The Ponchon–Savarit diagram provides a graphical method for solving coupled material and energy balances in separation processes involving binary mixtures. Here, we illustrate how the Ponchon–Savarit diagram can be computed for a non-ideal binary mixture that has an azeotrope.
Consider a binary mixture of ethanol and water at atmospheric pressure. The gas phase is assumed ideal, but the liquid phase is non-ideal. We plot the Ponchon–Savarit diagram, which is also called the enthalpy-composition diagram. Enthalpy is expressed in kcal/kg and composition is expressed in weight fraction of ethanol. Also shown is the vapor equilibrium curve for ethanol-water. The mole fractions of ethanol in the liquid and gas phases are denoted by
x
and
y
, respectively.
The Ponchon–Savarit diagram for
P=760mmHg
closely agree with Figure 2-4 given in [1] and reproduced below:​​
​​Finally, the "tie lines", displayed in green, show the composition of the two phases that exist in equilibrium at the specified temperature. ​At the azeotropic composition the tie line is shown in red; it is vertical, confirming that
x
ethanol
=
y
ethanol
at the azeotrope. ​At
P=760mmHg
, the azeotrope composition in terms of ethanol weight fraction is 96% and the boiling temperature is
T=78.16°C
.
Expressions for pure component vapor and liquid enthalpies were adapted from Aspen-HYSYS (see snapshots below).​Aspen-Hysys provides enthalpies above
0°C
(expressed in
kJ/kmol
).​​
Total pressure in mmHg
In[]:=
P=760;
Antoine Constants and equation for ethanol and water.
In[]:=
Aa1=7.68117;Ba1=1332.04;Ca1=199.200;​​Aa2=8.07131;Ba2=1730.63;Ca2=233.426;​​​​Psat1=10^(Aa1-Ba1/(T+Ca1));​​Psat2=10^(Aa2-Ba2/(T+Ca2));​​
Binary interaction parameters for the Van Laar activity coefficient model
In[]:=
A12=1.66480;A21=0.94010;​​​​Gam1[xa_]:=Exp[A12(A21(1-xa)/(A12xa+A21(1-xa)))^2];Gam2[xa_]:=Exp[A21(A12xa/(A21(1-xa)+A12xa))^2];​​
Computing VLE data for the binary system: Ethanol and Water
In[]:=
i=0;​​​​While[i<1001,{xa=i0.001,​​sol=FindRoot[Psat1xaGam1[xa]+Psat2(1-xa)Gam2[xa]P,{T,77,78}];xe[i]=xa,ye[i]=Psat1xaGam1[xa]/P/.sol,​​Te[i]=T/.sol,i++}];​​Tbl1=Table[{xe[i],Te[i]},{i,0,1000}];Tbl2=Table[{ye[i],Te[i]},{i,0,1000}];​​Tbl3=Table[{xe[i],ye[i]},{i,0,1000}];​​​​Tx=Interpolation[Tbl1,InterpolationOrder1];Ty=Interpolation[Tbl2,InterpolationOrder1];xy=Interpolation[Tbl3,InterpolationOrder1];​​​​solaz=FindRoot[xy[t]t,{t,0.9}];​​
In[]:=
solaz
Out[]=
{t0.904916}
In[]:=
Tx[t/.solaz]
Out[]=
78.1567
In[]:=
A=(0.0+76.28T+2.56510^-2T^2-1.12810^-004T^3+1.32610^-07T^4)/.T(273.15);​​hl2=0.0+76.28T+2.56510^-2T^2-1.12810^-004T^3+1.32610^-07T^4-A;​​​​B=(0.0+102.6T-6.98110^-2T^2-1.01110^-005T^3+5.09710^-07T^4)/.T(273.15);​​hl1=0.0+102.6T-6.98110^-2T^2-1.01110^-005T^3+5.09710^-07T^4-B;​​​​Hv2=47300+107.6T-0.2203T^2+3.66210^-004T^3-3.22810^-007T^4-A;​​Hv1=55930+83.61T-0.2218T^2+3.70610^-004T^3-3.80110^-008T^4-B;​​​​Hvhysys[y_]:=(yHv1+(1-y)Hv2)/.T(Ty[y]+273.15);​​hlhysys[x_]:=(xhl1+(1-x)hl2)/.T(Tx[x]+273.15);​​​​Hw[w_]:=Hvhysys[x]/(18(1-x)+46x)/4.18/.x-
9w
-23+14w
;(*vapor-phaseenthalpyinkcal/kg*)​​hw[w_]:=hlhysys[x]/(18(1-x)+46x)/4.18/.x-
9w
-23+14w
;(*liquid-phaseenthalpyinkcal/kg*)​​​​yw0=xy-
9w0
-23+14w0
;vw0=46yw0/(46yw0+18(1-yw0));w0az=46t/(46t+18(1-t))/.solaz;​​yw0az=xy-
9w0az
-23+14w0az
;vw0az=46yw0az/(46yw0az+18(1-yw0az));​​
Plot of the Ponchon-Savarit diagram at P=760 mmHg.
​
Tie-lines are given in Green. Dew line and bubble line are in Yellow and Blue. The tie-line for the azeotrope is given in Red.
In[]:=
p1=ShowPlot[{hw[w],Hw[w]},{w,0,1},FrameTrue,FrameLabel{Style["ethanol weight fraction",14],Style["enthalpy kcal/kg",14]},GridLinesAutomatic,ImageSize{600,350},PlotStyleThick,PlotRange{{0,1},{0,700}}],GraphicsThick,Green,Table[Line[{{w0,hw[w0]},{vw0,Hw[vw0]}}],{w0,0.01,0.04,0.01}],Table[Line[{{w0,hw[w0]},{vw0,Hw[vw0]}}],{w0,0.2,0.9,0.1}],Table[Line[{{w0,hw[w0]},{vw0,Hw[vw0]}}],{w0,0.06,0.14,0.02}],Red,Line[{{w0az,hw[w0az]},{vw0az,Hw[vw0az]}}],Black,TableStyleTextRowToStringNumberFormTx-
9w0
-23+14w0
,{4,2}," °C",{(w0+vw0)/2-0.025,(hw[w0]+Hw[vw0])/2},Automatic,{1000,(hw[w0]-Hw[vw0])/(w0-vw0)},10,{w0,0.2,0.9,0.1},TableStyleTextRowToStringNumberFormTx-
9w0
-23+14w0
,{4,2}," °C",{(w0+vw0)/2-0.025,(hw[w0]+Hw[vw0])/2},Automatic,{1000,(hw[w0]-Hw[vw0])/(w0-vw0)},10,{w0,0.06,0.14,0.02},TableStyleTextRowToStringNumberFormTx-
9w0
-23+14w0
,{4,2}," °C",{(w0+vw0)/2-0.025,(hw[w0]+Hw[vw0])/2},Automatic,{1000,(hw[w0]-Hw[vw0])/(w0-vw0)},10,{w0,0.01,0.04,0.01},Red,StyleTextRowToStringNumberFormTx-
9w0az
-23+14w0az
,{4,2}," °C",{(w0az+vw0az)/2-0.015,(hw[w0az]+Hw[vw0az])/2},Automatic,{0,1},10​​
Plot of the equilibrium curve at P=760 mmHg. The azeotrope is indicated by the Green dot.
Comparing our calculation results and digitized data (shown by red dots) of Figure 2-4 in [1].
Converting weight fraction (digitized data from Fig 2-4 of Ref 1) into mole fractions
Comparing our calculation results and digitized data (shown by red dots) obtained using the tie-lines of Figure 2-4 in [1].

References

[1] P. C. Wankat, Separation Process Engineering, 3rd ed., Upper Saddle River, NJ: Pearson, 2012.

CITE THIS NOTEBOOK

Ponchon-Savarit Diagram using Aspen-Hysys Thermodynamic Database​
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, January 13, 2024
​https://community.wolfram.com/groups/-/m/t/3102154