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106 3. Heterogeneous Processes and Reactor Analysis

The above equations are the same as those of the plug-flow tubular reactor for homoge-
neous reactions (Smith, 1981; Le 1972). v enspiel, ferential form of equation (3.122) The dif
v eral equi alent forms (Le enspiel, v can be written in se 1972): v

V )d
Fx i d r ( u V )d L r ( S (3.125)
s
v
( r )d S ( M ( R)d
r )d
V
s m S R
The gas-reactant liquid-phase mass balance is
Q L C  G,z  (3.126)
C ( L,i C L,o ) K a ( L )  C L,o  ( k a )( C L,o C S ) 0
L G
f c
V L  H 
where:
K L = the oerall gas-phase mass transfer coeficient as defined in equation (3.59) v f
k f = the liquid-solid mass transfer coef icient f
a c = the external surface area of the particles per unit volume of the liquid phase
as defined in equation (3.218)
a GL = the gas-liquid interfacial area as defined in equation (3.228)
Note that the gas-phase concentration C G,z varies with the distance from the entrance z due
to the plug-flow condition. If the gas phase is in complete mixed flo then , w C G,z = C G,o .
Finally, the component mass balance around the catalyst is

( ka )C C ( r )
fc L,o S u (3.127)

These material balances could be written for both reactants.
In a typical slurry bubble column operation, the liquid velocity is one order of magni-
tude lower than the one of gas, and in general, is very lo This mode of operation can be . w
approximated by a semibatch operation. The semibatch operation is frequently used and is
the case where the liquid and the catalyst comprise a stationary phase (slurry) in the reac-
tor. In this case, the material balance, eq. (3.122) is used along with the oerall rate based v
on the bulk gas-phase concentration (see Section 3.4.6). In the follo the semibatch
wing,
operation is presented.
Gas–Liquid reaction and batch liquid (semibatch oper ation)

If the liquid phase is reacting and batch, the system becomes dynamic as the liquid phase
concentrations change with time. o simplify the reactor model, we consider the common T
case of constant gas-phase concentration. Furthermore, the liquid phase is considered to be
under complete mixing condition.
The reaction can be represented as follo ws:

a A( B( liquid) products
ga
s)