Page 78 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 75

Diffusion in isothermal zeofite crystals
As discussed in Chapter 2, the class of adsorbents known as zeolites form
crystalline structures containing apertures (referred to as windows) of
molecular dimensions through which molecules of adsorbate smaller than
the aperture may enter the well-defined internal channels leading to the
larger cavities within the crystal where the sites for adsorption are located.
Diffusion into zeolites is therefore relatively slow because of the restricted
access. Diffusion coefficients Dc associated with zeolite crystal structures
have magnitudes in the range 10 -13 to 10 -15 m E s -1.
The rate of adsorption of gases by zeolites may be assessed from batch
experiments in which finite quantities of adsorbate are admitted to a vessel
containing the adsorbent and, either from weight changes of the adsorbent
or from information concerning gas concentration, the uptake of adsorbate
followed as a function of time (see Sections 4.3.2 and 4.3.4 for experimental
methods). Models of adsorption of gases by zeolites can also be formulated
and compared with experimental kinetic data. Assuming that a crystal of
zeolite may be regarded as an approximately spherical object, a steady state
isothermal (heat of adsorption rapidly dissipated) material balance (Fick's
second law of diffusion) on the adsorbate yields

(4.17)
r E Or = Ot
At the centre of the crystal, considerations of symmetry require that

r = 0 -Oq _- 0 for all t >- 0 (4.18)
Or

while at the periphery of the crystal
r= re q = qo (4.19)

The initial condition, provided the amount adsorbed is small in comparison
with the total quantity of adsorbate introduced, may be interpreted as a
constant concentration of adsorbate and is represented by
t = 0 q -" qoi for all r -> 0 (4.20)
The average adsorbate concentration through the crystal may be computed
from
re
qr 2 dr (4.21)
3 f