Page 37 - Distillation theory

P1: FCH
0521820928c01 CB644-Petlyuk-v1 June 11, 2004 17:45

1.6 Matrix Description of the Multicomponent Mixture 11

a) 2
1 2 3
1 1 1 1
2 1 1
3 1
1 → 2 → 3
1 3

b) 2
1 2 3 13
11
2 1 1 1 1
3 1
13 1 1 1
1 3 2 → 13 → 1
2 → 13 → 3

1 2 3 12 13 23 123
c) 2
1 1
2 1
3 1
12 1 1 1
13 1 1 1
1 3 23 1 1 1
123 1 1 1 1 1 1 1
123 → 12 → 1 123 → 12 → 2
123 → 13 → 1 123 → 13 → 3
123 → 23→ 2 123 → 23 → 3
Figure 1.8. The examples of three-component structures and their
structural matrices. Arrows, direction of residium curves; dotted
lines, separatrixes; thick line with arrow, bond; dotty lines, transfer
to next bond.

By the structural matrix of the azeotropic mixture concentration space, we will
name a square matrix, the columns and lines of which correspond to the stationary
points and the elements of which a ij = 1, if there is a bond directed from stationary
point i to stationary point j (a ij = 0, if such a bond is missing). For the purpose of
obviousness, some examples of three-component mixture structural matrices are
shown in Fig. 1.8.
Each line of a structural matrix corresponds to the ith stationary point and
each column to the jth one. Diagonal elements a ij = 1 (it is accepted conditionally
that each specific point is bonded to itself). The components are labeled 1, 2, 3;
binary azeotropes are designated by two-digit numbers, 12, 13, 23; and the ternary
azeotrope by a three-digit number, 123. Zero column corresponds to an unstable
−
+
node N and zero line to the stable N one (except for the diagonal elements).
Structural matrices provide an opportunity to easily single out all maximum-length