Appendix C

Solutions to end-of-chapter problems

C.1 Chapter 2

P2.1. QH=600 kW; QW=0 kW

P2.2. QH=540 kW; QW=1526 kW

P2.3. C1 (T: Met, Et, Prop; B: But); C2 (T: Met; B: Et, Prop); C3 (T: Et; B Prop)

P2.4. C1 (T: A; B: BCD); C2II (T: BC; B: D); C3 (T: B; B: C)

P2.5. C1(T: A; B: BC); C2 (T: B; B: C)

P2.6. ΔT=10K

P2.7. QH=50 kW; QW=30 kW

P2.8. QH=183 kW; QW=697 kW

P2.9. ΔT=25K

P2.10. C1 (AB, CDEF); C2(A, B); C3(CDE, F); C4 (CD, E); C5(C, D)

P2.11. C1 (AB, CDEF); C2(A, B); C3(CDE, F); C4 (C, DE); C5(D, E)

P2.12. QS=200 kW; QW=1600 kW; Matches: Above Pinch: H1-C1 (1000 kW); Heating C1 200 kW; Below Pinch: H2-C1 (2400 kW); Cooling H2 (1600 kW); H1-C1 (200 kW)

C.2 Chapter 3

P3.1. 160K

P3.2. 190K; Win=2802 kcal/h; Wout=697 kcal/h

P3.3. P1=150 atm; T4=300K; q=2 kcal/kg

P3.4. f=0.215

P3.5. D=4.47 ft h=18 in

P3.6. f=0.125; η=13%

P3.7. System II

P3.8. f=0.35; W1=60 kcal/kg; W1=54 kcal/kg

P3.9. With precooling T=163K; q=15 kcal/kg; Isentropic expansion; T=282K

P3.10. 6 Trays; 81% molar fraction in N2

P3.11. Ref III

P3.12. Pdesign=200 bar; Poperation=150 bar; η=0.95

P3.13. f=0.37; Linde with precooling q=30 kcal/kg; 4 trays

P3.14. q=22.7 kcal/kg

P3.15. 5 trays; f=0.76

P3.16. P=640 mmHg

C.3 Chapter 4

P4.1. 29.5 atm

P4.2. m=88.976 kg; Limestone: 11.024 kg;

Component%
CaO13.6
Ca(OH)269.6
CaCO316.8


5.18% excess of Ca(OH)2; Conversion 98%

P4.3. 105.7 m3

P4.4. Q=412808 kcal/h; U=1053kcalhm2Cimage

P4.5. m=89.39 kg

NaOH0.00296201
Na2CO30.16254275
H2O0.83449524


Limestone: 10.601 kg; 7.38% excess of Ca(OH)2; Conversion 97%

P4.6. T=700K

P4.7. Solution: 89.425 kg; Limestone: 10.574 kg

Solution (kg)89.42577
NaOH0.582368
Na2CO314.89163
H2O84.526
Limestone (kg)10.57423
CaO0.097362
Ca(OH)20.790953
CaCO30.111685

P4.8. Q=8246387 kcal/h; A=1645 m2; X=0.632

P4.9. 52% NaCl; 48% NH4HCO3; Required CaCO3, 860 kg; Production NaCl=1459 kg

P4.10. W=357,854 kW; No selection; 1200€/kW

P4.11. 0.28 kg/s H2; 2.23 kg/s O2; No selection; 1250€/kW

P4.12. 0.09434 kmol CO2

P4.13. A=21.68 m2; ΔP=7841 kPa.

P4.14. T=1473K; Q=−111,188 kJ

P4.15. −1.80 V

P4.16. 0.41 kg/s H2 and 3.26 kg/s O2; Solar

P4.17. Electrolysis: 4.5 GW; Oxygen Comp: 43.5 MW; Hydrogen Comp: 108 MW

P4.18. Gas:

H2O0.079
CO0.316
H20.509
CO20.095


20% via Electrolysis: Electrolysis: 46 MW; Oxygen Comp: 443 kW; Hydrogen Comp: 687 kW

P4.19. T=115°C; W=7744 kg/s; A=90 m2; AIQ1=41 m2; AIQ2=8.2 m2

P4.20. T=111°C; A=283 m2; AIQ1=65 m2; AIQ2=23 m2

P4.21. MR=175 kg/h; MP=825 kg/h; xR=171,917 ppm; xP=0.063 ppm

P4.22. 0.189 kmol/s of CaCO3; 0.696 kmol of flue gas

C.4 Chapter 5

P5.1. Air: 6 kmol per TM; Steam 8.34 kmol per TM; 8479 kcal/t

P5.2. H2O=1 kmol; CO=2 kmol; H2=3 kmol per kmol of C2H2; T=802K; alpha=0.75

P5.3. X=35% Recirculation (Syngas alone) 179.2; α=0.014

P5.4. Basis 1 kmol of Coal: Water gas 0.144 kmol; Generator gas 0.119 kmol; Qwater gas=4859 kcal; Qgenerator=1594 kcal; 91.5%

P5.5. T=252K

P5.6. P=1 atm; T=1215K; 0.2079 kmol of C

P5.7. 

Component%
N273.82
CO213.09
CO13.09
Total100.00
Component%
H248.39
CO31.61
H2O11.6
CO20.08
C0
Total100.00


T=894 K; Qgenerator gas=1014 kcal; Qwater gas=5552 kcal

P5.8. 974 kg/h of water; 12,959 kW

P5.9. 0.7 mol of CH4 per mol of H2

P5.10. Steam: 0.96 mol per mol of methane; Oxygen: 0.48 mol per mol of methane

P5.11. α=64.4%; CO2 removed=20.5 kmol

 Comp Gas %
H20.5027
CO0.2514
CH40.0492
N20.1967

P5.12. α=64.4%; CO2 removed=20.5 kmol; T=200 °C

P5.13. Purge=0.022; Recycle gas=275 kmol; Recycle ammonia=15.18 kmol

P5.14. Gas composition:

 % Molar
H2O9.90
CO18.24
CO26.76
H265.10


39 kmol flue gas/kmol of C3H8

P5.15. X=0.37; Purge=0.019; SG Recycle: 159.7 kmol/100 syngas fed; Methanol Recycle: 3.51 kmol/100 syngas fed

P5.16. 

 VaporLiquid
H20.613632820.02344087
CO0.303627180.02069322
CO20.075312640.00684493
MetOH0.007427360.94902098

P5.17. T=298.6 K

P5.18. T=784 K

P5.19. X=0.21

P5.20. 2 Beds

P5.21. X=0.35; 91% of the fed goes to 2nd Bed

P5.22. Efficiency=50%; 1.38 the minimum

P5.23. L=19.38 kmol/s with an excess of 34% with respect to the minimum

P5.24. T=494 K; Purge=0.038

P5.25. L/D=2

P5.26. Efficiency=63%

P5.27. Efficiency=25%

P5.28. 

Temp (K)573254254
P (bar)505050
Vapor fraction110
Enthalpy (MJ/h)141.8341−1147.413−3293.24
Total flow352.69306.034646.65541
Total flow unitkmol/hkmol/hkmol/h
Comp unitkmol/hkmol/hkmol/h
Hydrogen211.11211.02930.08069132
Nitrogen70.3770.304440.06556367
Argon9.129.0834070.03659212
Ammonia62.0915.6174346.47256

Image

P5.29. N/A

P5.30. 27% of C3H8 is used as fuel; Syngas composition: 19% H2O; 19% CO; 4% CO2; 58% H2

P5.31. Flash: 0.625 M€; T (273K); Column 1.003 M€; 3 Stages; 321 kmol/s of liquid (Raoult’s law holds)

P5.32. Fresh feeds to beds 2nd=2.1 kmol/s; 3rd=2.3 kmol/s

Stream No.FeedOut 1st bed2nd FeedExit HX to Bed 1
Stream Name    
Temp K373.0000*867.9598293.0000*673.0000
Pres Pa29999999.6374*29999999.637429999999.6374*29999999.6374
Enth MJ/s9.708347.4430.3111247.443
Vapor mole frac.1.00001.00001.00001.0000
Total kmol/s4.20003.75852.10004.2000
Total kg/s42.051042.051121.025542.0510
Total std L m3/h458.2150405.7532229.1075458.2150
Total std V m3/h338894.26303273.80169447.16338894.26
Flowrates in kg/s    
Nitrogen28.014021.830614.007028.0140
Hydrogen6.04744.71263.02376.0474
Ammonia0.00007.51840.00000.0000
Argon7.98967.98963.99487.9896

Image

Stream No.In 2nd bedOut 2nd Bed3rd FeedIn 3rd Bed
Stream Name    
Temp K671.9910814.7848293.0000*670.2527
Pres Pa29999999.637429999999.637429999999.6374*29999999.6374
Enth MJ/s47.13247.1330.3407646.793
Vapor mole frac.1.00001.00001.00001.0000
Total kmol/s5.85855.38252.30007.6825
Total kg/s63.076663.076823.027986.1047
Total std L m3/h634.8607578.2836250.9273829.2109
Total std V m3/h472720.96434306.26185585.00619891.22
Flowrates in kg/s    
Nitrogen35.837529.169115.341044.5101
Hydrogen7.73636.29673.31179.6084
Ammonia7.518415.62650.000015.6265
Argon11.984411.98444.375316.3597

Image

Stream No.Out 3rd BedFinal product
Stream Name  
Temp K789.4937636.1416
Pres Pa29999999.637429999999.6374
Enth MJ/s46.7949.0594
Vapor mole frac.1.00001.0000
Total kmol/s7.14547.1454
Total kg/s86.104886.1048
Total std L m3/h765.3866765.3866
Total std V m3/h576555.86576555.86
Flowrates in kg/s  
Nitrogen36.987436.9874
Hydrogen7.98457.9845
Ammonia24.773324.7733
Argon16.359716.3597


X1=0.221; X2=0.186; X3=0.169; XT=0.355

C.5 Chapter 6

P6.1. Kp=5.78 atm−1; T=27.25°C

P6.2. T=1492 K;

Composition%
N20.47660706
O20.0466796
H2O0.28999495
NO0.1867184


77% HNO3; 23% H2O

P6.3. X=0.93; T=1138K

P6.4. T=784K; T=505K; L=5.98kg H2O and 0.153 kg HNO3

P6.5. 

 Pfin (atm) (20 °C)
O20.03249854
N20.59247339
NOini0
NO20.08901046
N2O40.08048442
Total0.7944668
 Pfin (atm) (10 °C)
O20.03138935
N20.57225205
NOini0
NO20.06218873
N2O40.08962934
Total0.75545947
 Pfin (atm) (40 °C)
O20.03471692
N20.63291624
NOini0
NO20.15585831
N2O40.05559242
Total0.87908389

P6.6. T=502K

 % Molar
N20.80685892
O20.05068866
H2O0.002514
NO0
NO20.13976608
N2O40.00017234

P6.7. Sol1: 0.168; Sol2: 0.606

P6.8. 30 °C—200 s; 50 °C—300 s; 100 °C—450 s; 200 °C—t>1000 s

P6.9. 

 kmol
N20.45054664
O20.01559242
H2O0.002156928
NO0
NO20.013797762
N2O40.01790625

P6.10. L=5 cm.

C.6 Chapter 7

P7.1. 

image
Figure C.1
 After 1st BedAfter 2nd Bed
SO20.018560780.0033564
N20.790.79
O20.099280390.09204708
SO30.061439220.01446663


T=450°C

P7.2. 

 S→SO2SO2→SO3 
 InitialFinalInitial1st Bed2nd Bed
SO20.080.080.018560780.0033564
N20.790.790.790.790.79
O20.210.21–0.080.21–0.080.099280390.09204708
SO3  0.061439220.01446663

Image

P7.3. 

 S→SO2SO2→SO3 1st BedSO2→SO3 2nd Bed
 InitialFinalInitialFinalInitialFinal
SO20.10.010.031196720.031196720.0039281
N20.790.790.790.790.790.79
O20.210.21–0.10.21–0.10.075598360.075598360.06930267
SO3  0.068803280.006880330.02726863

Image


X=0.96

P7.4. Raw Material 0.5% H2O; 88.1% FeS2; 11.4% Slag; Losses 83,689 kcal/100 kg Pyrite

P7.5. X=0.21

 kmol
N215.56
O21.96
H2O1.41
SO21.19
NO0.16

P7.6. X=0.85

P7.7. X=0.975; 61.65 kg Water; Q=−93,500 kcal

P7.8. X=0.6; T=930K

P7.9. m=174.4 kg/s; T=498K

P7.10. T=711K

P7.11. H2SO4 (99%)=9.19 kg; H2SO4 (98%)=174.6 kg; Water added=22.25 kg; H2SO4 (Absorption)=182 kg

P7.12. y=0.0095 kg Water/kg as;

 kmol
N221.15
O22.81
H2O0.41
SO22.81


Losses=110,566 kcal

P7.13. 

N221.15
O21.49
H2O0.27
SO20.14
SO3 
NO0.014


Water=191. 44 kg

P7.14. 

a. 

Stream No.FeedExit 1st BedFeed 2nd bedExit 2nd bed
Temp K750.0000918.8530673.0000774.9077
Pres Pa1.0000101325.0000101325.0000101325.0000
Flowrates in kg/h    
Sulfur Dioxide640.6501264.5776264.577643.2041
SO30.0000469.9894469.9894746.6465
Oxygen351.9890258.0692258.0692202.7838
Nitrogen2213.10602213.10602213.10602213.1060

Image

Stream NoFeed 3rd bedExit 3rd bedFeed 4th bedExit 4th bed
Temp K673.0000689.7883623.0000625.7674
Pres Pa101325.0000101325.0000101325.0000101325.0000
Flowrates in kg/h    
Sulfur Dioxide43.20417.08847.08841.2328
SO3746.6465791.7814791.7814799.0995
Oxygen202.7838193.7643193.7643192.3019
Nitrogen2213.10602213.10602213.10602213.1060

Image

b. The conversion increases to almost 100%

C.7 Chapter 8

P8.1. MetOH added 2.9 kmol per kmol of Oil

P8.2. D=88 kg/s; R=5.12 kg/s; XD=0.8

P8.3. 42.2% Cellulose; 42.2% Hemicellulose; 15.6% Lignin; Xxylose=0.66; 18.6 kmol of ethanol

P8.4. MetOH=308 kmol; Purge=0.057

P8.5. 54% Starch; 21% Lipids

P8.6. t=12 h

P8.7. D=0.75 kg/s; R=3.75 kg/s; L/D=1; Number of trays 9

P8.8. C1HaOa/2; 13.4% of the biogas is used as fuel

P8.9. 

 HX1 Col Water–Ethanol Col 1 (Met–Eth/Prop/But) Col 2 (Eth–Prop/But)
Thermodynamics UNIFAC UNIFAC UNIFAC UNIFAC
Q (MJ/s) 11.8 18.9 19.3 5.8
Reflux ratio  2.8 8.2 0.15
Tin (K) 305 363 348 355.5
Tout (K) 363 351 (T) – 372 (B) 337.6 (T) – 355.5 (B) 351.1 (T) – 375 (B)
Ethanol prod (kg/s)  4.85  4.82

Image

P8.10. 38% H2; 32% CO

P8.11. C1H3.14O1.36; 45% CO2; 55% CH4

P8.12. 51.4 kg of steam; η=0.55

P8.13. 41.8% H2; 38.2% CO

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