quality of the two-phase solution leaving the evaporator (Q11) is 0.94. Solution: The example is first evaluated for an approach temperature of 0 K for all heat exchangers in connection with absorber and desorber. The solution is provided in file Ex11_3.ees. With the information given earlier and the usual assumptions that the outlet conditions for all heat exchangers with phase change are saturated, the model was solved, yielding properties for the state points and heat transfer rates given in Table 11.2. The results for an approach temperature of 0 K are shown in Table 11.2. The total heat transfer rate from the absorber amounts to Q abstot = 833 kW with Q abs = 362 kW being rejected as waste heat. The total absorber heat transfer rate increased, and the portion rejected as waste heat decreased slightly as compared to the conventional GAX cycle in Example 11.1. Both factors increase the GAX heat transfer rate (471 kW is being transferred to the desorber) by about 18%, as compared to Example 11.1. The total desorber heat requirement is 888 kW with 471 kW supplied by the absorber (GAX). In this branched GAX cycle, the absorber supplies 100% of the heat required by the GAX overlap portion of the desorber. The desorber receives 417 kW from an outside heat source, which is 5 kW less than in
248
Absorption Chillers and Heat Pumps
TABLE 11.2 State Points for the Branched GAX Cycle According to Figure 11.11 (Approach Temperatures 0 K) and Ex11_3.ees State Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
h (J/g)
(kg/sec) m
P (kPa)
–60.6 139.7 609.3 609.3 1440.4 139.7 1383.3 187.3 52.6 52.6 1198.0 1332.7
1.000 1.000 0.697 0.697 0.436 0.009 0.427 0.427 0.427 0.427 0.427 0.427
189.3 191.8 –58.0
0.124 0.124 1.000
478.4 1548.0 1548.0 478.4 1548.0 1548.0 1548.0 1548.0 1548.0 478.4 478.4 478.4 478.4 1548.0 478.4 1548.0 1548.0
Vapor Quality 0.000 0.000 0.000 0.095 1.000 0.000 1.000 0.000 0.033 0.940 0.993
0.000
T (°C)
x (kg/kg)
40.0 83.7 163.3 123.7 83.7 83.7 67.3 40.0 12.0 3.1 5.0 30.4 83.7 123.7 83.7 84.1 40.4
0.4893 0.4893 0.1393 0.1393 0.9845 0.4893 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950
0.2612 0.2612 0.4893
Summary of Energy Quantities /W W p p1
Pump power
Q gax Q
Generator/absorber heat transfer
471 kW
Heat transfer rate in absorber
362 kW
Q rect
Heat transfer rate in rectifier
36 kW
Q des
Heat transfer rate in desorber
417 kW
Q cond
Condenser heat transfer rate
510 kW
Q evap
Evaporator heat transfer rate
489 kW
Q CE
Condenser–evaporator heat transfer
57 kW
Q recirc
Absorber recirculation heat transfer
198 kW
COP
Cycle coefficient of performance
abs
2.6/0.3 kW
1.173
the nonbranched case from Example 11.1. Now 56.5% of the desorber heat requirement is supplied by the absorber, 8% more than for the conventional GAX system. The evaporator capacity, 489 kW, increased by 21 kW as a result of the branching modification, resulting in a cooling COP of 1.17, which is a 5% improvement over the conventional GAX cycle. The main solution pump work is 2.6 kW and the branch pump requires 0.31 kW, which reflects the fact that the flow rate in the branch is much lower (~12% of the main pump) than in the main solution pump. Rectifier heat and precooler heat duty are increased slightly as a consequence of the higher refrigerant mass flow rate, which increased by about 4%.
The results in Table 11.2 assume an approach temperature difference of 0 K. This approach temperature difference is varied between 0 and 14 K, to provide the results used to produce Figures 11.12 and 11.13. Figure 11.12 shows the cooling COP for both GAX and branched
249
Generator/Absorber Heat Exchange Cycles
1.2 Evaporator temperature = 5°C Heat rejection temperature = 40°C Mass fraction difference in solution loop = 0.35
1.15
Cooling COP
1.1 1.05 1 0.95
Branched GAX GAX
0.9 0.85 0.8
0
2
8 10 4 6 Heat transfer approach temperature (K)
12
14
12
14
FIGURE 11.12 COP versus approach temperature for branched GAX cycle of Example 11.3. 1200 · Qgentot
Heat transfer rate (kW)
1000 800
· Qabstot
600
· Qevap
400 Evaporator temperature = 5°C Heat rejection temperature = 40°C Mass fraction difference in solution loop = 0.35
200
0
2
· Qgax
4 6 8 10 Heat transfer approach temperature (K)
FIGURE 11.13 Branched GAX results for Example 11.3.
GAX as the approach temperature difference varies. The branch advantage is ~5% at 0 K but drops to ~2% at 14 K. Figure 11.13 shows several relevant heat transfer rates as a function of the approach temperature. As for the GAX cycle (Figure 11.8), the evaporator capacity is constant. However, now the flow rate in the branch solution pump is calculated to obtain an exact match between the heat available in the overlap region of the absorber and the heat required in the desorber, and thus both the total absorber heat and the total desorber heat increase with increasing approach temperature difference. The increase in the total desorber heat transfer rate is due to the fact that the desorber flow rate changes due to the branch pump and the desorber requires more heat to maintain the same mass fraction difference. The cooling COP, which is equal to the evaporator heat divided by the external heat to the
250
Absorption Chillers and Heat Pumps
desorber (which is the total heat minus the GAX heat), is larger than that for the conventional GAX over the entire range considered (see Figure 11.12). The improvement in COP is larger for low approach temperature differences because there is more GAX overlap. The degree to which the branched GAX performance exceeds that of the GAX depends on the mismatch of the heat supplied by the absorber and that required by the desorber in the same temperature interval. This mismatch changes with operating conditions. In Examples 11.1 through 11.3, the difference in mass fraction between the poor and rich solution was set to 0.35. When this parameter is varied, the heat deficit mismatch in the desorber/absorber heat exchanger varies as well, as shown in Figure 11.14, for an approach temperature difference of 5 K. The difference between the two curves is the deficit. It should be noted that depending on the operating and design conditions, this difference will become zero and may even reverse the sign. The relative performance of single-effect, GAX, and branched GAX cycles is summarized in Figures 11.15 and 11.16. In Figure 11.15, the cooling COP is plotted versus the heat rejection temperature for a fixed evaporator temperature and fixed heat transfer approach temperature. Although not shown, the temperature lift can be computed as the heat rejection temperature minus the evaporator temperature. Thus, it is observed that the advantage of branched GAX over GAX depends strongly on temperature lift. The advantage of GAX over single effect is slightly larger at low lift. It is noted that both the GAX and branched GAX models employ ideal absorber solution recirculation, and this assumption results in a somewhat biased comparison with single-effect models because the solution heat exchanger model used there was an effectiveness model (ε = 0.8). The single-effect prediction is the most realistic, and the GAX and branched GAX predictions are more idealized bounds on the performance of these cycles. The heating COP for the same three models is plotted in Figure 11.16 versus the evaporator temperature for fixed heat rejection temperature and fixed approach temperature. Once again, the importance of temperature lift can be seen. In this case, temperature lift increases from right to left. For heat pumping at very mild outdoor temperatures, the temperature lift is very small and both GAX and branched GAX provide a significant performance advantage. However, when outdoor temperature gets very cold, the temperature overlap goes away and the GAX advantage goes away as well. 600
Heat transfer rate (kW)
500 400 300
Required by desorber Available from absorber
200 100 0 0.2
0.35 0.4 0.45 0.25 0.3 Mass fraction difference between poor and rich legs
0.5
FIGURE 11.14 Energy mismatch between the absorber and the desorber for an approach temperature difference of 5 K.
251
Generator/Absorber Heat Exchange Cycles
2 Evaporator temperature = 5°C Heat transfer approach temperature = 5 K
Cooling COP
1.5
Branched GAX GAX
1
Single effect
0.5
0 30
32.5
35 37.5 40 Heat rejection temperature (C)
45
42.5
FIGURE 11.15 Cooling COP versus heat rejection temperature. 3.5
Heating COP
3
Condenser temperature = 30°C Heat transfer approach temperature = 5 K Branched GAX
2.5 GAX 2
1.5
1 –30
Single effect
–20
–10 0 Evaporator temperature (°C)
10
20
FIGURE 11.16 Heating COP versus evaporator temperature.
11.3 GAX Cycle Hardware To our knowledge, GAX systems have not been commercialized. There have been various attempts to commercialize GAX, but these efforts are dormant today (Fiskum et al. 1996). Various research groups have built and tested GAX systems (Erickson and Rane 1992; Erickson and Anand 1996; Gómez et al. 2005). A prototype GAX system was installed in The Netherlands by Colibri (as described in the first edition), but that system is no longer operating. GAX represents a compelling theoretical possibility, but it has proven to be
252
Absorption Chillers and Heat Pumps
elusive from a practical hardware perspective. The promise of higher COP depends on high-performance heat/mass exchangers that add cost. In the end, the GAX systems do have higher performance, but they also have higher cost than a single-stage system. In the current era of low energy costs, it is very difficult to justify increased capital cost. Thus, the GAX concept is one of several technologies described in this book that work but that have not been able to penetrate the market.
Homework Problems 11.1 Using the pressure–temperature diagram of Figure 3.18, describe the operating limitations of the GAX cycle. When the absorber and the condenser have to have a temperature of at least 40°C, to what temperature can the evaporator temperature drop until the GAX effect ceases to exist? What is the highest desorber temperature under these conditions? 11.2 Consider only the desorber of the GAX cycle of Figure 11.4. For the operating conditions given in Example 11.1, calculate and plot the heat transfer rate in the desorber versus the temperature. Discuss the results. 11.3 In Example 11.1 vary the approach temperature for the solution recirculation in the absorber so that the recirculation eventually ceases to exist. Plot the COP as a function of the approach temperature and discuss the result. 11.4 Consider the GAX model used in Example 11.1. Modify the model to employ desorber solution recirculation and compare the performance (COP) between the original model and this new variation.
References Altenkirch, E. and B. Tenckhoff. (1914). Absorptionskaeltemaschine zur kontinuierlichen Erzeugung von Kaelte und Waerme oder acuh von Arbeit. German Patent 278,076. Bassols, J. (1988). Experimental/Numeric Optimization of the Heat Exchange Surfaces of a Sorption Heat Pump. Proceedings of Absorption Heat Pumps Workshop, London, pp. 419–427. Erickson, D. C. and D. K. Anand. (1996). VX GAX Cycle Development. International Absorption Heat Pump Conference, Montreal. Erickson, D. C. and M. V. Rane. (1992). The GAX Family of Absorption Cycles. IEA Heat Pump Newsletter 10(4). Fiskum, R. J., P. W. Adcock, and R. C. DeVault. (1996). United States Department of Energy Thermally Activated Heat Pump Program. IECEC—Energy Conversion Engineering Conference, Vol. 2, Washington, DC, IEEE, pp. 736–741. Gómez, V. H., A. Vidal, C. García, O. García-Valladares, R. Best, J. Hernández, and N. Velázquez. (2005). Evaluation of an Indirect-Fired GAX Cycle Cooling System. International Sorption Heat Pump Conference, Denver, Paper #4, pp. 1–5. Herold, K. E., X. He, D. C. Erickson, and M. V. Rane. (1991). The Branched GAX Absorption Heat Pump Cycle. Proceedings of the Absorption Heat Pump Conference, Tokyo, pp. 127–132.
Generator/Absorber Heat Exchange Cycles
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Jawahar, C. P. and R. Saravanan. (2010). Generator Absorber Heat Exchange Based Absorption Cycle—A Review. Renewable & Sustainable Energy Reviews 14(8): 2372–2382. Kang, Y. T., W. B. Chen, and R. N. Christensen. (1996). Development of Design Model for a Rectifier in GAX Absorption Heat Pump Systems. ASHRAE Transactions 102(Pt 1): 963–972. Rane, M. V. and D. C. Erickson. (1994). Advanced Absorption Cycle: Vapor Exchange GAX. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 25–32. Scharfe, J., F. Ziegler, and R. Radermacher. (1986). Analysis of Advantages and Limitations of Absorber-Generator Heat. International Journal of Refrigeration 9(6): 326–333.
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12 Diffusion–Absorption Cycle
12.1 Introduction The diffusion–absorption refrigeration cycle was pioneered around 1920 by two Swedes named Von Platen and Munters (1928). The cycle is unique in that it runs without any mechanical work input. This is achieved by pumping the fluids using a bubble pump driven by heat. Another unique feature of the cycle is that it is essentially noise-free. These two characteristics provide solid niche markets for the cycle in the recreational vehicle and the hotel room refrigerator markets. The cycle has come a long way since its origin and is currently manufactured in numerous locations throughout the world, including Sweden, United States, Mexico, Argentina, China, and India. The diffusion–absorption cycle utilizes ammonia–water–hydrogen as working fluid. The roles of ammonia and water are familiar from absorption cycle experience. The hydrogen is used as a capping gas to equalize the pressure throughout the cycle to allow the low-head bubble pump to operate as the liquid circulator. In the diffusion–absorption cycle, the partial pressure of the ammonia gas varies from point to point instead of the overall system pressure. In reality, there are small variations in system pressure in the machine that are quite important for operation. The cycle utilizes a regenerative gas heat exchanger between the evaporator and absorber that is driven by gravity-induced pressure differences. The diffusion–absorption cycle has inherent irreversibilities that are larger than those found in typical absorption cycles. In particular, there is increased mass transfer resistance on the vapor side of the processes due to the presence of the hydrogen. There is also an additional heat exchanger called the auxiliary gas heat exchanger. These factors explain why the cycle performance is relatively low and why the cycle has never emerged from the shadows to capture more than the niche markets. A diffusion–absorption refrigerator (DAR) uses a three-component working fluid consisting of the refrigerant (ammonia), the absorbent (water), and the auxiliary gas (hydrogen). The refrigerant serves as a transporting medium to carry energy from a low-temperature source to a high-temperature sink. The water absorbs the refrigerant at low temperature and low partial pressure and releases it at high temperature against high partial p ressure. The auxiliary gas provides pressure equalization for the working fluid between the condenser and the evaporator. The number of possible working fluid combinations for this type of cycle is large, but in practice, the combination in the widest commercial use is ammonia–water–hydrogen. Helium can also be used as the auxiliary gas with a performance penalty. Other variations on the theme have been considered by a wide range of researchers (e.g., Einstein and Szilard 1930; Dannen 1997; Mazouz et al. 2005).
255
256
Absorption Chillers and Heat Pumps
The introduction of an auxiliary gas into an ammonia–water absorption cycle was first proposed by Geppert (1900). He suggested using air as a pressure equalizer. However, the use of air decreases the coefficient of performance (COP) of a DAR to such an extent that made it impossible for commercial use. Von Platen and Munters utilized hydrogen as the auxiliary gas but still found a low COP in early versions. To increase COP, Von Platen and Munters (1928) suggested that there should be a gas circuit between the evaporator and the absorber. This circulation reduces the diffusion resistance associated with the auxiliary gas considerably. With these changes, the DAR was widely used for domestic refrigerator applications during the 1930s and 1940s, but it was eventually replaced by vapor compression refrigerators that were more cost effective. The unique features of the DAR (silent operation and fuel-fired) were not that critical for household refrigerator applications. The DAR cycle is related to an ammonia–water absorption heat pump cycle since it uses ammonia as the refrigerant and water as the absorbent. Watts and Gulland (1958) reviewed the patents related to this technology and concluded that the development of the system was conducted by shrewd design rather than by a scientific approach. Stierlin (1971) contributed significantly to the gas circuit and made numerous contributions to the overall development. Eber (1975) discussed a compact auxiliary gas heat exchanger for the DAR. Modeling of such systems is complicated by the p resence of the auxiliary gas (Kouremenos 1973; Kouremenos et al. 1991; Herold and Wang 1992). Using the lead provided by Stierlin’s work and our own modeling, we demonstrated significantly improved cycle performance through heat integration (Chen 1995; Chen et al. 1996). The bubble pump was the focus of Albers et al. (2005). Yildiz et al. (2014) analyzed the effect of insulation on performance. Also in 2014, Rodriguez-Munoz and Belman-Flores performed a thorough review of the subject.
12.2 Cycle Physics The DAR with ammonia, water, and hydrogen as the working fluid has been used for the last 60 years. Millions of units have been put into service as refrigerators and freezers. The basic layout of a DAR cycle is shown in Figure 12.1. A notable difference as compared to the ammonia/water cycles in Chapters 9 through 11 is the gas loop, which circulates vapor between the evaporator and the absorber. The implementation of one such system is shown in Figure 12.2, which includes all of the components and the three fluid loops discussed with reference to Figure 12.1. The ammonia loop includes all the components since ammonia circulates through all the components. Ammonia–water solution circulates through the solution loop (circuit), which includes the desorber, bubble pump, absorber, and solution heat exchanger. The auxiliary gas circulates through the gas loop, which includes the evaporator, absorber, and auxiliary gas heat exchanger. The operation of the cycle is described next, starting with the absorber. The liquid reservoir at the base of the absorber contains approximately 0.35 mass fraction ammonia. This ammonia-rich liquid (weak absorbent) comes from the absorber, where liquid flows down by gravity in counterflow to the hydrogen–ammonia vapor mixture. From the absorber, the weak absorbent flows through the solution heat exchanger and arrives at the b ubble pump. Due to the heat input, some ammonia vapor is driven out of the solution and forms bubbles, which push liquid up in the bubble pump.
257
Diffusion–Absorption Cycle
Condenser Ammonia loop
Ammonia liquid
Evaporator
Ammonia vapor Ammonia/hydrogen vapor mixture
Ammonia/water liquid mixture Generator/ bubble pump
· Q Absorber Gas loop Solution loop FIGURE 12.1 Three loops in diffusion–absorption refrigerator.
The vapor passes through the rectifier, where water is removed and returned to the generator. The purified ammonia vapor flows to the condenser. After the bubble pump, the intermediate absorbent flows through the outer tube of the bubble pump and passes through the boiler, where more ammonia is vaporized. Finally, the strong absorbent, which typically contains 0.1–0.2 mass fraction ammonia as it leaves the boiler, flows through the inner tube of the solution heat exchanger. The vapor from the desorber is at a temperature of around 200°C. The vapor contains a small quantity of water vapor that can be removed by passing the mixed vapor through the rectifier where the purification takes place accompanied by heat rejection. The small amount of water in the ammonia drains to the generator along with the reflux ammonia. The water content of the vapor leaving the rectifier is close to zero. This vapor enters the condenser, which is a finned tube with natural convection air cooling. The ammonia vapor condenses by rejecting heat to the air, and the condensate flows to the evaporator. Ammonia-poor hydrogen enters the lower section of the evaporator and flows upward, in counterflow to the downward-flowing liquid ammonia. The auxiliary gas atmosphere accommodates the partial pressure of the ammonia vapor in accordance with Dalton’s law. As the ammonia evaporates into the hydrogen, the partial pressure of the ammonia gas rises and the evaporation temperature also rises.
258
Absorption Chillers and Heat Pumps
4
5
6 7
Condenser 10
Low-temperature evaporator
9
Rectifier
8
11
Alternate liquid ammonia
12
Hot ammonia 13
Vent tube High-temperature evaporator
14 Ammonia-poor hydrogen
Auxiliary gas heat exchanger
Fuse pipe
3
15 16
Absorber
Pump tube
17
2
18 Ammonia-rich hydrogen Strong absorbent
19 21
20
1 Reservoir
Weak absorbent
Generator 22 Electric heater
Solution heat exchanger
FIGURE 12.2 Diffusion–absorption refrigerator hardware schematic.
The ammonia-rich gas mixture leaves the bottom of the evaporator and passes down through the gas heat exchanger to the absorber. In the absorber, the ammonia is absorbed from the gas by the liquid solution. The auxiliary gas, which is almost insoluble in the liquid, passes up from the top of the absorber, through the outer tube of the auxiliary gas heat exchanger, and into the evaporator, together with some residual ammonia vapor. The hydrogen and ammonia gas circulation loop is driven by natural convection caused p rimarily by the large density differences associated with the ammonia fraction in the vapor. The hot and cold legs of the loop are brought together in the auxiliary gas heat exchanger. The liquid circulation in the cycle is driven by the heat-powered bubble pump shown schematically in Figure 12.3. Thus, it can be considered the heart of the system.
259
Diffusion–Absorption Cycle
Ammonia vapor
h
Strong absorbent d
Weak absorbent
Reservoir
Bubble pump tube
y1
y x
Heat input x
FIGURE 12.3 Schematic diagram of a bubble pump.
The height difference between the solution level in the reservoir and the level at which the bubbles are formed in the pump is a governing parameter. The determination of the required height difference was investigated by Narayankhedkar and Maiya (1985). Stierlin (1967) presented a new bubble pump/generator that is claimed to significantly improve the performance. By introducing the rectification heat into the liquid from the absorber before it goes into the generator, the COP of the cycle increases.
12.3 Choice of the Auxiliary Gas The DAR technology has traditionally used hydrogen as the auxiliary gas. The total amount of hydrogen in the DAR system is relatively small (~10 g), and DAR systems have an excellent safety record. However, the hydrogen does burn with a high-temperature flame when the DAR is exposed to excessively high temperatures, such as those encountered in a building fire. Leakage of the hydrogen and ammonia into conditioned spaces is another concern, although the amounts are small enough as to not cause problems. Stierlin and Ferguson (1988) reported that such leaks happen in the first 5 years at a total rate of approximately 2% of units. To exclude safety hazards associated with hydrogen, the hydrogen can be replaced by helium. The comparisons of hydrogen and helium as auxiliary gas have been investigated by Narayankhedkar and Maiya (1985), Kouremenos and Stegou Sagia (1988), Stierlin and Ferguson (1988), and Chen and Herold (1995). The results of these investigations indicate that hydrogen performs better than helium. The difference is apparently due to localized natural convection cells that form in the
260
Absorption Chillers and Heat Pumps
absorber as the ammonia is absorbed. Since the auxiliary gas remains in the vapor phase, the gas becomes less dense as absorption of ammonia occurs. This causes the formation of localized mixing cells, which bring additional ammonia close to the interface and augment the overall absorption process. The density difference between hydrogen and helium causes a significant difference in the strength of these convective cells. These differences were found to partially explain the measured performance differences for hydrogen and helium (Chen and Herold 1995). Another effect that contributes is the circulation rate in the gas loop. The gas-loop circulation is driven by natural convection caused by density differences due to ammonia content differences. Thermal effects, although also present, are secondary effects. As the gas passes through the evaporator and picks up ammonia, its density increases significantly. The density difference between the ammonia-poor gas rising through the hot leg and the ammonia-rich gas falling through the cold leg provides the driving force. The gas loop provides an interesting fluid flow problem primarily from two aspects: (1) the up-flowing leg is driven by a pressure difference, while the down-flowing leg is driven by gravitational forces and (2) the direction of flow of such a natural convection loop depends on small forces associated with asymmetrical design details.
12.4 Total Pressure of the System Due to the presence of the auxiliary gas, the system pressure in a DAR is uniform throughout the machine except for small hydrostatic and viscous effects. This is in sharp contrast to a conventional absorption heat pump, where the pressure difference between the high-pressure side (desorber, rectifier, and condenser) and low-pressure side (absorber and evaporator) is substantial. In the DAR, differences in vapor pressure of the working fluid, governed by temperature and liquid mass fraction, manifest as differences in the partial pressure in the vapor. The auxiliary gas partial pressure varies throughout the cycle in a complementary relationship to the working fluid vapor pressure so that the pressure differences in the cycle are small. Small hydrostatic pressure differences are important in a DAR both on the vapor and liquid sides of the machine. These pressure differences drive the liquid and vapor flows, which transfer energy from one component to another. On the liquid side, the bubble pump uses buoyancy-induced pressure differences to circulate liquid from the desorber to the absorber. On the vapor side, the auxiliary gas heat exchanger carries a recirculating flow of auxiliary gas that picks up ammonia in the evaporator and gives up ammonia in the absorber. The density difference between the ammonia-rich and ammonia-poor streams is the driving force for this recirculating flow. The amount of auxiliary gas charged into the system has a direct influence on the operating conditions in the cycle. In particular, the total pressure of the system governs the temperature at which the condenser operates. When the machine starts from room temperature, the internal flow rates are zero and the working fluid exists as a two-phase mixture consisting of the three components, NH3, H2O, and H2. Initially, the vapor phase is largely auxiliary gas with a small partial pressure of NH3 and almost no H2O. As heat is applied to the bubble pump (desorber), some of the liquid vaporizes and the bubbles rise through a small-diameter tube and “pump” liquid up to the top of the absorber.
Diffusion–Absorption Cycle
261
Until the vapor pressure of the liquid in the desorber exceeds the total pressure in the machine, the vapor leaving the desorber must diffuse through the auxiliary gas blanket. In this regime, the condensation process is controlled by diffusion through the auxiliary gas. When the vapor pressure exceeds the total pressure, a pressure-driven flow is started that sweeps the auxiliary gas out of the condenser. In this regime, the vapor is largely NH3, with a small amount of H2O, and the condensation coefficients are much higher than with auxiliary gas present. The actual steady-state operating regime in the condenser is some hybrid of these two regimes. The majority of the condensation process will take place in the regime where the auxiliary gas concentration is low. The auxiliary gas concentration will adjust according to the load on the system. Therefore, the temperature of the first drop of condensate is determined by the auxiliary gas charge. If the system is charged to 25 bar, and the assumption is made that the rectifier section strips out all the water, then the first condensate temperature will correspond to the saturation temperature of pure NH3 at 25 bar (58°C). This means that no matter what the temperature of the sink is, the first condensate will form at a temperature corresponding to the auxiliary gas charge. This operating characteristic of a DAR influences performance. If the auxiliary gas charge is large, leading to a high first condensate temperature, then the performance is degraded. However, if the auxiliary gas charge is too small, the system performance drops to zero in high ambient temperature situations. This situation can occur if the NH3 saturation pressure, corresponding to the ambient temperature, is greater than the system pressure. In such an operating condition, the bubble pump fails and the system shuts down. Thus, the total pressure of the system, which is a function of auxiliary gas charge pressure, should be just sufficient to provide the required temperature range across the condenser.
12.5 Cycle Performance The steady-state performance characteristics of a domestic refrigerator-sized DAR unit are shown in Figure 12.4. This unit was a production unit typical of units sold in 1994 (http://www.norcold.com). The unit has an air-cooled rectifier without any attempt at integrating the rectifier heat. Tests were run at typical ambient temperatures with the load supplied by heat leak into an insulated box in a typical refrigerator configuration. No attempt was made to control the temperature of the cooled space. Instead, the unit was run continuously, and the air temperature inside the unit was measured. The COP and capacity values reported were determined based on a heat transfer model of the insulated box. The model was calibrated against a series of heat input tests where a known amount of energy was dissipated inside the insulated box and the resulting temperatures were recorded. This allowed the heat transfer characteristics of the insulated box to be determined. Of course, the direction of energy flow is different between the calibration tests and actual refrigeration operation. However, because the thermal resistance of the system is dominated by the resistance of the insulation in the wall, and because the heat transfer in the wall is largely independent of the direction of energy flow, the model was found to work dependably. Both COP and capacity are plotted in Figure 12.4 versus the power input to the heater. The system was heated by an electric heater for these tests. Below approximately 175 W, the bubble pump did not start and the system did not run. This was due to heat loss from
262
Absorption Chillers and Heat Pumps
60
Unit #3 Cooling capacity
0.2
Cooling COP
COP
50 40
0.15
0.1
Under powered
Design conditions
Test number: 1, 2, 3, 4, 5, 26 Ambient temperature: 19–23˚C Gas type: hydrogen Charge pressure: 25.5 bar Ammonia concentration: 29.1%
0.05
0 100
30
Over powered
150
200
250 Input power (W)
300
350
20
Cooling capacity (W)
0.25
10 0 400
FIGURE 12.4 Measured DAR performance versus input power.
the bubble pump and the rectifier to the ambient. Once the start-up threshold power was exceeded, both COP and capacity rise rapidly to their maximum values. The COP decreases as input power is increased beyond 200 W. This behavior is due to a series of factors, but it is primarily due to liquid ammonia leaving the evaporator. When input power is high, the ammonia flow rate is high. However, the refrigerator cannot utilize all of the ammonia due to the dynamics of the insulated box. Increased capacity tends to decrease the air temperature inside the box, but this reduces the temperature difference between the evaporator and the air. Thus, at high power input, only a fraction of the ammonia that enters the evaporator is evaporated. The remainder flows through the gas heat exchanger back to the reservoir, where it mixes back into solution to start another circuit. This liquid carryover represents a loss to both COP and capacity because it does not provide refrigeration. The unit tested has a nominal power input of 300 W. Based on Figure 12.4, it is seen that this limit causes the machine to operate at full capacity but suboptimum COP. However, the high ambient operating characteristics are such that the machine does not attain full capacity, which is needed most at high ambient, until 300 W.
References Albers, J., F. Ziegler, and F. Asdrubali. (2005). Investigation into the Influence of the Cooling Water Temperature on the Operating Conditions of Thermosyphon Generators. International Sorption Heat Pump Conference, Denver, Paper #53, pp. 1–8. Chen, J. (1995). Further Development of the Diffusion Absorption Refrigerator. PhD Dissertation, University of Maryland.
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Chen, J. and K. E. Herold. (1995). Buoyancy Effects on the Mass Transfer in Absorption with a Nonabsorbable Gas. Int. J. Heat Fluid Flow. 16(6): 536–545. Chen, J., J. K. Kim, and K. E. Herold. (1996). Performance Enhancement of a Diffusion-Absorption Refrigerator. Int. J. Refrig. 19(3): 208–218. Dannen, G. (1997). The Einstein-Szilard Refrigerators. Sci. Am. 276(1): 90–95. Eber, N. (1975). New Compact Heat Exchanger for Absorption Cooling Units. XIVth International Congress of Refrigeration, Vol. 2, Moscow, No. B2.46, pp. 886–892. Einstein, A. and L. Szilard. (1930). Refrigeration, US Patent 1781541. Geppert, H. (1900). Process of Producing Cold, U.S. Patent 662,690. Herold, K. E. and L. Wang. (1992). Performance Modeling of Several Diffusion Absorption Heat Pump Cycles. Proceedings of the Florence World Energy Research Symposium, Florence, Italy, pp. 23–34. Kouremenos, D. A. (1973). The Thermodynamic Properties of Ammonia-Hydrogen Gas Mixtures; A Temperature Mass Fraction Diagram for Evaporation Purposes. Proceedings of the VIII International Congress of Refrigeration, pp. 437–443. Kouremenos, D. A., K. A. Antonopoulos, and A. Stegou-Sagia. (1991). Absorption of Ammonia in Refrigerators with Helium as Inert Gas. Analysis of Thermal and Energy System. Proceedings of the International Conference, Athens, Greece, pp. 701–717. Kouremenos, D. A. and A. Stegou Sagia. (1988). Use of Helium Instead of Hydrogen in Inert Gas Absorption Refrigeration. Int. J. Refrig. 11(5): 336–341. Mazouz, S., O. Chouaieb, and A. Bellagi. (2005). Thermodynamic Analysis of a New Refrigeration Cycle. International Sorption Heat Pump Conference, Denver, Paper #33, pp. 1–8. Narayankhedkar, K. G. and M. P. Maiya. (1985). Investigations on Triple Fluid Vapor Absorption Refrigerator. Int. J. Refrig. 8(6): 335–342. Rodriguez-Munoz, J. L. and J. M. Belman-Flores. (2014). Review of Diffusion-Absorption Refrigeration Technologies. Renew. Sustain. Energy Rev. 30: 145–153. Stierlin, H. (1967). Latest Developments in Domestic Absorption Refrigerators and the Future Outlook. XII International Congress of Refrigeration, Vol. 2, Madrid, pp. 1323–1337. Stierlin, H. (1971). Multiple Hydrogen Circuits in Absorption Deep Freezers. XIII International Congress of Refrigeration, Vol. 2, Washington, DC, pp. 526–533. Stierlin, H. and J. R. Ferguson. (1988). Diffusion Absorption Heat Pump (DAR). Proceedings of Workshop on Absorption Heat Pumps, London, pp. 247–257. Von Platen, B. C. and C. G. Munters. (1928). Refrigerator, U.S. Patent 1,685,764. Watts, F. G. and C. K. Gulland. (1958). Triple-Fluid Vapor Absorption Refrigerators. J. Refrig. Jul/ Aug: 107–115. Yildiz, A., M. A. Ersöz, and B. Gözmen. (2014). Effect of Insulation on the Energy and Exergy Performances in Diffusion Absorption Refrigeration (DAR) Systems. Int. J. Refrig. 44: 161–167.
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13 Applications of Absorption Chillers and Heat Pumps The primary worldwide application for absorption chillers is building cooling. Largecapacity (industrial-scale) chillers can be found in the mechanical rooms of large buildings, where they typically provide chilled water that is circulated to heat exchangers throughout the building to cool the air. The advantage of absorption chillers is that they use a nonelectric energy source and thus provide flexibility to the designer/owner/operator. Absorption chillers are also used as components in campus-scale “district” cooling applications, where chilled water, for air conditioning, is provided from a central cooling plant and distributed to multiple buildings in a district. The advantage of a district cooling approach is that it is often more efficient to run a single large chiller instead of multiple small chillers. District cooling is widely used worldwide in situations where a single entity (i.e., a company or a government organization) controls a group of buildings that are situated close together in a “campus.” District heating can also employ absorption heat pumps.
13.1 Industrial Waste Heat Utilization Beyond the air-conditioning applications, absorption chillers and heat pumps also have utility for industrial-scale heat integration alongside various other technologies, as indicated in Figure 13.1. Large process plants (e.g., chemical plants, oil refineries) often have subprocesses that operate at different temperatures and that require either heating or cooling. An example is distillation that typically requires heating to boil off the volatiles and cooling to condense the reflux. Such plants often have multiple distillation columns working at different temperatures. From an energy efficiency standpoint, as well as a costcutting standpoint, it is attractive to consider using the heat rejected from one process to provide the heat needed by another. When the temperatures line up favorably (i.e., this approach requires that heat transfer flows from high to low temperature), this type of heat integration can be done directly by incorporating a heat exchanger. However, it is more common that the temperatures and heat flows do not line up favorably. In such situations, heat integration usually requires a heat pump. As with any design modification, the decision to incorporate an absorption heat pump in a process plant comes down to life cycle costing. If the cost savings due to increased process efficiency are sufficient to justify the capital cost of the equipment, then the design option will be considered. The economics of this type of heat integration has not been particularly favorable in recent years due to the relatively low cost of energy. However, there have always been specific applications that are economically attractive, and the companies that build and operate these plants are well aware of heat-integration opportunities. The largest opportunities are usually addressed when the plant is constructed. Retrofit opportunities also exist and are implemented as costs change. 265
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Absorption Chillers and Heat Pumps
Industrial waste heat utilization Passive heat recovery Gas/gas
Gas/liq
Cogeneration
Liq/liq
Steam turbine
Gas turbine
Heat pumps I.C. engine
Closed cycle Absorption heat pumps
Type I
Mechanical compression heat pumps
Open cycle
Mechanical Thermocompression compression
Type II
FIGURE 13.1 Overview of industrial waste heat utilization options, including absorption heat pumps. (Adapted from EPRI [1988].)
Absorption heat pumps interact with their surroundings at three temperature levels, as shown in Figures 1.3 and 1.4 for Type I and Type II heat pumps, respectively. Both of these types can find applications in industrial heat integration. A search of the literature yields examples of both types. It is difficult to determine the number of industry installations, but it is thought to be small. A guess based on literature references is a few hundred Type I installations and less than a hundred Type II units. This base may be sufficient to provide an experience level that will act as a seed for such applications if and when energy prices rise. Two overviews of industrial absorption heat pump applications can be found in Erickson et al. (2005) and Herold (2007). An overview that focusses on high-temperature applications can be found in Howe and Erickson (1991). Key applications include oil refineries and power generation. Examples of several representative Type I installations in refineries include Brant et al. (1998), Erickson and Kelly (1998), and Kalinowski et al. (2009). A broad range of applications can be found on the Colibri website (http://www.colibri-bv.com). One example is reproduced here as Figure 13.2 showing a two-stage 10 MW refrigeration plant. This indicates the potential scale of the industrial applications. Examples of Type II installations include a rubber plant (Ma et al. 2002) and a laboratory facility at Battelle Memorial Institute that was used as a demonstration plant for marketing to industry (Herold 1985). Other representative publications include Alefeld and Scharfe (1991), Arh (1994), and Fukusumi et al. (2014). The manufacturer Thermax includes a reference to a Type II product line (Thermax 2015).
13.2 Gas Turbine Inlet Air Cooling Stationary gas turbines are widely used today for electricity generation because natural gas is plentiful, relatively cheap, and causes less CO2 emission per kilowatt of
Applications of Absorption Chillers and Heat Pumps
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FIGURE 13.2 Two-stage 10 MW absorption cooling plant installed in Egypt. (Courtesy of Colibri, Vaals, The Netherlands.)
electricity produced. In addition, gas turbine power plants are generally less costly than other options, and they have favorable control characteristics in that they can be started and stopped without major time delays. Thus, gas turbines have many positive factors that have led to an increasing market share over the last 30 years (EIA 2012). On the negative side of the ledger, gas turbine system capacity is impacted by the ambient temperature. As the temperature goes up, the capacity goes down. This is due to the fact that the capacity is a strong function of the mass flow rate of air ingested by the compressor, and the mass flow rate is a strong function of the air density. Since the air density decreases when the ambient temperature rises, the capacity decreases. It can be shown from an ideal gas analysis that when the temperature changes from 0°C to 30°C, the air density decreases by about 10%. This temperature range is arbitrary, but it is meant to show the scale of the effect. A complicating factor is that as the ambient temperature rises, the demand for electricity often rises, particularly in regions where electric-powered air conditioning is used. Thus, the gas turbine capacity goes down just when the demand is increasing. One way to level the power output is to utilize turbine inlet air cooling. This can be done using an absorption chiller fired by waste heat from the turbine. Type I systems used for gas turbine inlet air cooling include Hwang (2004) and Erickson et al. (2014). An example of installation is shown in Figure 13.3 (Erickson et al. 2015). This unit produces 7000 kW of cooling.
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FIGURE 13.3 Gas turbine power plant with absorption inlet air cooling. (Courtesy of Energy Concepts, Annapolis, MD.)
13.3 Solar Absorption Cooling The use of solar energy to provide the energy source for cooling is a straightforward concept. This can be done using photovoltaic (PV) electricity and an electricity-driven vapor compression chiller or using solar thermal energy with an absorption (or adsorption) chiller. There are also some interesting desiccant-based concepts, but those systems are less developed and are not discussed here. The economics associated with solar cooling have been long debated, but the recent price reductions for PV panels tend to favor the electric systems. For any of these systems, the implementation encounters several practical challenges in addition to the chiller details. The fact that a large fraction of a building cooling load is due to solar input (at least in some buildings) provides a good match for solar cooling. However, there is always a thermal lag associated with the thermal capacitance of the system, so the match is not perfect. In addition, many buildings have cooling requirements that are not directly related to solar input and, thus, must have cooling even when the sun is not shining. A major source of heat load in a building is often computer and other office equipment. These machines generate heat whenever they are turned on. Thus, although the cooling load does tend to follow the solar input, the match is not perfect. These features tend to lead to a hybrid approach, where there is a baseline chiller using nonsolar energy in combination with a solar chiller to handle the portion of the load that follows the sun. Generally, this implies a larger chiller footprint than one would have for a traditional design without any solar equipment. The coefficient of performance (COP) of a solar cooling system is composed of contributions from the solar collector and the cooling equipment as COPsys = εsolarCOPcool
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TABLE 13.1 Comparison of Three Solar Cooling Options System PV: electric cooling Solar thermal: single-effect absorption cooling Solar thermal: double-effect absorption cooling
Collection Temperature (°C)
Collection Efficiencya
Cooling COP
System COP
NA 70
0.15 0.65
3b 0.7
0.45 0.46
110
0.54
1.2
0.65
Collection efficiency depends strongly on system design and operating conditions. Values given are just nominal values. Values for the solar thermal systems were taken from the model in Assilzadeh et al. (2005), which is a function of collection temperature. b Cooling COP for electric cooling is generally dependent on operating conditions. Given value is just a nominal or average value. a
The efficiency of the solar collector (εsolar) depends on the collector design but, in general, decreases as the energy collection temperature increases, due to heat loss to the environment (Assilzadeh et al. 2005). For the absorption cooling systems, the COP of the cooling system depends on the cycle design (and the collection temperature), as discussed at great length in this book. A general idea of these effects can be seen in Table 13.1. For the nominal values given, the double-effect (Li et al. 2014) absorption system gives the best performance (modestly better than the other two options). Although detailed economic data are not provided here, it is generally true that electric cooling machines (of the same cooling capacity) are less expensive than absorption cooling machines, by a wide margin. On the solar side, the collector costs (per m2) for PV or solar thermal are comparable (depending on the details of the installation). As the system COP is comparable and the costs are significantly lower, PV-driven electric cooling systems are the preferred solar cooling option in most cases today. This bottom line has been solidified by the steadily falling prices of PV panels in recent years due to low-cost manufacturing, primarily in China. Thus, although solar absorption cooling is technically feasible, it is not economically favorable in most situations. Numerous studies on solar absorption cooling can be found in the literature going back to the 1980s when Carrier produced and demonstrated a machine called the SAM-15 (Biermann 1980). A recent compilation of work on solar cooling can be found in Albers and Auracher (2014). Included in that volume is a review article that provides a good summary of recent work (Al-Alili et al. 2014). Among the many interesting studies on the subject, a solar-powered icemaker stands out as a unique application (Erickson 1991).
References Al-Alili, A., Y. Hwang, and R. Radermacher. (2014). Review of Solar Thermal Air Conditioning Technologies. International Journal of Refrigeration-Revue Internationale Du Froid 39: 4–22. Albers, J. and H. Auracher, Eds. (2014). Special Issue on Solar Cooling. International Journal of Refrigeration 39: 1–120.
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Alefeld, G. and J. Scharfe. (1991). An Absorption Heat Pump Transformer (Heat Pump Type III) for Distillation Plants. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 321–327. Arh, S. (1994). Absorption Heat Pump Transformer Cycle for Simultaneous Heating and Cooling. Proceedings of the International Absorption Heat Pump Conference, New Orleans, ASME AES-Vol. 31, pp. 79–84. Assilzadeh, F., S. A. Kalogirou, Y. Ali, and K. Sopian. (2005). Simulation and Optimization of a LiBr Solar Absorption Cooling System with Evacuated Tube Collectors. Renewable Energy 30(8): 1143–1159. Biermann, W. J. (1980). Prototype Modular 15 Ton Solar Absorption Air Conditioning System. Proceeding Annual DOE Active Solar Heating and Cooling Contractors Meeting, Incline Village, NV, pp. 2–13. Brant, B., S. Brueske, D. C. Erickson, and R. A. Papar. (1998). New Waste-Heat Refrigeration Cuts Flaring, Reduces Pollution. Oil & Gas Journal 96(20): 61–65. EIA. (2012). US Energy Information Agency, Annual Energy Outlook. EPRI. (1988). Industrial Heat Pump Manual: Technical and Application Resource Guide for Electric Utilities. EM-6057. Electric Power Research Institute, Palo Alto, CA. Erickson, D., D. K. Anand, and E. Makar. (2015). Absorption Refrigeration Cycle Turbine Inlet Conditioning. International Journal of Air-Conditioning and Refrigeration 23(1): 11. Erickson, D., G. Anand, and E. Makar. (2014). Absorption Refrigeration Cycle Turbine Inlet Conditioning. International Sorption Heat Pump Conference, College Park, MD, Paper #76, pp. 1–9. Erickson, D. C. (1991). Isaac Solar Refrigerator Environment-Friendly Technologies for the 21st Century. Proceedings of the Japanese Association of Refrigeration Absorption Heat Pump Conference, Tokyo. Erickson, D. C., G. Anand, I. Kyung, E. Makar, and C. B. Panchal. (2005). Absorption Refrigeration and/or Power Cycles for Industrial Waste Heat Applications. International Sorption Heat Pump Conference, Denver, Paper #3, pp. 1–8. Erickson, D. C. and F. Kelly. (1998). LPG Recovery from Refinery Flare by Waste Heat-Powered Absorption Refrigeration. IECEC-98 (Intersociety Energy Conversion Engineering Conference), Colorado Springs, CO. Fukusumi, Y., H. Yamada, T. Irie, K. Saito, N. Inoue, and Y. Nakagawa. (2014). Experiment of a Two-Stage Absorption Heat Transformer Generating Steam. International Sorption Heat Pump Conference, College Park, MD, Paper #135, pp. 1–10. Herold, K. E. (1985). Projects at Battelle Memorial Institute. Columbus, OH. Herold, K. E. (2007). Absorption Heat Pumps for Waste Heat Recovery Applications. In Encyclopedia of Energy Engineering and Technology, Vol. 3, B. Capehart, Ed. Taylor and Francis, Boca Raton, FL, pp. 1541–1547. Howe, L. A. and D. C. Erickson. (1991). High Temperature Industrial Absorption Heat Pumping. Proceedings of Absorption Heat Pump Conference, Tokyo, pp. 165–170. Hwang, Y. H. (2004). Potential Energy Benefits of Integrated Refrigeration System with Microturbine and Absorption Chiller. International Journal of Refrigeration-Revue Internationale Du Froid 27(8): 816–829. Kalinowski, P., Y. Hwang, R. Radermacher, S. Hashimi, and P. Rodgers. (2009). Application of Waste Heat Powered Absorption Refrigeration System to the LNG Recovery Process. International Journal of Refrigeration-Revue Internationale Du Froid 32(4): 687–694. Li, Z. Y., X. Y. Ye, and J. P. Liu. (2014). Performance Analysis of Solar Air Cooled Double Effect LiBr/ H2O Absorption Cooling System in Subtropical City. Energy Conversion and Management 85: 302–312. Ma, X., J. Chen, S. Li, Q. Sha, A. Liang, W. Li, J. Zhang, G. Zheng, and Z. Feng. (2002). Industrial Application of Absorption Heat Transformer for Waste Heat Recovery in Synthetic Rubber Plant. Proceedings of the International Sorption Heat Pump Conference, Shanghai, pp. 141–145. Thermax. (2015). http://www.thermaxglobal.com/thermax-absorption-cooling-systems/heat-pump/, accessed on 2 Dec 2015.
Appendix A: Using EES (Engineering Equation Solver) to Solve Absorption Cycle Problems
A.1 Overview EES (pronounced “ease”) is an acronym for Engineering Equation Solver. The basic function provided by EES is the numerical solution of nonlinear algebraic and differential equations. EES provides built-in thermodynamic and transport property functions for hundreds of fluids, including water, dry and moist air, most refrigerants, cryogens, and others. Included in the property database are thermodynamic properties for lithium bromide/water and ammonia/water mixtures, which are of special interest for absorption cycles. EES can also solve parametric tables, do optimization, provide uncertainty analyses, perform linear and nonlinear regression, convert units, check unit consistency, and generate publication-quality plots. These capabilities allow EES to be a powerful tool for analysis and design of absorption systems. A demonstration version of EES for computers running under Windows XP/7/8/10 or newer operating systems is available for download from F-Chart Software (http://fchart. com/ees/demo.php). All of the example problems in this book have been solved using EES. If you already have an EES license, you can download just the example problems from http://fchart.com/ees/books.php. The demonstration version of EES is useful only for solving and modifying the example problems. A complete version of the program can be purchased from F-Chart Software (http://fchart.com; email:
[email protected]). EES is in widespread use in academia and industry, and much information on using the program is available. If you are new to EES, the best starting point is likely the YouTube videos or written materials available at http://fchart.com/ees/. The best source of information concerning the use of EES for both new and experienced users is the Mastering EES ebook (Klein and Nellis 2015).
A.2 Recommended Way to Use EES (Example Problem 2.2) The zero-order model represented by Equations 2.17 through 2.22 is a simple representation of an absorption cycle operating at finite capacity. However, considerable computational effort is needed to solve this problem because the equation set is nonlinear, and repeated calculations are needed to identify the optimum heat exchange area distribution. Also some attention to guess values is needed to ensure that the iterative calculations produce the desired result. This example will be used to illustrate how best to use EES to obtain the desired results. 271
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As explained in chapter 5 of Mastering EES (Klein and Nellis 2015), it is best to enter a few equations at a time into EES and ensure that they are working properly and that the guess values are appropriate. Entering the equations in an organized way, starting with the input information, is the best way to ensure that the program will solve with minimal effort on your part. Start EES and enter the following information from the problem statement. Note that text within quotes is comments and need not be entered. “Zero Order Model - Single or Double Effect Absorption Cycle Ex 2.1” $TabStops 0.2 4 in “Inputs” U=0.5 [kW/m^2-K]
“heat exchange conductance per unit area”
T_h=convertTemp(C,K,200 [C]) T_c=convertTemp(C,K,50 [C]) T_e=convertTemp(C,K, -20 [C])
“high temperature” “condenser temperature” “evaporator temperature”
A_tot=10 [m^2]
“total area for all three heat exchangers”
These equations are direct and involve no iteration. In general, it is recommended that, after entering each subset of equations, you press F2 to ensure that the equations are entered properly and that they solve. Examine the Solution window and ensure that the values shown there are reasonable. If so, select the Update Guesses from the Calculate menu (Ctrl-G) to set the guess value of each entered variable to the most recent calculated value. This example is an optimization problem with two degrees of freedom. Although there are some alternatives, it is most reasonable to choose two of the three heat exchanger areas to be the optimization variables. In this case, we choose A_h and A_c, the areas of the generator and condenser. The third area is constrained by the requirement that the sum of the areas is A_tot. If you were to also enter a value for A_e, the equation set would be overconstrained and EES would issue an error message. The optimization should be the last task in solving the problem. At this time, we will just enter reasonable values for the optimization variables. “Specify values if not optimizing” $ifnot MinMax A_h=4 [m^2] A_c=3 [m^2] $endif A_tot=A_h+A_c+A_e
“area of the generator” “area of the condenser” “total area”
Note the use of the $ifnot MinMax directive in these equations. This directive simplifies the input. It will allow A_h and A_c to be set to the specified values when the optimization is not involved, but these specifications will be ignored while doing the optimization. Press F2 to check the equations. We next start the analysis, which begins by specifying the relations between area, heat transfer conductance, and heat transfer resistance. Enter the following equations and press F2.
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“Relate areas, conductances and resistances” A_h=UA_h/U “area of the generator” A_c=UA_c/U “area of the condenser” A_e=UA_e/U “area of the evaporator” UA_h=1/R_h “conductance of the generator” UA_c=1/R_c “conductance of the condenser” UA_e=1/R_e “conductance of the evaporator” The heat transfer rates are described by Equations 2.17 through 2.20. These equations involve temperatures T_c_i, T_h_i, and T_e_i, which are not known. These temperatures will eventually be determined by the reversibility criterion and single-effect constraints entered later, but it is best to enter reasonable values here to ensure that equations entered up to this point solve. Only two of these three temperatures can be specified because the third is fixed by the energy balance on the entire cycle. Temporarily, enter reasonable values of T_h_i and T_e_i. Note that, in order for heat to flow in the correct directions, T_h_i must be lower than the heat source temperature, T_h, and T_e_i must be lower than the temperature of the cold source, T_e. “Heat transfer relations” Q_dot_h=(T_h-T_h_i)/R_h Q_dot_c=(T_c_i-T_c)/R_c Q_dot_e=(T_e-T_e_i)/R_e Q_dot_h+Q_dot_e=Q_dot_c
“rate of heat transfer to the generator, Eqn. 2.17” “rate of heat transfer from condenser, Eqn. 2.18” “rate of heat transfer to evaporator, Eqn 2.19” “energy balance on the entire cycle, Eqn 2.20”
“temporary values to allow step by step testing of equations.” T_h_i=T_h-10 [K] “guess for saturation temperature in the desorber” T_e_i=T_e-10 [K] “guess for saturation temperature in the evaporator” Press F2 to solve the equations. Look at the heat flow rates and ensure that they are all positive values. Update the guess values (Ctrl-G) now so that guess values of the temperatures are set to reasonable values. Then, comment out temporary equations and continue entering the final part of the analysis. {“temporary values to allow step by step testing of equations.” T_h_i=T_h-10 [K] “guess for saturation temperature in the desorber” T_e_i=T_e-10 [K] “guess for saturation temperature in the evaporator”} “Property relations” T_h_i-T_c_i=T_c_i-T_e_i “Single effect, Eqn 2.22” Q_dot_e/Q_dot_h=T_e_i/T_h_i*((T_h_i-T_c_i)/(T_c_i-T_e_i)) “Second law - reversible requirement, Eqn 2.21” “Results” CAP=Q_dot_e “definition of evaporator capacity” COP=Q_dot_e/Q_dot_h “COP, Eqn 2.21” COP_Carnot=T_e/T_h*((T_h-T_c)/(T_c-T_e)) “Carnot COP”
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Solve the equations and examine the results. If the heat transfer rates and temperatures are reasonable, we are ready to complete the problem by doing the optimization to find the heat exchanger areas that maximize the cooling capacity. If you entered the $ifnot MinMax directive as suggested earlier, it will not be necessary to comment out the equations that set the values of two of the areas. Just select Min/Max from the Calculate menu (or press F4) to bring up the optimization dialog. Select CAP to be the optimization variable and A_c and A_h to be the optimization variables.
The optimization algorithms in EES require that bounds be specified for A_c and A_h. Press the Bounds button and enter reasonable values for the lower and upper bounds (e.g., 1 and 9 m2). Click the OK button to enter these bounds and again to exit the Min/Max dialog and start the optimization calculations.
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When the calculations are completed, the Solution window will show that the maximum cooling capacity is 17.486 kW and the areas of the high, low, and intermediate heat exchangers are 2.705, 2.286, and 5.009 m2, respectively. This example has illustrated the recommended way to use EES. Enter a few equations at a time and ensure that they solve and that the answers appear reasonable. If the equations involve variables that do not yet have values, temporarily enter reasonable values for these variables and remove them later as the analysis is developed. Update the guess values using the Update Guesses command as you go. It may also be necessary to enter lower and upper bounds for some variables, but this should be avoided unless it is necessary to prevent numerical problems. This method of working problems will generally result in EES providing correct results with the least effort. See Chapter 5 of Mastering EES for additional suggestions (Klein and Nellis 2015).
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A.3 Property Data in EES One of the most useful features of EES is its built-in functions for the thermodynamic and transport properties of fluids. Property data for many pure fluids (e.g., steam, ammonia, air, and many others) are built into the program and these property functions can be integrated with entered equations, such as mass and energy balances, to determine state-point information in an absorption cycle. As a very simple example, we can calculate the enthalpy change of vaporization of pure water and pure ammonia at 5°C with the following simple program.
Note the use of the $UnitSystem directive. It is good practice to include this directive at the top of the EES program to explicitly indicate what unit system is in effect. The specified units are shown in the status bar of the Equations window. Clicking on the units panel in the status bar will bring up the Unit System dialog, which provides an alternative way to specify the unit system. EES expects that the units of all inputs and outputs to and from the property routines will be as in the specified unit system. If the Unit Checking is on, EES will issue warnings if the units of any input or output are not specified or differ from the units expected by the property function. The units of any variable can be set in the Variable Information dialog (Options menu) or by right-clicking on the variable name in the Solution window. See the Units YouTube video (http://fchart.com/ees/) for details related to setting units of variables in EES. The property functions in EES are designed to accept any independent set of input values. For pure real fluids, two intensive (mass independent) properties fix the intensive state (Klein and Nellis 2012). Any combination of inputs, such as temperature and pressure or pressure and specific enthalpy, could be supplied. See the online help (Thermophysical Functions, http://fchart.com/ees/eeshelp/thermophysical_functions.htm) for a complete
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list of all property functions and inputs. In the aforementioned example, the inputs have been chosen to be the temperature (identified with the T= preceding the value or variable that holds the temperature) and quality (identified with x=). A quality of 1 designates saturated vapor, whereas a quality of 0 indicates saturated liquid. View the Property Data YouTube video (http://fchart.com/ees/) if you would like more information concerning the internal EES property data. The difference between the enthalpies of the vapor and liquid provide the enthalpy of vaporization shown in the Solution window. The enthalpy of vaporization of water is about double that of ammonia at 5°C. A mixture of two components has three degrees of freedom, requiring three intensive properties to fix the state. The current EES property database only provides data for four mixtures, which are air–water, lithium bromide/water, lithium chloride–water, and ammonia– water. Except for the air–water property data, which assumes ideal gas behavior, the property functions for all of the mixtures are actually provided by external programs called by EES. Their use differs somewhat from that of the built-in functions, although the ammonia–water routines have been formulated to look quite similar to the pure fluid routines. The use of the lithium bromide/water and ammonia–water property functions is central to the mission of this book, and they are described in detail next in Sections A.4 and A.5.
A.4 Lithium Bromide/Water Property Libraries There are actually three separate property libraries for mixtures of lithium bromide and water. The original library that was used with the first edition of this book is provided in file LiBr.DLL located in the ..\USERLIB\LIBR folder within the EES directory. These property functions are based on information from the ASHRAE Handbook of Fundamentals (ASHRAE 1989). Use of these property functions is not recommended because more accurate property functions are available. The LiBr.DLL properties are provided in EES solely for backward compatibility. A second property package for lithium bromide/water mixtures is provided with EES in the form of an external EES library, named LiBrH2O.LIB. The properties in this library are based on the property correlation provided by Patek and Klomfar (2006). The library includes functions for viscosity (Lee et al. 1990) and thermal conductivity (DiGuilio et al. 1990). The third lithium bromide/water property library, which is used for the examples in the second edition of this book, were developed by Yuan and Herold (2005) as a part of the Sorption Systems Consortium at the University of Maryland. The library is written in C++ and provided as a dynamically linked library named LiBrSSC.DLL. This library resides in the same LiBr folder as the other two libraries. Older versions of EES may not provide this library, but it can be downloaded from http://fchart.com/ees/add-ons.php. The property routines in this library are summarized in Table A.1. Additional information on the use of these property routines can be obtained from the online help provided with the library using the Function Information command in the Options menu. A disadvantage of using the LiBrSSC external library directly is that all properties must be in the unit system expected by the library. For example, all temperatures are in degree Celsius. If EES is configured to operate in K or in °F, conversions must be made before the call is issued. A set of LiBrSSC helper functions has been prepared to allow the LiBrSSC library to be used with the unit system set in EES using the Unit System dialog or the $UnitSystem directive. The helper functions are listed in Table A.2.
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TABLE A.1 Summary of LiBrSSC Routines Functions
Output Units
Thermal conductivity Dynamic viscosity Specific heat Enthalpy
W/m-K cP J/g-K J/g
Chemical potential of water Chemical potential of LiBr Volume Entropy
J/g J/g m3/kg J/g-K
Saturation pressure Saturation temperature Crystallization temperature Index of refraction
kPa °C °C —
Procedures Partial mass Gibbs function Partial mass enthalpy Partial mass entropy Partial mass volume Flashing process
J/g J/g J/g-K m3/kg *
Call Format k = LiBrSSCCond(Tc,X) µ = LiBrSSCVisc(Tc,X) c_p = LiBrSSCCp(Tc,X,P) or c_p_sat = LiBrSSCCp(Tc,X) h = LiBrSSCh(Tc,X,P) or h_sat = LiBrSSCh(Tc,X) µ_w = LiBrSSCuw(Tc,X, P) µ_LiBr = LiBrSSCus(Tc,X, P) v = LiBrSSCv(Tc,X) s = LiBrSSCs(Tc,X,P) or s_sat = LiBrSSCs(Tc,X) P_sat = LiBrSSCp(Tc,X) T_satt = LiBrSSCT(P,X) T_cryst = LiBrSSCTCryst(X) N = LiBrSSCRefIndex(Tc,X) CALL LiBrSSCpart_g(Tc, X, P : g, dgdx, mu_w, mu_s) CALL LiBrSSCpart_h(Tc, X, P : h, dhdx, h_w, h_s) CALL LiBrSSCpart_s(Tc, X, P : s, dsdx, s_w, s_s) CALL LiBrSSCpart_v(Tc, X : v, dvdx, v_w, v_s) CALL LiBrSSCflash(h, P, x_in : q, T, x, hl, hv)
Input units: Tc, °C; X, mass fraction of LiBr; P, kPa. Overloading: LiBrSSCCp, LiBrSSCCh, and LiBrSSCCs all employ overloading such that if you do not input a value for pressure, the saturation pressure is assumed. *See details on units in the procedure description in the EES built-in help.
TABLE A.2 Summary of LiBrSSC Helper Functions Function Thermal conductivity Dynamic viscosity Specific heat Enthalpy Volume Entropy Saturation pressure Saturation temperature Crystallization temperature
Example k = Cond_LiBrH2OSSC(T,X) mu = Visc_LiBrSSC(T,X) cp = Cp_LiBrSSC(T,X) h = h_LiBrSSC(T,X) v = v_LiBrSSC(T,X) s = s_LiBrSSC(T,X) Psat = Psat_LiBrSSC(T,X) Tsat = Tsat_LiBrSSC(P,X) Tcryst = Tcryst_LiBrSSCT(X)
Note: The units of the properties for these functions are as selected with the $UnitSystem directive or the Unit System dialog. The units of properties are converted as needed to the unit system required by the LiBrSSC routine in Table A.1.
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The following example demonstrates the use of the lithium bromide/water property functions and the plotting capability in EES. The objective is to plot the enthalpy of a lithium bromide/water solution as a function of composition at temperatures of 10°C and 100°C for mass fractions between 0.4 and 0.75. This is a very simple problem, and all the needed equations can be entered directly and tested at one composition before creating the parametric table and the plot. The LiBrSSC library compositions are provided as a LiBr mass fraction. The following equations using the functions in Table A.2 determine the specific enthalpy of a saturated solution at both temperatures. These functions will operate in the unit system specified with the $UnitSystem directive. $UnitSystem SI C kPa kJ $IFNOT ParametricTable x=0.5 $endif T_lo=10 [C] T_hi=100 [C] h_lo=h_LiBrSSC(T_lo,x) h_hi=h_LiBrSSC(T_hi,x) Note the use of the $IFNOT directive. As we are not using a parametric table at this point, the composition specified in variable x is set to 0.5. When a parametric table is used, this equation will be ignored. Solve the equation set to ensure that the equations are entered properly and that the LiBrSSC property library is installed. The Solution window should appear as follows.
We need to vary the value of x between 0.4 and 0.7 and plot the specific enthalpies. This is most easily accomplished using a Parametric table, which is similar to a spreadsheet. Select New Parametric Table from the Tables menu. The list on the left initially shows all of the variables appearing in the equations. The list on the right holds the variables that will appear in the parametric table. Click on variables h_hi, h_lo, and x to select them and then click the Add button to include them in the parametric table. Set the number of
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runs (rows) in the parametric table to 20. Click the OK button and a table with three columns and 20 rows is generated.
We next need to enter values of x between 0.4 and 0.7. Click on the triangular control at the upper right of the header cell for variable x. The following dialog will appear, where you can enter the first and last values to appear in the x column.
Click OK and EES will fill in equally spaced values of x between the two limits specified. Next, select Solve Table from the Calculate menu (or press F3) to solve the Parametric table. The values of h_lo and h_hi for each value of x in the table are calculated and displayed in the table.
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Appendix A
Once the values are determined, they can be plotted using the New Plot Window command in the Plots menu. Select x to appear on the x-axis and h_lo and h_hi for the y-axis. EES will automatically set the scales, but you may wish to adjust them.
Click the OK button and provide a label for the y-axis when prompted to do so and the plot will then be displayed, as shown in Figure A.1. Labels for 10°C and 100°C can be added to the plot to identify the lines. See the Plotting in EES YouTube video (http:// fchart.com/ees/) for more information. 300 100°C
Specific enthalpy (J/g)
250 200 150
10°C
100 50
0 0.4
0.5
x
0.6
FIGURE A.1 Plot of specific enthalpy versus mass fraction of lithium bromide at 10°C and 100°C.
0.7
282
Appendix A
A.5 Ammonia/Water Property Library The ammonia/water property library is provided in an external file named NH3H2O.DLP that is located in the ..\USERLIB\EES_SYSTEM folder in the EES directory. The thermodynamic property data are based on the mixture equation of state developed by Ibrahim and Klein (1993). Ammonia/water mixtures require three independent properties to fix each state. The original implementation of this library, which was used in examples of the first edition of this book, provided access to the data through a Call function with the following format: CALL NH3H2O(Code, In1, In2, In3 : T, P, x, h, s, u, v, Q) The four parameters to the left of the colon (Code, In1, In2, and In3) are inputs. The parameters to the right of the colon are outputs calculated by the NH3H2O program. The NH3H2O routine only operates in SI units with T = [K], P = [bar], x = [ammonia mass fraction], h = [kJ/kg], s = [kJ/kg-K], u = [kJ/kg], v = [m3/kg], and Q = [vapor mass fraction]. For saturated states, 0 ≤ Q ≤ 1. Subcooled states are indicated with Q = –0.01; superheated states have Q = 1.01. The first input, Code, is a three-digit number that indicates which three properties are supplied in In1, In2, and In3, as indicated in the table. For example, Code = 128 implies that In1 is temperature, In2 is pressure, and In3 is vapor quality. Property
T
P
x
h
s
u
v
Q
Code
1
2
3
4
5
6
7
8
Ammonia/water property data can still be accessed with the CALL statement, but a simpler implementation that is consistent with the format of built-in property functions has been developed, and it is this implementation that is used in the examples of this book. Their use is summarized in Table A.3. TABLE A.3 Calling Ammonia/Water Property Routines in EES Using a Simplified Interface NH3H2O Fluid Mixture—Simplified Calling Interface Property functions that accept NH3H2O as the fluid name: Conductivity Density Enthalpy Entropy IntEnergy MassFraction Pressure Quality Surface tension Temperature Viscosity Volume
Inputs: each of the functions in the first column needs three input properties from the following list H = specific enthalpy P = pressure Q = quality (saturated states, 0 ≤ Q ≤ 1) S = specific entropy T = temperature U = specific internal energy V = specific volume X = mass fraction
Example: Compute pressure of NH3H2O given temperature, mass fraction, and quality. P[1] = pressure(NH3H2O,T=T[1],x = x[1],Q = Qu[1]).
283
Appendix A
Note that X designates mass fraction for NH3H2O, whereas it designates quality for all of the pure fluids. Q is used to designate quality for NH3H2O. Also, the quality function will return a value of –0.001 for a subcooled state and 1.001 for a superheated state, whereas –100 and 100 are used for the pure fluids. Otherwise, the use of the NH3H2O property functions is the same as for the pure fluids. In particular, the property inputs and returned property value are in the unit system designated with the unit system selected in EES using the $UnitSystem directive or Unit System dialog, just as with the pure fluids. Example 4.2 demonstrates use of the NH3H2O library. The EES code and results for this example are shown next. A rich ammonia/water saturated solution at 370 K having an ammonia mass fraction of 0.3 flows into a desorber. Saturated liquid and vapor streams exit in equilibrium. The liquid stream has an ammonia mass fraction of 0.20. The entire process occurs at constant pressure. The objective is to calculate the mass flow rate of the rich solution and the required heat transfer per kilogram of vapor generated. First, specify the units system that will be used with the $UnitSystem directive. $UnitSystem SI K kPa mass Three properties are needed to fix each state. The temperature, quality, and mass fraction are known for the inlet rich solution (state 1). This information can be used with the ammonia/water property library to determine the pressure and the specific enthalpy of state 1. “Properties of incoming rich solution (state 1)” T[1]=370 [K] Qu[1]=0.0 x[1]=0.30 P[1]=pressure(NH3H2O,T=T[1],x=x[1],Q=Qu[1]) h[1]=enthalpy(NH3H2O,T=T[1],x=x[1],Q=Qu[1])
“temperature of rich solution” “Quality (saturated liquid)” “mass fraction at inlet, inlet” “pressure at state 1” “specific enthalpy at state 1”
Solve these equations to ensure that they have been entered properly and the ammonia/ water property library is available. The process occurs at constant pressure, so the pressure for the exiting states is the same as for state 1. The mass fraction of the exiting liquid (state 3) is known, and it is a saturated liquid state, which completely specifies state 3. “Properties of saturated liquid at outlet (state 3)” x[3]=0.20 Qu[3]=0.0 P[3]=P[1] h[3]=enthalpy(NH3H2O,P=P[3],x=x[3],Q=Qu[3])
“mass fraction” “saturated liquid” “isobaric process” “specific enthalpy at state 3”
Solve. Next, the temperature and pressure of the exiting saturated vapor (state 2) are the same as for the exiting liquid (state 3). The quality of the vapor is 1. The mass fraction and specific enthalpy can be determined.
284
Appendix A
“Properties of saturated vapor at outlet (state 2)” T[2]=T[1] “thermal equilibrium” P[2]=P[1] “isobaric” Qu[2]=1.0 “saturated vapor” x[2]=massfraction(NH3H2O,T=T[2],P=P[2],Q=Qu[2]) “mass fraction” h[2]=enthalpy(NH3H2O,T=T[2],P=P[2],Q=Qu[2]) “specific enthalpy” The mass flow rate of entering rich solution (state 1) per kilogram of vapor (state 2) can now be calculated. “Summary of results” f=(x[2]-x[3])/(x[1]-x[3]) q=h[2]-h[3]+f*(h[3]-h[1])
“flow rate f of rich solution per kg of vapor” “heat transfer per kg of vapor generated”
The Solution Window that appears after solving these equations should appear as follows once you enter units for P[1], h[1], and q (kPa, J/g, and J/g, respectively). The results agree with those provided in Example 4.2 with the small difference due to the fact that the temperature is 370 K in this example and 373.15 in Example 4.2.
A.6 Coaxing a Set of Equations to Converge (Example 10.1) The discussion in Section A.2 focused on how best to enter equations into EES in a manner that will provide a solution. This discussion is most appropriate when entering a new set of equations. However, it is often the case with absorption cycle models that you have a working EES program for one set of inputs and you now want to use the existing model to calculate the performance of this cycle at a different set of conditions. Modifying the
285
Appendix A
inputs to the EES code and then solving can result in an error message from EES indicating that convergence on a solution was not attained. This section describes how to coax the model to provide a solution. This convergence problem is exemplified with Example 10.1, which provides a model for the two-stage system shown in Figure A.2. This system is challenging to model because of the cyclic flows that occur within the cycle. See Appendix C for a discussion of redundant mass balances common in absorption cycle analysis. The original model for this cycle was developed and solved following the recommendations provided in Section A.2, which involves a systematic procedure that focuses on adding one equation at a time and testing each equation when it is added. Although tedious, this procedure is the most effective way to model a completely new cycle. Once the model is running, variations on the model can be studied by changing the inputs. In Example 10.1, the effectiveness of both solution heat exchangers and the condensate precooler (identified as RHX in Figure A.2) were set to 0.8. If you wish to follow along with this example, open file Ex10_1.EES and solve it (press F2). EES should quickly converge to a solution for which the cycle COP is 0.496. The purpose of a model is to allow the effects of changes in a design to be estimated without having to build and test the equipment. In this case, it is of interest to determine how the cycle COP would be affected if the condensate precooler was not included in the system. Ideally, all that would be necessary to answer this question is to change one input value and e-solve. Locate the following equation in the Equations window “effectiveness of condensate precooler”
epsilon_cpc=0.8 and change this equation to
“effectiveness of condensate precooler”
epsilon_cpc=0
˙ Q cond C
˙ Q rect,1
25 9
R1
8
10
Desorber 1 4
3
SHX 1
W˙ p1
RHX 11
24
˙ Q rect,3
˙ =Q ˙ +Q ˙ Q des,1 abs,2 rect,2 ˙ W p2
R2
23
28
26 14 15
Absorber 1
17
˙ Q abs,1
FIGURE A.2 Schematic of a two-stage absorption system with condensate precooling.
18
20
21
Absorber 2 29
Desorber 2
SHX 2
16
6
1
Q˙ evap
R3
˙ Q des,2
22
13
12 E
5
2
˙ Q rec,2
˙ 27 Q des,1
7
Q˙ abs,2
19
286
Appendix A
Setting the effectiveness of the condensate precooler to 0 is equivalent to removing it from the cycle. However, when you try to solve the equation set with this new input, you will find that EES does not converge. The equations representing the performance of this cycle are coupled and nonlinear, and the guess values resulting from the original case when the effectiveness was 0.8 do not provide a set of guess values, for the new case where the effectiveness is 0.0, that is sufficiently close to the solution to allow convergence. The best way to get this set of equations to converge with the new input is to incrementally change the value of epsilon_cpc from its original value to the desired value. To illustrate this point, return the value of epsilon_cpc to 0.8 and solve. EES should converge readily. Next, update the guess values using the Update Guess menu item in the Calculate menu or more simply by entering Ctrl-G. Now change the value of epsilon_cpc to 0.6. If the equations converge, as they will in this case, update the guess values and continue lowering the value of epsilon_cpc. For example, reducing epsilon_cpc by 0.2 each time will result in the desired solution at epsilon_cpc=0 after four iterations. In general, if the equations do not converge, taking a smaller increment in the variable often resolves the problem. For this example, the equation set will converge with epsilon_cpc=0 and the resulting COP is 0.411, but only with a set of guess values that is sufficiently near the solution. It is noted that this heat exchanger has a significant effect on the cycle performance and that that implies large changes in most of the variables in the problem as epsilon_cpc changes. There are two ways to simplify this stepwise process of finding a good set of guess values. The first is to include $UpdateGuesses in the Equations window. This directive will automatically update the guess values after a successful solution is obtained. The second option is to employ the Parametric table to incrementally vary the value of epsilon_cpc from its original value (0.8) to the desired value (0.). Ensure that the Update guess values check box is checked in the Solve Table window. EES will then automatically run a series of calculations that vary the value of the parameter (epsilon_cpc) and update the guess values after each calculation. This allows you to automate the stepwise process. In some cases where the equations are very sensitive, it may be necessary to use a small step size (which implies a large number of runs in the Parametric table). If a given step size does not converge, you can try adding some runs to reduce the step size and trying again. One caution in this process is that, in some cases, varying the value of an input parameter may drive the solution toward a constraint of some kind, which could be a variable constraint in EES or a physical constraint in the problem, such as the fact that the ammonia concentration cannot go below zero. If you are unable to get your equations to converge with a small increment size, a next step would be to investigate the closest converged solution for clues as to possible constraint violations. This ability to leverage a converged solution to obtain neighboring solutions of the same equation set is a fundamental concept behind the presentation in this book. If the cycle you are interested in already appears, you should be able to readily modify it for your unique application.
Appendix A
287
A.7 Conclusion This appendix has described a number of more important capabilities of EES with respect to modeling absorption systems. EES is a very versatile program with many other features. Additional information on the program operation can be obtained from the Help menu or from the program manual. Like any tool, EES requires some effort to master. The effort expended in learning how to use EES efficiently will prove to be a worthwhile investment in that it will allow you to easily solve problems that would have otherwise been intractable.
References ASHRAE. 1989. ASHRAE Handbook of Fundamentals. Atlanta, GA: ASHRAE, 1989. DiGuilio, R.M., Lee, R.J., Jeter, S.M., and Teja, A.S. Properties of Lithium Bromide-Water Solutions at High Temperatures and Concentrations—I Thermal Conductivity, ASHRAE Transactions, 96, 702–708, 1990. Ibrahim, O.M., and Klein, S.A. Thermodynamic Properties of Ammonia-Water Mixtures, ASHRAE Transactions, 21(2), 1495–1502, 1993. Klein, S.A., and Nellis, G.F. Mastering EES, ebook published by F-Chart Software. 2015. http://www. fchart.com Klein, S.A., and Nellis, G.F. Thermodynamics. Cambridge University Press, New York, NY, 2012. Lee, R.J., DiGuilio, R.M., Jeter, S.M., and Teja, A.S. Properties of Lithium Bromide-Water Solutions at High Temperatures and Concentrations—II Density and Viscosity, ASHRAE Transactions, 96, 709–714, 1990. Patek, J., and Klomfar, J. A Computationally Effective Formulation of the Thermodynamic Properties of LiBr-H2O from 273 to 500 K Over Full Composition Range. International Journal of Refrigeration, 29, 566–578, 2006. Yuan, Z., and Herold, K.E. Thermodynamic Properties of Aqueous Lithium Bromide Using a Multiproperty Free Energy Correlation, HVAC&R Research, 11(3), 377–393, 2005a. Yuan, Z., and Herold, K.E. Specific Heat Measurements on Aqueous Lithium Bromide, HVAC&R Research, 11(3), 361–375, 2005b.
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Appendix B: Absorption Cycle Modeling
B.1 Introduction The discussion of modeling in this appendix is based primarily on a generic single-effect cycle without advanced features. The discussion applies equally well to both water/ lithium bromide and ammonia/water systems, and it can be readily extended to advanced cycles. The models of interest are steady-state system models. The objective is to create a model that is a useful representation of a real absorption cycle. Thus, the inputs and outputs are chosen to obtain as much connection to real practice as possible. A schematic of the generic single-effect cycle is included as Figure B.1. The inputs and outputs associated with the model are indicated in Table B.1. In the following sections, this cycle is examined from various perspectives with the goal of assembling the overall system model. For simplicity in the presentation, it is useful to concentrate on the physics of the cycle itself and to postpone consideration of the external heat transfer processes until after a full understanding of the cycle is obtained. This approach, which has been termed an “internal model” in this book requires a cycle schematic as shown in Figure B.2. Both of the schematics in Figures B.1 and B.2 represent the same cycle, but in the case of Figure B.2, the heat transfer processes are not modeled as heat transfer mechanism relations but instead are represented by heat transfer rates (Q ′s). This simplified view avoids some clutter in the analysis. Sections B.2 and B.3 are based on Figure B.2, and then the external heat transfer processes are integrated in Section B.4.
B.2 Mass Balance Considerations Mass balances can be routinely written on each of the components in the absorption cycle in Figure B.2, as shown in Table B.2, Equations B.1 through B.8. Although we expect all of these mass balances to be satisfied by a valid solution, the set shown in Table B.2 turns out to include redundant entries that can cause trouble in modeling. A complete understanding of the unique mass balance issues associated with absorption cycles is critical if one is to be successful in modeling new cycles. As the working fluids are mixtures, it is necessary to obtain a mass balance for each species in the mixture. Once the species mass balances are satisfied, the overall mass balance will also be satisfied by definition. Thus, for each component in the cycle, one expects to write a number of mass balances equal to the number of species in the working fluid. For binary mixtures such as water/lithium bromide and ammonia/water, this means two mass balances for each cycle component. The analyst can write either (1) mass balances for each of the species or (2) the overall mass balance plus one species mass balance. In Table B.2, each cycle component is represented by 289
290
Appendix B
˙ 15 Q c
16
12 7
Condenser
4 Solution heat exchanger
Refrigerant expansion valve 2
· W
9
5 Pump Solution expansion valve
1
Evaporator
6 Absorber
10 18
˙ Q d Desorber
3
8
˙ Q e
11
17
13
14
˙ Q a
FIGURE B.1 Schematic of single-effect cycle with external heat transfer processes.
TABLE B.1 Model Inputs and Outputs Inputs Solution pump flow rate External heat transfer fluid flow rates External heat transfer fluid inlet temperatures Heat exchanger sizes
Outputs Refrigerant and solution loop flow rates Thermodynamic state points Heat transfer rates System performance
an overall mass balance and a balance on one of the mixture components. It is important to avoid including a redundant third mass balance because such an equation does not contribute any additional information and, if included, tends to lead to a discontinuity during attempts at solution of the set of equations. Another redundancy in mass balances can be easily introduced when one is dealing with cycles because of the cyclic nature of the flow systems. This is seen by examining some specific cases. Assuming a binary working fluid, there are two variables for each stream. These are the mass flow rate and the mass fraction (i.e., the composition). From a mass balance perspective, the specification of these two variables completely defines the streams. For the purpose of the mass balance discussion in this section, the mass fractions of the streams are viewed as being defined by other constraints, namely the other equations in the model such as the energy balances and heat transfer equations.
291
Appendix B
˙ Q c
˙ Q d 7
Condenser
Desorber 3
8
4 Solution heat exchanger
Refrigerant expansion valve 2 · W
Pressure
9
Pump Solution expansion valve 6
1
Evaporator
Absorber
10 ˙ Q e
5
˙ Q a
Temperature FIGURE B.2 Schematic of single-effect cycle without external heat transfer processes (internal model).
From this perspective, then, the mass fractions of all the streams are assumed known. Note that in certain cases, it is not possible to independently specify all of the mass fractions, in which case only the independent set is assumed. This point is returned to later in this section. Furthermore, it is assumed that the solution pump mass flow rate is known. This corresponds to turning on a pump with a known flow rate characteristic. If it is assumed that the flow rate in stream 1 (Figure B.2) is known, then there are nine unknown flow rates to be determined in Equations B.1 through B.8 listed in Table B.2. For the components that involve only a single inlet and single outlet, the mass balance considerations are largely trivial. These include the pump, both expansion valves, the condenser, and the evaporator. Furthermore, the solution heat exchanger also falls into this category because the solution streams on the hot and cold sides do not mix. For all of these components, the overall composition of the working fluid does not change across the device and the mass flow rate in equals the mass flow rate out. The redundancy in Equations B.1 through B.8 can be demonstrated by combining Equations B.1 through B.4 and B.6 through B.8 in such a way as to eliminate the mass flow 8, m 9 , and m 1. The resulting equations are identical to Equation B.5, 1, m 2, m 5, m 6, m rates m which implies that Equation B.5 is redundant to the remaining set. A similar redundancy occurs in all absorption cycles because of recirculating flows. The redundancy becomes clearer if all the trivial mass balances are removed from the system of equations. This can be done by ignoring the components with a single inlet and single outlet. With this in mind, the single-effect cycle mass flows can be represented as in Figure B.3. There are only two components in the cycle that have nontrivial mass balances. The mass balances on the two components in Figure B.3 are identical. Although this may seem obvious for the simple systems shown in Figures B.2 and B.3, more complex systems can introduce significant
292
Appendix B
TABLE B.2 Mass and Energy Balances for Cycle in Figure B.2 Mass Balances for Each Component Pump
1 = m 2 m
Solution heat exchanger
2 = m 3 m
x2 = x3
4 = m 5 m
x 4 = x5
(B.1)
x1 = x2
Solution expansion valve
5 = m 6 m
(B.2)
(B.3)
x5 = x6 Absorber
10 + m 6 = m 1 m
(B.4)
10 x10 + m 6 x6 = m 1 x1 m Desorber
3 = m 4 +m 7 m
(B.5)
3 x3 = m 4 x4 + m 7 x7 m Condenser
7 = m 8 m
(B.6)
x7 = x8 Refrigerant expansion valve
8 = m 9 m
(B.7)
x8 = x9 Evaporator
9 = m 10 m
(B.8)
x9 = x10 Energy Balance for Each Component Pump
=m 1 h1 + W 2 h2 m
(B.9)
Solution heat exchanger
2 h2 + m 4 h4 = m 3 h3 + m 5 h5 m
(B.10)
Solution expansion valve
h5 = h6
(B.11)
Absorber
10 h10 + m 6 h6 = m 1 h1 + Q a m
(B.12)
Desorber
3 h3 + Q g = m 4 h4 + m 7 h7 m
(B.13)
Condenser
7 h7 = m 8 h8 + Q c m
(B.14)
Refrigerant expansion valve
h8 = h9
(B.15)
Evaporator
9 h9 + Q e = m 10 h10 m
(B.16)
confusion as to which equations should be included in a well-posed model. By breaking the problem down and analyzing the mass balance equations separately, this confusion can be avoided. The b ottom-line conclusion is that there are two redundant mass balance equations in a simple single-effect absorption machine. A slightly more complicated flow scheme is illustrated in Figure B.4. This flow scheme is similar to that found in a parallel-flow, double-effect absorption cycle. In this case there are seven flow streams. It is assumed that the mass flow rates of streams 1 and 3 are fixed by their respective pumps. Thus, there are five unknown flow rates. It can be shown that there are six independent mass balance equations. One possible set can be written as shown in Table B.3.
293
Appendix B
Desorber 1 3 2 Absorber FIGURE B.3 Mass flows in simple single-effect cycle. High desorber 3
5
4 Mixer
7
6
Low desorber 1 2 Absorber
FIGURE B.4 Mass flows in a double-effect cycle.
TABLE B.3 Nonredundant Set of Mass Balances for System in Figure B.4 Component Low desorber
Mass Balances 2 + m 3 + m 6 = m 1 + m 4 m 2 x2 + m 3 x3 + m 6 x6 = m 1 x1 + m 4 x4 m
High desorber
3 = m 4 +m 5 m 3 x3 = m 4 x4 + m 5 x5 m
Mixer
5 + m 6 = m 7 m 5 x5 + m 6 x6 = m 7 x7 m
The pair of mass balances for the absorber can be shown to be dependent on the set included in Table B.3 and, therefore, would be redundant in a cycle model. Note that another complete set would include the Absorber balances but omit the High Desorber balances. In this case, there are six independent mass balance equations and five unknown flow rates. Thus, we can only specify six of the mass fractions independently since the outlet
294
Appendix B
mass fraction from the Mixer (state 7) is fully determined from the inlet conditions and the two mass balances. This situation is typical of a device that has multiple inlets and only one outlet. So, our count is six independent mass balances and six variables (five flow rates and one mass fraction). The number of independent mass balances for a new cycle with a binary working fluid can be determined by the following procedure. Step around the cycle schematic, component by component, and write a pair of mass balances for each one. To enable those balances, draw a control volume for each component. The control volumes should be contiguous, as shown in Figure B.5. When you get to a component where all of the connections are already included in mass balances written for other components, then you know that the balances written for that component will be redundant. Count two mass balances for each of the nonredundant components. It is observed that this procedure always results in two redundant mass balances for any cycle involving a binary fluid. Another very useful exercise in thinking about the mass balances for a new cycle is to enter the mass balance equations into EES to see if they will solve. For example, consider Figure B.5; if you enter the equations in Table B.3 into EES along with the specification of the flow rates in streams 1 and 3 and the specification of the mass fractions in streams 1–6, you find that the model produces reasonable values for all of the unknown flow rates as well as the dependent mass fraction at state 7. This model is provided in file AppB_1.ees. Although the discussion in this section is based on the assumption that certain mass fractions in the cycle are known, the overall result (i.e., the number of independent mass balances) is independent of that assumption. This assumption was convenient to introduce the discussion of mass balance redundancy because it allowed the mass balance considerations to be uncoupled from the remaining equations in the model. In the following sections, this restriction is lifted to allow the full coupling expected in an actual absorption machine where the mass balances may influence the mass fractions and the energy balances may influence the mass flow rates. A proper, nonredundant set of mass balances forms the basis of a more complete model that includes coupling between the mass and energy balances in the problem.
High desorber 3
5
Mixer
7
6
4
Low desorber
1
2 Absorber
FIGURE B.5 Mass balance equation counting schematic with control volumes.
295
Appendix B
Example B.1: Resorption Cycle Determine the number of independent mass balances that can be written for the resorption cycle in Figure 8.5. Figure B.6 is a simplified version of Figure 8.5 showing only the components that have nontrivial mass balances. Solution: After redrawing the schematic to only include the nontrivial components, we end up with four components connected by six streams, as shown in Figure B.6. If the counting procedure is applied, we find that after drawing control volumes around three of the components, then the final component has no new streams (i.e., none that are not already connected). Thus, we conclude that there are six nonredundant mass balances. After specifying two solution flow rates, we can independently specify only four mass fractions. Note that it is not possible to independently specify the mass fraction of states 3 and 6 because x3 = x6 is required for a steady-state solution (and the mass balances enforce that). As Absorber 2 has a mixer configuration (two inlets and one outlet), it is not possible to independently specify the mass fraction of state 5. See file ExB_1.ees. Example B.2: Mass Balances in Ammonia/Water Cycles Determine the number of independent mass balances in the ammonia/water singleeffect cycle pictured in Figure 9.3. Figure B.7 is a simplified version of Figure 9.3 showing only the components that have nontrivial mass balances. Solution: The counting procedure finds three nontrivial components, but only two yield independent mass balances. Thus, we obtain a count of four independent mass balances. As there are five streams and one solution pump, all five mass fractions can be independently specified. However, it is noted that not all mass fraction specifications will give physically meaningful results. See file ExB_2.ees.
3
Absorber 2 5
Desorber 1
4
Desorber 2
1
6
2
Absorber 1
FIGURE B.6 Mass balance schematic for resorption cycle. 4 Rectifier
Desorber 3
5
1 Absorber
FIGURE B.7 Mass balance schematic for single-stage ammonia/water cycle.
2
296
Appendix B
The mass balance models discussed here, and implemented in EES, are a very promising way to start the analysis of a new cycle. If you can start the simulation without any errors in the mass balance formulation, you can avoid considerable confusion.
B.3 Energy Balances An energy balance can be written for each component of the system. The energy balance accounts for the energy flowing into (or out from) the system with mass flows and any heat transfer or work interactions. The component energy balances for the cycle shown in Figure B.2 are given in Table B.2 as Equations B.9 through B.16. The energy flows are assumed positive in the direction of the arrows shown in Figure B.2. The specific enthalpy values needed to evaluate these equations must be obtained from property data sources for the working fluid of interest. The enthalpy values depend on the thermodynamic state, and the state depends on the operating conditions of the adjoining state points. Thus, there is coupling between the system components and the system equations must, in general, be solved simultaneously.
B.4 Heat Transfer Processes Heat transfer processes are of fundamental importance in modeling the performance of an absorption cycle. The primary function of the cycle is to transfer heat from a low temperature to a high temperature, and this function is achieved by proper choice of the size and type of heat exchanger components. The modeling approach described in Section 4.10 gives the modeler a tool to examine the effect of heat exchanger size on cycle performance. There are five heat exchangers in the cycle described in Figure B.1. These are the desorber, absorber, condenser, evaporator, and solution heat exchanger. The first four exchange heat between the cycle and its surroundings, while the solution heat exchanger transfers heat internally within the cycle. These components have been described in some detail in Chapters 4, 6–11. With the exception of the solution heat exchanger, these components are combined heat and mass exchangers. The mass transfer and heat transfer processes are closely coupled. As discussed in Section 4.10, a model of the overall transfer process must account for both the heat transfer and mass transfer. The simplified approach described in Section 4.10 utilizes an overall transfer characteristic of the heat and mass transfer device to describe the component. The transfer characteristic is defined in terms of the temperature-driving potential. The overall transfer characteristic of a particular device will certainly depend on both heat transfer and mass transfer resistances, but because the two processes are closely coupled, the model can be written in terms of the temperature driving potential. In general, the heat transfer models allow the coupled heat and mass transfer characteristics of the device to be modeled by a single equation. For example, a UA formulation for any of the heat exchangers will involve an equation of the form
Q = UA∆ Tlm (B.17)
Appendix B
297
with the log mean temperature difference defined in terms of the temperature differences at the two ends of the device (as discussed in Section 4.10).
B.5 Equation and Variable Counting The equations representing an absorption cycle include those already described in Sections B.1 through B.4 and also include assumptions about the thermodynamic state at various points within the cycle. As of the number of equations involved, particularly for cycles with more complexity than a single-effect cycle, it is necessary for the modeler to count the equations to ensure that the problem being solved is well posed. If a problem is underspecified or overspecified (i.e., if there are too few or too many equations), the solver will typically fail and give a diagnostic. However, if you have the right number of equations but the wrong equations, the solver will not generally be able to give a clear diagnostic. Thus, it is useful to have a step-by-step procedure for understanding your equations, as was introduced in Sections B.2 for mass balances. Equation counting is an art in the sense that there is not a single answer to the problem. Given a particular cycle, two modelers might be expected to come up with a different count as to the number of equations needed to model the cycle. Both can be right. The choice of variables to include in the count explains the different answers. The rule that ties all such analyses together (assuming they are correct) is that the number of equations for a well-posed problem must equal the number of variables. Consider the cycle in Figure B.1. It is perhaps best to first count the variables in the system. Based on the mass balance discussion in Section B.2, there are three mass flow rates internal to the cycle. This count ignores all devices with a single inlet and single outlet and assumes that the flow rate in equals the flow rate out of such devices (under steady-state conditions). There are 10 internal state points indicated by number on the schematic. Assuming a binary fluid at each state point, the Gibbs phase rule requires three properties to specify the thermodynamic state at each point. However, a number of assumptions are commonly made that reduce the number of variables significantly. It is common to assume that there are only two pressures in the system. Thus, instead of 10 pressures, there are only 2, because the small pressure losses occurring in all components other than throttle valves are assumed to be negligible. For the mass fractions, there are three because there are no mass fraction changes across the single inlet/single outlet devices. Similarly, there are three mass flow rates. There are 10 temperatures. And finally, the pump work is also determined by the model and so it must be counted as a variable. There are three variables (inlet and outlet temperature and flow rate) associated with each of the external water loops. The variables are summarized in Table B.4. The total number of variables for the single-effect cycle in Figure B.1 is then 31. In the discussion that follows, these variables will be specified either as inputs or by the equations that represent the model. The next step is to count the equations in order to determine the number of required inputs. Some of the equations have already been discussed in Sections B.2 through B.4. From that discussion, we know that there are two independent mass balances, there are eight energy balances, and there are five heat transfer equations. In addition to those, an equation is usually included to compute the solution pump work based on the pressure
298
Appendix B
TABLE B.4 Variables, Equations, and Inputs in the Single-Effect Model of Figure B.1 Variables Internal Pressure Mass fraction Mass flow rates Temperatures Pump work
2 3 3 10 1
External Inlet temperatures Outlet temperatures Mass flow rates Total variables
4 4 4 31
Equations Mass balance Energy balance Heat transfer Pump work Total equations
2 8 5 1 16
Inputs Mass flow rates Inlet water temperatures Vapor quality Temperature and mass fraction at state 7 Total inputs
5 4 4 2 15
difference and the flow rate. This is a total of 16 equations. By subtracting the number of equations from the number of variables, the number of inputs required to close the system is found to be 15. The temperature and mass fraction of the vapor stream exiting the desorber (point 7) have not been specified by any of the equations in the model. Thus, the user must specify a value for these two to close the system. From heat transfer considerations, the vapor temperature should fall between the highest and lowest temperatures present in the desorber. As the vapor evolves from the liquid surface, it will be in local equilibrium. But as the liquid moves through the desorber, the temperature changes. Thus, the temperature of the mixed vapor stream leaving the desorber can take a range of values depending on the hardware design. Similar thinking applies to the vapor mass fraction. From an equation-counting viewpoint, the specification of the temperature and mass fraction at point 7 can be thought of as either inputs (if values are specified by the analyst) or as equations if the temperature and mass fraction are related to other properties in the system. Whether counted as inputs or equations, both the temperature and mass fraction at point 7 must be specified. With these two, there are 13 remaining inputs required.
Appendix B
299
It is common in a system-level analysis of an absorption system to assume that the working fluid leaving the desorber, absorber, and condenser is saturated liquid (points 1, 4, and 8) and that the fluid leaving the evaporator is saturated vapor (point 10). These assumptions ignore sensible heat effects but yield a good combination of accuracy and modeling simplicity. These assumptions are imposed by specifying four vapor qualities. (Note that the specification of the saturated liquid states is done by specifying a vapor quality of zero.) With the four vapor qualities specified and the temperature and mass fraction at point 7 specified, nine additional inputs are required. A typical set of inputs corresponding closely to the physical inputs to an actual cycle are (1) the solution pump flow rate and (2) the flow rate and inlet temperature of each of the four external water loops. With these additional nine inputs, a well-posed problem is formed where it is observed that the number of equations plus inputs equals the number of variables. Variations on the set of variables and inputs are possible. For example, it is possible to specify the capacity of one of the heat exchangers instead of the mass flow rate of the external loop for that heat exchanger. If one wishes to include the component heat transfer rates as variables in the variable count, then the energy balance equations on those components must be included in a form that computes the component heat transfer rates. When this is done, there are five additional energy balance equations that are associated with the five heat transfer rates. Under this alternate analysis, the conclusion would be that there are 36 variables and 21 equations, which still require 15 inputs. Thus, it is seen that the number of equations and variables is not unique. This explains why the equation and variable counts coming from different absorption cycle software packages are not the same even when the cycle solved is identical. It is important to count the equations if a full understanding of the model is to be obtained. For those who wish to generate models for new cycles, the equation-counting step represents an important discipline since it is not always obvious during model development. As another specific example of equation counting, the cycle represented by Figure B.2 is considered and the result is summarized in Table B.5. This is the internal model version of the cycle in Figure B.1. The key difference is that the four external water loops are not modeled, but they are replaced, in a sense, by four heat transfer rates. Thus, instead of 12 external variables, this cycle has four. This results in a variable count of 23. On the equation side, there is only one heat transfer equation associated with the solution heat exchanger. The resulting equation count is 12, and it is concluded that 11 inputs are required. On the input side, there is only one mass flow rate (the solution flow rate). Instead of four inlet water temperatures, four temperatures are specified internal to the cycle. The remaining entries are identical to those for the cycle in Figure B.1. As required, the number of equations plus inputs equals the number of variables. Equation counting can be quite confusing unless a rigid methodology is established to assist in deciding which variables to include and whether to consider certain constraints as equations or as inputs. For example, no mention has been made in this description of the property relations for the working fluid. This choice is made here because it simplifies the view of the problem and allows more insight. It is not necessary to consider the specific enthalpy as a variable since it is determined once the thermodynamic state is determined (as per the Gibbs phase rule). However, this formalism is just one of many possible choices in how to count equations. As mentioned already, the art of equation counting in such a system depends on the analyst’s viewpoint and the assumptions made in choosing the variables.
300
Appendix B
Example B.3: Resorption Cycle Equation Counting Determine the number of equations, variables, and the number of inputs required to close the system for the resorption cycle pictured in Figure 8.5. Solution: The formalism introduced in this section results in the following tables.
Variables Internal Pressure Mass fraction Mass flow rates Temperatures Pump work
2 6 6 14 2
External Inlet temperatures Outlet temperatures Mass flow rates Total variables
4 4 4 42
Equations Mass balance Energy balance Heat transfer Pump work Total equations
6 10 6 2 24
Inputs Mass flow rates Inlet water temperatures Vapor quality Temperature and mass fraction at Desorber 1 outlet Temperature at Desorber 2 outlet Mass fraction Total inputs
6 4 4 2
1 1 18
Observations: The comments here refer to each entry in the tables, in order, starting from the top arranged according to the column headings. Variables-Internal: The cycle is assumed to be a two-pressure machine. The mass fractions in each of the four solution legs and the vapor are counted as variables. Note that for water/lithium bromide the vapor mass fraction would be zero. There are six internal mass flow rates. There are 14 internal state points, and the temperature at each is counted. There are two solution pumps, and the work rate for each is counted. Variables-External: Each of the four heat transfer loops has a flow rate and an inlet and outlet temperature associated with it. Thus, there are 12 external variables.
301
Appendix B
TABLE B.5 Variables, Equations, and Inputs in the Single-Effect Model of Figure B.2 (Internal Model) Variables Internal Pressure Mass fraction Mass flow rates Temperatures Pump work
2 3 3 10 1
External Heat transfer rate Total variables
4 23
Equations Mass balance Energy balance Heat transfer Pump work Total equations
2 8 1 1 12
Inputs Mass flow rates Cycle temperatures Vapor quality Temperature and mass fraction at state 7 Total inputs
1 4 4 2 11
Equations: There are six independent mass balance equations, as discussed in Example B.1. There are 10 components, each of which generates an energy balance. There are six heat exchangers, each of which generates a heat transfer equation. There are two solution pumps, each of which generates a pump equation. Inputs: The total number of inputs required is determined by subtracting the number of equations from the number of variables. In this case, 18 inputs are required. Six mass flow rates are input, including the four heat transfer loop flow rates and two solution flow rates. The inlet temperatures to the four heat transfer loops are inputs. The vapor quality at the liquid outlet of each of the absorbers and desorbers is input. The temperature and mass fraction of the vapor leaving Desorber 1 must be specified in some manner. Similarly, the temperature at the outlet of Desorber 2 must be specified. For Desorber 2, the mass fraction at the outlet is already constrained by a mass balance. Here, these three specifications are counted as three inputs. The final input listed (labeled “Mass fraction”) was chosen to close the system. Although such an input is not needed for a traditional single-effect cycle, it is needed for the resorption cycle, as shown by this formal count. The exact nature of the additional input was chosen after the count revealed that it was needed. See the discussion in Section 8.3 for additional detail about this input. In the model provided in Section 8.3, the mass fraction of one of the solution legs was specified.
302
Appendix B
It is a useful exercise to try replacing this input by one of the redundant mass balance equations. The result is a system with the correct number of equations, but the system is not well posed and will not give a meaningful solution. This type of dilemma is met often when writing the model for a new cycle. The equation-counting formalism is one more tool to help the modeler keep organized.
B.6 Convergence Issues and the Importance of Selecting an Initial Guess The systems of equations that result from the modeling process described in this appendix are difficult to solve because they are nonlinear and coupled. Large sets of equations are required even for the simplest cycle configuration. The nonlinearity arises because the fluid properties are nonlinear functions of the P–T–X (pressure–temperature–mass fraction) variables and also because the mass flow rates, which are variables, are multiplied by statepoint properties in the mass and energy balances. Furthermore, the heat transfer equations are usually nonlinear. Large sets of nonlinear equations always present a challenge to solve. The iterative solution methods that are available to handle such sets of equations are sensitive to several characteristics. The two main problems that crop up are (1) multiple solutions and (2) sensitivity to initial guess values. Multiple solutions are possible in nonlinear systems, such as those resulting from absorption cycle models. It is sometimes possible to anticipate these solutions and to include additional constraints on the variables that avoid convergence to an unwanted solution. One source of unwanted solutions is the set that comes about when the heat transfer potentials in a heat exchanger are inverted with respect to the actual solution. For example, in a condenser the temperatures internal to the cycle are always greater than the temperatures external to the cycle. However, if the solver does not know this, it may be possible to find a solution where the condenser becomes a heat input device. Although this does not make sense physically, it is mathematically possible unless it is strictly forbidden by imposing constraints on the variables. It is possible to avoid such unwanted solutions if the iteration is started close to the actual solution, which implies that a “good” initial guess is available. Iterative solvers require initial guesses for each of the unknown variables. A good initial guess is simply one that allows the iteration to converge on the correct solution. It is not always easy to obtain a good initial guess. If a converged solution is available for a given model, one very useful technique is to step away from that solution in small steps using the output from one run as the initial guess for the next run. If the steps taken are sufficiently small, the model will converge at each step and, by taking many small steps, a new solution can be obtained far away from the original solution. This process can be tedious if the desired operating conditions are far away from the operating conditions of the available converged solution and small steps are required. In general, some variables are more sensitive than others. The sensitivity of a particular model must be determined by experimentation; some models (and some variables) are much more sensitive than others. If a converged solution is not available, as is often the case when a new cycle is being modeled, it is often sufficient to simply specify reasonable values for all of the temperatures and mass fractions. As the mass fractions are known to only range between 0 and 1, it is often stabilizing to make these constraints explicit. For the temperatures, reasonable values can be determined by looking at the heat transfer processes and ensuring that the temperature differences are in the expected direction. If the mass fractions in the solution
303
Appendix B
loop are specified, the property routines for the fluid pair of interest can be used to guide the choice of reasonable temperatures. If the new cycle is a derivative of an existing cycle, it may be possible to import the initial guess for most of the variables from the original cycle and then use the methods described herein to guide the choice of guesses for the new variables.
B.7 Equation Solvers The set of equations resulting from the steady-state, system-level modeling approach described in this appendix are nonlinear, coupled, algebraic equations. The equations are coupled by the connections to other components in the cycle and, in particular, by the loop structure of these connections. The operating conditions in one component influence the downstream component (or components) through changes in the flow rate and state of the working fluid. The equations reflect this coupling and require that the equations must be solved simultaneously. The equations are algebraic as opposed to differential. Algebraic equations result from dealing with a steady-state, lumped component models. Once the equations have been identified in this manner, the type of solver needed is clear. Many routines have been developed for this type of system with the most familiar being the Newton–Raphson method. The Newton–Raphson method can be formulated in multiple dimensions so that each unknown variable in the cycle represents one dimension. The method requires that the number of equations equals the number of unknowns. An initial guess value is required for each of the unknowns. At each iteration, the method calculates a correction to each of the unknowns designed to bring the entire system closer to a solution. The problem can be formulated in vector notation where the unknowns are a vector. Then, the correction at each iteration is a correction vector. The correction vector is computed by linearizing the set of equations around the current guess value of the solution. The linearization is done numerically and involves evaluating the derivative of each equation with respect to each of the independent variables. The method is summarized next. The system of equations to be solved can be represented in vector form as
F ( x ) = 0 (B.18)
so that each individual equation can be written as
Fi ( x ) = 0,
i = 1, 2,..., n (B.19)
where n is the number of equations. For a well-posed system, n is the number of independent variables as well. The iterative solution process begins by specifying an initial guess for the vector of unknowns. The iteration step values of the independent variables are represented by a superscript so that the initial guess is denoted as x 0. In general, the equations will not be exactly satisfied at the initial guess value, which is denoted as
( )
F x 0 = F 0 ≠ 0 (B.20)
304
Appendix B
If the system were linear, the following equation would allow the analyst to solve for a correction vector that would locate the solution in one step. However, for the more general case of nonlinear equations, the method amounts to linearizing the system of equations about the current guess and solving for a correction vector. As a result of the nonlinearity, the procedure requires multiple steps to converge. For each of the n equations, we write
∇Fi ⋅ xc1 = − Fi0 ,
i = 1, 2, … , n (B.21)
This results in n equations in the n unknown components of the correction vector. This system is linear and can be solved explicitly for the correction vector. The updated guess for the solution is then
x 1 = x 0 + xc1 (B.22)
This iterative procedure is repeated until the solution is sufficiently close to satisfying the original equations. Several difficulties can be encountered in the solution of such sets of nonlinear algebraic equations. The primary problems are (1) multiple solutions and (2) lack of convergence from a particular guess value. Nonlinear equations can, in general, have multiple solutions. Thus, when an iterative solver converges on a solution, it may not be the solution of interest to the analyst. Care must be taken to examine the solution and to establish that it does represent a valid solution to the problem of interest. Another problem is divergence of the iterative scheme. Particularly when the guess values for the independent variables are far away from a solution, it is common for nonlinear equations to exhibit divergence using the Newton–Raphson scheme. When the scheme works, it usually converges very rapidly. However when it fails, other measures must be taken to find a solution. Numerous alternative solution techniques have appeared in the literature. These methods include various schemes to accelerate convergence and to avoid divergence. A classical scheme to avoid divergence is the Marquardt–Levenberg algorithm (Levenberg 1944; Marquardt 1963), which represents a hybrid between the Newton–Raphson method and a steepest descent method. Another powerful scheme for loosely coupled systems is to block the equations into groups that can be solved independently. The computational effort required to perform an iteration is related to n. Thus, any reduction in n gives significant acceleration of convergence. Blocking essentially splits the problem into minimum-size subproblems that can be solved more efficiently while still leading to the solution of the global set of equations. The EES program described in Appendix A uses a sophisticated solver that is based on these general ideas.
References Levenberg, K. (1944). A Method for the Solution of Certain Non-Linear Problems in Least Squares. Quarterly of Applied Mathematics 2: 164–168. Marquardt, D. (1963). An Algorithm for Least-Squares Estimation of Nonlinear Parameters. SIAM Journal on Applied Mathematics 11(2): 431–441.
Appendix C: Modeling a Water/Lithium Bromide Absorption Chiller The process of creating a new model of an absorption cycle can be challenging because there are a moderately large number of equations and it can be confusing to write down a well-posed problem without making some error. Once the error is introduced, it becomes even more difficult to find the error. Thus, a systematic procedure is recommended that breaks the larger task into a series of steps which can be checked individually. This process is described in this appendix focusing on the cycle models described in Sections 6.1 and 6.2.
C.1 Mass Balances On the surface, the mass balances for an absorption cycle may appear straightforward. However, it has been found repeatedly, by us and others, that it is easy to make mistakes in the mass balance part of a model which then will corrupt the rest of the model (see Appendix B for a broader discussion of these mass balance issues). Thus, focus here is on a strategy to understand the mass balances first before other considerations are introduced. The main aspect of the strategy is to assume a reasonable set of mass fractions throughout the cycle and then to solve the mass balances based on those assumed values to determine the unknown mass flow rates. The formulation, based on Figure C.1, is summarized in Table C.1. Mass balances for all of the components are entered as shown with the exception of the two for the absorber. Due to the cyclic structure of the solution loop, two mass balance equations are redundant for this cycle. The absorber balances were selected as the redundant pair and were not included explicitly in the formulation. Instead, the absorber mass balances were written in a residual form that should be zero if they are satisfied. The solution is summarized in Table C.2. Note that the absorber mass balances, and all of the other component mass balances, are satisfied. The mass balance formulation described here is included as file ExC_1.ees.
C.2 Temperature Inputs For the simple internal model considered here, temperature inputs are used in each of the corner components. Those inputs are summarized in Table C.3 along with how they are used in the model. The next step in creating the model is to graft these equations onto the mass balance model that was already created. Two of the equations involve aqueous lithium bromide states and set the two mass fractions that were previously specified. Thus, when these 305
306
Appendix C
. Qd
. Qc 7
Condenser
Desorber 3
8
4 Solution heat exchanger
Refrigerant expansion valve
9
Pressure
2
. W
5 Pump Solution expansion valve
1
Evaporator
Absorber
10
. Qe
6
. Qa
Temperature FIGURE C.1 Schematic of a water/lithium bromide absorption chiller.
TABLE C.1 Mass Balance Formulation (File ExC_1.ees) Specified Mass Fractions
Specified Mass Flow Rate
x1 = 0.55
1 = 1 kg/sec m
x4 = 0.60 Component
Overall Mass
LiBr Mass
Absorber
1 = m 10 + m 6 m 4 +m 7 = m 3 m
1x1 = m 6 x6 m 4 x4 = m 3 x3 m
8 = m 7 m 9 = m 8 m
x8 = x7 x10 = x9
Pump
10 = m 9 m m2 = m1
Solution valve
6 = m 5 m
x6 = x5
SHX hot side
5 = m 4 m 3 = m 2 m
x5 = x4
a
Desorbera Condenser Refrig. valve Evaporator
SHX cold side a
x9 = x8 x2 = x1
x3 = x2
These two are removed as redundant.
two temperature inputs are added (T1 and T4), it is necessary to comment out the specifications of x1 and x4. These two temperature inputs replace the mass fractions because of the assumption of saturated states at 1 and 4. The remaining two temperature specifications set the two pressures in the system using the properties of pure water. These pressures will be used in the next section to evaluate the state-point properties. When these four
307
Appendix C
TABLE C.2 Mass Balance Solution Based on Formulation in Table C.1 and Figure C.1 (File ExC_1.ees) State Point
i (kg/sec) Mass Flow Rate, m
1 2 3 4 5 6 7 8 9 10
Mass Fraction, x i
1 1 1 0.9167 0.9167 0.9167 0.08333 0.08333 0.08333 0.08333
0.55 0.55 0.55 0.6 0.6 0.6 0 0 0 0
TABLE C.3 Temperature Inputs Used in File ExC_2.ees Temperature Inputs Aqueous LiBr states Absorber outlet temperature T1 = 30°C Desorber outlet temperature T4 = 90°C Pure water states Condenser outlet temperature T8 = 30°C Evaporator outlet temperature T10 = 4°C
Saturation Relation
Effect on Model
T1 = Tsat(PL, x1)
Sets x1
T4 = Tsat(PH, x4)
Sets x4
T8 = Tsat, liquid(PH)
Sets PH
T10 = Tsat, vapor(PL)
Sets PL
TABLE C.4 Results after Entering Temperature Inputs (File ExC_2.ees) Pressure Results Ph = 4.246 kPa Pl = 0.8136 kPa
Mass Fraction Results x1 = 0.5322 x4 = 0.6711 Mass Flow Rates
1 = 1 kg/sec m
4 = 0.793 kg/sec m
7 = 0.207 kg/sec m
equations are added and the two mass fraction specifications that were set originally are commented out, the results in Table C.4 are obtained. The code used to obtain the results in Table C.4 is in file ExC_2.ees. The additions and deletions from the previous example are highlighted in the EES file in green and red, respectively. The mass fractions obtained are somewhat different than the ones used previously to test the mass balance formulation. As a result, all of the mass flow rates are different as well. The new mass flow rates are summarized in Table C.4. Only three flow rates are reported because there are only three unique flow rates in the system.
308
Appendix C
C.3 Energy Balances The next step is to write the energy balances. The results from the previous solution are needed for the energy balances so the approach is to build on the previous computer program as a starting point for the next step. The energy balances for all of the components are summarized in Table C.5. Enthalpy terms are included and the specific enthalpy values need to be related to the other state-point variables, as indicated in Table C.6. If you enter all of these equations, your model will still not be complete. Models need to be added for (1) solution heat exchanger heat transfer, (2) temperature of vapor at outlet of desorber, and (3) a pump model. These three models are summarized in Table C.7. When these equations are added to the model (see file ExC_3.ees), EES converges to the solution indicated in Table C.8. (It may be necessary to set variable limits on the vapor quality Q9 to restrict it to be between 0 and 1 to get it to converge.) TABLE C.5 Energy Balance Formulation Used in File ExC_3.ees Component Absorber Desorber Condenser Refrig. valve
Energy Balance 1h1 + m 10 h10 + m 6 h6 Q a = m 4 h4 + m 7 h7 + m 3 h3 Q d = m h +m h Q = − m c
8 8
7 7
Evaporator
h9 = h8 10 h10 − m 9 h9 Q e = m
Pump
=m 2 h2 − m 1h1 W
Solution valve
h6 = h5 5 h5 + m 4 h4 Q shx = − m h −m h Q =m
SHX hot side SHX cold side
shx
3 3
2 2
TABLE C.6 Evaluation of Specific Enthalpies Used in File ExC_3.ees State Point
Enthalpy Relation
Aqueous LiBr solution states 1 h1 = h(T1, x1) 2 h2 = h(T2, x2) 3 h3 = h(T3, x3) 4 h4 = h(T4, x4) 5 h5 = h(T5, x5) 6 h6 = h(T6, x6) Pure water states 7 h7 = h(T7, Ph) 8 h8 = hsat,v(T8) 9 h9 = h(PL, Q9) 10 h10 = hsat,v(T10)
Superheated water vapor Assumed to be saturated liquid Vapor/liquid two-phase state Assumed to be saturated vapor
309
Appendix C
TABLE C.7 Three Final Models to Complete the Cycle Model Used in File ExC_3.ees Model
Comments 1. Need to specify value for ε 2. Temperature formulation works because desorber outlet always has the minimum capacitance in such a cycle
Solution heat exchanger T − T5 ε= 4 T4 − T2 Desorber outlet temperature T7 = Tsat(x3, PH) Pump model h2 = h1 + v1ΔP
Vapor leaving desorber is assumed in equilibrium with incoming solution stream concentration (state 3). This is a standard assumption that represents the best possible case Isentropic pressure change on an incompressible fluid. Standard pump model for a liquid
TABLE C.8 Complete Solution for the Internal Cycle Model in Figure C.1 (File ExC_3.ees) State Points
h (J/g)
(kg/sec) m
1 2 3 4 5 6 7 8 9 10
71.1 71.1 137.9 255.2 171.1 171.1 2610.3 125.7 125.7 2507.9
1.000 1.000 1.000 0.793 0.793 0.793 0.207 0.207 0.207 0.207
Vapor Quality
T (°C)
x (kg/kg)
30.00 30.00 61.82 90.00 42.00 42.00 59.12 30.00
0.5322 0.5322 0.5322 0.6711 0.6711 0.6711 0 0 0 0
0.0437 4.00
Summary of Energy Quantities W Q
Pump power
0.00216 kW
a
Heat transfer rate in absorber
583.6 kW
Q d
Heat transfer rate in desorber
604.9 kW
Q e
Heat transfer rate in evaporator
493.1 kW
Q c
Heat transfer rate in condenser
514.3 kW
Q hx
Heat transfer rate in solution heat exchanger
66.7 kW
COP
Coefficient of performance
0.815
C.4 UA Models Once the internal model in the previous section is working, it can be converted to a UA model based on Figure C.2 (i.e., a model that considers heat transfer with the external streams). Start by updating the guess values for problem ExC_3.ees and save the file as ExC_4.ees. Then follow these steps for each component that involves heat exchange: (1) assume a reasonable temperature difference in the outside water loop; (2) calculate
310
Appendix C
. 15 Qc
16
12 7
Condenser
Desorber 3
8
4 Solution heat exchanger
Refrigerant expansion valve 2 Pump
Solution expansion valve 6
1
Evaporator
. Qe
5
. W
9
Absorber
10 18
17
11 . Qd
13
14
. Qa
FIGURE C.2 Schematic of a water/lithium bromide absorption chiller including heat exchanger models at the four corner components in the cycle.
TABLE C.9 UA Model Calculations Used as Inputs for File ExC_4.ees Component Desorber Absorber Condenser Evaporator
Fluid Loop Temperatures
Fluid Loop Flow Rate
Log Mean Temperature Difference
UA Value
T11 = 110°C T12 = 100°C T13 = 25°C T14 = 30°C T15 = 25°C T16 = 28°C T17 = 12°C T18 = 7°C
11 = 14.4 kg/sec m
ΔTIM = 29.21 K
UAd = 20.71 kW/K
13 = 27.79 kg/sec m
ΔTIM = 7.996 K
UAa = 72.989 kW/K
15 = 40.82 kg/sec m
ΔTIM = 3.274 K
UAc = 157.1 kW/K
17 = 23.48 kg/sec m
ΔTIM = 5.098 K
UAe = 96.73 kW/K
the water mass flow rate that is consistent with that temperature difference and the known heat transfer rate; and (3) calculate the UA value consistent with the temperatures and the heat transfer rate. Although tedious, this procedure works reliably. These steps are performed for each of the four corner components, and the results are summarized in Table C.9. The UA model is provided as file ExC_4.ees. This model converges smoothly (results shown in Table C.10), but it has arbitrary values of UA and fluid loop mass flow rates. Once you update the guess values to the current solution, the next step is to edit the input values to some more reasonable set. To complete this exercise, all
311
Appendix C
TABLE C.10 Results from Initial UA Model (File: ExC_4.ees) State Points
h (J/g)
(kg/sec) m
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
71.1 71.1 137.9 255.2 171.1 171.1 2610.3 125.7 125.7 2507.9
1.000 1.000 1.000 0.793 0.793 0.793 0.207 0.207 0.207 0.207 14.400
Vapor Quality
0.0437
27.790 40.820 23.480
T (°C)
x (kg/kg)
30.00 30.00 61.82 90.00 42.00 42.00 59.12 30.00 4.00 4.00 110.00 100.00 25.00 30.00 25.00 28.00 12.00 7.00
0.5322 0.5322 0.5322 0.6711 0.6711 0.6711 0 0 0 0
Summary of Energy Quantities W COP
Coefficient of performance
Component
Heat Transfer Rate (kW)
Log Mean Temperature Difference ΔT IM (K)
Desorber Absorber Condenser Evaporator Solution HX
604.9 583.6 514.3 493.1 66.72
29.21 7.996 3.274 5.098 18.95
Pump power
0.216 W 0.815
the UA values are set to 50 kW/K and all the flow rates to 20 kg/sec. The model with the uniform inputs is provided as file ExC_5.ees (results not shown). In this case, the model converged smoothly with the new inputs. In going from the internal model represented by the results in Table C.8 to the UA model shown in Table C.10, the four temperature inputs internal to the cycle are replaced by four temperature inputs at the inlet to each of the four heat transfer fluid loops. The four fluid loops are new features in the UA model. In addition to the four temperature inputs, the fluid loops require specification of the mass flow rate of the fluid, the specific heat of the fluid, and the size of each heat exchanger (i.e., the UA value). The log mean temperature difference calculation performed in these models is implemented as an EES function. This is particularly convenient because the same calculation is repeated several times with different input values. The function includes two checks for typical problems that can occur during the calculation. One is the case when the temperature differences at each end of the heat exchanger are equal. This case is perfectly reasonable physically but represents a singularity in the log function. This situation is easily
312
Appendix C
avoided by testing for that case and avoiding calling the log function when it occurs. The second case is when, during the course of the iteration, the temperature profiles cross such that the temperature difference at one (or both) end of the heat exchanger is in the wrong direction. This situation is not expected physically but can easily occur during the iteration. It has been found that setting the log mean temperature difference to zero when this nonphysical situation arises tends to push the iteration away from this condition and to allow the solver to find a valid solution. These checks, which are built in to the UA models here, provide a significant increase in model utility because they stabilize the iteration and largely avoid the nonconvergence issues common when you do not include the checks. The code in EES functions operates differently than the code in the Equations window. Inside functions, the code operates like a typical procedural language such as FORTRAN or C. There is no automatic iteration inside an EES function. Statements are assignment statements instead of equations as in the Equations window. The function definition must appear at the top of the Equations window before any other code and must have a Function header statement at the beginning and an End statement at the end. More detail on EES functions can be found in the EES online help. The solution heat exchanger model, which is formulated as an effectiveness model (εshx = 0.8) in the code, could also be formulated as a UA-log mean temperature difference model. These alternative heat exchanger models are equivalent. To illustrate this, the log mean temperature difference is calculated from the effectiveness solution and then the UA value that would be required to obtain the specified effectiveness is also calculated.
C.5 Summary The objective of Appendix C is to provide a step-by-step procedure of how to build an absorption cycle model using water/lithium bromide. The task is simplified by breaking the creation down into a series of well-defined steps. Although the illustration here is for a simple cycle, the steps are the same for modeling a more complex cycle. The end result is a complete system model that can be utilized to study absorption cycle performance, as discussed in Chapter 6.
Appendix D: Modeling an Ammonia/Water Absorption Chiller Creating a model of an absorption cycle is complicated by the recyclic flows, property data, and heat transfer relations, all of which introduce complexity into the modeling process. The appendix provides detailed step-by-step instructions to create a new model of an ammonia/water absorption cycle using EES. The governing equations are entered component by component, and the corresponding EES code follows. The example considered here is the same as that used in Example 9.2. A single-stage ammonia/water absorption system is shown in Figure D.1 (which is a duplicate of Figure 9.3). The evaporator saturation temperature at the outlet is –10°C with two-phase fluid leaving at a vapor quality of 0.975 (this feature minimizes the evaporator temperature glide). The mass flow rate of solution through the solution pump is 1 kg/sec. The temperature of the saturated liquid streams leaving both the absorber and the condenser is 40°C. The difference in ammonia mass fraction of the two solution streams (i.e., x1 – x4) is 0.10. The rectifier produces a vapor with an ammonia mass fraction of 0.9996. It is assumed that the pump efficiency is 100% and that the effectiveness of the solution heat exchanger is 80%. Find: The COP, all heat transfer rates, and the pump power. Solution: It is good practice in using EES to begin a problem by specifically entering the unit system that will be used. This is done with the $UnitSystem directive. $UnitSystem SI C kPa kJ mass The solution begins by processing all of the information provided in the problem statement. Referring to Figure D.1 for the locations of states, we can immediately recognize that the temperatures at state 13 is –10°C, and the temperature at both states 1 and 10 is 40°C. The ammonia mass fraction at state 9 is 0.9996. The quality of the state 13 is 0.975. The quality at states 1, 8, and 10 is 0 (liquid), and it is 1 (vapor) at states 7 and 9. The solution mass flow rate driven by the pump is 1 kg/sec, and the effectiveness of the solution heat exchanger is 0.8. The pump is assumed to be isentropic. Finally, we know the difference between the ammonia mass fractions at states 1 and 4 is 0.1. $UnitSystem SI C kPa kJ mass “Input Parameters from the problem statement” “temperatures (for state point, see diagram window)” T[13]=-10 [C] “temperature at exit of the evaporator” T[10]=40 [C] “temperature at the exit of the condenser” T[1]=40 [C] “temperature at the exit of the absorber” “mass fractions” x[9]=0.9996
“mass fraction at the exit of the rectifier” 313
314
Appendix D
“quality” Q[1]=0 Q[4]=0 Q[7]=1 Q[8]=0 Q[9]=1 Q[10]=0 Q[13]=0.975
“quality of liquid exiting absorber entering pump” “quality of liquid exiting the generator” “quality at vapor exit of generator” “quality of liquid returning from rectifier” “quality at exit of rectifier” “quality at exit of condenser” “quality at exit of evaporator”
“efficiencies” eta_pump=1.0 epsilon_shx=0.8
“isentropic efficiency of pump” “solution heat exchanger effectiveness”
DELTAx=0.1 m_dot[1]=1 [kg/s]
“difference between the mass fraction to and from the generator” “mass flow rate through solution pump”
Since pressure losses in the cycle are neglected in this analysis, there are only two p ressure levels in this cycle, and pressure drops occur only across the valves. The low pressure is fixed by the saturation conditions at the evaporator exit (state 13), which is known through property relations since the temperature, overall mass fraction, and quality at state 13 are specified.
P1 = P6 = P12 = P13 = Psat(T13, x13, Q13)
The high pressure is fixed by the saturation conditions at the condenser exit (state 10)
P2 = P3 = P4 = P5 = P7 = P8 = P9 = P10 = Psat(T10, x10, liq)
These pressure specifications are entered next. Rectifier
Condenser 9 . Qcond
. Qrect
10 2 Expansion device
Pump
12
1 13
Evaporator . Qevap
. Qabs
FIGURE D.1 Schematic of an ammonia/water absorption chiller.
5
6 Absorber
Expansion device
Desorber
7 8
3
4 . Qdes Solution heat exchanger
315
Appendix D
“pressures” P_high=pressure(NH3H2O,T=T[10],x=x[10],Q=Q[10]) “pressure at condenser exit” P_low=pressure(NH3H2O,T=T[13],x=x[13],Q=Q[13]) “pressure at evaporator exit” P[1]=P_low “set all pressures” P[2]=P_high P[3]=P_high P[4]=P_high P[5]=P_high P[6]=P_low P[7]=P_high P[8]=P_high P[9]=P_high P[10]=P_high P[12]=P_low P[13]=P_low One last piece of information in the problem statement is the difference between the mass fractions at states 1 and 4, which is defined to be Δx. x[1]-x[4]=DELTAx
“definition of the difference between mass fractions”
As explained in Appendix A, it is best when using EES to enter a few equations and then solve them to ensure that they have been entered correctly. It is not possible to solve the equations entered up to this point since the mass fractions x[1], x[10], and x[13] are not yet known. However, we can temporarily enter reasonable values for x[1], x[10], and x[13] and then solve the equations entered up to this point. These equations will be removed as the solution progresses. It is helpful to highlight the equations so that you remember that they are temporary and will be eventually commented out or deleted. x[10]=0.99 x[13]=0.99 x[1]=0.3
“temporary equations for refrigerant mass fraction” “temporary equations for refrigerant mass fraction” “temporary equation for solution mass fraction”
The ammonia mass fractions throughout an absorption cycle are determined by the operating conditions, and they fluctuate to match the conditions. In this example, the vapor mass fraction leaving the rectifier (state 9) has been specified. The mass fractions of the ammonia-poor stream (states 1, 2, and 3) are determined by the given absorber temperature and the evaporator pressure. The mass fractions of the ammonia-rich stream (states 4, 5, and 6) are determined by the specified difference between the rich and poor streams. Thus, in the following, it is assumed that the pressures and the mass fractions are known throughout the cycle. We next need to enter the governing equations, which for the most part consist of mass, ammonia, and energy balances on each component. As noted in Appendix B, cyclic flows result in a redundancy for mass and ammonia balances. One component in the loop does not require mass and ammonia balances. We have arbitrarily chosen this component to be the absorber. We will use the mass and ammonia balances for the absorber as a check.
316
Appendix D
Since there are loops in this cycle, these balances are coupled and the equations will need to be solved simultaneously. We will start at the pump. 1 = m 2 m 1 x1 = m 2 x2 m
pump = m 2 h2 − m 1 h1 W
The pump power is the product of the volumetric flow rate and the pressure increase.
1 ν1 ( P2 − P1 ) pump = m W ηpump
The temperature, pressure, and quality at state 1 are known, which allows the mass fraction and specific enthalpy at state 1 to be determined. The energy balance on the pump determines the specific enthalpy at state 2, which can be used to calculate T[2]. The EES code for the pump is as follows. The specification of x[1] = 0.3 entered above needs to be deleted or commented out at this point. Solve these equations to ensure that they are entered properly. Update the guess values. “PUMP” m_dot[1]=m_dot[2] x[1]=x[2] v[1]=volume(NH3H2O,T=T[1],P=P[1],Q=Q[1]) swp=v[1]*(P[2]-P[1])/eta_pump h[2]=h[1]+swp W_dot_pump=m_dot[1]*(h[2]-h[1]) x[1]=MassFraction(NH3H2O,T=T[1],P=P[1],Q=Q[1]) h[1]=enthalpy(NH3H2O,T=T[1],P=P[1],Q=Q[1]) T[2]=temperature(NH3H2O,P=P[2],h=h[2],x=x[2])
“mass balance” “ammonia balance” “specific volume” “specific work of the pump” “energy balance on the pump” “pump power” “mass fraction at state 1” “specific enthalpy at state 1” “temperature at state 2”
The solution heat exchanger requires mass and ammonia balances on each of the two streams, an overall energy balance, and a heat transfer rate equation based on the known heat exchanger effectiveness. 2 = m 3 m 4 = m 5 m 2 x2 = m 3 x3 m 4 x4 = m 5 x5 m
2 h2 − m 4 h4 = m 3 h3 − m 5 h5 m
317
Appendix D
To calculate the heat transfer rate between the two streams, it is necessary to determine the minimum capacitance rate (the product of mass flow rate and specific heat) and apply the definition of heat transfer effectiveness Q shx = ε shx C min (T4 − T2 )
where
(
C min = min C 2 −3 , C 4−5 C23 =
( h2 − h3 ) , (T2 − T3 )
) C45 =
( h4 − h5 ) , (T4 − T5 )
2 c23 , C 2 −3 = m
4 c 45 C 4−5 = m
2 ( h3 − h2 ) Q shx = m
4 ( h4 − h5 ) Q shx = m
Enter these equations. They cannot be solved because we do not yet know m_dot[4]. We do know that m_dot[4] will be somewhat smaller than m_dot[2], and we can temporarily enter a guess equation for m_dot[4]. This equation will be removed shortly. Solve the equations and update the guess values. “SOLUTION HEAT EXCHANGER” m_dot[2]=m_dot[3] m_dot[4]=m_dot[5] x[2]=x[3] x[4]=x[5] cp_23=(h[2]-h[3])/(T[2]-T[3]) cp_45=(h[4]-h[5])/(T[4]-T[5]) C_dot_23=m_dot[2]*cp_23 C_dot_45=m_dot[4]*cp_45 C_dot_min=min(C_dot_23,C_dot_45)
“mass balances” “ammonia balances”
“specific heat of stream 2-3” “specific heat of stream 4-5” “capacitance rate of stream 2-3” “capacitance rate of stream 4-5” “minimum capacitance rate in SHX” Q_dot_shx=epsilon_shx*C_dot_min*(T[4]-T[2]) “so lution heat exchanger heat transfer rate” m_dot[2]*(h[3]-h[2])=Q_dot_shx “energy balance for stream 2-3” m_dot[4]*(h[4]-h[5])=Q_dot_shx “energy balance for stream 4-5” h[3]=enthalpy(NH3H2O,P=P[3],T=T[3],x=x[3]) “specific enthalpy at state 3l” h[4]=enthalpy(NH3H2O,P=P[4],x=x[4],Q=Q[4]) “specific enthalpy at state 4” T[4]=temperature(NH3H2O,P=P[4],x=x[4],Q=Q[4]) “temperature at state 4” T[5]=temperature(NH3H2O,P=P[5],h=h[5],x=x[5]) “temperature at state 5” m_dot[4]=0.9*m_dot[2]
“temporary equation for solution flow rate”
318
Appendix D
As the desorber and rectifier are so closely coupled, it is perhaps best to enter and solve the equations for both components. Mass, ammonia, and energy balances on the desorber result in 3 +m 8 = m 7 +m 4 m 3 x3 + m 8 x8 = m 7 x7 + m 4 x4 m 3 h3 + m 8 h8 + Q des = m 4 h4 + m 7 h7 m
For the rectifier, 7 =m 9 +m 8 m 7 x7 = m 9 x9 + m 8 x8 m
7 h7 = m 9 h9 + m 8 h8 + Q rect m
In addition, it is necessary to know the temperature and ammonia mass fraction of the liquid returning from the rectifier (state 8). This information would normally require a specification of the rectifier design and a detailed heat and mass transfer analysis. However, a simple approximation that provides reasonable results is to make two assumptions: (1) assume that the vapor leaving the desorber (state 7) is in equilibrium with the entering liquid (state 3) and (2) that the liquid leaving the rectifier (state 8) is in equilibrium with the entering vapor (state 7). The first assumption represents the ideal counterflow desorber limiting case. The second assumption represents the reversible rectifier. Taken together, these conditions require
T8 = T7 x8 = x3
The specific enthalpy at state 8 can be calculated from property relations. State 9 is assumed to be saturated vapor (quality = 1), and the pressure is known. The mass balance provides the ammonia mass fraction, so property relations then fix the temperature and specific enthalpy at state 9. Enter the following equations “DESORBER” m_dot[8]+m_dot[3]=(m_dot[7]+m_dot[4]) m_dot[8]*x[8]+m_dot[3]*x[3]=(m_dot[7]*x[7] +m_dot[4]*x[4]) m_dot[3]*h[3]+m_dot[8]*h[8]+Q_dot_des= m_dot[7]*h[7]+m_dot[4]*h[4] x[7]=massfraction(NH3H2O,T=T[7],P=P[7],Q=Q[7]) h[7]=enthalpy(NH3H2O,T=T[7],P=P[7],Q=Q[7]) T[8]=temperature(NH3H2O,x=x[8],P=P[8],Q=Q[8])
“mass balance” “ammonia balance” “energy balance” “saturated liquid in equilibrium with x[3]” “specific enthalpy at state 7” “liquid in equilibrium with point 7”
319
Appendix D
“specific enthalpy at state 8”
h[8]=enthalpy(NH3H2O,x=x[8],P=P[8],Q=Q[8]) “RECTIFIER” T[8]=T[7]
“thermal equil. Btwn states 7 & 8” x[8]=x[3] “fo rces chem equil btwn states 7 & 8” m_dot[7]=m_dot[9]+m_dot[8] “mass balance” m_dot[7]*x[7]=m_dot[9]*x[9]+m_dot[8]*x[8] “energy balance” m_dot[7]*h[7]=m_dot[9]*h[9]+m_dot[8]*h[8]+Q_dot_rect “energy balance” h[9]=enthalpy(NH3H2O,P=P[7],x=x[9],Q=Q[9]) “sa turated vapor at given mass fraction” T[9]=temperature(NH3H2O,P=P[7],x=x[9],Q=Q[9]) “temperature at state 9” If you attempt to solve the equations at this point, you will see that the system of equations is overdefined. Delete or comment out the temporary equation that we entered for m_dot [4]. “Remove this equation”
{m_dot[4]=0.9*m_dot[2]}
Now the equations should solve. Update the guess values. For the expansion valve between the solution heat exchanger and the absorber, mass and energy balances are written as 5 = m 6 m
5 x5 = m 6 x6 m
⇒
x5 = x6
5 h5 = m 6 h6 m
⇒
h5 = h6
The temperature and quality at state 6 are found using property relations. Enter the equations for the expansion valve, solve and update the guess values. “EXPANSION VALVE” m_dot[5]=m_dot[6] x[5]=x[6] h[5]=h[6] Q[6]=Quality(NH3H2O,P=P[6],h=h[6],x=x[6]) T[6]=temperature(NH3H2O,P=P[6],h=h[6],x=x[6])
“mass balance” “ammonia balance” “energy balance on the valve” “obtain vapor quality” “and temperature”
For the condenser, the balances are =m 10 m 9 x9 = m 10 x10 m
⇒ x9 = x10
9 h9 − m 10 h10 Q cond = m
320
Appendix D
The condensate at state 10 is assumed to be saturated liquid, and a property relation determines the specific enthalpy. Enter the equations for the condenser. “CONDENSER” m_dot[9]=m_dot[10] x[9]=x[10] Q_dot_cond=m_dot[9]*(h[9]-h[10]) h[10]=enthalpy(NH3H2O,T=T[10],x=x[10],Q=Q[10])
“mass balance” “ammonia balance” “energy balance” “saturated liquid”
When you try to solve, EES will present an error indicating that x[9] or x[10] is already set to a value. Remove the temporary equation that was entered above for x[10]. “Remove this equation”
{x[10]=0.99}
The equations should now solve. Update the guess values. Mass, ammonia, and energy balances for the refrigerant expansion valve between the condenser and the evaporator are as follows. 10 = m 12 m
10 x10 = m 12 x12 m
⇒
x10 = x12
10 h10 = m 12 h12 m
⇒
h10 = h12
The corresponding EES code is entered. Solve and update the guess values. “REFRIGERANT EXPANSION VALVE” m_dot[10]=m_dot[12] “mass balance” x[10]=x[12] “ammonia balance” h[10]=h[12] “energy balance on the valve” Mass, ammonia, and energy balance for the evaporator are as follows. Property relations can determine the temperature and quality at state 12 and the specific enthalpy at state 13. 12 = m 13 m 12 x12 = m 13 x13 m
⇒ x12 = x13
13 h13 − m 12 h12 Q evap = m
The EES code for the evaporator follows. To enable testing, it will be necessary to comment the temporary equation that set the value of x[13] entered at the start. Solve and update guess values. {x[13]=0.99}
“Remove this equation”
321
Appendix D
“EVAPORATOR” m_dot[12]=m_dot[13] x[12]=x[13] Q_dot_evap=m_dot[13]*(h[13]-h[12]) T[12]=temperature(NH3H2O,P=P[12],h=h[12],x=x[12]) Q[12]=Quality(NH3H2O,P=P[12],h=h[12],x=x[12]) h[13]=enthalpy(NH3H2O,x=x[13],T=T[13],Q=Q[13])
“mass balance” “ammonia balance” “energy balance on evaporator” “temperature at state 12” “quality at state 12” “specific enthalpy at state 13”
The final component in the system is the absorber. It is tempting to also enter mass and ammonia balances for the absorber. However, these equations are redundant, since the mass flows are cyclic and mass and ammonia balances have been written for all other components. Instead, it is recommended to introduce mass and ammonia error terms, as follows. 13 + m 6 = m 1 + ∆m m 13 x13 + m 6 x6 = m 1x1 + ∆a m
Upon solution, the values of Δm and Δa should both be very close to zero, confirming that the mass and ammonia balances on all components in the cycle are satisfied. An energy balance on the absorber determines the rate at which heat must be rejected from the absorber 13 h13 + m 6 h6 = m 1 h1 + Q abs m
“ABSORBER” m_dot[13]+m_dot[6]=m_dot[1]+err_absmass m_dot[13]*x[13]+m_dot[6]*x[6]=m_dot[1]*x[1]+err_absammonia m_dot[13]*h[13]+m_dot[6]*h[6]=m_dot[1]*h[1]+Q_dot_abs
“mass balance” “ammonia balance” “energy balance”
The cycle calculations are completed. All that is necessary now is to calculate the COP and some other quantities of interest. Also, it is a good idea to do an overall energy balance on the cycle to ensure that the model is entered correctly. “OVERALL” COP_1=Q_dot_evap/(W_dot_pump+Q_dot_des) COP_2=Q_dot_evap/Q_dot_des P_ratio=P_high/P_low DELTAt_glide=T[13]-T[12] f=(x[9]-x[4])/(x[3]-x[4])
“definition of coefficient of performance including pump power” “de fi nition of coefficient of performance” “pressure ratio” “definition of temperature glide” “definition of solution circulation ratio”
“check the energy balance” checkQ=Q_dot_des+Q_dot_evap+W_dot_pump-(Q_dot_rect+Q_dot_cond +Q_dot_abs) The properties at each state and a summary of the energy quantities are given in Table 9.2.
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Appendix E: The ABSIM Software Package
E.1 Overview ABSIM (an acronym for ABsorption SIMulation) is a computer code for simulation of absorption systems in flexible and modular form. It has been developed by Professor Gershon Grossman and coworkers at the Technion – Israel Institute of Technology, supported initially (up to version 5.0, 1997) by ORNL/DOE. This modular code is based on unit subroutines containing the governing equations for the system’s components and on property subroutines containing thermodynamic properties of the working fluids. The components are linked together by a main program that calls the unit subroutines according to the user’s specifications to form the complete cycle. When all the equations for the entire cycle have been established, a powerful mathematical solver routine is employed to solve them simultaneously. Thirty-one absorption fluids are presently available in the code’s property database, and 15 units/components are available to compose practically every absorption cycle of interest, including the ones described in this book. The code in its present form may be used not only for evaluating new cycles and working fluids but also to investigate a system’s behavior in off-design c onditions, to analyze experimental data, and to perform preliminary design optimization. The code is user oriented and requires a relatively simple input containing the given operating conditions and the working fluid at each state point. A graphical user interface enables the user to draw the cycle diagram on the computer screen, enter the input data interactively, run the program, and view the results either in the form of a table or superimposed on the cycle diagram. Special utilities enable the user to plot the results and produce a PTX diagram of the cycle. The code has been employed successfully to simulate a variety of single-effect, doubleeffect, and dual-loop absorption chillers, heat pumps, and heat transformers employing the working fluids LiBr–H2O, LiCl–H2O, H2O–NH3, LiBr/ZnBr2–CH3OH, NaOH–H2O, and more, in both closed- and open-cycle configurations. The same code has been used to simulate the rather complex generator–absorber heat exchanger (GAX) cycle in two variations, advanced GAX cycles employing ammonia–water in several cycle variations, a variety of double- and triple-effect chillers employing lithium bromide/water, and several opencycle and hybrid air-conditioning systems employing lithium chloride/water. To obtain a free copy of the latest development version of ABSIM with a user’s manual and several examples, please contact: Prof. Gershon Grossman, Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel 32000. Phone: (972)48292074; Fax: (972)4-8295711; E-mail:
[email protected]
323
324
Appendix E
E.2 Introduction to ABSIM Development of the ABSIM program began in the 1980s with the objective of creating a simulation tool for evaluating absorption systems in varying cycle configurations and with different working fluids. This period saw renewed interest in heat-actuated heat pumps in general and in absorption systems in particular, as promising alternatives to electric-driven heat pumps. The potential for utilizing available heat sources—lowgrade heat such as solar and waste on one hand, and high-temperature heat from natural gas on the other hand—seemed to offer new opportunities. The absorption community has begun to search for advanced cycles in various multistage configurations, and for new working fluid combinations with the potential for enhanced performance and reliability. The US Department of Energy (DOE) in particular had supported this search under an Advanced Cycles/Advanced Fluids program, aimed at evaluating many promising ideas for new cycles and working fluids (Biermann 1984; Phillips 1990; Modahl and Hayes 1992). The development of working absorption systems has created a need for reliable and effective system simulations. Several system-specific computer models had been developed (Grossman et al. 1979; Vliet et al. 1982; Grossman and Childs 1983; McLinden and Klein 1985) that have proven to be very valuable tools for research and development and for design optimization. These system-specific models were, however, limited to the particular systems for which they were created; modifying them to simulate other systems would require rewriting major parts of the code, particularly the iterative sequence, for each new cycle. As part of the effort under the DOE Program, attempts were made at comparison of the different candidate cycles using software employed by the chemical industry for process simulation (Evans 1982), which possesses the flexibility to consider cycle variations. Experience has shown that for simulating common heat pump cycles these codes are much too powerful and, at the same time, require the user considerable investment in time and training before being able to employ them. The extensive libraries containing many modules and working substances do not contain most of those required for absorption systems. Codes employing sequential algorithms require the user to program the sequence by which the simulator is to proceed through the cycle; this is easy to do in the open cycles most often employed in the chemical industry, but convergence problems are often encountered when dealing with closed cycles with several interconnected loops typical of multistage absorption systems. Equation-oriented codes do not have this problem and seem more suitable for the purpose. One such code containing a good library of working fluid properties suitable for heat pumps is the Engineering Equations Solver (Klein 1992–2015). Here the user must write the equations governing the cycle and make sure the set is well defined. In the case of a nonlinear set of equations, the user must check the results to make sure that the mathematical solution is also a physical one. In one form or another, the user has to enter detailed information about the cycle of interest to lead the simulator toward convergence to the correct solution. The objective of developing ABSIM has been a user-oriented, modular computer simulation code, specifically designed for absorption systems in different cycle configurations and with different working fluids. The usefulness of such a simulation tool has emerged during repeated attempts under absorption research programs to evaluate new ideas for absorption cycles and working substances and to compare them with existing ones. In developing the code, care has been taken to avoid most of the aforementioned
Appendix E
325
requirements imposed on the user in common process simulators. One particular feature of ABSIM is that the user does not have to do any programming. The complete set of governing equations is generated automatically, by drawing the cycle on the computer screen (thereby indicating to the code the components of the cycle and their interconnections), and by specifying the working fluids and the operating conditions. The set of equations is solved in a manner that eliminates mathematically valid results that are not physically valid. Several publications (Grossman and Wilk 1994; Grossman and Zaltash 2001) have described the modular approach taken to achieve this flexibility without the need for the user to worry about the iterative scheme or even see the equations. A Windows graphical interface enhances user-friendliness considerably, by enabling the user to create the cycle diagram on the computer screen, supply the data interactively, observe the results superimposed on the cycle diagram, and plot them.
E.3 ABSIM Program Structure Based on the fact that any absorption system consists of a number of basic units/components (e.g., absorber, evaporator, desorber), and that each of these components can employ a multitude of working fluids, the code is built upon unit subroutines and property subroutines in separate modules. A main program manages and activates these subroutines. Each basic component is simulated by a unit subroutine containing the physical equations required to fully describe its behavior, such as energy balance, conservation of mass for each material species, heat and mass transfer, and thermodynamic equilibrium. By drawing the cycle diagram on the computer screen, the user conveys to the program an “image” of the cycle to be simulated: the number and types of units contained in it and their interconnections. Data entered specify each unit’s properties such as transfer characteristics, where applicable, and the working fluid at each state point in the system. The input must also specify the given operating conditions—the values of the parameters set fixed by the user, for example, temperatures, flowrates, and so on at specific state points. The main program interprets the input and creates a variable vector containing all the independent unknown quantities. It then calls the unit subroutines, thereby linking the components and establishing the system’s governing equations. Each unit subroutine, when activated, calls upon the property subroutines, contained in the property database, for thermodynamic properties of the working fluids. This separation between the unit subroutines and property subroutines provides the flexibility for each unit to operate with different working fluids. All the equations and variables are normalized and brought to the same order of magnitude. The solver is then activated, and the values of the unknowns are calculated to a user-specified accuracy. Recognizing that the set of nonlinear equations may have more than one mathematical solution, the physical validity of the solution is ensured by applying constraints on the variables. The output contains the temperature, enthalpy, flowrate, concentration, pressure, and vapor fraction at each of the cycle’s state points as well as the heat duty and transfer characteristics of each unit. From these quantities, other performance data such as COP and capacity may be calculated. To prepare an input, the user first draws the cycle diagram on the computer screen using the graphical interface, in terms of the basic 15 units available in the code. The units and state points are numbered automatically, in an arbitrary order that may be changed at
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the user’s discretion. Input data are then entered by the user as prompted for, consisting of the following three parts: 1. Global parameters: containing a user-supplied problem title, scaling parameters for normalization, limits on the number of iterations, and convergence criteria. Default options are available for all of these. Input and output may be either in SI or in British units. 2. Unit parameters: showing the characteristics of the units composing the cycle, as applicable, for example, heat transfer characteristics of a condenser, pressure difference/ flowrate characteristic of a valve, isentropic efficiency of a compressor, and the like. Heat transfer characteristics of a unit may be specified by one of six methods: The user can supply the UA (overall heat transfer coefficient times area), the NTU (number of transfer units), the EFF (effectiveness), the CAT (closest approach temperature), the LMTD (logarithmic mean temperature difference), or the heat duty. Mass transfer characteristics are not as simple to specify; hence, the mass transfer resistance of a unit is specified by a temperature deviation from equilibrium at the outlet streams. 3. State-point data: showing for each of the state points in the cycle the working fluid in it, and five pairs of numbers for the temperature, flowrate, concentration, vapor pressure, and vapor fraction in that state point. Each pair of numbers consists of an integer index and a real value. The former can be either zero or nonzero, indicating a fixed or variable quantity, respectively. The latter gives a fixed value or an initial guess for the quantity in question. Fifteen units/components are presently available in the code. A description of these units and their governing equations is given in detail in the user’s manual and was given in part and in a shorter form by Grossman and Wilk (1994). The units are Absorber, Desorber, Heat Exchanger, Condenser, Evaporator, Valve, Mixer, Splitter, Rectifier, Analyzer, Compressor, Pump, Evaporative Cooler, Air–Solution Contactor (ASC), and Expander. Each of the units has several versions, differing from each other by geometry, location of inlet and outlet streams, co-flow versus counterflow, and so on. Experience has shown these 15 units to be sufficient to create most absorption cycles of interest. The governing equations apply to each unit as a whole and are formed from some or all of the following physical laws: conservation of total mass; conservation of mass for each material species (absorbent– absorbate); energy balance; heat transfer; vapor–liquid equilibrium; and mass transfer. From the earlier equations for each unit, a set of nonlinear equations is formed for the entire system that must be solved simultaneously. The thermodynamic properties of working fluids have been incorporated in the code in the form of a property database external to the unit subroutines. This was done to allow different parts of a system to operate with different working fluids, thereby enhancing modularity and flexibility. Under this approach, each unit subroutine calls the property database several times and retrieves from it the properties required by its various equations. Also, the working fluid may vary from one state point to another, as specified by the user. The property database presently contains the following working fluids: water (H2O), moist air, flue gas, NH3, CH3OH, LiBr–H2O, LiCl–H2O, H2O–NH3, LiBr–H2O–NH3, LiBr/ZnBr2–CH3OH, silica gel, NaOH– H2O, LiNO3/KNO3/NaNO3–H2O, LiNO3–NH3, R–12, R–22, R–32, R–114, R–123, R–124, R–125, R–134a, R–143a, R–152a, R–290 (propane), R–143a/R–125/R–134a(52/44/4), R–32/R–125(60/40), R–32/R–125(50/50), R–502, R–143a/R–125(55/45), and R–143a/R–125(50/50). A graphical user interface operating under MS Windows has been added to the code, which enhances user-friendliness considerably. Figure E.1 is a screen view of ABSIM,
FIGURE E.1 Screen view of the ABSIM program.
Appendix E 327
328
Appendix E
displaying a sample problem—a cycle diagram of a single-effect LiBr–H 2O chiller that had been drawn in the white area of the screen and properly specified. Results of calculations are displayed, superimposed on the cycle diagram: in this example, the temperatures (in degrees Celsius) at various state points of the system. The menu bar shows several entries, each comprising several subentries in their respective pull-down menus. The ABSIM code has been employed over the past years by many users worldwide to simulate a wide variety of absorption systems in different multieffect configurations and working fluids. The following chapter describes some of these cycles along with the results.
E.4 Selected Examples of ABSIM Simulations Earlier versions of ABSIM have been employed to simulate more than 50 various cycles of interest with the working fluids LiBr–H2O, H2O–NH3, LiBr–H2O–NH3, and LiBr/ZnBr2– CH3OH. These cycles included single-effect, double-effect, and dual-loop chillers; heat pumps; and heat transformers in various configurations. Some results for typical cases showing design point performance have been described by Grossman et al. (1991). Studies of absorption cycles conducted by others using the earlier versions of ABSIM have been described by Garimella et al. (1996, 1997). This chapter aims at describing simulation capabilities for some of the more complex cycles, achieved with the code in its present version. Due to the wide variety of cycles simulated, a detailed discussion of all the results is beyond the scope of this chapter. It is therefore attempted to give a general overview with the most interesting cycles. For the purpose of this discussion, the cycles have been divided into three groups according to the two working fluids pairs of most practical interest in closed-cycle absorption, LiBr–H2O and H2O–NH3; and in open-cycle absorption, LiCl–H2O. E.4.1 LiBr–Water Cycles An early version of ABSIM has been employed to conduct a detailed parametric study to investigate the performance of various cycles using lithium bromide–water (Gommed and Grossman 1990). Complete performance maps under varying operating conditions have been generated for systems in single-stage and several double-stage configurations, in series, and in parallel connection. Using a more advanced version of ABSIM (Grossman and Wilk 1994), this study has been extended to triple-effect systems in several configurations (Grossman et al. 1994). Among those were the double-condenser coupled cycle, which recovers heat from the hot condensate leaving the h igh-temperature condensers and adds it to the lower-temperature desorbers; and the dual-loop cycle comprising two complete single-effect loops, recovering heat from the condenser and absorber of one loop to the desorber of the other loop and generating a cooling effect in the evaporators of both loops. The present version of the code makes it possible to simulate cycles with a degree of complexity never attempted before. One such example is the extension of the LiBr–H2O studies of single-, double-, and triple-effect systems to quadruple-effect cycles. Figure E.2 describes schematically a four-effect lithium bromide–water chiller, formed as an extension of the corresponding double-effect cycle (Gommed and Grossman 1990),
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46
CND(22)
X X 58
47
DES(27)
60
62 XX
61
VLV(23) HEX(21)
MIX(26) 35
CND(20)
X X 51
36
MIX(24)
DES(19)
46
49 XX
47
SPL(25) VLV(18) HEX(17)
MIX(26) 21
CND(13)
X X 33
22
MIX(15)
DES(14)
35
38 XX
36
SPL(12) VLV(11) HEX(10)
MIX(16)
16
CND(5)
X X 17
15
MIX(8)
DES(7)
21
24 XX
22
SPL(6) VLV(4) HEX(3)
9
10 XX
8
EVP(2)
FIGURE E.2 Schematic description of a 4-effect LiBr–H2O absorption cycle.
6 XX ABS(1)
4 3
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or of the three-condenser–three-desorber (3C3D) triple-effect cycle (Grossman et al. 1994). The system comprises an evaporator, an absorber, and three pairs of desorbers/condensers coupled together for internal heat recovery. The system has 27 components or subunits and 62 state points. Absorber (1) and condenser (5) are externally cooled; desorber (27) is externally heated. Chilled water is produced in evaporator (2). Heat rejected from condenser (13) powers desorber (7), heat from condenser (20) powers desorber (14), and heat from condenser (22) powers desorber (19). The coupling between each condenser–desorber pair is through a circulating (hidden) heat transfer fluid loop, as shown, but may also be achieved by physically combining the two components, such that the refrigerant condensing on one side of a heat exchange surface would heat up the solution desorbing on the other side of that surface. The absorbent solution is in parallel flow, where the weak (weak in LiBr concentration) solution from the absorber is split and divided among the four desorbers. According to simulation results of double-effect (Gommed and Grossman 1990) and triple-effect cycles (Grossman et al. 1994), the parallel flow arrangement is superior in performance to the series flow in terms of increased COP and a lower risk of crystallization. The condensate leaving the condensers (13), (20), and (22) is mixed with the superheated vapor leaving the desorbers (7), (14), and (19), respectively, before proceeding from each to the next lower-temperature condenser. This method, known as double-condenser coupling (DeVault and Biermann 1993), helps subcool each condensate stream and reject the heat to a corresponding desorber. Due to the limited scope of this chapter, corresponding diagrams for single-, double-, and triple-effect cycles are not provided. Instead, the reader is referred to Figure E.2 to picture these cycles as follows: the three-effect cycle is the same as the four-effect cycle depicted, with units 21, 22, 23, 24, 25, 26, and 27 eliminated; the two-effect cycle is the same as the three-effect cycle, with units 12, 15, 16, 17, 18, 19, and 20 eliminated; the one-effect cycle is the same as the two-effect cycle, with units 6, 8, 9, 10, 11, 13, and 14 eliminated. It should be noted that the four-effect cycle described in Figure E.2 is only one of several possible configurations. Further details on LiBr–H2O four-effect cycles are given in the publication by Grossman et al. (1995b). Results of simulations for the various LiBr–H2O cycles described in this chapter, including the effects of varying heat source and sink temperatures, solution and water flowrates, and size of units on COP and capacity, are given in part in the publication by Grossman and Zaltash (2001). E.4.2 Water–Ammonia Cycles Cycles employing ammonia–water have been recognized as promising candidates for residential and light commercial gas-fired heat pumps. They are particularly suitable for this application because they can provide the functions of both winter heating and summer cooling in a compact size, with air or hydronic external heat sources/sinks. Several cycles have been considered for this purpose, ranging from the simplest single-effect to the GAX (Generator–Absorber heat eXchange) with its different variations. ABSIM has made it possible to simulate a variety of ammonia/water heat pump cycles, with operating conditions and different design parameters varied over a wide range to compare their performance. Figure E.3 describes one of the proposed configurations (Phillips 1990) of the basic GAX system comprising 15 components or subunits and 42 state points. The absorber and desorber are each split into three units: absorber (analyzer) 4 is externally cooled, absorber (analyzer) 5 is solution cooled, and absorber 6 is GAX cooled. Similarly, desorber 7 is externally heated by primary energy (e.g., gas-fired), desorber (analyzer) 10 is solution heated, and desorber (analyzer) 11 is GAX heated. An external liquid loop, state points 22 and 23, employing water as the heat transfer fluid, transfers the heat of absorption between the
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MIX(12) 36
20 42
33
42 22
41 ANL(11) 39 39
23 38 38 21
38 ANL(10)
30
30 32
30
RCT(9)
CND(8)
31
34
37
25
26
25 28
25 DES(7)
35
33
8
29
26
27
36
29
21 23
24
7
10
1
DES(2)
9
6 6
1 1
3
DES(1)
6
2 2
5
MIX(3) 11
22
18 18
17 17 17
20
9
VLV(14)
4
7
8
ABS(6)
10
5
ANL(5)
19
13
12
13
12 12
19
15
MIX(13)
40 ANL(4) 11
14 16
PMP(15)
16
FIGURE E.3 Schematic description of the GAX cycle according to the configuration proposed by Phillips (1990).
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GAX absorber (unit 6) and desorber (unit 11). The vapor at state point 33 enters the rectifier (unit 9) and is distilled to state point 30, with the reflux at state point 36 mixed with the rich liquid in a mixer (unit 12) before entering the generator. Rectifier (9) is used to strip the majority of the water out of the vapor generated in the desorber. The rectified vapor condenses in a condenser (unit 8) and the condensate at state point 8 is subcooled to state point 9 in the precooler before expanding through valve 14 into the evaporator. The evaporator is simulated as the combination of desorber 1 and mixer 13 to allow for incomplete evaporation of the refrigerant leaving at state point 6. The precooler is also simulated as the combination of desorber 2 and mixer 3 for the same reasons. The precooler causes part or all of the liquid that remains in the refrigerant stream 6 to evaporate (state point 11). This stream enters the absorber, completing the cycle. A detailed investigation of the GAX cycle according to the Phillips (1990) configuration has been conducted by Grossman et al. (1995a), using ABSIM. Performance under both heating and cooling modes has been studied under a wide range of operating conditions. Numerous other hardware variations are feasible in the basic GAX cycle. The main variations result from the choice of indirect or direct heat transfer and flow splitting of ammonia/water solution and refrigerant in the cycle. The GAX is one of the more complex of ammonia–water cycles for gas-fired heat pump applications, and one would naturally like to know how it compares to other cycle candidates. In a comprehensive investigation using ABSIM (Engler et al. 1997), the following cycles were investigated: (1) a basic single-effect cycle (BSEC) comprising an evaporator, absorber, desorber, condenser, rectifier, recuperative heat exchanger, circulation pump, and expansion valve; (2) the same cycle as BSEC with the addition of a precooler (SECP, sometimes known as suction-line heat exchanger); (3) the same cycle as SECP with the addition of two solution heat recoveries, one in the absorber and one in the desorber, which employ the solution leaving the unit to cool and heat it, respectively, for increased efficiency; this cycle is referred to as AHE (absorber heat exchange); and (4) the same cycle as AHE with additional heat exchange between the desorber and the absorber, when a temperature overlap between the two permits it; this cycle is the GAX. Due to the limited space in this chapter, individual diagrams for each of these cycles cannot be provided. Instead, the reader is referred to Figure E.3 to picture the cycles as follows: the GAX cycle is the one depicted in the figure; the AHE cycle is the same, with units 6 and 11 (and the heat transfer loop between them) eliminated; the SECP is the same as the AHE with units 5 and 10 eliminated; the BSCE is the same as the SECP with units 2 and 3 eliminated. E.4.3 LiCl–H2O Open and Hybrid Cycles In conventional air-conditioning systems, dehumidification is achieved by overcooling the air below its dew point, which leads to both thermodynamic and practical inefficiencies. An optimal air-conditioning system would be hybrid, consisting of electricpowered vapor compression (VC) to handle the sensible heat load and a heat-driven liquid-desiccant system (LDS) to handle the latent heat load. The LDS is an open-cycle absorption system. The hybrid system has the added advantage of allowing independent control of temperature and humidity, thereby providing much-improved thermal comfort. Figure E.4 describes a hybrid air-conditioning system as simulated by ABSIM. The VC part of the system is located on the right side, comprising an evaporator (12), condenser (13), expansion valve (14), and compressor (15). The working fluid in this part of the system is R134a. The LDS is located to the left, employing LiCl–H2O. The dehumidifier shown
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ASC(7) 26 20 SPL(13) 28 27 54 25 30 29 19 56 25
20 19
ASC(6) 22
21
24
23
14
14
13
13
ASC(5) 16
15
18
17
12
10
10
53 9 MIX(16)
53
8 6
8
7 CMP(2)
VLV(4) 1
HEX(12) 55
6
11
9
56
54
CND(3)
2
52 32 SPL(15) 34 36 35 52 33 38 37 31 57 33 ASC(8) 57
32 31
42
41
44
43
ASC(9)
40 39
40 39
48
47
50
49
ASC(10)
46 45
46 45
51
HEX(11)
4
4 3
1 5
2
EVP(1)
55 3 MIX(14)
FIGURE E.4 Schematic description of a hybrid air-conditioning cycle comprising a vapor compression system for cooling and an LiCl–H2O liquid desiccant system for dehumidification.
at the bottom consists of three ASC units 38, 42, and 31, connected in series. The regenerator shown at the top consists similarly of three ASC 1, 11, and 6, connected in series. Process air at state 36 enters the dehumidifier on its right side and exits dehumidified (state 27) on the left. This air proceeds to heat exchanger 16, where its temperature is lowered further. The desiccant stream serving the dehumidifier is cooled by the evaporator of the VC, entering it at state 16 and leaving at 51. Regeneration air at state 4 enters the regenerator on the left side and is discarded (state 19) on the right. The desiccant stream serving the regenerator is heated by the condenser of the VC, entering it at state 14 and leaving at 18. A recuperative heat exchanger (7) is also part of the LDS. Numerous other configurations of stand-alone LDS and of hybrid air-conditioning systems have been simulated using ABSIM. Due to the limited space in this chapter, cycle diagrams for each of these systems cannot be provided. One of the more interesting cycles employs a closed-cycle LiBr–H2O absorption chiller instead of the VC in Figure E.4 and is fully powered by low-grade heat.
References Biermann, W.J. 1984. Advanced Absorption Heat Pump Cycles. ORNL/Sub/81‑17499/1, Oak Ridge National Laboratory, Oak Ridge, TN. DeVault, R.C. and Biermann, W.J. 1993. Triple-Effect Absorption Refrigeration System with DoubleCondenser Coupling. US Patent 5,205,136. Engler, M., Grossman, G. and Hellmann, H.-M. 1997. Comparative Simulation and Investigation of Ammonia-Water Absorption Cycles for Heat Pump Applications. International Journal of Refrigeration, 20, 504–516. Evans, L.B. 1982. Process Flowsheeting: A State of the Art Review. Proceedings, CHEM COMP 1982: Chemical Process Analysis and Design Using Computers, G.F. Forment, ed., K. Vlaam Ingenieursver, Antwerp, Belgium, 1–12.
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Garimella, S., Christensen, R.N. and Lacy, D. 1996. Performance Evaluation of a Generator-Absorber Heat Exchange Heat Pump. Applied Thermal Engineering, 16, 591–604. Garimella, S., Lacy, D. and Stout, R.E. 1997. Space Conditioning Using Triple-Effect Absorption Heat Pumps. Applied Thermal Engineering, 17, 1183–1197. Gommed, K. and Grossman, G. 1990. Performance Analysis of Staged Absorption Heat Pumps: Water—Lithium Bromide Systems. ASHRAE Transactions, 96(Pt 1), 1590–1598. Grossman, G. and Childs, K.W. 1983. Computer Simulation of a Lithium Bromide‑Water Absorption Heat Pump for Temperature Boosting. ASHRAE Transactions, 89(Pt 1b), 240–248. Grossman, G., DeVault, R.C. and Creswick, F.A. 1995. Simulation and Performance Analysis of an Ammonia-Water Absorption Heat Pump Based on the Generator-Absorber Heat Exchange (GAX) Cycle. ASHRAE Transactions, 101(Pt. 1), 1313–1323. Grossman, G., Gommed, K. and Gadoth, D. 1991. A Computer Model for Simulation of Absorption Systems in Flexible and Modular Form. ORNL/Sub/90‑89673, Oak Ridge National Laboratory, Oak Ridge, TN. Grossman, G., Lando, J.L., Vardi, I., Bourne, J.R., Kimchi, Y. and Ben‑Dror, J. 1979. Solar Powered Environment Control Criteria and Realization. Proceedings, International Solar Energy Society Conference, Vol. 1, K.W. Boer and B.H. Glenn, eds., Pergamon Press, Atlanta, GA, 720–724. Grossman, G. and Wilk, M. 1994. Advanced Modular Simulation of Absorption Systems. International Journal of Refrigeration, 17, 231–244. Grossman, G., Wilk, M. and DeVault, R.C. 1994. Simulation and Performance of Triple-Effect Absorption Cycles. ASHRAE Transactions, 100(Pt 1), 452–462. Grossman, G. and Zaltash, A. 2001. ABSIM—Modular simulation of advanced absorption systems. International Journal of Refrigeration, 24, 531–543. Grossman, G., Zaltash, A. and DeVault, R.C. 1995. Simulation and Performance Analysis of a FourEffect Lithium Bromide-Water Absorption Chiller. ASHRAE Transactions, 101(Pt 1), 1302–1312. Klein, S.A. 1992–2015. Engineering Equation Solver, F-Chart Software, Box 44042, Madison, WI, USA. McLinden, M.O. and Klein, S.A. 1985. Steady State Modeling of Absorption Heat Pumps with a Comparison to Experiments. ASHRAE Transactions, 91(Pt 2b), 1793–1807. Modahl, R.J. and Hayes, F.C. 1992. Development and Proof Testing of Advanced Absorption Refrigeration Cycle Concepts. ORNL/Sub/86‑17498/1, Oak Ridge National Laboratory, Oak Ridge, TN. Phillips, B.A. 1990. Development of a High-Efficiency Gas-Fired Absorption Heat Pump for Residential and Small Commercial Applications. ORNL/Sub/86-24610/1, Oak Ridge National Laboratory, Oak Ridge, TN. Vliet, G.C., Lawson, M.B. and Lithgow, R.A. 1982. Water‑Lithium Bromide Double Effect Absorption Cooling Cycle Analysis. ASHRAE Transactions, 88(Pt 1), 811–823.
Appendix F: Vapor Surfactant Theory The vapor surfactant theory addresses the heat and mass transfer enhancement mechanism of surfactant additives in water/lithium bromide (LiBr) absorption chillers. The vapor surfactant theory holds that the enhancement additives are surfactants delivered to the surface of the solution film from the vapor and that they produce enhancement by generating intense secondary flows on the liquid film. The secondary flows, driven by surface tension gradients (Marangoni convection), augment the coupled heat/mass transfer process by providing mixing and thinning of the film. The primary variable influencing the enhancement is the surface concentration distribution of the surfactant since the surface tension gradients arise due to nonuniformities in the surfactant surface concentration. The vapor surfactant theory is found to explain observations from all known experiments on surfactant-based enhancement. This theory is a significant departure from past theories in its emphasis on the primary role of the vapor in the process.
F.1 Introduction In an aqueous LiBr absorption chiller, water vapor is absorbed into aqueous LiBr solution. In such a chiller, the absorber is typically the largest component because of the relatively poor mass transfer characteristics and the high specific volume of steam at absorber conditions. In a typical absorber, aqueous LiBr solution flows as a film on the outer surface of internally cooled tubes and absorbs water vapor. The absorption is a strongly coupled heat and mass transfer process and is limited on the solution side by mass transfer in the liquid phase. One common method used to enhance the mass transfer and, thus, augment the overall absorption process is the use of a mass transfer enhancement additive such as 2-ethyl-1-hexanol or 1-octanol. Such additives, with trace concentrations in the range of 100 parts per million by mass of the solution charge (ppm), increase the film-side heat transfer coefficient of the coupled absorption process up to a value 2–3 times the value without the additive. Though enhancement additives have been commonly used in LiBr absorption machines since the 1950s, the mechanism by which they provide enhancement was long debated. The vapor surfactant theory provides a significant advance in understanding of the mechanism.
F.2 Background The subject of absorption enhancement additives has been an active area of research since the early patents (Bourne and Eisberg 1966; Albertson et al. 1971; Chi et al. 1971; Modahl and Lynch 1974). In addition to absorption enhancement, the observation of dropwise condensation in the condensers of absorption chillers with additives was mentioned, without details, in all of these patents. This observation is important in explaining the absorption 335
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enhancement mechanism but appears to have been largely ignored by later investigators. The research intensity on absorption enhancement increased considerably in the 1990s with multiple efforts in Japan (Kashiwagi 1988; Hozawa et al. 1991; Hihara and Saito 1993; Kashiwagi et al. 1993), Europe (Setterwall et al. 1991; Ji et al. 1993; Beutler et al. 1996, 1998; Hoffmann et al. 1996; Ziegler and Grossman 1996; Kren et al. 1999), and the United States (Cosenza and Vliet 1990; Elkassabgi and Perez Blanco 1991; Chandler 1993; Perez Blanco and Sheehan 1995; Chandler 1996; Kim et al. 1996a, 1996b; Kulankara 1996; Sheehan et al. 1996; Atchley et al. 1998). Many of these investigators mentioned vapor effects, but the primary importance of the vapor in the enhancement mechanism was made explicit by Kulankara and Herold (Kulankara 1999; Kulankara and Herold 2000, 2001), and their theory was termed the vapor surfactant theory.
F.3 Vapor Surfactant Theory The vapor surfactant theory holds that heat/mass transfer enhancement in both condensation and absorption is due to modifications of the liquid film structure by surface tension–driven secondary flows (Marangoni convection). The surface tension gradients that drive these flows are primarily caused by surfactant arriving at the liquid surface, as a vapor, along with the water vapor. As with surfactants in general, the key parameter that determines the surface tension is the surfactant surface concentration. Marangoni convection requires surface tension gradients that are caused by nonuniform surfactant surface concentration. Nonuniformities in surfactant surface concentration in absorption chillers are brought about primarily by nonuniform condensation or absorption flux of steam that carries surfactant along as a vapor mixture. Once the surfactant lands on the liquid surface it lowers the surface tension locally. Unless the surfactant was delivered in a spatially uniform manner, surface tension gradients will result. These gradients cause surface forces, which then cause surface flows. There is transport of surfactant from the surface to the bulk of the liquid not only via diffusion but also via Marangoni flow. These surfactants have a very low solubility in the liquid. Thus, there exists a low concentration of surfactant in the liquid, but the effect of the surfactant arriving with the vapor overwhelms the effect of surfactant in the liquid. Based on the critical liquid concentration (i.e., the concentration where the surface tension stops changing) from surface tension measurements, the solubility of 2-ethyl-1-hexanol (the most commonly used surfactant) is estimated to be less than 100 ppm in 60% LiBr at 20°C and on the order of 1000 ppm in pure water. Concentrations in excess of the solubility limit lead to a two-phase mixture, which separates due to density differences (surfactant tends to float). Whether the surfactant is dissolved or in a separate liquid phase, the surfactant can easily be transported to the higher pressure cycle components (i.e., the desorber) with the solution via the solution pump. The solution pump inlet design should include surface entrainment to transport liquid surfactant that floats on the surface. Once in the desorber, most of the surfactant is boiled off along with water vapor. It then arrives at the condenser surface along with the water vapor, where it provides condensation enhancement. When flow visualization is available, condensation with the surfactant supplied with the vapor takes on an appearance of dropwise condensation, which is apparently due to aggressive Marangoni convection that sweeps away the liquid in regions of high flux. The film thins locally due to these surface flows, and the thin film means that the resistance of
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the film thickness, which is the major condensation resistance, is significantly reduced. This condensation enhancement is significant but since the overall heat transfer coefficient in a condenser is typically controlled by the tube-side heat transfer process, the effect of this vapor-side enhancement on a typical absorption chiller is small, depending considerably on the overall design of the condenser bundle, especially on tube-side enhancement features. The condensate leaving the condenser is a mixture of water and surfactant. The solubility of the surfactant in pure water (~1000 ppm) is much higher than that in aqueous LiBr. Depending on the surfactant circulation rate, the condensate may be single phase (water + dissolved surfactant) or two phase with excess surfactant in liquid form. Related work on condensation of mixed vapors shows similar enhancement (Morrison and Deans 1997; Morrison et al. 1998). The surfactant is transported to the evaporator with the condensate (via bulk flow, either dissolved or as a two-phase liquid mixture). In the evaporator, the surfactant vaporizes and flows to the absorber with the water vapor (via bulk flow of a mixed vapor of water and surfactant), where it adsorbs/condenses. The absorption of water vapor as well as the condensation/adsorption of surfactant is expected to be nonuniform due to nonuniformities in the surface conditions. The nonuniform surfactant surface concentration results in surface tension–driven secondary flows that thin and mix the film, enhancing the absorption process. In the absorber, the secondary flows are observed as rivulets separated by regions with a very thin film. As in condensation, these regions of thin film significantly enhance heat transfer. The mixing provided by the surface flows provides advective mass transfer, resulting in significantly enhanced mass transfer (as compared to a laminar film). The resulting absorption enhancement is significant since both aspects of the coupled heat/mass transfer process are enhanced. As with the condenser, the overall effect is diluted if the absorber performance is controlled by the tube side. However, because the absorber component is the largest component in an absorption machine, significant improvements can be obtained in the overall machine design performance (i.e., cooling capacity per unit surface area) by careful bundle design, including steps to increase tube-side heat transfer performance (such as finned tubes and increased coolant flow rates). The surfactant cycle described here is a critical aspect in absorption enhancement and, to our knowledge, the surfactant cycle was never described prior to the vapor surfactant theory (Ghosh et al. 2002; Glebov and Setterwall 2002). Several experiments demonstrate that the delivery of surfactant from the vapor is much more important to enhancement than the presence of dissolved surfactant in the liquid (Qiao et al. 2000; Zhou and Herold 2002; Zhou et al. 2002; Herold 2003, 2005; Yuan 2005). One of the many observations that led to development of this theory was the observation of surfactant buildup on the liquid surface in the evaporator of a newly developed machine by a major manufacturer. In an effort to improve performance during development, a large amount of alcohol was added to the machine, but it was not circulating because the evaporator recirculation pump design did not entrain the alcohol on the liquid surface. Thus, the surfactant cycle was broken and the absorber operated poorly. Once this design was adjusted to entrain the alcohol, performance jumped up to the expected level. Another key observation that made it clear that the alcohol undergoes a cycle was the observation that you can inject the alcohol in the upper drum (i.e., in the desorber/condenser vessel) and the enhancement begins very rapidly (on the order of 20 sec in one experiment, but depending on the machine size and the operating condition). This made it clear that the alcohol moves easily from high pressure to low and that the enhancement seems to occur well before there is time for the solution charge to become saturated in surfactant. Although such effects were observed by many investigators prior
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to the introduction of the vapor surfactant theory, it appears that the first discussion of the surfactant cycle appeared in the literature around 2002. The surfactant cycle is critical to a clear understanding of the enhancement mechanism because it explains how the surfactant arrives at the liquid surface, where it causes the surface tension changes that are the fundamental mechanism of action. The surfactant cycle also explains the effects of the surfactant in the condenser. In both condensation and absorption, the surfactant-induced secondary flows on the surface can be quite dramatic in their velocity and intensity. Flow visualization shows an unstable film surface with rapid temporal and spatial fluctuations. The enhancement is not a steady-state effect locally. Averaged over the entire bundle, the absorption rate is relatively steady, but locally the absorption rates fluctuate dramatically due to the surfactant effects, which tend to magnify local variations in flux, leading to local flow instability. This flow instability is easy to observe in a flow visualization facility. A key observation is that the intensity of the flow instability is a function of the flux. As this is a tightly coupled heat/mass transfer process, heat flux and mass flux go together. When the flux is high, the intensity of the flow instability is high and the enhancement is high. The flow instability is key to the enhancement. The flow instability occurs because a slight increase in flux at one location causes more surfactant to be delivered to that location, which further enhances transport (flux) at that location, leading to runaway process. The process is eventually limited by saturation of the liquid surface with surfactant. However, before reaching that saturated condition, significant absorption and condensation enhancement can be observed. In the range before the liquid surface becomes saturated with surfactant, the enhancement sweet spot exists, where device performance actually gets better as flux increases. In general, film absorption and film condensation follow the rule of thumb that increased flux causes a thicker film that inhibits the process. Thus, the base case for an understanding of these processes is that device performance should decrease as the flux increases. A very intriguing aspect of the surfactant enhancement mechanism is that it breaks this rule of thumb, at least for a range of flux values, and provides an inverted flux characteristic. This rule breakage is made possible because the surfactant-induced flows actually thin the film, at least locally, causing the increased transport. At very high flux, the surfactant effect disappears due to surfactant saturation. The range of flux values where the inverted flux characteristic operates includes the range of typical absorption machine operating conditions. Surfactant enhancement of absorption and condensation in aqueous LiBr technology is standard practice, but it has never been well understood. A key reason for this is that the inverted flux characteristic interacts with several other bundle design variables in complex ways. Enhancement in a vertical single-tube experiment can easily reach 300%, but typical enhancement in a horizontal tube bundle may only be 30%. A major challenge in large-bundle design is to approach uniform flux throughout the bundle. If uniform flux could be easily engineered, then it would be easy to scale a bundle and obtain predictable performance. Even without the inverted flux characteristic, bundle design is complex and some areas of the bundle experience much higher flux than others due to the combined effects of the mass transfer and heat transfer processes, either of which can control the overall process. Mass transfer is strongly affected by pressure, solution distribution, and solution flow rate. The pressure varies throughout the bundle when the tubes are closely spaced and the vapor velocities are high. The low vapor pressure of aqueous LiBr makes the absorption process extraordinarily sensitive to pressure drop effects. Heat transfer is strongly affected by the temperature difference between the solution on the outside
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of the tubes and the water on the inside. The ideal temperature difference design would be counterflow, but a horizontal bundle design is more like crossflow. Thus, the highest flux is often at the end of a long bundle, where the coolant enters the tubes. For these reasons, and other secondary affects not mentioned, the flux in the bundle is generally not uniform. The surfactant tends to enhance the flux in regions of high flux. Thus, the surfactant tends to amplify bundle flux nonuniformity. It is not uncommon that the heat/mass transfer area of the bundle is not utilized effectively overall, and this fact is made worse by the surfactant. It is a relatively simple matter to address this issue in a small absorber, where you have more control over the heat and mass transfer potential differences. However, in a large bundle, with many practical, geometrical, and economic constraints, it is much more complex. Manufacturers have often observed that scaling a bundle design does not always work well because of the interplay of all these variables. The implication of the vapor surfactant theory for absorber bundle design is that the importance of achieving uniform potential differences throughout the device is greater than without the surfactant. The enhancement factor in a bundle can only approach that found in a single vertical tube if the heat and mass transfer potentials are balanced throughout the bundle (e.g., counterflow design). In a bundle design with poor balance, there may be sections of the bundle with very low flux that could be excised from the design without much effect on performance. However, in a balanced design all sections of the bundle would carry close to the same flux. Achieving balanced design is difficult in a large bundle, but the value of the vapor surfactant theory is that it shows the path toward improvement. Although difficult to achieve a fully balanced design, there are many design features that can be adjusted to come closer to a balanced design such as (1) variable tube spacing to account for pressure drop, (2) multipass water circuiting for tall bundles to provide water temperatures that follow the solution mass fraction changes, and (3) variable tube-side enhancement with no enhancement at the cold water entrance. These are standard ideas in bundle design that are independent of the surfactant, but the surfactant makes them doubly important because of the inverted flux characteristic. The data on surfactants, other than the two most common ones mentioned earlier, has historically been confusing because some surfactants that are very effective at reducing surface tension in aqueous LiBr are not very effective at producing absorption/ condensation enhancement. However, with the help of the vapor surfactant theory, these confusing observations are explainable. Since the surfactant vapor enters the absorber/ condenser in vapor form, the vapor pressure of the surfactant is also an important factor that determines its effectiveness in producing enhancement. The effect of surfactant vapor pressure can be deduced from the data presented by Beutler et al. (1996), who report that the surface tension of aqueous LiBr with 1-decanol is lower than the surface tension with either 2-ethyl-1-hexanol or 1-octanol. However, the enhancement brought about by 1-decanol is reported to be lower than that produced by either 1-octanol or 2-ethyl-1-hexanol. This apparently contradictory data for 1-decanol has been used to raise questions about the Marangoni convection enhancement mechanism. However, this seeming contradiction can be explained by the low vapor pressure of 1-decanol. Vapor pressure data presented in Yaws (1994) show that the vapor pressure of 2-ethyl1-hexanol and 1-octanol is approximately 12 and 7 times higher than that of 1-decanol, respectively (at typical absorber operating conditions). As a result, 1-decanol tends to stay more in the liquid phase while the more effective surfactants have a much higher concentration in the vapor and, thus, can perform better in a multiphase application like the surfactant cycle in an absorption chiller.
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Based on the vapor surfactant theory, the key characteristics of an effective surfactant additive can be deduced. An effective additive is a surfactant and should have a low plateau value of surface tension (to make it effective at causing Marangoni convection), a low critical concentration in the liquid (the surfactant acts primarily in the vapor space so storing it in the liquid is not productive), and a vapor pressure that is high enough to deliver the surfactant to the surface while not so high as to provide a vapor-side mass transfer resistance. The combination of a low plateau value of surface tension and a low value of critical concentration results in larger surface tension gradients when nonuniformities in surfactant surface concentration are present, which in turn results in more intense secondary flows and higher enhancement.
F.4 Key Experimental Results The experiments and results summarized here highlight the unique nature of the surfactant in aqueous lithium bromide absorption technology. The importance of the transport of the surfactant to the liquid surface via vapor flow is critical in every example. Other experimental results supporting the theory can be found in Schultz and Patnaik (2002) and Harm et al. (2005). F.4.1 Drop Proximity Experiment The importance of the surfactant vapor can be observed in a very simple benchtop experiment where a sample of either water or aqueous LiBr is loaded into a Petri dish to some nominal depth. If the Petri dish is allowed to sit undisturbed for a few minutes, the surface can be observed to be quiescent. Close observation, at the optimum angle of view, will usually show small dust particles sitting on the surface, and these are useful to help the visualization. A droplet of 2-ethyl-hexanol is loaded onto the tip of a pipet or a dropper such that the droplet is exposed to the air. The droplet is brought into proximity of the liquid surface in the Petri dish without touching the surface. Under these conditions, a welldefined surface flow is observed emanating radially away from the droplet position. This is interpreted to be a Marangoni flow caused by adsorption of surfactant vapor. In this case, the surfactant diffuses through the air to get to the surface. This is in contrast to the absorption/condensation cases where surfactant arrives at the surface by bulk flow along with water vapor. However, the experiment shows clearly that surfactant-driven surface flows can occur when the surfactant is not initially present in the liquid. This realization was one of the important steps in the development of the vapor surfactant theory. F.4.2 Active Surface Experiment Another benchtop experiment that highlights the physics of this system is done by mixing the surfactant (at or slightly above the solubility limit) into the liquid solution in a Petri dish. If too much surfactant is added, it will begin to cover the surface in a surfactant liquid layer. After mixing, a cover is placed over the Petri dish, and there is a wait of a few minutes until the system is quiescent. When the cover is removed, nothing happens until one disturbs the air above the sample, perhaps by blowing gently across the surface. An initial disturbance causes the surface of the system to begin jumping back and forth in an agitated pattern that appears perpetual. It is observed that the motion stops if the lid is
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put back on the dish. It also stops after the system has been exposed to air for a long time (such as overnight). This is apparently caused by evaporation of the surfactant in a spatially nonuniform manner that causes surface tension gradients which drive local surface flows. Once the surfactant is completely evaporated, or if the vapor phase is saturated in surfactant (when the lid is in place), the flow stops. In this experiment, the surfactant transfers from the liquid phase to the vapor phase, so it is rather different than the condensation and absorption situations. However, this experiment helps to highlight the fact that the surfactants under consideration interact with both the liquid and vapor phases. This experiment also demonstrates Maranogoni convection in this system. F.4.3 Surface Tension Measurements The surface tension changes caused by the surfactant are fundamental to understanding vapor surfactant effects. However, the traditional methods and techniques used to measure surface tension tend to obscure the most important aspects for this system. If the measurements are performed in a closed vessel with sufficient time to allow the surfactant surface concentration to equilibrate with the surrounding vapor concentration, then you get static surface tension results. Such results have often been plotted as a function of the concentration, defined as the amount of surfactant divided by the volume of the liquid. Such data show considerable scatter between investigators, and the reason is that the concentration used has very little meaning because the surfactant does not stay in the liquid but instead redistributes itself on the solid surfaces and in the vapor phase (Zhou et al. 2002). The more important variable is found to be the vapor concentration of the surfactant, which is more difficult to control and to measure. However, it is possible to control the concentration of the surfactant in the vapor if you redesign the experiment, as in Figure F.1. In this case, the liquid enters the system free of surfactant, but the surfactant adsorbs on the surface of the liquid droplets as they form. A mixture of air and surfactant vapor sweeps gently past the test section with controlled (low) velocity. The advantage of this configuration is that it defines the surfactant vapor concentration to which the droplets are exposed. Results from such experiments are Drop creator Clear pipe
Rotameter
Filter
Compressed air Valve
Additive flask
Heating mantle
Flask
Variac
Test chamber
Balance
FIGURE F.1 Schematic of the surface tension measurement facility designed to control the surfactant vapor concentration. (Reprinted from Applied Thermal Engineering, 21, Yuan, Z., Herold, K.E., Surface tension of pure water and aqueous lithium bromide with 2-ethyl-hexanol, 881–897. Copyright 2001. With permission from Elsevier.)
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120 110
Temperature = 24.3 ± 1.3°C Air velocity = 0.06 m/sec
100 Surface tension (mN/m)
90 80 70 60 50 40
Symbol Concentration of 2EH in air (ppm) 0 43 100 200
30 20 10 0
0.01
0.1 Drop frequency (Hz)
1
FIGURE F.2 Surface tension data for 60% lithium bromide in water obtained from the apparatus in Figure F.1 showing the strong effects of vapor concentration and drop frequency. 2EH = 2-ethyl-1-hexanol. (Reprinted from Applied Thermal Engineering, 21, Yuan, Z., Herold, K.E., Surface tension of pure water and aqueous lithium bromide with 2-ethyl-hexanol, 881–897. Copyright 2001. With permission from Elsevier.)
shown in Figure F.2. It is observed that the concentration of surfactant in the air has a major effect on the measured surface tension. It is a dynamic effect since it is influenced by the droplet generation rate. The most interesting aspect of these data is the fact that a very low vapor concentration of 200 ppm in air is sufficient to reduce the surface tension to the lowest plateau values ever reported for this system. Thus, the delivery of surfactant from the vapor phase to the liquid surface is very effective, even at low vapor concentration, at reducing the liquid surface tension. These results provide data that are directly relevant to the enhancement method in an absorption chiller. F.4.4 Effect of Flux on Enhancement One of the most important observations about the enhancement process is that enhancement is a strong function of transport flux (i.e., the flux of vapor condensing or absorbing) with increasing enhancement as the flux is increased from zero. Data for two values of flux (measured as heat flux) are shown in Figure F.3 for absorption. It can be seen that the heat transfer coefficient is considerably higher at higher heat flux. The trend expected from condensation and absorption in the absence of surfactant is that the heat transfer coefficient should decrease as the flux goes up, correlating well with the liquid film thickness on the surface. However, in this case the reverse is observed. It is noted that this inverted flux characteristic is not expected to hold true as the flux is increased without bound. Eventually, the enhancement will reach a plateau, and the film thickness effect will again become dominant. However, there is a range of flux and surfactant vapor concentration where the inverted flux characteristic is observed. The inverted flux characteristic is also observed for condensation (Kulankara and Herold 2000).
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Heat transfer coefficient [kW/(m2.K)]
2
1.5
1
0.5 2EH at 10.5 kW/m2 flux 2EH at 20.5 kW/m2 flux 0
100
200
300
400 500 600 700 Additive concentration (ppm)
800
900
1000
FIGURE F.3 Heat transfer coefficient versus surfactant liquid concentration showing the effect of heat flux. 2EH = 2-ethyl1-hexanol. (Kulankara, S., Herold, K.E., theory of heat/mass transfer additives in absorption chillers, HVAC&R Research, 6(4):369–380, 2000. Reprinted by permission of the American Society of Heating, Refrigerating and Air Conditioning Engineers, www.ashrae.org)
F.5 Modeling Marangoni Flows with Vapor Surfactant Effects It would be useful to model absorption and condensation processes with vapor surfactant effects to gain a more complete understanding of these processes. This appears to be a very worthy new problem for the fluid dynamics community. It is complicated by several aspects, including (1) it involves two-phase flow with a (potentially) moving boundary; (2) it involves mixtures that segregate at the phase boundary; (3) it requires data on the relationship between surfactant surface concentration and surface tension; (4) it requires a shear stress boundary condition on the flow; and (5) the observed flows appear very chaotic. Simplified models are more tractable. For example, we considered condensation on a flat, horizontal liquid surface with nonuniform cooling from below and solved the timedependent model numerically (Qiao et al. 2000). The nonuniform cooling automatically provides the nonuniform flux that is needed to start the Marangoni convection. We used our own surface tension data along with a Gibbs analysis to define the surface concentration (Zhou et al. 2002). The model we created definitely showed enhancement due to the surfactant. The model proved to be very sensitive to the input data and the numerical grid density. Our efforts on this were only a first step in the direction of vapor surfactant modeling. Another problem related to this that may be of interest to the fluid dynamics community is the instability problem. The flow visualization of these Marangoni flows seems to exhibit randomness in both space and time. The chaotic nature of the flows provides one more model system to study complex flows.
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F.6 Summary The vapor surfactant theory provides a physical explanation for all of the available data on surfactant-enhanced heat and mass transfer in absorption refrigeration systems. In addition, it makes predications about absorber design that provide a path to the next generation of system enhancements. Smaller and cheaper machines are the potential payoff from this deeper understanding. Physics-based absorber design, based on vapor surfactant physics, has the biggest potential for performance improvement of absorption chillers going forward.
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