Page 246 - Adsorption Technology & Design, Elsevier (1998)

Selected adsorption processes 223

describing concentration conditions into, co, and out of, CL, a number, n, of
equilibrium stages.
Numerical computation of the simulated moving bed system provides a
second alternative description to the continuous countercurrent and equil-
ibrium stage models (Barker et al. 1983, Ching 1983, Hashimito et al. 1983,
Carta and Pigford 1986, and Ching et al. 1987). Each bed of total volume V is
considered to be equivalent to a number, n, of ideal mixing cells in which the
fluid and adsorbed phases, volumes VL and V~, respectively, are distributed
according to

VL = e V/n and V~ = (1 -e) V/n (7.19)

Assuming mass transfer equilibrium in each cell, a differential mass balance
for component A across the ith cell gives

d c i ( u )
i = 1,2,...,(n- 1),n (7.20)
d-T = ' VL + KVs' (ci-t- ci)
Here u is the constant volumetric flow rate within each of the bed sections
but will differ for each of the four sections due to the introduction of feed and
withdrawal of products. Similarly, fluid concentration (moles/volume)
remains constant within each bed section but will differ between sections 2
and 3 where feed is introduced and between sections 4 and 1 where
desorbent make up is added (see Figure 7.16). Both the differences in fluid
flow u and concentration c at each stage can easily be represented by simple
mass balances over appropriate sections and at the feed and desorbent input
points. The unsteady state linear first-order differential equation for n cells
within each bed section coupled with the two sets of mass balances can be
solved by standard numerical techniques from zero time with defined initial
conditions. The calculation is continued by advancing the feed, raffinate,
extract and recirculation points at chosen time intervals until a steady state is
approached. Figure 7.17 illustrates, for fructose and glucose separation,
(Ching et al. 1985, Ruthven and Ching 1989) the extent of agreement
obtained between the numerical simulation and the countercurrent models.
Isothermal operation is not necessarily suitable for all simulated moving bed
systems. The concentration of extract and raffinate streams can never exceed
the concentration of feed components for a system with a linear isotherm.
Furthermore, when the operating and equilibrium lines are close an excessive
number of theoretical plates (to use the parlance of distillation and absorption
technology) or height of each bed would be required for separation.
Constraints such as these may be circumvented by non- isothermal operation of
a simulated moving bed (Ching and Ruthven 1986). By maintaining bed section
1 at an elevated temperature with sections 2, 3 and 4 at a lower temperature,