Biomedical Engineering Reference
In-Depth Information
which is conducted in a plug flow reactor. The feed is 50% A, 30%
B
B, and 20% inert on
a molar basis. The total inlet molar flow rate 10 mol/s which gives a total volumetric
flow rate of 0.1 m
3
/s.
(a) determine the reactor volume required to achieve 50% conversion of A.
(b) determine the reactor volume required to achieve 80% conversion of A.
The rate equation is
$
s
1
.
5.41. The intermediate R is to be produced in a steady isothermal liquid CSTR:
10
4
m
3
$
mol
1
r
A
¼
kC
A
C
B
with
k
¼
5
A
/
R
;
r
1
¼ k
1
C
A
/
;
r
2
¼ k
2
C
R
R
S
2s
1
and
k
2
¼
0.5 s
1
. Calculate the value of residence time for maximum
with
k
1
¼
yield of R,
s
maxR
. What is the conversion of A, yields of R and S if the residence time
in the reactor is
s
maxR
.
5.42. The reaction system:
A
/
R
;
r
1
¼ k
1
C
A
A
/
S
;
r
2
¼ k
2
C
B
Have activation energies of 8 and 10 kcal/mol, respectively. In a 1-L batch reactor at
100
C, the fractional yield of R is 50% and the conversion is 50% in a reaction time
of 10 min with
C
A0
¼
1 mol/L. The solvent is water and the reactor can be pressurized
as needed to maintain liquids at any given temperature.
(a) What temperature and reactor volume are required to produce 90% fractional
yield of R at 90% conversion in a CSTR using a feed of 2 mol/L A at a flow rate
of 10 L/min?
(b) Repeat a. if a PFR is used instead.
5.43. We wish to produce ethylene by the oxidative dehydrogenation of ethane. Over
a suitable catalyst the reactions and rates are found to be
C
2
H
6
þ 0:5
O
2
/
C
2
H
4
þ
H
2
O
;
r
1
¼ k
1
C
C
2
H
6
C
O
2
; r
2
¼ k
2
C
C
2
H
6
C
2
O
2
The reaction is to be run at 1000 K, where it is found that
k
1
¼
C
2
H
6
þ 3:5
O
2
/ 2
CO
2
þ 3
H
2
O
9 L/(mol
$
s) and
1670 L
2
/(mol
2
k
2
¼
$
s). The feed pressures are
p
C
2
H
6
¼
2 atm,
p
O
2
¼
1 atm, and
p
N
2
¼
4 atm. Neglect the pressure drop in the reactor and the reaction is to have a resi-
dence time such that the product contains 0.05 atm of O
2
. Assume that there is sufficient
diluent that the density remains constant.
(a) Will a PFR or a CSTR give a higher ethylene fractional yield?
(b) Will a PFR or a CSTR require the longer residence time?
(c) Calculate the fractional yield to ethylene on a carbon atom basis in PFR and CSTR
for this O
2
conversion.
(d) Set up the problem to calculate the residence times required in PFR and CSTR. (This
illustrates how complex multiple reaction systems can become and why the
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