Page 156 - Adsorption Technology & Design, Elsevier (1998)

144 Designprocedures

ueAdc = - kfA (1 -e) ap (c-ci)dz (6.15)
where A is the cross sectional area of the column
ap is the external surface area of the adsorbent particle per unit
volume of particle
u is the fluid superficial velocity
c is the adsorbate concentration in the fluid bulk
ci is the adsorbate concentration at the fluid-adsorbent interface
e is the bed voidage.
In this example it is assumed that the mass transfer process is fluid film
controlled, and that the fluid film mass transfer coefficient is kf. Equation
(6.15) cannot be readily integrated since the interracial concentration ci is
not known. The rate of mass transfer is therefore expressed in terms of an
overall driving force (c-c*) in which c* is the adsorbate concentration in
equilibrium with the mean sorbed phase concentration. The length of the
adsorbent bed L is then given by equation (6.16),
CE
_ ue f dc (6.16)
L (1-e)koap ~, c-c*

or

L = NTU x HTU (6.17)
where k0 is the overall mass transfer coefficient
CE and cB are the fluid phase adsorbate concentrations into and out of
the moving bed
NTU is the number of transfer units
HTU is the height of a transfer unit.
An analytical solution to the continuous equivalent countercurrent
representation of a simulated moving bed process is provided in Section
7.7.4.

6.4 FIXED BEDS

Two extreme approaches can be taken for the design of fixed beds. One
involves rigorous solution of the conservation, transport and thermo-
dynamic equations and the other makes use of short-cut techniques which
are based on laboratory-scale, pilot-scale or industrial-scale data. In the
former approach, a certain amount of experimental work may be required
where data is lacking in the literature.