Page 72 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 69

front (upstream) face and the back (downstream) surface of a particle due to
differing flow conditions which prevail at these positions. However, average
values, known as average film coefficients, are used in practice. Correlations
exist for the estimation of these coefficients as functions of fluid properties
and particle size.
Wakao and Funazkri (1978) revealed that when mass transfer coefficients
were measured by experiments involving adsorption or evaporation, the
mass balance for the bed (see Chapter 6) should include a term accounting
for axial dispersion. Previous correlations of experimental data were based
upon a mass balance equation for the packed bed ignoring axial dispersion.
It was shown that the mass transfer coefficient could be expressed in terms of
the dimensionless Sherwood number (Sh) by the relation
Sh = kdp/D = 2.0 + 1.1 Sc 0'33 Re ~ (4.4)

if axial dispersion were included in the analysis of experimental results and
that the value of k was about twice that for a value of Re = 10 if axial
dispersion were neglected. The dimensionless Reynolds number, Re, in
equation (4.4) is defined as pudp/p (where p is the fluid density, u the
superficial fluid velocity,/z the fluid viscosity and dp the particle diameter)
while the dimensionless Schmidt number, Sc, is defined as lt/pD (where D is
the diffusion coefficient for bulk Maxwellian transport of the component
being transported from fluid to solid). Should one have to rely on
experimental data obtained which excludes any consideration of axial
dispersion, then it is best to estimate the mass transfer coefficient from the
use of the so-called j factor, which for mass transfer is
jD = (kp/p) Sc ~ = (0.458/e) (Re) ~
(4.5)
and where e is the bed voidage.
Alternatively the Ranz and Marshall (1952) correlation,
Sh "- 2.0 q- 0.6 Sc 0"33 Re ~ (4.6)
may be used when axial dispersion is not included in the bed mass balance.
The heat transfer coefficient h from solid to fluid may be estimated from a
correlation for the Nusselt number, Nu, suggested by Lemcoff et al. (1990)
and which is similar to the correlation given by equation (4.4) for mass
transfer,
Nu = hdp/A,f = 2.0 + 1.1 er 0'33 Re ~
(4.7)
The dimensionless Prandtl number Pr is defined as cf/~/Af, cf being the heat
capacity of the fluid and Zf the corresponding thermal conductivity. At
moderate and higher values of the Reynolds number the correlation appears
to be good but at low values of Re a significant scatter of data is evident. The