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3.5 Agitated Slurry Reactors 133

Component mass balance around the catalyst:

(
(ka f c A )C AL,o C u A r s m ) m A r ( ) (3.241)
AS
( ka f c B ) C BL,o C u B ( r ) (3.242)
BS

where
( r ) m
( r ) uA s ( r ) (3.243)
uB mA
a a
and
Q the volumetric flow rate (G for gas and L for liquid as subscripts)
V R the reactor v olume
v
(– r ) A the oerall rate of reaction (disappearance) per unit mass of catalyst
m
A based on component
(– r ) u A the oerall rate of reaction (disappearance) per unit volume of b ubble-
v
free liquid based on component A
(– r ) u B the oerall rate of reaction (disappearance) per unit volume of b ubble-
v
free liquid based on component B.
Subscripts i and o denote the inlet and outlet concentrations of reactants, respecti . v ely
Constant gas-phase concentration In the case of constant gas-phase concentration of
A, eq. (3.236) is not needed. The rest of the model remains the same.

Gas–liquid reactions and batch liquid
Consider the reaction of the form

a A( B(1) products
g)
In this case, the model equations deri ubble column reactor are applica- ed for the slurry b v
ble. Note that if the gas-phase concentration is constant, the gas-phase material balance is
not needed (where the two reactors haferent model equations). e dif v

Gas-phase reactions and batch liquid
Consider the reaction of the form
a A(g) B(g) product s

In this case, the material balance in the liquid phase (3.238) is not applicable as both reac-
tants are gases. Furthermore, as in slurry bubble columns, if the liquid is batch, the o er- v
all rate based on the bulk gas-phase concentration is used and the oerall mass-transfer v
coefficient K o is found in the solution of the model (Chapter 5).
The gas-phase material balances can be written in the classic form of CSTR reactor
enspiel, v material balances (Le 1972):
V x
L A (3.244)
C AG,i F A,i ( r ) uA