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86 3. Heterogeneous Processes and Reactor Analysis

where:
C C
x i t (3.74)
C i

erall
v
and r u is the o rate of reaction (disappearance) per unit volume of the fluid phase.
Note that this is identical to the definition of the (homogeneous) reaction rate. This is
because the restrictions of uniform concentration and temperature are satisfied in an ideal
BSTR and the volume has been assumed to be constant. Since BSTR is used mainly for
liquid-phase reactions, the latter assumption usually holds.
It should be noted here that while in catalytic systems the rate is based on the moles dis-
appearing from the fluid phase – dC / dt , and the rate has the form ( ) f ( k , C ) ,i n
r
u
adsorption and ion exchange the rate is normally based on the moles accumulated in the
solid phase and the rate is expressed per unit mass of the solid phase dq / dt where q is in
moles per unit mass of the solid phase (solid loading). Then, the rate is expressed in the
form of a partial differential diffusion equation. For spherical particles, mass transport can
fusion equation, be described by a dif written in spherical coordinates r :

q d  2 q 2 q 
r D s  (3.75)
m 2 
r
t d  t r 
where D s is the solid diffusion coefficient and q is the solid-phase concentration of the solute.
Finally, the rate of change of a species is related to the stoichiometry. For the general
reaction of the form

a A B b c C d D

, ogler the rates are (F 1999)

1 1 1 1
r A r B r r (3.76)
D
C
a b c d
Continuous flow r s eactor
In the ideal CSTR, the fluid concentration is uniform and the fluid flows in and out of the
reactor. Under the steady state condition, the accumulation term in the general material
balance, eq. (3.70), is zero. Furthermore, the exit concentration is equal to the concentra-
tion in the reactor. For a volume element of fluid ( V L ), the mass balance for the limiting
enspiel, v reactant becomes (Le 1972)

F r V ) 0 (3.77)
(
F
i o u L
where F is the molar feed rate of the limiting reactant. Subscripts i and o denote the inlet
and outlet parameters, respecti. In analogy to the batch reactor v ely ,
F
F
x i o (3.78)
F
i