Effect of Dimerization on Vapor Liquid Equilibrium of Binary Systems
Authors: Housam Binous and Ahmed Bellagi
Effect of Dimerization on Vapor Liquid Equilibrium of Binary Systems
Authors: Housam Binous and Ahmed Bellagi
Authors: Housam Binous and Ahmed Bellagi
Vapor liquid equilibrium data for the binary system: acetic acid - water, are computed . Gas-phase dimerization for the this carboxylic acid (acetic acid) is taken into account . We compare our calculations with available experimental data .
Similar computations could be performed (not show here) for another important binary system (formic acid–water mixture) where gas-phase dimerization needs to be considered in order to properly predict VLE data.
Vapor liquid equilibrium data for the binary system: acetic acid - water, are computed . Gas-phase dimerization for the this carboxylic acid (acetic acid) is taken into account . We compare our calculations with available experimental data .
Similar computations could be performed (not show here) for another important binary system (formic acid–water mixture) where gas-phase dimerization needs to be considered in order to properly predict VLE data.
Reference:
H. Binous, U. Zahid, A. Bellagi, Batch Distillations of Mixtures Containing Water and Acetic Acid : Experiment and Theory, Advances in Engineering Research, Hauppauge: Nova Science Publishers, vol 36, pp. 187-216, 2020.
H. Binous, U. Zahid, A. Bellagi, Batch Distillations of Mixtures Containing Water and Acetic Acid : Experiment and Theory, Advances in Engineering Research, Hauppauge: Nova Science Publishers, vol 36, pp. 187-216, 2020.
Binary system: Acetic Acid - Water
Gas Constant and Pressure
In[]:=
P=101325;R=1.987204;
Modified Antoine Equation
In[]:=
Aa[1]=61.34090;Ba[1]=-6768.88;Ca[1]=0;Da[1]=-6.72663;Ea[1]=4.8410^-6;Fa[1]=2;Aa[2]=65.92780;Ba[2]=-7227.53;Ca[2]=0;Da[2]=-7.17695;Ea[2]=4.0310^-6;Fa[2]=2;Psat1[i_,t_]:=10^3Exp[Aa[i]+Ba[i]/(Ca[i]+T[t])+Da[i]Log[T[t]]+Ea[i]T[t]^Fa[i]];
Acetic Acid (component 1) b.p. 117.801
In[]:=
FindRoot[Psat1[1,t]P,{T[t],300}]
Out[]=
{T[t]390.951}
In[]:=
390.951-273.15
Out[]=
117.801
water (component 2) b.p. 100.003
In[]:=
FindRoot[Psat1[2,t]P,{T[t],300}]
Out[]=
{T[t]373.153}
In[]:=
373.153-273.15
Out[]=
100.003
Dimerization constant for Acetic Acid obtained from Venimadhavan, Malone and Doherty, AIChE Journal, Vol. 45, No 3, pp. 546-556
1- expression versus temperature
2- value at ≈25°C
1- expression versus temperature
2- value at ≈25°C
In[]:=
K=10^(-12.5454+3166/(273.15+T))
Out[]=
-12.5454+
3166
273.15+T
10
In[]:=
K/.T24.85
Out[]=
0.0119884
Activity coefficients using UNIQUAC Model
Component 1= Acetic Acid
Component 2= Water
Component 1= Acetic Acid
Component 2= Water
In[]:=
tau[j_,i_,t_]:=Exp[-(U[j,i]-U[i,i])/(RT[t])];G1[1,t_]:=GamC[t,1]GamR[t,1];G1[2,t_]:=GamC[t,2]GamR[t,2];GamC[t_,i_]:=ExpLog[phi[i]/x[i]]+z2q[i]Log[v[i]/phi[i]]+l[i]-phi[i]x[i]x[j]l[j]/.x[1]x1[t]/.x[2]x2[t];l[i_]:=z/2(r[i]-q[i])-(r[i]-1);z=10;GamR[t_,i_]:=Expq[i]1-Logv[j]tau[j,i,t]-v[k]tau[k,j,t];phi[i_]:=r[i]x[i]r[j]x[j]/.x[1]x1[t]/.x[2]x2[t];v[i_]:=q[i]x[i]q[j]x[j]/.x[1]x1[t]/.x[2]x2[t];U[1,1]=0.0;U[1,2]=427.7405;U[2,1]=-305.4517;U[2,2]=0.0;r[1]=2.20230;r[2]=0.920000;q[1]=2.07200;q[2]=1.39970;Ksym[t_]:=10^(-12.5454+3166/(T[t]));
2
∑
j=1
2
∑
j=1
2
∑
j=1
v[j]tau[i,j,t]
2
∑
k=1
2
∑
j=1
2
∑
j=1
In[]:=
x2[t_]:=1-x1[t];
Here we compute the VLE data
In[]:=
i=1;While[i≤99,{x1[t]=(i)0.01,x[i,1]=x1[t],SOL=FindRoot[{PPsat1[1,t]G1[1,t]x1[t]/((1+Sqrt[(1+4Ksym[t]Psat1[1,t])])/(1+Sqrt[(1+4Ksym[t]Py1[t](2-y1[t]))]))+Psat1[2,t]G1[2,t]x2[t]/((2(1-y1[t]+Sqrt[(1+4Ksym[t]Py1[t](2-y1[t]))]))/((2-y1[t])(1+Sqrt[(1+4Ksym[t]Py1[t](2-y1[t]))]))),y1[t]Psat1[1,t]G1[1,t]x1[t]/((1+Sqrt[(1+4Ksym[t]Psat1[1,t])])/(1+Sqrt[(1+4Ksym[t]Py1[t](2-y1[t]))]))1/P},{T[t],390},{y1[t],0.3},MaxIterations10000]//Chop,y[i,1]=y1[t]/.SOL,T[i]=T[t]/.SOL,Print[i," ",x[i,1]," ",y[i,1]," ",T[i]],i++}]
1 0.01 0.00548162 373.282
2 0.02 0.011409 373.4
3 0.03 0.0176566 373.511
4 0.04 0.0241285 373.614
5 0.05 0.0307517 373.713
6 0.06 0.0374715 373.807
7 0.07 0.0442473 373.897
8 0.08 0.0510496 373.985
9 0.09 0.0578573 374.07
10 0.1 0.0646558 374.154
11 0.11 0.0714359 374.236
12 0.12 0.0781919 374.318
13 0.13 0.0849214 374.398
14 0.14 0.0916242 374.479
15 0.15 0.0983017 374.559
16 0.16 0.104957 374.639
17 0.17 0.111593 374.719
18 0.18 0.118214 374.799
19 0.19 0.124826 374.88
20 0.2 0.131434 374.962
21 0.21 0.138042 375.044
22 0.22 0.144656 375.127
23 0.23 0.151282 375.211
24 0.24 0.157924 375.296
25 0.25 0.164589 375.383
26 0.26 0.171282 375.47
27 0.27 0.178007 375.559
28 0.28 0.18477 375.649
29 0.29 0.191575 375.741
30 0.3 0.198428 375.834
31 0.31 0.205333 375.929
32 0.32 0.212294 376.026
33 0.33 0.219316 376.124
34 0.34 0.226403 376.224
35 0.35 0.233559 376.326
36 0.36 0.240788 376.43
37 0.37 0.248094 376.536
38 0.38 0.25548 376.644
39 0.39 0.26295 376.754
40 0.4 0.270509 376.867
41 0.41 0.278158 376.981
42 0.42 0.285902 377.098
43 0.43 0.293744 377.218
44 0.44 0.301686 377.34
45 0.45 0.309733 377.464
46 0.46 0.317888 377.591
47 0.47 0.326152 377.72
48 0.48 0.33453 377.853
49 0.49 0.343024 377.987
50 0.5 0.351638 378.125
51 0.51 0.360373 378.266
52 0.52 0.369233 378.409
53 0.53 0.378221 378.556
54 0.54 0.387338 378.706
55 0.55 0.39659 378.858
56 0.56 0.405977 379.014
57 0.57 0.415502 379.174
58 0.58 0.425169 379.336
Molecular weight for water and acetic acid
plotting computed VLE data:
1 - equilibrium curve
2- isobaric VLE diagram
1 - equilibrium curve
2- isobaric VLE diagram
VLE data at 101.325 kPa obtained from the open-literature:
Othmer, D. F., Silvis, S. J., & Spiel, A. (1952). Composition of Vapors from Boiling Binary Solutions: Pressure Equilibrium Still for Studying Water–Acetic Acid System. Industrial & Engineering Chemistry, 44(8), 1864–1872.
The experimental data are indicated by the colored dots.
VLE data at 101.325 kPa obtained from the open-literature:
Othmer, D. F., Silvis, S. J., & Spiel, A. (1952). Composition of Vapors from Boiling Binary Solutions: Pressure Equilibrium Still for Studying Water–Acetic Acid System. Industrial & Engineering Chemistry, 44(8), 1864–1872.
The experimental data are indicated by the colored dots.