WINPROP USER GUIDE PHASE-BEHAVIOUR & FLUID PROPERTY PROGRAM VERSION 2014
14.WI.M4
This publication and the application described in it are furnished fur nished under license exclusively to the licensee, for internal use only, and are subject to a confidentiality confidentiality agreement. They may be used only in accordance with the terms and conditions of that agreement. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, ele ctronic, mechanical, or otherwise, including photocopying, recording, or by any information storage/retrieval system, to any party other than the licensee, without the written permission of Computer Modelling Group. The information in this publication is believed to be accurate in all respects. However, Computer Modelling Group makes no warranty as to accuracy or suitability, and does not assume responsibility for any consequences resulting from the use thereof. The information contained herein is subject to change without notice.
Copyright
2014 Computer Modelling Group Ltd.
All rights reserved.
The license management portion of this program is based on: Reprise License Manager (RLM) Copyright (C) 2006-2014, Reprise Software, Inc. WinProp uses Intel(R) Compilers. WinProp, CMG, and Computer Modelling Group are registered trademarks of Computer Modelling Group Ltd. All other trademarks are the property of their respective owners. Computer Modelling Group Ltd.
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Tel: (403) 531-1300
Fax: (403) 289-8502
E-mail:
[email protected]
Preface WinProp is CMG's equation of state (EOS) multiphase equilibrium and properties determination program. WinProp features techniques for characterizing the heavy end of a petroleum fluid, lumping lumping of components, matching laboratory PVT data through regression, simulation of first and multiple contact miscibility, phase diagrams generation, asphaltene and wax precipitation modeling, compositional grading calculations as well as process flow simulation. This User Guide presents a comprehensive description of the steps involved in obtaining a PVT data suitable for inclusion in data files for CMG's GEM, STARS or IMEX simulators. This User Guide is aimed at reservoir engineers who want to use WinProp to predict phase behavior of reservoir fluids as well as characterize these fluids for reservoir simulation. It requires some knowledge of phase behavior as it pertains to the the different fluid types found in reservoirs. Every attempt has been made in the preparation of this User Guide to provide the user with all the necessary details. If questions arise, please contact: Computer Modelling Group Ltd. 200, 1824 Crowchild Trail N.W . Calgary, Canada T2M 3Y7 Telephone: (403) 531-1300 Fax: (403) 289-8502 E-mail:
[email protected]
Confidentiality: All components of CMG technology including software and related documentation are protected by copyright, trademark and an d secrecy. CMG technology can be used only as permitted by your license from CMG. By the license, you have agreed to keep all CMG technology confidential and not disclose it to any third party. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, elec tronic, mechanical, or otherwise, including photocopying, recording, or by any information storage/retrieval system, to any party other than the licensee, without the written permission of Computer Modelling Group. Corrections/Errors: CMG ENDEAVORS TO PRODUCE TECHNOLOGY OF THE HIGHEST QUALITY; NEVERTHELESS ERRORS OR DEFICIENCIES IN SUCH TECHNOLOGY ARE INEVITABLE. IF YOU FIND AN ERROR OR DEFICIENCY, YOU ARE REQUESTED TO PROVIDE DETAILS OF IT AND ILLUSTRATIVE DATA SET(S) TO CMG SUFFICIENT TO PERMIT CMG TO REPRODUCE THE ERROR OR DEFICIENCY. CMG SHALL ENDEAVOR TO REMEDY A DEFICIENCY IN A TIMELY MANNER AND SHALL PERIODICALLY REPORT TO YOU AS TO THE STEPS BEING TAKEN TO REMEDY THE DEFICIENCY. THE RESPONSE TIME FOR A DEFICIENCY MUST BE PRIORITIZED FOR THEIR GENERAL APPLICATION TO CMG MEMBERS AND WHETHER THEY FORM PART OF A CMG PROGRAM. CMG DOES NOT WARRANT THAT DEFICIENCIES WILL BE REMEDIED.
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Contents New Features
1
New Features in WinProp 2014.10 2014.10 .................. ........................... .................. .................. ................... ................... .................. ............... ......1 New Features in WinProp 2013.10 2013.10 .................. ........................... .................. ................... ................... .................. .................. ............... ......2 Simulator Calculation Engine Changes ........................................................... 2 Graphical User Interface Changes ................................................................... 3 New Features in WinProp 2012.10 2012.10 ................. .......................... .................. .................. .................. ................... ................... ................ .......3 Simulator Calculation Engine Changes ........................................................... 3 Graphical User Interface Changes ................................................................... 4 New Features in WinProp 2011.10 2011.10 ................. .......................... ................... ................... .................. .................. .................. ................ .......4 New Features in WinProp 2010.10 2010.10 .................. ........................... .................. .................. .................. .................. .................. ................ .......5 New Features in WinProp 2009.10 2009.10 .................. ........................... .................. .................. .................. .................. .................. ................ .......5 New Features in WinProp 2008.10 2008.10 .................. ........................... .................. .................. .................. .................. .................. ................ .......6 New Features in WinProp 2007.10 2007.10 .................. ........................... .................. .................. .................. .................. .................. ................ .......6 New Features in WinProp 2006.10 2006.10 .................. ........................... .................. .................. .................. .................. ................... ................ ......7 New Features in WinProp 2005.10 2005.10 .................. ........................... .................. .................. .................. ................... ................... ............... ......7 New Features in WinProp 2004.10 2004.10 .................. ........................... .................. ................... ................... .................. .................. ............... ......8 New Features in WinProp 2003.11 2003.11 .................. ........................... ................... ................... .................. .................. .................. ............... ......8 New Features in WinProp 2003.10 2003.10 ................... ............................ .................. .................. .................. .................. .................. ............... ......9 New Features in WinProp 2002.10 2002.10 ................... ............................ .................. .................. .................. .................. .................. ............. ....10 New Features in WinProp 2001.10 2001.10 ................. .......................... .................. .................. ................... ................... .................. .............. .....10 New Features in WinProp 2000.15 2000.15 ................. .......................... ................... ................... .................. .................. .................. .............. .....11 New Features in WinProp 2000.10 2000.10 ................. ........................... ................... .................. .................. .................. .................. .............. .....12 New Features in WinProp 1999.10 1999.10 .................. ........................... .................. .................. .................. .................. .................. .............. .....13 New Features in WinProp 98.00 98.00 ................. .......................... .................. .................. ................... ................... .................. .................. .........16 New Features in WinProp 97.00 97.00 ................. .......................... .................. ................... ................... .................. .................. .................. .........18
Introduction
21
WinProp Overview ..................................................................................................... 21 Use of this Manual ...................................................................................................... 21 Installation .................................................................................................................. 22 Confidentiality ............................................................................................................ 22 Template Data Files .................................................................................................... 22
User Guide WinProp
Contents i
Basic Operations
25
Overview .................................................................................................................... 25 Elements of the WinProp Program Window .............................................................. 25 Inserting Simulation Steps............................................................................. 26 Step Validation Status ................................................................................... 27 Including/Excluding Steps ............................................................................ 27 Comments ...................................................................................................... 28 Accessing On-Line Help ............................................................................................ 28 Creating, Opening and Saving Data Files .................................................................. 28 Running and Viewing Output ..................................................................................... 29 Copying Between Data Sets ....................................................................................... 29 Setting Up a Regression Run ...................................................................................... 29 Using the Update Component Properties Feature ...................................................... 31 Set up the Splitting Calculation: .................................................................... 31 Run WinProp ................................................................................................. 31 Remove Splitting Node ................................................................................. 31 View/Print the Data Set .............................................................................................. 31 Editing the Data Set .................................................................................................... 32 Operations with Multiple Calculation Modules ......................................................... 32
Titles/EOS/Unit s Selection
35
Overview .................................................................................................................... 35 Data Input ................................................................................................................... 35 Comments ...................................................................................................... 35 Title Line 1, Title Line 2, Title Line 3 .......................................................... 35 Equation of State ........................................................................................... 36 Units .............................................................................................................. 36 Feed ............................................................................................................... 36
Components
37
Component Selection and Definition ......................................................................... 37 Library Components ...................................................................................... 38 User Component with Known Properties ...................................................... 39 Component Properties ................................................................................................ 41 Notes on Component Properties.................................................................... 42 Interaction Coefficients .............................................................................................. 47 Hydrocarbon-Hydrocarbon Interaction Coefficients..................................... 48 Other Interaction Coefficients ....................................................................... 50 Viscosity Parameters .................................................................................................. 50 Jossi-Stiel-Thodos Correlation ...................................................................... 51 Pedersen Correlation ..................................................................................... 52
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Contents
User Guide WinProp
Aqueous Phase ............................................................................................................53 Aqueous Phase Salinity ................................................................................. 53 Henry’s Law Constant Correlation ................................................................ 54 Model Option .............................................................................................................. 54 Activation of Second Set of Component Properties ................................................... 55 GEM Fluid Model Generation and Component Properties Printing ........................... 55 GEM-GHG Parameter Selection................................................................................. 57
Common Data Required for All Options
61
Overview ..................................................................................................................... 61 Composition Specification ..........................................................................................61 Initial K-Values...........................................................................................................63 Output Level ............................................................................................................... 64 Stability Test Level ..................................................................................................... 64
Two-Phase Saturation and Phase Boundary Calculati ons
65
Overview ..................................................................................................................... 65 Saturation Pressure ..................................................................................................... 65 Saturation Temperature ............................................................................................... 66 Phase Boundary and Quality Line Calculations ......................................................... 66 Envelope Specification .................................................................................. 67 Envelope Construction Controls .................................................................... 70 Cricondenbar/Cricondentherm Calculation ................................................................ 70 Critical Point Calculation ............................................................................................71
Flash Calculatio ns
73
Overview ..................................................................................................................... 73 Common Input for Two-Phase Flash, Multiphase Flash and Asphaltene/Wax Modelling Calculations ............................................................................................ 73 Two-Phase Flash Calculations .................................................................................... 74 Multiphase Flash Calculations .................................................................................... 75 Asphaltene/Wax Modelling ........................................................................................ 77 Theoretical Background................................................................................. 77 Input Data - Asphaltene/Wax Modelling ....................................................... 78 Single-Phase Calculation ............................................................................................ 84 Isenthalpic Flash Calculations .................................................................................... 84 Theoretical Background................................................................................. 84 Input Data - Isenthalpic Flash ........................................................................ 86
Three-Phase Boun dary Calcu latio n
89
Background ................................................................................................................. 89 Input Data ................................................................................................................... 89 User Guide WinProp
Contents iii
Envelope Specification Tab........................................................................... 89 Envelope Construction Controls Tab ............................................................ 91 Initial K-Values Tab ...................................................................................... 92
Component Splittin g and Lumpi ng
93
Overview .................................................................................................................... 93 Characterization of Multiple Related Samples ........................................................... 94 Splitting the "Plus" Fraction ....................................................................................... 94 Numerical Cleaning of Mud-Contaminated Samples............................................... 100 Lumping of Components .......................................................................................... 102 Transferring Results to Other Data Sets ................................................................... 103
Laboratory Calcul ations
105
Overview .................................................................................................................. 105 Recombination of Separator Oil and Gas ................................................................. 105 Compressibility Calculation ..................................................................................... 108 Constant Composition Expansion ............................................................................ 110 Differential Liberation .............................................................................................. 113 Constant Volume Depletion ..................................................................................... 116 Separator Test ........................................................................................................... 120 Swelling Test ............................................................................................................ 123
Multiple Contact Miscibil ity Calcul ations
127
Overview .................................................................................................................. 127 Data Input ................................................................................................................. 128
Regression
133
Overview .................................................................................................................. 133 Organization of the Input Data ................................................................................. 133 Parameter Selection .................................................................................................. 135 Grouping Regression Variables ................................................................................ 138 Regression Variable Bounds .................................................................................... 140 Regression Control Parameters ................................................................................ 142 Transferring Results to Other Data Sets ................................................................... 143
Compositi onal Grading
145
Overview .................................................................................................................. 145 Data Input ................................................................................................................. 146
iv
Contents
User Guide WinProp
STARS PVT Data Generation
149
Overview ................................................................................................................... 149 Use of the STARS PVT Generation Option ............................................................. 149 Input Data (STARS) ................................................................................................. 150 Basic STARS PVT Data .............................................................................. 150 Gas-Liquid K-Value Tables ......................................................................... 154 Gas-Liquid and Liquid-Liquid K-Value Tables ..........................................156 Gas-Liquid and Solid-Liquid K-Value Tables .............................................158 Feed and K-Value Plotting Controls ............................................................ 159
Black -Oil PVT Data Generation
161
Overview ................................................................................................................... 161 Laboratory Procedure ............................................................................................... 174 Input Data ................................................................................................................. 175
References
179
List ............................................................................................................................ 179
Appendix A
183
Case Studies .............................................................................................................. 183 Case Study Number 1: Gas Condensate Modeling .....................................183 Case Study Number 2: Solubility of CO2 in Brine ..................................... 206 Case Study Number 3: Asphaltene Precipitation Modeling .......................223
Appendix B
241
Equations .................................................................................................................. 241 Cubic Equation of State ............................................................................... 241 Phase Stability Test ...................................................................................... 246 Two-Phase Flash Calculation ...................................................................... 248 Saturation Calculation.................................................................................. 249 Cricondenbar/Cricondentherm Equations .................................................... 251 Phase Diagram Construction ....................................................................... 251 Three Phase Flash Calculation with Equation of State ................................ 255 Three Phase with Isenthalpic Flash Calculation .......................................... 257 Flash Calculation Involving Water .............................................................. 259 Critical Point Calculations ........................................................................... 262 Viscosity Correlation ................................................................................... 264 Solution of Non-Linear Equations ............................................................... 265 Plus Fraction Characterization ..................................................................... 266 Interfacial Tension Calculations .................................................................. 270
User Guide WinProp
Contents v
Regression ................................................................................................................ 270 Introduction ................................................................................................. 270 The Regression Method............................................................................... 271 Application of the Regression ..................................................................... 272 Properties of Components ........................................................................................ 275 User Components ........................................................................................ 277 Interaction Coefficient ................................................................................. 279 Nomenclature ........................................................................................................... 281 References for Appendix B ...................................................................................... 283
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Contents
User Guide WinProp
New Features
New Features in WinProp 2014.10 Flash Enhancement
For performing negative flashes in difficult regions (e.g. near-critical) a new flash method using Newton iteration has been added. This technique is available for the Two-Phase Flash calculation by selecting Negative/Newton as the flash type. A new template data set illustrating use of the option is given in TwoPhase_negativeNewtonFlash.dat.
New Phase Split Calculation
The phase split calculation of Li, Johns and Ahmadi (Fluid Phase Equilibria 316 (2012) 85-97) has been implemented for use with multi-contact miscibility calculations, and also with the new flash option described above. This change, and other algorithm enhancements, has improved the efficiency and convergence of the multi-cell mixing method for MMP calculations.
STARS PVT generation enhancements
The option to specify the pressure-dependent enthalpy model for STARS PVT generation has been implemented. The PVT_DEPARTURE keyword and associated ideal gas enthalpy coefficient data will be written to the STARS fluid model file when this option is selected. The new Negative/Newton flash method described above is also available for generating STARS K-Value tables. A new template data set illustrating use of the option is given in stars_GLKTables_negativeNewton.dat.
Improved Property Estimation
Ideal Gas Heat Capacity coefficients for components lighter than C6 are now estimated according to molecular weight if these coefficients are not obtained from the component library or entered by the user. This will give improved results for these components compared to using standard correlations.
Graphical User Interface Enhancements
Experimental data points will now be shown in plots for all calculation options, inside or outside of the regression block.
User Guide WinProp
New Features 1
Context menu options for selection of volume shift correlation options have been improved. There is now a Preferences menu item that allows the user to choose which text editor is used when the option to display output data in an external editor is activated.
New Featur es in WinPro p 2013.10 Simulator Calculation Engine Changes Linear Temperature-Dependent Volume Shift
A linear temperature-dependent volume shift model has been implemented in WinProp. This model is useful for matching density data over a range of temperatures, especially for heavy oils. The temperature-dependent parameter in the model may be adjusted via regression, or estimated with a correlation. This model is also available in GEM. The old temperature-dependent volume shift formulation is still available; however the old model cannot be adjusted in regression and is not available in GEM. STARS PVT
It is now possible to specify both Basic STARS PVT and STARS K-value generation in a single calculation option. The previous behavior of running only one of these calculations is still available. Lumping of Non-Adjacent Components
The data entry window for the Lumping option has been modified. It is now possible to enter the pseudo-component number for any individual component directly in the lumping scheme table. This allows lumping of non-adjacent components. All existing Lumping data sets will run as before, but will be converted to the new data entry format when opened in WinProp. Phase Diagram for Pure Component
It is now possible to generate a pure component Pressure-Temperature diagram (vapor pressure curve) using the Two-Phase Envelope calculation option. No changes in input are required. This feature will be active if only one component is defined, or if only one component in a multi-component system has a non-zero composition. New Phase Property Plots
Phase Enthalpy, Heat Capacity and Entropy are now available to be plotted via the Plot Control tab for the two-phase flash, multiphase flash and multi-phase with solid flash. Other Changes
•
2
Default binary interaction parameters and volume shifts have been modified for some library components, particularly for the SRK EOS.
New Features
User Guide WinProp
•
Excess enthalpy, heat capacity and entropy may be calculated using the Lee-Kesler EOS/corresponding states model, to allow comparison of this model to excess properties calculated directly from the cubic EOS.
Graphical User Interface Changes Multiple Components Deletion
From the component GUI, multiple components can be selected (i.e. row-wise) and deleted. Single Component Duplication
With Copy and Paste buttons, a single component can be easily duplicated. Cleaner Component GUI
Action buttons for setting Volume Shift and Reference Henry Constant are replaced with the relevant context menus, which can be executed via the corresponding property column header. Plot Data Export
The functionality for exporting plot data to TXT or XML has been completed allowing the export of all plot data for all calculation options, export of all plot data for one calculation option, or export of plot data for one plot.
New Features in WinProp 2012.10 Simulator Calculation Engine Changes STARS Gas Viscosity Parameter Generation
The STARS “Basic PVT” calculation now has the option to write out component gas viscosity correlation coefficients. Since the STARS gas viscosity model is a low-pressure form, the coefficients are generated at atmospheric pressure. See template data set “starsgas_visc_withH2O.dat”. Multiple Mixing Cell Method for MMP
The multiple mixing cell method of Ahmadi and Johns (SPE 116823) for calculating minimum miscibility pressure has been implemented in WinProp. Recent research on analytical method-of-characteristics (MOC) techniques for calculating MMP indicates that the MOC methods may not always converge to the correct solution. The multiple mixing cell method is included as an alternative to check the results of MOC calculations, and possibly indicate if slim-tube simulations should be done. Additional Regression Variables for OGW Flash
The component mole fractions in non-aqueous phases and component gas-water and oil-water k-values can now be specified as experimental data for regression in the OGW flash.
User Guide WinProp
New Features 3
Enthalpy and Entropy Calculations
Phase Entropy is now output in the standard phase property table in WinProp, along with enthalpy and heat capacity. The database of ideal gas enthalpy coefficients used in the calculation of all of these quantities has been updated from the 2005 edition of the API Technical Data Book, to eliminate some inconsistencies in the earlier data. Format I and Format II Extended Black Oil Tables
The calculation of the alternate format extended black oil tables has been enhanced for better consistency with Equation-of-State results for density and viscosity.
Graphical User Interface Changes Operations with Multiple Calculation Modules
A new dialog has been implemented to allow operations to be performed on multiple calculation modules simultaneously. The dialog shows a list of the calculation modules in the data set that can be selected using the usual
and keyboard controls. The selected items can be included/excluded from the WinProp run, or cut/copied to the clipboard. The contents of the clipboard may then be pasted into any open data set. Other Interface Features
An option to temporarily disable regression has been implemented. The calculations in the regression block are still performed, but no regression is done.
New Featur es in WinPro p 2011.10 Re-designed Graphical User Interface
The main program window for WinProp has been completely redesigned, greatly improving the functionality and ease of use of the interface. The data entry windows for the calculation options are very similar to previous versions of the program, allowing existing users to quickly become familiar with the new software. Please see the Basic Operations chapter for a description of the new interface and how to use it. New features of the interface include:
•
The structure of the data set (order of calculation options) is now displayed in a tree view, as opposed to the “table -of-contents” style grid.
• •
All data entry windows are displayed within the main program interface.
•
4
For QC checks, plots are shown within the data entry windows of component properties vs. molecular weight, as well as plots of experimental data vs. pressure for CCE, CVD and DifLib laboratory experiments. Text and graphical output is now displayed within the main program window, accessed via the tree view.
New Features
User Guide WinProp
•
Text output can be sent to Windows Notepad, and graphs can be printed, copied to the clipboard, saved as a jpg file or graph data can be exported as a text file.
•
The Table Import Wizard is now obsolete, as tabular data can be pasted directly from spreadsheets into the data entry grids for laboratory PVT experiments. For component properties definition, the user-component data entry dialog has been expanded to include the functionality of the Table Import Wizard, allowing specification of properties for multiple components in one step.
New Features in WinProp 2010.10 New Approach for the Multiple Contact Miscibility Calculation
A Tie Line calculation method has been added to WinProp in the Multiple Contact Miscibility Calculations chapter to calculate the minimum miscibility pressure (MMP) or minimum miscibility enrichment (MME). This method takes the combined condensing and vaporizing displacement mechanisms into consideration, as well as the existing pure vaporizing or pure condensing mechanisms. With the pressure or enrichment increasing, all key tie lines, including the initial tie line, injection tie line and the crossover tie lines, can be found simultaneously based on the method of characteristics theory. The MMP or MME can be determined once any of these key tie lines’ length becomes zero. See the Multiple Contact Miscibility Calculations chapter for more details. Use of the feature is illustrated in the mcm-combined-U2002richMMP.dat template data set. Liquid Viscosity-Temperature Table for Multiple Pressures
The STARS PVT generation option can now calculate and output multiple liquid viscositytemperature tables over a defined pressure range. This is compatible with a new STARS option to allow pressure dependence of liquid viscosities available in STARS 2010.10.
New Features in WinProp 2009.10 Numerical Cleaning of Mud-Contaminated Samples
A new feature has been added to WinProp in the Component Splitting and Lumping chapter. WinProp now can determine the original composition of the reservoir fluids from mudcontaminated samples. WinProp uses the skimming method, subtraction method or a combination of both methods to numerically clean the mud-contaminated samples. If the level of mud contamination is available and the mud composition is also provided, a direct subtraction method will be used to numerically clean the contaminated sample. If the level of mud contamination is not available but the mud composition is provided, a combination of the skimming method and subtraction method will be used to estimate the level of contamination first, and then numerically clean the contaminated sample. If there is no information about the level of contamination and mud composition, WinProp can use skimming method to numerically clean the contaminated sample based on the first and last SCN in the mud. Please see the Component Splitting and Lumping chapter for more details. Use of the feature is illustrated in the mudclean_split.dat template data set. User Guide WinProp
New Features 5
New Featur es in WinPro p 2008.10 STARS PVT Generation
A number of enhancements have been made to improve the liquid density parameters. The feed composition is flashed at reference pressure and temperature so that a stable liquid composition is used for all calculations. Once this is done, Compressibility, first and second thermal expansion coefficients are determined from a perturbation calculation. Finally the cross coefficient (P and T) is determined by optimization to best fit surface conditions and a user-specified range of reservoir condition densities. These changes result in a decreased sensitivity to the choice of reference conditions, more accurate compressibility parameters, and a better match between the EOS and STARS fluid model densities, which are now shown in a table in the .out file. The reference phase for components can now be specified as AQUEOUS, the previous default was that all components are OLEIC. This means that K-values for gas-water systems can be generated. In addition, the solid K-value table generation has been improved, as well as the map of WinProp EOS vs. STARS k-value flash results. Aqueous Phase Property Models
Accurate models for the Henry’s constants of CO 2, N2, H2S and CH4 have been implemented, taking into account pressure, temperature and salinity (salting-out coefficient). These models are activated by selecting the option button for “Harvey’s Method (1996)” on the “Aqueous phase” tab of the Component properties dialog. These correlations are also implemented in GEM 2008.10. The existing aqueous phase solubility models are still available in WinProp. The Kestin correlation is now used for aqueous phase viscosity when the OGW flash is specified in WinProp. Calculation of Temperature-Dependent Asphaltene Parameters
It is now possible to enter multiple asphaltene onset pressures at different temperatures in the asphaltene flash dialog. These values are used to calculate the temperature-dependent parameters of the asphaltene precipitation model.
New Featur es in WinPro p 2007.10 IMEX Volatile Oil PVT Table Generation
Black oil PVT tables can be generated for the new IMEX volatile oil option. Undersaturated gas compressibility and viscosity may be represented using only the dry gas and saturated gas endpoints, or with a complete table of values between these endpoints. The “endpoints” form uses the new PVTVO table. To allow modeling of nonlinear effects in the gas compressibility and viscosity, undersaturated gas property tables are used in conjunction with the PVTCOND table, as for the Gas-Water with Condensate model in IMEX.
6
New Features
User Guide WinProp
Other Enhancements for IMEX PVT Table Generation
For all IMEX PVT tables, the user can now choose to generate gas formation volume factors, gas expansion factors, or gas Z-factors. This applies to the saturated tables (PVT, PVTG, PVTCOND and PVTVO) as well as the undersaturated gas tables, which can now take the form BGUST, EGUST or ZGUST. For IMEX PVTCOND and PVTVO tables, calculation of the condensate/gas ratio at low pressures has been modified modified for improved improved performance in the simulator. Scaling Differential Liberation Oil FVF and GOR to Bubble Point Oil Volume
For the differential liberation experiment, oil formation volume factor and solution gas/oil ratio can be scaled to the bubble point oil volume rather than the residual oil volume. This provides oil shrinkage and cumulative gas released per volume of bubble point oil, and eliminates the need for the EOS to accurately represent the residual oil volume. The scaled values can be used in regression. Summary plots show both the original ori ginal data and the scaled scal ed values. STARS PVT Generation
For STARS PVT generation, new methods have been implemented i mplemented to generate the component liquid viscosity table. Apparent liquid viscosities of light components can be generated by perturbing perturbing the the dead dead oil oil at each each temper temperature, ature, which will give accurate liquid liquid viscosit viscosities ies of solvent components which may vaporize at higher hi gher temperatures ("match dead oil" method). Smooth curves for all component viscosities may be generated by scaling the liquid viscosities at low temperatures, then extrapolating to higher temperatures ("scale viscosities" method). More accurate determination of phase viscosity and density, and reduced sensitivity to choice of reference condition, have been achieved a chieved by using stable liquid properties in STARS component property calculations. ca lculations. Saturation Pressure/Regression Enhancement
Saturation Pressure calculation results are checked for stability. This prevents the regression algorithm from converging to an unstable two-phase saturation condition, within a three phase region.
New New Featur Features es in i n WinProp Win Prop 2006.1 2006.10 0 Enhancements of existing features and code clean up.
New New Featur Features es in i n WinProp Win Prop 2005.1 2005.10 0 A number of WinProp’s calculation options have been enhanced, including the following: Irreversible Asphaltene Calculation
The asphaltene flash has been enhanced to allow specification of an equilibrium constant for conversion of reversible to irreversible asphaltene. The irreversible asphaltene can be interpreted as flocculated solid particles. This technique has been designed to allow the simulation of laboratory forward and reverse contact experiments with series of asphaltene flash calculations. User Guide WinProp
New Features 7
Oil-Gas-Water (OGW) Flash Calculations
The OGW flash has been improved to give greater stability and better convergence characteristics for difficult problems, for example light and intermediate hydrocarbons with steam. STARS Aqueous-Liquid and Aqueous-Vapor K-Value Generation
In addition to the improvements of the OGW flash listed above, the generation of STARS Kvalues including aqueous phases has been enhanced with improved extrapolation algorithms.
New New Featur Featur es in WinPro p 2004.10 2004.10 A number of WinProp’s calculation options have been enhanced, including the following: Compositional Gradient Calculation
For the non-isothermal model, temperatures are now output to the summary table, error trapping has been improved, and the input of the temperature gradient has been modified so that positive gradient values now indicate increasing temperature with depth. Viewing Simulator PVT Models
Menu items have been added to allow easy viewing of the files generated for GEM, IMEX or STARS component models, analogous to the WinProp output file viewing procedure. Temperature-Dependent Volume Shifts
The Rackett’s Z-Factor is now re-calculated during lumping or regression calculations, so that the temperature-dependent volume shift technique will maintain consistency with pseudocomponent specific gravities. STARS PVT Model Generation
Liquid-phase component component viscosities for light components are now back-calculated from live oil and dead oil viscosities, viscosities, rather than computing them directly from the WinProp viscosity model.
New New Featur Featur es in WinPro p 2003.11 2003.11 Gamma Distribution Characterization Enhancements
The following enhancements have been implemented for the gamma distribution characterization: (1) Specification of the bounds on the molecular weights has been improved when using the “variable molecular weight interval” method for fitting the distribution parameters to extended extended analysis data. data. (2) When specific specific gravity data is available with the extended analysis, coefficients in the specific gravity-molecular weight correlation are adjusted to best fit the data. (3) Use of the gamma distribution to extrapolate extended analysis data to higher carbon numbers has been improved to provide better consistency with input physical property data.
8
New Features Features
User Guide WinProp
Separator Calculation for Gas Condensates
Calculation of dry gas and wet gas formation volume factors has been implemented when the separator calculation is used with gas condensate fluids. The dry gas FVF is defined as the volume of gas at the dew point pressure divided by the volume of gas from f rom all separator stages evaluated at standard conditions. The wet gas FVF is defined as the volume of gas at the dew point pressure divided by a hypothetical surface wellstream volume, calculated under the assumption the entire wellstream is in the gas phase with a Z-factor of one. The T he condensate/gas ratio is also reported. r eported. In addition, the average separator gas gravity from all separation stages is now being output for oil and condensate fluids.
New New Featur Features es in i n WinProp Win Prop 2003.1 2003.10 0 IMEX GASWATER_WITH_CONDENSATE GASWATER_WITH_CONDENSATE PVT Table Generation
The black oil PVT option has been expanded to allow generation of PVT tables for the IMEX GASWATER_WITH_CONDENS GASWATER_WITH_CONDENSATE ATE fluid model. This model allows description of condensate liquid dissolved dissolved in the gas phase or present as a free liquid in the reservoir and at surface conditions. This option may be used for dewpoint fluids (gas condensates) only. The tables are generated by simulating a constant volume depletion experiment. experiment. For each pressure level in the constant c onstant volume depletion, a row in the *PVTCOND table for the saturated propertie prop ertiess is written. written. Indiv Individua iduall *BGUS *BGUST T and VGUST VGUST tables tables are writt written en for for the the gas form formation ation volume factors and gas viscosities corresponding corresponding to each saturation pressure in the *PVTCOND table. Use of the feature is illustrated in the imex_condensate.dat template template data set. Regression on Secondary Stream Mole Fr action
The ability to select the mole fraction of the secondary stream, used to define the feed composition for a calculation option, has been added to the regression calculation. The feed composition can be defined as a mole fraction weighted mixture of the primary and secondary compositions. This mole fraction can be adjusted during regression to match any of WinProp’s allowable experimental data types. One application of this feature is to determine the mole fraction of a separator gas stream necessary to recombine with a separator oil stream to achieve a specified GOR. Use of this feature is illustrated in the template data set regress_stream-frac.dat . Automatic Selection of Regression Parameters
For users with limited experience in tuning equation of state parameters to match experimental data, a facility is provided to automatically select regression parameters based on the types of experimental data entered in the calculation options within the regression block. WinProp will select a combination of critical properties of the heavy end pseudocomponents, volume shift parameter parameters, s, hyd hydrocar rocarbon bon binary binary interact interaction ion paramet parameter er expo exponent nentss and and viscosi viscosity ty paramet parameters ers to be adjusted during regression, depending on the experimental data entered. The automatic parameter selector will not remove any parameters already selected by the user. Also, once the automatic parameter parameter selectio selectionn proce process ss is comp complete lete,, you you may may add or remove remove regr regress ession ion paramet parameters ers manu manually ally..
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New New Featur Featur es in WinPro p 2002.10 2002.10 Minimum Miscibility Enrichment Level
A minimum miscibility enrichment level option has been added to the multi-contact miscibility calculation. This feature allows calculation of the minimum fraction of rich gas required to be added to a lean gas stream to achieve multi-contact miscibility with an oil at a specified pressure. pressure. A minimum minimum rich rich gas gas fraction fraction and and a numb number er of gas fraction fraction steps are specifie specified. d. WinProp performs multiple-contact calculations for each step in the rich gas fraction, and interpolates to determine the minimum enrichment level for multi-contact miscibility. Results of the calculations for each solvent gas mixture tested are displayed on ternary diagrams. This feature is an addition to the existing multi-contact calculation for determination of the minimum miscibility pressure for a given oil and solvent. K-Value Plotting
The phase property plotting feature has been enhanced to allow generation of K-value plots for the 2-phase flash, multiphase flash, and the STARS K-value calculation options. GasLiquid, Liquid-Liquid and Aqueous-Liquid K-value plots may be generated. The results are shown as the log of the K-value for each component, plotted against pressure, temperature temperature or composition, depending on which independent independent variable has been specified for the flash. STARS Fluid Model Generation Enhancements
The options for treatment of surface streams for STARS production reporting can now be specified in WinProp. This includes specifying the surface pressure and temperature, the flash options *SEGREGATED or *KVALUE and also the new option for specifying K-values which are used only for the surface flash. The ability to specify these K-values separately from the K-value tables allows the pressure and temperature range for the tables to be concentrated on the expected reservoir conditions, but still calculate accurate surface phase splits. Both Gas-Liquid and Liquid-Liquid Liquid-Liquid K-values at the surface can be specified. The extrapolation algorithm for determining component K-values K-values outside of the range of convergence of the flash calculations has also been improved.
New New Featur Featur es in WinPro p 2001.10 2001.10 Thermal Compositional Gradient Model
Beginning with the 97.00 release, WinProp has had the capability to perform isothermal gravity/chemical equilibrium equilibrium calculations for the determination of compositional grading due to gravity. The 2001.10 release includes the option to incorporate thermal effects on the gradient calculation. The model equations are developed based on the zero mass flux condition. Calculations may be performed without thermal diffusion (passive thermal gradient case) or with thermal diffusion coefficients determined from correlations or entered as constant values for each component.
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New New Featur Features es in i n WinProp Win Prop 2000.1 2000.15 5 STARS PVT Data Generation Enhancements
A number of features for f or creating STARS component property and K-value data have been added to WinProp. For component properties the following features have been implemented: optional use of WinProp’s viscosity model for component viscosities as opposed to the corresponding states model, optional output of viscosity versus temperature table instead of correlation coefficients, and the generation of viscosity and density nonlinear mixing functions. For K-value data, the features added include: generation of liquid-liquid and gasliquid K-value tables simultaneously, generation of composition dependent K-value tables, use of STARS defaults for water K-values, indication of which K-values have been extrapolated in the tables, and output of a map comparing the WinProp calculated phase split to that determined from the K-value tables. Please see the STARS PVT Data Generation chapter for more details. WinProp-ModelBuilder Integration
Several features have been introduced to enhance the data flow between WinProp and ModelBuilder. The concept of PVT “Meta-Data” has been introduced; this refers to the equation of state model and mixture composition used to generate the PVT data for IMEX or STARS (for GEM, the equation of state model used is the same as in WinProp, so Meta-Data is not required). In this release of WinProp, the PVT Meta-Data will be written out to the file with the IMEX fluid model. When this file is imported into ModelBuilder, ModelBuilder, the Meta-Data will be read in and stored stored in the simulator simulator data set. If it is desired desired at a later date to analyze or modify the PVT data in some way, WinProp can be launched from within ModelBuilder and the Meta-Data EOS description will be restored to WinProp. The GEM EOS model can also be sent to WinProp by launching from within ModelBuilder. In this case, compositions determined from the initial conditions section will be transferred to WinProp as well. Additional PVT Tables
An alternate format for black oil PVT tables has been added to the existing options for creating various IMEX or extended black oil PVT tables. The alternate format includes writing of the PVT table in order from highest to lowest pressure, and writing out a table of multiplying factors for the undersaturated oil compressibilities compressibilities and viscosities. Enhancements Enhancements to the extrapolation methods for generating PVT properties above the original saturation pressure of the oil oil have also been implemented. Laboratory Experiment Enhancements
The maximum number of separators which may be specified with the constant volume depletion experiment and also for the black oil PVT data generation option has been increased to 8. Liquid dropout for the constant composition and constant volume depletion experiments can now be specified as a percentage of the cell volume at the saturation pressure, or as a percentage of the cell cell volume at the current pressure step. User Guide WinProp
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Interface Enhancements
The differential liberation and constant volume depletion experiment data entry forms have been redesigned to allow entry of pressure step data in row format, for improved compatibility with experimental PVT reports. Data for material balance and consistency check calculations is now entered on a separate table which is linked to the main table with the pressure information. Pasting of data to any grid which allows a variable number of rows has been modified to automatically increase the number of rows in the table if required to hold all of the data being input.
New Featur es in WinPro p 2000.10 Automatic Generation of Quality Lines on Phase Diagrams
A feature has been added to the 2-phase envelope calculation option to allow the user to select lines of constant mole or volume fraction to be calculated and displayed on the plot of the phase envelope. In addition the algorithm has been improved so that the initial guess for the starting point is generated internally. The user no longer needs to initialize phase envelope calculations with a flash or saturation pressure calculation or provide a good guess for the starting point directly. It should now be possible to generate a 2 phase pressure temperature envelope with default selections reliably. Additional PVT Tables
For CMGL’s IMEX simulator, WinProp can now generate Gas-Water PVT tables. “Extended” Black Oil type PVT tables can be generated including the R v data describing oil solubility in the vapor phase. These data are generated by simulating a constant volume depletion or a differential liberation laboratory experiment. Oil properties are obtained by material balance calculations or directly through EOS separator calculations. A number of methods are available for extrapolating individual curves beyond the original saturation pressure. These tables are output in a generic format. The user can then customize this data for use with specific extended black oil reservoir simulation programs. Additional Experimental Data
The constant composition expansion experiment option has been enhanced to allow regression on the following experimental data: viscosity, density, compressibility factor and single phase oil compressibility. These data are included in the regression only when the corresponding property can be calculated by the program. For example single phase oil compressibility data will not be used in regression for a dew point fluid. Asphaltene Precipitation Modelling Case Study
A new case study is included in the User Guide and on-line help which describes the development of a model for prediction of asphaltene precipitation from a black oil under pressure depletion. The case study illustrates characterization of the oil, regression to match fluid phase behavior data, specification of the asphaltene model parameters, and calibration of the model with experimental precipitation data. 12
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All of the case studies are now included in Appendix A. Interface Enhancements
A feature has been added to allow calculation options to be temporarily excluded from the data set, rather than deleting them entirely. Options are excluded/included from the main control form by right-clicking on the desired row and making a selection from the pop-up menu. One application of this feature is to temporarily reduce the number of calculation options within a regression block to try and obtain a match to some key data. After an initial regression run, the component properties can be updated and calculation options that were excluded can be included again for further regression runs. Data entry and navigation on the grids has been improved by enabling use of the left and right arrow keys, in addition to the up, down and enter keys.
New Features in WinProp 1999.10 Enhancements to Aqueous Phase Solubility Calculations
WinProp supports calculation of solubility of light gas and hydrocarbon components in the aqueous phase using Henry’s law. This feature is enabled by selecting flash type OGW (OilGas-Water) on the OGW/EOS Multiphase Flash form. Henry’s law constants can be entered by the user or calculated internally using correlations fit to experimental solubility data. Two new features have been added for modeling aqueous phase solubility. First, modification of the internally calculated Henry’s constants to account for salinity of the aqueous phase has been implemented. By default, the internal Henry’s constants are for pure water. To predict solubility of components in brine, all that is required is brine salinity, in terms of equivalent NaCl concentration. This is entered on tab Aqueous phase of the Components Selection/Properties form. The second feature implemented is regression on the aqueous solubility parameters to match experimental solubility data. Component reference Henry’s constants, i.e. Henry’s constant at a specified reference pressure, and molar volume at infinite dilution can be adjusted to match experimental data. Please see the Components chapter for further description of Henry’s constants. Case Study Number 2: Solubility of CO2 in Brine illustrates the use of both of these new features. Pedersen Viscosity Correlation
WinProp now allows use of the Pedersen corresponding states viscosity correlation in addition to the Jossi-Stiel-Thodos (JST) correlation. The Pedersen correlation is expected to give better liquid viscosity predictions for light and medium gravity oils than the JST model. The Pedersen correlation is not dependent on having accurate density predictions as the JST technique is. Parameters in either correlation may be adjusted during regression to match experimental viscosity data. Please see the Components chapter for more information on viscosity models.
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Generation of PVT Properties for CMG’s IMEX Simulator
WinProp can now generate the PVT data corresponding to the light oil and the pseudomiscible models of CMG’s IMEX simulator. Earlier releases targeted the black oil model only. In addition, the aqueous phase properties can now be estimated from built in correlations as an alternative to entering the values directly. The PVT fluid model data with the associated IMEX keywords is written to an output file with the extension (.imx). This file can be referenced as an include file in an IMEX data file. Please refer to the Black-Oil PVT Data Generation chapter of this manual for a complete discussion. Consistency Checks and Material Balance Calculations
A number of tools are available in WinProp for evaluating the quality of PVT data provided to the reservoir engineer from laboratory or field measurements. The data is typically used to tune the EOS model. It is imperative therefore that the PVT data is analyzed critically prior to any detailed regression calculations. The tools available include Hoffman plots and material balance calculations. Material balance calculations for the constant volume depletion (CVD), differential liberation (DL) and separator options are performed if the required data is entered. For these experiments, the required data are generally reported in a typical PVT report from a laboratory. A Hoffman plot is generated for the recombination option based on the entered oil and gas compositions. Hoffman plots are also created with the CVD, DL and separator options if sufficient data is entered to calculate the oil phase compositions from a component material balance. Refer to the Laboratory Calculations chapter for more detail as well as template cases matbal-bo.dat and matbal-gc.dat . Changes to the Multiple Contact Miscibility (MCM) Option
A number of enhancements have been made to the MCM option with the objectives of 1) alleviating difficulties in interpreting the program results and 2) determining and reporting multiple and first contact miscibility pressures directly. With respect to point one, the criteria used for stopping the forward and backward contact flash calculations are reported in the output file. The most likely reasons are either miscibility is achieved or there is no change in the oil and gas compositions from the previous contact. With respect to point two, the user can now enter a range of pressures for the calculation. If multiple and/or first contact miscible pressure(s) are found in this pressure interval then these values are reported at the end of the output listing. Ternary diagrams are also automatically created at designated intervals. Specification of Mole Fraction Steps for Flash Calculations
The ability to specify steps in the primary mole fraction making up the feed to a flash calculation has been implemented for two-phase, multiphase and asphaltene/wax flash calculations. This allows the specification of flashes for a number of mixtures of the primary and secondary compositions on a single flash form. This feature is similar to the existing capability for specifying pressure and temperature steps. These steps can be defined with the feed specification on the first tab of each flash calculation.
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Plotting Capability Added to Two-Phase and Multiphase Flash
When a series of flash calculations have been specified by setting temperature, pressure or mole fraction steps, plots of the phase properties can be generated. Up to three phase properties, such as molecular weight, compressibility factor or phase mole fraction, can be selected for each flash calculation. One plot is generated for each property and each phase. When plotting is activated, steps can be specified in one or two of the variables: pressure, temperature and mole fraction. If steps are specified for only one variable, the plots are generated with that variable as the independent variable, and the phase property as the dependent variable. Up to 100 steps in the independent variable are allowed. When steps are specified for two variables, one variable is treated as a parameter variable, and curves of the phase property are displayed for each value of the parameter variable. Up to 8 steps in the parameter variable are allowed. The phase properties to be plotted are selected on tab Plot Control of the flash calculation forms. Plotting Capability Added to Asphaltene/Wax Flash
The asphaltene/wax flash has a plotting feature similar to the one described above for the two-phase and multiphase flashes. This allows generation of plots such as weight % precipitate as a function of solvent concentration or pressure. A special plotting feature implemented for the asphaltene/wax flash is the generation of a pseudo-ternary diagram to display the results of flash calculations in terms of the predicted phase split, i.e. liquid-vapor, solid-liquid etc. The results are shown for a number of dilution lines defined by the user. Plot specification is done on tab Plot Control of the asphaltene/wax flash calculation. Three-Phase Envelope Automatic Plot Generation
Automatic plot generation has been implemented for the three-phase boundary calculation. Excel plots can now be created for three-phase P-T, P-X and T-X diagrams. These plots can be created by selecting File | Create Excel plots after running a data set with a three-phase envelope calculation option. Ternary Diagram Two-Phase Envelope Generation
The capability to create ternary or pseudo-ternary two-phase boundaries has been added to the two-phase envelope calculation option. This calculation locates points in composition space defining the two-phase vapor-liquid phase boundary on a triangular diagram. This can be considered a static or single-contact calculation, as opposed to the multiple contact calculation option which performs a dynamic simulation of multiple contact miscibility processes. This feature is enabled by selecting Pseudo-Ternary Phase Envelope on the Two-phase envelope calculation option form. Table Import Wizard
A Table Import Wizard has been implemented in WinProp to assist the user in importing data into WinProp from existing Excel or ASCII format files. The wizard guides the user through the steps of selecting data to be imported, defining units and performing unit conversions, and User Guide WinProp
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inserting the imported data into the correct locations in WinProp’s data structure. Table import is available for the following forms: Component Selection/Properties, Plus Fraction Splitting, Constant Composition Expansion, Differential Liberation, Constant Volume Depletion and Swelling Test. An example illustrating the use of the Table Import Wizard is given in the “Tutorial” section of the manual. Information regarding the specific implementation for the forms listed above may be found in the “Components”, “Component Splitting and Lumping”, and “Laboratory Calculations” sections. Interface Enhancements
Two toolbars are provided for easier access to items previously available through the menus alone. The main toolbar contains buttons corresponding to items in the File and Edit menus. This toolbar targets frequently performed tasks such as opening and saving files, generating the results, viewing the output file and creating plots. This toolbar is not customizable and is permanently displayed. A second toolbar contains buttons corresponding to often used calculation options. These buttons are grouped to mirror the organization of the menus. This toolbar is customizable. The user can remove any of the buttons selected by default and add buttons corresponding to options not originally chosen. Once the toolbar is customized the settings are saved for subsequent sessions. The options toolbar can also be removed from the interface and reinstituted at a later time. The menu system is revised with the objective of creating more intuitive classes. Similarly, the names of the forms corresponding to the calculation options are modified to be more descriptive. Forms for the constant volume depletion, separator test and differential liberation are redesigned in light of the additional data that can now be entered for material balance calculations. Other enhancements include the addition of progress bars in specific situations. A progress bar is shown when loading or saving the component form for example.
New Features in WinProp 98.00 Additional Methods for Heavy Fraction Characterization
The three-parameter gamma distribution is now available in WinProp to describe the molecular weight versus mole fraction relationship for the heavy fraction of a petroleum fluid. The Gaussian quadrature method is used in evaluating the integral of this distribution function. The molecular weight of the pseudo components selected corresponds to the quadrature points. Good VLE results are obtained with this method with a small number of pseudo components. In addition the Gamma distribution and Gaussian quadrature can be used to generate a single set of pseudo components for multiple related samples with different plus fraction molecular weight and specific gravity. Related mixtures have the same compounds but in varying proportions, for example saturated oil and its equilibrium gas or fluids from different depths in a reservoir with a compositional gradient. Parameters of the Gaussian distribution function are obtained by nonlinear regression if extended analysis data is entered or from generalized correlations if only plus fraction specific gravity and molecular weight are available. Where multiple samples are involved each sample can have extended analysis data entered if available. Please refer to the Component Splitting and Lumping chapter of this manual for a more extensive discussion.
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Generation of PVT Properties for IMEX Black Oil Model WinProp can now generate the PVT data corresponding to the “black oil” model of CMG’s IMEX simulator. This data is written out to an output file with the extension blk. This file can
then be referenced as an include file in an IMEX data file. The properties of the oil phase (formation volume factor, gas oil ratio) are generated by flashing the equilibrium liquid at each stage of the “differential liberation” directly through the user specified separator train. The range of the PVT table can be extended to include pressures above the original oil bubble point pressure by generating the swelling curve. This way the table can handle variable bubble point scenarios arising for example from gas injection or solution gas migration followed by re pressurization. This option can be found under Options | "Black oil model PVT data." Please refer to the Black-Oil PVT Data Generation chapter of this manual for a complete discussion. Process Flow and Isenthalpic Flash Options
Data entry forms for the Process flow and Isenthalpic flash options have been added to WinProp. The process flow option can be added to the data file by selecting Calculations | Process flow from the menu and isenthalpic flash by selecting Calculations | Isenthalpic flash. For the process flow sample template are process1.dat, process2.dat and process3.dat. For isenthalpic flash the sample templates are isenth1.dat, isenth2.dat and isenth3.dat. Please refer to the chapter titled “Process flow” for detailed discussion of the process flow option and the Flash Calculations chapter for more details on the isenthalpic flash option. Support for Multiple Hydrocarbon-Hydrocarbon Binary Interaction Exponents
Hydrocarbon components are identified by a value of 1 on the HC column of the component table on the Component form. Binary interaction coefficients between two hydrocarbon components are calculated from a correlation, which involves the critical volume of each component and an exponent parameter. In contrast to previous versions of WinProp where all HC-HC binaries were calculated based on a single exponent parameter, the user can now group pairs of binary and specify a different exponent parameter value for each group. These individual group exponents can be also selected as regression parameter(s). Please see the Components and Regression chapters for more details. Handling of the “Regression Block” in a Data File
In WinProp the regression block refers to the calculation options that are between the “Regression” and “Start regression” forms. For a case to run successfully all options in this block must have at least one piece of experimental data entered and all options outside the regression block are required not to have any experimental data entered. WinProp will now attempt to ensure that these requirements are met when the user attempts to run a given case while preserving the data that has been entered. For example if there an option within the regression block then this option will be moved out of the regression block. If there is an option with experimental data outside the regression block then the experimental data will be written out to the data file with the accompanying keyword(s) commented out. This will also allow the user to retain the experimental data that were entered for regression when regression is removed from the data file, that is “Regression” and “End regression”
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forms are removed. The entered experimental data will be shown where appropriate with the program predictions on plots even if there is no regression involved in the run. Interface Enhancements
The list of the five most recently files accessed by WinProp is now available on the File menu. This is a faster way of selecting a case than through the file open dialog box. Interface enhancements include the ability to redirect the screen diary to an output file. To redirect select “Redirect to file DBPROP.XXX” under File | Screen menu. The user can now select an editor other than Notepad by invoking the Editor | “User editor select” option under the File menu. This will open a file dialog box. Using the file dialog select the executable file corresponding to the desired editor. WinProp allows up to open up to 8 different cases (data files) to be open simultaneously, primarily to allow various calculation option forms to be copied between different data files. This saves the user from having to type in data values multiple times. The MDI capability also facilitates comparing the data entered for a given form across data files. A number of checks have been implemented to avoid violating the internal design limitations of this option. For example forms can be opened only when a single case is loaded and a case cannot be closed until all the open forms are closed. In previous versions of WinProp the data in a table (grid) could be changed via a text box positioned outside the table. With WinProp 98.00 a floating text box positioned exactly on the desired cell is used for table (grid) edits. To erase the current value or text in a cell and enter a new value or text, position the cursor on that cell and start typing. To edit the contents of a cell, position the cursor on that cell and double click with the left mouse button. The cell contents are updated when the carriage return (Enter) key is pressed or if the cursor is moved to another cell. Please note that changing the focus to a new control will not update the grid (table) contents.
New Features in WinProp 97.00 Compositional Grading Calculations
Significant compositional variation with depth can occur in deep reservoirs with near critical fluids or for fluids where there is a large variation in molecular weight between the light and heavy constituents. This effect is important in estimating materials in place as well as field development and operation strategy. WinProp now has the capability of simulating this phenomena based on the isothermal gravity/chemical equilibrium (GCE) formulation. This option can be found under Calculation Options | Compositional Gradient . A complete discussion can be found in the Compositional Grading chapter. Generation of PVT Properties for STARS STARS is CMG's steam and additive thermal simulator. WinProp can generate the complete PVT data required by STARS. This includes component partial densities, compressibility and thermal expansion factors as well as liquid component viscosity coefficients. WinProp can also generate tabular K-value data between any two phases that STARS supports. STARS used K-
values to determine the number of phases in equilibrium and the composition of each phase. The PVT data is printed in a format suitable for direct inclusion in a STARS data file. The output of 18
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this option is directed to a file with a suffix .tbl. This option can be found under Options | Print STARS PVT Table. Please refer to the STARS PVT Data Generation chapter of this manual for a more extensive discussion. Regression Enhancements
It is now possible to specify more than one component for a given property such as the critical pressure as a single variable in regression. The members of the group will in general have individual initial values and bounds. In regression the same increment is applied to all members of the group. This feature can be useful if it is desired to maintain a certain trend or symmetry for a given property or in avoiding regressing on a property belonging to a component with a small mole fraction. For information on how to define group variables refer to the Regression chapter of this manual. Summary plots showing before regression, after regression and experimental data are now generated automatically when Excel plots are created from a regression run. Individual plots showing calculated results are still available, with new titles indicating before or after regression calculations. Conversion from CMGPROP to WinProp Format
A conversion utility is provided within WinProp to translate files created for CMGPROP on UNIX or PC platforms. This utility can be invoked by selecting Options | Convert from Cmgprop to WinProp. The user is advised to open each form and verify the results of the conversion carefully. Please use the Save As option under the File menu to save the WinProp compatible data file to avoid overwriting the original CMGPROP data file. The original file will be an important aid in case difficulties are encountered in conversion and in verifying the conversion. There are a number of situations that can pose difficulties for the converter including the use of wildcards in specifying array values and presence of comment marker on a line where array values are stipulated. Please edit the CMGPROP data file eliminating these situations prior to using the conversion utility. MDI Capability
The Multiple Document Interface (MDI) Feature is now implemented in WinProp. This allows the user to open up to eight files at once. This has significant advantages for example when the user desires to compare output files for two or more cases or in the ease with which data corresponding to various calculation options may be copied between different data files. Refer to the Copying Between Data Sets section in the Basic Operations chapter of this manual. Update Component Properties Feature
Upon completing a splitting, lumping or regression calculation where the number of components are changed or the component properties modified, WinProp writes out the revised component information in an output file with the suffix .rls. With the previous version of WinProp the user would run a file, for example test1.dat with a splitting calculation, use File | Open to open test1.rls, use File | Save As to rename to test2.dat for example and then continue working with this file by appending calculation options to it. This procedure is now automated with the introduction of the update component properties selection under the Options menu. The user still runs the splitting calculation with test1.dat. Once the calculation is User Guide WinProp
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carried out, update component properties is invoked. This updates the information on the Composition and Component forms. The user then removes the splitting calculation from the data file and appends the desired calculation options. Optionally the user may wish to save this file with a different file name say test2.dat to retain a complete work record of the session. Addition of Bounds Tab on the Regression Form
An additional tab showing the initial value and the lower and upper bound selected by WinProp for each regression variable specified has been added to the Regression form. The user may subsequently edit the bounds. The capability to restore values back to their default selections is provided as well. This provides the user greater flexibility in arriving at an EOS description based on the specific characteristics of the fluid being considered and the PVT data available. Volume Shift Specification
Additional flexibility is introduced in selecting values for the volume shift parameter for each component. Previously the default was a value of zero for all components. The new default is a value generated from the correlation for library components and a value of zero for user defined components. The user may apply the correlation values to all components by selecting Reset to Correlation Values from the Volume Shift menu on the component form. Alternatively the user may revert to the older default by selecting Reset to Zeros. The user can still specify a value for any component which is different from either correlation or zero by editing the cell directly. Support of Two Sets of EOS Parameters WinProp now supports the concept of two different EOS models. When two sets are enabled the
first set is used for calculations at reservoir conditions and the second set for surface or separator conditions. With this provision it is possible to match PVT experimental data at surface conditions (typically separator API and GOR data) independently from data at reservoir conditions. This makes it possible to obtain much more accurate predictions over the wide range of conditions encountered as the fluid is produced and processed on the surface with a realistic number of components for compositional simulation. Please refer to the Components and Regression chapters for details. Extended Separator Option
The conventional separator operation involves the liquid phase output from a given separator becoming the feed for the next separator in sequence downstream and the vapor phase joining the gas product stream. This arrangement is not always optimal particularly for rich gas condensates. For modeling alternative separation strategies the separator option is enhanced to allow additional product streams such as LPG and in providing flexibility in the selection of the destination of the liquid and vapor stream from each separator. Please review the Laboratory Calculations chapter for more information about this feature. Multicomponent Solid Precipitation Model
The solid precipitation model is now suitable for modeling both wax and asphaltene precipitation scenarios. The thermodynamic model has been enhanced as follows: the precipitate is now modeled as a multicomponent solid in contrast to the earlier single component pure solid phase assumption, non-isothermal conditions are treated, and up to three fluid phases in equilibrium with the solid are allowed. 20
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Introduction
WinProp Overview WinProp is CMG's equation of state multiphase equilibrium property package featuring fluid characterization, lumping of components, matching of laboratory data through regression, simulation of multiple contact processes, phase diagram construction, solids precipitation, and more. Laboratory experiments considered in WinProp include recombination of separator oil and gas, compressibility measurements, constant composition expansion, differential liberation, separator test, constant volume depletion and swelling test. You can use WinProp to analyze the phase behavior of reservoir gas and oil systems, and to generate component properties for CMG's compositional simulator GEM, black oil simulator IMEX and steam and additives thermal simulator STARS . WinProp features a graphical user interface that allows you to prepare data, view plots of the input, run the phase property calculation engine, then view the text and graphical results within the program window.
Use of this Manual This User Guide describes the different forms and options for entering data into WinProp. It is also available as on-line help. This User Guide is aimed at reservoir engineers with some background knowledge on the phase behavior and characterization of reservoir fluids. Good references on these topics can be found in Ahmed [1], Pedersen, Fredenslund, and Thomassen [30] and McCain [17] (see the References chapter). For more details on phase equilibrium thermodynamics, please see Sandler [35] or Walas [37]. Every attempt has been made in the preparation of this User Guide to provide you with all of the information necessary to run the program and understand the calculations being performed. If questions arise, please contact: Computer Modelling Group Ltd.
200, 1824 Crowchild Trail N.W. Calgary, Canada T2M 3Y7 Telephone: (403) 531-1300 Fax: (403) 289-8502 Email: [email protected] Website: www.cmgl.ca
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Introducti on 21
Installation All CMG software must be installed from the CD-ROM by running the Setup program. Please refer to the detailed installation instructions that are packaged with the software for additional information.
Confidentiality All components of CMG's technology including software and related documentation are protected by copyright, trademark and secrecy. CMG technology can be used only as permitted by your license from CMG. By the license, you have agreed to keep all CMG technology confidential and not disclose it to any third party. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, mechanical, or otherwise, including photocopying, recording, or by any information storage/retrieval system, to any party other than the licensee, without the written permission of Computer Modelling Group Ltd.
Template Data Files A number of example data files are located in the "TPL" directory located under the WinProp directory. A brief description of each of the available template data files is shown below: Data file name
Description
AqueousCO2-08-Harvey.dat case_study-1.dat case_study-2.dat case_study-3-asph.dat case_study-3-regress.dat case_study-3-split.dat cce.dat compgrad-blackoil.dat compgrad-voloil.dat compress.dat cricon.dat critical.dat cvd.dat diflib.dat envel_2ph-pt.dat envel_2ph-px.dat envel_2ph-tern.dat envel_3ph-pt.dat envel_3ph-px.dat extended_blackoil.dat
Aqueous phase properties calculation using Harvey’s method Data for case study number 1 (See Appendix A) Data for case study number 2 (See Appendix A) Data for case study number 3 (See Appendix A) Data for case study number 3 (See Appendix A) Data for case study number 3 (See Appendix A) Constant composition expansion calculation Compositional gradient calculation - black oil Compositional gradient calculation - volatile oil Single-phase liquid compressibility calculation Cricondenbar and cricondentherm calculation Critical point calculation Constant volume depletion simulation Differential liberation experiment simulation Two-phase pressure-temperature envelope construction Two-phase pressure-composition envelope construction Two-phase pseudo-ternary diagram construction Three-phase pressure-temperature envelope construction Three-phase pressure-composition envelope construction Extended black oil PVT tables with oil vaporization
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Data file name
Description
flash-2ph.dat flash-3ph.dat flash-isenth1.dat flash-isenth2.dat flash-isenth3.dat flash-ogw.dat format2_blackoil.dat imex_condensate.dat imex_voloil.dat imex-blackoil.dat labpvt-bo1.dat labpvt-bo2.dat labpvt-bo3.dat labpvt-gc1.dat labpvt-gc2.dat labpvt-gc3.dat lumping.dat matbal-bo.dat matbal-gc.dat mcm-condensing.dat mcm-vaporizing-co2.dat mcm-combined-H95-8lean.dat mcm-combined-U2002rich.dat mcm-Z12-5-MME.dat process-cvd.dat process-mcm.dat process-plant.dat recombine.dat regress-blackoil1.dat regress-blackoil2.dat regress-compress.dat regress-condensate1.dat regress-condensate2.dat regress-critical.dat regress-flash_2ph.dat regress-flash_3ph.dat regress-flash_ogw.dat regress-lightoil.dat regress-multicontact.dat regress-sat_pres.dat
Two-phase EOS flash calculation Three-phase EOS flash calculation Isenthalpic flash - 2 component system Isenthalpic flash - 6 component system Isenthalpic flash - single component system Three-phase oil-gas-water Henry's law flash calculation Alternate format black oil PVT tables IMEX gas-water with condensate PVT model data generation IMEX volatile oil PVT model data generation IMEX PVT model data generation Lab PVT experiment simulations – black oil no. 1 Lab PVT experiment simulations – black oil no. 2 Lab PVT experiment simulations – black oil no. 3 Lab PVT experiment simulations – gas condensate no. 1 Lab PVT experiment simulations – gas condensate no. 2 Lab PVT experiment simulations – gas condensate no. 3 Lumping "plus fraction" components Material balance checks for black oil PVT experiments Material balance checks for condensate PVT experiments Condensing gas drive multicontact miscibility calculation Vaporizing CO2 drive multicontact miscibility calculation Condensing and vaporizing combined drive MMP calculation Condensing and vaporizing combined drive MMP calculation Condensing and vaporizing combined drive MME calculation Process flow – simulation of constant volume depletion test Process flow – simulation of multiple contact experiment Process flow – simulation of a gas plant Recombination of separator oil and gas streams Black oil no. 1 regression Black oil no. 2 regression Liquid compressibility regression Gas condensate no. 1 regression Gas condensate no. 2 regression Critical point regression Two-phase flash regression Three-phase EOS flash regression Three-phase Henry's law flash regression Light oil regression Multiple contact data regression Saturation pressure regression
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Introducti on 23
Data file name
Description
regress-separator.dat regress-singlephase.dat regress-stream_frac.dat regress-viscosity.dat sat-pressure.dat sat-temperature.dat separator.dat singlephase.dat solid-asph_plots.dat solid-asph1.dat solid-asph2.dat solid-asph_temperature.dat solid-phenanthrene.dat solid-wax.dat split-mw_analysis.dat split-mwsg_analysis.dat split-mwsg_plus.dat split-mwsgtb_analysis.dat stars-comp_props.dat stars-vl_kvalues.dat stars-vlaq_kvalues.dat stars-vls_kvalues.dat stdrm017props.dat stflu008props.dat sttst26props.dat swelling.dat
Separator data matching with 2nd EOS set parameters Single phase properties regression Adjust gas and oil mixing ratio to match separator GOR Regression for viscosity matching Saturation pressure calculation Saturation temperature calculation Separator calculation Single-phase fluid properties calculation Plot construction for single component asphaltene model Single component solid asphaltene precipitation Heavy oil with 2 component solid precipitation Temperature-dependent asphaltene modeling Pure component solid (phenanthrene) precipitation Multicomponent wax precipitation Characterization - MW versus mole fraction data Characterization - MW, SG versus mole fraction data Characterization – plus fraction MW and SG only Characterization - MW, SG ,TB versus mole fraction data Component PVT properties generation for STARS Vapor -Liquid K-values generation for STARS Vapor -Liquid-aqueous K-values generation for STARS Vapor -Liquid-solid K-values generation for STARS Create fluid model for STARS stdrm017 template Create fluid model for STARS stflu008 template Create fluid model for STARS sttst026 template Swelling experiment simulation
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Basic Operations
Overview This chapter provides basic information for creating, editing, saving and running data sets in WinProp, as well as for viewing and printing output files. Examples of case studies with step-by-step instructions for performing PVT modeling tasks are included in Appendix A. Detailed instructions for using all of the calculation options available in WinProp are given in the remaining chapters.
Elements of the WinProp Program Window The following screen shows the main areas of the WinProp program window: Menu Bar
Toolbar
Tree View
Data Entryand Results Area
The tree view on the left side of the program window shows the structure of the data set. Selecting any node in the tree view by clicking it with the mouse or using the arrow keys displays the information associated with that node in the Data Entry and Results area to the right. The top level of the tree gives the data set name in all capitals, “Data Set Name” in the above example. The name of the file containing the data set is the data set name followed by .dat, for example, “Data Set Name.dat”. Underneath the top level are three nodes: User Guide WinProp
Basic Operations 25
• •
Simulation Data Set: Displays the keyword input file for the simulation run. Simulation Results: Displays the results of the simulation.
By default, Simulation Steps contains three nodes, in order:
•
Titles/EOS/Units: To document the run, select the unit system and choose the
equation of state (EOS) to be used for all calculations included in the data set.
• •
Component Selection/Properties: To select and edit components. Composition: To specify the composition of the system. Note that new
composition definition steps can be added at any point in the data set.
Inserting Simulation Steps Simulation steps can be inserted after a selected step in one of three ways. To illustrate, if we want to add Plus Fraction Splitting after Composition, we could do this in the following ways:
• Right-click Composition in the tree view, select Add After, select the step category (Characterization in our example), then the step type ( Plus Fraction Splitting in our example):
• Click Composition in the tree view then click the SPLT
icon in the toolbar.
Note: You can mouse over the icons in the toolbar to display their text description.
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• Click Components in the tree view then, in the menu bar, click the step category (Characterization in our example), then the step type ( Plus Fraction Splitting in our example):
Throughout this manual, operations may be stated in general terms; however, recognize that there are three ways to carry them out.
Step Validation Status As steps are added and configured, the step validation status is displayed in the tree view, as follows: Step is not validated because, for example, a parameter has not yet been defined. Step is validated and ready for simulation run. Note: If a step is not validated, you can mouse over the icon in the tree node to display a text
description of the reason.
Including/Excluding Steps If a simulation step is to be included in the simulation run, the name of the step will be displayed in normal font, as shown in the case of Plus Fraction Splitting below:
If a simulation step is to be excluded in the simulation run, the name of the step will be displayed in a light grey font, as shown below:
You may need to click somewhere off the step to view this status. To exclude a currently included step, right-click the step then select Exclude. To include a currently included step, right-click the step then select Include. User Guide WinProp
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Comments In some screens you have the option to record a comment about a form or parameter, such as “Based on sample from Lab xyz”. These comments are for your information and are not used in the simulation calculations.
Acces sing On-Line Hel p Selecting Help on the menu provides you with the following options: Contents
Displays Help table of contents
Search for Help on... Help on current form About CMG WinProp
Search for help on a particular topic Displays Help about the current form Displays WinProp version and copyright information
Help on the current form can also be displayed by pressing the F1 key or the Help
icon.
Creatin g, Opening and Saving Data Files You can create a new data file by selecting File | New from the menu. WinProp inserts three blank forms in the data set: Titles/EOS/Units, Component Selection/Properties, and Composition.
An existing data file can be opened in the following ways:
•
In Launcher, drag the desired data file from the file table on to the WinProp application icon. WinProp will open with the data file loaded.
• Select File | Open. A file browser will appear to assist you in the file selection. You save a data file by selecting File | Save. A data file can be saved under a different file name by selecting File | Save As. By convention all data set names have the (.DAT) suffix. The following files are created when running WinProp: File suffix
Description
.out
ASCII file containing calculation results.
.gem
Output of component properties in a format suitable for the compositional simulator GEM. This file is created if you select the GEM option in the CMG GEM EOS Model form.
.gmz
Output of composition versus depth data in format suitable for inclusion within the GEM simulator data file. This file is generated if the “Write GEM *ZDEPTH …” check box on the Compositional Gradient form is selected.
.str
Output of PVT data formatted for inclusion in a STARS simulator data file. This file is created if you select the CMG STARS PVT Data option.
.imx
Output of “black oil” PVT tables formatted for inclusion in an IMEX
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File suffix
Description
simulator data file or extended black oil tables in a “generic” format. This file is created if the calculation option to generate PVT data for simulation studies with IMEX is selected. .rls
Output of component properties from the regression or lumping and splitting procedure. This file can be opened to create a new data set (see the Component Splitting and Lumping and Regression chapters for more information).
.srf
Output for plotting.
To exit WinProp, select File | Exit.
Running and Viewin g Output To run the selected data set, select File | Run from the menu (or click Run Simulation in the toolbar or press the F2 key). The results of the calculations can be viewed and printed through Simulation Results in the tree view.
Copyin g Betw een Data Sets Note: In the following procedure, copying is carried out by right-clicking the item to be copied then selecting Copy. Pasting is carried out by right-clicking the destination then selecting Paste (or Paste After).
With the MDI implementation of WinProp, users can open as many as eight data or associated files (such as output files) for side-by-side comparison or to transfer data between files. To copy data between data sets: 1. Open the source and target files. 2. Right-click the desired component on the tree view of the source file then select Copy. 3. Right-click the destination on the tree view then select Paste (or Paste After).
Setti ng Up a Regressio n Run Certain calculation options, including the simulation of laboratory PVT experiments, allow the user to enter experimental data which can be used to tune the EOS model. To do this, you enter a Regression Parameters step in the tree view. This step will contain the calculation options for the data that is entered. Note: All options that appear within the Regression Parameters node must have at least one
experimental data point.
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Basic Operations 29
The Regression Parameters form is used to select EOS component properties for tuning. For calculation steps inserted before the Regression Parameters node, WinProp uses the original component properties. For steps inserted after the Regression Parameters node, component properties modified during the regression are used. Note: WinProp allows one Regression Parameters node per data set. To perform a second regression calculation, select File | Update component properties from the menu bar.
To insert a step in the Regression Parameters node, right-click Regression Parameters then navigate through the menus to the desired step, as shown in the following example:
Similarly, to insert a regression step after an existing one, right-click the existing step, select Insert After, navigate through the menus then click the desired new step, as shown below:
The regression node may be “Excluded”, in which case none of the calculations under the regression node will be performed, or the regression may be “Disabled”, meaning that no regression will be performed but all of the calculations under the regression node will still be executed. 30
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Using the Update Compo nent Propert ies Feature Quite often the user is in possession of limited information on the composition of the reservoir fluid. This typically means a breakdown from C 1 to C5 with the heavy end lumped as C 6+ for which only the molecular weight and specific gravity information is available. In order to obtain reasonably accurate results with an EOS the heavy end must be described by more than one pseudo-component. This step is known as characterization or splitting. Since this procedure requires approximating a continuous distribution with a number of discrete components with limited experimental data for the heavy end, the pseudo-components properties are considered to be approximate and therefore suitable candidates for tuning to match available PVT experimental data. The splitting - regression sequence needs to be done in two steps since prior to the splitting calculation the pseudo-components do not exist to enable various properties such P c or Tc to be selected for regression. The execution of this two-step process can be done efficiently using the Update component properties feature. The process generally involves the following sequence:
Set up the Splitti ng Calcul ation: 1. Add Plus Fraction Splitting to the tree view, immediately after the Composition node. 2. Select the Component Selection/Properties node. 3. The compositional analysis up to C5 involves components with known properties. Add these components by clicking the Ins Lib button to open the Library Components dialog then select CO2 through FC6 inclusive. 4. Select the Composition node then enter the mole fractions as they appear on the laboratory report. Ignore the warning message about the sum not being equal to one. 5. Select the Plus Fraction Splitting node then enter the plus fraction properties.
Run WinProp 1. Once the splitting calculation is performed, WinProp writes out the full set of component properties including data for the pseudo-components in a special output file with the suffix (.rls). 2. Click File | Update component properties in the menu bar. WinProp will read the (.rls) file and update the Composition and Component Selection/Properties forms based on the data in this file.
Remove Splitti ng Node Remove the splitting node from the data set by right-clicking Plus Fraction Splitting then selecting Delete. You can now proceed to set up the regression run as described in the Setting Up a Regression Run section.
View/Print the Data Set To view the data set click Simulation Data Set in the tree view. To print the data set click File in the menu then select Print data set. This is a useful aid in troubleshooting if the results are unexpected or if you are having difficulty running the program.
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Editing the Data Set To add a simulation step: 1. Select the point at which you want to insert a simulation step. 2. Select the desired simulation step in the toolbar, or use one of the other methods discussed earlier. Mouse over the simulation step icon in the toolbar to display its name. Once you click it, the simulation step will be added to the data set. To delete a simulation step: 1. Right-click the simulation step that you want to delete then select Delete. The simulation step is immediately deleted. To modify the data associated with a simulation step: 1. Click the simulation step that you want to modify. The available tabs, selections and fields will be displayed in the Data Entry and Results area. 2. Click the selection, field or table cell then enter the desired data value. 3. Select File | Save (or File | Save As if you want to create a new file) to save your edits. In addition to direct entry of data values into fields and table cells, you can highlight data with the left mouse button, then use standard Windows key strokes to delete or copy it: DELETE to delete, CTRL+C to copy, CTRL+X to cut, and CTRL+V to paste it into another field or table cell. You can use this copy and paste option to transfer data within one WinProp data set or from one data set to another. Note: In tables, DELETE clears the data in cells, but does not delete the corresponding rows.
Operations w ith Multiple Calcul ation Modules A dialog to perform operations on multiple calculation modules simultaneously can be launched by clicking the “Module Operations” button on the toolbar or by selecting it from the context menu that comes up when you right-click on the data set name in the tree view. The dialog appears like the example below. Calculation modules that are already temporarily excluded from the data set are shown with check boxes in the left-hand column. Any number of modules may be selected from this list using the standard and keyboard shortcuts. Once a set of modules is selected, radio buttons at the bottom of the dialog allow the user to include or exclude the modules from the data set, or to cut or copy the modules to the clipboard. The operation is completed when the “OK” button is clicked. For Include/Exclude or Cut operations, a confirmation message box appears listing the operations to be performed as soon as the selection dialog box closes. The user has the option of accepting or declining the changes. For the Copy operation, the confirmation message box does not appear until the user chooses to paste the contents of the clipboard. This is done by bringing up the right-click context menu in the tree view of any open data set.
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User Guide WinProp
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Titles/EOS/Units Selection
Overview This form is pre-selected by WinProp and appears as the first form in all WinProp data files. It is used for documenting the run, selecting the unit system and for choosing the equation of state (EOS) to be used for all calculations included in the data file.
Data Input Comments Enter your comments regarding this data set. These comments will be shown in the Data set structure form.
Title Li ne 1, Title Li ne 2, Title Lin e 3 Enter up to 3 titles to identify the runs.
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Equation of State Selection of the equation of state for the oil and gas phases. The default is PR (1978). PR(1978) PR(1976) SRK(G&D) SRK
Peng-Robinson equation of state with 1978 expression for constant "a". Peng-Robinson equation of state with 1976 expression for constant "a". This is the original equation of state. Soave-Redlich-Kwong equation of state with the constant "a" proposed by Grabowski and Daubert[6]. Original Soave-Redlich-Kwong equation of state.
Units psia & deg F kPa & deg C
Pressures in psia and temperatures in ºF. Pressures in kPa and temperatures in ºC.
kg/cm & deg C
Pressures in kg/cm2 and temperatures in ºC.
Mole
The feed on Form Composition is in moles, mole fractions, or mole percent. The feed on Form Composition is in mass (e.g. kg), mass fractions, or mass percent.
2
Feed
Mass
When the Mass option is selected, WinProp converts all mass fractions to mole fractions using the component molecular weights. All outputs will contain the corresponding mole fractions and not the input mass fractions.
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Components
Component Selection and Defini tion The equation of state requires the following properties for each component: critical pressure (Pc), critical temperature (Tc), acentric factor (ω), and interaction coefficients between different components (δij). The molecular weight is also required to calculate mass densities. Additional factors such as the volume shifts τ, and the parameters Ωa and Ω b can also be defined for each component to enhance the equation of state predictions. A complete description for all of the properties in the component table is given in the Component Properties section of this chapter. To select or edit components, click Component Selection/Properties in the tree view. This will bring up the Component Selection/Properties form:
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Components 37
You can select components from WinProp’s component library or define your own components as described below. Note: In the Component Selection/Properties tabs, when you make changes the Apply Changes button will be enabled. Clicking this button will apply the changes. Clicking the Discard button will restore the tabs to the state they were in the last time changes were applied. When you exit the Component Selection/Properties node, you will be prompted to
apply the changes if you have not done so already.
Library Components To choose library components, click the Ins Lib button in the Component tab. The Library Components dialog is displayed:
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Select the components from the Library Components list by clicking on them with the left mouse button. Use the and keys for multiple selections. Pure hydrocarbon components, light gases and water may be selected from the library, as well as generalized single carbon number (SCN) petroleum fractions FC6 through FC45. The specific gravities, molecular weights and boiling points of the SCN fractions are taken from Whitson (1983). The critical properties of these fractions are calculated with the Lee-Kesler correlations (Kesler and Lee, (1976)). The component molecular weights are shown in brackets for each component primarily to allow the user to select generalized SCN fractions to approximate a heavy end of known molecular weight. Once you have selected, or as you are selecting, click to move them into the Selected Components pane. The component order is important for lumping into pseudo-components, as only components that are adjacent to one another can be lumped together. Select components in Selected Components, then use and to change their order, as necessary, or to cancel a selection. After you have OK selected your components, click to save and return to the form.
User Component with Kn own Properties If you have a component with known critical properties, you can insert this component by clicking the Ins Own button in the Component Selection/Properties form. The Custom hydrocarbon component definition screen opens:
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Components 39
Click the New Row button to add a user component. Components can be defined either by specifying critical properties directly, or by specifying physical properties and calculating critical properties from correlations. Enter the component name (maximum 8 characters) then for direct critical property specification, as a minimum enter critical pressure, critical temperature, acentric factor and molecular weight. As necessary, select the desired Physical Properties Correlation, and Critical Properties Correlation. Values will be estimated for any of the optional data parameter fields that are left blank. Critical compressibility is used only to calculate critical volume. Critical volume is used in the calculation of binary interaction parameters (see the Interaction Coefficients section below). Specific gravity and boiling point temperature are used to estimate ideal gas enthalpy coefficients. Specific gravity is also used along with the critical properties to estimate Rackett’s compressibility factor, which is employed in calculating temperature dependent volume shifts. For many heavy hydrocarbon fractions, the measured properties are specific gravity (SG), normal boiling point (T b), and molecular weight (MW). For the physical property specification method, a minimum of two of these three properties must be entered. If one of the properties is not entered, it will be estimated using the selected Physical Properties Correlation. Note that critical properties are calculated from specific gravity and normal boiling point; molecular weight is used for determination of mass densities only. Thus if you enter SG and T b, the critical properties will be unaffected by the choice of Physical Properties Correlation. The stated ranges of accuracy for the correlations are as follows: Twu
T b up to 715 °C and SG up to 1.436 (Twu, 1984).
Goossens
MW from 76 to 1685 (C120), Density from 0.63 to 1.08 g/cc and T b from 33 to 740 °C (Goossens, 1996).
RiaziDaubert
T b up to 455 °C and MW from 70 to 300 (Riazi and Daubert, 1980).
For petroleum fractions up to about C20, all three correlations give similar results. For heavier fractions, the Riazi-Daubert correlation shows larger errors than the other two. The Goossens correlation gives very good predictions of MW from the other properties for alkanes up to C120. It should be noted that the form of this correlation limits boiling points to a maximum of 805 °C, regardless of the molecular weight and specific gravity. Once the physical properties are known, the critical constants for the component are determined using the selected Critical Properties Correlation. The ranges of applicability of the Twu and Riazi-Daubert correlations are as given above. The Lee-Kesler correlation was developed for T b up to 650 °C, but is internally consistent for extrapolation above this temperature (Kesler and Lee, 1976). For acentric factors, the Lee-Kesler correlation is recommended for petroleum fractions.
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Component Properties After components have been selected or defined, their parameters and properties are shown on the form Component Selection/Properties. A typical example is illustrated below.
This form contains several tabs. The properties shown on the Component tab are listed in the table below. Additional explanation regarding some of the parameters is given in the notes following the table. Use of the temperature-dependent volume shift feature is described under Rackett’s Compressibility Factor (ZRA) in the notes. Heading
Parameter or property
Component HC Pc(atm) Tc (K) Acentric fact. Mol. weight Vol. Shift
Component name (maximum 8 characters) Hydrocarbon flag (=1 for hydrocarbons) Critical pressure in atm Critical temperature in K Acentric factor Molecular weight Volume shift (dimensionless)
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Heading
Parameter or property
V Shift Coef1 V Shift Tref Z (Rackett) Vc (l/mol) Vc (viscosity)
Volume shift temperature coefficient (1/deg F or 1/deg C) Volume shift reference temperature (deg F or deg C) Rackett’s compressibility factor Critical volume in l/mol Critical volume in l/mol for viscosity calculations
Heading
Parameter or property
Omega A Omega B SG T b (deg F | deg C) Parachor Ref. Henry (atm) V inf. (l/mol) P ref. (atm) Enth. Coeff. A Enth. Coeff. B Enth. Coeff. C Enth. Coeff. D Enth. Coeff. E Enth. Coeff. F Enth. Coeff. G Heating Value
Ωa EOS parameter Ω b EOS parameter Specific gravity (water = 1) Normal boiling point in °F (field units) or °C (SI units) Parachor IFT parameter Reference Henry’s constant in atm Molar volume at infinite dilution Reference pressure for Henry’s constant in atm Ideal gas enthalpy coefficient A (for units see note below) Ideal gas enthalpy coefficient B (for units see note below) Ideal gas enthalpy coefficient C (for units see note below) Ideal gas enthalpy coefficient D (for units see note below) Ideal gas enthalpy coefficient E (for units see note below) Ideal gas enthalpy coefficient F (for units see note below) Ideal gas enthalpy coefficient G (for units see note below) Heating value (for units see note below)
Notes on Component Properties Hydrocarbon (HC) Flag: Binary interaction parameters between components with HC flags set
to 1 are calculated via a correlation as described in the Interaction Coefficients section below. The interaction parameters between all other pairs of components may be set individually. Thus, if you wish to set individual interaction parameters between one component and all others, change the value of the HC flag for that component to 0. Note that the HC flags for CO 2 and H2S have special values and should not be changed. Volume Shift: The volume translation technique of Peneloux et al. (1982) is available for
improving the prediction of phase density with the equation of state. There are three methods available for modeling the volume shift, selected via the drop-down list box on the Component tab: 1. Constant Volume Shift 2. Temperature Dependent Volume Shift Correlation 3. Linear Temperature Dependent Volume Shift
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The dimensionless volume shift S can be expressed by the following relation, as in Pedersen et al. (SPE 88364): S = S 0
+ S 1 (T − T ref )
For the Constant Volume Shift option only, parameter S 0 is used, corresponding to column Vol. Shift. Volume shift parameters S 0 are set to zero by default. The correlation of Jhaveri and Youngren (1988) can be applied to calculate volume shift parameters for all components by rightclicking the column header Vol. Shift and selecting Set to Interface Correlation Value. To reset S 0 to zero for all components, the Set to Zero context menu can be used. To calculate volume shift values that match the specified specific gravity for each component using the Rackett’s ZFactor method, select the context menu option Use Internal Zra Correlation. If Temperature Dependent Volume Shift Correlation is selected, volume shifts for each component are determined each time an EoS calculation is performed, at the temperature specified for that calculation. The calculation of temperature-dependent volume shifts is described next under Rackett’s Compressibility Factor (ZRA). When printing component properties to the output file or for export to the GEM simulator, the most recently used volume shift values will be output. For the Linear Temperature Dependent Volume Shift option, the full equation given above is used. S 1 corresponds to column V Shift Coef1 and T ref corresponds to column V Shift Tref . Values can be entered in the table for S 1 and T ref , or internal defaults may be used. The default for T ref is 60 F | 15.56 C. Volume shift temperature coefficients S 1 are set to zero by default. If the right-click context menu option Use Internal Zra Correlation is selected, when the data set is run the Rackett’s Z-Factor correlation is used to determine the saturated liquid density for each component at the specified Default Reservoir Temperature. The volume shift corresponding to this value of liquid density is determined as for the Temperature Dependent Volume Shift Correlation, then the linear volume shift correlation equation given above is used to backcalculate the value of S 1. If no value of Default Reservoir Temperature is entered, 80 C | 176 F is used. To reset S 1 to zero for all components the Set to Zero context menu can be used. Both S 0 and S 1 may be used as regression parameters to match experimental data. Rackett’s Compressibility Factor (ZRA): Temperature-dependent volume shifts are implemented using a technique similar to that described by Kokal and Sayegh (1990). Component volume shifts are evaluated at any temperature by taking the difference between the saturated liquid molar volume of a pure component calculated from the equation of state and the saturated liquid molar volume calculated using a modified Rackett equation: vs
[1+(1−T ) = ( RT c / Pc ) Z RA r
2/7
]
Rackett’s compressibility factors are available for all library components. For pseudocomponents, Rackett’s compressibility factors are back calculated from the critical properties and specific gravity using the assumption that the specific gravity is approximately equal to the saturated liquid density at 60 °F. Critical Volume: Critical volumes are used only in the calculation of hydrocarbonhydrocarbon binary interaction parameters as described below under Interaction Coefficients.
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Critical Volume for Viscosity: Critical volumes are used in the Jossi, Stiel and Thodos
viscosity correlation (Reid et al., 1977) as described in the Viscosity Parameters section in this chapter. These critical volume values are used only for the calculation of viscosity, and thus may be modified via regression to match experimental viscosity data without affecting the calculation of any other properties. Omega A and Omega B: The default values for Ωa and Ω b for the Peng-Robinson equation of
state are 0.45723553 and 0.077796074 respectively. For the Soave-Redlich-Kwong equation of state, these values are 0.4274802 and 0.08664035 respectively. Specific Gravity and Normal Boiling Point: Specific gravity is defined as the liquid density
of the component at 60 °F and 1 atm divided by the density of water at 60 °F and 1 atm. For components with normal boiling points below 60 °F, the liquid density is taken as the saturated liquid density at 60 °F. If SG and T b have been used to calculate critical properties and acentric factors, changing SG and T b in the table will not affect the other properties. If you wish to recalculate the properties of a particular component with revised values for SG and T b, delete that component from the table by clicking on the table row then clicking the Del button to the left of the table. Insert a new component with revised values for SG and T b, using the Ins Own button, described above. Parachor: The parachor value is used for calculating interfacial tension. Parachors are
available for all of the library components. For pseudo-components and user components, parachors are estimated based on molecular weight using a correlation proposed by Firoozabadi et al. (1988). Reference Henry’s Constant, Molar Volume at Infinite Dilution and Reference Pressure: These properties are used in calculating the solubility of components in the
aqueous phase. There are three methods available for specifying these parameters: (1) Entering nonzero values for these properties in the component table, (2) entering zero values in the component table to allow internal estimation of Henry’s constants, and (3) entering zero values in the table, but overriding the internal Henry’s constants with user input values entered for individual flash calculations. If nonzero values for the solubility parameters are entered in the component table, Henry’s constants are calculated from: ln H i
= ln H io + ν i∞ ( p − p io ) / RT
where the superscript “o” refers to the reference condition. If experimental solubility data is to be matched using regression, this method for defining the solubility parameters must be used. Correlation values can be entered by right-clicking column header Ref. Henry (atm) and selecting Calculate Aqueous Solubility. Methods (2) or (3) will be used if the solubility parameters are all set to zero. This can be done by right-clicking column header Ref. Henry (atm) and selecting Default Aqueous Solubility. The 3rd context menu item No Aqueous Solubility is for specifying all components insoluble. To change a single component’s Henry Constant, you can type in any value, the word Default, or the word Insoluble. If the reference solubility parameters are set to zero in the component table, Henry’s constants will be estimated internally for all components for each Oil-Gas-Water flash. 44
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User Guide WinProp
Method (2) may be overridden by specifying component Henry’s constants for individual Oil-Gas-Water flash calculations. Ideal Gas Enthalpy Coefficients: The ideal enthalpy at a given temperature T is calculated from a polynomial expression that takes the following form: H ideal
= H A + H B * T + HC * T 2 + H D * T3 + H E * T 4 + H F * T5
where the temperature T is in °R. The ideal enthalpy coefficients HA through HF should be specified in units to give H ideal in Btu/lb. Component Heating Values: The heating value of a component is the heat of combustion
assuming the reaction goes to completion; i.e., the reaction takes place with excess oxygen and the final products are carbon dioxide and water. In SI system the units are kcal/gmol and in Field units are Btu/gmol. Approximate values have been assigned to the Library components. These values were taken from the CRC Handbook of Chemistry and Physics, 65 th edition, CRC Press Inc, 1984, pages D275-D280 (see table below). WinProp will write out the HEATING_VALUES keyword and the associated values to the .gem output file. This file can then be referenced by a GEM data file using an include statement or the contents of the .gem file can be copied and pasted at the appropriate location in the GEM data file. Currently, for pseudo-components created by WinProp’s splitting and or lumping options, no method has been coded for estimating the heating value; accordingly, for pseudo-components values of zero are assigned. However heating values for pseudo components can be estimated based on the values assigned to the library components given the actual composition of the pseudo component is known. Once these values are estimated simply edit the values in the last column of WinProp’s component properties form and save the form. For example for pseudocomponent C2-C3 assuming a split of 50% C 2 and 50% C3 and using the built in values in WinProp the heating value is calculated by mole fraction averaging as: 0.5*1478.46+0.5*2105.16 = 1791.81 Btu/gmol. Values for other pseudo components such as C4-C6 can be estimated in a similar manner. For the plus fraction such as C 10+ if the breakdown of the carbon number vs. mole fraction is known then mole fraction averaging can be applied. If the distribution is not known then assign the value corresponding to the presumed largest mole fraction carbon number, for example for C 10+ this might be C 12. The heating value for the library component FC 12 of 7722.09 Btu/gmol would then be assigned to C10+. GEM will calculate and report the heating value of all the well streams in the output file using the known composition of the stream by mole fraction averaging the entered component heating values supplied by the user. Once the HEATING_VALUES keyword appears in a GEM data file a heating value for the separator gas stream for wells and groups will be calculated and be available for plotting with RESULTS. The heating value assigned to the library components in WinProp are shown below.
User Guide WinProp
Components 45
For the carbon fraction FC 7-FC45 the heating value equals 1002.57 kcal/gmol + 157.44 kcal/gmol increment for every carbon number greater than 6. Same values are used for NC6 and FC6 and NC7 and FC7 etc. For pseudo components values of zero will be assigned, as at present there is no method implemented for estimating these values.
46
Component Name
Heating Value (Btu/gmol)
H2S N2 CO2 CH4 (or C1) C2H6 (or C2) C3H8 (or C3) IC4 NC4 IC5 NC5 FC6 FC7 FC8 FC9 FC10 FC11 FC12 FC13 FC14 FC15 FC16 FC17 FC18 FC19 FC20 FC21 FC22 FC23 FC24 FC25 FC26 FC27 FC28 FC29 FC30 FC31 FC32 FC33 FC34 FC35 FC36
0.0 0.0 0.0 844.29 1478.46 2105.16 2711.54 2711.54 3353.66 3353.66 3975.91 4600.28 5224.64 5849.00 6473.36 7097.73 7722.09 8346.45 8970.82 9595.18 10219.54 10843.91 11468.22 12092.63 12717.00 13341.36 13965.72 14590.08 15214.45 15838.81 16463.17 17087.54 17711.90 18336.26 18960.63 19584.99 20209.35 20833.71 21458.08 22082.44 22706.80
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User Guide WinProp
Component Name
Heating Value (Btu/gmol)
FC37 23331.17 FC38 23955.53 FC39 24579.89 FC40 25204.26 FC41 25828.62 FC42 26452.98 FC43 27077.35 FC44 27701.71 FC45 28326.07 NC6 3975.91 NC7 4600.28 NC8 5224.64 NC9 5849.00 NC10 6473.36 NC16 10219.54 TOLUENE 3705.97 BENZENE 3097.15 CYCLO-C6 3715.32 H2O 0.0 Example: Consider an 8-components fluid, with the last three components being pseudocomponents. In Field units, the heating values as written out by WinProp would result in the following lines appearing in the .gem output file: *NC 8 3 *COMPNAME ' CH4' ' C2H6' ' C3H8' ' NC4' ' NC5' ' FRAC1' ' FRAC2' ' FRAC3' *HEATI NG_VALUES 844. 29 1478. 46 2105. 16 2711. 54 3353. 66 0. 0 0. 0 0. 0
Interaction Coeffici ents Interaction coefficients (δij) are introduced to account for the molecular interaction between dissimilar molecules. Their values are generally obtained by fitting the predicted saturation pressures to experimental data. Interaction coefficients for component pairs are shown on the Int. Coef. tab. An example is shown below.
User Guide WinProp
Components 47
Hydrocarbon-Hydrocarbon Interaction Coeffic ients The hydrocarbon (HC) components are identified by a value of 1 in the “HC” column on the Component tab. The interaction coefficients between HC components are calculated from
2v1ci/ 6 v1cj/ 6 δij = 1 − 1 / 3 1 / 3 v +v ci ci
θ
where vci is the critical volume of component i, and θ is the hydrocarbon – hydrocarbon interaction coefficient exponent. It has been shown that a value of 1.2 provides a good match of the paraffin – paraffin interaction coefficients of Oellrich et al (1981). However, it is recommended that this value be obtained by matching experimental data (e.g. saturation pressure data). To avoid cluttering the table of interaction coefficients, the HC interaction coefficients are not shown when the form is loaded. To view them, click the Show HC Int. Coef. button at the bottom of the table. To hide them, click the Hide HC Int. Coef. button. With this version of WinProp, it is possible to define multiple HC:HC interaction coefficient groups, each with its own value of the exponent. HC:HC groups can also be selected as independent parameters in regression, as shown n the Regression chapter. The list of groups currently defined is shown in the list box with the caption HC Int. Coef. Exp.. The entries 48
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User Guide WinProp
include a name and, in brackets, the value of the exponent. To see the group ID for all HC-HC pairs on the interaction coefficient table, click the Show HC-HC Group(s) on grid button. The value of the exponent for a given group(s) can be changed by invoking a custom form designed to handle the tasks associated with managing these groups. This form, shown below, is invoked by clicking the HC-HC Groups / Apply value to multiple non HC-HC pairs… button.
The currently selected group is shown under the Name label. The list of pairs that belong to this group is shown in the list box labelled Selected pairs. The user can scroll through all defined groups in the drop down list box under the Name label. The full list of pairs that do not currently belong to an ygroup can be seen on the list box under the Select pairs frame. These pairs can be assigned to any defined group(s). If any “orphans” remain when this form is saved then these are assigned to the default group, i.e. group # 1. Initially only a single group is created with the exponent value of 1.2. The value of the exponent can be changed via the text box with the label Exponent value. All HC:HC pairs initially belong to this group. To create a new group first select the HC:HC option button under Type and then click on the Create New button. This new group will be assigned the name HcIntCoefExp-2 with a value of 1.2 for the exponent. For pairs to be assigned to this new group # 2, group #1 must first relinquish these. This is done by first selecting group # 1 from the group list, identifying the pairs that will be removed (by pressing the left mouse button while holding the CTRL key down) from the Selected pairs list box and then clicking on the Delete selection(s) button. These pairs will be removed from group # 1 as reflected in the revised list in the Selected pairs box. To pick these pairs up for group # 2, change the name to group # 2, select pairs by highlighting and then pressing the Apply selection(s) button. At least one pair must be assigned to each group and a given pair can be assigned to a single group only. To delete a group click on the Delete Group button. User Guide WinProp
Components 49
If you select Non-HC-HC pairs, the selected pairs are displayed in the right pane. To add a selection, first select the 1 st Index then select the pair then click Apply Selection as above. This is illustrated below:
Other Interactio n Coefficients Interaction coefficients between nonhydrocarbons, and between hydrocarbons and nonhydrocarbons from the WinProp library are displayed in the table. They may be edited in one of two ways, either directly on the grid, or if a common value is to be assigned to multiple pairs, say CO2 and all pseudo-components then a faster way is through a special form invoked by the clicking the button on the Int. Coef. tab with the caption HC-HC Groups / Apply value to multiple non HC-HC pairs…. Select pairs through the 1st index (single) and 2nd index [multiple] lists and then click on the Apply selection(s) button. The list of pairs chosen is shown in the Selected pairs box. Specify the value to be applied in the text box labelled Value and finally click on the Apply value button. On exiting the form, the interaction coefficient table should now show the revised value for the pairs selected. Note that as δij ≈ δ ji, changing one also changes the other.
Viscosity Parameters There are two types of viscosity correlation available in WinProp: the Jossi, Stiel and Thodos (JST) correlation as described in Reid et al. (1977), and the Pedersen corresponding states correlation as presented in Pedersen et al. (1984) and Pedersen and Fredenslund (1987). The viscosities of liquid and vapor phases are calculated with the same correlation. The choice of correlation is made on the Viscosity tab of the Component Selection/Properties form by selecting one of the option buttons under Viscosity Model Type. 50
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User Guide WinProp
Joss i-Stiel-Thodos Correlation An example of the data entry form for the JST correlation is shown below.
The JST correlation determines the mixture viscosity from the low-pressure mixture viscosity according to the following function:
[ ( µ − µ )ξ + 10 − ] *
4 0.25
= a 0 + a 1ρ r + a 2 ρ 2r + a 3ρ 3r + a 4 ρ 4r
Where Oil or gas viscosity in cP or MPa ⋅s Low-pressure viscosity in cP or MPa ⋅s Group Tc1/6 M-1/2 Pc-2/3 where Tc is in K and P c is in atm M molecular weight ρr Reduced molar density, ρ/ρc = vc/v Two options are available for calculating the low-pressure mixture viscosity. The Yoon-Thodos + Herning-Zipperer method computes low pressure component viscosities according to a formula developed by Yoon and Thodos and then computes the mixture viscosity according to the mixing rule of Herning and Zipperer. Both of these formulas are reported in Reid et al. (1977). The Lee-Eakin method calculates the low-pressure mixture viscosity directly using a correlation based on the molecular weight of the mixture presented by Lee and Eakin (1964).
µ µ∗ ξ
= = = =
The value of ξ is calculated by first obtaining mole – fraction weighted average values for the mixture critical temperature, pressure and molecular weight.
User Guide WinProp
Components 51
The mixture critical volume vc is calculated from: 1/ α
n c α v c = ∑ x i v ci i =1
where α is the mixing exponent parameter, xi is the composition and vci is the critical volume for viscosity calculation (vc(viscosity) on the Component tab).
α, a0, a1, a2, a3, and a4 are entered on the Viscosity tab. Default values are shown when the form is first activated. As well as the correlation coefficients (α, ai) and critical volumes for viscosity (and to a lesser extent, the critical temperatures and pressures), the JST method depends very strongly on the density of the mixture predicted by the equation of state. Thus, use of the JST correlation may result in large errors if the phase densities are incorrect. It is recommended that the EOS be tuned to match volumetric data before attempting to predict or match viscosities with the JST correlation.
Pedersen Correlation The Pedersen viscosity correlation uses the principle of corresponding states to calculate the viscosity of a component or mixture, knowing the viscosity of a reference substance at the same conditions of reduced pressure and temperature. The deviation from simple corresponding states is accounted for by a “rotational coupling coefficient,” α. The viscosity of the mixture is calculated according to the following formula:
T µ mix (P, T) = c,mix µ o (Po , To ) Tc,o
−1 / 6
Pc,mix Pc,o
2/3
MWmix MWo
1/ 2
α mix α o
where
µ
= Tc = Pc = MW = = α
Viscosity Critical temperature Critical pressure Molecular weight Rotational coupling coefficient
The subscript “mix” refers to the mixture property, and the subscript “o” refers to the reference substance property. The reference substance for the Pedersen model is methane. The mixture critical temperature and pressure are calculated using mixing rules that are a function of the component critical temperatures and pressures and mole fractions. The molecular weight of the mixture is determined from:
(
2 MWmix = b1 MW b w
− MW bn2 ) + MWn
where MWw is the weight fraction averaged molecular weight, and MWn is the mole fraction averaged molecular weight. The rotational coupling coefficient is calculated as follows:
α = 1 + b 3 ρ br 4 MW b5 where ρr is the reduced density of the reference substance. 52
Components
User Guide WinProp
The viscosity of a mixture calculated using the Pedersen model depends strongly on the critical pressures, critical temperatures and molecular weights of the components, and the coefficients bi shown in the above two equations. Two different versions of the Pedersen correlation may be chosen. The one labelled Modified Pedersen (1987) uses a modification to the methane viscosity equation as described in Pedersen and Fredenslund (1987). This modification showed improved results for mixture viscosities up to approximately 10 cP. Each modification has a set of default coefficients. These coefficients may be modified during regression to match experimental viscosity data.
Aqueous Phase The Aqueous Phase tab is used for setting properties of the water phase for use in multiphase Oil-Gas-Water calculations. The form is shown below.
Aqueous Phase Salinity The salinity of the aqueous phase is expressed as NaCl concentration. The units available for specifying the brine salinity are weight fraction, molality, grams of NaCl per litre of water, molarity, and mole fraction. All other water properties are determined from correlations. The brine salinity is used to adjust the internally estimated Henry’s constants for the library components N2, CO2, H2S, C1, C2, C3, iC4, nC4, iC5, nC5, nC6, nC7 and nC8 to account for the salting-out effect. Note that this adjustment is not performed when solubility parameters are specified in the component table, or when Henry’s constants are entered for individual flash calculations.
User Guide WinProp
Components 53
Henry’s Law Constant Correlation There are two correlations available in WinProp to calculate Henry’s law constant: the Harvey’s method (1996), and the Li-Nghiem’s method (1986). The effect of salt on the gas solubility in the aqueous phase is modeling either by salting-out coefficient or the scaled particle theory, depending on the component. The choice of Henry’s constant correlation is made by selecting one of the option buttons in the Henry’s law constant correlation frame in the Aqueous Phase tab. The correlation is set to Harvey’s method (1996) by default.
Model Option The Model Option tab is used for setting the options for calculating excess properties. The Lee-Kesler EOS/corresponding states method is available in other software, and is implemented here to allow comparison to excess properties calculated directly with the cubic equation of state. The Lee-Kesler mixing rule associated with this method is expected to give better results than Kay’s mixing rule. The form is shown below:
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User Guide WinProp
Activation of Second Set of Comp on ent Pro perti es WinProp supports the specification of a second set of EOS component properties. It is often difficult for a single EOS description to perform adequately over a wide range of conditions encountered in reservoir phase behavior modeling. This can be alleviated by the introduction of a second EOS model that is applied to calculations performed at surface (separator) conditions, while the first EOS set is used for calculations at reservoir conditions. Therefore separator data can then be matched separately from other PVT data gathered at reservoir temperature, for example by CVD and differential liberation experiments. To add a second set of component properties, in the Component tab select in the drop-down list at the lower left of the tab. This should be done after the component selection is completed. WinProp will duplicate the first set properties for the second set. The user can toggle between the first and second set through the drop-down list. Certain operations, for example addition or removal of components on the component form, can be performed only if the first set is active. Currently, critical pressure, critical temperature, volume shift, omega-A, omega-B, interaction coefficient exponent and interaction coefficients for pairs with a nonhydrocarbon component are supported for the second set. The user can edit the values of these properties from the default assignments. The user can also reset back to the original values by selecting Reset to 1st Set. The second set parameters can also be used in regression. To use a second set parameter in regression the user does not have to enable the second set component properties first. The second set parameters can be selected directly on the Component Properties tab in the Regression Parameters form. The initial value of the property will be set equal to the corresponding first set parameter. The second EOS parameter set, when enabled, is used in performing the following calculations: separator, separator calculation associated with the constant volume depletion experiment (to determine yields at surface) and in differential liberation experiment when flashing the residual oil (at atmospheric pressure and reservoir temperature) to standard conditions (atmospheric pressure and temperature).
GEM Flui d Model Generation and Component Properties Printing The EOS model description in WinProp can be written to a file in a format suitable for CMG's compositional simulator GEM. This file can be imported into a GEM data set using Builder. The model information includes EOS type, component critical properties, volume shifts, EOS omega parameters, parachors, aqueous solubility parameters and viscosity model coefficients. The component properties can also be echoed to the output file. The option to write out the EOS model can be included in the data set by selecting Simulator PVT | CMG GEM EOS Model from the menu. A form entitled CMG GEM EOS Model will be included in the data set, as shown in the following example:
User Guide WinProp
Components 55
In the File Selection area of this form there are two check boxes for printing the component properties. Select the upper check box to print detailed component properties to the output file, and select the lower check box to write out the EOS model for GEM. This file will have the same root name as the data file and the extension (.gem). To complete the model description for GEM, a reservoir temperature must be specified. If the data set includes a laboratory experiment simulation such as a CCE, CVD or Differential Liberation calculation, the temperature from the first calculation of this type in the data set will be taken as the default reservoir temperature, otherwise this field must be filled in by the user. There are also options to Write solid model parameters for GEM , and to Write component heating values for GEM. To use the solid model in GEM, the number of solidforming components must be set to one on the “Asphaltene/Wax Modelling” dialog. GEM’s solid model is used for asphaltene precipitation, not for waxes. To have accurate parameters for GEM, the reference fugacity for the model should be determined from experimental data, as described in the Asphaltene/Wax Modelling section in the Flash Calculations chapter. Parameters for the isothermal precipitation model will always be written for GEM. Temperature-dependent parameters will only be written if additional onset pressures have been specified with the reference fugacity calculation. There are three options for water modeling in GEM. By default, GEM does not allow vaporization of the water component, water density is calculated from a linear model in terms of compressibility, and water viscosity is constant. To allow vaporization of the H 2O component in GEM, this component must exist in the WinProp data set and it must be included in the GEM component list. Even if the component “H2O” is present, it is not written out to the GEM component properties file unless Include H2O in GEM component 56
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User Guide WinProp
list is checked. To allow the water density in GEM to be calculated as a function of pressure, temperature and salinity, check Use Rowe-Chou aqueous density correlation. To allow the
water viscosity in GEM to be calculated as a function of pressure, temperature and salinity, check Use Kestin aqueous viscosity correlation. In the Interaction Coefficient Table frame, the format of the table can be selected as either upper or lower triangular form. By default, the aqueous phase solubility parameters are not printed with the other component properties. To turn on this option, select the check box in the Solubility Parameters area. If an Oil-Gas-Water flash is included in the data set before the print options form, the Henry’s constants and molar volumes at infinite dilution used in the flash will be available for printing. Optionally, the parameters may be recalculated at a specified pressure and temperature before printing.
GEM-GHG Parameter Select ion CMG’s GEM simulator is an Equation of State compositional and Green-House Gas (GHG) model. The GHG features include modeling of aqueous reactions and mineral precipitation or dissolution. To generate the data required to model aqueous and mineral reactions in GEM, check the Print GEM-GHG parameters box then click Select Reactions on the main CMG GEM EOS Model data entry area. The following data entry window will be displayed:
On the Reaction Selection tab of this window, option buttons can be selected to display Aqueous Species Reactions or Mineral Species Reactions. All of the available reactions of User Guide WinProp
Components 57
the selected type will be displayed in the “Available Reactions” list. Reactions are chosen by selecting them from this list and using the arrow buttons to move them to or from the “Selected Reactions” list. When the WinProp data set is run, lists of aqueous and mineral species are generated from the chosen reactions. If the selected reactions do not include Na+ or Cl- ions but it is desired to use these in the simulation to track changes in salinity, check Include Na+ and Cl- ions on this tab. By default, the derivatives of the chemical equilibrium equations and the mineral precipitation/dissolution rate equations are calculated analytically. There may be some situations where numerical derivatives are advantageous. To choose the derivative calculation method select the Analytical or Numerical option buttons. The parameters required for modeling the mineral precipitation/dissolution rate reactions are entered on the Mineral Reaction Data tab shown below. There is little standardized data of this type, so it is not included in most geochemical reaction databases. These parameters can be found in the literature or provided by geochemists familiar with the mineralogy for a given area. The parameters required are the Reactive Surface Area for the mineral (m2), the log of the Rate Constant (mol/m 2s) at a given Reference Temperature (°C), and the Activation Energy (J/mol) for the reaction. To model permeability changes, check Reduce permeability as a function of porosity change due to mineral precipitation according to CarmanKozeny equation.
Further options for aqueous modeling in GEM can be selected on the Aqueous Phase Models/Data tab:
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User Guide WinProp
Aqueous Phase Activity Model: The most accurate model available in GEM is the B-Dot model, this is the default. For low salinity cases, the Debye-Huckel model may be used. The Ideal (activity coefficients equal one) is in general not accurate, but may be used to simplify difficult models to determine if the activity coefficient model chosen is causing convergence problems. Please see the GEM documentation for the equations used in these models. Aqueous Phase Salinity: The default in GEM is the option Use constant salinity. To specify a non-zero salinity, enter the molality of the brine in the text box labelled: Equivalent NaCl molality (mol NaCl/kg H2O) . To calculate the salinity in GEM based on composition of the water in each grid block, select Calculate equivalent salinity from Cl- or Na+ concentration. Hydrocarbon Trace in Aquifer: The default in GEM is to include a trace of hydrocarbon in all water blocks. To over-ride this default and have exactly 100% water saturation in aquifer blocks, check Aquifer is completely filled with H2O (no trace hydrocarbon used). Aqueous Phase Threshold Mole Fractions: To allow better convergence in GEM when amounts of dissolved gaseous species are small, GEM will stop reaction modeling when the concentration of a component goes below a specified threshold value. Values of mole fraction of 0.01 or less are recommended.
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Components 59
Common Data Required for All Options
Overview This chapter describes the common data required for most calculations. These include Composition specification, Initial K-values, Output level, and Stability test level. Generally, the built in default values are used in the calculations. The saturation pressure calculation, which is common to most laboratory experiment simulation options, is discussed in the next chapter.
Composition Specification Compositions are entered in moles or in weight units, specified as fraction or percent. Values will always be normalized internally when the simulation is run. To normalize values in the composition table, click the Normalize command button. If weight fractions or percents are entered, they are converted internally to mole fractions. To use weight units, select the appropriate option on form Titles/EOS/Units. The table on form Composition contains two columns for composition input. The primary composition corresponds generally to the composition of the oil or gas in place. Values must be entered for the primary composition. The secondary composition corresponds normally to the injected fluid. The secondary composition need not be entered and will default to zero. An example of the Composition form is shown below.
User Guide WinProp
Common Data Required for All Options 61
Several composition sections can be defined in a data set. All calculations following a composition specification will use that composition until the end of the run or another composition specification is encountered. In the following example, the fluid composition from Well 16 is used for a series of calculations. Similar calculations are then performed with the fluid composition of Well 20.
CompositionforWell16 CalculationsforWell16
CompositionforWell20 CalculationsforWell20
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Common Data Required for All Options
User Guide WinProp
Composition Used in Calculations
The feed composition used for all calculation options can be
• • • • •
a mixture of the primary composition and the secondary composition the feed from the previous calculation option the vapor composition from the previous calculation option the liquid composition from the previous calculation option the composition from Phase n from the previous calculation option
The feed composition is specified from the Combo Box Feed, located on the last tab of most calculation options. The selection of the feed composition for a two-phase saturation pressure calculation is shown above. In this example, the composition that enters into the two-phase calculations is a mixture containing 80 mole % of the primary composition and 20 mole % of the secondary composition. When Phase is selected, you enter the Phase Number in the adjacent text box. Some calculations accept only the Mixed and Previous option. The Feed Combo Box displays only these items in this case.
Initi al K-Values Initial K-values are required to start most calculations. These can be
• estimated internally from Wilson’s equation (Internal), i.e. ln K i =5.37 (1 + ωi ) (1 − Tci / T )+ln ( p ci / p)
• from a previous two-phase calculation (Previous) • from Phase n of a previous multiphase calculation (Phase) When Phase is selected, the Phase Number is entered in the adjacent text box.
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Common Data Required for All Options 63
Output Level The Output level for a normal run is 1. If more information is required, for example the results of each iteration of a flash calculation, select an Output level value of 2.
Stabilit y Test Level In phase behavior calculations, the number of phases is generally unknown a priori. WinProp assumes that the system is initially single-phase and performs a stability test on that system. The stability test is a calculation that determines whether a system needs to split into additional phases to achieve stability. The stability test searches the multidimensional Gibbs free energy surface for stationary points. For a phase to be stable, the Gibbs free energy must be lower than the value at all stationary points. The Stability test level determines the thoroughness of the search for the stationary points. Values are from 0 to 4. For most two-phase oil/gas systems, Level 1 is normally sufficient. For systems with more than two phases, a value of 4 may be required. The Stability test level is set to its default value when the form for a particular calculation is first activated. If you suspect that your system may have more phases than those predicted, increase the level value and rerun the data set. See Nghiem and Li (1984) for a detailed discussion of stability test calculations.
64
Common Data Required for All Options
User Guide WinProp
Two-Phase Saturation and Phase Boundary Calculations
Overview This chapter describes calculations for mixtures on the phase boundaries:
• Bubble point and dew point calculations • Phase boundary diagram construction (pressure-temperature, pressure-composition, temperature-composition and pseudo-ternary)
• Critical-point calculation • Multiple-contact calculation The phase boundary calculations can also generate lines of constant phase mole fraction or lines of constant volume fraction (quality lines).
Saturation Pressure This option is invoked by selecting the Saturation Pressure node. An example data set for this option is sat-pressure.dat . For data entry in the Feed/K values/Output level/Stability test level tab, see the Common Data Required for All Options chapter. A value of the temperature at which the saturation pressure is to be calculated is required. In the Calculations tab, enter a value in the text box labelled Temperature. An estimate of the saturation pressure is also required; enter a value in the text box labelled Saturation Pressure Estimate. If this is a poor estimate, ask WinProp to generate internally a better initial guess for saturation pressure calculation by checking the box Improve saturation pressure estimate. Details of the calculation techniques can be found in Nghiem et al. (1985). Finally, at a given temperature there are two saturation pressures, the upper and lower values respectively. The upper value can be a dew point or bubble point fluid, the lower is a dew point fluid. By default the upper value is calculated as this corresponds to the reservoir saturation pressure at the given temperature. The lower value can be chosen instead by selecting the button Lower dew point in the Calculation option area. Experimental data related to a saturation pressure calculation that can be matched via regression are shown on the Calculations tab. These include saturation pressure, liquid and vapor mass densities, compressibilities and viscosities. The weight assigned to each experimental data value can also be specified. User Guide WinProp
Two-Phase Saturation and Phase Boundary Calculations 65
Satur ation Temperature This option is invoked by selecting Calculations | Saturation Temperature. An example data set for this option is sat-temperature.dat . For data entry in the Feed/K values/Output level/Stability test level tab, see the Common Data Required for All Options chapter. A value for the pressure at which the saturation temperature is to be calculated is required. In the Calculations tab, enter a value in the text box labelled Pressure. An estimate of the saturation temperature is also required; enter a value in the text box labelled Saturation Temperature Estimate. If this is a poor estimate, ask WinProp to generate internally a better initial guess for saturation temperature calculation by checking the box Improve saturation temperature estimate. Generally there are two possible values for the saturation temperature at a given pressure. The larger value corresponds to a dew point fluid whereas the lower value corresponds to a bubble point fluid. By default the larger value is calculated. The lower value is chosen by selecting Lower sat. temperature in the Calculation option area. Details of the calculation techniques can be found in Nghiem et al. (1985). Experimental data related to a temperature pressure calculation that can be matched via regression are shown on the table provided on the Calculations tab. These include saturation temperature, liquid and vapor mass densities, compressibilities and viscosities. The weight assigned to each experimental data value can also be specified.
Phase Boundary and Qualit y Lin e Calcul ations This option is invoked by selecting Calculations | Two-phase Envelope. Example data sets for this option are envel_2ph-pt.dat (PT diagram), envel_2ph-px.dat (PX diagram) and envel_2ph-tern.dat (ternary diagram). The two-phase envelope calculation generates the boundaries between the single-phase and two-phase regions. The bubble point envelope corresponds to the boundary between a single phase liquid region and a two-phase vapor-liquid region; the dew point envelope corresponds to the boundary between the single-phase vapor region and the two-phase region. There are two main classes of diagrams that can be generated: X-Y phase diagrams and pseudo-ternary phase diagrams. Pseudo-ternary phase diagrams depict the boundaries between single-phase and two-phase regions in composition space at a fixed temperature and pressure. The results are displayed on a triangular diagram, where each apex of the triangle corresponds to 100% of one pseudocomponent. Each component in the system is assigned to one of the three pseudo-components. X-Y phase diagrams are displayed on regular Cartesian coordinates. The types of envelopes or diagrams that can be generated are:
• Pressure-Temperature (PT) diagram • Pressure-Composition (PX) diagram • Temperature-Composition (TX) diagram In the process of constructing the envelope, WinProp also calculates the location of critical points through interpolation. This is a very efficient method for estimating critical points if they exist on the portion of the phase envelope being constructed. A direct method of 66
Two-Phase Saturation and Phase Bound ary Calculations
User Guide WinProp
calculating critical points is also available (see the Critical Point Calculation section in this chapter). A typical PT diagram is shown below: Gas condensate Phase Envelope Pressure-Temperature Diagram 14,000
2-Phase boundary 99.000 volume % 90.000 volume % 75.000 volume % 60.000 volume % 55.000 volume % 50.000 volume % 45.000 volume % 40.000 volume %
12,000
10,000 ) a i s p ( e r u s s e r P
8,000
Critical 95.000 volume % 80.000 volume % 70.000 volume % Critical 55.000 volume % 50.000 volume % 45.000 volume % 35.000 volume %
6,000
4,000
2,000
0 -200
0
200
400
600
800
Temperature (deg F)
Envelope Specification The type of envelope to be calculated is specified on the Specification tab, shown below:
First, select either X-Y Phase Envelope or Pseudo-Ternary Phase Envelope in the Envelope Type area at the top of the tab. This selection will activate the corresponding data entry area. User Guide WinProp
Two-Phase Saturation and Phase Boundary Calculations 67
X-Y Phase Envelope
For X-Y phase envelopes, you must select which variable to use on the X-axis (independent variable) and the Y-axis (dependent variable). The choices are Temperature or Composition for the X-axis and Pressure or Temperature for the Y-axis. For a Pressure-Temperature (P-T) diagram select Temperature as the independent variable and Pressure as the dependent variable. For a Pressure-Composition (P-x) or swelling curve select Composition as the independent variable and Pressure as the dependent variable. Finally for a Temperature-Composition (T-x) diagram select Composition as the independent variable and Temperature as the dependent variable. The envelope is generated by taking steps in terms of the independent variable, and determining the corresponding value of the dependent variable on the phase boundary. Minimum and maximum values for the X- and Y- variables are specified along with the axis definitions. The calculation stops when any of these limiting values are exceeded. When composition is selected as the independent variable, minimum and maximum independent variable step sizes are also specified, as well as the upper and lower limits for the axis. P-x and T-x diagrams are generated by adding a fluid defined by the secondary composition on the last Composition form to the fluid defined as the feed for the envelope calculation. For P-T diagram the value entered in the Temperature area is taken as the initial starting point for the calculation on the upper saturation pressure curve. Two types of curve(s) can be generated, line(s) of constant mole fraction of the vapor phase or line(s) of constant volume fraction vapor phase. The latter are also known as quality lines. These are specified on the Construction Controls tab, shown below, on the table in the Quality/Mole Fraction Lines Specification area:
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All values should be between 0 and 1. A maximum of 25 such lines can appear on a single plot. By default a single value corresponding to vapor phase mole fraction equal to 0.0 is preselected. If x = 1.0 is selected and both an upper and lower dew point exist, the starting point on the upper dew point will be selected. If starting points on both upper and lower dew point curves is desired then select Trace from all potential starting points on the Construction Controls tab. The value entered in the Pressure area on the Specification tab, either a number or the selection Unknown may be used as the initial guess for saturation pressure at T = Ts if a 2 phase region cannot be found at T= T s by scanning the interval from P max to Pmin. For the majority of cases a value is not required for the Pressure. When composition is selected as the independent variable, both pressure and temperature must be entered, although the value corresponding to the dependent variable will be determined internally. In the unlikely scenario that this cannot be done the value entered for the dependent variable will be used as an initial guess in the saturation calculation. The initial composition is taken as that defined by the Feed specification for the envelope calculation. In the Quality/Model Fraction Lines Specification area, the values entered for Mole fraction vapor (Fv) or Volume fraction vapor (Vv) are used to define the lines that are generated on the phase envelope. You can add values by selecting a line in the table then clicking the Tools button to add or delete rows. If a critical point is encountered, the line corresponding to (1- F v) will also be calculated. For example, with F v=1, the entire phase boundary (starting on the dew point side) will be calculated. If a value is specified for volume fraction vapor, the quality line corresponding to Vv will be calculated. Again, if a critical point is encountered, the line corresponding to (1-Vv) will also be calculated. To calculate phase boundaries, select F v = 0.0 and/or 1.0 or Vv = 0.0 or 1.0. When tracing lines of constant volume fraction, an additional stopping constraint can be placed on the calculation by specifying minimum and maximum allowed values of vapor mole fraction. By default these values are set to –10 and +10 respectively, thus the calculation will not halt unless large nonphysical values of the vapor mole fraction are calculated. Pseudo-Ternary Phase Envelope
The first step in generating the pseudo-ternary phase envelope is the specification of the pseudo-components. When the Pseudo-Ternary Phase Envelope option is selected, a grid listing all of the components is displayed in the Pseudo-Ternary Phase Envelope area. The primary and secondary compositions are shown to assist the user in defining the pseudocomponents. Components are assigned to pseudo-components by entering the number 1, 2 or 3 in the Pseudo column. Pseudo-component 1 is at the lower left corner of the triangle, 2 is at the lower right, and 3 is at the top. The diagram is generated by locating the point on the diagram corresponding to the specified mole or volume fraction vapor for the feed composition. The composition of the phase in equilibrium with this phase is obtained from the K-values. A step in the construction is taken by adding fluid with the secondary composition, and the next point is calculated with this new composition. Note that different pseudoization schemes will result in different envelopes being generated. As for the X-Y diagram, minimum and maximum values for the mole fraction of secondary fluid can be specified, as well as minimum and maximum secondary fluid step sizes.
User Guide WinProp
Two-Phase Saturation and Phase Boundary Calculations 69
Pressure and temperature must be specified, as they are fixed for the ternary diagram. Mole fraction vapor, volume fraction vapor, minimum mole fraction vapor and maximum mole fraction vapor may be specified as discussed under X-Y Phase Envelopes.
Envelope Construction Controls The following are available through the Construction Controls tab: Maximum Number of Points
This value corresponds to the maximum number of points calculated on the phase diagram. Initial Step Size
The Initial step size controls the spacing between the calculated points on the envelope. Both positive and negative values may be used. For positive values, the diagram is traced initially in the direction of increasing x-values. For negative values, the diagram is initially traced in the direction of decreasing x-values. WinProp internally estimates the step size for subsequent points on the envelope. Independent Variable Interpolation Points
These correspond to x-values for which you want calculated y-values. Because the step size in the envelope calculation is automatic, these interpolation values must be entered to force calculations at desired x-axis values. The following is available through the Feed/K values/Output level/Stability tab: Stability Test
WinProp checks the stability of each phase for every calculated point on a phase envelope. The envelope generation routine can be set to terminate when instability is detected, or to continue calculations. Letting the calculation continue along unstable lines is sometimes useful, as it allows determination of two stable portions of a phase envelope that are connected by an unstable line.
Cricondenbar/Cricondentherm Calcul ation The cricondenbar corresponds to maximum pressure on the PT phase envelope whereas the cricondentherm corresponds to the maximum temperature. These are estimated in a two phase PT envelope construction (see Phase Boundary and Quality Line Calculations in this chapter) or can be calculated directly by selecting Calculations | Criconden--bar/-therm:
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An example data set for this option is cricon.dat . For Feed, K-values, Output level and Stability test level specifications, see the Common Data Required for All Options chapter. As initial guesses for pressure and temperature, you can specify Unknown or Previous (value from the previous calculation option), or type in the value of the initial guess.
Critical Point Calculation The phase-boundary and quality-line calculations estimate the critical point through interpolation. This method is efficient and yields both the phase boundary and critical points. However, if you want a direct calculation or want to match a critical point in a regression calculation, you should use the Critical Points Calculation option. The critical points calculation is invoked by selecting Calculations | Critical Points :
User Guide WinProp
Two-Phase Saturation and Phase Boundary Calculations 71
An example data set for this option is critical.dat . This option uses the calculation method of Heidemann and Khalil (1980). The required numerical data are the Lower dimensionless volume limit and the Upper dimensionless volume limit. These dimensionless volumes are equal to the ratios of molar volume v over the parameter b of the EOS. All critical points between these two volume limits are calculated. Default values for these limits are 1.0 and 5.0 respectively. You can enter the experimental critical pressure and temperature for regression purposes.
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Flash Calculations
Overview Flash calculations determine the split of a system at a given pressure, temperature and feed composition. The number of phases and the properties for each phase are calculated. WinProp can perform many types of flash calculations: 1. Two-phase vapor-liquid 2. Three-phase vapor-liquid_1-liquid_2 3. Three-phase vapor-liquid-aqueous 4. Four phase flash calculation (fluid phases only) 5. Multiphase flash calculations with a solid phase 6. Isenthalpic flash calculation In the above calculations, the fluid phases are modeled with an EOS, except for Calculation No. 3 where the component solubility in the aqueous phase is modeled by Henry's law. Calculation No. 5 can be used for modeling asphaltene and wax precipitation. Flash calculations performed in the single-phase region will yield a single-phase system. An option for single-phase calculation is also available in WinProp and is described in this chapter. Common input for two-phase flash, multiphase flash and asphaltene/wax modeling calculations is described below, followed by descriptions of each of the flash types.
Common Input f or Two-Phase Flash, Multi phase Flash and Asphal tene/Wax Mod ell ing Calc ul ati on s For Feed, K-values, Output level and Stability test level specifications, see the Common Data Required for All Options chapter. Flash calculations are performed at the pressure and temperature specified in the Calculations tab, in the text boxes labelled Pressure and Temperature. You can perform a series of calculations by specifying the Pressure Steps, Temperature Steps, or Mole Fraction Steps with the associated number of steps. The steps can be positive or negative. Step No. 1 corresponds to a calculation at the specified pressure and temperature or mole fraction. Specifying steps for the primary mole fraction allows calculations for a number of mixtures of the primary and secondary fluids.
User Guide WinProp
Flash Calculatio ns 73
When a series of flash calculations have been specified by setting temperature, pressure or mole fraction steps, plots of the phase properties can be generated. Specification of the phase properties (maximum of three) to plot is done on the Plot Control tab. When plotting is activated, steps can be specified in one or two of the variables: pressure, temperature and mole fraction. If steps are specified for only one variable, the plots are generated with that variable as the independent variable, and the phase property as the dependent variable. Up to 100 steps in the independent variable are allowed. When steps are specified for two variables, one variable is treated as a parameter variable, and curves of the phase property are displayed for each value of the parameter variable. Up to 8 steps in the parameter variable are allowed. If mole fraction steps are specified, mole fraction is always used as the independent variable. If pressure and temperature steps are both specified, pressure is used as the independent variable.
Two-Phase Flash Calcul ations This option is invoked by selecting Calculations | Two-Phase Flash from the menu:
An example data set is flash-2ph.dat . For specification of data on the Calculations and Plot Control tabs, see the Common Input for Two-Phase Flash, Multiphase Flash and Asphaltene/Wax Modelling Calculations section at the beginning of this chapter. Flash Type may be set to one of QNSS/Newton, Negative or Negative/Newton. Selecting QNSS/Newton specifies that the two-phase flash equations will be converged initially using
a Quasi-Newton successive substitution algorithm, followed by Newton’s method to refine the roots. If the system is in the single-phase region, properties for that phase will be reported, and k-values will not be calculated. When the Negative flash is selected, the QNSS algorithm 74
Flash Calculations
User Guide WinProp
is used without further refinement of the roots. If the system is in the single-phase region, properties for two phases will be reported, with one phase being present in a negative (non physical) amount. This option allows generation of k-value estimates outside of the two phase region. The Negative/Newton method will use the same method as QNSS/Newton but will still converge the flash outside of the single-phase region to generate K-values as for the negative flash method. Experimental data to be included in a regression calculation are entered on the Experimental and Experimental K-values tabs. Data on the Experimental tab include mass densities, mole fractions, volume fractions, compressibility factors, and viscosity of both the vapor and liquid phases. Experimental K-values are entered on the Experimental K-values tab.
Multiphase Flash Calcul ations This option is invoked by selecting Calculations | OGW/EOS Multiphase Flash :
An example data set is flash-3ph.dat . For specification of data on the Calculations and Plot Control tabs, refer to the Common Input for Two-Phase Flash, Multiphase Flash and Asphaltene/Wax Modelling Calculations section at the beginning of this chapter. The type of multiphase calculation to be performed is selected through Flash Type at the bottom of the Calculations tab. The 3-phase and 4-phase calculations use the techniques described in Nghiem and Li (1984). This is a stage-wise procedure where the number of phases is gradually increased. All phases are modeled with an EOS. The number of phases selected in User Guide WinProp
Flash Calculatio ns 75
Flash Type corresponds to the maximum number of phases. Thus, selection of a 4-phase
calculation for a two-phase system will yield the same results as a two-phase flash calculation. The Oil-Gas-Water (OGW) calculation involve a three-phase calculation where the vapor and liquid phases are modeled with an EOS while the aqueous phase is modeled with Henry' law. An example data set is flash-ogw.dat . As the EOS was developed for gas-like hydrocarbon systems, it may not model accurately the aqueous phase. Li and Nghiem (1986) recommended the use of Henry's law constants for component solubility in the aqueous phase. The fugacity coefficient of Component i in the aqueous phase φiw is given by lnφiw =ln( H i / p) where Hi is Henry's law constant of Component i. H i for each component may be entered on the Henry's Law tab:
If Hi is not specified, WinProp will estimate it internally. See the Components chapter for more information on Henry’s constants. Experimental data for 3-phase and OGW calculations may be entered on the Experimental tab. These include mass densities, mole fractions, volume fractions, and viscosities of the different phases. When the flash type is set to OGW, experimental data for the solubility of components in the aqueous phase may be entered on the Exp. Solubility tab. The units available for specifying the component solubilities are mole fraction, weight fraction, moles per mole of water, weight per weight of water, SCF per Std. bbl of water and std m 3 per std m3 of water. Enter a value of “-1” in the table to exclude that data point from the regression. 76
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User Guide WinProp
For the OGW flash, experimental data may also be entered for component mole fractions in the vapor and liquid phases, and for gas-water and liquid-water k-values. Note: When a regression is being performed on aqueous phase solubility parameters, all
OGW flashes specified within the regression block must be at the same temperature. WinProp does not accept experimental data for 4-phase calculations.
Asphal tene/Wax Mod ell ing Theoretical Background Thermodynamic Model
The precipitation of asphaltene and wax phases is modelled using a multiphase flash calculation in which the fluid phases are described with an equation of state and the fugacities of components in the solid phase are predicted using the solid model described below. The solid phase can consist of one or more components. The approach for modeling asphaltene and wax precipitation is described in detail in Nghiem et al. (1993, 1996) and Kohse et al. (2000). The precipitated phase is represented as an ideal mixture of solid components. The fugacity of a precipitating component in the solid phase is: ln f s = ln f s*
−
v s p − p tp
+ R
T
∆H tp 1 1 ∆C p − − R R T T *
− p tp − * T T * 1 1 ln − Ttp − * T T T p
*
where f s is the fugacity at pressure p and temperature T, f s* is the fugacity at pressure p * and temperature T*, vs is the solid phase molar volume of the component, ∆C p is the solid-liquid heat capacity difference, ∆Htp is the heat of fusion at the triple point, p tp and T tp are the triple point pressure and temperature, and R is the universal gas constant. For isothermal predictions, this equation can be simplified to give: ln f s
= ln f s* + v s ( p − p * ) / RT
Characterization of the Solid Forming Components
The crucial step in modeling wax and asphaltene precipitation is the characterization of the solid forming components, both in solution and in the solid phase. It was found that by splitting the heaviest components into two components, a non-precipitating and a precipitating fraction, good quantitative match with experimental data was obtained. This has been independently verified for both wax and asphaltene precipitation problems. Irreversible Asphaltene Calculations
WinProp has the capability to separate asphaltene precipitate into reversible and irreversible parts. This can be useful for simulating laboratory forward or reverse contact experiments with a series of asphaltene flash calculations.
User Guide WinProp
Flash Calculatio ns 77
Asphaltene is described as a reversible solid (S1) and an irreversible solid (S2). The conversion of S1 to S2 is described by a simple chemical reaction: S1 ←→ S 2 K The rate of formation of S2 is given by: r = k 12 C1 − k 21C 2
where C1and C2 are the molar concentrations of S1 and S2 respectively. At equilibrium, the rate is zero and the following equilibrium constant can be derived: K =
k 21 C1 = k 12 C 2
The mole fraction of reversible solid relative to the total amount of solid is: x1
=
C1 C1 + C 2
=
K K + 1
and the mole fraction of irreversible solid is x2 =
C2 1 = C1 + C 2 K + 1
The procedure for simulating forward and reverse contact experiments is as follows: The first stage of the experiment can be modeled using the solid flash with the first stage oil and gas mixture. The total amount of solid precipitate will be determined from the thermodynamic model. At the completion of this calculation, the amounts of reversible and irreversible solid (x1 and x2) can be calculated from the above equations with a user-specified value of K. K = 0 indicates that all of the solid is irreversible, K = 1 gives equal amounts of reversible and irreversible solid, and K >> 1 implies that the solid is essentially all reversible. For backward contacts, the feed to the next flash calculation is defined by taking the liquid plus the reversible solid, and combining it with injection gas. The irreversible solid is removed from the system for this flash. For forward contacts, the equilibrium vapor phase with no asphaltene is combined with fresh oil. Therefore, for forward contacts, the degree of irreversibility will not affect the calculations.
Input Data - Asphaltene/Wax Modelli ng You can model asphaltene or wax precipitation by selecting Calculations | Asphaltene/Wax Modelling:
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The approach is described in detail in the references cited above. It is recommended that you go through the example data sets solid-asph1.dat , solid-phenanthrene.dat , solid-wax.dat and solid-asph2.dat to get familiar with the approach. For specification of data on the Calculations and Plot Control tabs, refer to the Common Input for Two-Phase Flash, Multiphase Flash and Asphaltene/Wax Modelling Calculations section at the beginning of this chapter. Additional plotting options are available on the Asphaltene/Wax Modelling | Plot Control tab. If X-Y Plots is selected, the amount of solid in terms of weight percent precipitated can be plotted in addition to three other phase properties. Selecting Pseudo-Ternary Phase Diagram in the Plot Control tab allows creation of a triangular diagram, displaying the results of flash calculations in terms of phase split (e.g. liquidvapor, solid-liquid-vapor, and solid-liquid) along dilution lines:
User Guide WinProp
Flash Calculatio ns 79
The first step is to assign each component to one of three pseudo-components by entering the number 1, 2 or 3 in the column labelled “Pseudo” in the table. Pseudo-component 1 is at the lower left apex of the triangle, pseudo-component 2 is at the lower right and 3 is at the top. Definition of the dilution lines is done by first selecting which two pseudo-components will be held at a fixed ratio along each dilution line. For example, setting pseudo-components A to 1 and B to 2 indicates that the base of the dilution lines will be along the bottom of the diagram, between apexes 1 and 2, and the lines will terminate at the top of the diagram at apex 3. The molar ratios of the two pseudo-components along each dilution line are then defined by entering the mole fraction of pseudo-component B for each desired line in the table under Dilution Line Definition. The number of flashes desired on each dilution line must also be specified.
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On the Ref. State tab (shown as follow), the following information is entered:
Number of Components in Solid
Of the Nc total components, the user may specify the last N 1 as the number of solid forming components. The default is set to 1, that is the only component number N c can precipitate. Once this number is specified, the component number and name for all the precipitating components are shown on the first and second columns of the table on this tab. Depending on the method selected for computing the reference fugacity, columns 3-5 of this table will also be updated automatically. Calculation Method Identifier
The three-phase flash algorithm performs flash and stability calculations in an alternating sequence. The calculation begins with a stability test on the single-phase fluid. If the phase is unstable, a two-phase flash calculation is performed, followed by a stability test on the converged two-phase system and so on. Three calculation methods are available. They differ in the sequence in which the stability tests are performed. In Method 1, the stability test is performed first with respect to the solid phase. In Method 2 (default), the stability test is performed with respect to all fluid phases prior to a stability test with respect to the solid phase. Method 3 is a special case of Method 1; with Method 3, a stability test on the converged two phase fluid-solid system is not performed. Thus, Method 3 is more efficient but not as rigorous as Method 1. For most cases, Methods 1 and 2 converge to the same results. In exceptional cases, it has been found that only one method converged while the other one failed.
User Guide WinProp
Flash Calculatio ns 81
Reference Fugacity [ln (solid fugacity (atm))]
Four options are available for specifying Reference fugacity: The reference fugacity at the specified pressure and temperature is set equal to the fugacity of the solid forming component after the system has converged to a single liquid phase or a two-phase vapor-liquid system. Use the value for the reference fugacity from a previous multiphase solid flash Previous calculation. This is used for wax only. The reference fugacity at the specified pressure and Lcorrelate temperature will be correlated with the pure component liquid fugacity at the same pressure and temperature. This selection implies that the value of the natural logarithm of the reference User Input fugacity in units of atmospheres as well as the corresponding reference pressure and temperature will be input by the user for each precipitating component on the table provided. The user must select this option before the values can be entered in the table If the reference fugacity specification is set to Calculate, solid onset pressures for the same mixture but at different temperatures may be specified in the Additional Onset Points table, which will be displayed at the bottom of the Ref. State tab. ∆C p and ∆Htp (optionally vs) can be calculated so the solid model will match these onset points. Calculate
Additional Onset Points
Solid onset pressures at different temperatures may be used to calculate parameters in the solid model for performing temperature-dependent precipitation predictions. The requirements for doing this calculation are:
•
Two, three or four solid precipitation onset pressures at different temperatures must be known for one fluid composition.
•
The solid phase must be modeled with a single component, as is normally done for asphaltene precipitation modeling. The pressure and temperature for one of the onset points must be entered on the Calculations tab as the pressure and temperature for the flash. This will be used as the reference condition, and will define the reference fugacity. Calculation of the other parameters will depend on the number of additional onset points entered, as described below. Normally v s is adjusted to match a known amount of solid at a given condition (bulk precipitation experiment), otherwise it will default as described under Solid-Phase Molar Volume.
82
•
1 additional onset point – ∆C p is set to the user-input value or defaults to zero. ∆Htp is calculated to match the specified onset point.
•
2 additional onset points – ∆C p and ∆Htp are calculated to match the specified onset points.
•
3 additional onset points – ∆C p, ∆Htp and vs are calculated to match the specified onset points. This is not normally done, as it is preferable to use v s to match a bulk precipitation experiment.
Flash Calculations
User Guide WinProp
Reference Pressure (psia | kPa | kg/cm2)
This corresponds to the reference pressure for calculating reference fugacity. This pressure is required only if a reference fugacity is actually entered. If Field units is selected enter value in psia, for SI units in kPa and for modified SI units in kg/cm 2. When the Calculate, Previous or Lcorrelate options are selected for the reference fugacity, the reference pressure is set internally by the program and need not be entered on the table. Reference Temperature ( C for SI or F for field units)
This corresponds to the reference temperature for calculating the reference fugacity. This temperature is required only if a reference fugacity is actually entered. When the Calculate, Previous or Lcorrelate options are selected for the reference fugacity, the reference temperature is set to appropriate values internally by the program and need not be entered on the table. Solid-Phase Molar Volume (l/mol)
This corresponds to the component solid-phase molar volume for the calculation of the component solid-phase fugacity. If the molar volume is not specified, the following value is assigned:
•
If the reference fugacity option is Calculate, the solid-phase molar volume is calculated from the EOS, unless 3 additional onset points have been specified.
•
If the reference fugacity option is Lcorrelate then the molar volume is obtained from a correlation by Won (1986).
•
If the reference fugacity option is Previous, the solid-phase molar volume from the previous calculation is used.
•
If a value for the reference fugacity is entered, the solid-phase molar volume is calculated from the EOS.
Heat Capacity (cal/K/mol)
This corresponds to the component solid-liquid heat capacity difference for calculation of the component solid-phase fugacity. If this quantity is not explicitly specified for each precipitating component, the following value is assigned:
• If the reference fugacity option is Calculate, the solid-liquid heat capacity difference defaults to zero, unless 2 or more additional onset points have been specified.
•
If the reference fugacity option is Lcorrelate then the heat capacity difference is obtained from a correlation by Pedersen (1991).
•
If the reference fugacity option is Previous, the solid-liquid heat capacity difference from the previous calculation is used.
•
If a value for the reference fugacity is entered, the solid-liquid heat capacity difference defaults to zero.
Heat of Fusion (cal/mol)
This corresponds to the component heat of fusion for the calculation of the component solid phase fugacity. If this quantity is not explicitly specified for each precipitating component, the values are obtained from a correlation by Won (1986). User Guide WinProp
Flash Calculatio ns 83
Triple Point Pressure (psia, kPa orkg/cm2, as defined in Titles/EOS/Units)
If the triple point pressure for each precipitating component is known then these may be specified under the column heading Triple Pres. Enter Triple Pres. in psia, in kPa or in kg/cm2, as indicated in the table header. If the triple point pressure is not known then the default is a value of zero, which is realistic for high molecular weight compounds. Triple Point Temperature ( C or F, as defined in Titles/EOS/Units)
If the triple point temperature for each precipitating component is known then these may be specified under the column heading Triple Temp. If not known then the values are estimated from an internal correlation that was developed by Won (1986). Ratio of reverse over forward rate for conversion to irreversible solid
This is the equilibrium constant “K” described above under Irreversible Asphaltene Calculations.
Single-Phase Calculation A flash calculation in the single-phase region yields a single-phase system. However, if the fluid is known a priori to be single phase, its properties can be calculated directly with the single-phase calculation option. This option is invoked by selecting Calculations | Singlephase Fluid. Note: With this option, WinProp assumes single-phase for all calculations even if the fluid is
multiphase. An example data set for this option is singlephase.dat .
Isenthalpic Flash Calcul ations Theoretical Backgroun d Isenthalpic flash calculations correspond to finding the temperature, phase splits (phase mole fractions) and phase compositions, given the pressure, composition and enthalpy of the feed, together with the net enthalpy added to the system (Agarwal et al, 1988). For isenthalpic flash calculations, in addition to the material and phase equilibrium relations applicable to isothermal flash calculations, there is an energy balance equation, i.e. n p
g n p
≡ H − H spec = ∑
j =1
nc
F j
∑ (y ijh ij ) − H spec = 0
i =1
where Hspec is the specified molar enthalpy of the system and h ij is the partial molar enthalpy of Component i in Phase j which is also obtained from an EOS. Calculation Method Identifier
Two schemes for isenthalpic flash calculations are discussed below. The final scheme is a hybrid of these two schemes.
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Scheme 1
Scheme 1 consists of performing a series of multiphase isothermal flash calculations by adjusting the temperature to satisfy the energy equation. In other words, the temperature is varied in an outer loop, and the isothermal flash equations are solved in an inner loop. Techniques for solving the multiphase isothermal flash equations are taken from Nghiem and Li (1984) and Nghiem et al (1985). The isenthalpic flash calculations are initiated by an isothermal flash calculation at the specified feed composition z, the specified pressure p and an initial guess for temperature, T(0). A new temperature T(1) is then determined from the energy equation by assuming that the phase mole fractions, compositions and specific enthalpies are constant. With T(0) and T(1), a secant method for solving the energy equation is set up in the outer loop. As discussed later, Scheme 1 does not work for systems with a degree of freedom equal to unity, for example, a one-component two-phase system or a two-component three-phase system. Scheme 2
Scheme 2 basically follows Michelsen's approach (Michelsen, 1987), but the implementation is different. This scheme is a stage-wise procedure where the system is assumed to be initially single-phase, and where the number of phases is increased if necessary between iterations. Furthermore, this scheme attempts to converge the material balance equation, the energy balance equation and the equilibrium equation in a sequential manner. This method also works for systems with a degree of freedom equal to unity. Hybrid Scheme
When the Hybrid Scheme is specified, the flash calculation uses iterations of both Scheme 1 and Scheme 2. Users can specify the number of iterations of Scheme 2 to be used for every iteration of Scheme 1. Special Considerations
Isenthalpic flash calculations are more complex than isothermal flash calculations because of the lack of the a priori knowledge of temperature (and phases) and because of the presence of narrow boiling mixtures. The implications of these two factors are discussed in the following sections. Phase Information
Since temperature is not known a priori in isenthalpic flash calculations, the traditional stability analysis of the Gibb's free-energy surface (Nghiem and Li, 1984) cannot be used to determine the number of phases that actually exist at convergence. A stability analysis can only give the number of phases at the initial temperature estimate, which may not be the same as the number of phases at convergence. This leads to the appearance and disappearance of phases during the iterative process. This does not create any difficulties for Scheme 1 but could cause convergence problems for Scheme 2. Narrow-Boiling Systems
Narrow-boiling systems are those where the enthalpy changes drastically for a small change in temperature during phase transition. Although many multicomponent fluids exhibit this behavior, a single-component fluid in the two-phase region and two-component fluid in the three-phase region are extreme examples of narrow-boiling mixtures. User Guide WinProp
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From the phase rule, the degree of freedom F of a system with n c components and n p phases is F = nc+ 2 - n p Thus for a single-component system in the two-phase region, F = 1. This implies that, if the pressure is fixed, the two-phase temperature is also fixed. In other words, pressure and temperature are dependent on each other in the two-phase region. The enthalpy for this system is determined by the phase split in the two-phase region. The same analysis applies to a two-component system in the three-phase region. Effect of Narrow-Boiling Systems on the Calculations
Scheme 1 is not applicable to systems with a degree of freedom equal to unity (e.g. onecomponent two-phase systems or two-component three-phase systems) because it attempts to satisfy the energy equation by adjusting the temperature. For these systems, the energy equation can only be satisfied by adjusting the phase split; otherwise, Scheme 1 works for any multicomponent systems with n c ≥ 3 even if they exhibit narrow-boiling behavior. Calculation Procedures
A hybrid scheme, where five Scheme-2 iterations are performed for every Scheme-1 iteration, is very stable and robust. Of course, only Scheme 2 is used for one and two component systems.
Input Data - Isenthalpic Flash Add this option to your data set by selecting Calculations | Isenthalpic Flash :
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A number of examples are provided in the template test bed. These cases are named flashisenth1.dat through flash-isenth3.dat and can be found under the template (.tpl) directory. For Feed, K-values, Output level and Stability test level specifications, see the Common Data Required for All Options chapter for further information Flash calculations are performed at the pressure specified in the Pressure field. Enter a value for the enthalpy in the Enthalpy field. In the Temperature field, enter an initial guess for the temperature. This initial guess for the temperature is required input and must be specified by the user. If you select the Hybrid Scheme, you will be able to enter the number of iterations of Scheme 2 to be used for each iteration of Scheme 1. Calculation Method Identifier
As detailed above in the Calculation Method Identifier subsection of the Theoretical Background section, two methods are implemented to solve the nonlinear set of equations corresponding to isenthalpic flash. A hybrid scheme in which five Scheme-2 iterations are performed for every Scheme-1 iteration is very stable and robust, and is the default choice. If Hybrid Scheme is selected, the integer number entered in the Calculation Model field indicates the number of iterations of Scheme 2 to be used for every iteration of Scheme 1. A value of zero therefore implies the selection of Scheme 1 exclusively. A value equal to or greater than 101 will be interpreted as the selection of Scheme 2 alone.
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Thre hr ee-Phase -Phase Bound Bou nda ary Calcul lc ula ation ti on
Background For systems that exhibit three-phase behavior, there exist conditions where one of the phase mole fractions goes to zero. Under these conditions, there are two phases in equilibrium with an infinitesimal amount of a third phase. The locus of all these conditions corresponds to a three-phase boundary. Nghiem and Li [21] describe calculation techniques for constructing the three-phase boundary; these are extensions of the two-phase boundary calculations described in a separate chapter. You can calculate the following envelopes:
• Pressure-Temperature (PT) diagram • Pressure-Composition Pressure-Composition (PX) diagram • Temperature-Composition Temperature-Composition (TX) diagram
Input Data The three-phase boundary calculation is invoked by selecting Calculations | Three-phase Envelope. Examples of three-phase PT envelope and PX envelope e nvelope are in envel_3ph-pt.dat and envel_3ph-px.dat respectively. respectively. This calculation requires good initial guesses for convergence. Therefore the pressure, temperature, and K-values must be obtained from a previous three-phase flash flash calculation near the boundary as in envel_3ph-pt.dat , or entered by the user as in envel_3ph-px.dat .
Envelope Envelope Specifi Specifi cation Tab Tab Specify the type of envelope (PT, PX, or TX) to be calculated by selecting the variables for the x- and y-axes on this tab. For the PT diagram the composition is fixed. The composition is determined based on the data entered on the Composition form and the feed specification entered on the Feed/Output/Stability tab. For the PT envelope, also specify the first point to be calculated by entering a value for the x-variable and an estimate for the y-variable in the combo boxes labelled labelled Pressure and Temperature respectively. The x-variable and y-variable are also called independent and dependent variables respectively. The choices for the combo box for the y-variable are: Previous, or enter a value explicitly. For PX and TX diagrams the composition changes as the envelope is traversed. The x-axis variable in these cases is the mole fraction of the secondary fluid. The initial value of this mole fraction is as defined by the feed specification. For the PX diagram, enter the initial guess for the pressure in the combo box labelled Pressure. Also enter a value for the temperature (fixed) in the combo box labelled Temperature.
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Similarly for the TX diagram, enter an initial guess for the temperature in the combo box labelled Temperature and a value for the pressure (fixed) in the combo c ombo box labelled Pressure. For all cases an initial guess for the mole fraction of either the vapor phase or the second (intermediate) liquid phase is also required. For the boundary corresponding to zero vapor phase, enter a value value for the “second “second liquid” or intermediate phase mole mole fraction. For For the boundary corresponding corresponding to zero second second liquid phase, phase, enter a value value for the vapor phase phase mole fraction initial guess. If Use values from previous calculations is selected, WinProp will calculate the boundary corresponding to the phase with the lowest mole fraction (in the previous calculation) calculation) equal to zero. Defaults for the maximum and minimum values for the x- and y-variables can be overridden by entering values values in the appropriate appropriate text boxes. The calculations stop when the maximum maximum or minimum values are exceeded or when the maximum number number of points has been calculated (see Envelope Construction Controls Tab) Tab ). The calculations will also stop if the mole fraction of any phase falls outside the limits specified by the values in the text boxes Minimum phase mole frac and Maximum phase mole frac. The default values of –10 and 10 for the minimum and maximum are chosen such that the calculation will not stop unless large non physical values of the phase mole mole fractions are encountered. encountered. The Envelope Specification tab corresponding to envel_3ph-px.dat is is shown below:
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Envelope Envelope Constructi on Controls Tab Tab
Maximum Number of Points
This value corresponds to the maximum number of points calculated on the phase diagram. Initial Step Size
The Initial step size controls the spacing between the calculated points on the envelope. Both positive and negative negative values may may be used. For positive values, values, the diagram is traced initially initially in the direction of increasing x-values. For negative values, the diagram is initially traced in the direction of decreasing x-values. WinProp internally estimates the step size for subsequent points on the envelope. Average Number of Iterations
This value is used to adjust the distance between two consecutive points on the diagram. The distance is increased if the actual ac tual number of iterations is less than the entered values, and is decreased in the opposite case. Independent Variable Interpolation Points
These correspond to x-values for which you want calculated y-values. Because the step size in the envelope calculation is automatic, these interpolation values must be entered to force calculations at desired x-axis values.
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Initi al K-Values Tab Tab
The estimates of the K-values for the first point on the boundary can be from f rom a previous calculation, or entered in the appropriate table as shown in the above figure.
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Component Splitting and Lumping
Overview Our experience shows that two representations of the components are normally required in the modeling of the phase behavior of reservoir fluids. In the first stage, the fluid system is represented by a large number of components (e.g. C1, C2, C3, ..., C 29, C30+). Simple calculations such as saturation pressure calculations are performed on this many-component system to verify the adequacy of the EOS. We found that in most cases the EOS can predict accurately the saturation pressure with only minor adjustment to the Hydrocarbon Interaction Coefficient Exponent (HICE). See the Regression chapter for more details. This manycomponent representation is not practical for compositional simulation because of the excessive run time and memory requirements. The second stage involves the lumping of the many-component system into fewer components (e.g. 10). Reservoir fluids typically consist of pure, well-defined components such as CO 2, N2, C1, C2, etc., and many hundreds of heptanes and heavier components (C 7+). The laboratory analysis of a reservoir fluid includes generally a gas chromatograph analysis of the C 7+ fraction into Single Carbon Number (SCN) fractions up to C 30+ for example. Characterization of the C 7+ fraction as a number of pseudo-components is accomplished using WinProp’s Plus Fraction Splitting and Component Lumping calculation options. If a full extended analysis is available with mole fraction, MW and SG or T b given for each SCN fraction, the SCNs may be entered as user components directly on the Component Selection/Properties form. If a complete analysis is not available, the Plus Fraction Splitting calculation is used to define a distribution function relating mole fractions to molecular weights of the C7+ fraction. Three distribution functions are available in WinProp: exponential, two-stage exponential, and gamma distribution. The implementation of the distribution functions depends on the experimental data available. If a partial extended analysis is given (e.g. only MW and mole fraction of the SCN fractions) and one of the exponential distribution types is selected, the splitting calculation does not use the distribution function. SG and T b values for the SCN fractions are determined from correlations based on the SG and MW of the plus fraction. Subsequently, critical properties of the SCNs may be generated. After the splitting, the SCNs representing the C 7+ fraction can be lumped into fewer components based on K-values estimated from Wilson's correlation using the Lee-Kesler mixing rules, (Lee and Kesler [15] ).
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Component Splitting and Lumpin g 93
If a partial extended analysis is given and the gamma distribution is selected, the α parameter in the distribution is determined by minimization to obtain the best fit of the distribution to the experimental data. At this point, the analysis may be extended by using the distribution function to generate mole fraction and molecular weight data for SCNs beyond the last fraction in the experimental analysis. SG, T b and critical properties of the SCNs may be generated and lumping to fewer components may be done as for the exponential distribution case. Alternatively, the Gaussian quadrature technique may be used to determine MW and mole fractions of the pseudo-components from the distribution function. Correlations are then used to generate the SG, T b and critical properties of the pseudo-components directly, rather than using mixing rules. If no extended analysis is available, i.e. only mole fraction, SG and MW of the C 7+ fraction are known, the parameters in the chosen distribution function are adjusted to match the known data. The distribution function is then used to generate SCN mole fraction and MW. Once this is done, the characterization may proceed as described for the partial extended analysis cases above. Due to the larger number of adjustable parameters in the gamma distribution, the α parameter must be specified if no extended analysis is available. If it is not input by the user, the program will estimate a value for this parameter. The Component Lumping calculation may be specified in a data set if the SCNs were not lumped within a splitting calculation, or to further reduce the number of components. The lumping scheme may be input by the user, or the program can generate the pseudocomponents using an internal algorithm. We recommend specifying a lumping scheme based on the K-values of the many-component system at a prevailing condition in the reservoir, e.g. the saturation condition.
Characterizatio n of Multip le Related Sampl es Multiple related samples can be characterized using the gamma distribution and Gaussian quadrature techniques as described by Whitson et al [40]. This results in a single set of C 7+ fraction pseudo-components for all samples. Plus fraction MW and SG for each sample are matched by determining the correct mole fractions of each pseudo-component for the sample. Data for each sample is entered in exactly the same manner as for single sample characterization. The same type of data need not be entered for each sample; i.e. an extended analysis may be entered for one sample and only plus fraction SG, MW and mole fraction for another sample.
Splitting the "Plus" Fraction This option is invoked by selecting Characterization | Plus Fraction Splitting. An example data set for this option is split-mwsg_plus.dat .
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General splitting model controls are entered on General tab of the Plus Fraction Splitting calculation form as shown and described below.
Distribution Function Type
Three choices are available for the distribution function for splitting the plus fraction: Exponential
Exponentially decreasing function appropriate for gas condensates and lighter fluids
2-Stage Exponential
Approximation to the gamma function suitable for black oil type fluids
Gamma
Three-parameter gamma distribution suitable for all fluid types
Number of Fluid Samples
If the gamma distribution is chosen, up to 8 related fluid samples may be characterized simultaneously. If the exponential distributions are chosen, this text box is not enabled. First Single Carbon Number in Plus Fraction
Enter the carbon number of the lightest SCN in the plus fraction (e.g. enter 6 to characterize a C6+ fluid fraction). Number of Pseudo-Components
The SCNs can be used as is in subsequent calculations or lumped into pseudo-components right after the splitting procedure. The following options are available: No lumping Determined internally Input value
User Guide WinProp
The SCNs will be used as is. WinProp will estimate internally the number of pseudocomponents for the plus fraction. Specify the desired number of pseudo-components.
Component Splitting and Lumpin g 95
When using the gamma distribution and Gaussian quadrature without extended analysis, the number of pseudo-components cannot be estimated via correlation and will be set equal to 3. Lumping Method
Log(K) lumping is available when characterizing a single sample with any of the distribution functions. Gaussian quadrature lumping may be used with the gamma distribution, and is required for characterizing multiple samples. Log(K) lumping defines pseudo-components as having equal ranges of log(K). Gaussian quadrature lumping defines pseudo-components via analytical integration of the gamma distribution. Critical Properties Correlation
Three correlations are available to calculate the critical properties of the SCNs. 1. Lee-Kesler (Kesler and Lee [12]) 2. Riazi (Riazi and Daubert [34] ) 3. Twu (Twu [36]) On the Distribution tab, shown below, parameters relating to the chosen distribution are entered.
Three of these properties are common to both exponential and gamma distribution types, as follows. SCN Fraction MW Interval
This corresponds to the interval in molecular weight for each single carbon number group. For the gamma distribution, if a variable MW is selected this value is ignored. The default is 14.026. 96
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“Bias” Parameter for SCN MW End Points
This parameter is used for setting the minimum molecular weight for the plus fraction distribution. A value of 0 means that the minimum MW will be equal to the normal alkane MW of the same carbon number as the first SCN fraction in the plus fraction. A value of 1 means that the minimum MW will be equal to the normal alkane MW of one lower carbon number than the first SCN fraction in the plus fraction. The default value is 0.75. Distribution Function Cutoff
This parameter is used in determining the number of pseudo-components for lumping. This calculation requires specification of a maximum SCN number. Setting the cutoff to 1.0 means that the maximum SCN number will be set equal to the last SCN number in the analysis. This often leads to over-prediction of the required number of pseudo-components. Setting the cutoff less than 1.0 indicates that the maximum SCN number will be taken as the one at which the ratio of the sum of the individual SCN mole fractions to the total plus fraction mole fraction exceeds the cutoff. The value should be less than 1. The default is 0.95. Parameters specific to the exponential distributions are: Mole Fraction of Component Preceding Plus Fraction
This value is used to set the “Y-Axis” intercept of the two-stage exponential distribution function. For C6+ fraction characterization, this value should be set equal to the mole fraction of the C5 components, for C7+ fraction characterization, this value should be set equal to the mole fraction of the C6 components, etc. “Y” Axis Intercept of the Distribution Function
This is usually set equal to the mole fraction of the component preceding the plus fraction (default). Parameters specific to the gamma distribution are: SCN MW Interval Type
When fitting the gamma distribution to extended analysis data, the SCN fractions can have fixed or variable intervals in molecular weight. Choosing Constant sets the MW interval equal to the value entered under SCN fraction MW interval. Choosing Variable (match mole fraction) or Variable (match weight fraction) indicates that the upper MW boundary of the SCN fraction is varied until either the experimental mole fraction or the experimental weight fraction (default) of the SCN is matched. Eta Parameter (Minimum MW in Distribution)
The eta (η) parameter specifies the minimum molecular weight in the gamma distribution. By default, it will be calculated as described under “Bias” Parameter for SCN MW End Points.
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MW of Heaviest Pseudo-Component
The choices for molecular weight of the heaviest pseudo-component are No Restriction, Internal Default or entering a value. Specifying No Restriction implies no upper limit in MW on the gamma distribution, and is not recommended. It leads to prediction of very high molecular weights for the heaviest pseudo-component. The default setting obtained by selecting Internal Default sets the heaviest pseudo-component MW equal to 2.5 times the MW of the plus fraction. If multiple samples are used and No Restriction is selected, it will automatically be reset to Internal Default. SG-Tb-MW Correlation
When Gaussian quadrature is used with the gamma distribution, the following correlations are available for determining pseudo-component boiling point from specific gravity and molecular weight. 1. Twu (Twu [36]) 2. Goossens (Goossens [7]) 3. Riazi (Riazi and Daubert [34] ) Characterization Factor
There are four options available for defining the characterization factor that is used to calculate specific gravity of the pseudocomponents once the molecular weight is known: 1. Whitson (default) – gives good results for most fluids. 2. Watson (UOP) – similar to Whitson correlation, but will use the selected SG-TbMW correlation to determine Tb. 3. Soreide – characterization factor based on analysis of database of conventional oils and condensates. 4. Jacoby – the Jacoby aromaticity factor can be useful for gas-condensate systems. Characterization Factor Variation
By default the characterization factor for all pseudocomponents is assumed to be equal to the average characterization factor for the entire plus fraction. Alternatively, the method of Haaland can be used to define the characterization factor of each pseudocomponent as a function of the average characterization factor and the MW of the component. The controls available for determining gamma distribution parameters by minimization are: Residual Value
The choices for residual value depend on what is selected under SCN MW interval type. The residual value setting indicates what experimental data for each SCN is used in defining the error function to be minimized. The choices are Molecular Weight, Mole Fraction and Weight Fraction. If a constant MW interval is chosen, then molecular weight is not available as a choice of residual value. Similarly, if a variable MW interval is chosen to match the mole fraction, then mole fraction is not available as a choice of residual value. The default is to vary the MW interval to match the weight fraction of the SCN, and adjust the distribution α parameter to minimize the error function defined in terms of the molecular weights.
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Residual Type
The choices for residual type are Sum of Squares, Chi Square Goodness-of-Fit Test or Sum of Scaled Squares. The default is sum of squares. For most applications, the difference in minimization results between the residual types will be small. Final SCN Fraction Data
The residual calculation can be specified to include or not include the data from the final SCN fraction in the analysis. On each Sample tab, shown below, the properties of the plus fraction are entered. The number of sample tabs appearing is set according to the Number of Fluid Samples entered on the General tab.
If extended analysis data is available from a true or simulated boiling point (distillation) analysis, the data can be entered in the table on the Sample tab. In column 2 enter the mole fraction of each fraction. In column 3 enter the average molecular weight of the fraction. Note that if any extended analysis data are to be entered, mole fraction and molecular weight are required for each cut. If data is available then values for the specific gravity can be entered in column 4 and normal boiling point in °C in column 5. Please note that if data for normal boiling point is entered then data for specific gravity must also be entered. Sample data sets with extended analysis data are split-mw_analysis , split-mwsg_analysis and split-mwsgtb_analysis . User Guide WinProp
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Number of SCN Fractions
If this entry is left blank, the value will default to the number of fractions in the analysis, or to 25 if there is no extended analysis. If the exponential distributions are used with extended analysis, and a value for number of SCN fractions is entered, it will be ignored. If the gamma distribution is used with extended analysis, and a value for number of SCN fractions is entered that is greater than the number of fractions in the analysis, the analysis will be extended using the distribution function to the specified SCN number. MW+
Molecular weight of the plus fraction must be entered in the text box unless extended analysis data is given. SG+
Specific gravity of the plus fraction must be entered in the text box unless SG data is given in the extended analysis table. Z+
Mole fraction of the plus fraction must be entered in the text box unless extended analysis data is given. If one of the exponential distribution function types is selected then the following data entry box will be available: Slope
This is the slope of the exponentially decreasing curve of the distribution function. If not specified then it is determined internally based on data for a typical oil. If the gamma distribution function is selected then the following data entry box will be available: Alpha
This parameter is analogous to the slope parameter used for the exponential distribution types. If α>1, the distribution has a peak in mole fraction for an SCN greater than the initial SCN in the distribution. If α=1, the gamma distribution reduces to an exponential distribution, and if α<1 the function decreases more rapidly than an exponential distribution. In general, α is larger for heavier fluids, and smaller for lighter fluids. The normal range is from 0.5 to 2.5. If extended analysis data is available and α is not specified, it is determined by minimization to best fit the experimental data. If extended analysis data is not available and α is not specified, an estimate is determined internally based on plus fraction SG and MW.
Numerical Cleaning of Mud-Contamin ated Samples This option can be used to determine the original composition of reservoir fluids from mudcontaminated samples. WinProp uses a skimming method, subtraction method or a combination of both methods, depending on the user’s input. On any of the Sample tabs in the Plus Fraction Splitting interface, the user decides if that sample needs to be numerically cleaned by checking “Conduct Contaminated Sample Analysis”. If the sample needs to be cleaned, the level of mud contamination should be entered in the text box if it is available. On a separate Mud Info tab, the user needs to provide additional information about the mud, including the first and last SCN in the 100
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mud (required) and the mud composition (optional). An example interface for the Mud Info tab is shown below. Please see the template data set mudclean_split.dat for example data input.
First and Last Single Carbon Number in the Mud
The first and last SCN in the mud must be entered in the text box on the Mud Info tab. Mud Composition Table
If the mud composition data is available, the data can be entered in the table on the Mud Info tab. In column 2 enter the mole fraction of each mud fraction. In column 3 enter the average molecular weight of that mud fraction. Level of Contamination
This parameter can be input under each Sample tab, if available. The level of mud contamination is expressed as the weight fraction of the mud. If this parameter is available and the mud composition is also provided, a direct subtraction method will be used to numerically clean the contaminated sample. If this parameter is not available but the mud composition is provided, a combination of the skimming method and subtraction method will be used to estimate the level of contamination first, and then numerically clean the contaminated sample. If there is no information about the level of contamination and mud composition, WinProp can use the skimming method to numerically clean the contaminated sample based on the first and last SCN in the mud. User Guide WinProp
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Lumping of Components This option is invoked by selecting Characterization | Component Lumping. An example data set for this option is lumping.dat . An example interface for this option is shown below.
Two options are available to the user for specifying the lumping method: explicitly entering the lumping scheme or relying on the internal algorithm to determine the number of pseudocomponents. This algorithm is documented in Appendix B. The lumping method selection is made with the selections located in the Lumping Method area. The user-defined scheme is specified in the table shown on this form. The first column shows the component name from the many-component system. For information purposes, the primary and secondary compositions are shown in the second and third column. To perform user-defined lumping, first set the Number of Lumped Components in the selection box above the grid. In the Scheme column of the table, enter an integer corresponding to the desired pseudo-component number for each individual component in the table. Only integers less than or equal to the specified Number of Lumped Components may be entered in the table. Components do not have to be adjacent to belong to the same pseudo-component. 102
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Users have control in selecting the last component N l in the original list of the N c component system that will be involved in the lumping. That is component 1 in the list through component N l will be lumped. This selection is made through the Group up to component box. The critical properties of the pseudo-components are estimated using the mixing rules of Lee and Kesler [15].
Transferring Results t o Other Data Sets The results of the splitting and lumping calculation options are component properties and compositions that can be used in subsequent calculations. For example, when these calculations are made with file test1.dat, WinProp will generate a file called test1.rls as well as the standard output test1.out. The file with the (.rls) extension contains the component properties and composition in a format that can read back in by WinProp. This is achieved by selecting File | Update component properties. Three forms will be updated: Titles/EOS/Units, Component Selection/Properties, and Composition. Calculation options can then be inserted from the menu. After these calculation options have been defined, use File | Save as to save this file with a different name, e.g. test2.dat if desired. A similar procedure applies to the Regression option.
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Laboratory Calculations
Overview WinProp performs the following laboratory calculations: 1. Recombination of separator oil and gas 2. Compressibility measurements 3. Constant composition expansion 4. 5. 6. 7.
Differential liberation Separator test Constant volume depletion Swelling test
Descriptions of the above laboratory procedures can be found in Pedersen et al. [29] and McCain [17]. You can also include experimental data in these calculations for regression purposes. Convention for Experimental Data Input
Many experimental data are entered in tabular form. You are required to enter data for all pressures or mixtures. For missing data, enter "-1.0" in the corresponding cell. The program will ignore all negative data in the regression. WinProp will put "-1.0" into empty cells corresponding to pressures or mixtures that have values in some other cells. You can also enter a negative sign ("-") in front of any piece of data to exclude it from the regression.
Recombin ation o f Separator Oil and Gas Overview
When downhole samples of hydrocarbon fluids are not available, the separator oil and gas are recombined to obtain a representative sample of the reservoir fluid. The recombination is performed at the separator gas-oil ratio (GOR) in the laboratory. For the recombination calculation, the ratio of oil and gas volumes needs to be converted to a molar ratio. This allows the wellstream molar composition to be calculated from the known separator oil and gas molar composition. The conversion of GOR to a molar ratio requires the densities of the two streams to be known. The calculated recombined fluid composition is therefore sensitive to the values assigned to the oil and gas densities. Normally the densities are calculated from the equation of state (EOS). While the EOS based gas density is reliable, User Guide WinProp
Laboratory Calculations 105
the EOS calculated oil phase density is generally not as accurate. A number of options in addition to the EOS are therefore provided for specifying the densities. These are 1. Entering the densities directly and 2. Use of the Alani-Kennedy correlation for calculating the oil phase density and Dranchuk et al. [4] correlation for calculating the gas phase density. Further discussion of these correlations follows in the next section. A key concern is the quality of the compositional data collected in the field for the recombination calculation. A fast and reliable way of evaluating the consistency of the data is through a graphical technique, known as the Hoffman plot [9]. This plot is created by plotting the logarithm of the product K-value times pressure versus a component characteristic factor, F. If the data is good, that is the oil and gas samples are reasonably in equilibrium at the separator conditions and the measurement of the oil and gas compositions is generally error free, then the points for components C1-C6 should fall on a straight line. Compositions corresponding to components N 2 and C7+ are generally not measured as accurately. The parameter, F, is defined as follows: F=
(log Pc − log Pa ) 1 1 − T b Tc
1 1 T − T b
Where Pc = critical pressure, Tc = critical temperature, Pa = atmospheric pressure, T b = normal boiling point and T = Temperature Input Data
Invoke the Recombination calculation option by selecting Lab | Recombination from the menu. An example data set is recombine.dat , shown below:
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The separator pressure, temperature and gas-oil ratio are the required inputs to be specified in the text boxes under the frame labeled Separator condition. The compositions of the separator oil and gas are also required and are entered on the form Composition, with the oil entered as the primary composition and the gas as the secondary composition. The default method is to calculate the oil and gas densities from their respective compositions and the separator pressure and temperature using the equation of state (EOS). Generally, the EOS calculated oil density is not reliable. Therefore, if an experimentally determined value for the oil density or oil specific gravity is available, enter it directly instead. In the case of specific gravity, select the button Specific gravity entered and enters a value in the adjacent text box. If the oil density is available select the Mass density entered button and enter a value in the adjacent text box in the units stipulated. A third choice is to use some model other than the EOS to predict the oil density. Since the composition is known the Alani and Kennedy correlation is a good choice. To use this method select “From Alani Kennedy correlation...” button and enter values of the C 7+ specific gravity and molecular weight. This method is considered to be quite accurate even for highly volatile oils. The authors used experimental density data to develop a cubic equation for the oil molar volume: v
3
− (R (T + 460) / P + b )v 2 + av / P − ab / P = 0
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where, v = Molar volume, ft 3/lbmol T = Temperature, F P = Pressure, psia R = 10.7335, (psia) (ft 3/lbmol)/R The parameters a and b depend on the temperature and on component specific constants; for pure compounds a and b are given by: a = λe n / (T + 460) b = m (T + 460) + C
The values of λ, n, m and C are available in the literature for common compounds, see for example Danesh [3]. For the C7+ fraction, a and b are obtained from an equation with the specific gravity and molecular weight as well as the temperature being the inputs. Provision is made to enter the specific gravity and molecular weight of the C 7+ fraction on the Recombination form. The values of a and b for the mixture are determined by molar averaging. Please refer to reference [3], page 76-77 for more extensive presentation of this material including an example calculation. For the gas density the EOS value is reliable. However, a value may be entered directly or calculated from the entered compressibility factor. A third option is to use the correlations of Dranchuk, Purvis and Robinson [4]. Two methods are available for calculating the pseudocritical temperature and pressure: Kay’s rule and the Wichert and Aziz correlation [42] . The Hoffmann plot for the recombination will be created automatically when the recombination calculation is done. The gas and oil are not in equilibrium from an EOS calculation viewpoint. Thus, a separator calculation on the recombined fluid will not give the measured gas-oil ratio or oil and gas compositions. Another approach for doing recombination is to use the Separator calculation, and through regression find the fraction of gas in the gas/oil mixture that will give the measured gas-oil ratio. The composition of the gas and oil are entered as the primary and secondary compositions on Form Composition. An initial guess for the feed is specified on the second tab of the Separator calculation by selecting the mole fraction of the primary fluid. The “Mole fraction of secondary stream” can be selected as the regression variable to match the experimental GOR entered for the Separator calculation.
Compressibility Calculation Overview
This option calculates the single-phase compressibility as defined by the following equation: c = −1 / V(∂V / ∂P )
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You invoke this option by selecting Lab | Single-phase Compressibility. An example data set for this option is compress.dat , shown below:
Note that, in the output file, compressibilities are reported under column headings labeled “global” and “liquid”. For the case where the mixture is single phase at the given pressure and temperature these two values will be the same since the global and liquid composition are identical. For the case where there are 2 phases, the compressibility under “global” is the overall mixture (oil and gas) compressibility calculated using the equation valid for single phase and the value under the “liquid” column is the oil phase compressibility. Input Data
Once the primary fluid (usually oil) and secondary fluid (usually gas) compositions have been entered on the Composition form, compressibilities for any number of fluids defined by combining the oil and gas streams in different proportions can be determined . On tab 1, Calculations tab, shown above, enter the temperature and on the table below, enter for each mixture the initial pressure, the pressure increment, the mole fraction of the secondary fluid in the mixture and the number of pressure steps.
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The experimental compressibilities can be entered on the table provided on the Experimental tab:
Note that this table accommodates all the mixtures defined on the previous tab. If a given experimental value is not available, enter a value of –1.0. In the example data set compress.dat , compressibility calculations are carried out for four fluid mixtures. For each mixture, the compressibility of the fluid is calculated for three pressures equal to 24000 kPa, 25000 kPa and 26000 kPa respectively.
Constant Compos itio n Expansion Laboratory Procedure
A sample of the reservoir fluid is placed in a laboratory cell. Pressure is adjusted to a value equal to or greater than the initial reservoir pressure. Temperature is set to the reservoir temperature. Pressure is reduced by increasing the volume of the cell in increments. No gas or liquid is removed from the cell. At each step, the pressure and total volume of the reservoir fluid (oil and gas) are measured. Additional data that can be determined include the liquid phase volume, oil and gas densities, viscosities, compressibility factors or single phase compressibility above the saturation pressure. The procedure is also called flash vaporization, flash liberation, flash expansion or constant mass expansion. 110 Laboratory Calculations
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Input Data
You invoke this option by selecting Lab | Constant Composition Expansion. Alternatively add the option by clicking on the CCE button on the options toolbar. An example data set is cce.dat . Enter data on the Pressure Levels tab, shown below:
For a description of the data entry related to the saturation pressure fields, refer to the Saturation Pressure section in the Two-Phase Saturation and Phase Boundary Calculations chapter. The reservoir or experimental temperature is entered in the text box labeled Temperature. The pressure levels of CCE test are entered on the table provided under the Pressure column. Enter values starting with the highest pressure to the lowest. At least one value is required. The following experimental data can be entered for regression for this option: For a bubble point fluid: 1. Exp ROV: Relative total volume ( total fluid volume at current pressure / fluid volume at saturation conditions) above and below saturation conditions, dimensionless quantity, 2. Liq Vol: Liquid saturation as a percentage (volume occupied by the liquid phase / total cell volume * 100) above and below saturation conditions, dimensionless quantity,
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3. Oil Visc: Oil viscosity above and below saturation conditions in cP, 4. Gas Visc: Gas viscosity below saturation pressure in cP, 5. Gas Z Factor: Gas compressibility factor below saturation conditions (dimensionless), 6. Oil Z Factor: Oil compressibility factor above and below saturation conditions (dimensionless), 7. Gas Density: Gas density below saturation conditions, in units of kg/m3 for SI units and lbm/ft3 in field units, 8. Oil Density: Oil density above and below saturation conditions, in units of kg/m3 for SI units and lbm/ft3 in field units, 9. Oil Compressibility: Single phase oil compressibility, at and above saturation conditions, in units of 1/kPa for SI units and 1/psia in field units. For a dew point fluid: 1. Exp ROV: Relative total volume ( total fluid volume at current pressure / fluid volume at saturation conditions) above and below saturation conditions, dimensionless quantity, 2. Liq Vol: Liquid saturation as a percentage ( volume occupied by the liquid phase / total cell volume * 100) above and below saturation conditions, dimensionless quantity, 3. Oil Visc: Oil viscosity below saturation conditions in cP, 4. Gas Visc: Gas viscosity above and below saturation pressure in cP, 5. Gas Z Factor: Gas compressibility factor above and below saturation conditions (dimensionless), 6. Oil Z Factor: Oil compressibility factor below saturation conditions (dimensionless), 7. Gas Density: Gas density above and below saturation conditions, in units of kg/m 3 for SI units and lbm/ft 3 in field units, 8. Oil Density: Oil density below saturation conditions, in units of kg/m 3 for SI units and lbm/ft3 in field units. If experimental values are not available at all pressure levels for a given data type, a value of 1.0 may be entered for the unknown values. Refer also to Convention for Experimental Data Input in the Overview section at the beginning of this chapter. For a given piece of data if the corresponding (predicted) value cannot be calculated, for example single phase compressibility for a dew point fluid, then that specific piece of data will not be included in regression.
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Differential Liberation Laboratory Procedure
This procedure is generally performed for a black-oil fluid to simulate the conditions encountered in the reservoir. The sample of reservoir liquid in the laboratory cell is brought to the bubble point pressure, and the temperature is set to the reservoir temperature. Pressure is reduced by increasing the cell volume. All the gas is expelled from the cell while pressure is held constant by reducing the cell volume. The gas is collected, and its quantity and specific gravity are measured. The process is repeated in steps until atmospheric pressure is reached. The temperature is then reduced to 15 °C or 60 °F, and the volume of the remaining liquid is measured. This corresponds to the residual oil from the differential liberation. Each of the values of liquid volume in the cell is divided by the volume of the residual oil to obtain the relative oil volume or formation volume factor, B o. The compressibility of the gas (Z-factor), the gas density and the formation volume factor of gas (B g) are also measured. The total volume of gas removed during the entire process is the amount of gas in solution at the bubble point. The solution gas-oil ratio (R s) is calculated by dividing the total volume of gas by the volume of residual oil. The solution gas at any lower pressure is obtained by subtracting the sum of gas removed down to the pressure of interest from the total volume of gas removed. A schematic of the differential liberation process is shown below: Gas off
Gas
All gas displaced
Gas Oil
Gas
Oil Oil Oil
Oil Hg
Hg
Hg Hg
Hg P1 = Psat
P2 < P sat
P 2 < P sat
P 2 < P sat
P3< P 2 < Psat
Input Data
This option is invoked by selecting Lab | Differential Liberation or by selecting the DIFF LIB button on the options menu. An example data set is diflib.dat , shown below:
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Also the data set , matbal-bo.dat illustrates consistency checks calculations for the differential liberation experiment. You enter data on the Pressure Levels, Consistency Checks and Feed/K values/Output level/Stability test level/Standard Conditions tabs. On the Pressure Levels tab, for a description of the data requirements for the saturation pressure related fields, specifically the saturation pressure entered on the first row and first column of the main differential liberation table and the check box labelled Improve saturation pressure estimate, refer to the Saturation Pressure section in the Two-Phase Saturation and Phase Boundary Calculations chapter. The standard conditions are entered on the Feed/K values/Output level/Stability test level/Standard Conditions tab. The default values are 14.696 psia and 60 °F or 101.325 kPa and 15.56 °C. The basic data required on the Pressure Levels tab are the temperature and the pressure levels. Enter the reservoir temperature in the text box labelled Temperature. Enter the pressure levels in column one of the main table. At least one pressure level must be specified, in addition to the saturation pressure. Note that row one is reserved for the saturation pressure. The specified pressures on row two and subsequent pressures may be higher than the saturation pressure. However, for rows 2 and greater, specify the pressures from the highest value to the lowest. Do not leave any empty rows.
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Quite often experimental data such as oil specific gravity (SG), oil formation volume factor (FVF), solution gas-oil ratio (GOR), gas Z-factor, gas formation volume factor, gas specific gravity, oil and gas viscosities as well as properties of the residual oil are available from the laboratory. These data may be used in WinProp in two ways: 1. Material balance and consistency check calculations to evaluate the quality of the data and 2. In regression to tune the EOS model to match the observed data. Generally, material balance calculations would be done first to evaluate the data prior to the regression calculation. The required data for performing an overall material balance are the gas oil ratio at each step, the specific gravity of the gas at each step, the specific gravity of the oil at saturation conditions, oil formation volume factor at saturation conditions and the residual oil specific gravity. For component material balances the gas phase composition at each stage is also required. Please note that in going from reservoir temperature and standard pressure to standard temperature and pressure, it is assumed that no gas will be evolved. The component balance calculates the composition of the oil phase in the cell at each stage of the experiment. These data are entered on the Consistency Checks tab. The data fields required to be filled for overall material balance calculations are shown in cyan. For component material balance in addition to the data for performing the overall material balance, the gas composition for each step of the differential liberation experiment is also required. These fields are shown in yellow. Since some of the data measured in the laboratory can be used for both regression and for material balance calculations, a button on the Consistency Checks tab labeled, Copy Main Table Contents is provided to avoid having to specify the same data twice on the main table on the Pressure Levels tab and the table in the Consistency Checks tab. The pressure values however have to be entered on the main table on the Pressure Levels tab. Therefore if the experimental data are initially entered on the main table, then clicking on the command button Copy Main Table Contents will copy the common data from the main table to the consistency checks table. If sufficient data is entered for the material balance then WinProp will automatically perform that calculation. Similarly if sufficient data is entered for component material balance then that calculation will be performed by WinProp. However the user has the option to suppress the consistency or material balance checks by checking off on the check box labelled Perform consistency checks if sufficient data is entered at the bottom of the Consistency Checks tab. Data for regression can be entered on columns 2 through columns 9 of the main table on the Pressure Levels tab 1 as well as the Residual oil specific gravity… and API gravity text boxes, also on the Pressure Levels tab. For a given property such as GOR if experimental data is not available for a given pressure, then enter a value of -1.0 for that row. A table below the main table on the Pressure Levels tab 1 can be used to assign weights to the different types of data entered. Refer also to Convention for Experimental Data Input in the Overview section at the beginning of this chapter. If data has been entered on the Consistency Checks tab that the user would also like to use for regression purposes then clicking on the button labelled Copy Consistency Checks Table will copy the data in fields common to both tables. On the Pressure Levels tab there is a check box labeled Scale ROV and GOR to oil shrinkage and cum. gas released relative to bubble point. Selecting this option will enable calculation of oil shrinkage as the ratio of oil volume to saturated oil volume, and cumulative gas released as the ratio of standard volumes of gas liberated to saturated oil volume. If the Differential Liberation calculation is not being used in regression, this option will generate a plot of these quantities vs. User Guide WinProp
Laboratory Calculations 115
pressure when the Excel plots are generated, in addition to the normal Relative Oil Volume and Gas-Oil Ratio plot. If regression to experimental data is being performed, the experimental values are converted to oil shrinkage and cumulative gas released, and the regression is done on these quantities. The regression summary table will show the match to the scaled quantities, and the regression summary plots will show the fit to both the scaled and un-scaled quantities. The advantage of this technique is that the EOS will not be penalized for poor prediction of the residual oil density, which is a quantity that will never be encountered in the field. Note: Refer to the Common Data Required for All Options chapter for information about entering fields in the Feed/K values/Output level/Stability test levels tab.
Constant Volume Depletion Laboratory Procedure
This procedure is usually performed for a gas condensate to simulate the conditions encountered in the reservoir. The sample of reservoir liquid in the laboratory cell is brought to the dew-point pressure, and the temperature is set to the reservoir temperature. Pressure is reduced by increasing the cell volume. Part of the gas is expelled from the cell until the volume of the cell equals the volume at the dew point. The gas collected is sent to a multistage separator. The process is repeated for several pressure steps. A schematic of the constant volume depletion process is shown below: Gas off
Gas
Gas
Gas
Gas
Oil
Gas
Oil Hg
Oil
Hg
Hg
Hg P 1 = P sat
P 2 < P sat
Oil Hg
P 2 < P sat
P 2 < P sat
P 3< P 2 < P sat
Input Data
You invoke this option by selecting Lab | Constant Volume Depletion from the menu or by selecting the CVD button on the options toolbar. An example data set is cvd.dat , shown below:
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For illustration of consistency checks calculations on CVD experimental data, see the template case, matbal-gc.dat . You enter data on the Pressure Levels, Consistency Checks, Separator and Feed/K-values/Output level/Stability test level tabs. On the Pressure Levels tab, enter the reservoir or CVD test temperature in the text box labeled Temperature. For this test, an initial guess for the saturation pressure is required. This value is entered on row 1 and column 1 of the main table on the Pressure Levels tab, shown above. The program can use this value directly in a saturation pressure calculation or refine the guess with a stability test. The latter choice is selected by checking off the check box labeled Improve saturation pressure estimate. Further details are provided in the Saturation Pressure section in the Two-Phase Saturation and Phase Boundary Calculations chapter. The only other required data are the values of the pressure steps. These are entered in the column labeled Pressure on the main table provided on the Pressure Levels tab. The first row of this table is reserved for the saturation pressure. Enter values from highest pressure to the lowest pressure starting on row 2. Do not leave any empty rows. Columns 2 through 4 are to be used for entering experimental data which can be used for regression. On the column labeled Cum. Gas Prod. (%), enter the percentage recovery, that is, total moles removed as a percentage of the initial moles (at saturation pressure) charged to the cell. On the column labeled Liq. Sat (% of CVS) enter the percent of the cell volume occupied by the liquid phase at each pressure step, relative to the volume occupied at saturation conditions. For fluids with a dew point, at saturation pressure, this value is 0.0. For volatile oils which exhibit User Guide WinProp
Laboratory Calculations 117
a bubble point enter a value of 100 at the saturation pressure. On the column labeled Gas Z factor enter the gas phase compressibility factor at each pressure. For a given property such as Gas Z factor, if experimental data is not available for a given pressure, then enter a value of –1.0 for that row. In the first row of the main table on the Pressure Levels tab you can assign weights to the different types of data entered. Refer also to Convention for Experimental Data Input in the Overview section at the beginning of this chapter. If data has been entered on the Consistency Checks tab and the user would also like to use this data for regression purposes then clicking on the button labeled Copy Consistency Checks Table will copy the data in fields common to both tables. Material balance calculations can be used to check the quality of the laboratory data collected. The overall material balance can be used to determine the total mass of the gas and liquid phases and their densities as a function of pressure. If the compositional analysis of the gas phase from each stage is also available then the liquid phase composition at each stage can also be calculated. These data are entered in the table on the Consistency Checks tab. The required data for performing an overall material balance are the cumulative percent recovery at each pressure step, the Z factor of the gas at each pressure step, the specific gravity of the gas at each pressure step and the liquid saturation at each pressure step. The data fields required to be filled for overall material balance calculations are shown in cyan. For component material balance in addition to the data for performing the overall material balance, the gas composition for each step of the constant volume depletion experiment is also required. These fields are shown in yellow. Since some of the data measured in the laboratory can be used for both regression and for material balance calculations, a button on the Consistency Checks tab labelled, Copy Main Table Contents is provided to avoid having to specify the same data twice on the main table on the Pressure Levels tab and in the consistency checks table on the Consistency Checks tab. The pressure values however have to be entered on the main table on the Pressure Levels tab. Therefore if the experimental data are initially entered on the main table, then clicking on the Copy Main Table Contents button will copy the common data from the main table to the consistency checks table. If sufficient data is entered for the material balance then WinProp will automatically perform that calculation. Similarly if sufficient data is entered for component material balance then that calculation will be performed by WinProp. However the user has the option to suppress the consistency or material balance checks by selecting the check box labeled Perform consistency checks if sufficient data is entered at the bottom of the Consistency Checks tab. A brief description of the material balance calculations for CVD is outlined below. For more detailed information please refer to Whitson and Torp [41]. Assume as a basis 1 mole of initial fluid charged to the CVD cell. The total mass in the cell at a particular stage k, denoted as ntk is then equal to: n tk = 1 −
i = k
∑ ∆n pi
i=2
where ∆n pi is the incremental moles of vapor produced from the cell during stage i. In terms of the table entries, ∆n pi is the difference in the values of “gas produced %” expressed as fraction between stage i and stage (i-1). Note the initial stage (saturation conditions) is being denoted as stage 1. The corresponding material balance equation for a component j is:
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n tk z jk = z j1 −
i = k
∑ ∆n pi .y ji
i=2
where z jk is the overall composition of the fluid remaining in the cell at stage k and y ji is the composition of the vapor phase removed from the cell at stage i. For density calculations the mass and volume of each phase in the cell is required. The cell volume can be calculated from the knowledge of initial fluid properties: Vcell
=
Z1RT P1
For gas condensates the gas compressibility factor Z 1 is generally available, for volatile oils, however, the bubble point density is usually measured. Provision is made to enter Z factors only in WinProp. The measured bubble point density can be used together with the real gas law (PV=nZRT) to obtain the required Z factor. At each stage the liquid volume in the cell is measured and reported as the liquid saturation. The liquid volume in the cell, can then be calculated as: VLk = S Lk .Vcell
From a volume balance, the vapor volume is then V vk = (1-SLk ).Vcell. Using the real gas law, the corresponding moles of vapor in the cell at stage k are calculated as n vk = pk .Vvk /Zk RT. The composition of the liquid phase remaining in the cell at each stage k can now be computed as: x jk =
n tk .z jk − n vk .y jk n tk − n vk
The compositions calculated in this manner are analyzed by plotting the corresponding logarithm of K values versus a component characterization factor, F, known as the Hoffman plot. WinProp will automatically create this plot if component material balance calculations are performed, which will be done if the required data is entered by the user. The densities of the liquid and vapor phases can also be calculated from a mass balance [41]. The multistage separator conditions and standard conditions are entered on the Separator tab. Enter stages from the highest pressure down to the lowest pressure. A maximum of 8 stages excluding stock tank are allowed. The multistage separator does not include the stock tank conditions which are entered as Standard conditions. A lower carbon-number component and an upper carbon-number component are also specified. The molecular weight of components between those two is computed at each pressure level. This enables the tracking of the molecular weight of the plus fraction during the depletion process. You can also enter experimental data on mole % of gas produced, liquid dropout (% liquid saturation), and gas compressibility factor for regression purposes. Refer also to Convention for Experimental Data Input in the Overview section at the beginning of this chapter. Note: Refer to the Common Data Required for All Options chapter for information about entering fields in the Feed/K values/Output level/Stability test levels tab.
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Separator Test Laboratory Procedure
The reservoir fluid is sent to a multistage separator where the pressure and temperature are selected to optimize liquid production. The last stage of the separator corresponds to the stock tank. A schematic of a conventional three-stage separation process is shown below:
1
st
STAGE P1 , T1
GAS (ST)
GAS (2)
GAS (1)
2
nd
STAGE P 2, T2
3
rd
STAGE
P 3, T3
OIL to stock tank
The overall gas-oil ratio, the stock-tank specific gravity or API, and the oil formation volume factor Bo are measured. The implementation of the Separator option provides for considerable flexibility in modeling separation strategies which do not conform to the conventional scheme described above. This is often encountered with gas condensate fluids. Each separator has the limitation of a single required input and two outputs corresponding to the vapor and liquid streams. However the liquid output need not feed the next separator and the gas output is not limited to join the gas product stream. For a given separator one of these output streams can potentially become a product stream or feed a separator downstream. Recycling is not allowed. The user can also specify new product streams aside from oil and gas such as LPG. The oil and gas product streams however must always be present. Quantities that can be used for regression calculation such as GOR will always therefore be defined. Two examples via schematics are shown below of alternative separator calculations. In the first case the oil product stream is made up of contributions from the liquid phase from the 3 separators. This is essentially a reversal of the conventional case where the gas product stream is made up of the vapor phase from all the separators. In the second case a third product stream labeled as LPG is defined. GAS
FEED
1
st
STAGE P1 , T1
2
nd
STAGE P 2, T2
STOCK-TANK P s , Ts
OIL
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LPG
FEED
1
st
STAGE P1 , T1
2
nd
STAGE P 2, T2
GAS
STOCK-TANK P s , Ts OIL
Input Data
This option is invoked by selecting Lab | Separator or alternatively by selecting the SEP button on the options toolbar. An example data set is separator.dat , shown below:
Specification of the separator stage conditions and stage data for performing Hoffmann plots and material balance calculations is done on the Pressure Levels tab. Initially there are 2 columns corresponding to the saturation conditions and stock tank conditions in the main table on the Pressure Levels tab. The minimum data requirements are the temperature and pressure for each defined “stage”. For the saturation column, the reservoir temperature is required along with the known saturation pressure or an initial guess for the saturation pressure. The program will calculate the saturation pressure. The user-supplied value will be used directly as an initial guess in the saturation pressure calculation or the user-supplied value will be refined further via a stability test prior to the saturation pressure calculation being invoked. The default is to refine the initial value as indicated by the check box labelled User Guide WinProp
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Improve saturation pressure estimate. For the stock tank, the default values for the
temperature and pressure are shown on the table. The user may edit these values. The Liquid to and the Vapor to rows in the middle table indicate the destination of the liquid and the vapor stream from each stage. When there is only one stage, “stock tank,” then these destinations have to be the “oil” product stream and the “gas” product stream since these 2 streams have to be present in all cases. For reporting volumes, conditions other than the stock tank pressure and temperature can be selected for each product stream. These are to be specified in the table labeled Product Streams Reporting Table at the bottom of the Pressure Levels tab. To add a separator, select a cell in the column before which you want the new stage to be inserted and click on the button labeled Insert Sep. To delete a separator, select a cell in the appropriate column(s) and click on the button Delete Sep. The highest separator stage should be added first, followed by lower pressure stages to the stock tank. The default destination for the liquid phase is as feed to the next separator downstream while the default for the vapor phase is the “gas” product stream. Once all the separators are added and the conditions specified then the destinations can be changed, possibly defining a new product stream such as an LPG or intermediate product stream. This is done through a dropdown menu in the appropriate cell of the stream destinations (middle) table. Once added, such a stream will also have an entry added to the Product Streams Reporting Table. For overall material balance calculation and Hoffmann plots, the required data are the specific gravity of the gas removed from each separator stage, the gas-oil ratio (with respect to stock tank oil) at each stage, the stock tank API, the density at the saturation conditions and the oil formation volume factor at saturation conditions. For component material balance calculations the composition of the gas stream from separator stage is required as well. The GOR values correspond to the amount of gas liberated and not gas in solution. The formulation of the material balance equations is based on the fact that the mass or moles placed at the start of the experiment must equal the mass of the residual oil plus the mass of gas removed from the cell [18]. M init −
∑stages M gas − M resid = 0
Assuming a basis of 1 stb of residual (stock tank) oil, then M resid = 1(stb) * 0.158987( m3 / stb) * ρ stc ( kg / m3) M init = 1(stb) * Bo ( rb / stb) * ρ s ( kg / m3) M k gas
= 0.034514R s k (scf / stb) * λk
The above equations all yield mass of initial in place fluid, gas removed and residual oil in units of kg. The gas oil ratio appearing in the expression for the gas removed in stage k is the liberated GOR and λk is the specific gravity of the gas coming out of solution in stage k. ρstc is the stock tank density of the oil and ρs is the saturated fluid density. Bo is the formation volume factor at saturated conditions. The experimental data for regression are entered on the Experimental Data tab, shown below:
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The three experimental data values available for regression are the overall solution gas oil ratio, the oil formation volume factor and the residual oil API gravity. Note: Refer to the Common Data Required for All Options chapter for information about entering fields in the Feed/K values/Output level/Stability test levels tab.
Swelling Test Laboratory Procedure
This experiment provides information on the fluid behavior under gas injection processes. When a gas is injected into a reservoir, it can go into solution and swell the oil, i.e., the volume of the oil becomes larger. Measurements of this effect can be performed as follows. The reservoir oil is loaded in a cell, and the temperature is set at the reservoir temperature. The bubble point of the oil and the corresponding volume are measured. A small amount of injection gas is transferred into the cell. A new saturation pressure is determined and a new saturation volume recorded. This process is repeated until the upper bound of injection-gas concentration is reached or the saturation pressure of the fluid is equal to the estimated injection pressure. A constant composition expansion experiment may be performed for each mixture of injection-gas and oil in the above process. Input Data
This option is invoked by selecting Lab | Swelling Test or alternatively by clicking on the SWL TEST button on the options toolbar. An example data set is swelling.dat , shown below:
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You enter data on the Mixtures, Feed/K values/Output level/Stability test level and CCE tabs. Note: Refer to the Common Data Required for All Options chapter for information about entering fields in the Feed/K values/Output level/Stability test levels tab.
The required data on the Mixtures tab, shown above, include the temperature at which the experiment is performed and an initial guess for the saturation pressure of the oil at the specified temperature. If the Improve saturation pressure estimate box is checked, this value will be refined further via a stability test. Further details are provided in the Saturation Pressure section in the Two-Phase Saturation and Phase Boundary Calculations chapter. The original oil is labelled as mixture #0. The initial guess for saturation pressure entered in the Saturation Pressure Estimate text box is also shown on the table on the Mixtures tab to be used to specify the data for the other mixtures. The oil and gas compositions are entered on the Composition form as primary and secondary fluids respectively. On the table provided for specifying mixture properties, the first column corresponds to the mole fraction of injection gas, and the second column corresponds to the saturation pressure estimate of the injection-gas and oil mixture. The row corresponding to the original oil, i.e., with mole fraction equal to zero, is added automatically by WinProp. The saturation pressure estimate value appearing in the table for this row is taken from the Saturation Pressure Estimate text box. Additional data for at least one mixture is required on this table. Enter data for these mixtures in consecutive rows starting with the smallest value of the gas mole fraction to the largest value. A guess for the corresponding saturation pressure is required for each mixture. As data is added to 124 Laboratory Calculations
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the table, the total number of mixtures defined is indicated by the label No of swelling experiments. Insert or remove rows from this table by clicking in the row that you want to delete, or the row below which you want to insert another row, then click the Tools button and select the desired operation. The above example shows a case with 5 mixtures. For regression purposes, the experimental saturation pressure data and/or swelling factor (volume of swelled fluid at saturation pressure/volume of original fluid at saturation pressure) may be entered in the third and fourth columns respectively. Either of the two properties may be assigned, in the first row, a weight greater than the default of 1.0, to reflect the relative importance of the data to the process for which the EOS model is being developed or the relative accuracy of the measurements. Refer also to Convention for Experimental Data Input in the Overview section at the beginning of this chapter. If required, the pressure levels of a constant composition expansion process are entered on the CCE tab, shown in the following example:
The CCE experiment will be performed at the entered pressures for each of the mixtures stipulated. The CCE plots are generated automatically when you run a simulation if pressures are specified for the CCE experiment.
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Multiple Contact Miscibility Calculations
Overview The design of gas or solvent injection processes often involves a multiple-contact calculation to study the vaporization or extraction process. There are two methodologies to analyze the gas drive mechanism and miscible process in WinProp. Traditionally, with cell-to-cell simulation, a pseudo-ternary diagram is generated from the calculations to help with the interpretation of the results. Most gas or solvent injection floods operate in a regime where true miscibility is not achieved, rather near miscible conditions are realized. High recoveries can be achieved even though miscibility is not truly realized. As compared to conditions required for miscibility, operation in this regime translates to lower operating costs as compression costs increase with pressure and feedstock costs increase with the solvent enrichment level. These are known as vaporizing/condensing processes (Zick [44]), and the resulting ternary diagram has an hourglass shape. By analyzing the ternary diagrams from the MCM option in conjunction with slim tube or core flood experiments, optimal operating conditions or solvent composition can be determined. Please refer to Nutakki et al. [25] for a detailed discussion of this subject. Besides the pure vaporizing or pure condensing processes, there is a combined drive mechanism that has features of both vaporizing and condensing drives. In such a system, the crossover tie line controls the development of miscibility, instead of initial oil tie line or injection gas tie line. Geometric construction in the composition space is used to locate all the key tie lines. The MCM option in WinProp is used to calculate the minimum miscibility pressure (MMP) or first contact miscible pressure (FCM) for a given oil and solvent at a particular temperature or the minimum miscibility enrichment level (MME) required for multiple or single contact miscibility at a given temperature, pressure, oil composition, primary and make up gas compositions. Users can select the traditional Cell-to-Cell simulation method which will determine only vaporizing or condensing drive mechanisms, the Tie Line method or a Multiple Mixing Cell Simulation method. The latter two methods will determine miscibility due to the combined vaporizing/condensing mechanism. The minimum miscibility pressure may be determined for a given solvent composition by entering a range of pressures to be tested. Conversely, the minimum rich gas enrichment level may be determined to achieve miscibility at a specified pressure by entering a range of rich gas mole fractions to be tested. In both cases, the program reports the MMP or MME if found and the mechanism by which miscibility is achieved, that is vaporizing or condensing drive User Guide WinProp
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mechanism, or the combined vaporizing/condensing drive mechanism. If FCM is within the entered pressure limits then it is reported as well. For the MMP calculation, the program divides the entered pressure range into 400 equally spaced intervals. The calculation begins with the lowest pressure (P min) terminating at the maximum pressure (Pmax) or at the FCM pressure. Similarly for the MME calculation, the entered mole fraction range is divided into equally spaced intervals, and the calculation terminates at the maximum solvent enrichment level, or at the enrichment level which gives first contact miscibility at the specified pressure. The results are output based on the pressure step, or mole fraction step, used to specify the range and at the pressure corresponding to the MMP or MME. If Cell-to-Cell method is used, the ternary diagrams will also be output. If Tie Line method is used, detailed liquid/vapor composition, as well as the k-value for each key tie line will be output.
Data Input The multiple-contact calculation option is invoked by selecting Calculations | Multiple Contacts or by selecting the MCM button on the options toolbar. Example data sets for this option are mcm-condensing.dat , mcm-vaporizing-co2.dat, mcm-combined-H95-8leanmmp.dat and mcm-Z12-5-mme.dat , as shown in the following example:
The required data include the temperature, entered in the text box on the Conditions/Method tab, and a pressure or alternatively a pressure range for the calculation. For calculation at a single pressure, enter the value in the Pressure text box. To specify a pressure range enter the minimum pressure, Pmin, in the Pressure text box and enter a value for Pressure step, Pstep, and No. of pressure steps, Nsteps. The maximum pressure, P max = Pmin + Pstep * Nsteps. The user 128
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needs to select one of the calculation methods: Cell to Cell Simulation, Semi-analytical (Key Tie Lines) Method or the Multiple Mixing-Cell Method. The other required data are the oil composition, entered on the Composition form, and the primary and make up gas compositions, the make up gas fraction or range of fractions, and the pseudoization scheme for the ternary diagram entered on the Compositions tab on the Multiple Contacts form. For calculation at a single solvent enrichment level, enter a value between 0.0 and 1.0 in the Make-up gas fraction text box. The default value for the make-up gas fraction is zero, implying the solvent composition equals the primary gas composition. In this case the makeup gas composition is not required and values of zero can be entered. To specify a range of make-up gas mole fractions, enter the minimum value in the Make-up gas fraction text box, and enter values for the Make-up gas fraction step and for the No. of make-up gas fraction steps. If Cell-to-Cell simulation is selected, the pseudoization scheme needs to have a value of 1, 2 or 3 to group a given component into the first, second or third pseudo-component respectively. The pseudoization scheme is used in the post-processing step, which is just for ternary plots; the actual calculations are done with the full set of components. Note that if a range of pressures is specified (MMP calculation), only one solvent composition may be entered; i.e., the Make-up gas fraction step must be 0.0 and the No. of make-up gas fraction steps must be 1. Similarly for the MME calculation where a range of make-up gas fractions is specified, only one pressure value may be entered. If the Semi-analytical (Key Tie Lines) Method is selected, the Method of Characteristics is used as described in the text “Gas Injection Processes”, by Franklin Orr, Tie-Line Publications, 2007. At any pressure, a system of equations is solved to determine the original oil tie-line, the injection gas tie-line, and the nc-3 crossover tie-lines. At the specified temperature, if the length of any tie-line goes to zero, that is the minimum miscibility pressure. If the Multiple Mixing-Cell Method is selected, the method presented by Ahmadi and Johns in SPE 116823 is used. The following steps are used in the Cell-to-Cell Simulation calculation (the points referred to by letter are shown on the diagram following step 4). 1. A solvent is first formed by mixing a primary gas (e.g. dry gas) with a specified mole fraction of make-up gas (e.g. LPG). The compositions of the primary and make-up gases, and the fraction of make-up gas, are entered on the Compositions tab. The oil composition is specified on the Composition form. 2. Solvent is added to the oil such that the solvent to oil molar ratio increases by a specified value for each mixture. This solvent increment ratio is entered on the Conditions/Method tab as the Solvent increment ratio. The default value is 0.01. Flash calculations are performed for a maximum of 100 mixtures of solvent and oil. If no two-phase region is detected, the process is judged to be first contact miscible and the calculations stop. In the event that a two-phase region is encountered, the calculation procedure proceeds to Steps 3 and 4.
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3. Using the first point (A) in the two-phase region detected in Step 2, all liquid is removed. The remaining gas is combined with the original oil in the gas oil ratio RATIO:(1-RATIO) to form B1. The value of RATIO is entered on the Conditions/Method tab as Equilibrium gas/original oil mixing ratio (default value: 0.10). A flash calculation is performed, and the liquid is removed. The procedure is repeated. This simulates a vaporizing or extraction process, and generates the portion of the phase envelope marked B. A maximum of 50 flash calculations is performed. 4. Again, using the first point (A) in the two-phase region detected in Step 2, all vapor is removed. The remaining liquid is combined with the original solvent in the solvent liquid ratio RATIO:(1-RATIO) to form C 1. A flash calculation is performed, and the vapor is removed. The procedure is repeated until the oil cannot be enriched further or after a maximum of 50 flash calculations are performed. This process simulates a condensing gas drive process, and generates the portion of the phase envelope marked C. Heavy
B
Oil
C
A
C1 B2
C2
B1
Critical Point
Light
Dry Gas
Solvent
Intermediate
Pseudo-Ternary Diagram
If Cell-to-Cell simulation is selected, the last column of the table on the Compositions tab needs to have a value of 1, 2 or 3, which determines the grouping of components into three pseudo-components for the ternary diagram. In the following example:
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N2 and C1 belong to Pseudo-Component 1; IC5, NC5, NC6 and FC20 belong to PseudoComponent 3, while the remaining components belong to Pseudo-Component 2. The resulting ternary diagram from this multiple contact calculation is shown below, where the bottom left apex corresponds to Pseudo-Component 1, the bottom right apex corresponds to Pseudo-Component 2 and the top apex represents Pseudo-Component 3.
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Regression
Overview The regression feature of WinProp can be used to “tune” the equation of state to match experimental measurements. The parameters used in the regression are component properties and interaction coefficients. Most of the calculation options of WinProp allow experimental data to be entered for regression purposes. WinProp uses the regression procedure of Agarwal et al. [2]. From the specified list of parameters, the procedure orders the parameters such that the most sensitive parameters are used first. The regression is performed on a small number of parameters at a time. The default is to use a subset of 5 parameters, although this number can be modified. Once a parameter reaches the maximum or minimum value allowed or does not contribute any longer to improving the match, it is replaced by the next parameter that has not been used from the ordered list. Thus, a large set of parameters can be specified, and WinProp will regress on a small number of parameters at a time, working from the most sensitive parameters to the least sensitive parameters.
Organization of the Input Data A sample regression data set structure is shown in the following:
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Example data sets for regression begin with the word regress. There are 16 template cases that involve regression from regress-blackoil1.dat through regress-separator.dat . Please refer to the Introduction chapter of this manual for a brief description of each of these data files. In the tree view, the Regression Parameters node contains the calculation options which in turn contain the experimental data that will be used for the regression. Insert the Regression Parameters node and sub-nodes using one of the methods described in the Basic Operations chapter. A weight is associated with each data item or group of data. The weights w i are used to assign a degree of importance to each data point. The default value is 1.0. A larger value gives more importance to the data while a lesser value gives less importance. The regression is performed by minimizing the objective function F=
∑ [w (x i
i , calc
−x i, meas ) / x i, meas ] 2
i
where xi,calc and xi,meas correspond to the calculated value and measured value respectively. To exclude any measured value from the regression, precede it with a negative sign ("-"). Please see Convention for Experimental Data Input in the Overview section at the beginning of the Laboratory Calculations chapter.
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All calculations before the Regression Parameters node use the parameter values before regression. All calculations after the Regression Parameters node use the parameter values after regression. For the calculation options that are included in the regression, the output and plots contain both results before and after regression. In the above example, the CMG GEM EOS Model option was used to print component properties before and after the regression (see GEM Fluid Model Generation and Component Properties Printing in the Components chapter).
Parameter Selection Component properties for regression are selected on the Component Properties tab of the Regression Parameters node, shown in the following example.
Select or cancel component properties by clicking cells on the grid. Clicking the first time selects the property. Clicking a second time cancels that property. If temperature-dependent volume shifts have been activated on the Component Properties tab, volume shift will not be available as a regression parameter. Non-zero values of the aqueous phase solubility parameters, such as Henry’s constant and molar volume at infinite dilution, must be set on the Component Selection/Properties form to enable these variables as regression parameters.
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The mole fraction of the secondary stream, used to define the feed for calculation options, can be selected as a regression variable by clicking the Mole fraction of secondary stream check box below the grid. Interaction coefficients are selected as regression parameters on the Interaction Coefficients tab, shown below.
The interaction coefficients between hydrocarbon components are calculated from the equation described in the Interaction Coefficients section in the Components chapter. The HC-HC Int. Coef. Exponent is an important parameter for matching reservoir fluid saturation pressure. The list of HC-HC groups, defined earlier in the Component Selection/Properties form, is shown in the list box in the Hydrocarbon Groups area. To select specific groups as regression parameters, first select Select from list then highlight entries from the list by holding down the CTRL key and clicking with the left mouse button. The interaction coefficients involving non-hydrocarbon components are selected by clicking on the grid. Parameters specific to the viscosity correlations are selected on the Viscosity Parameters tab, shown in the following example:
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As discussed in the Components chapter, there are two types of viscosity correlations available in WinProp: Jossi-Stiel-Thodos (JST) and Pedersen. When JST is being used, the correlation coefficients and the component critical volumes for viscosity are available to be selected as regression parameters. When the Pedersen correlation is active, only the correlation coefficients appear as possible regression variables on this tab. Both correlations also depend on the component critical pressures, critical temperatures and molecular weights. By leaving these values fixed, however, and regressing only on the parameters appearing on the Viscosity Parameters tab, the process of matching experimental viscosity data can be completely decoupled from the process of tuning the EOS to PVT data. A second set of EOS parameters can be specified as regression variables in the same way as the first set. The user can toggle between the component properties and interaction coefficient tables belonging to the first and second sets through the set selection menu. To activate the second set when the first set is active select Second Set in the Component Set list at the bottom of the Component Properties tab. The second set of regression variables currently supported are the critical pressure, critical temperature, volume shift, omega A, omega B, interaction coefficient exponent and the binary interaction coefficients for pairs with a nonhydrocarbon species. The default variable bounds for a given property are the same regardless of which set the component belongs to. The selection of bounds is discussed in more detail below. The grouping feature discussed below can also be used for the second set parameters. User Guide WinProp
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Grouping Regression Variables It is possible to treat a given property, for example, critical pressure, for a group of components (for example, all pseudo-components) as a single variable under regression with the grouping feature of WinProp. The initial value of each member of the group and the lower and upper bound will in general be unique. To ensure that the individual bounds for each member are properly applied, WinProp recalculates the lower and upper bound for the reference component (reference component is the first component specified for the group) replacing the default or user specified bounds. The grouping feature is particularly useful when it is desired to maintain a certain trend or symmetry or avoiding regressing on a variable with a small mole fraction. During regression, all members of a group may be varied either by equal increments or by equal ratios. Using the equal increment method means that each variable in the group is incremented or decremented by the same amount during a regression iteration. The equal ratio method indicates that each variable in the group is increased or decreased by the same fraction of its original value during a regression iteration. Parameters that have zero initial values cannot be used with the equal ratio method. The method is selected through the Regression Controls tab. The default is to use equal increments. To create and apply a group, select the Components Properties tab. Click the button to the right of the Selection/Group at the bottom of the tab then select New Group. The Selection/Group combo box will now contain a group titled Grp#1 - empty:
To select components for inclusion in the group, click the appropriate grid cells for a particular property such as Pc (atm). Instead of an X indicating a selection, a group id of Grp#1 will be assigned. As well, the Selection/Group combo box will now indicate that group 1 is associated with the Pc property, as follows:
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To remove a cell from the group, click the cell a second time. To delete a group, select the group in the Selection/Group combo box then click the button then select Delete Group. The group is immediately deleted and group assignments are removed from the grid. To stop group selection, click Single Selection in the Selection/Group combo box. Component data of one type (e.g. Pc, Tc, etc.) can be grouped together. This implies that in the Component Properties grid groups must selected in columns. In the Interaction Coefficients grid, interaction coefficients for any pairs of components can be included in the same group. To create a second group, click the button then select New Group. The Selection/Group combo box will now contain a group titled Grp#2 - empty:
As before, click on the cells that you want to assign to Group 2. Repeat this process for any other groups that you want to add. The Component Properties tab for a regression run specifying the critical pressures and volume shifts for the last four components in the plus fraction as grouped variables is shown below:
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Regression Variable Bounds The Variable Bounds tab has a summary table that shows the initial value, the lower bound and the upper bound for each regression variable currently selected, as shown for our example:
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Column 1 shows the variable number. If the component is a member of a group then the group id is shown. A description of the variable is given in column 2. Whether the variable belongs to the first set or second set is indicated here. Column 3 shows the initial value of the variable. This value cannot be edited here. It can only be modified on the Component Selection/Properties form. For each variable, WinProp sets a default lower and upper bound. For most properties, the maximum change allowed is 20% above or below the original value. For the hydrocarbon interaction coefficient, other interaction parameters and volume shifts, the bounds are set according to limits found appropriate for typical petroleum fluids. For hydrocarbon components, these bounds are modified to ensure that certain trends are maintained: as the molecular weight increases critical temperature and acentric factor increase while the critical pressure decreases. To give experienced users the flexibility to restrict the variation of certain component properties and allow larger changes in others, however, the default variable bounds can be edited on this table. As mentioned above, changing the bound of a group member may lead to the bound for the reference component of the group (first group component in the list) to be adjusted automatically. The user can revert to the WinProp defaults for the bounds by clicking the Reset to Default button.
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Regression Control Parameters Parameters for the numerical methods and grouping options are entered on the Regression Controls tab, as shown below:
In the Numerical Controls area, the following information is entered: Convergence tolerance
If the change in the objective function between two iterations, or the absolute value of the objective function, is less than this value, the regression stops.
Maximum number of iterations
The regression stops after the specified number of iterations.
Number of simultaneous regression parameters
Number of parameters to be regressed on at one time. The default value is 5. If the number of regression parameters is less than this number, the former will be used instead. Note that increasing this value can significantly increase the run time for the regression.
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In the Grouping Controls area, an option is given to specify how the members of a group are varied during regression. Selecting Vary group variables by equal increments specifies that a change ∆x will be applied to all group members as x new = xold + ∆x. Selecting Vary group variables by equal ratios specifies that all group members will be multiplied by a common factor as xnew = xold x F∆. The default method is to vary the group members by equal increments.
Transferring Results t o Other Data Sets The results of the regression option are component properties that will be used in subsequent calculations. If calculation options are appended after the Regression Parameters node then the component properties used will correspond to values modified by the regression procedure. However, it is prudent to examine the results of the regression calculation before proceeding further. This can be done easily using WinProp’s Update component properties feature. For example, when a regression is performed with a file named regress.dat, besides the standard output regress.out, WinProp also outputs a file named regress.rls. This (.rls) file contains the component properties from the regression process in a format readable by WinProp. The contents of the (.rls) file can be used to update the component properties in the current data set by selecting File | Update component properties. Three nodes are updated: Titles/EOS/Units, Component Selection/Properties and Composition. The Regression Parameters node can now be removed from the file, and prediction of phase behavior using the tuned model can be performed. To keep a record of the work done, use File | Save as to save this file with a different name, e.g. regress1.dat. Note that a number of back-to-back regression runs can also be performed in this way with the same data but using different regression variables. A similar procedure applies to Plus Fraction Splitting and Component Lumping in terms of updating component properties.
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Compositional Grading
Overview The compositional grading phenomenon refers to a variation in fluid composition with depth in a reservoir. As depth increases, the mole fraction of light components decreases, density increases and GOR decreases. Near critical oils and volatile fluids exhibit the largest compositional grading effects, while black oils have the least variation in properties with depth. Compositional grading is reduced if the system is highly undersaturated. Assessment of compositional grading is important in estimation of fluid in place, initialization of reservoir simulators and consideration of production alternatives. For example, when considering gas injection in a reservoir with compositional grading the solvent composition required to achieve miscibility will vary with depth. There are two model formulations available for performing the compositional gradient calculation: the isothermal model or the thermal model. The isothermal compositional gradient calculation solves the gravity/chemical equilibrium problem. Given the composition and pressure at a reference depth, the composition and pressure at any other specified depth can be determined. The saturation pressure at the specified depth is also calculated. If there is transition from bubble point to dew point saturation conditions over the calculation interval, the GOC depth will be estimated. This is done with a simple halving algorithm to locate the depth at which the transition from bubble point to dew point occurs. This ultimately requires saturation determination in the vicinity of the critical point, which can cause failure of the saturation calculation. The GOC calculation continues until an interval of 0.1m is reached or until the saturation calculation fails. For this reason, the accuracy to which the GOC depth was determined is reported in the summary table. Formulation of the problem and the required solution algorithms are given in Whitson and Belery [39]. The thermal model incorporates the effect of the geothermal temperature gradient on the compositional gradient. Thermal diffusion effects as well as the variation of fluid properties as a function of temperature can be included in the model. As for the isothermal model, the location of the GOC will be estimated if it exists. When the temperature is not constant, the system is not in equilibrium. The model solves for a stationary state, or zero mass flux condition, as described in Hoier and Whitson (SPE 63085). Please note that the equation of state must predict a single-phase system for the reference composition at the reference pressure. If the system is unstable, the calculation cannot be performed. If experimental data indicate that the initial condition should be stable, some EOS tuning may be required before the compositional gradient calculation can be carried out.
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With the default output level of 1, only the summary table is shown in the output (.out) file. This gives the reservoir pressure, saturation pressure, density and two key mole fraction values as a function of depth. With output level 2, for each depth, the full phase property table and the saturation calculation results are printed in addition to the summary table. When the detailed output is requested it will be printed in the order the calculation is carried out which is described below. The calculation is carried out in the following steps: 1. The first depth level above the reference depth is calculated, using the reference conditions as the initial guess for the calculation. 2. Continuing for each depth level from the first calculation to the top of the interval, each calculation is performed using the previous converged results as the initial guess. 3. The first depth level below the reference depth is calculated, using the reference conditions as the initial guess. 4. Continuing for each depth level from the calculation in step 3 to the bottom of the interval, each calculation is performed using the converged results from the previous calculation as the initial guess.
Data Input Example data sets for the compositional grading calculation are given in compgrad-blackoil.dat (shown below) and compgrad-voloil.dat . For field units, temperature is entered in °F, pressure in psia and depth in feet. For SI units, temperature is entered in °C, pressure in kPa and depth in meters.
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For Feed/K values/Output level/Stability test level specifications, see the Common Data Required for All Options chapter. Specification of the primary calculation options is done on the General tab, shown above. Enter the reservoir temperature at the reference depth in the Reference Temperature text box. In the Reference Pressure text box enter a value for the pressure corresponding to the reference depth entered in the Reference Depth text box. Enter the depth to the top and bottom of the formation in text boxes Depth to Top and Depth to Bottom respectively. The total height of the fluid column as defined by these depths is divided by the number of calculation intervals specified in the text box No. of Calculation Intervals to determine the evenly spaced points at which the calculation is performed. The default value is 10. If the user desires the calculation to be performed at certain specific depths, these can be entered in the table provided, using the button to add and delete rows. Enter each depth in the column headed Depth Value. The user can monitor the composition changes with depth for a given component or a range of components. This information will be printed in the summary table in the output file. When a range is selected the mole fractions of the specified components are summed and the total reported. For the first component or range of components to be tracked select the lower and upper limits through the combo boxes in the Key Component 1 area. For the second key component or range select the lower and upper limits through the combo boxes in the Key Component 2 area. The upper component must have a component index greater than or equal to the index for the lower component. The thermal model data is specified on the Thermal tab:
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To activate the thermal model check the box labelled Use Thermal Model, as shown above. The temperature gradient imposed is constant and is entered in the Temperature Gradient text box. Entering a positive value for the thermal gradient implies increasing temperature with depth. The units are °F/ft for field units or °C/m for SI and modified SI. Various models for calculating the thermal diffusion coefficients can be selected. In addition, constant thermal diffusion coefficient terms for each component can be entered in the table labelled Thermal Diffusion Coefficient Terms. Note that values entered in this table are not the thermal diffusion coefficients usually defined in the literature, but are the terms identified as Ft in Hoier and Whitson (SPE 63085). This table can also be used to enter multiplying factors for each component which will multiply the thermal diffusion coefficients calculated from the chosen model. If you select Enter constant thermal diffusion coefficient terms for each component or Enter thermal diffusion coefficient multiplying factors for each component, a table will open to the right for you to enter the thermal diffusion coefficient terms or multiplying factors respectively. CMG’s GEM compositional simulator allows input of tables of composition vs . depth for initialization of the reservoir via the keyword *ZDEPTH. The results of the compositional grading calculation can be written out with this keyword in the format expected by GEM. The data will be written to a file with the same root name as the data file and the extension (.gmz). This option is activated by selecting the check box in the General tab labelled “Write GEM *ZDEPTH keyword with composition vs. depth data …”.
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STARS PVT Data Generation
Overview You can use this option of WinProp to generate the complete PVT data required by CMG’s steam and additives thermal simulator STARS. The data which may be generated includes: 1. Initial composition data 2. Liquid component densities, compressibility and thermal expansion coefficients, plus nonlinear mixing function data for density 3. Liquid component viscosity tables or correlation coefficients, plus nonlinear mixing function data for viscosity 4. Gas component viscosity correlation coefficients 5. Simple analytical correlation for component vapor-liquid K-values 6. Tabular gas-liquid K-values 7. Tabular liquid-liquid K-values 8. Tabular solid-liquid K-values 9. Gas-liquid and liquid-liquid K-values at surface conditions
Use of the STARS PVT Generati on Opt ion At any stage in a WinProp data file (before or after regression for example) a basic STARS component description can be generated based on the current WinProp component information and the currently specified mixture composition. This option is invoked by selecting Simulator PVT | CMG STARS PVT Data. The data is written out to a special file with the input data file root name and extension (.str). Examples are included in the WinProp template directory as stars-vl_kvalues.dat (shown below), stars-vlaq_kvalues.dat , starsvls_kvalues.dat and stars-comp_props.dat to illustrate the use of this option. Please refer to the Introduction chapter for a brief description of each data file.
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The data written out to the (.str) file may be imported directly into Builder for all of the calculation options except the Gas-Liquid and Solid-Liquid K-Value Tables option. Please see the discussion below for details.
Input Data (STARS) Through the Calc. Type tab, you can choose to generate Basic STARS PVT data and/or Kvalue Tables by checking the corresponding boxes. If the K-value Tables box is checked, one of the following table options can be selected: Gas-Liquid K-Value Tables, Gas-Liquid and Liquid-Liquid K-Value Tables, or Gas-Liquid and Solid-Liquid K-Value Tables. Input data for each of these options is described below. At the end of this section, the options for plotting the component K-values are described.
Basi c STARS PVT Data Selection of this option allows calculation of all of the required pure component properties for a STARS fluid model. When the Basic STARS PVT Data option is selected, the Basic PVT and Density/Surface Control, tabs are activated. The following data may be entered on these tabs.
Reference Conditio ns Reference pressure and temperature, corresponding to STARS keywords PRSR and TEMR, are entered in the Reference Conditions area on the Basic PVT tab, shown below:
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Using small variations in pressure and temperature from the reference condition, a perturbation method is used to obtain the compressibility and first/second thermal expansion coefficients required by the STARS liquid density model. The pressure-temperature cross coefficient for liquid density is obtained by minimizing the difference between STARS density model and the EOS over a specified range of pressure and temperature. See Density Optimization Range (P, T). The liquid density in STARS is equal to that given by WinProp at the reference state.
Component Viscosity Model Pure component viscosities can be calculated using the currently selected WinProp viscosity model or using the two-parameter corresponding states (CS) model of Teja and Rice. Note: If you select Write liquid viscosity correlation coefficients as the component viscosity format, the 2-Parameter corresponding states model is automatically selected. If you select Write liquid viscosity-temperature scale as the component viscosity format, the associated parameter text boxes will become accessible and you will be able to select any of the three component viscosity models. The CS model uses the component acentric factor as an interpolating parameter, with the viscosities of ethane (C 2) and eicosane (C20) used as reference values. If the WinProp viscosity model is used, two calculation techniques are available: 1) “match dead oil” or 2) “scale viscosities”. Option 1 will use WinProp’s viscosity model to calculate the viscosities of all components that are liquid at the reference pressure and the specified temperature in the table, then calculate the apparent liquid viscosities of the gaseous components using STARS mixing rule. Option 2 will locate 2 temperatures for each component at which the component is in the liquid state. The viscosities at these two temperatures are extrapolated over all temperatures in the table. Option 1 will give more accurate intermediate component User Guid e WinPro p
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viscosities, whereas option 2 will give smoother curves. With any of the component viscosity model options, the component viscosities are scaled by the viscosity of the mixture calculated using the WinProp viscosity model. This ensures that the STARS viscosity model and the WinProp viscosity model give the same results for the specified mixture composition at the reference conditions.
Component Viscosity Format The viscosity information for STARS can be written out as Andrade correlation coefficients only if the two-parameter corresponding states model is used. If the component viscosity versus temperature/pressure table is used, any of the component viscosity models can be selected. If the tabular output is selected, the component viscosities are scaled by the WinProp mixture viscosity as described under Component Viscosity Model for each temperature/pressure in the table. For the tabular output, minimum and maximum temperature limits and the number of temperature steps must be input. A maximum of 40 steps for temperature or pressure may be specified. Use of the pressure steps for the liquid viscosity-temperature/pressure table is optional. If the pressure limits are left blank, one viscosity-temperature table will be calculated at the specified reference pressure. If pressure steps are specified, one viscosity-temperature table will be generated for each pressure step. There is a check-box available to “Write gas viscosity correlation coefficients.” If this is selected, WinProp will first calculate the viscosities of all components that are gas at low pressure (1 atm) and the specified reference temperature. Apparent gas viscosities of the liquid components are determined by perturbing the gas system with each liquid component individually, then back-calculating using STARS mixing rule. The component viscosities are scaled by the viscosity of the mixture calculated using the WinProp viscosity model. This ensures that the STARS viscosity model and the WinProp viscosity model give the same results for the specified mixture composition at the reference temperature and low pressure. For very heavy components the apparent gas viscosity calculation may fail. In this case the viscosity coefficients for these components will be written out as 0.0s, indicating that STARS default gas viscosity will be used.
Viscosity and Density Nonlinear Mixin g Controls For mixture viscosity and density calculations, functions can be defined describing the nonlinear effect of the composition of one key component on these properties. For each property, one key component may be selected from the component list then minimum and maximum mole fractions of that component specified. The nonlinear mixing function values are calculated such that the STARS property model gives the same result as the WinProp model over the specified composition range of the key component, with the ratios of all other components kept fixed.
K-Value Correlation Option K-Value correlation coefficients can optionally be output with the other basic STARS PVT data, by selecting Write K-Value correlation coefficients. The correlation coefficients are derived from Wilson’s equation, which combines Raoult’s law and the definition of acentric factor with a simple vapor pressure equation. Note that these coefficients are not adjusted to match WinProp’s equation of state flash calculations, and should be regarded as 152
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approximations which will be valid at low pressures only. If K-value tables are being generated, the generation of correlation coefficients should be turned off, as only one form of K-value data should be entered in a STARS data set.
Enthalpy Model Selecting Use pressure-dependent enthalpy will write out the PVT_DEPARTURE keyword and the associated ideal gas enthalpy coefficient data along with the other basic STARS PVT data. This will activate the Kesler-Lee EOS/corresponding states method for hydrocarbon phase enthalpy and heat capacity calculation in STARS. It is possible to turn on this same method in WinProp, which allows comparison to the default EOS method for enthalpy and heat capacity. Surface conditions, surface flash options, surface K-value options, and density optimization range are configured through the Density/Surface Control tab, shown below:
Surface Condit ions Surface pressure and temperature corresponding to STARS keywords PSURF and TSURF are entered on the Density/Surface Control tab. The STARS default for these values is 101 kPa and 16.85 C. The surface conditions are used for reporting well rates and accumulations in terms of standard densities. Values can be entered in the Pressure and Temperature text boxes, and buttons are provided to reset the text boxes to the WinProp and STARS default values.
Density Optim ization Range (P, T) This range is used to define a grid of pressure and temperature points at which densities are calculated from the EOS. The density optimization technique is used to simultaneously determine the pressure-temperature cross-coefficients for all components in the STARS fluid model to minimize the difference between the EOS densities and densities calculated from STARS mixing rule. User Guid e WinPro p
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Density at surface conditions is always included in the optimization by default. To obtain the best match between the EOS and STARS fluid model for density, enter the range of pressure and temperature expected to be encountered in the reservoir during the STARS simulation in the Density Optimization Range (P, T) area. The default values, which can be entered by clicking Default P Range and Default T Range buttons below the text fields, are 400~40000 kPa and 30~330 C.
Surface Flash Method There are two options available in WinProp for specifying how STARS will perform the flash at surface conditions for production reporting. One option is to Segregate components in product streams according to K-values, corresponding to the STARS keywords *SURFLASH *SEGREGATED. For all oleic components, this means that a component will be in the oil phase if its gas-liquid K-value is less than one, otherwise it will be in the gas phase. The other option is to Use the K-value flash for production, corresponding to the STARS keywords *SURFLASH *KVALUE. For both of these options, K-values at surface conditions must be determined. In the Surface K-Value Options area, Generate Gas-Liquid K-values at surface conditions and Generate Gas-Liquid and Liquid-Liquid K-values at surface conditions can be selected to force WinProp to output K-values calculated at the specified surface pressure and temperature. If Generate Gas-Liquid and Liquid-Liquid K-values at surface conditions is selected, the user can specify either oleic or aqueous as the reference phase for each component (through the Henry Const./Ref. Phase tab). If these check boxes are not selected, K-values will be determined from the correlations or tables. If K-value correlations are being used, the K-values at the surface temperature will be calculated from the correlations. If Kvalue tables are being used, surface K-values will be interpolated from the tables provided the surface conditions lie within the pressure and temperature range of the tables. If the surface conditions lie outside the range of the tables, the K-values corresponding to the pressure and temperature closest to the surface conditions will be used, that is the tables will not be extrapolated.
Gas-Liq uid K-Value Tables The Gas-Liquid K-Value Table option is used to generate gas-liquid K-values for hydrocarbon components, and optionally for a water component as well. Hydrocarbon and light gas components are all assumed to be oleic. That is, the K-value is defined as the gas phase mole fraction of the component divided by the oil phase mole fraction of the component. If water is present as a component in the system, it is defined as an aqueous component, and the gas-liquid K-value is defined as the gas phase mole fraction of water divided by the aqueous phase mole fraction of water. In this case, the aqueous phase mole fraction of water is assumed to be equal to one. K-values are calculated using a two-phase negative flash which allows generation of Kvalues outside of the two-phase region. See the Flash Calculations chapter for more details. There are limits in pressure and temperature beyond which the negative flash will be unable to converge. These limits normally lie quite far from the two-phase boundary, except near the critical point of the mixture. K-values which lie outside the range of convergence of the negative flash are estimated by linear extrapolation. Values which have been extrapolated are marked in the tables with the notation “”. 154
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The check box Use negative Newton flash option can be selected to specify that Newton’s method will be used to converge the flash equations. This method is expected to give better results in difficult (e.g. near-critical) regions. Following the last K-value table in the (.str) file, a map entitled “Comparison of WinProp (W) and STARS K-value (S) phase split calculations” is given. At each pressure and temperature specified for the tables, the phase split determined from WinProp’s flash calculation is compared to the phase split calculated from the STARS K-value tables which have been generated. For example, the notation indicates that WinProp’s equation of state flash has determined there is a Liquid-Vapor phase split (W: LV), and that a flash done with the K-values from the STARS tables has produced the same result (S: LV). This map allows a check on the phase behavior which will be predicted when the K-value tables are used for flash calculations. Differences between WinProp’s results and the STARS K-value results may be due to extrapolation of K-values, selection of water component options, or use of the K-value threshold as discussed below. When the Gas-Liquid K-Value Table option is selected, the K-Value tab is activated, as shown in the example below.
The following data may be entered on the K-Value tab.
Pressure Data In the Pressure Data area, enter the following pressure data: initial Pressure, Pressure Step, and No. of pressure steps. K-values are written out starting with the initial pressure, and continuing for the specified number of pressure steps, incrementing the pressure by the specified pressure step for each calculation. A minimum of 2 pressure steps must be specified.
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Temperatu re Data In the Temperature Data area, enter the following temperature data: initial Temperature, Temperature Step, and No. of Temperature Steps. K-values are written out starting with the initial temperature, and continuing for the specified number of temperature steps, incrementing the temperature by the specified temperature step for each calculation. A minimum of 2 temperature steps must be specified.
Compositi on-Dependent K-Value Control s The dependence of component K-values on the concentration of a single key component can be determined by WinProp and output in the form of composition-dependent K-value tables. Currently two of STARS composition dependence options may be enabled using WinProp: (1) global mole fraction of the key component and (2) Hand’s rule using the ratio of the mole fraction of the key component to the mole fraction of the heaviest oleic component. The input data in each case is the same: selection of the Key component from the component list, specification of the minimum and maximum global mole fractions of the key component (Min. global mole fraction and Max. global mole fraction), and specification of the number of mole fraction steps ( No. of mole fraction steps). A K-value table will be generated for each component for each of the specified mole fraction steps. When Hand’s rule is used, the heaviest hydrocarbon component in the system must be the first component in the component list. Please see the STARS User Guide for more information on Hand’s rule.
Water Component Optio ns The option to Use STARS default gas-liquid K-values for water causes no K-value table to be written out for the water component, allowing STARS internal defaults to be used. Note that when the phase split map is generated, the k-values from the default correlation are used. Use WinProp calculated gas-liquid K-values for water results in output of a table for the water component with the equation of state determined k-values. The option labelled Don’t allow water component to vaporize causes a table with all zero entries to be output for the water component. This last option can be used even when water is not present in the WinProp component list.
Minimum K-Value Threshol d The Minimum K-Value Threshold allows specification of a minimum value to be used in the K-value tables. Any number smaller than this will be replaced by the threshold value. The default value of 1.0E-16 will be used if this entry is left blank.
Gas-Liquid and Liqu id-Liquid K-Value Tables The Gas-Liquid and Liquid-Liquid K-Value Table option is used to generate gas-liquid and liquid-liquid K-values for hydrocarbon components and the water component. A water component must exist in the WinProp component list to use this option. User can specify either oleic or aqueous as the reference phase for each component. When you select the Gas-Liquid and Liquid-Liquid K-Value Table option, the K-Value and the Henry Const./Ref. Phase tabs are enabled. Instructions for using the K-Value tab can be found above, under Gas-Liquid K-Value Tables. The Henry Const./Ref. Phase tab is shown below: 156
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Through the Henry Const./Ref. Phase tab, the user can enter Henry Law constants for the components in the left hand pane, if they are left blank the Henry’s constants will be calculated based on the model parameters entered in Component Selection/Properties. The Reference Phase Aqueous grid in the right hand pane is used to define which components are referenced to the aqueous phase. Selected components are defined as aqueous components and unselected components are defined as oleic components. Water is always defined as an aqueous component. The gas-liquid K-value is defined as the gas phase mole fraction of the component divided by the reference phase mole fraction of the component. For the liquid-liquid K-value calculation: if the reference phase is aqueous, it is defined as the oleic phase mole fraction of the component divided by the aqueous phase mole fraction of the component. If the reference phase is oleic, it is defined as the aqueous phase mole fraction of the component divided by the oleic phase mole fraction of the component. Water is always defined as an aqueous component, thus the gas-liquid K-value is defined as the gas phase mole fraction of water divided by the aqueous phase mole fraction of water and the liquid-liquid K-value is defined as the oil phase mole fraction of water divided by the aqueous phase mole fraction of water. Generation of the gas-liquid and liquid-liquid K-value tables is done simultaneously using the Oil-Gas-Water flash, which models the aqueous phase with Henry’s Law and the vapor and liquid phases with the equation of state. See the Flash Calculations chapter for more details. If a stable oil-gas-water system exists at a specified pressure and temperature, all of the gas-liquid and liquid-liquid K-values are defined and may be calculated directly. If one or more of the three phases does not exist, a two-phase negative flash using Henry’s Law for one phase is attempted. Following this flash, a split of the hydrocarbon phase is attempted using the negative flash with the EOS for both phases. At the end of this process, K-values for all of the phases which have been located are calculated, and the remaining K-values are extrapolated. User Guid e WinPro p
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As described under Gas-Liquid K-Value Tables, the map entitled “Comparison of WinProp (W) and STARS K-value (S) phase split calculations” is again generated. An additional phase indicator (A) indicating the aqueous phase is used. Differences between the WinProp and STARS K-value calculated results may exist for the reasons described in the section on Gas-Liquid K-Value Tables, and also because the step-wise two-phase negative flash procedure may give slightly different results than the simultaneous three-phase flash which is used as the basis for the WinProp phase split results. The only differences in input data as compared to the Gas-Liquid K-value Tables option are that Hand’s rule is not available as a composition-dependent K-value option and an additional water component option may be selected: Use WinProp calculated liquid-liquid K-values for water. This allows generation of a table for calculating the amount of water in the liquid hydrocarbon phase. The default is to not allow any partitioning of water into the oil phase.
Gas-Liquid and Solid-Liquid K-Value Tables The Gas-Liquid and Solid-Liquid K-Value Table option is used to generate gas-liquid Kvalues for hydrocarbon components and solid-liquid K-values for the solid-forming components. A water component cannot exist in the WinProp component list when this option is used. Hydrocarbon and light gas components are all assumed to be oleic. That is, the gas-liquid K-value is defined as the gas phase mole fraction of the component divided by the oil phase mole fraction of the component. The solid-forming components are also assumed to be oleic, thus the solid-liquid K-values are defined as the mole fraction of the component in the solid phase divided by the mole fraction of the component in the liquid phase. The solid-liquid K-values are used with the partial equilibrium reaction keywords in STARS. Note that the complete keyword specification for use of the solid-liquid K-values is not written out to the (.str) file. Before importing into Builder or including in a STARS data set, the required keywords must be added to the k-value specification. Please see the STARS documentation for details. Generation of the gas-liquid and solid-liquid K-value tables is done simultaneously using the Asphaltene/Wax Modelling method described in the Flash Calculations chapter. As for the Gas-Liquid and Solid-Liquid K-Value Tables, if a stable three-phase system exists at a specified pressure and temperature, all of the gas-liquid and solid-liquid K-values are defined and may be calculated directly. If one or more of the three phases does not exist, a two-phase negative flash using the solid model for one phase is attempted. Following this flash, a split of the hydrocarbon fluid phase is attempted using the negative flash with the EOS for both phases. At the end of this process, K-values for all of the phases which have been located are calculated, and the remaining K-values are extrapolated. As described under Gas-Liquid K-Value Tables, the map entitled “Comparison of WinProp (W) and STARS K-value (S) phase split calculations” is again generated. An additional phase indicator (S) indicating the solid phase is used. Differences between the WinProp and STARS K-value calculated results may exist for the reasons described in the section on GasLiquid K-Value Tables, and also because the step-wise two-phase negative flash procedure may give slightly different results than the simultaneous three-phase flash which is used as the basis for the WinProp phase split results.
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The only differences in input data as compared to the Gas-Liquid K-value Tables option are that Hand’s rule is not available as a composition-dependent K-value option and none of the water component options are enabled.
Feed and K-Value Plotting Controls On the Feed/Controls/Plots tab, shown below, the feed composition can be specified along with some other controls as described in the Common Data Required for All Options chapter.
On this tab the check boxes for plotting the component K-values can also be selected. Depending on the calculation c alculation option selected, both the gas-liquid and liquid-liquid liquid-liquid K-values may be plotted. The results are always shown as log of the component K-values plotted against pressure, with a separate plot generated for each temperature in the table. ta ble.
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Black-Oil PVT Data Generation
Overview This option can be used to generate the PVT data for simulation studies with CMG’s CMG’s blackoil simulator IMEX as well as other commercially available black-oil black-oil simulators . In the latter case, some of these simulators implement the Extended Black-Oil Formulation. In addition to the standard black-oil parameters an additional parameter, the condensate gas ratio, often denoted as Rv is added to account for oil component vaporization in the gas phase at reservoir conditions. WinProp can generate PVT data for the extended black-oil model. Unlike models for CMG’s own simulator IMEX the data is presented in a “generic” format. The keywords do not exactly correspond to a specific simulator. The calculations should be done once an EOS model is obtained for the oil, generally through characterization of the heavy end followed by regression to match the available data. The PVT data is written out to a file with the root name corresponding to the input-data-file and with the extension (.imx). For example if the input file name is test.dat, the PVT data file will be test.imx. If the PVT data is designed for IMEX then it may be referenced as an include file in an IMEX data set or imported with Builder. If the PVT data is targeted at some other simulator then the information in the .imx file may require editing prior to use in the specific simulator of choice. A total of thirteen different fluid component models may be specified with IMEX. At present, WinProp can be used to generate six of those models, namely Black-Oil, Pseudo-miscible with chase gas, Pseudo-miscible without chase gas, Gas-Water, Gas-Water with Condensate and Volatile Oil. Please refer to the IMEX user guide for more information on these fluid models. For PVT data aimed at one of IMEX’s models, the following information is written out to the output file: 1. The *PVT *BG|*EG|*ZG 1 keyword and associated table (1 is always written out for the table number) are written for the oil models. The columns of this table are pressure, gas-oil ratio, oil formation volume factor, gas formation volume factor | gas expansion factor | gas Z-factor, oil viscosity and gas viscosity. For the pseudo-miscible option with chase gas, the solution gas always remains in solution. The solution gas-oil ratio is fixed and input through a field on the Solvent tab (writes out keyword *GORINT). The bubble point pressure versus solution gas-oil ratio curve in the table belongs to the chase gas. This is NOT taken into account when values are written to the PVT table . The total amount of solution gas is the value given by *GORINT and the dissolved chase gas given by the R s vs. bubble point pressure curve.
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For the Gas-Water model, a *PVTG *BG|*EG|*ZG table is written. The columns of this table are pressure, gas formation volume factor | gas expansion factor | gas Z-factor and gas viscosity. For the Gas-Water with Condensate table, ta ble, the *PVTCOND *BG|*EG|*ZG *BG|*EG|*ZG table is written with columns: pressure, gas-oil ratio, condensate-gas ratio, oil formation volume factor, facto r, gas formation volume volume factor | gas expansion expansion factor | gas Z-factor, oil viscosity and gas viscosity. For this option, a series of *BGUST|*EGUST|*ZGUST and *VGUST tables are also written, giving the formation volume factor and viscosity of the gas at saturation pressures lower than the corresponding mixture pressures given in the *PVTCOND table. BOT tables tables are not generated generated for this option, as the oil is assumed to be saturated at all times. For the Volatile Oil option, either the PVTCOND or PVTVO table can be written. Using the PVTCOND table with associated *BGUST|*EGUST|*ZGU *BGUST|*EGUST|*ZGUST ST and VGUST tables allows non-linear behavior of undersaturated gas to be modeled. Using PVTVO allows a simpler linear treatment of undersaturated gas properties by specifying only saturated gas and dry gas formation volume factors and viscosities. The *PVTCOND table specification is the same as for the Gas-Water with Condensate model, including use of *BGUST|*EGUST|*ZGUST and VGUST tables. The *PVTVO *BG|*EG|*ZG table is written with columns: pressure, gas-oil ratio, condensate-gas ratio, oil formation volume factor, fac tor, gas formation volume factor | gas expansion factor | gas Z-factor, oil viscosity, gas viscosity, dry gas formation volume factor | dry gas expansion factor | dry gas Z-factor and dry gas viscosity. *BOT tables are allowed with either table type for the volatile oil option. The units for these properties are indicated in the output file and are the same as in IMEX. Field, SI and modified SI units are supported. 2. Water phase properties properties are optional. optional. The keywords written out are *REFPW, *BWI, *CW, *VWI, *CVW and *DENSITY *WATER. 3. Gas phase density density at surface surface conditions, conditions, *DENSITY *DENSITY *GAS or *GRAVITY *GAS. 4. Oil phase density density at surface conditions, conditions, *DENSITY *DENSITY *OIL. *OIL. Pressure dependence of oil viscosity, *CVO. Oil compressibility at the original oil bubble point pressure *CO, or *BOT tables for the undersaturated oil may be output. Not required for the gas water option. 5. For the pseudo-miscible fluid m models odels a *PVTS *BS table. The entries of the table are pressure pressure,, solv solvent ent water water ratio ratio,, solv solvent ent expansi expansion on facto factor, r, solvent solvent viscosi viscosity ty and mixing mixing parameter parameter between between solvent solvent and oil. oil. The The solvent solvent den density sity is writt written en out with with the the keywords *DENSITY *SOLVENT. The mixing parameter between solvent and gas is written out with the *OMEGASG keyword. If the pseudo-miscible model with chase gas is chosen then the initial solution gas-oil ratio is written with keyword *GORINT. To generate the PVT data for the IMEX black-oil model the following information is required: 1. Composition of oil and, if the the swelling curve is to be generated, the gas composition. These These are entered on the Composition form. Oil is entered as the primary fluid and gas is the secondary secondary fluid. For For gas water option option enter the gas composition as the primary fluid on the composition form.
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2. The reservoir temperature temperature and a guess for the saturation saturation pressure pressure of the original oil. oil. These are entered on the Sat. Pressure tab of the Black-Oil PVT Data form:
For the Gas-Water option, only the reservoir temperature is required. 3. At least one pressure step for the differential liberation experiment on the grid with the label No. of pressure levels on the Pres. Levels tab:
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For Gas-Water option, these are pressures at which the properties gas formation volume factor and gas viscosity are to be calculated. The differential liberation experiment is not performed for the Gas-Water option. 4. The number of separators, excluding the stock tank and the operating conditions is displayed on the Pres. Levels tab. A maximum of 8 separators may be specified. For Gas-Water case only the standard (stock tank) conditions are required. 5. If the swelling curve is to be generated then the composition of the injection gas is entered on the Composition form as the secondary fluid. If the solution gas is to be used for swelling calculation, then select the appropriate option button on the Gas Properties tab in the Injection gas composition for swelling test area:
On the grid labelled No. of swelling experiments on the Pres. Levels tab, enter the mole fraction of the gas, an initial guess for the saturation pressure of the oil/gas mixture and the saturation pressure flag. For the Gas-Water option, these data are not required. 6. Water phase properties may be input by the user directly on the Water Properties tab or alternatively, estimated from built-in correlations. This data is optional. 7. For the pseudo-miscible options, the solvent composition can be the secondary fluid on the Composition form or values entered on the Solvent Properties tab. The oil solvent mixing ratio as a function of pressure is entered on the grid provided on this tab. These values are echoed as column 5 of the *PVTS table. The remaining entries of this table, that is, the solvent water ratio, the solvent expansion factor and the solvent viscosity, will be calculated by the program. Add the water component from the library for the solvent solubility in the aqueous phase calculations. Enter a composition of zero for the water component. The fields for entering the solvent gas mixing parameter and the minimum solvent saturation are on the Solvent Properties tab. If the Pseudo Miscible with Chase Gas option is selected on the Model tab
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then the Initial solution GOR text box in the Solvent Properties tab is enabled and a value is required. 8. For the Gas-Water with Condensate option, the method for calculating oil phase properties (Bo and GOR) must be selected on the Oil Properties tab. Oil phase properties can be obtained by flashing a sample of the oil phase at each depletion pressure through the user-defined separators (Method of Whitson and Torp) or alternatively, from material balance equations (Method of Coats). For PVT data aimed at an extended black-oil model, the following information is written out to the output file: 1. The *PVTO keyword and associated table. Typical output is shown below. *PVTO * * s ol ut i on pr e ss ur e , oi l oi l ** GOR( 2) psi a FVF( 1) vi s, cp ** - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0. 2606 515. 00 1. 2279 0. 16615 1115. 00 1. 2158 0. 17475 1915. 00 1. 1996 0. 18621 2715. 00 1. 1834 0. 19768 3515. 00 1. 1673 0. 20914 5000. 00 1. 1372 0. 23043 6034. 82 1. 1163 0. 24526 6500. 00 1. 1069 0. 25192 0. 5045 1115. 00 1. 3730 0. 14572 1915. 00 1. 3503 0. 15714 2715. 00 1. 3275 0. 16856 3515. 00 1. 3048 0. 17998 5000. 00 1. 2626 0. 20118 6034. 82 1. 2332 0. 21595 6500. 00 1. 2199 0. 22259 0. 8261 1915. 00 1. 5462 0. 12408 2715. 00 1. 5150 0. 13452 3515. 00 1. 4839 0. 14497 5000. 00 1. 4262 0. 16436 6034. 82 1. 3859 0. 17787 6500. 00 1. 3678 0. 18394 1. 1532 2715. 00 1. 7100 0. 10950 3515. 00 1. 6720 0. 11872 5000. 00 1. 6015 0. 13582 6034. 82 1. 5523 0. 14774 6500. 00 1. 5302 0. 15310 1. 4574 3515. 00 1. 8505 0. 10135 5000. 00 1. 7735 0. 11634 6034. 82 1. 7198 0. 12679 6500. 00 1. 6956 0. 13149 1. 6255 5000. 00 1. 8713 0. 10344 6034. 82 1. 8290 0. 11189 6500. 00 1. 8100 0. 11568 1. 7044 6034. 82 1. 8751 0. 10689 6500. 00 1. 8590 0. 11031 1. 7399 6500. 00 1. 8768 0. 10845
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The columns of this table are the gas-oil ratio (GOR), pressure, oil formation volume factor, and oil viscosity. For each GOR value the first row shows the saturated fluid values. For a GOR of 0.2606 mscf/stb for example, the saturation User Guide WinProp
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pressure is 515 psia, the formation volume factor equals 1.2279 and the viscosity is 0.16615 cP. Second and subsequent rows of data for a given GOR define the undersaturated curves for the oil formation volume factor and viscosity as a function of pressure as specified in column 2. 2. PVTG (gas phase properties) and associated table. Typical format is shown below: *PVTG ** pr essur e, sol ut i on, gas gas ** psi a CGR( 4) FVF( 3) vi s, cp ** - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 515. 00 0. 000597 5. 73365 0. 01262 0. 000000 5. 73597 0. 01263 1115. 00 0. 001038 2. 37473 0. 01441 0. 000597 2. 37631 0. 01441 0. 000000 2. 37845 0. 01440 1915. 00 0. 005019 1. 27344 0. 01926 0. 001038 1. 28264 0. 01905 0. 000597 1. 28366 0. 01903 0. 000000 1. 28504 0. 01900 2715. 00 0. 020711 0. 90464 0. 02658 0. 005019 0. 92026 0. 02516 0. 001038 0. 92444 0. 02481 0. 000597 0. 92491 0. 02477 0. 000000 0. 92555 0. 02472 3515. 00 0. 057092 0. 75257 0. 03598 0. 020711 0. 75975 0. 03208 0. 005019 0. 76457 0. 03045 0. 001038 0. 76597 0. 03004 0. 000597 0. 76613 0. 02999 0. 000000 0. 76634 0. 02993 5000. 00 0. 186452 0. 69119 0. 06067 0. 057092 0. 64409 0. 04474 0. 020711 0. 63417 0. 04032 0. 005019 0. 63060 0. 03844 0. 001038 0. 62977 0. 03797 0. 000597 0. 62968 0. 03792 0. 000000 0. 62956 0. 03785 6034. 82 0. 265054 0. 69762 0. 07772 0. 186452 0. 66087 0. 06746 0. 057092 0. 60205 0. 05014 0. 020711 0. 58698 0. 04532 0. 005019 0. 58085 0. 04326 0. 001038 0. 57933 0. 04274 0. 000597 0. 57916 0. 04268 0. 000000 0. 57894 0. 04261 6500. 00 0. 300389 0. 70479 0. 08562 0. 265054 0. 68800 0. 08103 0. 186452 0. 64996 0. 07045 0. 057092 0. 58755 0. 05249 0. 020711 0. 57093 0. 04747 0. 005019 0. 56402 0. 04533 0. 001038 0. 56230 0. 04479 0. 000597 0. 56210 0. 04473 0. 000000 0. 56185 0. 04464
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Sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas Sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Under sat ur at ed Dr y gas
gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas gas
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3. The columns of this table are the pressure, the condensate gas ratio, the gas formation volume factor and viscosity respectively. The first row corresponds to saturated values. Subsequent rows show the properties of the mixture of saturated gas and dry gas. These combinations are done such that the mixtures correspond to condensate gas ratios that are specified at lower pressures. For example at a pressure of 1800 psia there is one row for undersaturated gas with a CGR of 0.00104 stb/mscf which is the CGR ratio at the previous pressure value of 1100 psia. 4. The stock tank densities of the oil, gas and water phase as well as the water phase properties. To generate the PVT data for the extended black-oil model the following information is required: 1. Composition of oil and, if the swelling curve is to be generated, the gas composition. These are entered on the Composition form. Oil is entered as the primary fluid and gas is the secondary fluid. The injection gas composition can alternatively be chosen to be the solution gas. The selection is made on the Gas Properties tab in the Injection gas composition for swelling test area:
2. Selection of the PVT Experiment. For black-oils, differential liberation corresponds best to the depletion process occurring in the reservoir. For light oils, differential liberation or constant volume depletion may be chosen. For gas condensates the constant volume depletion experiment is appropriate. The PVT experiment provides samples of the gas and oil phase which are then flashed through the user defined separators to obtain the oil and gas properties. The selection is made in the PVT Experiment area of the Model tab of the Black Oil PVT Data node.
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Black-Oil PVT Data Generation 167
The PVT Experiment area is accessible based on the model selection, as shown in the following example:
3. Selection of the method for calculating oil phase properties. Oil phase properties can be obtained by flashing a sample of the oil phase at each depletion pressure through the user defined separators (Method of Whitson and Torp) or alternatively from material balance equations (Method of Coats). This choice is made in the Oil FVF and GOR calculation area on the Oil Properties tab, which will be accessible based on the model selection, as shown below:
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4. Option for calculating oil phase properties above the original saturation pressure. This selection is made in the Calc. of Oil Prop. Above Original Sat. Pressure area on the Model tab:
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Black-Oil PVT Data Generation 169
If values for the oil and gas properties are required for pressures greater than the original saturation pressure then a choice of three techniques is available. Option 1 is to simulate a swelling test to extend the curves. This requires the injection gas composition. This method generally works well for black-oils. Option 2 is to extrapolate the curves while honoring certain relationships between the parameters. For black-oils (but generally not for light oils and condensates) there is a linear relationship between oil phase formation volume and GOR. There is also a linear relationship between oil density and viscosity. Option 3 is to simply extrapolate the curves individually without assuming any specific relationship between the parameters. Option 3 appears to be the only viable option for light oils and gas condensates. 5. The reservoir temperature and a guess for the saturation pressure of the original oil. These are entered in the Reservoir temperature / saturation pressure estimate area on the Sat. Pressure tab of the Black-Oil PVT Data form.
6. At least one pressure step for the differential liberation experiment or constant volume depletion experiment on the No. of pressure levels grid on the Pres. levels. tab. 7. The number of separators excluding the stock tank and the operating conditions can be specified in the Separator conditions area on the Pres. Levels tab. A maximum of 8 separators may be specified.
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8. If the swelling curve is to be generated then the composition of the injection or solution gas is entered on the Composition form. On the No. of swelling experiments grid on the Pres. levels tab enter the mole fraction of the gas, initial estimate for the saturation pressure of the oil/gas mixture and the saturation pressure flag:
9. Water phase properties may be input by the user directly on the Water Properties tab or alternatively estimated from built in correlations. PVT data can also be generated for a commercial black oil simulator, i.e., not for IMEX. This format is referred to as Format II, with Format I corresponding to IMEX. There are four “models” in this case, as shown in the Black Oil Tables, Format II area below:
Model 1 writes out differential liberation and separator calculation results separately, that is, differential liberation data is not adjusted for surface (separator) conditions. Model 2 writes out the “corrected” differential liberation data. Model 3 is for simulating an oil water system. The differential liberation data is not corrected for surface conditions for model 3. Model 4 corresponds to a gas water system. PVT data for a black oil simulator written in Format II, the following information is written out to the output file:
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Black-Oil PVT Data Generation 171
1. The *BOTAB 1 keyword and associated table (1 is always written out for the table number) for models 1-3, including oil water and BGTAB 1 for gas water option. For models 1 and 2, this is followed DOS WTOS and PSAT keywords and the corresponding values. DOS is the density of saturated oil at reservoir temperature and the original oil saturation pressure in units of gm/cc. WTOS is the molecular weight of the oil in gm/gmol and PSAT is the saturation pressure of the original oil in psia or kPa units. For the oil water option, model 3, the BOTAB keyword is followed by DOB WTRO and GR keywords and the corresponding values in a new line. The values are the density of the residual oil from differential liberation experiment in gm/cc, molecular weight of the residual oil in gm/gmol and gas gravity of the solution gas. For the gas water option, model 4, the BGTAB keyword is followed by the GR keyword and a value for the gas gravity. Typical results for model 1 are shown below: BOTAB 1 C** VALUES I N TABLE DI FLI B RESULTS, NOT CORRECTED FOR C** SURFACE CONDI TI ONS DOS WTOS PSAT 0. 5897 99. 48 2179. 86
2. The columns of the BOTAB table for models 1 and 2, are the saturation pressure, gasoil ratio, oil formation volume factor, gas formation volume factor, gas gravity, oil viscosity and gas viscosity. The table is arranged with highest pressure first and the lowest pressure last in monotonic order. The units for these properties are indicated in the output file. For model 1 where the entries in the BOTAB table are not adjusted for surface conditions, the values shown correspond to those calculated by the differential liberation test. For model 2 the values in the table have been corrected for surface conditions. For model 3, Oil Water option, the values in the BOTAB have not been adjusted for surface conditions. Since gas properties are not required the columns of the oil water table are saturation pressure, gas oil ratio, oil formation volume factor and oil viscosity. The columns of the BGTAB table are the pressure, gas formation volume factor and gas viscosity. Typical results for model 1 are shown below: C** pr essur e, sol ut i on C** psi a GOR( 2) C** - - - - - - - - - - - - - - - - - - - - PSAT RS 3970. 15 1. 5087 3726. 70 1. 3440 2872. 26 0. 8910 2179. 86 0. 6192 2100. 00 0. 5915 1850. 00 0. 5094 1600. 00 0. 4334 1350. 00 0. 3625 1100. 00 0. 2959 850. 00 0. 2325 600. 00 0. 1707
oi l gas FVF( 1) FVF( 3) --------- ---------BO BG 1. 8045 0. 74298 1. 7254 0. 78048 1. 5086 0. 98604 1. 3788 1. 30766 1. 3651 1. 35951 1. 3242 1. 55392 1. 2864 1. 81437 1. 2510 2. 17750 1. 2174 2. 71317 1. 1851 3. 57349 1. 1528 5. 16455
gas oi l gas gravi t y vi s, cp vi s, cp ---------- ---------- -------GR VO VG 0. 85325 0. 20414 0. 0303 0. 83804 0. 22407 0. 0283 0. 79643 0. 30972 0. 0224 0. 77723 0. 40449 0. 0189 0. 77610 0. 41726 0. 0186 0. 77425 0. 46041 0. 0177 0. 77564 0. 50903 0. 0168 0. 78143 0. 56684 0. 0160 0. 79374 0. 61839 0. 0154 0. 81701 0. 67266 0. 0147 0. 86209 0. 74204 0. 0141
3. For models 1-3 the undersaturated oil formation volume factors and oil viscosities curves as a function of pressure for each saturation pressure. These are defined by a table with columns corresponding to saturation pressures as shown on the BOTAB table and rows corresponding to pressure elevation above the saturation pressure i.e. dp = p-psat. For each pressure a value for the formation volume factor
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and a value for the oil viscosity divided by the corresponding values at saturation pressure is shown. Typical results are shown below: PSAT 3970. 15 3726. 70 2872. 26 2179. 86 1350. 00 1100. 00 850. 00 600. 00
2100. 00
1850. 00
1600. 00
DP BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC BOFAC VOFAC 243. 44 0. 9921 1. 02010 0. 9925 1. 02042 0. 9937 1. 02213 0. 9945 1. 02421 0. 9946 1. 02449 0. 9949 1. 02541 0. 9952 1. 02642 0. 9954 1. 03114 0. 9957 1. 03619 0. 9960 1. 03787 0. 9963 1. 03973 1097. 89 1. 10918 1. 14044
0. 9645 0. 9757 0. 9807
1. 09065 1. 11044 1. 16320
0. 9662 0. 9770 0. 9819
1. 09209 1. 11461 1. 17077
0. 9714 0. 9782 0. 9831
1. 09979 1. 11914 1. 17917
0. 9753 0. 9794
1790. 29 1. 17804 1. 22902
0. 9422 0. 9604 0. 9685
1. 14781 1. 18009 1. 26613
0. 9448 0. 9624 0. 9704
1. 15017 1. 18688 1. 27847
0. 9534 0. 9645 0. 9725
1. 16273 1. 19428 1. 29216
0. 9597 0. 9665
1870. 15 1. 18598 1. 23923
0. 9396 0. 9586 0. 9670
1. 15441 1. 18812 1. 27800
0. 9424 0. 9608 0. 9691
1. 15686 1. 19522 1. 29089
0. 9513 0. 9629 0. 9713
1. 16999 1. 20294 1. 30519
0. 9579 0. 9650
2120. 15 1. 21084 1. 27121 2370. 15 1. 23571 1. 30319
0. 9315 0. 9531 0. 9626 0. 9234 0. 9475 0. 9582
1. 17505 1. 21327 1. 31517 1. 19569 1. 23842 1. 35233
0. 9347 0. 9555 0. 9650 0. 9270 0. 9503 0. 9609
1. 17783 1. 22132 1. 32978 1. 19880 1. 24741 1. 36866
0. 9448 0. 9579 0. 9674 0. 9383 0. 9530 0. 9636
1. 19271 1. 23007 1. 34599 1. 21543 1. 25720 1. 38679
0. 9523 0. 9603
2620. 15 1. 26057 1. 33518
0. 9154 0. 9420 0. 9538
1. 21633 1. 26356 1. 38949
0. 9193 0. 9450 0. 9568
1. 21977 1. 27351 1. 40755
0. 9318 0. 9480 0. 9598
1. 23816 1. 28433 1. 42759
0. 9410 0. 9509
2870. 15 1. 28543 1. 36716
0. 9073 0. 9365 0. 9494
1. 23697 1. 28871 1. 42666
0. 9116 0. 9398 0. 9526
1. 24074 1. 29961 1. 44643
0. 9253 0. 9430 0. 9559
1. 26088 1. 31146 1. 46838
0. 9354 0. 9462
3120. 15 1. 31029 1. 39914
0. 8992 0. 9309 0. 9450
1. 25761 1. 31386 1. 46382
0. 9039 0. 9345 0. 9485
1. 26171 1. 32570 1. 48532
0. 9188 0. 9381 0. 9521
1. 28360 1. 33859 1. 50918
0. 9298 0. 9416
0. 8911 0. 9254 0. 9406
1. 27825 1. 33901 1. 50098
0. 8962 0. 9293 0. 9444
1. 28268 1. 35180 1. 52421
0. 9123 0. 9331 0. 9483
1. 30633 1. 36572 1. 54998
0. 9242 0. 9369
0. 9467 0. 9556
1. 33515 1. 43112
4. For models 1 and 3 the oil properties of the original oil are calculated by flashing through the user defined separator battery. Typical output is shown below:
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Black-Oil PVT Data Generation 173
C** SEPARATOR TEST DATA SEPTEST 1 PVTTABLE 1 PSATF BOF 2179. 86 1. 3447 P T GOR 300. 00 75. 00 0. 42 200. 00 75. 00 0. 03 100. 00 75. 00 0. 04 14. 70 60. 00 0. 08
BOSTG 1. 0788 1. 0654 1. 0484 1. 0000
GR 0. 7100 0. 7588 0. 8849 1. 3454
To generate the PVT data for the Black Oil PVT Model (Format II), the following information is required: 1. Composition of oil and, if the swelling curve is to be generated, the gas composition. These are entered on the Composition form. Oil is entered as the primary fluid and gas is the secondary fluid. Alternatively the user can choose to use the solution gas at the original oil saturation pressure as the injection gas. This option can be selected in the Injection gas composition for swelling gas area on the Gas Properties tab. For gas water option enter the gas composition as the primary fluid on the Composition form. 2. The reservoir temperature and an estimate for the saturation pressure of the original oil. These are entered in the Reservoir temperature / saturation pressure estimate area on the Sat. Pressure tab of the Black-Oil PVT Data form. For the Gas-Water option, only the reservoir temperature is required. 3. At least one pressure step for the differential liberation experiment on the No. of pressure levels grid on the Pres. levels tab. 4. The number of separators, excluding the stock tank, and the operating conditions, are entered in the Separator conditions area on the Pres. Levels tab. A maximum of 8 separators may be specified. 5. If the swelling curve is to be generated then the composition of the injection or solution gas is entered on the Composition form. On the No. of swelling experiments grid on the Pres. levels tab, enter the mole fraction of the gas, initial guess for the saturation pressure of the oil/gas mixture and the saturation pressure flag. For the Gas, Water option, these data are not required. 6. Water phase properties may be input by the user directly on the Water Properties tab or alternatively estimated from built in correlations.
Laboratory Procedure This procedure is generally performed to obtain PVT data for black-oil simulation. The sample of reservoir liquid in the laboratory cell is brought to the bubble-point pressure, and the temperature is set to the reservoir temperature. Pressure is reduced by increasing the cell volume. All the gas is expelled from the cell while pressure is held constant by reducing the cell volume. The gas is collected and its composition and volume are measured at the experiment conditions as well as standard conditions. This enables the formation volume factor of gas (B g) to be calculated. The gas viscosity is also measured. A sample of the oil phase is removed at each pressure and its viscosity is measured. The oil sample is then flashed through the separators to obtain the 174
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formation volume factor and gas-oil ratio. The process is repeated in steps until atmospheric pressure is reached. For the light oil model the gas sample at each step is also put through the separators to obtain the gas shrinkage as well as condensate production at the surface. To obtain data corresponding to the swelling curve, the procedure for the swelling experiment is followed to obtain the saturation pressure. The reservoir oil is loaded in a cell, and the temperature is set at the reservoir temperature. The bubble point of the oil is measured. A small amount of injection gas is transferred into the cell. A new saturation pressure is determined. This process is repeated until the upper bound of injection-gas concentration is reached (e.g. 60 mol %) or the saturation pressure of the fluid is equal to the estimated injection pressure. Each oil/gas mixture is then flashed through the separators to get the oil formation volume factor and GOR. In addition the properties of the equilibrium gas are measured and reported (gas formation volume factor, viscosity).
Input Data This option is invoked by selecting Simulator PVT | Black-Oil PVT Data or by clicking on the options toolbar button BLK PVT. The template files imex-blackoil.dat, imex_condensate.dat and imex_voloil.dat show the data entry for all of the supported fluid models for IMEX. Normally only a single Black-Oil PVT Data form should be included in a data set. There are also two additional template cases, extended_blackoil.dat illustrating generation of PVT data for an extended black oil model and format2_blackoil.dat for black oil model with the results written out in format type 2. On the Model tab select either “CMG IMEX PVT Models”, “Extended Black-Oil Models” or “Black Oil PVT Model (Format II)”. If “CMG IMEX PVT Models” is chosen then select further one the six available fluid models. For “Black Oil PVT Model (Format II)”, choose one of the four available models. Then enter data on the Sat. Pressure, Pres. Levels, Water Properties (optional), Oil Properties and Gas Properties tabs. The Solvent Properties tab is also enabled for data entry if one of the pseudo-miscible fluid models of IMEX is selected. For “CMG IMEX PVT Model” select Volatile Oil in the CMG IMEX PVT Models area then, on the Oil Properties tab, select the method of calculating oil properties, one of either “Method of Whitson and Torp” or “Method of Coats”. Selection of “Method of Whitson and Torp” implies oil phase properties are calculated by flashing a sample of the oil phase at each pressure step of the differential liberation, constant volume depletion or swelling test simulation. By selecting “Method of Coats”, oil phase properties are calculated by material balance principles where possible, that is, for pressures less than the original oil saturation pressure. If data for pressures greater than original oil saturation pressure is required then select the method for generating this data in the Calc. of Oil Prop. Above Original Sat. Pressure area of the Model tab, one of: Simulation of a swelling experiment (gas injection) Extrapolation based on linear relationship between GOR and FVF and viscosity as a function of density Extrapolation of individual properties without assuming any relationship between properties. In this case, you will be prompted to enter the extrapolation order: “1” for linear, “2” for quadratic, and so on. User Guide WinProp
Black-Oil PVT Data Generation 175
For a description of the data on the Sat. Pressure tab, please refer to the Saturation Pressure section in the Two-Phase Saturation and Phase Boundary Calculations chapter. On the Pres. Levels tab, enter the pressure levels for the differential liberation calculation underneath the grid in the No. of pressure levels area. These pressures should all be less than the saturation pressure if the swelling option is being used to generate data for pressures greater than the original oil saturation pressure. If the extrapolation option is being used, enter all pressures in the “differential liberation” table including pressures greater than the original oil saturation pressure. Enter values starting from the highest pressure value to the lowest pressure value. As values are entered, the No. of pressure levels value will be updated accordingly. Rows can be added or deleted from this table by using button at the top of the table. At least one value is required. The pressure and temperature for the separator stages can be defined in the table in the Separator conditions area. A maximum of eight separator stages excluding the stock tank is allowed. The stock tank pressure is entered in the Stock tank pressure text box and the stock tank temperature in the Stock tank temperature text box. The stock tank stage is always included in the calculation whereas the inclusion of other separators is optional. The separator pressure and temperature are entered directly on the table. Please enter values starting from the highest pressure to the lowest pressure on the table. If there is only one separator then the pressure and temperature for this separator should be entered on row 1. For two separators use the first two rows. If the swelling curve is to be generated then enter the mole fraction of the gas in column 2 of the table labelled No. of swelling experiments. In column 3 enter the initial estimate for the saturation pressure of this mixture and in column 4, enter the saturation pressure flag. Valid entries here are either 2 or –2. A value of 2 indicates that the initial guess for saturation pressure will be improved via stability analysis, while a value of –2 indicates that the initial guess entered on the table will be used directly. The Pressure Levels tab corresponding to imex-blackoil.dat is shown below:
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On the Water Properties tab, enter the properties of the water phase. These may be input directly by the user or calculated from internal correlations by the program. To calculate from correlations enter data for salinity, water bubble point and the reference pressure, then click the “Apply:...” button at the bottom of the form. Alternatively, data can be entered directly in the required fields reference pressure, formation volume factor of the water, compressibility, viscosity at the reference pressure, pressure dependence of viscosity and water phase density. On the Oil Properties tab, the user can enter values for certain oil properties directly instead of accepting the values calculated internally by WinProp. To enter oil density (or alternatively oil gravity) directly, select that option in the Oil density / API gravity area then enter the value in the text box provided. To enter the oil viscosity pressure dependence directly, select Input oil viscosity pressure dependence then enter a value for this property in the text box. For undersaturated oil compressibility, three options are available in the Oil compressibility area. The default is Generate undersaturated oil formation volume factor tables to create a table of undersaturated compressibility as a function of saturation pressure. Alternatively, if only the compressibility of oil corresponding to the original oil composition at the saturation pressure is desired, select Calculate undersaturated oil compressibility at the original oil bubble point . To enter the oil compressibility of the original oil at saturation pressure, select Input undersaturated oil compressibility then enter an appropriate value in the text box provided. On the Gas Properties tab, several options for writing out the gas phase density or specific gravity are provided. The user can either accept the WinProp-generated value or enter the appropriate value directly. If one of the two pseudo-miscible models is selected then additional data is required on the Solvent Properties tab. This includes the solvent composition, gas-oil mixing ratio as a function of pressure, the solvent gas mixing ratio, the minimum solvent saturation and for the pseudo-miscible fluid model with chase gas, the initial gas-oil ratio. Extended Black Oil Model: Coats Material Balance equations
In the Coats method, only the reservoir vapor is taken through the separators . The oil phase properties formation volume factor (Bo) and gas-oil ratio (R s), are obtained from material balance equations at each expansion step of the CVD or differential liberation experiment from V1 to V2. These equations are: ρ sto V2 b gS g + b o R sS o 2 = ρ sto V1 b gS g + b o R sS o 1
ρ stg V2 b g R v S g + b oS o
2
= ρstg V1 b g R v S g + b oS o
1
Where ρsto and ρstg are fixed surface densities and bo = 1/Bo, bg = 1/Bg. The stock tank densities are obtained from the output of the separators at saturation pressure. The values at the saturation pressure are obtained by the Whitson-Torp method. Compressibility test
Oil and gas properties calculated for IMEX or for the extended black-oil simulator are checked to ensure that the total compressibility is greater than zero . This requires that the oil and gas compressibilities (C o and Cg) respectively as defined by the following equations are greater than zero:
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Black-Oil PVT Data Generation 177
C0
=
− dBo dR s Bg − R v Bo ) + B0 dp dp (1 − R s R v ) 1
− dBg dR v B0 − R s Bg ) + Bg dp dp (1 − R s R v ) For conventional black-oil model, R v and dR v/dp are both zero Cg
=
1
.
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References
List 1. Ahmed, T.: Hydrocarbon Phase Behavior, Gulf Publishing Company, Houston, 1989. 2. Agarwal, R.K., Li, Y.-K., and Nghiem, L.: "A Regression Technique With Dynamic Parameter Selection for Phase-Behavior Matching", SPE Reservoir Engineering, February 1990, pp. 115-120. 3. Danesh, Ali: Developments in Petroleum Science 47, PVT and Phase Behaviour of Petroleum Reservoir Fluids, Elsevier, 1998. 4. Dranchuk, P.M., Purvis R.A., and Robinson D.B.: "Computer Calculations of Natural Gas Compressibility Using the Standing and Katz Correlation", Institute of Petroleum Technical Series, No IP 74-008, 1974. 5. Firoozabadi, A., Katz, D.L., Soroosh, H., and Sajjadian, V.A.: "Surface Tension of Reservoir Crude-Oil-Gas Systems Recognizing the Asphalt in the Heavy Fraction", SPE Reservoir Engineering, February 1988, pp. 265-272. 6. Grabowski, M.S., and Daubert, T.W.: "A Modified Soave Equation of State for Phase Equilibrium Calculations", I. & E.C. Process Design and Development, Vol. 17, No. 4, 1978, pp. 443-454. 7. Goossens, A.G.: "Prediction of Molecular Weight of Petroleum Fractions", Ind. Eng. Chem. Res., 35, 1996, pp. 985-988. 8. Heidemann, R.A., and Khalil, A.M.: "The calculation of Critical Points", AIChE J., Vol. 26, September 1980, pp. 769-779. 9. Hoffman, A.E., Crump, J.S., and Hocott, C.R.: "Equilibrium Constants for a Gas Condensate System", Trans. AIME, 198, pp. 1-10, 1953. 10. Jhaveri, B.S., and Youngren, G.K.: "Three-Parameter Modification to the PengRobinson Equation of State to Improve Volumetric Predictions", SPE Reservoir Engineering, Vol. 3, No. 3, August 1988, pp. 1033-1040. 11. Katz, D.L., and Firoozabadi, A.: "Predicting Phase Behavior of Condensate/CrudeOil Systems Using Methane Interaction Coefficients", J. Petrol. Technol., Vol. 30, November 1978, pp. 1649-1655. 12. Kesler, M.G., and Lee, B.I.: "Improve Prediction of Enthalpy of Fractions", Hydro. Proc., March 1976, pp. 153-158.
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References 179
13. Kokal, S.L., and Sayegh, S.G.: "Gas-saturated bitumen density predictions using the volume-translated Peng-Robinson equation of state", Journal of Canadian Petroleum Technology, Vol. 29, No. 5, September-October 1990, pp. 77-82. 14. Lee, A.L., and Eakin, B.E.: "Gas-Phase Viscosity of Hydrocarbon Mixtures", Society of Petroleum Engineers Journal, Vol. 4, September 1964, pp. 247-249. 15. Lee, B.I., and Kesler, M.G.: "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., Vol. 21, May 1975, pp. 510-527. 16. Li, Y.-K., Nghiem, L.X.: "Phase Equilibria of Oil, Gas and Water/Brine Mixtures from a Cubic Equation of State and Henry's Law", Can. J. Chem. Eng., Vol. 64, 1986. 17. McCain, W.D. Jr.: The Properties of Petroleum Fluids, Second Edition, PennWell Books, Tulsa, Oklahoma, 1990. 18. Merrill, R.: EEC Summer School 1993; Sampling and Characterization of Reservoir Fluids, Course Notes, 1993. 19. Nghiem, L.X., Hassam, M.S., Nutakki, R., and George, A.E.D.: "Efficient Modeling of Asphaltene Precipitation", paper SPE 26642, presented at the 68th Annual Technical Conference and Exhibition of SPE, Houston, Texas, 3-6 October 1993. 20. Nghiem, L.X., Coombe, D.A., and Hassam, M.S.: "Modelling effects on Asphaltene Precipitation", Hydrocarbon Technology International, Autumn 1996. 21. Nghiem, L.X., and Li, Y.-K.: "Computation of Multiphase Equilibrium Phenomena With an Equation of State", Fluid Phase Equilibria, Vol. 17, 1984, pp. 77-95. 22. Nghiem, L.X., Li, Y.-K., and Heidemann, R.A.: "Application of the Tangent Plane Criterion to Saturation Pressure and Temperature Computations", Fluid Phase Equilibria, Vol. 21, 1985, pp. 39-60. 23. Nghiem, L.X., and Li, Y.-K.: "Phase-Equilibrium Calculations for Reservoir Engineering and Compositional Simulation", Proceedings of the Second International Forum on Reservoir Simulation, Alpbach, Austria, September 4-8, 1989. 24. Nutakki, R., Nghiem, L., Li, Y.-K., and George, A.: "Optimal Representation of Heavy Fractions in the Simulation of Multiple-Contact Processes", paper CIM/AOSTRA 91-57, presented at the 1991 CIM/AOSTRA Technical Conference, Banff, April 21-24. 25. Nutakki, R., Hamoodi, A.N., Li, Y.-K., and Nghiem, L.X.: "Experimental Analysis, Modelling, and Interpretation of Recovery Mechanisms in Enriched-Gas Processes", paper SPE 22634, presented at the 66th Annual Technical Conference and Exhibition of SPE, Dallas, Texas, 6-9 October 1993. 26. Oellrich, L., Plocker, U., Prausnitz, J.M., and Knapp, H.: "Equation-of-State Methods for Computing Phase Equilibria and Enthalpies", Int. Chem. Eng., Vol. 21, No. 1, January 1981, pp. 1-15. 27. Pedersen, K.S.: Energy and Fuels, v. 5, pp. 924, 1991. 28. Pedersen, K.S., and Fredenslund, Aa.: "An improved corresponding states model for the prediction of oil and gas viscosities and thermal conductivities", Chemical Engineering Science, Vol. 42, No. 1, pp. 182-186, 1987.
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References
User Guide WinProp
29. Pedersen, K.S., Fredenslund, Aa., Christensen, P.L., and Thomassen, P.: "Viscosity of Crude Oils", Chemical Engineering Science, Vol. 39, No. 6, pp. 1011-1016, 1984. 30. Pedersen, K.S., Fredenslund, Aa., and Thomassen, P.: Properties of Oils and Natural Gases, Gulf Publishing Company, Houston, Texas, 1989. 31. Peneloux, A., Rauzy, E., and Freze, R.: "A Consistent Correction for RedlichKwong-Soave Volumes", Fluid Phase Equilibria, Vol. 8, 1982, pp. 7-23. 32. Peng, D.-Y., and Robinson, D.B.: "A New Two-Constant Equation of State", Ind. Eng. Chem. Fundam., Vol. 15, 1976, pp. 59-64. 33. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K.: The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill, New York, 1977. 34. Riazi, M.R., and Daubert, T.E.: "Simplify Property Predictions", Hydro. Proc., March 1980, pp. 115-116. 35. Sandler, S.I.: Chemical and Engineering Thermodynamics, John Wiley and Sons, New York, 1977. 36. Twu, C.H.: "An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights for Petroleum and Coal-Tar Liquids", Fluid Phase Equilibria, Vol. 16, 1984, pp. 137-150. 37. Walas, S.M.: Phase Equilibria in Chemical Engineering, Butterworth Publishers, Boston, 1985. 38. Whitson, C.H.: "Characterizing Hydrocarbon Plus Fractions", Society of Petroleum Engineers Journal, August, 1983, pp. 683-694. 39. Whitson, C.H. and Belery, P.: "Compositional Gradients in Petroleum Reservoirs", SPE 28000, University of Tulsa Centennial Petroleum Engineering Symposium, Tulsa, OK, Aug 29-31, 1994. 40. Whitson, C.H., Anderson T.F., and Soreide I.: "C7+ Characterization of Related Equilibrium Fluid Using the Gamma Distribution", paper in "C7+ Characterization", Edited by Mansoori, Chorn, Taylor and Francis, New York, 1989. 41. Whitson, C.H., and Torp, S.B.: "Evaluating Constant Volume Depletion Data", SPE 10067, JPT, March 1983, pp. 610-620. 42. Wichert, E and Aziz, K.: "Calculate Z’s for Sour Gas Hydrocarbon Processing", Vol. 51, pp. 119, May 1972. 43. Won, K.W.: "Thermodynamics for Solid-Liquid Equilibria: Wax Formation from Heavy Hydrocarbon Mixtures", Fluid Phase Equilibria, Vol. 30, 1986, pp. 265-279. 44. Zick, A.A.: "A Combined Condensing/Vaporizing Mechanism in the Displacement st of Oil by Enriched Gases", SPE 15493, Proc. of 61 Ann. Conf., Oct 1996.
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Appendix A
Case Studi es Introduction
The case studies presented in this section are designed to guide the user step-by-step through practical phase-behavior modeling problems. Case Study Number 1 describes in detail the steps involved in heavy fraction characterization and equation of state tuning for a gas condensate. Working through this case study will provide practice in techniques for data set editing, the component properties updating procedure, data specification for a number of calculation options, as well as possible methods to use in your own regression problems. Case Study Number 2 illustrates the use of the Oil-Gas-Water flash for predicting solubility of gases in brine and regression on the aqueous phase solubility parameters. Generation of the required equation of state parameters to define the fluid model for CMG’s GEM compositional simulator is also shown. Case Study Number 3 shows how to develop a model for predicting precipitation of asphaltene from a black oil under pressure depletion.
Case Study Number 1: Gas Condensate Modeli ng In this case study, the Peng-Robinson equation of state will be tuned via regression to match the PVT behavior of a gas condensate fluid. Data for this example are taken from the Petroleum Engineering Handbook (H.B. Bradley, Editor-in-Chief, Society of Petroleum Engineers, 1987, pp. 39-6 to 39-9). The data given are typical for a fluid of this type, including hydrocarbon analyses of separator products, and results of constant composition expansion and constant volume depletion laboratory experiments. Create Data Set for Splitting Calculation
Begin by double-clicking the WinProp icon in the CMG Technologies Launcher (accessed from the Windows Start Menu). This will open WinProp with a new blank data set ready for editing. The required forms Titles/EOS/Units, Component Selection/Properties and Composition are placed in the new data set by default, as shown below:
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Click File | Save As then enter a file name and save the file. The file name will now appear at the top of the tree view. The first step in modeling the condensate fluid will be to split the heptanes plus fraction. The splitting calculation is inserted into the data set by clicking Composition in the tree view then clicking the SPLT (Plus Fraction Splitting) button in the toolbar or selecting Characterization | Plus Fraction Splitting from the main menu. Click Plus Fraction Splitting in the tree view to display the associated form:
Set EOS Model and Unit System
Click Titles/EOS/Units in the tree view to open the form for selecting the EOS model and units system. Text entered in Comment Line will appear on the main form for the data set, while text entered in Title Line 1, 2 and 3 will appear in output files. The text from Title 1 will also be used to label any plots that are created. Equation of state, Unit and Feed can be left at their default values, as shown below.
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Click Save Current Dataset in the toolbar, or File | Save in the menu bar to accept your data and return to the main WinProp form. Specify System Components to C6
To specify system components, click Component Selection/Properties in the tree view. Click the Ins Lib button to open the Library Components dialog:
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In the Library Components pane, select CO2 through FC6 (all components up to hexane) then click to select, as shown below:
Click OK to accept the selection and return to the Component Selection/Properties form. The Component table will be populated with the selected components, as shown below:
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Click the Apply Change button at the bottom of the tab, click OK in the message asking you to verify the compositions, then click File | Save to save your component selection. All other information on this form can be left at the default values. Refer to the Components chapter for information on modifying any of the default component properties. Specify System Composition
To specify the composition of the selected components, click Composition in the tree view. The Composition form is displayed. Enter the values shown below:
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As shown, in Case Study 1, the primary composition will sum to 90.01. Specify C7+ Fraction Properties
To characterize the heavy fraction properties, in the tree view, click Plus Fraction Splitting then select the Sample 1 tab. Enter the plus fraction properties (MW+, SG+ and Z+) shown below:
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Specify Plus Fraction Splitting and Lumping Calculation
Select the General tab to enter the parameters that will be used for the splitting and lumping calculations. The plus fraction will first be split into 7 single carbon number fractions. Select LeeKesler as the critical property correlation to be used to generate the properties of these fractions. By default, WinProp will automatically determine the number of pseudo-components. The General tab should now appear as follows:
The mole fraction of the component immediately preceding the plus fraction also has to be entered through the Distribution tab. Information on this tab can be found in the Component Splitting and Lumping chapter. In our case, the component is FC 6 with mole fraction equal to 0.0173, as shown below:
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Save the Data Set and Run the Splitting Calculation
The splitting calculation is now ready to run. If you have not done so already, select File | Save and enter a file name. The file extension (.DAT) will be added automatically if it is not specified. Now select File | Run or click Run Simulation in the toolbar to run the data set. When control returns to WinProp, the output file can be viewed by selecting Simulation Results | Simulation Output in the tree view, as shown below. The distribution of single carbon number fractions and the final properties of the lumped components are shown in the output file.
Update the System Component Specification
The next step in the tuning process is to match the available experimental data through regression. First, the component specification must be updated to reflect the results of the splitting calculation. This is done by selecting File | Update component properties from the main menu, or clicking Update Component in the toolbar, which will modify the first three forms in the data set. Click Yes when asked if you want to proceed. Open the Titles/EOS/Units form and enter a new comment and descriptive title for this data set.
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On the Component Selection/Properties form the properties of the full component specification, including the heavy pseudo-components, can be viewed and a new comment entered, as shown below:
Select Constant Volume Shift in the box in the upper right, as shown above.
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Open the Composition form to verify that the mole fractions now sum to one, as shown below:
At this point, the splitting calculation can be removed from the data set by right-clicking Plus Fraction Splitting in the tree view then selecting Cut. If you want to avoid overwriting the original data set, select File | Save As and enter a new name for the data set.
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Set Up the Regression Data Set
To begin setting up the regression run, click Composition in the tree view. Click STRT REG (Regression Parameters) or select Characterization | Start Regression from the toolbar. The Regression Parameters branch opens in the tree view, as follows:
Copy the Data for Regression
The saturation pressure, constant composition expansion and constant volume depletion specification experimental data can now be copied from the template file Case_study-1.dat . This file is located in the WinProp templates directory, for example cmg\WinProp\2013.01\tpl. Open the Case_study-1.dat data file. Click Module Operations in the toolbar to open the Calculation Module Operations dialog box:
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Select all three modules after Regression Parameters (Regression variable selection) as shown above then click OK to copy them. Right-click Regression Parameters in your case study then select Paste Into Reg-Block. Click Yes when asked to confirm. Click the Case_Study-1.dat tree node and then File | Close to close this dataset. The tree view should appear similar to the following:
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Select Initial Regression Parameters
The parameters to be used in the regression can now be selected by clicking Regression Parameters then selecting the Component Properties tab. Select the critical pressures of the C7+ pseudo-components as regression variables by clicking on the last five cells in the first column (labelled Pc). The Component Properties tab should appear as follows:
Select the Interaction Coefficients tab then, in the same manner as for the critical pressures, select the Hydrocarbon Interaction Coefficient Exponent and the interaction coefficients between CO2 and Methane, and between CO2 and the C7+ pseudo-components, as shown below:
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Save the dataset. For more details refer to the Regression chapter of the manual. Run the Regression Data Set
To run the regression data set, select File | Run or click Run Simulation . If you have not saved your data, a message box appears asking if you would like to save the data set before running. Click Yes to save your changes. While the data set is running, the progress of the regression can be tracked by noting the values of the residuals in the window displaying the run status messages. This information is also echoed to the output file. It is important to note that the magnitude of the change from the initial value of the residual is more important than the values of the residuals themselves.
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Regression Summary Plots
Summary plots of the before regression and after regression results, along with the experimental data, can be viewed through tabs in Simulation Results | Simulation Graphs in the tree view, as shown below:
Viewing the summary plots for this run shows that only minimal improvement in the fit was obtained. Note particularly that the liquid dropout values for the constant volume depletion have large errors. Check the Regression Summary Table
To check the numerical values for the before and after regression calculation errors, open the output file through Simulation Results | Simulation Output in the tree view, as shown below:
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At the end of the file, as shown above, there is a table with a summary of the regression results. Check if there has been any improvement of the match to the saturation pressure, shown in the first row of the summary table. Modify the Regression Specification
Modifications to the data set can now be made to improve the predictions of the volumetric data and the saturation pressure. Begin by opening the Component Selection/Properties form and viewing the column for the Volume Shift parameters. Note that some of the components have a default volume shift of zero. Right-click the Vol. Shift column heading then select Set to Interface Correlation Value to insert volume shift values:
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Click the Apply Change button. Next, open the Regression Parameters | Saturation Pressure form, and on the Calculations tab, enter a value of 50.0 for the weight associated with the experimental saturation pressure value. This is to ensure that the saturation pressure is more closely matched. On the Constant Volume Depletion form, Pressure Levels tab, enter a weight of 5.0 for the liquid saturation value, as shown below:
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Now, open the Regression Parameters form and add the volume shift parameters for methane and the C7+ pseudo-components as regression variables, as shown below:
Run the Modified Regression Data Set
Save and run the data set again. Note the decrease in the residual values. Check the match to the liquid dropout on the CVD summary plot. View the summary table in the output file to observe the effect of increasing the weight for the saturation pressure experimental data. Specify Group Variables for Regression
Further improvement of the fit can be attempted using WinProp’s regression variable grouping method. The grouping method ensures that existing trends in the original component properties are maintained, by incrementing or decrementing all of the members of a group by the same amount during regression. Since each group is treated as a single regression variable, this also provides a method for varying a large number of component properties without having to select them all as individual regression parameters. Open the Regression Parameters | Component Properties tab, and clear the selection of the critical pressures and volume shifts for the components C 07-C09 through C15-C17 by clicking on the cells marked with an “X” for those components. Leave P c and Vol shift selected for component C18+, and then select critical temperature and acentric factor for C18+.
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In the Selection/Group field at the bottom of the form, click the arrow then select New Group. Click on the cells for components C 07-C09 through C15-C17 in the critical pressure column. Repeat this procedure to specify groups for critical temperature, acentric factor and volume shift. The Component Properties tab should look like the following:
The interaction coefficients can be left as they were selected for the last run. Run the Data Set and Create Final Summary Plots
Save and run the data set with the new regression specification. In this case, the residual is reduced significantly, indicating that a much better fit has been obtained. Check the output file to verify that the predicted saturation pressure now matches the experimental value quite closely. The CVD summary should now show a good match of the liquid dropout as shown below.
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Predict VLE Behavior with Tuned Model
Now that the EOS is tuned, it can be used to predict the phase behavior of the gas condensate. Begin by updating the component properties in the data set to reflect the results of the regression as was done after the splitting calculation. Select File | Update component properties or click Update Component in the toolbar. Click Module Operations in the toolbar to open the Calculation Module Operations dialog box. Select all calculation modules after Composition, select Cut the selected calculation modules, and then click OK.
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Save the file under a new name. Specify a Two-Phase Envelope Calculation
Click Composition in the tree view. Select Calculations | Two-phase Envelope from the main menu, or click 2P ENVP in the toolbar. On the Specification tab, change the pressure specification to Unknown, the starting temperature specification to 60, and change the minimum temperature for the X-Axis to 32. Leave all other envelope specification controls on the Specification tab at the default values. The Specification tab should now appear as follows:
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On the Construction Controls tab, the phase boundary and quality line calculation can be specified. A value of 0.0 is already entered in the table for Vol. frac. vapor phase. Using the Tools button, enter additional rows for values of 0.1, 0.2 and 0.3 to generate quality lines. Also set the Initial step size to 0.1.
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The Construction Controls tab should now appear as follows:
Save and run the data set to perform the envelope calculation. In the output file, a table showing the pressure, temperature, Z-factors and K-values at all points for the two-phase boundary and all of the specified quality lines, is given. In Simulation Results | Simulation Graphs in the tree view, select the P-T Diagram, which should appear as follows:
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Case Study Number 2: Solubili ty of CO 2 in Brine In this case study, a fluid model is generated which can be used in CMG’s compositional simulator GEM to simulate a CO 2 injection recovery process, including modeling of the solution of CO2 into the aqueous phase. The model reservoir fluid is taken from Killough, J.E. and Kossack, C.A.: “Fifth Comparative Solution Project: Evaluation of Miscible Flood Simulators,” SPE paper no. 16000, presented at the Ninth SPE Symposium on Reservoir Simulation, San Antonio, TX, 1987. For this case study, the injection fluid described in the above paper will be replaced with pure CO2. This case study consists of three major steps: 1. Estimation of CO2 solubility in brine at several pressures using WinProp’s internal model for calculation of Henry’s constants for gaseous components in aqueous brines. 2. Fitting the parameters for the Henry’s law solubility model used in GEM to the predicted CO2 solubilities via regression. 3. Generation of a file containing the GEM fluid model keyword specifications. Note: If experimental solubility data existed for the gas in brine of the desired concentration,
step (1) could be bypassed. In this case study it is assumed that experimental solubility data are not available.
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Create Data Set for Prediction of CO2 Solubility in Brine
The reservoir fluid components with properties as given in the SPE Fifth Comparative Solution Project have been defined in the data set Case_study-2.dat . This file is located in the WinProp templates directory, for example cmg\WinProp\1999.10\Tpl. Open this data set by dragging the file onto the WinProp icon in the CMG Technologies Launcher, or by starting WinProp by double-clicking on the icon then selecting File | Open from the main menu. To avoid overwriting the template data set, save the file under a new name by selecting File | Save As from the main menu and entering a new file name in the Titles/EOS/Units form:
Modify the Default Aqueous Phase Solubility Parameters
Click the Component Selection/Properties form. The Component tab will be active. Notice that the components CO2 and H2O are defined, in addition to the components in the reservoir fluid. Using the horizontal scroll bar, scroll until the Ref. Henry column (component Henry’s constant), V inf. (molar volume at infinite dilution) and P ref. (reference pressure for Henry’s constant) columns are visible. These cells are blank by default, which indicates that the internal model for calculation of these values will be used. WinProp will estimate solubilities for all components up to C8 by default. In this study, it is desired to model only the solubility of CO 2 in the aqueous phase. Rightclick the column header Ref. Henry (atm), select No Aqueous Solubility, and then change its value from Insoluble to 0.0 (default) for both CO2 and H2O. Edit the component Henry’s constants so the form appears as follows:
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Click Apply Change then File | Save. Specify the Brine Salinity
Select the Aqueous Phase tab of the Component Selection/Properties form. On this tab, the aqueous phase salinity can be specified in a variety of units. The salinity is defined in terms of NaCl concentration. Brines are modeled by assuming that the total salinity is due only to Na+ and Cl- ions. In this case it is assumed that total salinity of the brine is 100,000 ppm, thus a value of 0.1 can be entered for the NaCl concentration with the units selected as Weight Fraction. The Aqueous Phase tab should now appear as follows:
By default, Henry’s constants, determined using the internal model, are for pure water. The value entered for the brine salinity is used to adjust the Henry’s constants to account for the reduced solubility of gases in solutions with electrolytes present.
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Check the Stream Compositions
Open the Composition form to observe the definition of the primary and secondary compositions, as shown below.
The secondary composition is usually defined as the injection fluid, in this case pure CO 2. The primary composition is usually defined as the reservoir fluid, thus the hydrocarbon component mole fractions corresponding to the initial reservoir fluid composition are entered here. In this case, the composition of water in the system must also be defined. The mole fraction of water is entered as 1.0 in the primary composition column. Click Normalize Composition. The resulting mole fraction of water in the primary stream will now be 0.5 (50%), as shown below:
Save your file.
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Add Flash Calculations to the Data Set
Click Composition in the tree view. To add an Oil-Gas-Water flash to the data set at this point, select Calculations | OGW/EOS Multiphase Flash from the menu bar. Your data set should appear as follows:
Specify Conditions for P-T Flash
In the Calculations tab, Feed specification area, specify the Primary mole fraction as 0.5. This means that the feed to the flash calculation will consist of 50 mole % of the combined reservoir oil/water stream and 50 mole % CO2. At the bottom of the tab, select OGW (OilGas-Water) from the Flash Type combo box. Next, in the Temperature Data area, enter the specified reservoir temperature of 160 °F in the Temperature (deg F) text box. The initial reservoir pressure is 4000 psia . To predict the solubility of CO 2 in brine over the full range of expected pressures, a series of flashes from 500 to 4500 psia will be performed. This is accomplished by entering 500 psia in the Pressure (psia) text box, a Pressure step of 1000 psi, and 5 for No. of pressure steps. Save your file.
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The Calculations tab should appear as follows:
Run the Data Set
Specification of the data set to predict the solubility of CO 2 in brine at 5 pressures is now complete. Save the data set by selecting File | Save from the main menu. Perform the calculations by selecting File | Run. The results of the calculations can now be viewed by selecting Simulation Results | Simulation Output in the tree view. Scroll through the output file until you reach the table with the results for the first flash calculation at 500 psia.
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The results table should appear similar to that shown below:
The table consists of three sections: phase compositions (mole percent), K-values and phase properties. Note that in the third section of the results table, Phase01 is identified as the aqueous phase. The mole% of CO2 in this phase is reported in the first section of the table as being 0.41267 %. Verify in your results that the only components present in the aqueous phase are CO 2 and water. Write down the mole% CO 2 in the aqueous phase calculated for each of the five flash calculations reported in the output file. These are required for the next stage of the modeling process. Set Up the Regression Run
The next phase of the modeling process is to perform a regression run using the predicted solubilities of CO 2 in brine as pseudo-experimental data. The results of the regression will be a reference Henry’s constant and molar volume at infinite dilution for CO 2 which may be included in a GEM data set.
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Modify the Initial Component Properties
Save the data set used for performing the flash calculations in the previous step under a new name using File | Save As. This will be used as the basis for the regression data set. To perform regression on aqueous phase solubility parameters, valid initial values of the parameters must be present in the component table. Select the Component Selection/Properties node in the tree view, select the Component tab and then scroll over the table until the column with Henry’s constants is visible. Right click the Ref. Henry (atm) column header and select Calculate Aqueous Solubility. This will open the Calculate Component Solubility Parameters dialog box, through which you can enter the temperature and pressure at which you want the initial solubility parameters evaluated:
The pressure entered will be used as the reference pressure for calculating Henry’s constants during regression. In this case 500 psia is used. The temperature entered should be the same as the temperature specified for your flash calculations (160 °F). After you enter the values, click OK to return to the Component tab. Note that molar volumes at infinite dilution and reference pressures have been filled in for all components. Valid Henry’s constants have also been entered in the table for CO 2, C1 and C3, as these components are considered to be soluble in the aqueous phase by default. Since we are concerned only with the solubility of CO2, manually enter (or copy from another cell) the Henry’s constants for C1 and C3 to Insoluble then click Apply Change. The aqueous solubility parameters should now appear as follows:
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Before leaving the Component Specification/Properties node, select the Aqueous Phase tab then clear NaCl Concentration or set it to zero, as follows:
This value is used only for predicting the effect of salinity on Henry’s constants and should not be used during regression on aqueous phase solubility parameters.
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Specify the Regression Parameters
Click the Composition node in the tree view then select Characterization | Start Regression. The Regression Parameters node is inserted in the tree view after the Composition node, as follows:
The only parameters that we want to modify are the reference Henry’s constant and molar volume at infinite dilution for CO 2. Scroll over the grid shown on the Component Properties tab to display the last two columns. Click in the row corresponding to CO 2 under the Henry const. and V inf. columns to select the parameters to use in regression. The form should appear as follows:
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Click Save
.
Specify the Experimental Data
The experimental data must be entered in the data set by specifying a flash calculation for each pressure that we have solubility data for. Click OGW/EOS Multiphase Flash in the tree view. In the Calculations tab, change the Pressure step to 0.0 and the No. of pressure steps to 1. You may want to edit the Comment field to reflect the new specification, “Flash at 500-1500 psi”, for example. The Calculations tab should now look as follows:
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Click on the Exp. Solubility tab to enter the data generated earlier for solubility of CO2 in brine. Make sure that the unit selected for entering the solubility is Mole Fraction then enter the value predicted for the amount of CO2 in brine from the first part of this case study. For the flash at 500 psia, the amount of CO 2 in the aqueous phase was calculated to be 0.41267 mole%, thus the entry in the table should be 0.0041267 as shown below. All of the other entries in the table can be left blank. They will default to a value of “-1”. A negative value indicates that a given experimental data point will not be used in the regression.
Click Save
.
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The flash specification with experimental data constructed above can now be copied multiple times into the regression and modified for the other pressures: 1. Right-click OGW/EOS Multiphase Flash then select Copy. 2. Right-click Regression Parameters then select Paste into Reg Block. 3. Repeat step 2 four times. 4. Click the second OGW/EOS Multiphase Flash node then select the Calculation tab. Change the pressure to 1500 psia, then click on the Exp. Solubility tab and enter the value of CO2 solubility recorded for this pressure from the first part of this case study. This should be a mole fraction of 0.0087940, or similar. 5. Create flash specifications and enter the CO2 solubility data for 2500 psia (0.0105154 mole fraction CO2), 3500 psia (0.0114117 mole fraction CO 2) and 4500 psia (0.0121093 mole fraction CO 2). 6. Delete the OGW/EOS Multiphase Flash node outside and below the Regression Parameters node (right-click then select Cut). The tree view should now appear as follows:
Complete and Run the Regression Data Set
Click Save
then Run Simulation
. If the following message is displayed, click Yes:
View the output by selecting Simulation Results | Simulation Output. At the end of the output file, two summary tables are printed: “Summary of Regression Variables” and “Summary of Regression Results.” Looking at the before and after regression values in the regression results table in comparison to the experimental values shows that the fit has been considerably improved. Investigation of the regression variables table, however, shows that both of the regression variables have reached the default upper bound imposed: 218 Appendix A
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This indicates that further improvement to the fit could be obtained by increasing this limit for one or both of the parameters chosen. A summary of the regression iterations appears roughly in the middle of the output file. Examination of this table shows that the Henry’s constant for CO2 (indicated by the name HEN1 in the table) reached its limit first during the regression iterations, as shown below:
Thus, we will try increasing the upper bound for this parameter. Modify the Regression Data Set
Click the Regression Parameters node then select the Variable Bounds tab, and change the upper bound for the CO2 Henry’s constant to 5500 atm. At this point the convergence tolerance can also be tightened on the Regression Controls tab. Click Save then Run Simulation . Viewing the summary tables at the end of the output file now shows that an excellent match of the CO2 solubility data has been obtained. Create a New Data Set
Once the process of tuning the model has been completed, a new data set can be created with all of the updated model parameters. Select File | Update component properties from the main menu or click the Update Component button in the toolbar. This will overwrite the first three forms in the data set with the model parameters obtained from the regression run. Use File | Save As to save the file under a new name. This new file will be used to generate the fluid model specification for GEM. First, remove all of the calculation options below the composition form. Click the Module Operations button in the toolbar. Select all modules after Composition in the Calculation Module Operations dialog box. Select Cut the selected calculation modules and then click OK. Click Yes when prompted.
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Add GEM Fluid Model Creation to the Data Set
Click the Composition node then, in the menu bar, select SimulatorPVT | CMG GEM EOS Model or click the GEM EOS button in the toolbar. This will insert a CMG GEM EOS Model node into the data set. Click this node to open the data entry form:
In the File Selection area, select Print component properties for GEM to CASE_STUDY-2C.GEM. Your file name may be different. It is also possible to send a copy of the component properties to an output file by selecting Print detailed component properties to *.OUT. GEM does not need to have the water component included in the component list, therefore leave Include H2O in GEM component list in its default cleared state. To output Henry’s constants and molar volumes, in the Solubility Parameters area, select Print aqueous phase component solubility parameters. Note: When the solubility parameters are defined on the Component Selection/Properties form, they are constant for a data set, and the option buttons available under Solubility Parameters will have no effect. Selecting these options only affects the results when the
internal model is used to generate Henry’s constants and other solubility parameters.
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In the File Selection area, set Reservoir temperature for GEM fluid model to 180°F . The completed CMG GEM EOS Model form should now appear as follows:
Run the Data Set for the GEM Fluid Model
Click Save
then Run Simulation
then view the output file through Simulation Results | Simulation Output. The table in the output file shows a listing of the properties for all of the components, including the aqueous phase solubility parameters.
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The GEM fluid model is saved in a file with the same root name as your data file and output file, but with the (.gem) extension (e.g. for the Case2b.dat data file, the GEM fluid model is stored in the file Case2b.gem). The file can be viewed by selecting File | View GEM EOS Model from the main menu.
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This file contains the same information as shown in tabular form in the output file, but written out in the keyword format required for GEM. The GEM fluid model file can be referenced in a GEM data set using an “include” statement, or it can be imported into a data set using CMG’s Builder program.
Case Study Number 3: Asphaltene Precipitation Modeling This case study describes the procedure for modeling the precipitation of asphaltene from a live reservoir oil due to pressure depletion. The thermodynamic model used to describe the precipitation of asphaltene and the flash algorithm for solving the equations are given in references 19 and 20. Please refer to the Flash Calculations chapter for further information on asphaltene/wax modeling. User Guide WinProp
App end ix A 223
The steps required to develop a precipitation model are: 1. Fluid characterization 2. Regression on fluid PVT 3. Specification of solid model parameters 4. Prediction of precipitation behavior Fluid analysis and asphaltene precipitation data are taken from Burke, Hobbs and Kashou, “Measurement and Modeling of Asphaltene Precipitation,” Journal of Petroleum Technology, November 1990, pp. 1440-1446. The following data for “Oil 1” taken from Table 1 of Burke et al will be used in this example. Component
Nitrogen Carbon Dioxide Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes plus Total C7+ molecular weight C7+ specific gravity Live oil molecular weight Stock tank oil API gravity Asphaltene content in stock tank oil, wt% Reservoir temperature, °F Saturation pressure, psia
Oil 1
0.57 2.46 36.37 3.47 4.05 0.59 1.34 0.74 0.83 1.62 47.96 100.00 329 0.9594 171.4 19.0 16.8 212 2950
Fluid Characterization
To begin this case study, a data set has been prepared to characterize the fluid by defining the compositions of components up to C 6 and pseudo-components describing the C7+ fraction. The data set is named Case_study-3-split.dat and is located in the WinProp templates directory, for example cmg\WinProp\2000.10\Tpl. You can begin by using this file, or by constructing your own data set as described in Case Study Number 1. From the table above, the composition data to C6 has been used, and a Plus Fraction Splitting calculation has been specified with the C 7+ molecular weight and specific gravity. The plus fraction will be lumped into 4 pseudocomponents, and the Lee-Kesler critical property correlations will be used. Perform the splitting calculation either by running your own data set, or by running the Case_study-3-split.dat data set:
224 Appendix A
User Guide WinProp
Update the System Component Specification
After splitting, the equation of state model can now be tuned to any available PVT data via regression. 1. If you are using the Case_study-3-split.dat data set, save this file under a new name to avoid overwriting the original file by selecting File | Save As and entering the new name. 2. Click Run Simulation . 3. To reflect the results of the splitting calculation, select File | Update component properties from the menu bar or click Update Component in the toolbar. This will modify the first three forms in the data set. If the following message screen is displayed, click Yes:
User Guide WinProp
App end ix A 225
4. Remove the splitting calculation from the data set by right-clicking Plus Fraction Splitting then selecting Cut. 5. Click the Titles/EOS/Units node then enter a new Comment Line and Title Line 1, for example:
6. Click the Component Selection/Properties node. The Component tab is displayed. Select Temperature Dependent Volume Shift Correlation in the upper right box. This will allow good initial predictions of the volumetric properties of the fluid. 7. Click Save . Set up the Regression Data Set
1. Click the Composition node. 2. Click Characterization | Start Regression in the menu bar to insert a Regression Parameters node below the Composition node. 3. Click the Regression Parameters node then click Sat Pres insert a Saturation Pressure node into the regression block.
226 Appendix A
in the toolbar to
User Guide WinProp
The screen should now appear as follows:
4. Click the Saturation Pressure node then select the Calculations tab. Enter a temperature of 212 °F, a saturation pressure estimate of 2500 psia, and an experimental saturation pressure measurement of 2950 psia. The Calculations tab will appear as follows:
User Guide WinProp
App end ix A 227
5. Click the Regression Parameters node then select the Interaction Coefficients tab. 6. Choose Select from then click HCIntCoefExp – 1(1.2) from the list. This selects the hydrocarbon interaction coefficient exponent as a regression variable. For more information about this parameter, please refer to the Components chapter in this User Guide. 7. In the Regression Controls tab, Convergence tolerance should already be set to 1E-06, which will achieve a good match with the experimental data. 8. Click Save . Note: A copy of this data set, Case_study-3-regress.dat is available in the templates
directory for comparison to your own work. 9. Click
to run the data set then view the output from the run through Simulation Results | Simulation Output. The regression summary table at the end of the output file shows that an exact match to the saturation pressure was achieved.
10. The model is now ready to be modified for asphaltene precipitation prediction. Specification of Asphaltene Component
1. If desired, rename Comment Line and Title Line 1 in the Titles/EOS/Units form. Note: The asphaltene component is specified by splitting the heaviest component of the oil
into precipitating and non-precipitating components. These two components have the same critical properties and acentric factors, however the precipitating component has higher binary interaction coefficients with the light components up to about C5. This is achieved in WinProp by adding a new component to the component list, then copying the properties of the heaviest component, onto the newly added component. 2. Select the Component Selection/Properties node.
228 Appendix A
User Guide WinProp
3. In the Component tab, select Constant Volume Shift in the upper right box. This allows the volume shifts to be fine-tuned to density data.
4. In the component table, click the row containing the component C 31+. 5. Click the Copy button on the left, then the Paste button. This will insert a duplicate C31+ component, as shown below:
User Guide WinProp
App end ix A 229
6. Rename the component names in rows 14 and 15 to C31A+ and C31B+ respectively. To do this, click in the cell to reach the editing level you desire (one click selects the cell and you can type over, three clicks allows you to edit the existing contents, for example). 7. To be able to specify interaction coefficients with the other components individually for the C31B+ component, as opposed to calculating them with the hydrocarbon interaction coefficient exponent, the HC flag in the column next to the C31B+ component name should be set to 0. 8. Click Apply Change. The Component tab should now appear as follows:
9. Select the Int. Coef. tab to view the magnitude of the binaries between C31A+ and the light components. As described in references 19 and 20, the binaries for the precipitating component must be considerably higher than those for the non precipitating component to give the correct shape of the precipitation curve below the bubble point. Values on the order of 0.2 are expected to give good results. For C31B+, enter the same binaries as C31A+ for CO2 and N2, then enter values of 0.2 for the interactions with C1 through nC5. All other values for C31B+ should be left as zero. Click Apply Change to complete the component specification.
230 Appendix A
User Guide WinProp
The Int. Coef. tab should appear as follows:
Specification of Asphaltene Composition
The mole fraction of the asphaltene component can be determined from the relation: xAsph MWAsph = wAsph MWOil. From the output of the regression run, the molecular weight of the oil is calculated as 171.343, as compared to the reported value of 171.4. The asphaltene content of the stock tank oil is given as 16.8 wt%. As the weight fraction of gas in the live oil is usually small, the value of 16.8 wt% will be used for the live oil. From the component table, the molecular weight of the C31B+ component is 665.624. This results in a mole fraction of 0.04324607 for the precipitating component. 1. Open the Composition form then enter 0.04324607 for the mole fraction of C31B+. Subtract this amount from the original mole fraction of C 31+, and enter 0.07424660 (which is 0.11749267 – 0.04324607) as the mole fraction for C31A+, as follows:
User Guide WinProp
App end ix A 231
2. Click Normalize Composition. 3. Click Save
.
Specification of Additional Regression Data
When the heaviest component is split into precipitating and non-precipitating parts, and the binaries for the asphaltene component are adjusted, the fluid phase behavior predictions will be affected. For this reason, regression must be performed again to ensure that the model will predict the correct fluid and solid phase behavior. In this data set, we will add regression on the stock tank oil API as well as the saturation pressure. 1. Click Saturation Pressure in the tree view then click the SEP a separator calculation into the regression node of the data set.
button to insert
2. Select the Separator node then enter an estimate for the saturation pressure of 2500 psia and a temperature of 212 °F in the first column of the separator specification. 3. Click the Experimental Data tab and enter 19.0 for Stock tank oil, API. 4. To match the experimental API, we will modify the volume shift parameters of the heavy fraction pseudo-components. As the volume shift of the asphaltene component affects the amount of precipitate, as well as the liquid density, it will not be adjusted during regression. Open the Regression Parameters | Component Properties node and click the cells in the Vol Shift column in the rows corresponding to the components C07-C15, C16-C25 and C26-C30 to select these parameters as regression variables. 5. Click Save .
232 Appendix A
User Guide WinProp
Specification of Reference Fugacity for Asphaltene Model
The equation describing the fugacity of the solid component in the solid phase is given in the Flash Calculations chapter of this User Guide. Writing this equation for isothermal conditions gives: ln f s = ln f s* + v s ( p1 − p o ) / RTo
(1.1.1)
where f s*is referred to as the reference fugacity, at the reference conditions po and To. vs is the molar volume of the solid. The reference fugacity is usually set equal to the fugacity of the precipitating component calculated by the equation of state at an experimentally determined asphaltene precipitation onset pressure for a given temperature. This ensures that the model will predict the correct onset pressure. At other pressure conditions, the fugacity of the solid component in the solid phase is compared to the fugacity of the solid component in the liquid phase as predicted by the equations of state, if the fugacity of the solid component in the solid phase is lower then asphaltene will precipitate. With modern solid precipitation detection systems, onset pressures can usually be determined quite accurately. In the Burke et al data, an exact onset pressure is not given, instead, a pressure point above the saturation pressure at which a small amount of asphaltene precipitates is determined. The data given (in Burke et al Table 5) is 0.402 wt% asphaltene precipitated at 4014.7 psia and 212 °F. To use this data, the reference fugacity is determined at the given pressure and temperature, but with the precipitated amount of asphaltene removed from the system. The reported wt% of precipitated asphaltene must again be converted to a mole fraction to enter into WinProp. Using the same formula and molecular weights as before, the mole fraction of precipitated asphaltene is determined as 0.001034817. 1. Click the Composition node then use Ctrl-C (or right-click then Copy) to copy the node. 2. Right-click Regression Parameters then select Paste After. 3. Click the new Composition node, and subtract the amount of precipitated asphaltene from the mole fraction of component C31B+. The resulting mole fraction should be 0.042211253. 4. Right-click the new Composition node then select Add After | Calculations | Asphaltene/Wax Modelling. 5. Click Asphaltene/Wax Modelling. 6. In the Calculations tab, enter a Pressure of 4014.7 psia and a Temperature of 212 °F. 7. In the Ref. State tab, select Calculate for the Reference fugacity. This will set the reference fugacity equal to the fugacity of the precipitating component in the liquid phase calculated by the equation of state.
User Guide WinProp
App end ix A 233
8. Click Save
. The data set should now appear as follows:
Specification of Solid Molar Volume
As discussed in reference 19, the solid molar volume should be set to a value slightly higher than the molar volume for the precipitating component predicted by the equation of state. At this point we can run the data set to check the regression on the fluid PVT data and to view the solid molar volume predicted by the EOS. Run the data set and view the output file. The regression summary table shows that both the saturation pressure and stock tank API are matched exactly. At the end of the file, a listing of the parameters of the solid model are given. The solid molar volume is given as 0.65883 L/mol. A good initial value to enter for the solid molar volume is 0.67 L/mol. 1. Return to the data data set set and click the Asphaltene/Wax Modelling node. 2. On the Ref. State tab, scroll over the properties of the C31B+ component and enter 0.67 under Molar Vol. This molar volume will be used by all a ll subsequent asphaltene precipitation calculations. 3. Click Save . Prediction of Asphaltene Precipitation
To perform predictions of asphaltene precipitation, we need to use the whole live fluid composition, not the composition adjusted for the reference fugacity calculation. 1. Right-click the first Composition node then Copy. 2. Right-click the Asphaltene/Wax Modelling node then select Paste After. A new Composition node is now inserted after the Asphaltene/Wax Modelling node. 3. Right-click the new Composition node then click Add After | Calculations | Asphaltene/Wax Modelling to add a new Asphaltene/Wax Modelling node at the end of the data set.
234 Appendix A
User Guide WinProp
4. In the Calculations tab, enter a Temperature of 212 °F. We want to predict the amount of asphaltene precipitated at various pressures. Enter a Pressure of 14.7 psia, a Pressure step of 200 psia and a No. of pressure steps of 31. This specification results in flashes being performed every 200 psi from 14.7 to 6014.7 psia. The Calculation tab should appear as follows:
5. Click the Ref. State tab. By default, Reference fugacity should already be set to Previous. This specifies that the reference fugacity f ugacity for the asphaltene model will be set to that value value determined in the previous asphaltene asphaltene flash, where the reference fugacity was set to Calculate. The molar volume, reference pressure and reference temperature set previously will also be used.
User Guide WinProp
App end ix A 235
6. In the Plot Control tab, click X-Y Plots in the Plot Type area then select the Plot weight% solid phase check box, as shown below:
7. Click Save . The final data set is now ready to run. 8. Click to run the data set then view the output from the run through Simulation Results | Simulation Graphs.
236 Appendix A
User Guide WinProp
The Phase Properties graph is shown below:
You should see that the shape of the asphaltene precipitation curve from the upper onset pressure to the saturation pressure shows the expected trend of increasing precipitation with decreasing pressure. pressure. Note also that the predicted amount of asphaltene at the reference pressure pre ssure of 4014.7 psia is exactly equal to the experimental value of 0.402 wt%. The shape of the curve at lower pressures is incorrect. The final step in this case study discusses how to adjust the solid model parameters to achieve the correct shape of the precipitation precipitation curve. Adjustment of Solid Model Parameters P arameters
As the solid precipitation model used in WinProp is thermodynamic, as opposed to kinetic, reversibility of precipitation is possible; i.e., precipitated solids can redissolve in the liquid phase. This phenomenon phenomenon has been observed in the laboratory for pressure depletion. depletion. Usually the maximum amount of precipitation occurs around the saturation pressure of the fluid. Below this pressure, liberation of gas from the oil changes the solubility parameter of the liquid phase and allows redissolution of the precipitated asphaltene. It is possible that all of the precipitated asphaltene will go back into solution at sufficiently low pressures. The parameters that control this behavior in the solid model are the solid molar volume and the interaction parameter between the precipitating component and the light ends of the oil. Increasing the solid molar volume increases the maximum amount of precipitation at the saturation pressure. Increasing the interaction parameter with the light ends will force the asphaltene to redissolve at lower pressures. The experimental data given in Burke et al (Table 5) indicates the maximum amount of precipitation from this fluid should be about 1%, and that the amount of precipitation should decrease to 0.403 wt% at 1014.7 psia. User Guide WinProp
App end ix A 237
Judging from the results of the initial run, it is seen that the molar volume of the solid must be increased slightly to increase the maximum amount of precipitation from approximately 0.8 wt% to 1 wt%. The interaction parameter between the precipitating component and the light ends must also be increased to give the correct shape of the precipitation curve below the saturation pressure. As noted earlier, performing the regression within the asphaltene modeling data set allows the model to predict the correct fluid PVT behavior when the interaction parameters for the asphaltene component are changed. 1. Click the Component tab. Select Linear Temperature Dependent Volume Shift in the upper right box. Right-click the Vol. Shift column heading and select Use Internal Zra Correlation. Repeat for the V Shift Coef 1 column heading. 2. In the Int. Coef. tab of the Component Selection/Properties node, adjust the interaction parameters between the C31B+ component and the components C 1 through nC5. Use a constant c onstant value of 0.224, as shown below:
Using a constant value of 0.224 for all of these interactions gives a good shape to the precipitation curve, although it doesn’t match exactly the experimental data. 3. Click Apply Change to save the component changes. 4. Select the Regression Parameters node. Select the cells in the V Shift Coef 1 column for C07-C15, C16-C25, and C26-C30. 5. Adjust the solid solid molar molar volume volume in the Ref. State tab of the final Asphaltene/Wax Modelling node to achieve the desired maximum amount of precipitation. In this case, a value of 0.675 L/mol was found to give good results, as shown below:
238 Appendix A
User Guide WinProp
6. Click Save in the toolbar to save the dataset. Click to run the data set then view the output from the run through Simulation Results | Simulation Graphs. The Phase Properties graph is shown below:
For comparison with your work, the final model is given in the template data set Case_study3-asph.dat
User Guide WinProp
App end ix A 239
Appendix B
Equations The following are the equations used in WinProp.
Cubic Equation of State A cubic equation of state takes the general form RT
p =
v − b
−
a v2
+ vb(1 + c ) − cb 2
(2.1.1a)
or RT
p =
v − b
−
a
(v + δ1 b )(v + δ 2 b)
(2.1.1b)
where
= (1 + c) − (1 + c)2 + 4c
2δ1
δ1 δ 2 = − c When c=1, Equation (2.1.1a) becomes the Peng-Robinson Equation of State and when c=0, it becomes the Soave-Redlich-Kwong Equation of State. For pure components, the parameters a and b are expressed in terms of the critical properties and the acentric factor: a
=
ac
a cα
= Ω a (RTc ) /
α = 1 + κ(1 − b = Ω b RTc / p c
p c
T / Tc
) (2.1.2)
Define A ≡ ap /(RT ) 2
and B ≡ bp / RT User Guide WinProp
App end ix B 241
the compressibility factor Z ≡ pv/RT can be expressed as: E ≡ Z 3 − Z 2 (1 − cB) + Z A − B(1 + c) − B 2 (1 + 2c) − AB − c(B 3 + B 2 ) = 0
(2.1.3)
For mixtures, the parameters a and b are defined using the following mixing rule
∑
a=
x i Si
i
Si
≡
ai
∑ x (1 − d ) j
ij
a j
j
b =
∑
x i b i
i
(2.1.4)
where d ij is an empirically determined interaction coefficient. The fugacity coefficient is derived from the equation of state (Michelsen, 1981)
∂~F − ln Z ln φ = ∂ n T, v where ~ F≡
∞
p N dV − RT V
∫ v
(2.1.5)
Resulting in ln φ i
=
b i b
(Z − 1) − ln(Z − B) −
1
A 2S i
δ 2 − δ1 B
a
−
Z + δ 2 B ln b Z + δ1 B
b i
(2.1.6)
Calculation of Parameters
The above equations require the knowledge of Ωa, Ω b and κ. The two parameters Ωa, Ω b are obtained from the critical condition. At the critical point, the compressibility factor will have three real and equal roots (Martin, 1979).
(Z − Z c )3 = 0 Comparing with the above Z equation results in
Ω b = 1 / (3Z1 + c) Ω b = (Z13 + c + c / Ω b )Ω b2 Zc
= Ω b Z1
where Z1 ≡ 1 + Z 2 + 2 / Z 2 1/ 3 Z 2 ≡ (3 + c + Z 3 )
Z 3 ≡ c 2 + 6c + 1 242 Appendix B
User Guide WinProp
Setting the value of c results in the usual equation of state: Equation of State
c
Peng-Robinson (PR)
1
Soave-Redlich-Kwong (SRK)
0
δ1 -0.4142
δ2
Ωa
Ω b
Zc
2.4142
0.45724
0.07780
0.307
1
0.42747
0.08664
0.333
0
Equation (2.1.7)
The κ is obtained from the following empirical correlations. For the PR equation of state, Peng and Robinson (1976) proposes
κ = 0.37464 + 1.54226 ω − 0.26992 ω 2 and for hydrocarbons heavier than n-decane (Robinson and Peng, 1978)
κ=
0.379642
+ 1.48503 ω − 0.164423 ω 2 + 0.016666 ω3
For the SRK equation of state, Soave (1972) proposes
κ = 0.480 + 1.574 ω − 0.176 ω2 While the following equation is suggested by Grabowski and Daubert (1978)
κ = 0.48508 + 1.55171 ω − 0.15613 ω 2 Selection of Compressibility Root and Vapor/Liquid Identification
The cubic Z-factor equation may yield two real roots. In which case, the one that results in the lowest Gibb's free energy (i.e. most stable) will be selected. Let Z A and ZB be the two real roots resulting in free energy G A and GB respectively. Since free energy G
=∑
x i ln f i ,
i
Z − B 1 A Z B + δ 2 B Z A + δ1 B + − (Z B − Z A ) G A − G B = ln B ln Z A − B δ 2 − δ1 B Z A + δ 2 B Z B + δ1 B
(2.1.8)
If GA - GB > 0, ZB will be selected and vice versa. For single-phase fluids, if the above scheme selects the largest Z root, the fluid is said to be vapor. Similarly, if the smallest positive Z root is chosen, the fluid is said to be liquid. In cases where the Z-factor equation yield only one real root, the naming of the phase to be vapor or liquid is irrelevant. For identification purposes, the criteria according to Gosset et al (1986) is used. The fluid is designated as liquid when A/B > Ωa / Ω b and Z < (Zc/Ω b)B, else it is designated as vapor. For simplicity, the EOS Z c as shown in Equation (2.1.7) is used in the above criteria. For multiphase fluids, the phases are identified according to their mass densities. The lower density phase is arbitrarily denoted as vapor.
User Guide WinProp
App end ix B 243
Volume Translation Technique
The volume translation technique of Peneloux et al (1982) is used to improve the density prediction capability of the SRK and PR equation of states. Consider pressure-explicit equation of state of the form: p = p (T, V, n1, n 2, n 3, ... )
The fugacity of component i is ln f i =
p
∫
o
(v i / RT − 1 / p )dp + ln(x i p)
(2.1.9)
where vi is the partial molar volume. The equilibrium conditions require that ln f iL = ln f iv
(2.1.10)
A volume translation modifies the molar volume of the system v predicted by the equation of state as follows:
= v o − ~v
vt
~ v= r i
(2.1.11)
∑ x r i i
= t i Bc
i
and B ci
= Ω b
RTc p c
where ti is the dimensionless individual translation value for each component and the superscripts o and t correspond respectively to the results before and after the volume translation. Bci is the hard core molecular volume of component i. By using equation (2.1.11), the fugacities of the component i after the volume translation become: ln f it = ln f io − pr i / RT
(2.1.12)
Thus if
( ) = ln (f ) , then ln (f )
ln f iL
v i
L i
t
= ln (f iv )
t
,
i.e. the volume translation has no effect on the equilibrium conditions. Therefore, it will not alter the saturation pressures, saturation temperatures, equilibrium compositions, etc. However, it will modify the molar volumes, compressibility factors and densities of the fluid. The following equations show the effect of equation (2.1.11) on the parameters of interest to petroleum engineers. Compressibility Zt
= Z o (v t / v o )
(2.1.13)
Gas oil ratio, GOR GOR t
= GOR o (v o / v t )stc
244 Appendix B
(2.1.14) User Guide WinProp
Mass density, ρ
ρ t = ρ o (v o / v t )
(2.1.15)
where the subscript stc denotes the stock tank (standard) conditions. Other equations of interest can be derived easily using equation (2.1.11). The use of the volume translation technique requires the knowledge of r i for each component. These can be estimated from equation (2.1.13) at the critical conditions
(Z c )i = ( Z c ) EOS (v c − r i ) / v c i
i
Where (Zc)EOS is the compressibility factor from the equation of state as shown in Equation (2.1.7). Peneloux et al (1982) have tabulated values of t i for the first ten components in the alkane series. Jhaveri et al (1984) have also developed empirical equations for t i. Generally, for phase behavior matching, it is advantageous to treat t i as regression variables. Experience shows that it is sufficient to introduce non-zero ti's for the C6+ components and methane only. Furthermore, for the C6+ components, it is preferable to have one t i value for all components, e.g.
= t C13− C 20 = t C 21+ .
t C 6 − C12
Enthalpy and Heat Capacity
The excess enthalpy, HE, of a fluid which follows the EOS in Equation (2.1.1) is given by:
≡ H − H*
HE
= pv − RT +
T(∂a / ∂T ) − a
(δ 2 − δ1 )
v + δ 2 b + δ v b 1
ln
(2.1.16)
and the excess capacity Cp E
≡ (∂H E / ∂T ) p
(2.1.17)
where H is the system enthalpy and H* is the enthalpy at the ideal gas state, calculated from H*
=∑
x i H *i
i
Hi* is a function of temperature only and can not be derived from the EOS and has to be input by the user in the form of a polynomial H *i
= H A + H BT + HCT 2 + H DT3 + H E T 4 + H FT 5
With T in deg. R and H i* in Btu/lb. H A through HF are user specified parameters. Passut and Danner (1972) have compiled the values of HA through HF for components commonly encountered in Petroleum Engineering. In most practical uses, the important variables are the enthalpy differences and not the absolute enthalpies. Thus, the reference point for H can be chosen arbitrarily. In WinProp enthalpy is assigned zero when the component is at ideal gas state at zero Kelvin.
User Guide WinProp
App end ix B 245
Phase Stability Test The tangent-plane criterion of stability analysis of a phase with compositions X results in solving the following set of equations (Nghiem and Li, 1984): ~
Di
≡ ln K ip + ln φ i (U ) − ln φ i (X ) = 0
K ip
= ui / xi
(2.2.1)
where and ~ ui
= ui / ∑
u k
k
for the primary variables U. The phase will be stable if
∑
ui
<1
i
and vice versa. If the phase is unstable, the equilibrium ratio K ip is a good first guess to initiate equilibrium calculation. Equation (2.2.1) is solved using the QNSS method described in the Viscosity Correlation section. To solve the above stability test equation, the following initial guess can be used: Initial Guess
Description
i
Pure component ui
Nc+1
= 1, u j, j≠i = 0
= ln φ i (X ) + ln (x i )
Average ui
Nc+3
= (y il + y iv ) / 2
Wilson's equation ui = xi
Nc+4
= 1,..., N c
Ideal gas ln u i
Nc+2
i
p ci p
e+
5.373(1+ ωi )(1− Tc i / T )
Inverse Wilson's equation ui
= xi
p p ci
e
+ 5.373(1 + ωi ) (1 − Tc i
/ T)
Initial guess (Nc+2) is generally used to test the stability of a liquid-vapor two-phase system only.
246 Appendix B
User Guide WinProp
The initial estimates of the stability test is set according to the input variable LEVEL. Level
Initial guess used for stability test
0 1
Nc+3, Nc+4 H1, L1, Nc+3, Nc+4
2 3
H1, L1, Nc+1, Nc+3, Nc+4 H1, H2, L1, L2, Nc+1, Nc+3, Nc+4
4
Ii,i=1,...,N c, Nc+1, Nc+3, Nc+4
where H1, H2 correspond to the heaviest and next heaviest component in the system and L 1, L2 correspond to the lightest and next lightest component. START
Solve Equation (2.2.1) for U
Σ ui <1
No
Phase unstable
Yes
Phase stable
Yes
Tried all initial guesses
No
Load the next initial guess
Flow Chart for Tangent Plane Criterion Stability Test
User Guide WinProp
App end ix B 247
Two-Phase Flash Calculation Two-phase flash calculation requires the solution of the following equilibrium and material balance equations: Equilibrium equation: G i ≡ ln K i − ln φ i (X L ) + ln φ i (X V ) = 0
i=1,...,Nc
Material balance equation: G n c +1
≡∑ k
z k (K k − 1) 1 + Fv (K k − 1)
=0
(2.3.1)
where K i
= x iV / x iL
z = global composition of the feed Fv = vapor phase mole fraction and x iL
= z i /[1 + Fv (K i − 1)]
When 0 < Fv < 1, the feed splits into two equilibrium systems. When F < 0, the feed is stable at the specified pressure and temperature but addition of a phase with composition X V to the feed Z will result in a phase with composition X L in equilibrium with X V. The equilibrium equation is solved using the QNSS method described in Solution of NonLinear Equations section, the primary variables are ln K i with initial guesses from the Wilson's equation: ln K i
T = 5.37 (1 + ωi ) 1 − c + ln ( p c T i
i
/ p )
(2.3.2)
In solving the material balance equation, the method of Nghiem, Aziz and Li (1983) is used for quick single-phase detection. With f o
=∑
z k K k
=∑
z k / K k
k
f 1
k
(2.3.3)
the system is a single-phase liquid when f o < 1 and a single-phase vapor when f 1 < 1.
248 Appendix B
User Guide WinProp
START
Initialization
Solve material balance equation for vapor phase mole fraction and composition
No
Use QNSS to solve the equilibrium equation once and update K-values
Single Phase
Yes
Stability Test No
Convergence
Yes
Unstable
Stable
Single Phase System
Two-Phase System
STOP
Flow Chart for Two-Phase Equilibrium Calculations
Saturation Calculation Saturation condition of a mixture X L at a particular pressure p and temperature T requires that the tangent plane to the Gibb's free energy surface at XL is also tangent to the surface at some other composition X V. The p and T are the saturation pressure and temperature and X V is the equilibrium composition (Nghiem, Li, and Heidemann, 1985), i.e.
User Guide WinProp
App end ix B 249
G i ≡ ln K i + ln φ iV − ln φ iL = 0 D≡
∑ i
V xi V ∑ x j j
[ln K
i
1=1,2,...,Nc
+ ln φ iV − ln φ iL ] = 0
(2.4.1)
(2.4.2)
where G is the equilibrium equation and D is the normalized distance from the Gibb's free surface to the tangent plane at x, evaluated at a composition y where:
φ iV = φ i (X V , p, T ) φ iL = φ i (X L , p, T ) K i
= x iV / x iL
(2.4.3)
For saturation pressure (temperature) calculation, the primary variables are ln K i and p(T). The Nc equilibrium equation (2.4.1) can be solved by the QNSS method and during each QNSS iteration, update p(T) from the distance equation (2.4.2). This is similar to the general scheme used to solve the two-phase flash problems. Initialization and Convergence
In the calculations performed in WinProp, an initial set of K-values, K i(0), is first generated from a stability test calculation (Michelsen, 1982; Nghiem and Heidemann, 1982; Nghiem and Li, 1984) at a specified pressure and temperature. These values of K i(0) will satisfy equation (2.4.1) at the given T and p, which need not be close to the phase boundary. The following sets of yi(0) are then defined from the initial K-values, K i(0). y i(,01) = K (i ,01) x i ; K (i ,01) = K (i 0) y i(,02)
(2.4.4)
= K i(,02) x i ; K (i,02) = 1 / K (i 0)
Let D1*(0) and D2*(0) be the distances in equation (2.4.2) corresponding to y (i ,01) and y (i ,02) respectively. These distances can be regarded as functions of a single variable (temperature or pressure) as long as the mole fractions y are held constant at values derived from equation (2.4.4). When the saturation temperature is specified, a one-dimensional search is performed to locate all the pressures which satisfy D1(0) = 0 and D *2(0 ) = 0
(2.4.5)
Similarly, these equations are solved for all the temperature roots at a specified saturation pressure. The technique used to solve equation (2.4.5) for temperature or pressure is a one-dimensional search combined with bisection or Newton's method. The saturation calculation using one of 250 Appendix B
User Guide WinProp
the Newton methods or QNSS is then initialized with the y i values given by equation (2.4.4) and the pressure and temperature conditions that satisfy equation (2.4.5). In some cases, equation (2.4.5) was found to have more than one pressure root (at the given temperature) or more than one temperature root (at the given pressure). The saturation calculation can be initialized with any one of these starting guesses. It has been observed that convergence can be obtained to a different solution for each of the starting guesses. In some problems, several of the converged solutions are physically meaningful, such as lower and upper dew point pressures in retrograde systems or points where liquid-liquid separations occur. Some of the converged points are found to lie inside the two-phase region, however, and are "trivial" solutions in the sense that the calculated V phase is identical to the starting L phase. It has been observed that such trivial solutions, when they are found, lie on the stability limit of the homogeneous fluid.
Cricondenbar/Cricond entherm Equations The cricondenbar/cricondentherm for phase X is taken as a saturation point with additional constraints. It solves the N c+1 saturation equations (Nghiem, Li and Heidemann, 1985): Gi
≡ ln K i + ln φ i (X V , p, T ) − ln φ i (X L , p, T ) = 0
D≡
∑ y [ln K + ln φ (X i
i
i
V
, p, T
) − ln φ (X
L
i
, p, T
) ]= 0
i
with
∂ ln φ iV ∂ ln φ iL = 0 for cricondenbar − ∂ ∂ T T
∂D = ∂T ∑ i
y i
∂D =∑ ∂ p i
∂ ln φ iV ∂ ln φ iL = 0 for cricondentherm − y i p p ∂ ∂
or (2.5.1)
Analytical derivatives for ln φ could be used. The primary variables are ln K i, p and T.
Phase Diagram Constru ctio n Thermodynamic criterion for phase equilibrium is that the Gibb's free energy is minimized at equilibrium. This yields the following necessary conditions: G i ≡ ln K i + ln φiV − ln φiL = 0
i = 1,..., N c
(2.6.1)
Material balance constraint gives N c
G N c +1
≡∑ i =1
(K i − 1)z i =0 1 + Fv (K i − 1)
(2.6.2)
where K i
= x iV / x iL
User Guide WinProp
App end ix B 251
Let the feed composition, z, be a mixture of two fluids z1 and z2. zi
= (1 − ζ ) z 1 + ζ z 2 i
i
For specified z1 and z2, the variables required to completely determine the system are p, T, F v, K1, K2,..., KN c, ζ. A total of N c+4 variables with N c+1 equations (2.6.1 and 2.6.2). All variables are designated into three groups: i Nc+1 primary variables, α ii 1 specified variable, β iii 2 fixed variables The values of the fixed variables will be kept constant throughout the calculations. For each point in the phase envelope, the value of the specified variable is fixed and the N c+1 equations solved to give the N c+1 primary variables. The value of the specified variable is then incremented and the whole process is repeated to form the complete phase diagram. The secondary variables xiL and xiV are computed from x iL
= z i /[1 + Fv (K i − 1)]
(2.6.3)
x iV = z i K i /[1 + Fv (K i − 1)] Various phase diagrams are formed by different designation of variables: Types of Phase Diagram
Variable
p-T
p-X
T-X
Ternary
Primary, α
ln K i ln T
ln K i ln p
ln K i ln T
ln K i Fv
Specified, β
ln p
ζ
ζ
Fixed
ζ
ln T Fv
ln p Fv
ζ ζ
Fv
ln T
The natural log is used to bring the magnitude of all the variables to a comparable basis. General Phase Envelope Construction Algorithm
Michelsen (1980) presented a very efficient algorithm for P-T envelope construction. His algorithm is summarized in the following. Other phase envelopes are generated with a similar scheme (Li and Nghiem, 1982). Let the subscript k denote the k-th point on the phase envelope. The temperature and Kvalues of the first point on the phase envelope (vector α1) are found by solving the n+1 governing equations (2.6.1 and 2.6.2) at a specified pressure ( β1) after the global composition and F are fixed. The first specified pressure is usually low ( ≤2000 kPa or 290 psia) so that a good estimate of the K-values can be obtained from the following equation:
252 Appendix B
User Guide WinProp
K i
=
p ci p
exp [ 5.4.2 (1 − Tci / T ) ]
i=1,...,n
Newton's method is used to solve for α1. After convergence has been achieved, i.e. n +1
∑= (α ( + ) − α ( ) ) k 1 k ,i
k 2 k ,i
<ε
i 1
one proceeds to the next point on the phase envelope. The efficiency of the method depends upon: 1. the initial guess α2(0), and 2. the specified variable β2 Once β2 is specified, Michelsen obtained the initial guess α2(0) by linear extrapolation. Let J1 be the Jacobian (∂G / ∂α)1. The inverse J1-1 is known from the last Newton's iteration of the first point on the phase envelope. Differentiation of the equation G- = 0 (equation 2.6.1) with respect to β at α1 and β1 yields:
∂α ∂G = −J 1-1 ∂β 1 ∂β 1 The above equation is used to obtain the initial guess α2(0) at β2 by linear extrapolation:
∂α α (20 ) = α1 + (β 2 − β1 ) ∂β 1 for the k-th point on the phase envelope with k ≥ 3, Michelsen used a third order extrapolation of the form:
α (20,k ) = a k 0 + a k 1β k + a k 2 β 2k + a k 3 β 3k
(2.6.4)
where akj, j=0,1,...,3, are the coefficients of the polynomial computed using the information of the last two points (i.e. k-1, k-2). The step size, or in other words, the difference between two subsequent specifications ∆βk-1 is chosen within prescribed limits such that an increase takes place if less than 3 iterations are used to solve the equations, and a decrease takes place if more than 4 iterations are used. Usually, the step size is multiplied by a factor greater than one in the former case, and multiplied by a factor less than one in the latter. Although the phase envelope construction starts with a specification of pressure, another variable can become a specified variable at its place during the construction of the phase envelope. Indeed, if (∂α/∂β)k-1 is large in magnitude making the extrapolation inappropriate, the variable corresponding to βk-1 will become a primary variable for the k-th point, and the one corresponding to αk-1,i will become the specified variable.
User Guide WinProp
App end ix B 253
The phase envelope construction does not restrict to the bubble point locus (F=0) or dew point locus (F=1) construction. The locus of any given F(0≤F≤1) can also be generated. For convenience, the locus corresponding to 1-F is always generated along with the one corresponding to F. Michelsen also uses an interpolation polynomial of the form (2.6.4) based on points on each side of the critical point to estimate the latter. The criteria used are that the Kvalues are equal to one at the critical point. He reported that the p c and Tc obtained are accurate to 1 kPa and 0.01 °K respectively. The same approach is used to estimate the cricondentherm where ∂T/∂ p = 0 and the cricondenbar where ∂ p/∂T = 0. START Specify α, β Set up initial guess Calculate one point on the phase diagram Set up Jacobian matrix Solve the equations Update variables Yes
Trivial root
STOP
No Unphysical results
Yes
Reduce step size
No One point in the phase diagram converged Yes Extrapolate variables
Stability check Output
Adjust new step size Complete phase diagram constructed
Yes
Printer plot
STOP
Flow Chart for Phase Diagram Construction
254 Appendix B
User Guide WinProp
Three Phase Flash Calculation with Equation of State For a liquid 1-liquid 2-gas system, the conditions for phase equilibrium are as follows: Equilibrium equation: ln K iv + ln φ iV − ln φ iL = 0 ln K iq + ln φ iQ
− ln φ iL = 0
(2.7.1)
where K iv
= x iV / x iL
and K iq = x iQ / x iL
i=1,...,Nc Material balance equations N c
∑= (
x iV
−
x iL
i 1
N c
∑= (x i 1
Q i
N c
(K iv − 1) z i
i =1
Fl + Fv K iv + Fq K iq
N c
(K iq − 1) z i
)= ∑
− x iL ) = ∑ i =1
Fl
+ Fv K iv + Fq K iq
=0
=0
(2.7.2)
with the constraint Fl + Fv + Fq = 1. Subscript L and Q denote the liquid 1 and 2 respectively. A three phase flash calculation corresponds to solving the 2Nc+3 nonlinear equations for the 2Nc+2 primary unknowns ln(K iv), ln(K iq ), Fl, Fv and Fq . The mole fractions are treated as dependent variables: x im
= K im z i / (K iv Fv + K il Fl + K iq Fiq )
(2.7.3)
A stage wise procedure is used for the three phase flash calculation. A two phase calculation is first performed. The initial guess for the third phase is then obtained from the stability test. QNSS method is used to solve the equilibrium equations. During each iteration, equations (2.7.2) are used to update F l, Fq and Fv.
User Guide WinProp
App end ix B 255
START
Two phase L-V flash calculation
Single phase 2 phases
Stability test
Stable
Unstable Solve material balance equation for phase split
3 phases Update K-values by QNSS method
Program converged
No
Yes Sort phases according to density L-V
V = Vapor Phase L = Liquid phase 1 Q = Liquid phase 2 - = Equilibrium
L
L-Q-V
STOP
Flow Chart for Three Phase Liquid-Liquid-Gas Flash Calculation
256 Appendix B
User Guide WinProp
Three Phase with Isenthalpic Flash Calculation Isenthalpic flash calculations correspond to finding the temperature, phase splits (phase mole fractions) and phase compositions, given the pressure, composition and enthalpy of the feed, together with the net enthalpy added to the system (Agarwal et al, 1988). Consider one mole of feed of composition z in a nc-component, n p-phase system (Figure B.1). After defining the thermodynamic model, there are n p independent governing equations for an isenthalpic flash calculation, one energy balance and n p-1 material balance constraint equations.
Figure B.1: Isenthalpic Flash Calculations
Let the equilibrium ratios (K-values) be K ij =
y ij y i R i
i = 1,..., n c j = 1,..., n p
(2.8.1)
where yij is the mole fraction of Component i in Phase j and R is the reference phase for the Kvalue definition. Note that R i need not be the same for all components. This gives extra flexibility to define K-values in the cases that components are not always present in all phases. The values of these K-values are obtained from an EOS by solving equilibrium equations. By definition K iR, = 1. Let F j be the mole fraction of phase j in the system, the compositions can be obtained from material balances as follows y ij
=
z i K ij
ξi
(2.8.2)
and n p
ξi = ∑
Fk K ik
k =1
User Guide WinProp
(2.8.3)
App end ix B 257
In addition, the mole number of Component i in phase j, n ij, is given by n ij
= F j y ij =
z i F j K ij
(2.8.4)
ξi
From the constraints that the mole fractions must sum up to unity, (n p-1) independent equations can be derived nc
g j
≡∑ i =1
(y
ij
− y in ) = 0
j=1,...,np-1
p
(2.8.5)
Substituting Equation (2.8.2) into (2.8.5) results in nc
g j
≡∑
− K in =0 ξi
z i K ij
i =1
p
j=1,...,np-1
(2.8.6)
The above are the material balance equations used in isothermal flash calculations. For isenthalpic flash calculations, there is an additional energy balance equation, i.e. g n p ≡ H − H spec =
n p
nc
∑= F ∑= (y h ) − H j
j 1
ij
ij
spec
=0
(2.8.7)
i 1
where Hspec is the specified molar enthalpy of the system and h ij is the partial molar enthalpy of Component i in Phase j which is also obtained from an EOS. Equations (2.8.6) and (2.8.7) form a system of n p equations for the n p unknowns T and F j (j=1,...,n p-1). As the phase mole fractions must sum up to unity, it follows that Fn p
=1−
n p −1
∑=
F j
(2.8.8)
j 1
The equations can readily be solved by the Newton-Raphson method. Thermodynamic Model
The K-values are obtained from the following thermodynamic equilibrium equation ln K ij
+ ln φ ij − ln φ iR = 0 i
i = 1,..., n c j ≠ R i
(2.8.9)
Equation (2.8.9) is derived from the equality of fugacities.
φij is the fugacity coefficient of Component i in Phase j estimated from an EOS and is a function of pressure, temperature and phase compositions. In using an EOS, the compressibility root corresponding to the minimum Gibb's free energy is selected unless stated otherwise. Note that Equation (2.8.9) represents a system of n c nonlinear equations and is solved iteratively with the material balance and energy balance equations.
258 Appendix B
User Guide WinProp
Flash Calculatio n Involvin g Water For a liquid-gas-water system, the conditions for phase equilibrium are as follows: Equilibrium equations: ln K iv
+ ln φ iV − ln φ iL = 0
ln K iw
+ ln φ iW − ln φ iL = 0
(2.9.1)
where K iv
= x iV / x iL
K iv
= x iW / x iL
and Material balance equations: N c
∑= (x
V i
i =1
i 1
N c
∑= (x i 1
W i
(K iv − 1)z i
N c
− x iL ) = ∑
Fl
(K iw − 1)z i
N c
− x iL ) = ∑ i =1
+ Fv K iv + Fw K iw
Fl
+ Fv K iv + Fw K iw
=0 =0
(2.9.2)
with the constraint F l + Fv + Fw = 1. A three-phase flash calculation corresponds to solving the 2N c+3 nonlinear equations for the 2Nc+3 primary unknowns K iv, K iw, Fl, Fv and Fw. The mole fractions are treated as dependent variables: x im
= K im Z i / (K iv Fv + Fl + K iw Fw )
(2.9.3)
For the components j which are assumed not soluble in the aqueous phase, take K jw = 0 and remove the corresponding equilibrium equation from the equation set. The system of equations can be solved by the quasi-Newton successive substitution method discussed in Nghiem and Li (1984) and Mehra et al (1984). Thermodynamic Models
The liquid and vapor phases are modelled by the cubic EOS, and the solubility in the aqueous phase is handled by Henry's law. Henry's law for a component sparingly soluble in the aqueous phase states ln φ iW = ln(H i / p )
i≠w
(2.9.4)
where the bold superscript w denotes the water component, and the regular subscript w denotes the aqueous phase. Hi is the Henry's law constant of component i in the aqueous phase. The variation of Henry's law constant with respect to pressure and temperature follows the equation:
User Guide WinProp
App end ix B 259
ln H i = ln H *i + v i∞ p / (RT )
(2.9.5)
where H* is a reference Henry's law constant. The molar volume at infinite dilution v i∞ is computed from the correlation of Lyckman et al (1965) reported by Heidemann and Prausnitz (1977) in the form:
p ci v i∞ T p ci = 0.0095 + 2.35 C T R Tci ci
(2.9.6)
where C is the cohesive energy density of water given by: C = (h ow − h sw + p sw v sw − RT ) / v sw
(2.9.7)
pws is the saturated vapor pressure of water at the temperature T, p ws is the molar volume of water at pws and T, and h ws - hwo is the enthalpy departure of liquid water p ws and T. The fugacity of the component water in the aqueous phase can readily be obtained from the fugacities of the solutes using the Gibb's-Duhem equation as in Prausnitz (1969): w
f w
p = x w φ w p w exp ∫ p w
s
w
s
w
vw RT
dp
(2.9.8)
where φws is the fugacity coefficient of pure water at p ws and vpws is the molar volume of pure water. The vapor pressure of water p sw and (h ow − h sw ) can be calculated respectively from the Frost-Kalkwarf-Thodos and the Yen-Alexander equation reported in Reid et al (1977). The molar volume vws is estimated from a correlation due to Chou reported in Rowe and Chou (1970). The fugacity coefficient φws is obtained from the following correlation which was found to match reasonably well the data in Canjar and Manning (1967):
φ sw = 0.9958 + 9.68330 x 10 −5 T ' − 6.1750 − 3.08333 x 10 −10 T '3 ; T ' > 90 =1 ; T ' ≤ 90 T = 1.8T − 459.67
x 10 −7 T '2
(2.9.9)
where T is the temperature in K, and T' is the temperature in °F. Initial guesses for the K-values are: K iv = p ci / p exp 5.42(1 + ω i ) (1 − Tci ) K iw
= K iv p / H i
260 Appendix B
User Guide WinProp
The following table summarizes the reference Henry's law constant stored in WinProp (Li and Nghiem, 1986). Coefficients Component
A
B
C
Methane
10.9554
11.3569
1.17105
0.4907
Ethane
13.9485
13.8254
1.66544
0.4911
Propane
14.6331
14.4872
1.78068
0.5469
n-Butane
13.4248
13.8865
1.71879
0.5080
n-Pentane
16.0045
16.2281
2.13123
0.5000
n-Octane
31.9431
28.6725
4.37707
0.4500
Carbon Dioxide
11.3021
10.6030
1.20696
(1)
Carbon Monoxide
10.7069
11.1313
1.08920
0.2000
Nitrogen
10.7090
11.4793
1.16549
0.2750
Hydrogen Sulfide
10.8393
9.8897
1.11984
0.1200
(1) 0.2 0.49852 - 0.0008 (T),
Water Interaction Coefficient
T ≤ 373 K T > 373 K
where
H *i 10 3 10 6 − C 2 ln s = −A + B T f w T T f ws
: :
temperature, K fugacity of saturated water, atm
Hi*
:
reference Henry's constant, atm
User Guide WinProp
App end ix B 261
START
Call hint for initialization
Two phase L-W flash calculation
L Disappears
2 Equilibrium phases W Disappears
Unstable
Stability Test
Unstable
Stable Disappears
Unstable
L-V flash calculation
L
W
Stability Test
Stability Test
Stable
W=Aqueous phase L = Liquid phase V = Vapor phase - = Equilibrium
W-L-V flash calculation
W-L
L-V
V or L Disappears
L-V-W
STOP
Flow Chart for Three Phase Water-Oil-Gas Flash Calculations
Critical Point Calculation s A critical point is a stable point on the stability limit. The Heidemann and Khalil (1980) method for calculating critical points consists of solving the following two criterion for T c and Vc: Q ∆N = 0
(2.10.1)
and C=
∑∑∑ i
j
k
∂ 3 A ∂n i ∂n j ∂n k ∆n i ∆n j ∆n k = 0
(2.10.2)
where A is the Helmholtz' free energy and
∂ 2 A = RT ∂ lnf i Q ij = ∂n i ∂n j ∂n j T, V T ,V
(2.10.3)
An efficient successive substitution solution procedure of the above equations has been proposed by Michelsen and Heidemann (1981) and summarized as follows: Select an initial value of λ (≡ vc/b). Calculate Tc such that det(Q) = 0 by Newton's method.
262 Appendix B
User Guide WinProp
Evaluate ∆N such that Q∆N= 0. To avoid discrete jumps in ∆ N, normalize ∆N by ∆NT∆N= 1. Evaluate the cubic form C* ≡ C (λ-1)2 and update λ
λ(k +1) = λ( k ) − C *
(k )
(λ( ) − λ( − ) )/ (C ( ) − C ( ) ) k
k 1
* k
* k -1
The factor (λ-1)2 is added to enhance stability. Repeat this process until C* = 0.
∑
Initial estimates suggested are λ = 3.5, Tc = 1.3
x i Tci . Another method to initiate the
i
calculation is to start with fixed step size of λ (say 0.1) until the cubic form (equation 2.10.1) changes sign. Then follow the above solution procedure. START
Initialization
Solvematerialbalanceequationforvapor phasemolefractionandcomposition
No
UseQNSStosolvetheequilibrium equationonceandupdateK-values
SinglePhase
Yes
Unstable StabilityTest
Convergence
No
Stable
SinglePhaseSystem Yes
Two-PhaseSystem
STOP
Flow Chart for Critical Point Calculation
User Guide WinProp
App end ix B 263
Viscosity Correlation In analogy to the Jossi, Stiel and Thodos equation, the following viscosity correlation is used (Fong and Nghiem, 1980):
[(µ − µ )ξ + 10 − ]
4 1/ 4
*
= a 0 + a 1 ρ r + a 2 ρ 2r + a 3 ρ 3r + a 4 ρ 4r
(2.11.1)
The reduced density ρr is defined as
n ρ r = ρv cµ = ρ∑ x i v αcµ i =1 c
1/ α
(2.11.2)
i
where vcµ is the critical molar volume used in the viscosity correlations. Generally v cµ is identical to the critical volume of the component. In WinProp, these are user input parameters which may be obtained from regression by matching experimental viscosity measurements. If no information is available, they are defaulted to v c. The mixture viscosity parameter is given by 1/ 6
∑ x i Tc i 1/ 2 2/3 x i MWi ∑ x i p c i i
ξ=
∑ i
(2.11.3)
i
and the low pressure viscosities of the mixture
∑ x µ MW ) = ∑ (x MW ) * i
i
µ*
1/ 2 i
i
i
1/ 2 i
(2.11.4)
i
where µi*, the low pressure viscosities for pure substances are from the Stiel and Thodos (1961) equation:
µ *i ξ i =
4.610Tr 0i .618
− 2.04 exp(− 0.449Tr ) i
+ 1.94 exp(− 4.058Tr ) + 0.1 ]x10 − 4 i
(2.11.5)
with
ξ i = Tc1 / 6 MWi−1 / 2 p c−2 / 3 i
i
(2.11.6)
and Tr i
= T / Tc
264 Appendix B
i
(2.11.7)
User Guide WinProp
The parameter vcµi resembles the critical volume for component i. In fact for most usage v cµi = v ci . The parameters α and a0 through a4 are usually obtained by regressing the available data. If no viscosity information is available, the following values can be used:
α
= = = = = =
0
a a1 a2 a3 a4
1 1.0230 x 10-1 2.3364 x 10-2 5.8533 x 10-2 -4.0758 x 10-2 9.3324 x 10-3
These values usually produce good estimates for gas viscosities.
Solution of Non-Linear Equations Governing equation:
G
≡ (G 1 , G 2 , ... , G 4 )T = 0
Primary variable: ξ ≡ ( ξ1 , ξ 2 , ..., ξ Ν ) Τ Solution: ξ (k +1) = ξ (k ) + ∆ξ ( k )
(2.12.1)
Newton's Method ( k )
∆ξ (k ) = −(J −1 )
G
( k )
J = Jacobian matrix ∂G/∂ξ
(2.12.2)
QNSS Method
Quasi-Newton Successive Substitution (Nghiem and Heidemann, 1982):
∆ξ (k ) = −
( k )
G
( k )
( k )
∆ξ (k −1) G ( k -1) = (k −1) ( k -1) ∆ξ ∆G
(0 )
= QSTEP ≡ 1
(k −1)
with and limited to
≤ DGM ≡ 30
∆ξ m limited to ≤ DVMAX ≡ 6
(2.12.3)
The QNSS method is restarted at every IREST iterations. Generally, IREST has the same magnitude as the total number of components.
User Guide WinProp
App end ix B 265
Plus Fraction Characterization Characterization Method
Reservoir fluid analyses usually report composition of all light and intermediate components. Heavy components are lumped into a 'plus' fraction, e.g. C 6+ where only the molecular weight and specific gravity are reported. It is advantageous to split the plus fraction into the single carbon number (SCN) fractions using model distribution e.g., C 6, C7, ..., C 45. The properties for each SCN are then estimated by empirical correlations. The synthetic distribution is then regrouped into a smaller number of hypothetical components (e.g., C 6-C12, C13-C20, C21+) via mixing rules. Distribution Model
A two-stage weighting exponential function is used as a probability function to describe the molar distribution as a function of molecular weight x ci
=
MWi +1
∫
ξdMW
MWi
with
ln ξ = (1 − f )C o
+
C1 − C o M1 − M o
MW < M 1 MW > M 1
0; f = 1;
(MW − M o ) + f [C1 + C 2 (M − M 1 )]
(2.13.1)
The parameters Co, Mo are from the 'minus' fraction, the fraction immediately preceding the plus fraction. Co = Mole fraction of the minus fraction / 14.0 Mo = Molecular weight of the minus fraction The parameter M1 and C1 are calculated by matching the molar distribution to the molecular weight and mole fraction of the plus fraction, X+ and M+ ∞
X+ =
∫
Mo
M1 e C1 C1 Co (e − e ) − ξdMW = C1 − C o C2 ∞
(M + − M o )X + =
∫
Mo
M 1 MW ξd (MW ) = C1 − C o
2
[
e Co 1 + (C1
− C o − 1)e C −C 1
o
]
2
1 + (1 − C 2 M 1 )e C C 2
266 Appendix B
i
(2.13.2)
User Guide WinProp
The parameter C2 is left as an adjustable parameter. It represents the final decline in the molar density function. The following equation was found to represent well the conventional oil in Canada: C2 = - ln 10 / (14.C 3 ) C3 = A(M + - F) 2 + B(M + - F) + C(SG + - G) 2 + D(SG + - G) + E where A B
= =
2.8297 x 10-3 4.0001 x 10-1
C D
= =
-8.4344 x 10-3 -6.3014 x 102
E F
= =
12.0 200.0
G
=
0.853
and SG+ is the specific gravity of the plus fraction. It can be used when no other information is available. Selection of Molecular Weight Range of SCN Group
The molecular weight range of each SCN group, say SCNi, is chosen to be between M1(i) = DERM(i-η) and M2(i) = DERM(i+1-η). The defaults are DERM = 14.026 and η(bias) = 0.75. Properties of Single Carbon Number Fraction
With the model distribution the mole fraction and molecular weight of each single carbon number (SCN) fraction, i, is easily calculated from the integral and the first moment: x ci
M2
∫
=
ξdMW
(2.13.3)
M1
MWci
=
1 x ci
M2
∫
MWξdMW + M o
M1
The specific gravity and normal boiling point for the SCN fraction are calculated from the Hariu-Sage (1969) correlation and assuming a constant Watson's characterization factor, K uop, which is adjusted to match the measured specific gravity of the plus fraction SG +: 2
2
j 0
k 0
log10 (MWi )= K uop
∑= ∑=
A jk T bk i K juop
= (Tb i + 459.67)1/3 / SG i
User Guide WinProp
i=6,7,8,... i=6,7,8,...
App end ix B 267
SG +
= ∑ i
X i MWi /SG i
−1
(2.13.4)
where A00 A10 A20 A01 A11 A21 A02 A12 A22
= = = = = = = = =
0.6670202 4.583705 x 10-3 -2.698693 x 10-6 0.1552531 -5.755585 x 10-4 3.875950 x 10-7 -5.378496 x 10-3 2.500584 x 10-5 -1.566228 x 10-8
The critical properties of the SCN fractions are calculated using, for example, Twu's correlations. Lumping into Hypothetical Components
Following Whitson (1983), the number of hypothetical components, NG, required to characterize a plus fraction is estimated as NG = 1 + 3.3 log10 (N-n) where n is the first SCN fraction in a C n+ fraction and N is the SCN fraction corresponding to 95 mole % of a C n+ fraction. The SCN fractions are then assigned to the hypothetical components according to their log (K) value. The K-values are calculated using the Wilson's equations. The Lee-Kesler (1975) mixing rules are then used to calculate the critical properties of the hypothetical components:
ω(1) = ∑
x j ω j
j
Vc(1) = Tc(1) p (c1)
=
1 8
∑∑ j
1 8Vc
1/ 3 ) x j x k (Vcj1 / 3 + Vck
3
k
∑∑ j
(
x j x k Vcj1 / 3
1/ 3 ) + Vck
Tcj Tck
k
= Z c RTc(1) / Vc(1) = (0.2905 − 0.085ω)RTc(1) / Vc(1)
where the superscript (1) denotes lumped properties.
268 Appendix B
User Guide WinProp
START Specify α, β Set up initial guess Calculate one point on the phase diagram Set up Jacobian matrix Solve t he equations Update variables Trivial root
Yes
STOP
No Unphysical results
Yes
Reduce step size
No One point in the phase diagram converged Yes Extrapolate variables
Stability check Output
Adjust new step size Complete phase diagram constructed
Yes
Printer plot
STOP
Flow Chart for Plus Fraction Characterization
User Guide WinProp
App end ix B 269
Interfacial Tension Calcul ations The general equation for calculating the interfacial tension is (Reid et al, 1977, p. 614); 1/4
= p ar (ρ L − ρ V )
(2.14.1)
where σ is the interfacial tension in dyne/cm between the phases L and V. ρ j is the molar density in mol/cm3 of phase j and p ar is the parachor. For hydrocarbon systems p ar i
= ξCN i
(2.14.2)
where
ξ = 40 40.3
CN ≤ 12 CN > 12
(2.14.3)
CN is the carbon number of the component i given by CNi = MWi/14 (2.14.4) where MWi is the molecular weight of i. For multicomponent systems 1/4
nc
= ∑ p ar (x i ρ L − y i ρ V ) i =1
i
(2.14.5) where xi are the mole fractions in phase L and y i the mole fractions in phase V.
Regression The major problem associated with phase-behavior matching with a cubic equation of state is the selection of regression parameters. There are many parameters that can be selected as the best set of parameters, and therefore a dynamic parameter-solution scheme is desired to avoid tedious and time-consuming trial-and-error regression runs. WinProp uses a regression technique where the most significant parameters are selected from a large set of parameters during the regression process. This reduces the regression effort considerably and alleviates the problem associated with the a priori selection of regression parameters (Agarwal, Li and Nghiem, 1987).
Introduction It is well known that cubic equations of state (EOS) will not generally predict accurately laboratory data of oil/gas mixtures without the tuning of the EOS parameters (Coats and Smart, 1986). It has often been the practice to adjust the properties of the components (usually the heavy fractions, e.g. p c, Tc, ω, etc., to fit the experimental data.
270 Appendix B
User Guide WinProp
The objective function of the regression involves the solution of complex nonlinear equations such as flash and saturation-pressure calculations. A robust minimization method is therefore required for rapid convergence to the minimum. In WinProp a modification of the adaptive least-squares algorithm of Dennis et al (1981) is used. The modification involves the use of some other nonlinear optimization concepts on direction and step-size selection due to Chen and Stadtherr (1981). The dynamic selection of the most meaningful regression parameters from a larger set of variables is described in Application of the Regression Method to EOS Tuning section. This feature is extremely useful in EOS fitting because it alleviates the problem of deciding apriori the best regression variables, which is extremely difficult. It should be stressed that the regression procedure will not correct the deficiencies of the EOS used, and the EOS predictive capability depends entirely on the type and the accuracy of the data used in the regression. For predictive purposes, attempts should be made to ensure that the "tuned" parameters are within reasonable physical limits.
The Regression Method The implementation of the dynamic-parameter-selection strategy for tuning the EOS requires the solution of a nonlinear optimization problem. In terms of least-squares, the optimization problem may be stated as minimize f (x ) = R (x ) R (x ) = T
x
nm
∑ i =1
r i (x )
2
(2.15.1)
where x = [x 1 , x 2 ,..., x n t
]T
is the regression-parameter vector, with n r being the number of regression parameters and nm the number of measurements to be fitted. Usually n m > nr . The elements of R(x) are denoted by r i (x) which are nonlinear in x. When the equation of state is adjusted to match a set of experimental data y r i
=
e i (x ) − y i yi
with
[
E(x ) = e1 (x ), e 2 (x ),..., e n
m
(x )]T
and y = [y i , y 2 ,..., y n m ]
T
where E(x) are the equation-of-state results and y the experimental data points. In this case the nonlinear least-squares problem consists of adjusting x so that the EOS results match the experimental measurements.
User Guide WinProp
App end ix B 271
The problem (2.15.1) may be solved by various methods for nonlinear parameter estimation (Bard, 1974), and for nonlinear optimization (Himmelblau, 1972; Schittkowski, 1981). The general purpose optimization methods however do not take advantage of the special structure of the nonlinear least squares optimization problem (2.15.1). Several strategies are available to exploit this structure. Coats and Smart (1986) used a modified linear programming least squares algorithm to solve (2.15.1). Watson and Lee (1986) use a modification of the Levenberg-Marquardt algorithm (see More', 1978) to solve a nonlinear least-squares problem. In WinProp a modification of the adaptive least-squares algorithm of Dennis et al (1981) is used. The algorithm departs from the method of Dennis et al in using some other nonlinear optimization concepts on step-direction and step-size selection due to Chen and Stadtherr (1981).
App li catio n of the Regr ess io n Method to EOS Tuning
It was found that the key to an efficient algorithm would be the fast and accurate (as far as possible) estimation of the Jacobian matrix J. It has been shown that the matrix J also determines the second derivative Hessian matrix ∇2f. Consequently, a small change in the determination of J affects the performance of the regression method quite dramatically. The derivatives of the residuals R are calculated by numerical differentiation, since in most cases it is not practical to obtain exact analytical derivatives. The calculation of R at all times involves iterative processes, where the solution is only available to some accuracy εi. If the Jacobian J is to be calculated by finite differences, the perturbation in the independent variables x must be such that it is not masked by the convergence accuracy εi or the truncation and round-off errors associated with the computation. It has been found that a perturbation of 1% in the independent variables is adequate to compute J by numerical differentiation. Choice of Regression Parameters
Given a global set of regression parameters x j, j=1,...,n p, the method selects an active subset of nr parameters with which regression will be performed. The global set of regression parameters is supplied by the user and may include any of the following parameters: pci
Critical pressure of Component i
Tci vci
ϖi
Critical temperature of Component i Critical volume of Component i which affects the interaction coefficients between hydrocarbons (see Equation 2.16.1) Acentric factor of Component i
vit
Volume translation of Component i (see the Equations section)
MWi
Molecular weight of Component i
272 Appendix B
User Guide WinProp
d ij
Interaction coefficient between Components i and j Exponents for computing interaction coefficients between hydrocarbons (see Equation 2.16.1)
θ
The interaction coefficients between hydrocarbons are estimated from the following equation (Li, et al, 1985)
2v1ci/ 6 v1cj/ 6 d ij = 1 − 1 / 3 1/ 3 v ci + v cj
θ
(2.16.1)
The volume translation technique of Peneloux et al (1982) is used to correct the molar volume (see the Equations section). The parameters x j are scaled by using the upper bound x j,max and lower bound x j,min of the corresponding parameter such that they always lie between zero and unity. x j
= (x j −
x j,min ) / (x j,max
−
x j,min )
(2.16.2)
The regression scheme sorts the n p parameters in the descending order of |∂f / ∂x j|. From these n p parameters, the first nr parameters are chosen for regression, i.e. the nr parameters with the largest |∂f / ∂x j|. nr is supplied by the user. The regression proceeds on these nr parameters and if at any time during the regression, |∂f / ∂x j| becomes less than r i |, i=1,...,n m, the variable x j is dropped from the regression set and the next variable on the original sorted list is added on. Indeed, since all x j are scaled between zeros and unity, if |∂f / ∂x j| is less than all |r i|, it is likely that x j has to go beyond its bounds to further reduce r i. Therefore, it is logical that x j should be dropped from the active parameter set. Another condition where x j is dropped is when it tries to go out of bonds for more than two iterations. At convergence, if the total number of regressed variables (including those which have been dropped) is less than five, then new variables are added to the active regression set and the original active regression variables with the smallest |∂f / ∂x j| are removed from the active set such that nr is preserved.
User Guide WinProp
App end ix B 273
The flow chart of the parameter selection procedure is given in Figure B.2. START
Load the initial values of the n p regression variables
Calculate ∂f / ∂x j j=1,2,...,n p and sort x j in the descending order of magnitude of ∂f / ∂x j
Choose the first n r regression variables from the sorted set
Regress on the n r variables
Is
∂f / ∂x j < r i for all i x j
= x j,min
or
for two iterations
or
No
x j = x j,max
Yes
Drop x j from the activ e regression set. Add the next variable from the sorted list to the active set
No
Converged? Yes Regressed on at least five variables?
Yes
STOP
No Add mo re v ariables to th e activ e regression set
Figure B.2: Flow Chart for Selecting the Active Regression Parameters
274 Appendix B
User Guide WinProp
Properties of Components The equations-of-state requires the critical properties as input. The critical properties for common single real molecules have been measured and tabulated in numerous handbooks. A fraction of the reservoir fluid, on the other hand, consists of numerous real molecules and generally only their specific gravity, boiling point and molecular weights are measured. Their critical properties are not determined. The components making up the reservoir fluid are thus identified into two types: the built-in components and the user components. Built-in components are those whose critical properties are known and have been stored in the phase behavior package WinProp. User components are those whose properties are not stored and must be supplied as input to WinProp. Real Components Component
CH4 C2H6 C3H8 iC4 nC4 iC5 nC5 nC6 nC7 nC8 nC9 nC10 nC16 N2 CO2 H2S H2O Toluene Benzene Cyclo-C6 FC6 FC7 FC8 FC9 FC10 FC11 FC12 User Guide WinProp
pc, atm.
vc, l/gmole
45.400 48.200 41.900 36.000 37.500 33.400 33.300 29.300 27.000 24.500 22.800 20.800 14.000 33.500 72.800 88.200 217.60 40.600 48.300 40.200 32.460 30.970 29.120 26.940 25.010 23.170 21.630
0.0990 0.1480 0.2030 0.2630 0.2550 0.3060 0.3040 0.3700 0.4320 0.4920 0.5480 0.6030 0.9560 0.0895 0.0940 0.0985 0.0560 0.3160 0.2590 0.3080 0.3440 0.3810 0.4210 0.4710 0.5210 0.5740 0.6260
Tc, deg. K
190.60 305.40 369.80 408.10 425.20 460.40 469.60 507.40 540.20 568.80 594.60 617.60 717.00 126.20 304.20 373.20 647.30 591.70 562.10 553.40 507.50 543.20 570.50 598.50 622.10 643.60 663.90
acentric factor
0.00800 0.09800 0.15200 0.17600 0.19300 0.22700 0.25100 0.29600 0.35100 0.39400 0.44400 0.49000 0.74200 0.04000 0.22500 0.10000 0.34400 0.25700 0.21200 0.21300 0.26370 0.30240 0.33720 0.37810 0.41650 0.45530 0.49220
MW, g/mol
16.04300 30.07000 44.09700 58.12400 58.12400 72.15100 72.15100 86.17800 100.2050 114.2320 128.2590 142.2860 226.4480 28.01300 44.0100 34.0800 18.01500 92.14100 78.11400 84.16200 86.0000 96.0000 107.0000 121.0000 134.0000 147.0000 161.0000 App end ix B 275
Component
FC13 FC14 FC15 FC16 FC17 FC18 FC19 FC20 FC21 FC22 FC23 FC24 FC25 FC26 FC27 FC28 FC29 FC30 FC35 FC36 FC37 FC38 FC39 FC40 FC41 FC42 FC43 FC44 FC45
pc, atm.
v c, l/gmole
20.430 19.330 18.250 17.150 16.350 15.650 15.060 14.360 13.830 13.260 12.830 12.380 11.840 11.480 11.130 10.760 10.490 06.310 09.910 08.660 08.530 08.290 08.130 07.900 07.780 07.600 07.460 07.250 07.140
0.6740 0.7230 0.7770 0.8350 0.8840 0.9300 0.9730 1.0270 1.0730 1.1260 1.1700 1.1510 1.2020 1.2400 1.2790 1.3230 1.3560 2.0060 1.5890 1.6320 1.6570 1.7020 1.7340 1.7800 1.8060 1.8440 1.8780 1.9280 1.9550
Tc, deg. K
682.40 700.70 718.60 734.50 749.20 760.50 771.00 782.90 793.30 804.40 814.00 823.20 832.70 841.20 849.60 857.70 864.30 832.80 905.90 912.10 917.30 923.40 928.20 934.30 938.50 942.80 947.60 953.70 957.80
acentric factor
MW, g/mol
0.52480 0.55720 0.58990 0.62250 0.64960 0.67240 0.69280 0.71670 0.73610 0.75690 0.77350 0.93510 0.96690 0.99090 1.01450 1.03960 1.05850 1.23760 1.17720 1.19660 1.20850 1.22780 1.24120 1.26020 1.27070 1.28560 1.29880 1.31730 1.32750
175.0000 190.0000 206.0000 222.0000 237.0000 251.0000 263.0000 275.0000 291.0000 300.0000 312.0000 324.0000 337.0000 349.0000 360.0000 372.0000 382.0000 394.0000 445.0000 456.0000 464.0000 475.0000 484.0000 495.0000 502.0000 512.0000 521.0000 531.0000 539.0000
The properties for the first 20 are obtained from Reid et al (1977). The next 30 components, FC6 to FC45 represent typical hydrocarbon fractions C6 to C45. Their critical properties are calculated with the correlations of Kesler and Lee (1976), using the averaged normal boiling points and specific gravities of C 6 to C45 reported by Whitson (Whitson, 1983; Katz and Firoozabadi, 1978). These components can be used for rough calculations if no other information about the heavy ends are available.
276 Appendix B
User Guide WinProp
User Compo nents For User components, usually only the physical properties molecular weight, boiling point and/or specific gravity are known. The critical properties are calculated from empirical correlations. Numerous such correlations are available in the literature. A survey by Whitson (1982) suggested the use of Kesler-Lee correlations for conventional oil. For heavy hydrocarbons the correlation of Twu (1984) generally yields reasonable results (Fu et al, 1986). These two methods are available in WinProp to calculate the required critical properties. In view of its simplicity, the method of Riazi-Daubert is also available. The correlations are summarized below. Kesler and Lee (1976)
=
− 0.0566 SG − ( 0.24244 + 2.2898 / SG + 0.11857 / SG 2 ) 10 −3 T b + ( 1.46850 + 3.6480 / SG + 0.47227 / SG 2 ) 10 −7 T b2 − ( 0.42019 + 0.0000 / SG + 1.69777 / SG 2 ) 10 −10 T b3
ln p c
Tc
8.3634
= 341.7 + 811 SG + (0.4244 + + (0.4669 − 3.2623 SG )10 5 / T b
0.1174 SG ) T b
For θ > 0.8
ω = −7.904 + 0.1352 K c − + (1.408 − 0.01063 K ) / θ
0.007465 K c2
+
8.359θ
For θ < 0.8
ω=
− ln ( p c / 14.7 ) −
+ 1.28862 ln θ − 0.169347θ 6 − 15.6875 / θ − 13.4721ln θ + 0.43577θ 2
5.92714
15.2518
+
6.09648 / θ
where p c in psia T b , Tc in o R θ = T b / Tc 1/ 3 K c = (CABP ) / SG CABP = cubic average boiling point in o R
(2.17.1)
Twu (1984)
Critical temperature: Tc
= Tco [( 1 +
f T
= ∆ SG t − 0.362456
∆ SG T =
2 f T ) / ( 1
(
exp 5 SG o
User Guide WinProp
−
−
2 f T ) ]
2
/ T b1 / 2 SG 1
+
(0.0398285 − 0.948125 /
T b1 / 2
) ∆ SG
t
) −1
App end ix B 277
Critical volume:
[( 1 +
Vc
=
f V
= ∆ SG V
Vco
∆ SG V =
2 f V ) / ( 1
−
2 f V )]
2
0.466590 / T b1 / 2
(
+ ( − 0.182421 +
3.01721 / T b1 / 2
) ∆ SG
V
− SG 2 ) − 1
exp 4 SG o 2
Critical pressure: p c = p oc ( Tc / Tco ) (Vco / Vco ) [( 1 + 2 f p ) / ( 1 − 2 f p f p
= ∆ SG p
( 2.53262 − 46.1955 /
+ ( − 11.4277 +
T b1 / 2
252.140 / T b1 / 2
−
+
)]2
0.00127885 T b
0.00230535 T b
)
) ∆ SG
p
∆ SG p = exp 0.5 (SG o − SG ) − 1 Molecular weight: 2 ln MW = ln MW o [( 1 + 2 f M ) / ( 1 − 2 f M )]
f M x
= ∆ SG M =
+ ( − 0.0175691 +
x
0.0123420
−
0.193168 / T b1 / 2
) ∆ SG
M
0.328086 / T b1 / 2
(
∆ SG M =
exp 5 SG o
(
+
− SG ) − 1
where Tco
=
T b 0.533272
− 0.284376
0.191017 x 10 −3 T b
x 10 −10 T b3
+
+
0.779681 x 10 −7 T b2
0.959468 x 10 28 / T b13
)−
1
p oc
(1 − 0.419869 − 0.505839 α − 1.56436 α − 9481.70 α ) − = (3.83354 + 1.19629 α + 34.8888 α + 36.1952 α + 104.193 α )
T b
=
Vco
=
3
1/ 2
exp ( 5.71419 - 0.122488 /
+
2.71579
θ2 )
14
8
2
4
2
θ − 0.286590 θ 2 − 39.8544 / θ
- 24.7522
θ + 35.3155 θ 2
with
θ = ln MW o α =1
T b / Tco
(2.17.2)
All temperatures in oR, volume in ft 3lb-mol and pressures in psia.
278 Appendix B
User Guide WinProp
Riazi and Daubert (1980)
p c = 3.12281 x 10 9 T b−2.315 SG Tc
= 24.2787
T b0.58848 SG
2.3201
0.3596
where p c in psia T b , Tc in o R
(2.17.3)
Interaction Coeffic ient The importance of interaction coefficients, d ij, in the accuracy of phase behavior calculations, especially the saturation pressures, has been demonstrated by Peng and Robinson (1976), Conrad and Gravier (1980) and Whitson (1982) among others. Theoretically, d ij is introduced to account for the molecular interaction between dissimilar molecules. Their values are usually obtained by fitting the predicted saturation pressure curves to experimental data. Hydrocarbon-Hydrocarbon Interaction
Katz and Firoozabadi (1978) have published the binary interaction coefficients between methane and other heavy hydrocarbon fractions. Their values have been fitted to the density, ρ, of the fraction by Conrad and Gavier (1980) as: d = 0.12903 ρ - 0.05871 Whitson and Torp (1981) have fitted the same set of data using specific gravity, SG, as correlating parameters: d = 0.14 (SG) - 0.0668 The Institute of Thermodynamics (Technical University of Berlin) has accumulated a comprehensive collection of data on vapor-liquid equilibrium. It contains approximately 55,000 experimental data for more than 120 binary systems. These have been evaluated by Oellrich, Plocker, Prausnitz and Knapp (1981) to determine the interaction coefficients (both hydrocarbon and non-hydrocarbon systems) for the commonly used equations-of-state including PR and SRK. Mehra (1981) and Li (1983) both used the following relations for hydrocarbon-hydrocarbon systems:
2 Vc1 / 3 Vc1 / 3 d ij = 1 − 1 / 3 Vc + Vc1 / 3 i
i
n
j
(2.18.1)
j
with the constant n = 1. The same form is also proposed by Chueh and Prausnitz (1967) and Chaudron, Asselineau and Renon (1973). Examining the paraffin-paraffin d ij of Oellrich et al (1981) shows that they could roughly be correlated using this equation with n = 1.2. Mehra (1981) has also shown that this equation reproduces satisfactorily the methane interaction coefficients of Katz and Firoozabadi (1978). Equation (2.18.1) is used in WinProp with n as a user input parameter.
User Guide WinProp
App end ix B 279
Hydrocarbon-Nonhydrocarbon Interaction
Besides Oellrich et al (1981), other researchers have also reported values of interaction coefficients for hydrocarbon-nonhydrocarbon systems. The reported interaction coefficient values between CO2 and hydrocarbons, dCO2-HC, generally ranges from 0.1 to 0.13 for PR EOS (Oellrich et al, 1981; Hughes, Matthews and Mott, 1981; Katz and Firoozabadi, 1978; Mehra, 1981). In addition, dCO 2-HC correlations have been proposed by Kato, Nagahama and Hirata (1981); Mulliken and Sandler (1980) and Turek, Metcalfe, Yarborough and Robinson (1980). These correlations are generally temperature dependent and complicated. The reported interaction coefficient values between N2 and hydrocarbons, dN2-HC, generally increases with increasing carbon number in the hydrocarbon, and range from 0.03 to 0.15 (Mehra, 1981; Oellrich et al, 1981; Katz and Firoozabadi, 1978). The following table shows the interaction coefficients for nonhydrocarbons stored in WinProp. N2
CH4 C2H6 C3H8 iC4 nC4 iC5 nC5 nC6 nC7 nC8 nC9 nC10 nC16 Toluene Benzene Cyclo-hexane FC6-FC45 N2 CO2 H2S H2O
280 Appendix B
.031 .042 .091 .095 .095 .095 .095 .100 .100 .100 .100 .100 .130 .120 .120 .120 .120 .000 -.020 .176 .275
CO2
.103 .130 .135 .130 .130 .125 .125 .125 .120 .115 .110 .110 .090 .120 .078 .106 .150 -.020 .000 .096 .200
H 2S
.080 .070 .070 .060 .060 .060 .060 .050 .040 .040 .030 .000 .000 .000 .000 .000 .000 .176 .096 .000 .120
H2O
.4907 .4911 .5469 .5080 .5080 .5000 .5000 .4500 .4500 .4500 .4500 .4500 .4500 .4800 .4800 .4800 .4800 .2750 .2000 .1200 .0000
User Guide WinProp
Nomenclature a b c C p d ij D f i F F j G GOR hij Hi Hspec K i K ij L1 L2 MW n N Nc N p NHYP p r i R T T3p ui U v V xi X zi Z
User Guide WinProp
equation of state parameter equation of state parameter equation of state parameter heat capacity interaction coefficient stability test distance fugacity for component i degree of freedom from the phase rule mole fraction of phase j Gibb's free energy gas-oil ratio partial molar enthalpy of component i in phase j enthalpy, or Henry's law constant for water flash for component i specified molar enthalpy equilibrium ratio for component i equilibrium ratio for component i in phase j first liquid phase second liquid phase molecular weight mole number total number of moles total number of components number of phases number of hypothetical components pressure volume translation for component i universal gas constant temperature three phase temperature number of component i in stability test vector of u partial molar volume vapor phase phase composition of component i, mole fraction vector of x global composition of component i, mole fraction compressibility factor (pv/RT)
App end ix B 281
Subscript
c i j k,m l q R i v w
critical property component number component number, phase phase liquid phase 1 liquid phase 2 reference phase for component i vapor phase water phase
Superscript
E k L o Q t V W *
excess property iteration number liquid phase 1 non-translated volume liquid phase 2 translated volume vapor phase water phase ideal state, reference state
Other Symbols
Ωa Ω b φ δ1 δ2 ϖ β ζ µ ξ ρr ρ
282 Appendix B
equation of state parameters equation of state parameters fugacity coefficient equation of state parameter equation of state parameter acentric factor specified variables for phase diagram construction fraction of injection fluid for phase diagram construction viscosity mixture viscosity parameter reduced density density
User Guide WinProp
References for Appendix B Agarwal, R., Li, Y.-K., and Nghiem, L., "A Regression Technique with Dynamic-Parameter Selection for Phase Behavior Matching," paper SPE 16343, presented at the SPE California Regional Meeting, Ventura, California, April 8-10, 1987. Agarwal, R.K., Li, Y.-K., Nghiem, L.X., and Coombe, D.A., "Multi-Phase Multi-Component Isenthalpic Flash Calculations with a Cubic Equation of State," presented at the 39 th Annual Technical Meeting of CIM, June 12-16, 1988, Calgary, Alberta. Bard, Y., "Nonlinear Parameter Estimation," Academic Press Inc., 1974. Canjar, L.N., and Manning, F.S., Thermodynamic Properties and Reduced Correlations for Gases, Gulf Publishing Co., Houston, Texas, 1967. Chaudron, J., Asselineau, L., and Renon, H., "Mixture Properties and Vapor-Liquid Equilibria by Modified Redlich-Kwong Equation of State," Chem. Eng. Sci., Vol. 28, 1973, pp. 1991. Chen, H.-S., and Stadtherr, M.A., "A Modification of Powell's Dogleg Method for Solving Systems of Nonlinear Equations," Comp. and Chem. Eng., Vol. 5, No. 3, 1981, pp. 143-150. Chueh, P.L. and Prausnitz, J.M., "Vapor-Liquid Equilibria at High Pressures: Calculation of Partial Molar Volumes in Nonpolar Liquid Mixtures," AIChE J., Vol. 13, No. 6, November 1967, pp. 1099-1107. Coats, K.H., Smart, G.T., "Application of a Regression-Based EOS PVT Program to Laboratory Data," SPE Reservoir Eng., Vol. 1, No. 3, May 1986, pp. 277-299. Conrad, P.G. and Gravier, J.F., "Peng-Robinson Equation of State Checks Validity of PVT Experiments," Oil and Gas J., April 1980, pp. 77-86. Dennis Jr., J.E., and Schnabel, R.B., "Numerical Methods for Unconstrained Optimization and Nonlinear Equations," Prentice-Hall Series in Computation Math, Cleve Moler, Advisor, 1983. Dennis Jr., J.E., Gay, D.M., and Welsch, R.E., "An Adaptive Nonlinear Least-Squares Algorithm," ACM Trans. Math. Software, Vol. 7, No. 3, September 1981, pp. 348-368. Fong, D.K.S., and Nghiem, L.X., "A Viscosity Model for Reservoir Fluids," Computer Modelling Group Research Report R7.02, March 1980. Fu, C.-T., Puttagunta, R., and Pors, D., "Estimation Methods in Pseudo-Critical Properties of Heavy Hydrocarbons," ARC/AOSTRA, Industry Access Report 8586-49, January 1986. Gay, D.M., "Computing Optimal Locally Constrained Steps," SIAM J. Sci. Stat. Comput., Vol. 2, No. 2, June 1981, pp. 186-197. Gosset, Heyen, and Kalitventzeff, "An Efficient Algorithm to Solve Cubic Equations of State," Fluid Phase Equilibria, Vol. 25, 1986, pp. 51-64. Grabowski, M.S., and Daubert, T.W., "A Modified Soave Equation of State for Phase Equilibrium Calculations," I.&E.C. Process Des. Dev., Vol. 17, No. 4, 1978, pp. 443-454. Harin, G.H., and Sage, R.C., "Crude Split Figured by Computer," Hydro. Proc., April 1969, pp. 143-148. Heidemann, R.A., and Khalil, A.M., "The Calculation of Critical Points," AIChE J., Vol. 26, 1980, pp. 769-779. User Guide WinProp
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Himmelblau, D.M., "Applied Nonlinear Programming," McGraw-Hill Inc., 1972. Hughes, D.S., Matthews, J.D., and Mott, R.E., "Theoretical Aspects of Calculating the Performance of CO2 as an EOR Process in North Sea Reservoirs," Proceedings, 1981 European Symposium on EOR, September 21-23, 1981, Bournemouth, England. Jhaveri, B.S., and Youngren, G.K., "Three-Parameter Modification of the Peng-Robinson Equation of State to Improve Volumetric Predictions," SPE paper 13118, presented at the 59 th Annual Technical Conference and Exhibition, Houston, Texas, September 16-19, 1984. Kato, K., Nagahama, K., and Hirata, M., "Generalized Interaction Parameters for the PengRobinson Equation of State: Carbon Dioxide-n-Paraffin Binary Systems," Fluid Phase Equil., Vol. 7, 1981, pp. 219-231. Katz, D.L., and Firoozabadi, A., "Predicting Phase Behavior of Condensate/Crude-Oil Systems Using Methane Interaction Coefficients," J. Petrol. Technol., Vol. 30, 1978, pp. 1649-1655. Kesler, M.G., and Lee, B.I., "Improve Predictions of Enthalpy of Fractions," Hydro. Proc., March 1976, pp. 153-158. Lee, B.I., and Kesler, M.G., "A Generalized Thermodynamic Correlation Based on ThreeParameter Corresponding States," AIChE J., Vol. 21, May 1975, pp. 510-527. Li, Y.-K., and Nghiem, L.X., "The Development of a General Phase Envelope Construction Algorithm for Reservoir Fluid Studies," paper SPE 11198, presented at the 57 th Annual Fall Meeting of SPE-AIME, September 26-29, 1982, New Orleans, Louisiana. Li, Y.-K., "Heavy Fraction Characterization and Hypothetical Component Selection for Oil and Gas Mixtures," Computer Modelling Group Research Report R12.04, May 1983. Li, Y.-K., and Nghiem, L.X., "Phase Equilibria of Oil, Gas and Water/Brine Mixtures from a Cubic Equation of State and Henry's Law," Can. J. Chem. Eng., 1986. Li, Y.-K., Nghiem, L.X., and Siu, A., "Phase Behavior Computations for Reservoir Fluids: Effects of Pseudo-Components on Phase Diagrams and Simulation Results," J. Can. Pet. Tech., Vol. 24, No. 6, 1985, pp. 29-36. Martin, J.J., "Cubic Equations of State - Which?," Ind. Eng. Chem. Fundam., Vol. 18, No. 2, 1979, pp. 81-97. Mehra, R.K., "The Computation of Multi-Phase Equilibrium in Compositional Reservoir Studies," Ph.D., Thesis, University of Calgary, 1981. Mehra, R.K., Heidemann, R.A., and Aziz, K., "An Accelerated Successive Substitution Algorithm, "Can. J. Chem. Eng., Vol. 61, 1984, pp. 590-596. Michelsen, M.L., "Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures," Fluid Phase Equilibria, Vol. 4, 1980, pp. 1-10. Michelsen, M.L., and Heidemann, R.A., "Calculation of Critical Points from Cubic TwoConstant Equations of State," AIChE J., Vol. 27, No. 3, 1981, pp. 521-523. Michelsen, M.L., "The Isothermal Flash Problem, Parts I and II," Fluid Phase Equilibria, Vol. 9, 1982, pp. 1-40. Moore, J.J., "The Levenberg-Marquardt Algorithm: Implementation and Theory," In Lecture Notes in Mathematics, No. 630, Numerical Analysis, G. Watson, Ed., Springer-Verlag, New York, 1978, pp. 105-116. 284 Appendix B
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Mulliken, C.A., and Sandler, S.I., "The Prediction of CO 2 Solubility and Swelling Factors for Enhanced Oil Recovery," Ind. Eng. Chem. Process Des. Dev., Vol. 19, 1980, pp. 709-711. Nghiem, L.X., and Heidemann, R.A., "General Acceleration Procedure for Multiphase Flash Calculation With Application to Oil-Gas-Water Systems," paper presented at the 2nd European Symposium on Enhanced Oil Recovery, Paris, France, November 8-10, 1982. Nghiem, L.X., Aziz, K., and Li, Y.-K., "A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwong or Peng-Robinson Equation of State," Soc. Petrol. Eng. J., Vol. 23, June 1983. Nghiem, L.X., and Li, Y.-K., "Computation of Multiphase Equilibrium Phenomena of Reservoir Fluid," Fluid Phase Equil., Vol. 17, 1984, pp. 77-95. Nghiem, L.X., Li, Y.-K., and Heidemann, R.A., "Application of the Tangent Plane Criterion to Saturation Pressure and Temperature Computations," Fluid Phase Equil., Vol. 21, 1985, pp. 39-50. Oellrich, L., Plocker, U., Prausnitz, J.M., and Knapp, H., "Equation-of-State Methods for Computing Phase Equilibria and Enthalpies," Int. Chem. Eng., Vol. 21, No. 1, January 1981, pp. 1-15. Passut, C.A., and Danner, R.P., "Correlation of Ideal Gas Enthalpy, Heat Capacity, and Entropy," Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 4, 1972, pp. 543-546. Peneloux, A., Rauzy, E., and Freze, R., "A Consistent Correction for Redlich-Kwong-Soave Volumes," Fluid Phase Equil., Vol. 8, 1982, pp. 7-23. Peng, D.Y., and Robinson, D.B., "A New Two-Constant Equation of State," Ind. Eng. Chem. Fundam., Vol. 15, 1976, pp. 59-64. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K., The Properties of Gases and Liquids , 3rd Edition, McGraw-Hill, New York, 1977. Riazi, M.R., and Daubert, T.E., "Simplify Property Predictions," Hydrocarbon Processing, March 1980, pp. 115-116. Robinson, D.B, and Peng, D.Y., "The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs," Gas Processors Association, Research Report RR-28, March 1978. Rowe, A.M., and Chou, J.C.S., "Pressure-Volume-Temperature-Concentration Relation of Aqueous NaCl Solutions," J. Chem. Eng. Data, Vol. 15, No. 1, 1970, pp. 61-66. Schittkowski, K., "The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian Type Line Search Function - Parts I and II," Numer. Math, Vol. 38, 1981, pp. 83-127. Soave, G., "Equilibrium Constants from a Modified Redlich-Kwong Equation of State," Chem. Eng. Sci., Vol. 27, 1972, pp. 1197-1203. Stiel, L.I., and Thodos, G., "The Viscosity of Nonpolar Gases at Normal Pressures," AIChE J., Vol. 7, No. 4, 1961. Twu, C.H., "An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-Tar Liquids," Fluid Phase Equil., Vol. 16, 1984, pp. 137-150. User Guide WinProp
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