Adsorption - Principles of Chemical Separations with Environmental Applications - page 195

v s . This approach provides more contact time for
sorbate-sorbent equilibrium and a lower pressure drop across the bed. In practice, this
translates to the use of short bed lengths of large diameter (low

A better alternative is a low value of

v s ), in contrast to long,

v s ). The pressure drop across the bed can be estimated using

small-diameter beds (high

the Ergun equation:

150 1

75 ρ f v

s (1

P
L

− ε
Re

− ε )

= + 1 . , (7.3)

d p ε

3

where L = actual bed length

ε = bed void fraction (not particle).

Remember that the total pressure drop includes accounting for auxiliary components
(valves, piping, etc.).
Step 3 depends on the sorbent size and the effective diffusivity ( D eff ) within the sorbent
particle, which can be written as

D AB ε p
τ

D eff = , (7.4)

where ε p = particle void fraction

τ = tortuousity (correction factor > 1 to account for the tortuous nature of

pore structure).

Appendix C describes pulse analysis that can be used to obtain process parameters. One
measure of the ability of the sorbate to access the particle interior is D eff / r where r is the

characteristic sorbent size (radius for spheres). A large value of this parameter translates
to good interior access. This result favors small particle size. This result is usually out-
weighed by pressure-drop considerations since a larger P is needed as the particle size is

reduced.

7.8 Process design factors

Before considering the specifics of adsorption design factors, it may be useful to generalize
the process with some simplified analogies.
First, think of a large department store that has a parking lot next to it (Figure 7.3(a)).
Before the store opens on a busy day, the parking lot is empty. When the store opens, cars
arrive and typically park very close to the store. As more cars arrive, they have to park
further and further away. The car traffic is a dynamic situation with cars coming (at an
assumed constant rate) and going but one can observe that there is a net accumulation
of cars as the lot fills up. At some time during this period, if we plot the number of cars
vs position relative to the store (Figure 7.3(b)), the plot will look very similar to the one
described for an adsorption column (see Figure 7.5). As the lot fills up, cars will enter
and leave without stopping to park since the open spaces are isolated, far from the store