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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