Page 70 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 67

per unit time. If M is the molecular mass of the gas in question, p its pressure
and T the absolute temperature, the rate (measured in kg m -2 s -1) at which
molecules strike the surface may be expressed as

(4.1)
Rm "" p( M/2trRg T) '/~
We compare the intrinsic rate of adsorption of nitrogen with an experiment-
ally observed rate of adsorption of nitrogen at 6 bar and 25~ (Crittenden et
al. 1995). Appropriate substitution of numerical values into equation (4.1)
gives the maximum intrinsic rate of adsorption as 2 x 10 4 kg m -2 s -1. On the
other hand, the experimentally observed rate is approximately 4 x
10 -8 kg m -2 s -1 (c. 0.33 mol s -l at 6 bar, 25~ onto a surface of 250 m E g-l).
Thus the intrinsic rate of adsorption is some 1012 times faster than the
observed rate of adsorption. It is generally acknowledged throughout the
literature on physical adsorption processes that the dominant rate-control-
ling step is not the actual physical attachment of adsorbate to adsorbent
(normally referred to as very rapid) but rather intraparticle transport of gas
within the porous structure of the adsorbent to its available surface.
Interparticle transport from bulk fluid to the external surface of the porous
adsorbent may also have an effect on the overall rate of adsorption under
some circumstances.
Transport resistances which influence the overall rate of adsorption are:

(1) mass and heat transfer of adsorbate to and from the exterior surface
of the adsorbent (known as interparticle transport);
(2) Maxwellian diffusion (bulk molecular diffusion) in moderately
large pores (macropores) or Knudsen diffusion in pores (micro-
pores) which have a diameter smaller than the mean free path of the
adsorbate molecules;
(3) intracrystalline diffusion within the channel and cage-like structure
of molecular sieve materials such as zeolites and silicalites;
(4) surface diffusion when adsorbate molecules move freely over the
internal surface of adsorbents in parallel with intraparticle diffu-
sion;
(5) heat transfer within the interior of particles occasioned by the
exothermic nature of adsorption.

The relative importance of these resistances largely depends on the nature of
the adsorbent and adsorbate and the conditions of temperature and pressure
in which the adsorption occurs. As shown in Chapter 6 any model
representing an adsorber must include mass and heat balances for the fluid
phase and also transport processes within the porous particles.