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3.4 Slurry Reactors 123

Consider a bubble-free slurry. It is known that solid concentrations up to 10% can be
handled in slurry reactors (Perry and Green, 1999). Thus, for particle densities of 1–3
g/cm 3 and water as liquid phase, the maximum v alues of V / V L are 0.1–0.03, which means
S
that h S is 3.2–9.1%. Hover, for lo we w m , e.g. 2% (w/v) (g/100 cm 3 ), these values drop to
s
0.6–1.9%, which is f ol- w . Considering that on introducing the gas-phase, airly lo the total v
ume of the reactor will be een higher, the solid-phase holdup is decreased e v en more and v
becomes minimal in many practical applications.

Bubble velocity and diameter
Gogoi and Dutta (1996) proposed the Cliff–Grace–Webber correlation for the terminal bub-
ble rising velocity for turbulent slurry bubble columns (Cliff et al ., 1978; Shah et al ., 1982):

0.149
u bub,te r L M J ( 0.867) (3.180)
L d bub

where d bub is the bubble diameter and ,
4
g
)
(
M L L G (3.181)
2

3
L L
d bub bub,te u r L
Re (3.182)
bub

L
g ( d ) 2
Eo L G bub (3.183)

L
4 0.149 
 0.14
L
H EoM   (3.184)
3 

and W

J 0.94 H 0.747 for 2 59.3 H (3.185)

J 3.42 H 0.441 for H 59.3 (3.186)
The aboe equations are v v alid for M 10 3 , Eo 40, and Re 0.1.
bub
For bubble columns, the ubble oshida equation can be used for determining of b Akita–Y
diameter (Shah et al., 1982; K 1996): oide,

2
d  Dg 2  0.5 D g 3  0.12 u   0 ..12
bub 26  L   L   sG  (3.187)
D 
L  
2 L   Dg 
where D is the column diameterThis correlation has been deried for columns of 0.3 m v
.
maximum diameter and 0.07 m/s maximum gas superf. Futhermore, the b icial v elocity ub-
bles size and formation is affected by the orifice type and diameter (Figure 3.33).