Biomedical Engineering Reference
In-Depth Information
18.4. A medium containing a vitamin is to be sterilized. Assume that the number of
spores initially present is 10
5
/L. The values of the pre-Arrhenius exponential factor
and E
ad
for the spores are k
d0
¼
10
36
min
1
and E
ad
¼
270 kJ/mol. For the
inactivation of the vitamin, the values of E
ad
and k
d0
are 40 kJ/mol and 10
4
min
1
.
The initial concentration of the vitamin is 30 mg/L. Compare the amount of active
vitamin in the sterilized medium for 10-L and 10,000-L fermentors when both are
sterilized at 121
C when we require in both cases that the probability of an
unsuccessful fermentation be 0.001. Ignore the effects of the heat-up and cool-
down periods.
18.5. Consider the data given in
Table P18.5
on the temperature changes in a 10,000-L
fermentor, which includes the heat-up and cool-down periods. Use the values for the
Arrhenius parameters given in Problem 18.4 and assume an initial spore concentration
of 10
5
/L and a vitamin concentration of 30 mg/L.
TABLE P18.5
Time, min
0
10
20
30
40
50
55
60
65
70
90
100
120
140
Temperature,
C
30
40
54
70
95
121
121
121
106
98
75
64
46
32
(a) What is the probability of a successful sterilization?
(b) What fraction of the vitamin remains undegraded?
(c) What fraction of the vitamin is degraded in the sterilization period?
(d) What fraction of the vitamin is degraded in the heat-up and cool-down
periods?
(e) What is the fraction of spores deactivated in the heat-up and cool-down cycles?
18.6. E. coli has a maximum respiration rate,
m
O
2
max
of about 240 mg-O
2
/(g-cell
$
h). It is
desired to achieve a cell mass of 20 g/cell. The k
L
a is 120 h
1
in a 1000-L reactor (800-L
working volume). A gas stream enriched in oxygen is used (i.e. 80% O
2
) which gives
a value of C
¼
28 mg/L. If oxygen becomes limiting, growth and respiration slow; for
example,
m
O
2
max
C
L
0:2
mg
m
O
2
¼
=
þC
L
L
where C
L
is the DO concentration in the fermentor. What is C
L
when the cell mass
is at 20 g/L?
18.7. The temperature history of the heating and cooling of a 40,000-L tank during
sterilization of medium is: 0
e
15 min, T
85
C; 15
e
40 min, T
121
C; 40
e
50 min,
¼
¼
30
C. The medium contains vitamins,
the most fragile of the vitamins has an activation energy for destruction of 40 kJ/mol,
and the value of k
d0
is 1
85
C; 50
e
60 min, T
55
C;
T
¼
¼
>
60 min, T
¼
10
4
min
1
. Assume vitamin destruction is first order and
the initial concentration is 50 mg/L. R is 8.314 J/(mol
$
K). The medium contains
2.5
10
3
spores/L. The spores have an E
ad
¼
270 kJ/mol, and k
d
at 121
Cis
1.02 min
1
. Estimate:
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