Page 94 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 9!

this technique (Karger and Pfeifer 1976). The reader is referred to a review
article by Gladden (1994) for an overview of the PFG technique.

4.3.4 Isotopic labelling
Sargent and Whitford (1971) measured the self-diffusivity of carbon dioxide
in a 5A zeolite by exposing radioactive C1302 adsorbate at constant total
concentration to the adsorbent and measuring the radioactivity as a function
of time. This method provides an accurate means of following the C1302
concentration and thence deducing the self-diffusion coefficient by matching
the uptake curve with equation (4.22). Quig and Rees (1976) used a non-
radioactive isotopic labelling method when studying the self-diffusion of
hydrocarbons in a 5A zeolite, but followed the progress of the uptake with a
mass spectrometer.

4.4 MASS TRANSFER RESISTANCES IN SERIES

Provided chemical reaction does not occur simultaneously with the diffusion
processes in an adsorbent particle, analysis of the response to a pulse input
of an adsorbate to a column packed with an adsorbent provides a convenient
experimental method of deducing the separate contributions of inter- and
intraphase mass transfer and diffusion to the overall resistance to adsorp-
tion. This is because each one of the resistances to mass transfer is in series
and thus linearly additive.
Various researchers, including Thomas (1944), Lapidus and Amundson
(1952), Levenspiel and Bischoff (1963) and Rosen (1954) have produced
analytical solutions to the coupled differential equations describing flow of
adsorbate through a bed of adsorbent in which mass transfer and diffusion
processes occur. Their solutions differ in detail but numerical representation
of the breakthrough curves (see Chapters 5 and 6) of adsorbate from the
adsorbent bed produces very similar results. Glueckauf and Coates (1947)
and Glueckauf (1955) introduced a linear driving force expression for the
rate of adsorption

~q/at = ka (qo, -" q) = kaK (c - coo) (4.44)
where qoo and coo are the equilibrium concentrations of adsorbate at
the solid and in the gaseous phases respectively, K is the Henry's law
(Section 3.3.2) equilibrium constant and k~ the adsorption rate constant.
With this assumption of a linear rate expression it was shown that the various
analytical solutions could be made numerically equivalent, so reducing
computation considerably. By adopting the linear driving force assumption,