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3.4 Slurry Reactors 113

,
First-order in gas r saturated liquid-phase and constant gas-phase concen-
eactant,
tration : If the liquid phase is saturated with the gas reactant, the oerall rate can be
v
derived in terms of the bulk liquid concentration of the gas reactant by using the balance
around the catalyst:
( ka )C C ( r ) (3.146)
f c L S u
where
( r ) m k C (3.147)
u s s m S
Following the procedure described in Section 3.1.2, the rate per unit volume of bubble-free
liquid in terms of the concentration of the reactant in the liquid phase is
C
( r ) k G (3.148)
C
k
u L
H
where
1 1 1
(3.149)
k k a m k
f c s s m
Note that since the liquid is saturated with the gas reactant, the liquid-phase concentration
is in equilibrium with the bulk gas concentration.
First order in liquid reactant : In this case, the o xpressed only v erall reaction rate can be e
in terms of the bulk liquid concentration of the liquid reactant by using the mass balance
of the reactant around the catalyst:

( ka f c )C L,t C ( r ) (3.150)
u
S,t
where
k C
( r u ) m s s m S,t (3.151)

Following the procedure described in Section 3.1.2, the rate per unit volume of bubble-free
liquid in terms of the concentration of the reactant in the liquid phase is

( r u ) L,t (3.152)
C
k
where
1 1 1
(3.153)
k ka m k
f c s s m
v
In the aboe equations, the liquid and solid concentrations of liquid reactant are time-
dependent (note subscript t).