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126 3. Heterogeneous Processes and Reactor Analysis

with solids concentration higher than 36% v/v (Krishna et al., 2001). Finally the a , v erage
bubble diameter is
d bub 0.069( u s u ) 0.376
trans
d   10. 3376 (3.200)
u ( s u trans )  0.069  bub  

v
Since the velocity of a gien phase in the bubble column usually differs from the other
phases, the volumetric flow rate fraction of that phase is not equal to its corresponding
holdup, and hence the slip velocity is introduced to account for this dif ference:

u u
U sG sL (3.201)
s
h 1 h
G G
icial slurry v elocity If the operations run in the semibatch mode and the linear superf u sL is
zero, the aboould become the mean bubble rise velocity in the swarm (Shah v e equation w
et al ., 1982).

Dispersion in liquid and gas phase

Liquid phase Liquid dispersion is related to how well the gas flowing through
the reactor can mix the slurry phase. Ideal mixing is a theoretical limit whereby
any liquid molecule can moe to any other part of the reactor from one instant to the
v
next. In practice, when D LL is greater than 0.01 m 2 /s, a well-mixed behavior e xists
(NTIS, 1985).
The liquid-phase dispersion coefficient can be estimated using the Deckwer et al . (1974)
correlation (Ramachandran and Chaudhari, 1980):

D LL 2.7 D u 1.4 sG 0.3 (3.202)

where D is the reactor diameter. CGS units are used with this equation.
Koide provides correlations derived for three-phase systems and one of them is the Kato
oide, and Nishiwaki correlation (K 1995):

1 Fr 0.85
u D
D (3.203)
LL sG
13 Fr
where the Froude number is
u sG
Fr 0.5 (3.203)
gD ( )

SI units are used with this correlation. In general, the addition of solids reduces the liquid
mixing.