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3.4 Slurry Reactors 111

Then
 a 
N tot,( 1) x N tot,i   N A,i N B,i  N A,i  a N BB,i
b

R
N N b N
tot,i A,i A,i
Also
V a N B,i
1 x
V b N B
i A,i
and thus,
 N a 
a 1 B,i
N N x  x B B 
A,i B,i B N N b
C b A,i  A,i  C
A  N  V i  N a  A,i
V i  1 B,i a x B   1 B,i x B 
 N A,i b   N A,i b 
Note that in examples 4 and 5, which represent common cases in three-phase systems, the
concentration of a pure A gas-phase is unchanged throughout the reactor volume and is
equal to the inlet one. Ho moles and reaction volume (or the gas volumetric flo w
er
,
v
we
rate) are changing during the reaction.
3.4.6 On the overall rates
“Overall rate” means the expression of the rate of the process in terms of the bulk liquid
or gas-phase concentration. The oerall rate can be expressed in terms of the bulk liquid
v
er
v
,
concentration for continuous and semibatch operation. Ho the oerall rate can be v
we
expressed in terms of bulk gas-phase concentration only in the case of a semibatch opera-
tion, i.e. continuous flow of gas and batch liquid. Both cases are analyzed in detail in the
following sections.
ver The oall rate of reaction in semibatch systems (batch liquid)
Nonreacting liquid Under the assumption of complete mixing for the liquid phase and
at steady-state conditions, mass transfer from gas to the liquid phase is equal to the mass
transfer at the liquid–solid interf ace:

C  
( k a
( Ka L GL )   H G,z C L,o   f c )(C L,o C S ) 0 (3.139)

The component mass balance around the catalyst is

( ka f c )C L,o C ( r ) (3.140)
u
S