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222 3. Heterogeneous Processes and Reactor Analysis

Note that in this case, as in the case of slurry reactors, the material balances are based
on the unit volume of the fluid (bubble) phase. The relationship between the rate e xpres-
sions is (see Section 3.1.1 for deri ation) v

1d N V
( r ) S ( r )
u vs (3.531)
V L d t V L
For each one of the three-phases in the fluidized bed ( i b, c, or e ),

V
S (3.532)
V L i

Then, the oerall rate of reaction (– v r ) per unit volume of liquid is
u
1d N
( r ) ( r ) (3.533)
u i v s
V L d t
Apart from the basic assumption of the corresponding hydraulic model, the follo wing
approach is valid for a fairly high gas flow rate. The gas flow in both the emulsion and the
cloud volume becomes so small that the flow of gas in these regions can be ne glected.
Consequently, flow through the bed occurs only in the bubble phase (Le 1972). enspiel, v
This means that f bub = 1 or in more practical terms, u s – u fm u fm . This is a real situation
in industrial catalytic reactors, which are characterized by high gas velocities, much higher
than the minimum fluidization velocity (W 1980). erther,
The Kunii-Levenspiel model can be simplified by assuming that the derive terms of ati v
eqs. (3.529) and (3.530) are unimportant compared to the rest of the terms. Furthermore,
plug flow can be assumed for gas (bubble) phase. Under these assumptions, the set of
equations reduces as follo 1976; F 1999): , ogler
,
ws (Carberry
For the bubble phase (gas phase),
C d
u bub b K bc C ( b C ) ( b,vs ) 0 (3.534)
r
b
c
z d
or
C d
u bub b ) a ll r (3.535)
r
(
0
b,u ove
z d
The oerall rate of reactant disappearance in the gas phase is v
( r ) ( ) ( C C ) (3.536)
K
r
b,u ove ll a r b b,vs bc b c
where – r b,vs is the reaction rate per unit volume of solids and (– r b,u ) overall the reaction rate
ubbles. in bubbles per unit volume of b