Ponchon-Savarit Diagram for an Ethanol-Water Binary Mixture​
​Authors: Housam Binous and Ahmed Bellagi

​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.​Enthalpies for the liquid and vapor phases are computed using the following equations:​​
H
L
(
x
ethanol
,T)=
x
ethanol
C
P,L,ethanol
(T-
T
ref
)+(1-
x
ethanol
)
C
P,L,water
(T-
T
ref
)+
E
H
,​
H
V
(
y
ethanol
,T)=
y
ethanol
[
λ
ethanol
+
C
P,V,ethanol
(T-
T
ref
)]+(1-
y
ethanol
)[
λ
water
+
C
P,V,water
(T-
T
ref
)]
,​where
λ
i
is the latent heat of vaporization of chemical species
i
at
T
ref
=273.15Kelvin
and
C
P,L,i
and
C
P,V,i
are the heat capacities for the liquid and the gas phases of chemical species
i
, respectively;
λ
i
is a slowly-varying function of temperature and can be assumed constant [3]. ​The mole fractions of ethanol in the liquid and gas phases are denoted by
x
ethanol
and
y
ethanol
, respectively. ​Finally,
E
H
is the excess enthalpy, which accounts for the non-ideal behavior of the liquid mixture. ​We use the following correlation from [2] to compute the excess enthalpy as a function of composition and temperature: ​
E
H
=
x
ethanol
(1-
x
ethanol
)
a
0
(T)+
a
0.5
(T)
0.5
x
ethanol
+
a
1.5
(T)
1.5
x
ethanol
+
a
2.5
(T)
2.5
x
ethanol
+
a
4.5
(T)
4.5
x
ethanol

, where
T
is the mixture temperature and
x
ethanol
is the ethanol mole fraction. Here,
a
m
(T)=
b
m
+
c
m
T+
d
m
2
T
, where
m=0,0.5,1.5,2.5,4.5
and
b
m
,
c
m
, and
d
m
are appropriate constants tabulated in [2].​The Ponchon–Savarit diagram for
P=760mmHg
closely agree with Figure 2-4 in [1] given 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
.​We compare out results to the digitized data of the Figure given above.
References:
​​
[1] P. C. Wankat, Separation Process Engineering, 3rd ed., Upper Saddle River, NJ: Pearson, 2012.
[2] J. A. Larkin, "Thermodynamic Properties of Aqueous Non-Electrolyte Mixtures I. Excess Enthalpy for Water + Ethanol at 298.15 to 383.15 K," Journal of Chemical Thermodynamics, 7(2), 1975 pp. 137–148.
[3] R. H. Perry and D. W. Green, Perry's Chemical Engineers' Handbook, 7th ed., New York: McGraw–Hill, 1997.
​
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}];​​​​(*latentheatofvaporization.SeeRef.3*)​​​​C1A=5.690010^7;C2A=0.3359;C3A=0;C4A=0;​​C1B=5.205310^7;C2B=0.3199;C3B=-0.212;C4B=0.25795;​​​​TcA=513.92;​​TcB=647.13;​​​​λA=10^-3C1A(1-Ti2/TcA)^(C2A+C3ATi2/TcA+C4A(Ti2/TcA)^2);​​λB=10^-3C1B(1-Ti2/TcB)^(C2B+C3BTi2/TcB+C4B(Ti2/TcB)^2);​​​​Ti2=0+273.15;​​​​H[y_]:=y(λA+73.98(Ty[y]))+(1-y)(λB+38.29(Ty[y]));(*vapor-phaseenthalpy*)​​h[x_]:=x(118.1(Tx[x]))+(1-x)(75.66(Tx[x]))+x(1-x)(a0+a1x^0.5+a2x^1.5+a3x^2.5+a4x^4.5);(*liquid-phaseenthalpy*)​​​​(*excessenthalpyasafunctionofcompositionandtemperatureisadded.SeeRef.2​​Itisgivenby:x(1-x)(a0+a1x^0.5+a2x^1.5+a3x^2.5+a4x^4.5)*)​​​​a0=-3.6386810^5+1.8382910^3(Tx[x]+273.15)-2.32763(Tx[x]+273.15)^2;​​a1=9.2598210^5-4.8358610^3(Tx[x]+273.15)+6.37228(Tx[x]+273.15)^2;​​a2=-14.0489410^5+7.5166110^3(Tx[x]+273.15)-10.11280(Tx[x]+273.15)^2;​​a3=10.9131810^5-5.8949810^3(Tx[x]+273.15)+7.98868(Tx[x]+273.15)^2;​​a4=-2.7998610^5+1.5055710^3(Tx[x]+273.15)-2.03127(Tx[x]+273.15)^2;​​​​Hw[w_]:=H[x]/(18(1-x)+46x)/4.18/.x-
9w
-23+14w
;(*vapor-phaseenthalpyinkcal/kg*)​​hw[w_]:=h[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.
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].