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154 3. Heterogeneous Processes and Reactor Analysis

we hae two terms for dispersion: the axial term v

D 2 C 1 d 2 C
L p (3.322)
uZ s zZ ( ) 2 Pe p Z zZ ( ) 2
and the radial term
2
D Z  C 1 C 
R  
uR s o R o  rR ( o ) 2 rR ( o ) ( rR ) o 
1 d p Z  CC 2 1 C  (3.323)
 
Pe R R o  ( rR ) 2 rR ( ) ( rR ) 
p o o o o

,
v
ix
w
where R o is the fed-bed radius. To hae ideal flo omiting these two terms from the
equation of continuity, one of the following must apply (Carberry 1976): ,
• axial dispersion should be low (lo w D L ), thus axial Pe p should be high, and the bed
should be deep, i.e. high Z / d p
• radial dispersion should be high (high D R ), thus radial Pe p , should be lo and the bed w
should be deep and of small diameter, i.e. high Z / R o and low R / d . p The increase in Z/d p
o
fect. has the same ef
Clearly, in the absence of a radial temperature or v no radial mass trans- elocity gradient,
fer can exist unless, of course, a reaction occurs at the bed wWhen a system is adia- all.
batic, a radial temperature and concentration gradient cannot exist unless a seere radial v
,
velocity variation is encountered (Carberry 1976). Radial variations in fluid velocity can
be due to the nature of flow, e.g. in laminar flow, and in the case of radial variations in void
fraction. In general, an aerage radial velocity independent of radial position can be
v
assumed, except from pathological cases such as in very low Reynolds numbers (laminar
flow), where a parabolic profile might be anticipated.
Finally, certain geometrical analogies should be kept within the following limits to avoid
re
ybal, large-scale maldistribution of the flow (T 1980; Gunn, 1968, Carberry 1976; Chen
et al ., 1968):
Z
5
D
D
12 30
d p
(3.324)
Z
50 150
d p

where D is the bed diameter , Z is the bed height, and d p is the particle diameter. To “trans-
fer” experimental data from the small to the large unit, maldistribution and liquid holdup
should be kept at a satisfactory leel and similar in both scales. Large-scale maldistrib v u-
tion can result from inadequate initial distrib from structural deviations or patholo-
ution,
ix gies within the fed bed (Chapter 6).