# Pinch Composition versus Reflux Ratio for a Benzene-Ethylenediamine Mixture at 1 atm

Pinch Composition versus Reflux Ratio for a Benzene-Ethylenediamine Mixture at 1 atm

This Demonstration plots the bifurcation diagram (pinch composition versus reflux ratio) for a mixture of benzene and ethylenediamine at 1 atm. The tangent pinch is shown as a blue dot in the diagram.

For this particular binary mixture, the vapor-liquid equilibrium (VLE) relation is as follows:

y=+bx(1-x)

ax

1+(a-1)x

a=9

b=-0.6

The bifurcation diagram is obtained; this is the implicit function relating the reflux ratio and the pinch point location:

y-x-=0

r

r+1

x

D

r+1

r

x

D

The tangent pinch obeys the following conditions: = and .

dy

dx

r

r+1

y-x-=0

r

r+1

x

D

r+1

As decreases, the curve loses its distinctive S-shape. The critical point where this transition occurs is verified by the following relations: y=0, =, and .

x

D

2

d

d

2

x

dy

dx

r

r+1

y-x-=0

r

r+1

x

D

r+1