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

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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
.
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