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3.8 T Fluid–Solid Fluidized Bed Reactors o-Phase, w 203

1.3
3 g/cm 3
2 g/cm 3
1,5 g/cm 3
1.2
1 g/cm 3

ε fm
1.1
/
ε bm

1

0.9
0 0.05 0.1 0.15 0.2 0.25
d (mm) p
Figure 3.55 The values of and v ersus d .
bm fm p

lower than 1 are not acceptable since bm cannot be lower than . In these cases, the ratio
fm
. is set equal to unity
Foscolo and Gibilaro (1984) proposed the following criterion for both gas and
liquid–solid systems:

( gd p ) 0.5   0.5 0.5 n 1
h
f
  0.56 (1 ) n t t (3.483)
u ter  h 
where is the voidage at which a transition from particulate to bubbling fluidization
t
occurs, and n is the exponent in the Richardson–Zaki equation (2.4 n 4.8). In prac-
tice, is taken equal to . The terminal v elocity u ter can be estimated using Table 3.12.
bm
t
The Foscolo–Gibilaro equation indicates multiple solutions for . Ho two solu- , er v we
t
tions at maximum are to be expected in the operating range between 0.4 and 1. The sec-
ond solution exists because bubbling beds are known to reert to particulate behavior at v
high voidages (Foscolo and Gibilaro, 1984).
To demonstrate the behavior of the Foscolo–Gilibaro equation, the following form is
used:

FC [0.56 n (1 ) ] 0.5 n 1 0 A (3.484)
t t

where
gd ( p ) 0.5   0.5
A  h f  (3.485)
u ter  h 