Vapor-Liquid Equilibrium Diagram of Heptane-Hexane at 760 mmHg Using SRK EOS
Authors: Housam Binous and Ahmed Bellagi
Vapor-Liquid Equilibrium Diagram of Heptane-Hexane at 760 mmHg Using SRK EOS
Authors: Housam Binous and Ahmed Bellagi
Authors: Housam Binous and Ahmed Bellagi
In[]:=
Off[General::"spell1"]
In[]:=
Off[FindRoot::"lstol"]
Reduced Pressure and Temperature
In[]:=
Tre[i_]:=T/Tc[i]
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Pre[i_]:=P/Pc[i]
Equilibrium constants using the ϕ-ϕ method and the Soave-Redlich-Kwong (SRK) Equation of State (EOS)Binary interaction parameters (BIP) often labeled are all set equal to zero.
k
ij
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Ap[i_]:=0.42747a[i]Pre[i]/Tre[i]^2
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Bp[i_]:=0.08664Pre[i]/Tre[i]
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ϕ
v
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B
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B
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ϕ
l
Z
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B
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B
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A
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A
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B
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B
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l
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a[i_]:=(1+m[i](1-Tre[i]^0.5))^2
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m[i_]:=0.480+1.574ω[i]-0.176ω[i]^2
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A
v
2
∑
i=1
2
∑
j=1
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Ab[i_,j_]=(Ap[i]Ap[j])^0.5(1-k[i,j]);
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B
v
2
∑
i=1
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A
l
2
∑
i=1
2
∑
j=1
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B
l
2
∑
i=1
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K[i_]:=[i]/[i];
ϕ
l
ϕ
v
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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.
In[]:=
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).
In[]:=
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-^2+(--^2)-0,^3-^2+(--^2)-0},{y[1],0.999},{y[2],0.001},{T,350},{,0.01},{,0.95},MaxIterations1000000]//Chop;
Z
l
Z
l
Z
l
A
l
B
l
B
l
A
l
B
l
Z
v
Z
v
Z
v
A
v
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v
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ye[1]=y[1]/.Sol[1];Te[1]=T/.Sol[1];Print[Te[1]," ",ye[1]," ",/.Sol[1]," ",/.Sol[1]]
Z
l
Z
v
342.192 0 0.00557927 0.959987
Hexane boiling temperature ≈ 69 °C
In[]:=
342.192-273.15
Out[]=
69.042
In[]:=
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-^2+(--^2)-0,^3-^2+(--^2)-0},{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++]
Z
l
Z
l
Z
l
A
l
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2 342.392 0.00399102 0.00558522 0.960002
3 342.594 0.00803829 0.00559115 0.960017
4 342.797 0.0121428 0.00559707 0.960031
5 343.001 0.0163057 0.00560297 0.960046
6 343.207 0.0205279 0.00560885 0.960059
7 343.414 0.0248105 0.00561472 0.960073
8 343.622 0.0291547 0.00562058 0.960086
9 343.831 0.0335616 0.00562642 0.960099
10 344.042 0.0380322 0.00563225 0.960111
11 344.255 0.0425679 0.00563806 0.960123
12 344.468 0.0471698 0.00564385 0.960134
13 344.683 0.0518392 0.00564963 0.960145
14 344.9 0.0565772 0.00565539 0.960156
15 345.118 0.0613852 0.00566114 0.960166
16 345.338 0.0662646 0.00566687 0.960176
17 345.558 0.0712166 0.00567259 0.960186
18 345.781 0.0762426 0.00567829 0.960194
19 346.005 0.0813441 0.00568397 0.960203
20 346.23 0.0865224 0.00568963 0.960211
21 346.457 0.0917792 0.00569528 0.960218
22 346.686 0.0971158 0.00570092 0.960225
23 346.916 0.102534 0.00570653 0.960231
24 347.148 0.108035 0.00571213 0.960237
25 347.381 0.11362 0.00571772 0.960242
26 347.616 0.119292 0.00572328 0.960247
27 347.853 0.125052 0.00572883 0.960251
28 348.091 0.130902 0.00573436 0.960255
29 348.331 0.136843 0.00573987 0.960258
30 348.573 0.142877 0.00574537 0.96026
31 348.816 0.149007 0.00575085 0.960262
32 349.061 0.155233 0.00575631 0.960263
33 349.308 0.161559 0.00576175 0.960263
34 349.557 0.167986 0.00576717 0.960263
35 349.808 0.174515 0.00577258 0.960262
36 350.06 0.18115 0.00577796 0.96026
37 350.314 0.187892 0.00578333 0.960258
38 350.57 0.194744 0.00578868 0.960254
39 350.828 0.201707 0.00579401 0.96025
40 351.088 0.208785 0.00579933 0.960245
41 351.35 0.215978 0.00580462 0.96024
42 351.613 0.223291 0.0058099 0.960233
43 351.879 0.230725 0.00581515 0.960226
44 352.147 0.238283 0.00582039 0.960218
45 352.417 0.245967 0.0058256 0.960209
46 352.689 0.253781 0.0058308 0.960198
47 352.962 0.261726 0.00583598 0.960187
48 353.238 0.269806 0.00584113 0.960175
49 353.517 0.278024 0.00584627 0.960162
50 353.797 0.286382 0.00585139 0.960148
51 354.079 0.294883 0.00585649 0.960133
52 354.364 0.303532 0.00586156 0.960117
53 354.651 0.31233 0.00586662 0.9601
54 354.94 0.321281 0.00587165 0.960082
55 355.231 0.330388 0.00587667 0.960062
56 355.525 0.339656 0.00588166 0.960041
57 355.821 0.349087 0.00588663 0.960019
58 356.119 0.358684 0.00589159 0.959996
59 356.42 0.368453 0.00589652 0.959972
60 356.723 0.378395 0.00590143 0.959946
61 357.029 0.388517 0.00590631 0.959918
62 357.337 0.39882 0.00591118 0.95989
63 357.648 0.40931 0.00591602 0.95986
64 357.961 0.419991 0.00592085 0.959828
65 358.277 0.430866 0.00592565 0.959795
66 358.595 0.441941 0.00593042 0.959761
67 358.916 0.45322 0.00593518 0.959725
68 359.239 0.464707 0.00593991 0.959687
69 359.566 0.476408 0.00594462 0.959647
70 359.895 0.488327 0.00594931 0.959606
71 360.227 0.50047 0.00595398 0.959563
72 360.561 0.51284 0.00595862 0.959518
73 360.899 0.525445 0.00596324 0.959472
74 361.239 0.538289 0.00596784 0.959423
75 361.582 0.551378 0.00597241 0.959372
76 361.928 0.564717 0.00597697 0.95932
77 362.277 0.578313 0.00598149 0.959265
Heptane boiling temperature ≈ 98 °C
Plot of calculated VLE data
Validation: VLE Data from DISTIL by Hyprotech Limited at 760 mmHg.