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200 3. Heterogeneous Processes and Reactor Analysis

for 1 < Re fm gion, < 1000. In this re m is approximately between 2.5 and 4.2. The v alue of
m is between 4.2 and 4.5 for 0.1 < Re fm <1 and an aalue of 4.35 can be used as a v erage v
first approximation.

v Pavlov (1979) gies a simpler equation based on the Archimedes number ( Ar ), for u bm >
u s > u fm :
18  Re 0.36 Re 2  0.21
 p p  (3.475)
f
 Ar 

It is easy to show that for the same superficial velocity, smaller particles result in higher
bed porosity.

g Bed voidae in type B fluidization

The following analysis holds for Type B fluidization and for Type A bubbling fluidization,
when the region of particulate fluidization is so small that it can be ignored. In the frame-
work of the two-phase model (see the subsection Hydrodynamic modeling of bubbling flu-
idization), the bed e ubbles xpansion in terms of the fraction of the bed occupied by b is
bub

u
Z u
Z
f fm s fm
bub (3.476)
Z f u bub
where:
Z the bed height at incipient fluidization
fm
Z the fluidized bed height
f
u the mean rise velocity of a bubble in the bed.
bub
According to Grace (1984), in practice, the b ubble v olume fraction bub never exceeds 0.4.
If a higher value is calculated, should be taken as 0.4, or the bed may be operating in
bub
the turbulent fluidization regime, in ubbling bed v alidating the basis of the tw o-phase and b
models (see the subsection Hydrodynamic modeling of bubbling fluidization).
Then,
Z fm
Z (3.477)
f
1
bub
The mean bed voidage is

(1 ) (1 ) (3.478)
)(1
f bub fm
where is the bed voidage at the minimum fluidization value of velocity. Then, in order
fm
to evaluate the fluidized bed height and the corresponding voidage, the u value is needed
bub
(see the subsection Hydrodynamic modeling of bubbling fluidization).