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3.4 Slurry Reactors 107

The conservation equation for B in the liquid phase is a batch-reactor model:
d x d C
( r ) C B BL (3.128)
uB BL,i
d t d t
Here, the subscript i denotes the initial concentration of component B in the liquid at
t 0. the material balance is used along with the o Then, erall rate based on the b ulk gas- v
phase concentration (see Section 3.4.6).
The gas-phase mass balance for A is not needed as the concentration in this phase is con-
stant. In Chapter 5, a solution is gien for the case of variable gas-phase concentration. v

Gas–liquid reactions and continuous flow of both phases under plug flow
If the process is continuous and under plug flo w , for both the gas and slurry phases, the
equations derived for trickle bed reactors are applicable (see Section 3.7.2) (Hopper et al .,
f
2001) by using the appropriate mass transfer coeficients. Note that in trickle beds, the
material balances are based on the reactor v olume.

Gas–liquid reactions and continuous flow of both phases in complete mixed flow
ed-flo
If the process is continuous and in the complete mixw mode, for both the gas and
slurry phases, the equations deri ed for agitated slurry reactors are valid (see Section 3.5.1) v
(Ramachandran and Chaudhari, 1980) by simply applying the appropriate mass transfer
coefficients. Note that in slurry-agitated reactors, the material balances are based on the
volume of the bubble-free liquid. Furthermore, in reactions of the form a A(g) + B(l) →
products, if gas phase concentration of the same treatment holds for the plug A is constant,
flow of the gas phase.
Finally, the relationship between the seeral rate expressions for slurry bubble column v
reactors is (see Section 3.1.1 for deri v ation)

1d N V S
( r ) ( r )
u vs
V L d t V L
S M V (3.129)
( r ) S ( r ) m ( R ) R
s
V V V
L L L
For slurries,
V M ( ) m
S S p s (3.130)
V L V L p

M S m (3.131)
V s
L
V R 1
V h (3.132)
L L