Biomedical Engineering Reference
In-Depth Information
(a) At what rate must the product be pumped through the filter to make the product
acceptable within 2 days if the tank is mixed and the filtered product is continuously
fed back into the tank?
(b) At the pumping rate of part (a) how long will be required if the filtered product is
placed in a separate tank?
(c) Repeat parts (a) and (b) assuming the filter only removes 90% of the particles on each
pass.
5.12.
(a) Find
C
A
(
s
) and
C
B
(
s
) for the liquid reaction A
/
B with
r
¼
kC
A
C
B
in a PFR and
$
min
1
.
(b) Why cannot this reaction be carried out in a PFR with this composition?
(c) What modification would be required in a PFR to give finite conversion?
5.13. Sketch 1/
r
vs
C
A0
0.2 L mol
1
a CSTR with a feed of
C
A0
¼
2 mol/L and
C
B0
¼
0 with
k
¼
C
A
or
f
A
for A
/
products for the reactions
r
¼
kC
A
/(1
þ
KC
A
) for
0.1 min
1
, and
K
C
A0
¼
2 mol/L,
k
¼
¼
1 L/mol. From this graph, find
for 90%
s
conversion for
(a) a PFR,
(b) a CSTR,
(c) two equal-volume CSTRs,
(d) the optimal combination of reactors in series.
5.14. An irreversible first-order reaction gave 80% conversion in a batch reactor in 20 min.
(a) Calculate the total residence time for this conversion for CSTRs in series for 1, 2, 3,
and 4 equal-volume reactors.
(b) What residence time will be required for a very large number of equal-volume
CSTRs? What is the limit of (1
)
n
in the limit
n
?
5.15. (a) What is the optimum combination of ideal reactors for the reaction A
þ
k
/
N
s
/
Bifitis
autocatalytic with
r
¼
kC
A
C
B
and
C
A
¼
C
A0
,
C
B0
¼
0? What is the intermediate
concentration between reactors?
(b) Solve for 90% conversion if
C
A0
¼
$
min
1
.
5.16. In fermentation processes sugar (A) is converted to ethanol (C) as a by-product of yeast
(B) reproduction. In a simple model, we can represent this process as
0.25 L
$
mol
1
1 mol/L and
k
¼
A
/
B
þ 3C;
r ¼ kC
A
C
B
Starting with 10 weight percent sucrose (C
12
H
22
O
11
) in water and assuming that half of
the carbon atoms in the sucrose are converted into ethanol (the above stoichiometry),
find the times required to produce 3.5 weight percent alcohol (1% sucrose remaining)
for initial concentrations of yeast of 0.00001, 0.0001, 0.001, and 0.01 M. It is found that
2 h are required for this conversion if the initial yeast concentration is maintained at
1 M. Assume that the density is that of water.
5.17. The gas-phase reaction A
0.25 mol/L/h at
200
C. Starting with pure A at 1 atm, calculate the time for 95% conversion of A in
(a) a constant-volume batch reactor,
(b) a constant-pressure batch reactor.
Calculate the reactor volume to process 10 mol/h of A to this conversion in
(c) a constant-pressure PFR,
/
3B obeys zeroth-order kinetics with
r
¼
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