462
Chapter 10
Da.eg d
?
\
e
2
UJA
+ Ha
= 0
(O
where the radial distance from the center is denoted £>
. The boundary condition at the surface of the
particle is:
SA
~
SAj
fo r
4 - Rp
The symmetry of the solution requires
(
2
)
= 0 for £ = 0
(3)
d4
Eqs. (l)-(3) provide sufficient information for solving the concentration profile in the pellet.
For a zeroth order reaction, we have
Ha
=
~K
Integrating Eq. (1) and applying the boundary condition given by Eq (3) we get
d*A
_
K 4
d4
3
D a^
(4)
(5)
Eqs. (5) and (2) give
- R l )
(«)
Eq. (
6
) thus gives the concentration of A at any given position in the pellet. Since there is no
concentration dependence on the volumetric reaction rate for reaction order zero, one may get the
impression that the diffusion will have no effect at all. However, one should remember the restriction
sA
>
0
, which requires that
k R2
KorLP
6
D
(?)
If this requirement is not satisfied, the rate of diffusion will not be sufficient to provide substrate for the
reaction to proceed in the central part of the pellet, and thus
qA = 0
for
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