Page 99 - Distillation theory

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3.8 Conclusion 73

movement of point x B at the segments 4 and 2 at Fig. 3.3 and the segments 4, 5
and 6 at Fig. 3.4.
For azeotropic mixtures, there is no such monotony. That is, at movement of
points x D and x B along the line of products feasible compositions for fixed feed
composition x F , the value of parameter D/F goes through points of extremums if
the number of stationary points of distillation subregion exceeds that of compo-
nents (m > n). Such nonmonotony leads to existence of several products feasible
compositions at fixed feed composition and fixed value of parameter D/F. It was
shown in the work (Petlyuk & Avet’yan, 1971) for the mixture of type 9 at Fig.
3.16. The phenomenon of plurality of products composition for three-component
mixtures is elaborated in the work (Bekiaris et al., 1993), and it is shown that for
the mixture presented at Fig. 3.10b, in some interval of values of parameters D/F,
there are three feasible sets of products compositions. In Petlyuk & Serafimov
(1983), it is shown that for n > 3, sometimes infinite number of sets of products
compositions is feasible at one and the same value of parameter D/F. Prognosis
of plurality of products compositions is of great importance for the proper de-
signing of separation units because this phenomenon can lead to the obtaining of
undesired product.

3.8. Conclusion
At R =∞ and N =∞, distillation trajectories bundles fill up distillation re-
∞
gions Reg in concentration simplex limited by node and saddle stationary points
(points of components and azeotropes) and by boundary elements of various di-
mensionality, part of which are located at boundary elements of concentration
simplex and part of which are located inside it.
Product points at fixed feed composition and at various values of parameter
D/F fill up some line in concentration simplex connecting nodes of distillation
region Reg ∞ with the feed point.
Feasible splits are only those without distributed components or pseudocompo-
nents (azeotropes) at boundary values of parameter D/F or with one distributed
component or pseudocomponent at all the intermediate values of parameter D/F.
Split is feasible if points N and N coincide with each other or if there is bond
−
+
D
B
or bonds chain N → N (the rule of connectedness). This rule is fulfilled if the
+
−
D
B
feed point is located inside the concentration simplex, the vertexes of which are
stationary points entering in one link chain. The stationary points of the link chain
must include all the components, and the number of links must be no less than that
of components. Split is feasible if points x D and x B belong to boundary elements
of the same product simplex (the rule of product simpex) and if the number of
stationary points of the links chain equals the number of components. If the links
number exceeds the number of components, the rule of connectedness must be
checked for each split.
An azeotropic mixture can be separated in a sequence of columns with recycles
if the point x F is located at the concave side of separatrix between the distillation
∞
regions Reg .