We compute the vapor-liquid diagram of an ethane-benzene mixture at 25°C and 175°C. This binary mixture exhibits a peculiar behavior because the volatilities of ethane and benzene are very different. We use the SRK equation of state to compute equilibrium constants. This problem was presented in Ref. 1.
Reduced Pressure and Temperature
In[]:=
Tre[i_]:=T/Tc[i]
In[]:=
Pre[i_]:=P/Pc[i]
Equilibrium constants using the ϕ-ϕ methode and the Soave-Redlich-Kwong Equation of State
In[]:=
Ap[i_]:=0.42747a[i]Pre[i]/Tre[i]^2
In[]:=
Bp[i_]:=0.08664Pre[i]/Tre[i]
In[]:=
ϕ
v
[i_]:=Exp[(
Z
v
-1)Bp[i]/
B
v
-Log[
Z
v
-
B
v
]-
A
v
/
B
v
(2Ap[i]^0.5/
A
v
^0.5-Bp[i]/
B
v
)Log[(
Z
v
+
B
v
)/
Z
v
]];
In[]:=
ϕ
l
[i_]:=Exp[(
Z
l
-1)Bp[i]/
B
l
-Log[
Z
l
-
B
l
]-
A
l
/
B
l
(2Ap[i]^0.5/
A
l
^0.5-Bp[i]/
B
l
)Log[(
Z
l
+
B
l
)/
Z
l
]];
In[]:=
a[i_]:=(1+m[i](1-Tre[i]^0.5))^2
In[]:=
m[i_]:=0.480+1.574ω[i]-0.176ω[i]^2
In[]:=
A
v
=
2
∑
i=1
2
∑
j=1
y[i]y[j]Ab[i,j];
In[]:=
Ab[i_,j_]=(Ap[i]Ap[j])^0.5;
In[]:=
B
v
=
2
∑
i=1
y[i]Bp[i];
In[]:=
A
l
=
2
∑
i=1
2
∑
j=1
x[i]x[j]Ab[i,j];
In[]:=
B
l
=
2
∑
i=1
x[i]Bp[i];
In[]:=
K[i_]:=
ϕ
l
[i]/
ϕ
v
[i];
Critical Pressure and Temperature and acentric factor for Ethane and Benzene
In[]:=
Pc[1]=709.8;Tc[1]=550.0;ω[1]=0.1064;
In[]:=
Pc[2]=714.2;Tc[2]=1012.7;ω[2]=0.2116;
Temperature is 77 °F.
In[]:=
25×1.8+32
Out[]=
77.
In[]:=
T=25×1.8+32+459.67;
VLE Calculations at 77°F.
In[]:=
Sol=.
In[]:=
x[1]=0;x[2]=1-x[1];
In[]:=
Sol[1]=FindRoot[{y[1]K[1]x[1],y[2]K[2]x[2],y[1]+y[2]1,
Z
l
^3-
Z
l
^2+
Z
l
(
A
l
-
B
l
-
B
l
^2)-
A
l
B
l
0,
Z
v
^3-
Z
v
^2+
Z
v
(
A
v
-
B
v
-
B
v
^2)-
A
v
B
v
0},{y[1],0.999},{y[2],0.001},{P,150},{
Z
l
,0.1},{
Z
v
,0.9},MaxIterations1000,AccuracyGoal->4]//Chop;
In[]:=
ye[1]=y[1]/.Sol[1];Pe[1]=P/.Sol[1];Print[Pe[1]," ",ye[1]," ",
Z
l
/.Sol[1]," ",
Z
v
/.Sol[1]]
1.90308 0 0.00054508 0.994382
In[]:=
For[i=2,i<101,x[1]=0.01(i-1);x[2]=1-x[1];Sol[i]=Quiet@FindRoot[{y[1]K[1]x[1],y[2]K[2]x[2],y[1]+y[2]1,
Z
l
^3-
Z
l
^2+
Z
l
(
A
l
-
B
l
-
B
l
^2)-
A
l
B
l
0,
Z
v
^3-
Z
v
^2+
Z
v
(
A
v
-
B
v
-
B
v
^2)-
A
v
B
v
0},{y[1],y[1]/.Sol[i-1]},{y[2],y[2]/.Sol[i-1]},{P,P/.Sol[i-1]},{
Z
l
,
Z
l
/.Sol[i-1]},{
Z
v
,
Z
v
/.Sol[i-1]},MaxIterations1000]//Chop;ye[i]=y[1]/.Sol[i];Pe[i]=P/.Sol[i];Print[i," ",Pe[i]," ",ye[i]," ",
Z
l
/.Sol[i]," ",
Z
v
/.Sol[i]];i++]
2 8.59797 0.78453 0.00233028 0.992412
3 15.3517 0.87866 0.00414724 0.989025
4 22.1011 0.91526 0.0059512 0.985521
5 28.8455 0.934724 0.0077421 0.981973
6 35.5845 0.946802 0.00951988 0.978398
7 42.3175 0.955026 0.0112845 0.974801
8 49.0441 0.960986 0.0130358 0.971186
9 55.7637 0.965503 0.0147739 0.967553
10 62.4757 0.969044 0.0164986 0.963905
11 69.1797 0.971894 0.0182099 0.960241
12 75.875 0.974236 0.0199077 0.956562
13 82.561 0.976195 0.021592 0.952869
14 89.2372 0.977858 0.0232627 0.94916
15 95.903 0.979287 0.0249198 0.945437
16 102.558 0.980527 0.0265633 0.941699
17 109.201 0.981613 0.028193 0.937948
18 115.831 0.982573 0.029809 0.934182
19 122.449 0.983427 0.0314111 0.930402
20 129.053 0.984191 0.0329995 0.926608
21 135.643 0.984878 0.0345739 0.9228
22 142.218 0.985501 0.0361345 0.918978
23 148.777 0.986066 0.0376811 0.915143
24 155.319 0.986582 0.0392138 0.911295
25 161.845 0.987055 0.0407325 0.907433
26 168.352 0.98749 0.0422372 0.903558
27 174.841 0.987891 0.043728 0.89967
28 181.311 0.988261 0.0452046 0.895769
29 187.761 0.988605 0.0466673 0.891855
30 194.189 0.988925 0.048116 0.887929
31 200.596 0.989223 0.0495507 0.88399
32 206.98 0.989502 0.0509713 0.880039
33 213.341 0.989762 0.052378 0.876076
34 219.678 0.990007 0.0537708 0.872101
35 225.99 0.990237 0.0551497 0.868114
36 232.276 0.990453 0.0565148 0.864116
37 238.536 0.990657 0.057866 0.860107
38 244.768 0.99085 0.0592036 0.856086
39 250.972 0.991032 0.0605275 0.852055
40 257.147 0.991204 0.0618379 0.848013
41 263.291 0.991368 0.0631348 0.843961
42 269.405 0.991523 0.0644184 0.839899
43 275.488 0.991671 0.0656888 0.835827
44 281.538 0.991812 0.0669462 0.831745
45 287.554 0.991946 0.0681907 0.827653
46 293.537 0.992074 0.0694225 0.823553
47 299.484 0.992196 0.0706418 0.819444
48 305.396 0.992313 0.0718489 0.815326
49 311.271 0.992426 0.073044 0.811199
50 317.109 0.992533 0.0742274 0.807065
51 322.909 0.992636 0.0753994 0.802923
52 328.67 0.992735 0.0765603 0.798772
53 334.391 0.992831 0.0777106 0.794615
54 340.073 0.992923 0.0788506 0.79045
55 345.714 0.993012 0.0799807 0.786277
56 351.314 0.993097 0.0811015 0.782098
57 356.871 0.99318 0.0822135 0.777912
58 362.387 0.99326 0.0833174 0.773718
59 367.86 0.993338 0.0844136 0.769518
60 373.29 0.993414 0.0855031 0.765311
61 378.677 0.993487 0.0865865 0.761097
62 384.021 0.993559 0.0876647 0.756875
63 389.321 0.993629 0.0887387 0.752646
64 394.578 0.993697 0.0898095 0.748409
65 399.792 0.993764 0.0908782 0.744163
66 404.964 0.99383 0.0919461 0.739908
67 410.093 0.993895 0.0930146 0.735644
68 415.181 0.993958 0.0940851 0.731368
69 420.228 0.994021 0.0951594 0.72708
70 425.236 0.994084 0.0962393 0.722778
71 430.206 0.994145 0.0973269 0.718461
72 435.139 0.994207 0.0984244 0.714127
73 440.038 0.994268 0.0995344 0.709773
74 444.905 0.99433 0.10066 0.705396
75 449.742 0.994392 0.101804 0.700993
76 454.553 0.994454 0.102969 0.696561
77 459.342 0.994517 0.104161 0.692093
78 464.112 0.994581 0.105383 0.687586
79 468.869 0.994646 0.106641 0.683033
80 473.617 0.994713 0.10794 0.678426
81 478.365 0.994782 0.109287 0.673758
82 483.118 0.994853 0.110689 0.669017
83 487.886 0.994927 0.112156 0.664193
84 492.678 0.995004 0.113697 0.65927
85 497.507 0.995085 0.115323 0.654234
86 502.385 0.995171 0.11705 0.649063
87 507.328 0.995262 0.118894 0.643735
88 512.354 0.995361 0.120874 0.638221
89 517.486 0.995467 0.123014 0.632487
90 522.748 0.995583 0.125345 0.62649
91 528.174 0.995712 0.127903 0.620177
92 533.8 0.995855 0.130735 0.613482
93 539.674 0.996018 0.133901 0.606319
94 545.856 0.996205 0.137482 0.598577
95 552.423 0.996423 0.141588 0.590102
96 559.48 0.996684 0.146372 0.580685
97 567.168 0.997005 0.152064 0.570014
98 575.699 0.997412 0.159028 0.55761
99 585.402 0.997955 0.167891 0.542659
Temperature is 347 °F.
VLE Calculations at 347°F.

References

[1] Jean Vidal, Thermodynamique, Application au Génie Chimique et à l’Industrie Pétrolière, Technip, 1997.

CITE THIS NOTEBOOK

Vapor-liquid equilibrium diagram of Ethane-Benzene at 25°C and 175°C​
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, October 22, 2025
​https://community.wolfram.com/groups/-/m/t/3563287