Page 89 - Distillation theory

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3.5 Feasible Splits at R =∞ and N =∞ 63

structure is as in Fig. 3.12), the vertexes of the simplex enter in the link chain 12 →
1 → 3 → 23 → 24. Let’s consider this example in more detail because it has some
peculiarities. If the feed point belongs to the product simplex shown in this figure,
then the feasible top product compositions x D , according to the rule of connect-
edness, can be (1) point 12, which is the unstable node N of the whole distillation
−
∞
region Reg , (2) any point at the segment 12,3, and (3) any point in the triangle
+
12, 3, 23, for which the stable node N of the distillation region boundary ele-
D
ments Reg D = Reg ∞ is point 23. The feasible bottom product compositions
bound,D
can be (1) point 24, (2) any point at the segment 23,24 for which the unstable
−
node N of the distillation region boundary element Reg ∞ is point 23 (the
B bound,B
boundary element of distillation region Reg ∞ is separatrix 23 → 24), and (3)
bound,B
−
any point in the triangle 3, 23, 24, for which the unstable node N of the distil-
B
lation region boundary element Reg ∞ is point 3. Thus, the following splits
bound,B
without distributed components are possible: 12 : 3,23,24 (trajectory 12 → 1 →
3 → 3,23,24), 12,3 : 23,24 (trajectory 12,3 → 23 → 23,24), 12,3,23 : 24 (trajectory
12,3,23 → 23 → 24), with one distributed component: 12,3,23 : 23,24 (trajectory
12,3,23 → 23 → 23,24) is also possible, but the split 12,3 : 3,23,24 is impossible
+
because at this split N ≡ 23 and N ≡ 3; that is, the link N → N does not exist.
+
−
−
D B D B
This is why at m > n it is necessary to check the rule of connectedness for the sup-
posed possible splits inside the product simplex. Besides that, it is necessary to find
out if the boundary element to which the supposed product point belongs is one
of the first two types of boundary elements of distillation subregion Reg ∞ .
bound,D
Thus, if the feed point belongs to a product simplex x F ∈ Reg simp (m > n), the
components and pseudocomponents of this product simplex can be separated at
R =∞ and N =∞, just as components of ideal mixture if x D ∈ Reg ∞
bound,D and x B
∈ Reg ∞ , and if the rule of connectedness is not broken.
bound,B
The notion of product simplex coincides with the notion of region of batch
distillation that was used in Safrit & Westerberg (1997).
A method similar to that of product simplex and considering azeotropes as
pseudocomponents was proposed for synthesis of separation flowsheets in Sargent
(1994).
Division of main types of three-component mixtures phase diagrams according
to classification of Gurikov (1958) into product triangles is given in Fig. 3.16. Each
type pertains to two different antipodal phase diagrams, which differ from each
other by direction of all the bonds and replacement of stable nodes by unstable
ones and vice versa. This figure can serve as the basis for determination of feasible
sharp and semisharp splits of various azeotropic mixtures at any feed composition.

3.5.3. Algorithm of Product Simplex for n-Component Mixtures
For n-component mixtures, the method of product simplex is based on application
of structural matrix. It includes the following steps:

1. Determination from structural matrix by means of sorting out the bonds
chains, set of stationary points of which includes in itself in total all the