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3.6 T w o-Phase Fix ed Beds 153

where D R is the axial dispersion coefficient. Multiplying this number with the term D /2 d , p
,
ix
where D is the fed-bed diameter we obtain the vessel radial Peclet number A lo w v . es-
,
sel radial Peclet number means better flow quality thus closer to ideal floThis is . w
because complete mixing (high D R ) in radial flow is the ideal flo w condition.
Liquid–solid fixed beds. According to Gunn (1968), for random beds of spheres
( 0.4), the radial Peclet numbers are from about 10 – 40 for 0.08 Re p 1000.
Gas–solid fixed beds. The following correlation is provided by Gunn for random beds
of spheres (1968):
1 1
(3.320)
Pe 11 Re Sc
p p
actor
,
where is the tortuosity f whose typical v In Figure 3.38, the axial alue is around 1.5.
and radial Peclet numbers for gases are compared.
From Figure 3.38, it is clear that the radial Peclet number is greater than the axial Peclet
number in gas–solid systems for the same Reynolds number .
Other comments on nonideal flow Recalling the partial differential equation for a fixed
bed (eq. (3.286)):
Z Z C C D 2 C
( ) R L
u u t zZ ( ) uZ zZ ( ) 2
s s s (3.321)
D Z  2 C 1 C 
R  
uR s o R o  ( rR o ) 2 rR o ( rR o ) 
(

12

10
Mimum value of radial Peclet number for liquids ni

8

p 6
Pe

4

2
Axial (iby) H
(Gunn) Radial
0
0.01 0.1 1 10 100 1000
Re p *Sc
Figure 3.38 Comparison of axial (Hiby) and radial (Gunn) Peclet numbers for gases (for 0.45,
Sc 1). alue corresponds to 0.05 The minimum v Re and Re 80 and is gi en by Gunn (1968). v
p p