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196 3. Heterogeneous Processes and Reactor Analysis

and

u fm d p G d fm p
Re fm (3.455)

Note that as in the case of G , Re fm is constant when changing the fluid density .
Wen and Yu (1966) correlated the terms containing the bed voidage at incipient flu-
idization for 0.0508 < d p < 50 mm, 0.385 < < 0.935, 0.136 < < 1, and particle diam-
S
fm
eter to column diameter ratio ranging from 0.000807 to 0.25:
(1 )
fm 11 (3.456)
2 3
S fm
1 14
3 (3.457)
Sf m

Then, the minimum fluidization velocity can be calculated using the equation

Ar 1650 Re 24.5 fm Re fm 2 (3.458)

elocity This equation needs iteration to be solved for the minimum fluidization v. Wen and
Yu (1966) proposed the following correlation for the direct evaluation of the minimum flu-
idization velocity (Wen and Yu, 1966):

Re (1136 0.0408 ) 33.7 Ar 0.5 (3.459)
fm

It should be noted that eqs. (3.458) and (3.459) do not give the same results. In the case of
the gas fluidization equation, eq. (3.459) is considered to be more suitable for particles
larger than 100 µm and 0.1 Re fm 1000, whereas the minimum fluidization v elocity
for particles less than 100 µm is better estimated using the correlation of Bayens (Rhodes,
1998; Abrahamsen and Geldart, 1980):
[( ) g ] 0.934 d 1.8
u fm h G 0.87 0.066 p (3.460)
1110
G G

Here, d p is the mean siee size of the powder (SI units). v

On the fluid density variance
Eqs. (3.448) and (3.449) assume constant fluid density in other w they hold for
,
ords,
incompressible flo. However, in compressible flo the density of the fluid is a function w
,
w
of the pressure drop (see Section 5.3.4). Then, we hae to use the differential forms of
v