Page 71 - Distillation theory

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3.3 Distillation Trajectories of Finite and Infinite Columns 45

2
Figure 3.3. Product regions (shaded, bottom region
darker shaded) under infinite reflux for given x F and dif-
ferent number of trays and D/F. Ideal ternary mixture
3 4 (K 1 > K 2 > K 3 ), line 1 − x D at N =∞ and x F1 < D/F <
(x F1 + x F2 ), line 2 − x B at N =∞ and x F1 < D/F < (x F1 +
1 x 2 x F2 ), line 3 − x D at N =∞ and (x F1 + x F2 ) < D/F < 1,
D
x F x B
line 4 − x B at N =∞ and 0 < D/F < x F1 , line 5 − x D at
5 6 D/F = 0, line 6 − x B at D/F = 1.
1 3

In the case of a finite number of stages, we have nonsharp separation; in that
of an infinite number, we have semisharp (Fig. 3.2a) or sharp separation with a
distributed component (Fig. 3.2c), or sharp separation without distributed com-
ponents (Fig. 3.2b).
The set of product points at all values of parameters N and D/F is shown in Fig.
3.3 (Petlyuk & Avet’yan, 1971; Stichlmair, Fair, & Bravo, 1989). For each feasible
point of the top product, there is some corresponding point of the bottom product
lying at the intersection of the c-line, passing through the point of top product,
and the material balance line, passing through the points of the top product and
the feed point.
The set of product points is restricted by the limit values of parameters N =∞,
D/F = 0, and D/F = 1. At D/F = 0, only the bottom product is being withdrawn
from the column, and at D/F = 1, only the top product. Therefore, at D/F = 0,
the composition of the bottom product coincides with that of the feeding and,
at D/F = 1, composition of the distillate coincides with that of the feeding. As
far as in such mode the point of one of the products coincides with the point of
feeding, the distillation trajectory lies in the c-line passing through the feed point
(lines 5 and 6 at Fig. 3.3). With the increase of N, the point of the product, the
withdrawing of which is zero, is moving away along this c-line from the feed point
to the corresponding node.
The set of product points under the infinite reflux (R =∞) and at the infinite
number of stages (N =∞) is a subset of the total set of product points at infinite
reflux (R =∞). As far as the mentioned subset (R =∞ and N =∞) depends on
one parameter (the only parameter is D/F), it is the line in the concentration triangle
and, in general, in the concentration simplex of any dimensionality. In Fig. 3.3, this
subset for points x D consists of lines 1 and 3 and for points x B consists of lines 2
and 4.

3.3.3. Product Composition Regions for Ideal Four-Component Mixtures

Let’s examine a set of product points at R =∞ and its subset at R =∞ and N =
∞ for a four-component ideal mixture (Fig. 3.4). Some point of the bottom prod-
uct belonging to the possible bottom product region at set feed composition (dark
shaded region to the right of point F) corresponds to the top product point