Biomedical Engineering Reference
In-Depth Information
t
= 0, C
A
=C
A0
,
C
B
= 0,
C
C
= 0
A
B
C
A,
B,
C
t
=
t
,C
A
,
C
B
,
C
C
FIGURE E4-8.1
A schematic diagram of the batch reactor.
k
1
C
A
K
1
þ C
A
þ K
C
C
C
k
2
C
B
K
2
þ C
B
r
B
¼ n
1B
r
1
þ n
2B
r
2
¼ r
1
r
2
¼
(E4-8.7)
k
2
C
B
K
2
þ C
B
r
C
¼ n
1C
r
1
þ n
2C
r
2
¼ r
2
¼
(E4-8.8)
Substituting Eqn
(E4-8.6)
through
(E4-8.8)
into Eqn
(E4-8.5)
, we obtain the differential
equations for the system:
d
C
A
d
k
1
C
A
K
1
þ C
A
þ K
C
C
C
¼ r
A
¼
(E4-8.9)
t
d
C
B
d
k
1
C
A
K
1
þ C
A
þ K
C
C
C
k
2
C
B
K
2
þ C
B
¼ r
B
¼
(E4-8.10)
t
d
C
C
d
k
2
C
B
K
2
þ C
B
¼ r
C
¼
(E4-8.11)
t
Now we are ready to solve the problem with an automatic integrator.
Open the excel file:
odexlims.xls
. If prompted, enable the macro. If not prompted, make sure
the macros are allowed to run from this file. You will see
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