Page 244 - Adsorption Technology & Design, Elsevier (1998)

Selected adsorption processes 221

If each of the above conditions is met by the same separation factor a (with
a > 1) the inequalities may be written as mass balances
D/S = KA a in section 1 (7.9)
(D - E)/S = KB a in section 2 (7.10)
a (D - E + F)/S = KA in section 3
(7.11)
a (D - E + F- R)/S = Ka in section 4
(7.12)
The operating lines in sections 1 and 2 should lie above each of the
equilibrium lines while in sections 3 and 4 the operating lines should lie
beneath the equilibrium lines. As there are finite changes in flow at the feed
inlet and also the raffinate and extract ports, the equilibrium lines will be
crossed by operating lines at these positions because there will be sudden
changes in the fluid phase composition without any concomitant change in
adsorbed phase composition. The McCabe-Thiele diagrams pertaining to
components A and B in a simulated moving bed system will be identical to
the countercurrent cascade described in Section 7.7.2 and illustrated by
Figure 7.15. Most of the separation of components for the extract product E
occurs in sections 1 and 3 while the separation of components for the
raffinate product R is mainly in sections 2 and 4. Reducing the ratio L/S
forces the operating lines closer to the equilibrium lines thus reducing the
mass transfer driving force. By analogy with distillation technology this
could be interpreted as requiring a larger number of theoretical stages, or,
for the simulated moving bed, necessitating that each of the four beds be
increased in size. As the conditions for separation of components A and B
must be ~/A > 1 and ?'a < 1 then the inequality
D+F D
KA > ------->~ > KB (7.1.3)
S S
must hold and there is therefore an optimum choice to be made between the
size of each bed and the desorbent flow rate.

7.7.4 Modelling
Modelling both the continuous countercurrent and simulated moving bed
processes has been considered by a number of authors. The continuous
countercurrent separation process has been addressed by Ching and
Ruthven (1984), who assumed axially dispersed flow of fluid and counter-
current plug flow of solids in a column. The fundamental differential
equation describing the steady state operation of such a system is, for each
component,