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240 3. Heterogeneous Processes and Reactor Analysis

utions,
The pressure drop reflects the sum of single-particle drag-force contrib which is
(Foscolo and Gibilaro, 1984)
p NF (3.598)
d

Using this equation and the equations for F d and N ,
p (1 ) ( ) g (3.599)
Z
h f
From the analysis presented in the last two paragraphs, it is evident that the gra vitational
force acting upon the particle is used for the deriation of the equations for the terminal v
velocity and the pressure drop in the fluidized bed. Then, it is clear that the hydraulic den-
sity should be used in these equations as well as in any other equations that are deri v ed
from a similar force-balance analysis. For instance, this is the case of the Foscolo–Gibilaro
criterion for determining the fluidization pattern (Section 3.8.2).
As mentioned before, the hydraulic density is not used for gases, simply because the
density difference between the solid and the fluid phase is so big that this density is prac-
or this reason, . F tically equal to the particle density the particle density is found in all rel-
evant equations and correlations.
v
Much attention should be gien to correlations for liquid–solid suspensions or fluidiz-
ing systems deried e. If the experimental data hae been correlated to par- v xperimentally v
ticle density this kind of density and not the hydraulic density should be used. F or
,
instance, this is the case of the Liu–Kwauk–Li criterion for determining the fluidization
v we, pattern (Section 3.8.2). Ho for correlations that hae been deried using nonporous er v v
particles, the hydraulic density should be used. This is because the correlation accounts for
the whole mass included in the volume of the particle, which is the sum of the solid mass
and liquid mass in the pores for porous particles.
A problem arising when using hydraulic density is the possibility of partial internal wet-
ting of the porous particle. Using eq. (3.358), it is assumed that the pores are totally f illed
with liquid, which is generally but not al true. This is why seeral authors correlate ays, w v
,
data to particle density which normally is a gien and well-defined parameter .
v
,
,
Furthermore, for the same reason, some authors use models to indirectly determine
hydraulic density.
3.9.9 Diffusion and diffusion coefficients in porous solids

General
In porous solids, it is the diffusion within the solid particles that usually controls the mass
transfer in many applications, such as adsorption, ion e drying, and heterogeneous xchange,
catalysis. Bulk diffusion is considered to take place within the large pores, e xcept that it is
hindered by the pore walls (Perry and Green, 1999). This hindrance is expressed by the tor-
tuosity f actor , which is estimated from geometric arguments. However, this approach
p
often results in values far from reality. Hence, a diffusion model fed with e xperimental
measurements is generally employed for the evaluation of the effective diffusivity D eff and