Spreadsheet Problem Solving for ChE Faculty Triple-effect Triple-effect Evaporator Design
D. E. Clough 1/19/98
Basic Data
Feed Flow Rate: Feed Composition: Feed Temperature:
6.93 kg/s 0.14 ma mass fraction NaOH 21 degC
Product Composition:
0.47 ma m ass fraction NaOH
Steam Temperature:
164 degC
Final Vapor Condensation Pressure: & Equilibrium Temperature:
2 ps psia 39 degC
Overall Material Balance
Flow Rate [kg/s] Total NaOH
Stream Feed Product
6.93 2.06
W ater Evap.
4.87 or
W ater 0.97 0.97
5.96 1.09 4.87
Boilups in the Effects
Evaporation Ef E ffect [kg/s] -------------------------------------------------------------------------------------------------- ---------------------------------- ------------------------------------ Values Values from Linear Linear Set of Enthalpy Enthalpy Equations Equations 1 1.552 2 1.551 -------------------------------------------------------------------------------------------------- ---------------------------------- -----------------------------------3 4.866 [this from material balance]
Compositions Compositions in the Effects
Composition Effect [mass fraction NaOH] 1 2 3 [this last entry should confirm basic data]
Feeds [kg/s]
0.14 0.14 0.47
6.93 6.93 2.06
Boiling Point Elevations in the Effects
Effect
Boiling Point Elevation [degF] [degC]
1 2 3
8.0 8.0 69.0
Temperature Drops
Total temperature drop: Sum of elevations: Net temperature drop:
Solver Entries: Temperature Temperature Drop
125.3 degC 47.2 degC 78.1 degC
4.4 4.4 38.3
Temperature Drop Effect [degC] ----------------------------------------------------- ------------------ ----------------------------------Solver adjusts 1 these 2 ----------------------------------------------------- ------------------ ----------------------------------3 78.08 [this last one computed by difference]
0.00 Sum of Adjustable Delta-T's
Temperature Summary
Solution Saturation Effect Temperature Temperature [degC] [degC] 1 2 3
164.3 159.9 77.3
Heat Transfer Coefficient Effect [W/(m2 K)]
159.9 155.4 39.0
1 2 3
4500 2000 600
Effect 1 Stream Properties
Stream
Temp.
Sat.Temp.
Comp.
No Superht.
Enthalpy
Steam Feed 1 Vapor 1 Cond 1 Feed 2
164.30 21.00 164.3 164.30 164.3
164.30 -160 ---
-0.14 --0.14
--2750.5 ---
2750.5 76.1 2759.2 651.1 611.2
Duty: Temperature Drop: Area:
Flow Enthalpy Rate 3.19 6.93 0.00 3.19 6.93
8775 528 0 -2077 -4236 2990
6698 kW 0.0 degC #DIV/0! m^2
Set of Simultaneous Enthalpy Balance Equations
ws
e1
e2
const
soln
2099.40 0.00 0.00
-2148.04 2092.07 2053.22
0.00 -2164.12 4161.36
3707.90 -111.41 9641.66
3.354 1.552 1.551
Effect 2 Stream Properties
Stream Vapor 1 Feed 2 Vapor 2 Cond 2 Feed 3 Duty: Temperature Drop: Area:
No Comp. Superht.
Temp. Sat.Temp. 164.3 164.3 160 160 160
160 -155 --
-0.14 --
Enthalpy
2750.5 -2750.5
0.14
--
2759.2 611.2 2759.2 651.1 595.1
Flow Enthalpy Rate 0.00 6.93 0.00 0.00 6.93
0 4236 0 0 -4124 111
0 kW 0.0 degC #DIV/0! m^2
Effect 3 Stream Properties
Stream Vapor 2
Temp. Sat.Temp. 160
155
No Comp. Superht. --
2750.5
Enthalpy 2759.2
Flow Enthalpy Rate 0.00
0
Feed 3 Vapor 3 Cond 3 Product
160 77 155 77
Duty: Temperature Drop: Area:
-39.00 ---
0.14 --0.47
-2572.9 ---
595.1 2648.3 651.1 426.2
6.93 4.87 0.00 2.06
4124 -12886 0 -880 -9642
0 78 0.0
Summary of Areas
Effect Area (m^2) ft 1 2 3 Total
#DIV/0! #DIV/0!
2
#DIV/0! #DIV/0! 0
#DIV/0!
0
Variance of Areas:
#DIV/0!
#DIV/0!
Steam Summary
Steam Consumption:
3.19 kg/s
Overall Economy:
1.53
Economy-per-effect: Effect 1 2 3
Capital Cost
Operating Costs Steam Cash Flow Cost of Capital 10% Inflation 3% NPV ($2,634,711)
Economy 0.00 #DIV/0! #DIV/0!
$400,000 1990 index $511,370 1997 index
$388,443 per year 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
($511,370) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($388,443) ($4,395,797)
1.28 CPI
Steam Cost $1.5 $1.9 3.19 202563
per 1000 lb per 1000 lb kg/s Mlb/yr
1990.00 1997.00
Property Tables
Table Interpolation
Table Inter
Boiling Point Elevation
Steam an
Composition (mass fraction)
Boiling Pt. Elev. (degF)
Index
0.00 4.00 14.00 25.00 35.00 47.00 65.00 75.00 88.00 100.00 120.00 138.00
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00
0.00 0.10 0.20 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 data from McCabe, Smith & Harriott, p. 421
Page 4
Property Tables
olation
Table Inter
Condensate Enthalpy
NaOH-H2
Temperature Vapor Enthalpy degF degC BTU/lbm kJ/kg 90.00 95.00 100.00 110.00 120.00 130.00 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 212.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00
32.2 35.0 37.8 43.3 48.9 54.4 60.0 65.6 71.1 76.7 82.2 87.8 93.3 98.9 100.0 104.4 110.0 115.6 121.1 126.7 132.2 137.8 143.3 148.9 154.4
1100.9 1103.1 1105.2 1109.5 1113.7 1117.9 1122.0 1126.1 1130.2 1134.2 1138.1 1142.0 1145.9 1149.7 1150.4 1153.4 1157.0 1160.5 1164.0 1167.3 1170.6 1173.8 1176.8 1179.7 1182.5
2560.7 2565.8 2570.7 2580.7 2590.5 2600.2 2609.8 2619.3 2628.8 2638.1 2647.2 2656.3 2665.4 2674.2 2675.8 2682.8 2691.2 2699.3 2707.5 2715.1 2722.8 2730.3 2737.2 2744.0 2750.5
Liquid Enthalpy BTU/lbm kJ/kg 57.99 62.98 67.97 77.94 87.92 97.90 107.89 117.89 127.89 137.90 147.92 157.95 167.99 178.05 180.07 188.13 198.23 208.34 218.48 228.64 238.84 249.06 259.31 269.59 279.92
134.9 146.5 158.1 181.3 204.5 227.7 251.0 274.2 297.5 320.8 344.1 367.4 390.7 414.1 418.8 437.6 461.1 484.6 508.2 531.8 555.5 579.3 603.2 627.1 651.1
Index
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00
Reference: McCabe, Smith and Harriott, p. 926.
Page 5
Converted
Property Tables
olation Solution Enthalpy
Comp. Mass Fraction
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Temperature -- degF 50.00
90.00
150.00
200.00
250.00
300.00
350.00
18.00 18.00 17.00 16.00 17.00 20.00 22.00 38.00 64.00 74.00 112.00
58.00 55.00 52.00 49.00 48.00 49.00 56.00 68.00 82.00 112.00 130.00
120.00 115.00 108.00 102.00 99.00 102.00 108.00 120.00 137.00 158.00 180.00
170.00 160.00 152.00 147.00 142.00 143.00 149.00 162.00 177.00 196.00 220.00
223.00 210.00 200.00 192.00 187.00 188.00 191.00 202.00 220.00 235.00 263.00
265.00 257.00 242.00 238.00 235.00 236.00 238.00 245.00 259.00 277.00 297.00
320.00 306.00 290.00 280.00 277.00 276.00 279.00 282.00 300.00 318.00 338.00
148.9 616.4 597.8 562.9 553.6 546.6 548.9 553.6 569.9 602.4 644.3 690.8
176.7 744.3 711.8 674.5 651.3 644.3 642.0 649.0 655.9 697.8 739.7 786.2
Entries in BTU/lbm Reference: McCabe, Smith & Harriott, p. 429. able First column entries below indices are temperatures in degC. First row entries to right of indices are compositions in mass fraction. Main table entries are enthalpies in kJ/kg.
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
10.0 41.9 41.9 39.5 37.2 39.5 46.5 51.2 88.4 148.9 172.1 260.5
32.2 134.9 127.9 121.0 114.0 111.6 114.0 130.3 158.2 190.7 260.5 302.4
65.6 279.1 267.5 251.2 237.3 230.3 237.3 251.2 279.1 318.7 367.5 418.7
93.3 395.4 372.2 353.6 341.9 330.3 332.6 346.6 376.8 411.7 455.9 511.7
Page 6
121.1 518.7 488.5 465.2 446.6 435.0 437.3 444.3 469.9 511.7 546.6 611.7
Nomenclature
Variable Name A1 AEff1 A2 AEff2
Description Heat transfer area in effect 1, m
Location =Balances!$B$122
Heat transfer area in effect 2, m
=Balances!$B$150
A3
Heat transfer area in effect 3, m
q1
AEff3 BoilUp DeltaTs Duty1
Initial estimates of boilup from effects 1 & 2, ks/s Delta-T's for effects 1 & 2, degC Heat duty for effect 1, kW
=Balances!$B$167 =Balances!$C$53:$C$54 =Balances!$C$91:$C$92 =Balances!$B$120
q2
Duty2
Heat duty for effect 2, kW
=Balances!$B$148
q3
e1
Duty3 Econ Econ1 Econ2 Econ3 Evap1
Heat duty for effect 3, kW Overall Economy: boilup generated/steam supplied Economy of effect 1 Economy of effect 2 Economy of effect 3 Boilup rate in effect 1, kg/s
=Balances!$B$165 =Balances!$B$183 =Balances!$B$189 =Balances!$B$190 =Balances!$B$191 =Balances!$C$53
e2
Evap2
Boilup rate in effect 2, kg/s
=Balances!$C$54
e3
Evap3
Boilup rate in effect 3, kg/s
=Balances!$C$56
etot
EvapTot Sum of boilup rates in all three effects, kg/s
=Balances!$B$46
x1
Frac1
Mass fraction NaOH in effect 1
=Balances!$B$64
x2
Frac2
Mass fraction NaOH in effect 2
=Balances!$B$65
x3
Frac3
Mass fraction NaOH in effect 3
=Balances!$B$66
hc
hCond
Enthalpy of steam condensate in effect 1, kJ/kg
=Balances!$F$117
hc2
hCond2 Enthalpy of condensate from effect 2, kJ/kg
=Balances!$F$145
hc3
hCond3 Enthalpy of condensate from effect 3, kJ/kg
=Balances!$F$162
H1
HEvap1 Vapor enthalpy in effect 1, kJ/kg
=Balances!$F$116
H2
HEvap2 Vapor enthalpy in effect 2, kJ/kg
=Balances!$F$144
H3
HEvap3 Vapor enthalpy in effect 3, kJ/kg
=Balances!$F$161
hf
hf
Enthalpy of feed, kJ/kg
=Balances!$F$115
h1
hLiq1
Enthalpy of feed to effect 2, kJ/kg
=Balances!$F$118
h2
hLiq2
Enthalpy of feed to effect 3, kJ/kg
=Balances!$F$146
hp
hp
Enthalpy of product, kJ/kg
=Balances!$F$163
Hs
Hs
Steam enthalpy, kJ/kg
=Balances!$F$114
H1
HsEvap1Saturated enthalpy of vapor in effect 1, kJ/kg
=Balances!$E$116
H2
HsEvap Saturated enthalpy of vapor in effect 2, kJ/kg
=Balances!$E$144
H3 w1
HsEvap Saturated enthalpy of vapor in effect 3, kJ/kg =Balances!$E$161 LinVal Solution of enthalpy equations for boilup in effects 1 & =Balances!$E$129:$E$1 Liq1 Liquid rate out of effect 1 (feed to effect 2), kg/s =Balances!$D$64
w2
Liq2
Liquid rate out of effect 2 (feed to effect 3), kg/s
=Balances!$D$65
w3=wp
Liq3
Liquid rate out of effect 3 (product rate), kg/s
=Balances! $D$66
P3
PCond SumEle TCond TDel1 TDel2 TDel3 TDelNet TDelTot TEff1
Pressure of third effect, psia =Balances!$C$35 Sum of boiling point elevations in the three effects, de =Balances!$B$83 Saturation temperature of condensate from 3rd effect, =Balances!$C$36 Delta T in effect 1, degC =Balances!$C$91 Delta T in effect 2, degC =Balances!$C$92 Delta T in effect 3, degC =Balances!$C$94 Net delta T with boiling point elevations removed, deg =Balances!$B$84 Total delta T available, degC =Balances!$B$82 Temperature in effect 1, degC =Balances!$B$103
Ts3
T1
Page 7
Nomenclature
T2
TEff2
Temperature in effect 2, degC
=Balances!$B$104
T3
TEff3
Temperature in effect 3, degC
=Balances!$B$105
BP1
Tf
TElev1 Boiling point elevation in effect 1, degC TElev1F Boiling point elevation in effect 1, degF TElev2 Boiling point elevation in effect 1, degC TElev2F Boiling point elevation in effect 1, degF TElev3 Boiling point elevation in effect 1, degC TElev3F Boiling point elevation in effect 1, degF Tf Feed temperature, degC
=Balances!$D$74 =Balances!$C$74 =Balances!$D$75 =Balances!$C$75 =Balances!$D$76 =Balances!$C$76 =Balances!$B$29
Ts
Ts
Steam temperature, degC
=Balances!$B$33
Ts1
TsEff1
Steam saturation temperature in effect 1, degC
=Balances!$C$103
Ts2
TsEff2
Steam saturation temperature in effect 2, degC
=Balances!$C$104
Ts3
TsEff3
U1
UEff1
U2
UEff2
Steam saturation temperature in effect 3, degC =Balances!$C$105 Overall heat transfer coefficient in effect 1, W/(m K) =Balances!$C$16 Overall heat transfer coefficient in effect 2, W/(m K) =Balances!$C$17
U3
UEff3
Overall heat transfer coefficient in effect 3, W/(m K) =Balances!$C$18
BP2 BP3
4
=Balances!$F$176 =Balances!$B$27
xf
VarArea Variance of the areas of the three effects, m wf Feed flow rate, kg/s wfH2O Feed rate of H2O, kg/s wfNaOH Feed rate of NaOH, kg/s wp Product flow rate, kg/s wpH2O Product rate of H2O, kg/s wpNaO Product rate of NaOH, kg/s ws Steam flow rate, kg/s wsnew Steam flow rate from enthalpy balance equations, kg/ xf Mass fraction NaOH in feed
xp
xp
=Balances!$B$31
wf
wp
ws
Mass fraction NaOH in product
Page 8
=Balances!$D$43 =Balances!$C$43 =Balances!$B$44 =Balances!$D$44 =Balances!$C$44 =Balances!$G$114 =Balances!$E$128 =Balances!$B$28
Nomenclature
0
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