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3.4 Slurry Reactors 119

velocity of the gas phase will be much lower in a fluid of low viscosity than in a liquid of
much higher viscosity.
gime,
For the heterogeneous flow re the Akita–Yoshida correlation deried for b v ubble
oshida,
column reactors is proposed (Akita and Y 1973; Ramachandran and Chaudhari,
1984; Behkish, 2004; K 1996): oide,
2
h gD  2  18 gD  3  112 u
H G n L L sG (3.161)
AY 4    2  0 .. 5
(1 h ) G 
L  
L (  gD )
where n 0.2 for pure liquids and nonelectrolytes, and 0.25 for electrolyte solutions. SI
units should be used with this equation. Akita and estigated the ef oshida (1973) in v fect Y
of liquid flow for liquid superfelocities up to 0.044 m/s and found that the ef icial v fect on
gas holdup is negligible. Furthermore, Fox and Degen (1990) studied the Fisher–T ropsch
synthesis in slurry bubble columns and reported that the effect of liquid flow is important
only in systems where foam is present . to have an idea of the effect of liquid flow, the fol-
lowing correlation for bubble columns has been given by Hughmark (1967) (Saxena, 1991;
Koide, 1996):

1
h
G 13
0.35         (3.162)
2  u  sG,f     W L   W L   

 
 
where
u     u  
u h   sG   sL   (3.163)
sG,f G  1  h
 h   G,f G,f   
with
u sL the superficial liquid v elocity
h G,f the gas holdup in the case of liquid flo . w
For batch liquid, u sG,f u sG . The subscript “w” in symbols denotes w. SI units ater property
are used in this equation. For the deriation of this correlation, air velocities up to 0.305
v
m/s and liquid velocities up to 0.09 m/s were used. The Hughmark correlation has been
derived for the heterogeneous flow regime. In Figure 3.31, the ef fect of liquid flo w on gas
holdup for the air–water system is presented.
It has been reported that for diameters less than 7.62 cm, the gas holdup depends on the
,
column diameter whereas it is independent of it for diameters greater than 10.2 cm
(Hughmark, 1967; Saxena, 1991). The same has been found in studies of the Fisher–Tropsch
synthesis in slurry bubble columns, where it has been reported that the effect of the column
diameter is negligible when foam is not present in the system (Fox and Degen, 1990).
Reilley et al . (1986) proposed the following correlation for turbulent bubble columns at
ambient conditions (Reilly et al ., 1986; Behkish, 2004; Sax 1991): ena,

h G 0.009 296 u sG 0.44 L 0.98
L 0.16 0.19 G (3.164)