Adsorption - Principles of Chemical Separations with Environmental Applications - page 202

Upon completion of the adsorption step, draining of the adsorption liquid is usually
done by gravity flow, sometimes assisted by a pressure of 10-20 psig (69-138 kPa). The
liquid must be given at least 30 minutes to drain thoroughly. Even then, there can be
significant hold-up or retention of liquid in the bed. Even after careful draining, hold-up
can amount to 40 cm 3 of fluid per 100 g of adsorbent. This fluid is retained in the micro- and
macropores and bridges between particles. Retained liquids can adversely affect product
streams and regeneration requirements. For example, any liquid that is not drained in a
temperature-swing cycle will consume extra thermal energy when it is vaporized from the
bed, and the fluid will end up recovered with the adsorbate.
In liquid adsorption systems where liquids are also used for purge or displacement, care
must be taken to prevent “fingering.” Fingering is the displacing of one liquid by another
at their interface due to density or viscosity differences. The phenomenon creates columns
of the intruding fluid (fingers) even in uniformly packed beds of adsorbent. It is obvious
that a denser fluid above a less dense fluid will cause instability. However, it is also true
that when a less viscous fluid is displacing a more viscous one, any bulge in the interface
will grow because the resistance to flow is less, and the less viscous fluid will continue
to intrude. Operating such that the upper fluid is the less dense or more viscous fluid for
displacing, will tend to correct any flow instabilities that occur.

7.9 Evaluating the adsorption process

An evaluation of the adsorption (and desorption) steps can be accomplished using the
equilibrium isotherms. This will be discussed in this section. Two simplified analyses
(scale-up and kinetic) based on obtaining a breakthrough curve in a small, laboratory-
scale apparatus and using the results for the design of larger, process-scale unit will be
discussed in Section 7.10. A detailed approach that considers the various transport steps
allows performance to be predicted by the model under varying flow conditions. The
reader should consult Yang's text [4] for a detailed presentation.

7.9.1 Equilibrium-limited operating conditions

We can use the equilibrium isotherm to predict performance under equilibrium-limited
operating conditions [10]. A mass balance on the solute in the MTZ leads to an equation
for the velocity of the front:

Amount introduced = Amount retained

YG b At = q ρ s Az (7.10)

d z
d t =

G b ρ f v

V = velocity of solute front =

d Y = d Y ,

(7.11)

ρ s · d q / ρ s · d q /