Page 95 - Adsorption Technology & Design, Elsevier (1998)

92 Rates of adsorption of gases and vapours by porous media

a moments analysis of adsorbate breakthrough curves from a column
containing a zeolite adsorbent yields an expression which can be used to
determine the separate mass transfer and diffusion resistances. Denoting
the first moment of the response to an input signal by/~ and the second
moment by 0 "2, the ratio o'2/2/12 yields results for a general model formulated
by Haynes and Sarma (1973) which may be compared with the same ratio of
moments obtained for the simplified model employing a linear driving force
for the adsorption rate. When experiments are confined to a low Reynolds
number region of flow (u being the superficial fluid velocity through the bed
of voidage e) the result for the general model is
Rp2 e )-2
o'2L = DL(e+ 1[ Rp2 + ~ + ~ rc2 )(lq
2p 2 u u 2 i e]kaDm 15epDp 15KD~ K(I- e) (4.45)
-
where K is the Henry's law constant.
For the linear rate model of Glueckauf and Coates the corresponding
result is
(e)l(
2~ z u - u z + i-e) ~ 1 +(1-e)------K (4.46)

where ka is the rate coefficient corresponding to the linear driving force
model (equation 4.45).
Both models become equivalent if
1 Rp 2 Rp 2 re 2
= ~ + + (4.47)
kaK 3Dm 15epDp 15KDc
The individual axial dispersion term DL, the molecular diffusion coefficient
Dm and the intraparticle and intracrystalline diffusivities may thus be
extracted from equation (4.45) from a plot of (cr2/2ju 2) (L/u) against 1/u 2 for a
range of particle sizes. Figure 4.12 shows such an experimental plot for three
different adsorbates, N2, CF4 and i-C4H10 passed at low velocity through a
bed of 4A zeolite (Kumar et al. 1982). The slope of the lines yields the
numerical value of the dispersion coefficient DL while the intercepts provide
the determination of kaK. Repeating the experiments with different size
particles enables the evaluation of the molecular diffusion coefficient Dm
and the intraparticle diffusivity Dp. To estimate Ddr~ 2 an adsorbate such as
CF4 or i-C4H10- molecules too large to penetrate into the crystalline zeolite
cavities- is employed. The lines for N2 are temperature sensitive and this
reflects dominant intracrystalline diffusion resistance. Subtraction of the
intercepts (determined at the same temperature) for N2 and CF4 then
provides an estimate of the intracrystalline diffusivity. Crystallites of
different sizes would yield similar information.