Page 83 - Distillation theory

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3.5 Feasible Splits at R =∞ and N =∞ 57

azeotropes), fractions of coal tar (20 components, 38 binary and 16 ternary azeo-
tropes), and a mixture processed in the resin industry (9 components, 15 binary
and 3 ternary azeotropes).
In Safrit & Westerberg (1997), a heuristic algorithm is based on the information
about local characteristics of stationary points, and checked by the authors at large
amounts of three-component mixtures and at some four-component mixtures.
This algorithm takes into consideration azeotropes formed by any number of
components.
In industry, it is necessary to deal with very complicated mixtures for which
structural matrices can serve as an instrument of separation flowsheets synthesis.
In Wahnschafft (1997), the example of plant for separation of coal tar in South
Africa (20 components, more than 200 azeotropes) consisting of 40 columns is
given.
Having a structural matrix and knowing compositions of products x D and x B ,
it is easy to find the nodal points N and N in the boundary elements of the
−
+
D B
concentration space and to determine the availability of a bond or chain of bonds
−
+
N → N .
D B
3.5. Feasible Splits at R =∞ and N =∞
When dealing with practical tasks, the designer of separation flowsheet should
have on hand the set of feasible splits in the first column. Of course, this set of
splits will hardly allow the separation of the mixture in the system of columns into
pure components without the use of recycles or special methods. But frequently it
is sufficient to separate only some product components. Sometimes it is reasonable
to separate the mixture into several fractions that can be the subject of separation
by more complicated methods, for example, using entrainers. In any case, at first
stage the designer has to determine the set of the splits.
For mixtures of any number of components, it is the easiest to determine two
splits: the direct and the indirect one. To do that, it is enough to calculate from
x F point the line of conjugated liquid–vapor tie-lines and the line of conjugated
vapor–liquid tie-lines. The first of them will lead to the unstable node N of the
−
distillation region Reg , to which point x F belongs, and the other will lead to
∞
the stable node N . Full or partial separability of these components or pseudo-
+
components (azeotropes) from the mixture is always possible and corresponds
to the direct or indirect split. At direct split x D ≡ N , point x B belongs to the
−
distillation region boundary (i.e., x B ∈ Reg ∞ ≡ Reg ). At indirect split x B ≡
bound B
N , x D belongs to the distillation region boundary (i.e., x D ∈ Reg ∞ ≡ Reg ).
+
bound D
The distillation structural matrix allows determination of stationary points of the
boundaries between the distillation region and other regions, and states by cal-
culation to which of these boundaries the second product point belongs at direct
and indirect split. For three- and four-component mixtures, even for structurally
complicated ones, these operations may be rendered clear and demonstrable if
the necessary software is at hand. Figure 3.14 shows examples of which distillation