Biomedical Engineering Reference
In-Depth Information
Mole balance for species A over the differential volume between
V
and
V
þ
d
V
at steady
state leads to
d
ðQC
A
Þþr
A
d
V ¼ 0
(E5-1.1)
which leads to
d
f
A
r
A
¼
d
f
A
kC
A
¼ QC
A
0
d
f
A
kC
A
0
1 f
A
Q
0
C
A
0
d
V ¼ QC
A
0
(E5-1.2)
Therefore
Q
k
d
f
A
1 f
A
d
V ¼
(E5-1.3)
Integration of
Eqn (E5-1.3)
leads to
Q
k
lnð1 f
A
Þ
V ¼
(E5-1.4)
Substituting in the volumetric flow rate, rate constant, and conversion, we obtain
10
L
=
s
V ¼
s
lnð1 0:5Þ¼346:57
L
0:02=
Example 5-2. Calculate (a) the reactor volume,
V
, (b) the residence time,
t
, and (c) the space
time,
, and (d) explain any difference between the two time scales, for the gas-phase produc-
tion of C
2
H
4
from C
2
H
6
in a cylindrical PFR of constant diameter, based on the following data
and assumptions:
s
C
2
H
6
ð
A
Þ /
C
2
H
4
ð
B
Þþ
H
2
ð
C
Þ
r ¼ kC
A
1. The feed is pure C
2
H
6
at 1 kg/s, 1000 K and 2 bar.
2.
k
0.254/min at 1000 K.
3. The reactor operates isothermally with negligible pressure drop.
4.
f
A
¼
¼
0.20 at the outlet.
5. Side reactions are negligible.
6. Ideal gas law can be used.
Solution.
Figure E5-2
shows a schematic diagram of the PFR.
Mole balance for species A over a differential volume between
V
and
V
þ
d
V
at steady
state leads to
d
F
A
þ r
A
d
V ¼ 0
(E5-2.1)
V
V
d
V
+
F
Ae
F
Be
F
Ce
A B + C
F
A0
dV
FIGURE E5-2
A schematic diagram of the PFR showing a differential control volume (
V
,
V þ
d
V
).
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