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

distillate composition

0.84

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=

ax

1+(a-1)x

+bx(1-x)

, where

a=9

and

b=-0.6

.

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

y-

r

r+1

x-

x

D

r+1

=0

, where

r

is the reflux ratio and

x

D

the distillate composition.

The tangent pinch obeys the following conditions:

dy

dx

=

r

r+1

and

y-

r

r+1

x-

x

D

r+1

=0

.

As

x

D

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

2

d

y

d

2

x

=0,

dy

dx

=

r

r+1

, and

y-

r

r+1

x-

x

D

r+1

=0

.