Page 193 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 179

and 0.5, respectively. Equation (6.71) can be written in non-dimensional
form as follows:
1 DL ?'IDM ?'le
(6.72)
"- : = +~2 = ~ + ~ ' 2
Pe' udp ud v ReSc
The coefficient ?'1 is dependent on bed voidage as follows:

y~ = 0.45 + 0.55e (6.73)
The coefficient )'2 is dependent upon flow characteristics as follows:
1
~'2 -" ............
p ,t'm / (6.74)
ee'| 1+ ]

At high Reynolds numbers the asymptotic value of the Peclet number takes
the value of 2 for relatively large particles, i.e. d o > 0.3 cm. For smaller
particles, i.e. dp < 0.3 cm, experimental data show much smaller limiting
Peclet numbers, given approximately as follows:
Pe'oo = 1.68do (6.75)
This behaviour is believed to be due to the tendency of small particles to
form clusters which act effectively as single particles. Thus the advantage of
reducing pore diffusional resistances by using small particles could well be
offset to some extent by an increase in axial dispersion.
The variations of Peclet number with Reynolds number for gas and liquid
phase systems are compared in Figure 6.12. At high Re, the asymptotic value
of Pe' = 2 is reached for liquids, but at lower values of Re, the axial dispersion
is greater than that for gases. The increased dispersion with liquids is
believed to be due to the effect of greater liquid hold-up in the laminar
boundary layer surrounding particles, together with small random fluctua-
tions in the flow (Ruthven 1984).
If adsorption is fast and strong then the concentration profile through a
particle may become asymmetric. This can lead to a significant additional
contribution to axial dispersion for gases at low Re. The effect is likely to be
most significant when most of the adsorption occurs at the outside of the
particle, as would occur in the initial stages of uptake in a mass transfer zone.
Equation (6.76) has been suggested for a rectangular isotherm as an
alternative to equation (6.72). In this case ?'1 is typically 50, compared with
the value of 0.7 for non-porous particles:
1 20 1
= + - (6.76)
Pe' ReSc 2