Page 87 - Distillation theory

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3.5 Feasible Splits at R =∞ and N =∞ 61

3.5.2. Method of Product Simplex for Distillation Subregions (m > n)

Let’s examine the case of m > n. Here are the examples of such distillation sub-
regions:

1. 13 → 3 → 2 → 1 (13 ⇒ 1) at Fig. 3.10b
2. 12 → 1 → 3 → 4 → 24 and 12 → 1 → 3 → 23 → 24 (12 ⇒ 24) at Fig. 3.12

If we choose among m stationary points any n ones, then we return to the
previous case. Let’s call part of distillation subregion Reg sub , containing n stationary
points and having linear boundary elements, a product simplex Reg simp (Reg simp ∈
Reg sub ). It is noteworthy that here the linearity is assumed solely in order to
make it easier to determine if the point x F belongs to this or that product simplex.
For a product simplex, the separation in one column of a feed pseudocomponents
(stationary points) set into two product subsets is feasible if it meets the rule of
connectedness (if x F ∈ Reg simp , then x D ∈ Reg simp and x B ∈ Reg simp ). Product
simplex is an analog of distillation subregion under condition when distillation
subregion has n stationary points because the stationary points of the product
simplex are connected with one bonds chain and a number of stationary points is
also equal to n.
Product simplex for three-component mixtures is a triangle; for four-
component mixtures, it is a tetrahedron; for five-component mixtures, it is a pen-
tahedron; etc. Inside one distillation subregion at m > n, product simplexes cross
each other (i.e., one and the same feed point can simultaneously enter several
product simplexes).
Thus, the product simplex is an elementary cell in the general structure of
concentration space at R =∞ and N =∞. In the example shown in Fig. 3.15 (the

2

12 24
Figure 3.15. An example of product sim-
plex Reg simp of four-component azeotro-
23 pic mixture (shaded).

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