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200 Distillation Trajectories in Infinite Complex Columns and Complexes

6.8. Calculation of Minimum Reflux Mode for Distillation Complexes
with Thermal Coupling Flows

6.8.1. The Columns with Side Withdrawals of Flows

Before examining minimum reflux mode for complexes with branching of flows,
we discuss complex columns with side withdrawals of flows. Side products of such
columns cannot be pure components at finite reflux, but the number of com-
ponents in each side product can differ from the number of components in the
other side products, in the initial mixture, and in the top and bottom products.
In such complex columns in each section, the number of components at the exit
from the section is smaller, than at the entrance. The simplest example of sepa-
ration is: 1 : 1, 2 : 3 (Fig. 6.14). In this case, side product 1,2 is withdrawn above
feed. Such splits are sharp. We confine oneself to examining of complex columns
with sharp splits. The pseudoproduct of each intermediate section of the column
with side withdrawals of products is the sum of all the products above (below) the
section under consideration, if this section itself is located above (below) feed. For
such splits, all the pseudoproduct points of the intermediate sections are located
at the boundary elements of concentration simplex. Therefore, the structure of
trajectory bundles for the intermediate sections does not differ from the structure
of trajectory bundles for the top or bottom sections at sharp separation.
Figure 6.14 shows trajectories of the intermediate section for separation 1 : 1,
2:3at different modes. Pseudoproduct points x (D = D 1 + D) is located at side

D1
1-2, and joining of the intermediate and bottom sections in the mode of minimum
reflux goes on in the same way as for the simple column at indirect split. Trajectory
of the intermediate section r 1 tears off from side 1-2 in point S r1 , and point of side
product x D1 can coincide with point S r1 (Fig. 6.14a) or lie at segment 1− S r1 (Fig.
6.14b). The first of these two modes is optimal because the best separation between
top and side products (the mode of the best separation) is achieved at this mode.
Zones of constant concentrations in the top and intermediate sections arise in
+
point S r1 ≡ N . Therefore, in the mode of minimum reflux in the intermediate
r2
section, there are two zones of constant concentrations. At the reflux bigger than
minimum, point S r1 moves to vertex 2 and at R =∞ this point reaches it (i.e.,
at R =∞, pure component 2 can be obtained in the infinite column as a side
product). Therefore, for the columns with side withdrawals of the products, the
mode of the best separation under minimum reflux corresponds to joining of
+
sections in points S r1 and N of the trajectory bundle of the intermediate section
r1
(at sharp separation) or in its vicinity (at quasisharp separation). The trajectory
of the column with a side product at minimum reflux at best separation may be
described as follows:
(1) (2) (3) (3) (2) +(2) (1)
x → qS → x ⇐⇓ x ←− qS ⇒⇑ N → x
B s1 f f −1 r1 r2 D
x
D1
1,2 1 1 3 3 2 .
Reg Reg t Reg min,R N + Reg t Reg t Reg
B s1 sep,s r1 r1 r1 D
3 2,3 2,3 1,2 1,2 1