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178 3. Heterogeneous Processes and Reactor Analysis

 u  d  1.167 
  sG G pe   0.9



w
   G  0.767 
  (3.398)

d
 u  sL L pe   

L
   
L    
with µ being the dynamic viscosity of w ater and / Z is in dyn/cm 3 . To convert to N/m,
P
w
multiply by 10 (1 dyn cm/s 1 g 2 10 5 N). In these equations, CGS units should be used.
s Liquid holdup in trickle bed r eactor
Although liquid holdup is mainly affected by the liquid flow rate, the shape, size, and wet-
ting characteristics of the particles, the gas flo and the initial distribution of the liq- w rate,
uid are also factored. One of the simpler correlations is that of Midoux et al . (Perry and
Green, 1999):
h 0.66 X 0.81
e,t (3.399)
1 0.66 X 0.81

where h is the total liquid holdup based on the total volume of the empty bed (m 3 /m 3 ).
e,t
This relationship is valid for 0.1 X 80.
The correlation of Sato takes into account the wall effects (Ramachandran and
Chaudhari, 1984):

h
e,t 0.185 1 3 X 0.22 (3.400)
u,m

6(1 )
a (3.401)
u,m
d
p,m
d p
d p,m d 4
1 p (3.402)
D 6(1 )

where D is the bed diameter in cm. In this equation CGS units should be used.
Pironti et al v . (1999) deried the following correlation for high Re numbers:

h e,d 0.048 Re 0.403 L,m Re 0.077 (3.403)
G,m
where
11 Re L,m 90.4
9 Re G,m 110