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3.8 T Fluid–Solid Fluidized Bed Reactors o-Phase, w 197

eqs. (3.448) and (3.449), which lead to the same equation for the minimum fluidization
,
v
velocity. Still, we need a representatie value for the fluid density which appears in the
minimum fluidization equation (eqs. (3.451) and (3.452)). For this purpose, we can use the
equations developed in Section 5.3.4 for nonisobaric fed bed operation: ix
P  P d   Z 2  0.5
 1    (3.461)
P i  Z d   i P i 
where approximately Z = Z fm . Then,

P
(3.462)
P
i i
Further, an aalue of fluid density can be used: v erage v

i (3.463)
2
A trial-and-error procedure is needed. Note that when using correlations for the determi-
nation of minimum fluidization velocity (or other releant parameters) as in eqs. (3.459) v
and (3.460), it is reasonable to assume that the fluid-phase density in ed is measured at olv v
inlet or ambient conditions, and thus no correction is needed. This is why in analogy to ,
eloc- the case of the hydraulic density of solids (Section 3.9.6), the minimum fluidization v
ity is directly correlated to the inlet fluid density .

g Minimum voidae at incipient fluidization
v
The bed voidage at incipient fluidization can be ealuated using the approximations of
Wen and Wu (1996):
0.071   13
= (3.464)
fm    
S

0.091(1  )  13
fm (3.465)
fm  2 
 S 
In the case of spherical particles, the fwhich is v alue 0.414, irst equation results in the v ery
ix
close to the typical voidage of a fed bed consisting of spherical particles (0.39–0.40).
This is the reason that the voidage at incipient fluidization is considered to be approxi-
mately equal to the fixed-bed voidage for spherical particles. Using the Wen–Yu equations.
(3.456) and (3.457), the voidage at incipient fluidization is found to be between 0.41 and
0.5. For the determination of the minimum fluidization v the fed-bed porosity , elocity ix
is often used instead of the corresponding voidage at minimum fluidization . In this way,
fm
we can obtain a crude value of u v . Hoer, in practice, the voidage at the onset of flu-
we
fm
idization may be greater than When the particles are lar the predicted porosity could . ge,