Biomedical Engineering Reference
In-Depth Information
which is identical to Eqn (9.88) except we have used primes here for the kinetic constants. In
the reaction mixture (bulk fluid phase),
the concentration of A and B together are
C
0
¼
C
B
. Derive the effectiveness factor for this reaction system.
Solution
. This is a reversible kinetics case. From stoichiometry, we obtain
C
A
þ
C
A
þ C
B
¼ C
0
¼
constant
(E17-4.3)
and this is valid anywhere inside the catalyst when pseudo-steady state has established.
Thus,
Eqn (E17-4.2)
can be written in terms of
C
A
only by making use of this stoichiometry
relation,
Eqn (E17-4.3)
. That is,
k
0
½C
A
ðC
0
C
A
Þ=K
C
1 þ K
0
A
C
A
þ K
0
B
ðC
0
C
A
Þ
r
A
¼
(E17-4.4)
Let
C
0
1 þ K
C
C
0
A
¼ C
A
(E17-4.5)
Eqn
(E17-4.4)
can be further reduced to
k
0
K
0
A
K
0
B
C
0
A
1 þð
K
0
A
þ
K
C
K
0
B
Þ
C
0
=ð1 þ
K
C
Þ
K
0
A
K
0
B
1 þ
K
C
r
A
¼
þ C
0
A
(E17-4.6)
which can be reduced to
r
max
C
0
A
K
A
þ C
0
A
r
A
¼
(E17-4.7)
where
k
0
K
0
A
K
0
B
¼
ð1 þ K
C
Þk
0
K
C
ðK
0
A
K
0
B
Þ
1 þ
K
C
r
max
¼
(E17-4.8a)
K
A
¼
1 þð
K
0
A
þ
K
C
K
0
B
Þ
C
0
=ð1 þ
K
C
Þ
(E17-4.8b)
K
0
A
K
0
B
Therefore, this reversible kinetics is reduced to the same form as the irreversible kinetics
given by
Eqn (17.8)
with the exception that the concentration of A is replaced by the differ-
ence of concentration of A from the equilibrium concentration of A as given by
Eqn (E17-4.5)
.
Since the equilibrium concentration is constant, and from
Eqn (17.22)
d
d
x
D
eA
S
d
C
A
d
x
þ r
A
S ¼ 0
(17.22)
we obtain the governing equation inside the porous catalyst as
d
C
0
A
d
d
x
D
eA
S
d
x
þ r
A
S ¼ 0
(E17-4.9)
Search WWH ::
Custom Search