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136 3. Heterogeneous Processes and Reactor Analysis

v
w
,
ills,
baffled agitated system, in turbulent flo is gien by (Prasher and W 1973; Smith,
1981; Ramachandran and Chaudhari, 1984)
(3.257)
o
where is a correction f , actor
Q Q
, G 3.5 10 G 2 (3.258)
1.26
1
ND 3 ND
a a
Q G Q G 2
0.62 1.85 , 3 3.5 10 (3.259)
ND ND
a a
with Q G being the gas flow rate in cm 3 /s, D a in cm, and N in r/s. The presence of a gas
in the vessel contents results in lowering the power required to turn an impeller at a
given speed, probably because of the lowered mean density of the mixture (T ybal, re
1980).
v v The aboe correlations hae been suggested for gas–liquid systems. In the presence of
a solid, in three-phase systems , the energy of dissipation can be approximately 25–50%
higher depending on the loading and density of particles (Ramachandran and Chaudhari,
1984).

Gas holdup and bubble size
v
Simple impeller The Calderbank correlation has been deried for stirred gas–liquid
reactors (Calderbank, 1958; Laakk onen et al ., 2005):

 uh  0.5 P  g  0.4 0.2 u   0.5
h  sG G  0.000216   L  sG  (3.260)
G 0.265   V  L 
0.6 L 0 . .265  

where h G is the fractional holdup and P g is the power consumption in aerated liquid. Then,

P g  P  1
  L (3.261)
V L M  L  L
where
M the mass of the liquid
L
a correction f actor accounting for the influence in the liquid-phase of gas
injection on the po as defined in eq. (3.257) wer consumption,
P the power consumption in a gas-free liquid system.
Furthermore, the superf icial gas v elocity u in slurry reactors is equivalent to the super-
sG
ficial gas velocity in a f ix ed bed:
Q (3.262)
u G
sG
A
where A is the cross-sectional area of the v essel.