Page 86 - Adsorption Technology & Design, Elsevier (1998)

Rates of adsorption of gases and vapours by porous media 83

and heat transfer. In the steady state the mass flux across the film between
bulk adsorbate and particle surface is equal to the diffusive flux at the
interface between particle and bulk phase and hence
k(cg .- c) = De(aC/c3R) at R = Rp (4.32)
Similarly, heat transferred across the film from the particle periphery to the
bulk fluid will be equal to the heat flux in the steady state so
h(T- Tg) = k~(~T/aR) at g = Rp (4.33)
where ke is the effective thermal conductivity of the adsorbent (analogous to
the effective diffusivity).

Casting both of the above equations into dimensionless form by writing
c~ Cg = y, T/Tg = 0 and R/Rp = z the equations become, respectively,

(ay/az)/(1 - y) = kRp/De = Bim at z = 1 (4.34)
and
(~O/~z)/(O - 1) = hRp/ke = Bib at Z = 1 (4.35)
We see that the ratio of rates of interparticle mass transfer to intraparticle
mass transfer is given by the mass Biot number Bim (= kRp/De). The ratio of
rates of interparticle heat transfer to intraparticle heat transfer is similarly
given by the Biot number for heat transfer Bih (= hRp/k~). When either one
of the Biot numbers is large, the major resistance to the appropriate
transport process is within the pellet rather than external to the pellet.
Froment and Bischoff (1979) indicate that, for the majority of cases, the
major resistance to mass transfer is within the porous pellet whereas the
major resistance to heat transfer is in the gaseous boundary layer (the gas
film) between particle and bulk fluid. For heterogeneously catalysed
reactions this is generally the situation (Kehoe and Butt 1972, Carberry
1975) although exceptions are known. For physical adsorption processes,
however, mass transfer resistance is invariably within the adsorbent pellet.
Heat transfer resistance is generally external to the adsorbent pellet but
Brunovska et al. (1978) have shown that the relative rates of inter- and
intraphase particle transport depend on the adsorbate-adsorbent pair. In
some circumstances, particularly, for example, when the adsorbate is
chemisorbed, resistance to heat transfer within the particle should not be
eschewed.
For heuristic purposes we consider a zeolite crystal and assume that heat
transfer resistance is wholly within the gas film surrounding the crystal and
that intracrystalline diffusion is the rate-controlling mass transfer process.
The set of equations which have to be solved to yield an expression for the