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44 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

stages, on the contrary, trajectory should go through a stationary point or at least
start (end) in it.
As far as c-lines cannot cross each other and boundary elements of concen-
tration simplex are filled with their c-lines bundles, c-lines cannot pass from the
internal space of the simplex to its boundary element. Therefore, the distillation
trajectories at the infinite reflux can lie completely inside the concentration sim-
plex or inside its boundary elements.
As it follows from the aforesaid, at a finite number of separation stages, both
product points should lie on one c-line inside the concentration simplex. If the
number of separation stages is infinite, the following variants of the product point
location are feasible: (1) one product point lies inside the concentration simplex
and the second one coincides with one of the nodal stationary points; and (2) both
product points lie on two different boundary elements of the concentration simplex,
and the distillation trajectory goes through their common point, which is a saddle
stationary point of the concentration simplex, or goes through two saddle stationary
points belonging to these boundary elements.

3.3.2. Product Composition Regions for Ideal Three-Component Mixtures

Let us examine how the location of the product points should change for three-
component mixtures under the infinite reflux at a set value of parameter D/F with
the increase of stages number (Figs. 3.2a,b,c). With the increase of N, one of the
product points moves toward the node (Fig. 3.2a), or both product points move
toward sides of the concentration triangle (Fig. 3.2c), or one of the product points
moves toward the node and another one moves toward the side (Fig. 3.2b).
The split (Fig. 3.2a) corresponds to the condition D/F < x F1 , the split (Fig. 3.2b)
corresponds to the condition D/F = x F1 , and that in Fig. 3.2c corresponds to the
condition x F1 < D/F < (x F1 + x F2 ).

2 2 2
a) b) c)

x x
B(3) B(3)
x x x
B(2)
x B(1) x B(1) B(2) x B(3)
x F x F x x x x B(1) B(2)
x D(1) x D(1) D(3) x D(2) D(1) F
x x
D(2) D(2)
1 3 1 3 1 3
x D(3) x D(3)
Figure 3.2. Product points and distillation trajectories under infinite reflux for different number
of trays: (a) semisharp split, (b) sharp direct split, and (c) split with distributed component. Ideal
mixture (K 1 > K 2 > K 3 ), x D(1) , x D(2) , x D(3) , x B(1) , x B(2) , x B(3) , product points for different number
of trays, x F = const, D/F = const; short segments with arrows, conjugated tie-lines liquid–vapor
(distillation trajectories under infinite reflux); thick solid lines, lines product composition for
different number of trays.