Page 73 - Adsorption Technology & Design, Elsevier (1998)

70 Rates of adsorption of gases and vapours by porous media

poor correlation at low Re may well arise because of the inherent assumption
of a uniform interface boundary condition leading to errors in the evaluation
of the thermal conductivity Af. From the analogy between heat and mass
transfer due to Chilton and Colburn (1934) implying that the j factors for
heat (jH) and mass (jD) transfer are numerically equal, another correlation
frequently used is
jH = (h/cflt) (Cf~//~f) 0"66 "- (0.458/e) (Re) ~ (4.8)

Heat generated by the adsorption of a component in the gas or liquid phase
by the porous solid has to be transported not only between solid and fluid in
an operating column, but is subsequently dissipated by transport from fluid
to vessel wall and thence to the surrounding environment. A correlation due
to Leva (1949) may be used to assess the resistance to heat transfer between
fluid and vessel wall. A film heat transfer coefficient estimated from a
correlation described by McAdams (1954) enables the evaluation of heat
transfer resistance from the vessel wall to the surroundings.

4.2.2 Diffusion in porous materials
Adsorption is a surface phenomenon, so that the more surface that is
available for adsorption the greater is the capacity of the adsorbent for the
adsorbate. Hence, as discussed in Chapter 2, adsorbents have maximum
ability to adsorb when the internal structure of these materials is porous,
thus allowing access of adsorbate molecules to the largest amount of internal
surface. The total mass flux due to an adsorbate entering a porous structure
is the sum of fluxes due to gaseous diffusion (Maxwellian and/or Knudsen
diffusion, depending on the pore radii), convective diffusion (occasioned by
the displacement of one molecular species by another), surface diffusion (in
which molecules are transported across a surface rather than through the
gaseous phase contained by the pores of the material) and viscous flow
(usually negligible for physical adsorption when there is only a small
pressure gradient along pores).

Maxwellian and Knudsen diffusive fluxes
In pores of diameter much greater than the mean free path of a molecule,
diffusion occurs by a process of molecular collisions in the gas phase within
the pore (Maxwellian or bulk diffusion) but, if the molecular mean free path
is much greater than the pore diameter, diffusion occurs by molecules
colliding with the pore walls (Knudsen diffusion). Both of these transport
processes occur with a decreasing concentration gradient and may be
described by means of Fick's law of diffusion with an appropriate diffusion