Page 68 - Distillation theory

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42 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

' 2 3
2 ' 3
x = y
a) 2 1
4
' 1
' 4
1
5
x 1
Figure 3.1. Conjugated tie-line liquid–va-
y por, c-line, and residue curve: (a) conju-
b) gated tie-line liquid–vapor and c-line, (b)
c-line and residue curve, and (c) intersec-
tion c-line and residue curves. 1 → 2 → 3 →
x 4 → 5 and 1 → 2 → 3 → 4 , two conju-

gated tie-lines liquid–vapor on one c-line;
thick lines, c-lines; thin lines, residue curves.
c)
x = y
4 3
x = y 2
3
x = y 1
2
x 1

The distillation trajectory under infinite reflux is a line of conjugated liquid–
vapor tie-lines, each of which corresponds to one of the column plates, in accor-
dance with Eq. (3.2). In the works (Zharov, 1968; Zharov & Serafimov, 1975),
the broken line of conjugate liquid–vapor tie-lines is replaced with a continuous
c-line, for which the liquid–vapor tie-lines are chords (Fig. 3.1a). At the same time
it follows from Eq. (3.1) that the liquid–vapor tie-line is a tangent to the residue
curve. Therefore, liquid–vapor tie-line, on the one hand, is a tangent to residue
curve and, on the other hand, is a chord of the c-line. This fact determines the
similarity and the difference between the residue curves and the c-lines (see Fig.
3.1b). In Fig. 3.1c, it is shown that the distillation trajectory under the infinite reflux
(c-line) crosses the set of residue curves.
At the same time in the vicinity of stationary points of concentration space
(pure components and azeotropes), where the length of the liquid–vapor tie-lines
becomes close to zero, the c-lines and the residue curves coincide (i.e., the local
characteristics of stationary points of c-lines bundles and residue curves bundles
are the same). That means that topologically the c-lines bundles and the residue
curves bundles are identical; the structure of the concentration space is also the
same: bonds between stationary points, regions Reg ∞ and subregions Reg of
sub
distillation and boundaries between them. In other words, distillation regions
Reg ∞ and subregions Reg sub under infinite reflux and boundaries between them,
on the one hand, and open evaporation regions and subregions and boundaries
between them, on the other hand, contain the same sets of stationary points.
However, the exact location of boundaries between the c-lines bundles and the