Biomedical Engineering Reference
In-Depth Information
which leads to
1 þ
n
S
n
A
Q
0
¼
1
n
S
n
A
f
A
Q
0
P
0
T
PT
0
F
F
0
P
0
T
PT
0
F
A
F
A
0
F
0
P
0
T
PT
0
F
A
0
F
0
Q ¼
Q
0
¼
(5.21)
and
C
j0
n
j
n
A
C
A
0
f
A
1
n
S
n
A
F
j
Q
¼
PT
0
P
0
T
C
j
¼
(5.22)
F
A
0
F
0
f
A
Using the fractional conversion
f
A
, Eqn
(5.12)
is reduced to
d
f
A
r
A
d
V ¼ F
A
0
(5.23)
Integrating Eqn
(5.23)
gives the required volume of the steady PFR for the desired fractional
conversion of
f
Ae
,
f
Ae
V ¼ F
A
0
Z
d
f
A
r
A
(5.24)
0
Correspondingly, the space time (no side inlets or outlets) for a PFR is given by
f
Ae
Q
0
¼ C
A
0
Z
V
d
f
A
r
A
s
¼
(5.25)
0
Comparing Eqn
(5.25)
with Eqn (4.8), we can observe that the behavior for a PFR is very
similar to that of a Ba
tc
h reactor. In fact, one can show that the time
t
for a batch reactor
and the residence time
t
for a steady PFR are “interchangeable.”
Table 5.2
shows a list of solu-
tions for some single reactions with simple kinetics.
Example 5-1. An elementary first-order reaction:
B
is to be carried out in a PFR. If the rate constant
k
A
/
0.02 s
1
and the volumetric flow rate is
constant at 10 L/s, calculate the reactor volume required for 50% conversion.
Solution.
Figure E5-1
shows a schematic diagram of the constant density PFR.
¼
V
V
d
V
+
Q
0
= Q =
Q
e
C
Ae
C
Be
Q
e
C
A0
C
A
C
B
Q
A B
Q
0
C
B0
dV
FIGURE E5-1
A schematic diagram of a constant density PFR showing a differential control volume
(
V
,
V
þ
d
V
).
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