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202 3. Heterogeneous Processes and Reactor Analysis

ference,
specific density dif the particle size is kept within the appropriate re within gion,
0.035 d p 0.1 mm, depending on the density dif to be in the Group ference, A particles
regime (Type A fluidization). Since the minimum bubbling velocity could not be less than
the minimum fluidization v, the ratio is set equal to unity when elocity u bm u fm .
In Figure 3.54, it is clear that while approaching the limit of Group B particles (lar ge
particle density and particle size), u bm approaches u fm , as expected. On the other hand, the
difference between the two velocities is increased constantly for smaller particles and
lower particle density, while it is v ery high for d p 0.045 mm where X 0.45 = 1. This could
be useful in the case where an expanded region of particulate fluidization is desirable in
gas–solid systems.
Since in the re gion between u fm and u bm the fluidization is particulate, eq. (3.475) could
be used for the determination of bed voidage at minimum bubbling v setting , elocity u s
u bm . In Figure 3.55, bm and fm are compared to each other for Group A particles—an air
system at 20 °C ( 1, 0.4, 1000–3000 kg/m 3 , X 45 0 for d p 0.045 mm, and
p
S
X 45 1 for d p 0.045 mm). From Figure (3.52) and the specific density dif the ference,
gion, particle size is kept within the appropriate re within 0.035 d p 0.23 mm, depend-
ference, ing on the density dif to be in the Group A particles re gime.
Pavlov’s equation (3.475) is used for voidage determination at minimum b ubbling con-
ditions (for u s u bm ), and since d p 0.5 mm, the Broadhurst–Becker equation (3.466) is
used for . For a wide range of particle sizes, the values of fm and bm are close to each
fm
other, within a ratio between 0.95 and 1.1 for all particle densities. alues of V / fm ratio
bm

9
3000 kg/m 3
8 2000 kg/m 3
1000 kg/m 3
7

6

5
fm
/u
bm
4
u
3
2

1

0
0 0.02 0.04 0.06 0.08 0.1 0.12
d (mm) p

Figure 3.54 Ratio of minimum bubbling velocity to minimum fluidization v . F or d elocity p > 0.045
mm, X 45 = 0 and for d p < 0.045 mm, X 45 =1 is assumed.