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130 3. Heterogeneous Processes and Reactor Analysis

This equation has been also proposed for slurry bubble column reactors and has been
derived for water–air and glycol–air systems; 0.003 u sG 0.4, 0 u sL 0.44 m/s. SI
units should be used in this equation.
The following correlation by Yasunishi et al. has been used for slurry bubble bed
columns (Yasunishi et al., 1986; K 1996): oide,


    1  1. 55
7
k fg GL,tot 3.09 10 u1 sG   S 
L  (3.223)
   0.6(1 h ) G   
where is the volume fraction of solid in the bubble-free slurry (liquid and solid phase).
S
SI units are used for all parameters e xcept u which is in cm/s.
sG
Gas–Liquid interfacial area in slurry r eactor s
The total external bubble area per unit volume of bubble-free liquid ( a ) by definition is
GL
A l bubbles,tota
a GL (3.224)
V L

ubbles, For spherical b
A d n 2 (3.225)
bubbles,tota l bub

ubbles.
where n is the number of b The volume of liquid V can be determined as
L
follows:
V  L 
V L V  G   V  R   h L
V L V    V    h V G h V G (3.226)
 V  G  R G G
R 

where V is the total volume of the reactor, i.e. the volume of slurry (volume of liquid, g as,
R
and solids) and

d 3
V V n bub n (3.227)
G bubble
6
Then

A d 2 n 6 h
a l bubbles,tota bub G
GL 3
V L h L  d bub  d bub h L (3.228)
h G   6 n  