Page 128 - Distillation theory

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102 Trajectories of Thermodynamically Reversible Distillation

1,2 1
a) b)

4 3,4
x E x E
1,,,4 1,,,4
3
23
2
x F x F

3
3,4 2, ,4
Figure 4.22. Columns for reversible extractive distil-
lation of four-component mixtures: (a) mixture 1,2 is
overhead product, and component 4 is entrainer; (b)
component 1 is overhead product, and mixture 3,4 is
entrainer.

the concentration tetrahedron the straight line passing through liquid–vapor tie
line crosses the continuations of two faces: 1-2-4 and 1-3-4 (Fig. 4.23). At the first
flowsheet, the pseudoproduct point of the intermediate section should lie in the
continuation of face 1(D)-2(D)-4(E) and, at the second flowsheet, at continuation
of face 1(D)-3(E)-4(E). For any pseudoproduct point located in the continuation
of face 1-2-4, there is a point inside this face where the trajectory of extractive
t
reversible distillation x rev tears off from it. This trajectory joins point x t rev with
node N rev of the trajectory bundle – vertex 3. Therefore, the trajectory bundle
of extractive reversible distillation at the first flowsheet at various values of the
parameter E/F fills up the whole concentration tetrahedron and has vertex 3 as
its node (the component 3 does not rank among the top product components
and the entrainer). Similarly, at the second flowsheet, the tear-off point of the
extractive reversible distillation trajectories is located in face 1-3-4, the node is
vertex 2 (component 2 does not rank among the top product components and the
entrainer), and the trajectory bundle at various values of the parameter E/F fills
up the whole concentration tetrahedron.
It is possible to formulate a general structural condition that should be valid in
the tear-off point of the extractive reversible distillation trajectory from a (n − 1)-
component face or hyperface of the concentration simplex of any multicomponent
azeotropicmixture:thephaseequilibriumcoefficientofthecomponentthatisabsent
in this face or hyperface and does not rank among the top product components and
of the entrainer should be smaller than that of the top product components and
bigger than that of the entrainer components.

4.8. Boundaries of Nonsharp Reversible Distillation

4.8.1. Three-Component Azeotropic Mixtures

If, at reversible distillation of three-component azeotropic mixtures, the product
segment constitutes part of a side of the concentration triangle (e.g. Fig. 4.24) and