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3.6 T w o-Phase Fix ed Beds 151

The equation proposed by K ubo et al . (1983) can be used for 10 Re / 2000
p
w mode): (experiments took place in upflo

Pe 0.243 0.27 Re 0.27 (3.315)
p p
For ceramic rasching rings of diameters between 10 and 60 mm, Bennett and Goodridge
wing correlation: (1970) proposed the follo

Pe Re 0.1 0.51 (3.316)
p p

It should be noted here that particles of irregular shape result in higher degrees of axial dis-
persion and thus lower Peclet numbers.
Gas–solid fixed beds: For axial dispersion in gas–solid fixed beds, the
Edwards–Richardson correlation can be used (W 1975; en and F an, Andrigo et al ., 1999).

1 0.5 0.75

Pe p 1 9.5 Re Sc p (3.317)
Re Sc
p
This correlation has been tested on many experimental data and it is valid for 0.08 < Re
p
400 and 0.28 Sc 2.2.
For gases, Hiby proposed the following correlation for 0.04 < Re < 400 and random
p
beds of spheres (Gunn, 1968):
1 0.65 0.67

Pe   0.5 Re Sc
p p (3.318)
17  
 Re Sc p 

In Figure 3.36, the Edw ards–Richardson and Hiby correlations are compared for gas–solid
systems, while in Figure 3.37, the Edwards–Richardson and Kubo correlations are com-
pared for gas–solid and liquid–solid systems, respecti . ely v
From Figure 3.37, it is clear that the Peclet number is greater in gas–solid systems, and
thus the flow is closer to plug flow for the same Reynolds number .

Radial Mixing Radial dispersion can be viewed as a result of stream slitting and side-
stepping. A stream of fluid at a particular radial position strikes a solid particle in its axial
journey and is split into two by the collision. On a half the stream moes laterally erage, v v
to the right and the other to the left. This is happens repeatedly and the result is that the
original single stream is laterally dispersed toard the w all. w
The particle Peclet number is defined as (Carberry 1976) ,

ud p
Pe p (3.319)
D R