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3.8 T Fluid–Solid Fluidized Bed Reactors o-Phase, w 199

If we consider a total mass balance of the solids, assuming that no solids are entrained
and carried out of the bed in the case of fluidization, the total mass of the solids in the fixed
en by bed is constant and gi v

M (1 AZ ) (3.468)
tot p
where A is the cross-sectional area of the bed. Under different bed conditions, the poros-
ity and the bed height vary but the rest of the terms in this equation are constant. This
means that the porosities and the bed heights of fed and fluidized bed are related by ix

Z (1 ) Z(1 ) (3.469)
f f
At the minimum fluidization condition,

1
Z Z (3.470)
fm
1
fm
where Z fm is the bed height at incipient fluidization.
g Bed voidae in particulate fluidization
In particulate fluidization, for u s > u fm and Re p < 10, the relationship between the flu-
idized bed voidage and velocity can be deried from the Ergun equation (McCabe v et al .,
1983):

150
u 3
s f (3.471)
s 2 dg p 2 ( ) 1 f
h

The expanded bed height is
1
Z Z (3.472)
f
1 f

where Z is the fed bed height and ix is the fed bed v ix oidage.
For relatively large particles (of several millimeters) in water, the equation proposed by
Lewis, Gilliland, and Bauer (LGB) can be used (McCabe et al ., 1983):

u   1 m
 u  fm s   (3.473)
f

The e xponent m is a function of particle Reynolds number based on the minimum flu-
elocity idization v. It can be estimated by the follo wing correlation:

m 4.21 Re 0.0804 (3.474)
fm