Biomedical Engineering Reference
In-Depth Information
The sulfite method is conducted in the presence of Cu
2
þ
, where sulfite (SO
2
3
) is oxidized
to sulfate (SO
2
4
) in a zero order reaction. The reaction is very rapid and consequently C
L
approaches zero. The rate of sulfate formation is monitored and is proportional to O
2
consumption (½ mol O
2
consumed to produce 1 mol of SO
2
4
). Mass balance of oxygen in
the reactor leads to:
d
C
SO
2
4
d
1
2
¼ K
L
a$ðC
0Þ
(18.6a)
t
d
C
SO
2
4
d
1
2C
K
L
a ¼
(18.6b)
t
where
C
SO
2
4
is the concentration of sulfate (SO
2
4
)andC
is a constant dependent
on the medium composition, pressure, and temperature and can be measured
separately.
The steady-state method uses a fermentor with active cells and may be the best method to
determine K
L
a. This method requires accurate measurement of O
2
in all gas exit streams and
reliable measurement of C
L
. Mass balance on O
2
in the gas allows rate of O
2
uptake, OUR
according to the following equation:
OUR
C
C
L
K
L
a ¼
(18.7)
OUR can be estimated with off-line measurements of a sample in a respirometer, but infor-
mation from the actual fermentor is ideal. C
is proportional to pO
2
which depends on the total
pressure and fraction of the gas that is O
2
. At sparger point, pO
2
is significantly higher than at
exit due to higher pressure and consumption in the bioreactor. Knowledge of residence time
distribution of gas bubbles is necessary to estimate a volume-averaged value of C
.
The final method is the dynamic method. This method is a simpler method that only
requires the measurement of DO and can be used under actual fermentation conditions.
Mass balance on oxygen in the reactor leads to
d
C
L
d
t
¼
OTR
OUR
(18.8a)
or
d
C
L
d
t
¼ K
L
aðC
C
L
Þm
O
2
X
(18.8b)
5 min) then turned
back on. With the gas supply off, K
L
a will be zero, and the slope of the descending curve will
give the OUR or
This method requires the air supply to be shut off for a short period (
<
m
O
2
X
:
C
L
d
d
t
¼m
O
2
X
(18.9)
Fig. 18.6
provides an example of the response of DO in a bioreactor when stopping and
restarting airflow. The DO is kept at a relatively high level when air is continuous sparged
into the reactor. When air sparging is stopped, the continuous consumption of oxygen by
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