Vapor-Liquid Equilibrium Diagram of Heptane-Hexane at 760 mmHg Using PR EOS
Authors: Housam Binous and Ahmed Bellagi
Vapor-Liquid Equilibrium Diagram of Heptane-Hexane at 760 mmHg Using PR EOS
Authors: Housam Binous and Ahmed Bellagi
Authors: Housam Binous and Ahmed Bellagi
The VLE data are computed for the heptane/hexane binary mixture at 760 mmHg.
We use the phi - phi method to compute the equilibrium constants, and the Peng-Robinson equation of state.
Data computed using Mathematica are compared to those provided by DISTIL from Hyprotech Limited. Agreement between both data is observed.
The VLE data are computed for the heptane/hexane binary mixture at 760 mmHg.
We use the phi - phi method to compute the equilibrium constants, and the Peng-Robinson equation of state.
Data computed using Mathematica are compared to those provided by DISTIL from Hyprotech Limited. Agreement between both data is observed.
We use the phi - phi method to compute the equilibrium constants, and the Peng-Robinson equation of state.
Data computed using Mathematica are compared to those provided by DISTIL from Hyprotech Limited. Agreement between both data is observed.
Reference :
1. Z.Nasri and H.Binous, Applications of the Peng - Robinson Equation of State using Matlab®, Chemical Engineering Education, 43 (2), pp.115 - 124, 2009.
2. H.Binous, Applications of the Peng - Robinson Equation of State using Mathematica®, Chemical Engineering Education, 42 (1), pp.47 - 51, 2008.
3. Z.Nasri and H.Binous, Applications of the Soave - Redlich - Kwong Equation of State using Mathematica®, Journal of Chemical Engineering of Japan, 40 (6), pp.534 - 538, 2007.
Reference :
1. Z.Nasri and H.Binous, Applications of the Peng - Robinson Equation of State using Matlab®, Chemical Engineering Education, 43 (2), pp.115 - 124, 2009.
2. H.Binous, Applications of the Peng - Robinson Equation of State using Mathematica®, Chemical Engineering Education, 42 (1), pp.47 - 51, 2008.
3. Z.Nasri and H.Binous, Applications of the Soave - Redlich - Kwong Equation of State using Mathematica®, Journal of Chemical Engineering of Japan, 40 (6), pp.534 - 538, 2007.
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Off[General::"spell1"]
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Off[FindRoot::"lstol"]
Reduced Pressure and Temperature
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Tre[i_]:=T/Tc[i]
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Pre[i_]:=P/Pc[i]
Equilibrium constants using the ϕ-ϕ method and the Peng Robinson (PR) Equation of State (EOS)Binary interaction parameters (BIP) often labeled are all set equal to zero.
k
ij
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ap[i_]:=0.45724a[i]Tc[i]^2/Pc[i]
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Ap[i_]:=ap[i]P/(T)^2;
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bp[i_]:=0.07780Tc[i]/Pc[i]
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Bp[i_]:=Pbp[i]/(T)
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a[i_]:=(1+m[i](1-Tre[i]^0.5))^2
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m[i_]:=0.37464+1.54226ω[i]-0.26992ω[i]^2
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Ab[i_,j_]=(Ap[i]Ap[j])^0.5(1-k[i,j]);
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K[i_]:=[i]/[i];
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k[1,1]=0;k[2,2]=0;k[2,1]=k[1,2];k[1,2]=0.0;
Critical Pressure and Temperature and acentric factor for heptane and hexane.
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Pc[1]=27.37760/1.01325;Tc[1]=267.0+273.15;ω[1]=0.34979;
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Pc[2]=30.32760/1.01325;Tc[2]=234.7+273.15;ω[2]=0.30070;
Pressure is 760 mmHg.
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P=760;
VLE Calculations at 760 mmHg :
1- First, we calculate the VLE data for pure hexane.
2- Then, we adopt a zero-order continuation strategy (i.e., the latest solution serves as an initial guess for the subsequent VLE calculation).
1- First, we calculate the VLE data for pure hexane.
2- Then, we adopt a zero-order continuation strategy (i.e., the latest solution serves as an initial guess for the subsequent VLE calculation).
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Sol=.
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x[1]=0;x[2]=1-x[1];
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Sol[1]=FindRoot[{y[1]K[1]x[1],y[2]K[2]x[2],y[1]+y[2]1,^3+(-1+)^2+(-3^2-2)-+^2+^30,^3+(-1+)^2+(-3^2-2)-+^2+^30},{y[1],0.999},{y[2],0.001},{T,350},{,0.05},{,0.92},MaxIterations1000000]//Chop;
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ye[1]=y[1]/.Sol[1];Te[1]=T/.Sol[1];Print[Te[1]," ",ye[1]," ",/.Sol[1]," ",/.Sol[1]]
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342.122 0 0.00493306 0.958276
Hexane boiling temperature ≈ 69 °C
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342.122-273.15
Out[]=
68.972
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For[i=2,i<101,x[1]=0.01(i-1);x[2]=1-x[1];Sol[i]=FindRoot[{y[1]K[1]x[1],y[2]K[2]x[2],y[1]+y[2]1,^3+(-1+)^2+(-3^2-2)-+^2+^30,^3+(-1+)^2+(-3^2-2)-+^2+^30},{y[1],y[1]/.Sol[i-1]},{y[2],y[2]/.Sol[i-1]},{T,T/.Sol[i-1]},{,/.Sol[i-1]},{,/.Sol[i-1]},MaxIterations1000000]//Chop;ye[i]=y[1]/.Sol[i];Te[i]=T/.Sol[i];Print[i," ",Te[i]," ",ye[i]," ",/.Sol[i]," ",/.Sol[i]];i++]
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2 342.323 0.00404686 0.00493834 0.95829
3 342.526 0.00814997 0.00494361 0.958304
4 342.73 0.0123103 0.00494886 0.958318
5 342.935 0.016529 0.0049541 0.958331
6 343.141 0.0208069 0.00495933 0.958344
7 343.349 0.0251452 0.00496454 0.958356
8 343.558 0.0295451 0.00496974 0.958368
9 343.769 0.0340075 0.00497493 0.95838
10 343.981 0.0385336 0.0049801 0.958391
11 344.194 0.0431247 0.00498526 0.958402
12 344.409 0.0477818 0.0049904 0.958413
13 344.625 0.0525062 0.00499553 0.958423
14 344.842 0.0572992 0.00500064 0.958433
15 345.061 0.0621621 0.00500574 0.958442
16 345.282 0.067096 0.00501082 0.958451
17 345.503 0.0721025 0.00501589 0.958459
18 345.727 0.0771827 0.00502094 0.958467
19 345.952 0.0823382 0.00502598 0.958474
20 346.178 0.0875703 0.00503101 0.958481
21 346.406 0.0928805 0.00503602 0.958487
22 346.635 0.0982703 0.00504101 0.958493
23 346.866 0.103741 0.00504599 0.958498
24 347.099 0.109295 0.00505095 0.958503
25 347.333 0.114933 0.00505589 0.958507
26 347.569 0.120656 0.00506082 0.958511
27 347.806 0.126467 0.00506574 0.958514
28 348.045 0.132368 0.00507064 0.958516
29 348.286 0.13836 0.00507552 0.958518
30 348.529 0.144444 0.00508038 0.958519
31 348.773 0.150623 0.00508523 0.958519
32 349.019 0.156898 0.00509007 0.958519
33 349.266 0.163272 0.00509488 0.958518
34 349.516 0.169747 0.00509968 0.958517
35 349.767 0.176324 0.00510447 0.958514
36 350.02 0.183005 0.00510923 0.958511
37 350.275 0.189793 0.00511398 0.958507
38 350.532 0.196689 0.00511871 0.958503
39 350.79 0.203697 0.00512343 0.958497
40 351.051 0.210817 0.00512812 0.958491
41 351.313 0.218054 0.0051328 0.958484
42 351.578 0.225408 0.00513746 0.958476
43 351.844 0.232882 0.00514211 0.958468
44 352.112 0.24048 0.00514673 0.958458
45 352.383 0.248203 0.00515134 0.958448
46 352.655 0.256054 0.00515593 0.958436
47 352.929 0.264035 0.0051605 0.958424
48 353.206 0.27215 0.00516506 0.95841
49 353.485 0.280402 0.00516959 0.958396
50 353.765 0.288792 0.00517411 0.95838
51 354.048 0.297325 0.00517861 0.958364
52 354.333 0.306003 0.00518308 0.958346
53 354.621 0.314829 0.00518754 0.958328
54 354.91 0.323806 0.00519198 0.958308
55 355.202 0.332939 0.00519641 0.958287
56 355.496 0.342229 0.00520081 0.958264
57 355.793 0.351681 0.00520519 0.958241
58 356.091 0.361299 0.00520955 0.958216
59 356.392 0.371085 0.0052139 0.95819
60 356.696 0.381043 0.00521822 0.958163
61 357.002 0.391177 0.00522252 0.958134
62 357.31 0.401492 0.00522681 0.958104
63 357.621 0.411991 0.00523107 0.958072
64 357.935 0.422678 0.00523531 0.958039
65 358.251 0.433557 0.00523954 0.958004
Heptane boiling temperature ≈ 98 °C
Plot of calculated VLE data
Validation: VLE Data from DISTIL by Hyprotech Limited at 760 mmHg.