Biomedical Engineering Reference
In-Depth Information
We obtain by substituting
Eqn (E5-10.4)
into
Eqn (E5-10.3)
,
f
A
1 þ f
A
2
0 ¼ Pk
f
1
f
A
1 þ f
A
E
f
E
b
RT
2
RT
2
P
2
k
b
(E5-10.5)
Therefore,
f
A
k
f
E
b
E
f
1 þ f
A
1 f
A
k
b
¼ P
(E5-10.6)
Also
k
f
0
exp
E
f
RT
exp
E
b
E
f
RT
k
f
k
f
0
k
b
0
k
b
¼
k
b
0
exp
¼
(E5-10.7)
E
b
RT
Therefore, the optimum temperature in the PFR is given by
E
b
E
f
E
b
E
f
k
f
!
¼
f
A
P
!
T ¼
(E5-10.8)
k
b
0
k
f
0
E
b
k
b
0
k
f
0
R ln
k
b
R ln
1 f
A
E
f
Substituting in the known numbers, we obtain
4811:16
K
f
A
1 f
A
!
T ¼
(E5-10.9)
ln
þ 10:833477
From the above equation, we observe that as the conversion (
f
A
) is increased, the required
optimum temperature decreases. Therefore, at low conversions, the optimum temperature
calculated could exceed the maximum allowed temperature. At the maximum tempera-
ture
T
350
C
623.15 K, its corresponding conversion can be determined from
Eqn
(E5-10.9)
to be
f
A
¼
¼
¼
0.206357793. Therefore, the optimum temperature progression in the
PFR is given by
8
<
623:15 K
f
A
0:20636
4811:16
K
f
A
1 f
A
!
f
A
> 0:20636
T ¼
(E5-10.10)
:
ln
þ 10:833477
The temperature progression is plotted in
Fig. E5-10
. One can observe that temperature
decreases along the length of the reactor (or space time). The maximum temperature (at
which the reaction stops) is also shown as it progresses through the reactor.
2. To determine the space time (reactor size) requirement, we must perform a mole balance to
the PFR. At steady state, the mole balance of A in the differential volume is given by
d
F
A
þ r
A
d
V ¼ 0
(E5-10.11)
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