Tugas 2_bachtiyar_ Fixed-point Iteration Dan Wegstein Method.xlsx

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Successive substitution solution for v in the Redlich-Kwong EOS - Single Variabel Temperature Pressure Gas Constant R a for CO2

700.0000 oR 80.0000 atm 0.7302 f2.atm/(lbmol.oR) 21972.0000 atm.oR (f3/lbmol)2

b for CO2

0.4755 f3/lbmol �^𝑘=𝑅𝑇/𝑃−𝑎(�−𝑏)/(𝑇^0.5 �(�+𝑏)𝑃)+𝑏

�^𝑘=�^(𝑘−1) k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

x 100.000 6.762 5.430 5.107 5.005 4.971 4.959 43.478 6.665 6.595 6.533 6.518 6.512 6.510 15.303 6.493 6.888 6.792 6.807 6.803 6.803 8.646 6.581 6.933 6.836 6.859 6.853 6.854 7.235 6.743 6.905 6.851 6.866 6.862 6.863 6.941 6.825

g (gx) 6.762 5.430 5.107 5.005 4.971 4.959 43.478 6.665 6.595 6.533 6.518 6.512 6.510 15.303 6.493 6.888 6.792 6.807 6.803 6.803 8.646 6.581 6.933 6.836 6.859 6.853 6.854 7.235 6.743 6.905 6.851 6.866 6.862 6.863 6.941 6.825 6.882

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

6.882 6.858 6.866 6.864 6.865 6.881 6.853 6.871 6.862 6.866 6.864 6.865 6.868 6.862 6.867 6.864 6.865 6.865 6.865 6.865 6.864 6.865 6.864 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865

6.858 6.866 6.864 6.865 6.881 6.853 6.871 6.862 6.866 6.864 6.865 6.868 6.862 6.867 6.864 6.865 6.865 6.865 6.865 6.864 6.865 6.864 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865

87 88 89 90 91 92 93 94 95 96 97 98 99 100

6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865

6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865 6.865

/(𝑇^0.5

Successive substitution solution for v in the Redlich-Kwong EOS - Multi Variabel

0 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle Reactor_In Reactor_Out Water_Out Vapor_Out Organic_Out Product 0 100 35 0 0 35 0.35 0 0 65 0 0 65 64.35 0 0 65 0 65 0 0 0 3000 3000 3000 0 0 0 0 3100 3165 3000 65 100 64.7

1 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle Reactor_In Reactor_Out Water_Out Vapor_Out Organic_Out Product 34.65 134.65 47.1275 0 0 47.1275 0.47128 0.65 0.65 88.1725 0 0 88.1725 87.2908 0 0 87.5225 0 87.5225 0 0 0 3000 3000 3000 0 0 0 35.3 3135.3 3222.8225 3000 87.5225 135.3 87.7621

2 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 46.6562 0.88173 0 0 47.538

Reactor_In 146.656225 0.881725 0 3000 3147.53795

Reactor_Out Water_Out Vapor_Out Organic_Out Product 51.32967875 0 0 51.32967875 0.5133 96.20827125 0 0 96.20827125 95.2462 95.32654625 0 95.3265463 0 0 3000 3000 0 0 0 3242.864496 3000 95.3265463 147.53795 95.7595

3 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 50.8164 0.96208 0 0 51.7785

Reactor_In 150.816382 0.96208271 0 3000 3151.77846

Reactor_Out Water_Out Vapor_Out Organic_Out 52.78573369 0 0 52.78573369 98.99273099 0 0 98.99273099 98.03064828 0 98.0306483 0 3000 3000 0 0 3249.809113 3000 98.0306483 151.7784647

Product 0.52786 98.0028 0 0 98.5307

4 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 52.2579 0.98993 0 0 53.2478

Reactor_In 152.257876 0.98992731 0 3000 3153.2478

Reactor_Out Water_Out Vapor_Out Organic_Out 53.29025672 0 0 53.29025672 99.95754694 0 0 99.95754694 98.96761963 0 98.9676196 0 3000 3000 0 0 3252.215423 3000 98.9676196 153.2478037

Product 0.5329 98.958 0 0 99.4909

5

Feed

Recycle Reactor_In Reactor_Out Water_Out Vapor_Out Organic_Out Product

N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

100 0 0 3000 3100

52.7574 152.757354 53.46507395 0.99958 0.99957547 100.2918557 0 0 99.2922802 0 3000 3000 53.7569 3153.75693 3253.04921

6 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 52.9304 1.00292 0 0 53.9333

Reactor_In 152.930423 1.00291856 0 3000 3153.93334

Reactor_Out Water_Out Vapor_Out Organic_Out 53.52564813 0 0 53.52564813 100.4076936 0 0 100.4076936 99.40477509 0 99.4047751 0 3000 3000 0 0 3253.338117 3000 99.4047751 153.9333418

Product 0.53526 99.4036 0 0 99.9389

7 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 52.9904 1.00408 0 0 53.9945

Reactor_In 152.990392 1.00407694 0 3000 3153.99447

Reactor_Out Water_Out Vapor_Out Organic_Out 53.54663708 0 0 53.54663708 100.4478315 0 0 100.4478315 99.44375457 0 99.4437546 0 3000 3000 0 0 3253.438223 3000 99.4437546 153.9944686

Product 0.53547 99.4434 0 0 99.9788

8 N(C8H10) N(C8H8) N(H2) N(H2O) N(Total)

Feed 100 0 0 3000 3100

Recycle 53.0112 1.00448 0 0 54.0156

Reactor_In 153.011171 1.00447832 0 3000 3154.01565

Reactor_Out Water_Out Vapor_Out 53.55390975 0 0 100.4617393 0 0 99.45726096 0 99.457261 3000 3000 0 3253.47291 3000 99.457261

Product 0.53554 99.4571 0 0 99.9927

0 0 0 3000 3000

0 53.46507395 0.53465 0 100.2918557 99.2889 99.2922802 0 0 0 0 0 99.2922802 153.7569296 99.8236

Organic_Out 53.55390975 100.4617393 0 0 154.015649

New_Recycle 34.65 0.65 0 0 35.3

New_Recycle 46.656225 0.881725 0 0 47.53795

New_Recycle 50.816381963 0.9620827125 0 0 51.778464675

New_Recycle 52.25787635 0.9899273099 0 0 53.24780366

New_Recycle 52.757354155 0.9995754694 0 0 53.756929625

New_Recycle

52.930423215 1.0029185567 0 0 53.933341772

New_Recycle 52.990391644 1.0040769365 0 0 53.99446858

New_Recycle 53.011170705 1.0044783151 0 0 54.01564902

New_Recycle 53.018370649 1.0046173927 0 0 54.022988042

Single Variable Wegstein Method for Redlich-Kwong EOS Temperature Pressure Gas Constant R a for CO2

700 oR 80 atm 0.7302 f2.atm/(lbmol.oR)

b for CO2

0.4755 f3/lbmol

-10 10

21972 atm.oR (f3/lbmol)2

�^([𝑘])=�^([𝑘− 1]) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Theta min Theta max

x 300.000 6.830 5.437 5.005 4.954 4.952 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

�^([𝑘])=𝑅𝑇/𝑃−𝑎(�−𝑏)/(𝑇^0.5 �(�+𝑏)𝑃)+𝑏 g(x)

Slope 6.830 5.444 5.109 4.971 4.953 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

0.0047 0.2403 0.3203 0.3488 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Theta 0.0047 0.2403 0.3203 0.3488 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

1.0048 1.3163 1.4713 1.5357 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

1.0048 1.3163 1.4713 1.5357 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

�+𝑏)𝑃)+𝑏

Multidimentional Wegstein Method for Recycle Stream Using Excel Sheet

0 Feed N(C8H10) 100 N(C8H8) 0 N(H2) 0 N(H2O) 3000 N(Total) 3100

Recycle 0 0 0 0 0

Reactor_In 100 0 0 3000 3100

Reactor_Out Water_Out 35 0 65 0 65 0 3000 3000 3165 3000

Vapor_Out 0 0 65 0 65

Organic_Out 35 65 0 0 100

1 Feed N(C8H10) 100 N(C8H8) 0 N(H2) 0 N(H2O) 3000 N(Total) 3100

Recycle 34.65 0.65 0 0 35.3

Reactor_In 134.65 0.65 0 3000 3135.3

Reactor_Out Water_Out 47.1275 0 88.1725 0 87.5225 0 3000 3000 3222.8225 3000

Vapor_Out 0 0 87.5225 0 87.5225

Organic_Out 47.1275 88.1725 0 0 135.3

Slope N(C8H10) 0.347 N(C8H8) 0.356 N(H2) 0 N(H2O) 0 N(Total)

Theta Calc 1.530 1.554 1.000 1.000

Theta Lower Theta Upper

2 Feed Recycle Reactor_In Reactor_Out Water_Out N(C8H10) 100 53.02218822 153.0221882 53.55776588 0 N(C8H8) 0 1.01010101 1.01010101 100.4745234 0 N(H2) 0 0 0 99.46442234 0 N(H2O) 3000 0 3000 3000 3000 N(Total) 3100 54.03228923 3154.032289 3253.496712 3000

Slope N(C8H10) 1.03 N(C8H8) -1.847 N(H2) 0 N(H2O) 0 N(Total)

3

Feed

Theta Calc -33.650 0.351 1.000 1.000

Recycle

Theta Lower Theta Upper

Reactor_In

Reactor_Out Water_Out

Weigstein Recycle 53.0221882173 1.0101010101 0 0

Vapor_Out 0 0 99.4644223412 0 99.4644223412

Organic_Out 53.55776588 100.4745234 0 0 154.0322892

Weigstein Recycle 53.0221882173 1.0082200055 0 0

Vapor_Out

Organic_Out

N(C8H10) 100 53.02218822 153.0221882 53.55776588 N(C8H8) 0 1.008220006 1.008220006 100.4726423 N(H2) 0 0 0 99.46442234 N(H2O) 3000 0 3000 3000 N(Total) 3100 54.03040822 3154.030408 3253.494831

Slope N(C8H10) 0.612 N(C8H8) 1.529 N(H2) 0 N(H2O) 0 N(Total)

Theta Calc 2.576 -1.889 1.000 1.000

0 0 0 3000 3000

Theta Lower Theta Upper

4 Feed Recycle Reactor_In Reactor_Out Water_Out N(C8H10) 100 53.02218822 153.0221882 53.55776588 0 N(C8H8) 0 1.014821115 1.014821115 100.4792435 0 N(H2) 0 0 0 99.46442234 0 N(H2O) 3000 0 3000 3000 3000 N(Total) 3100 54.03700933 3154.037009 3253.501432 3000

Slope N(C8H10) 1.051 N(C8H8) 0.346 N(H2) 0 N(H2O) 0 N(Total)

Theta Calc -19.586 1.529 1.000 1.000

Theta Lower Theta Upper

5 Feed Recycle Reactor_In Reactor_Out Water_Out N(C8H10) 100 53.02218822 153.0221882 53.55776588 0 N(C8H8) 0 0.999487559 0.999487559 100.4639099 0 N(H2) 0 0 0 99.46442234 0 N(H2O) 3000 0 3000 3000 3000 N(Total) 3100 54.02167578 3154.021676 3253.486098 3000

0 0 99.4644223412 0 99.4644223412

53.55776588 100.4726423 0 0 154.0304082

Weigstein Recycle 53.0221882173 1.0148211148 0 0

Vapor_Out 0 0 99.4644223412 0 99.4644223412

Organic_Out 53.55776588 100.4792435 0 0 154.0370093

Weigstein Recycle 53.0221882173 0.999487559 0 0

Vapor_Out 0 0 99.4644223412 0 99.4644223412

Organic_Out 53.55776588 100.4639099 0 0 154.0216758

Product 0.35 64.35 0 0 64.7

New_Recycle 34.65 0.65 0 0 35.3

Product 0.471275 87.290775 0 0 87.76205

New_Recycle 46.656225 0.881725 0 0 47.53795

Product 0.535577659 99.46977812 0 0 100.0053558

New_Recycle 53.022188217 1.0047452335 0 0 54.026933451

Product

New_Recycle

0.535577659 53.022188217 99.46791592 1.0047264235 0 0 0 0 100.0034936 54.026914641

Product 0.535577659 99.47445102 0 0 100.0100287

New_Recycle 53.022188217 1.0047924346 0 0 54.026980652

Product 0.535577659 99.4592708 0 0 99.99484846

New_Recycle 53.022188217 1.004639099 0 0 54.026827316

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