470
Chapter 10
sulphate is given by Eq. 1.
c* = 5.909 10-6expf-602 1
\
T
0.9407c,
1
+ 0.1933c,
M atm
1
0
)
where cs is the molarity of the salt solution and T is in K (Linek and Vacek, 1981). All experiments were
carried out at 25 C, with 1 atm head space pressure and constant stirrer speed.
a.
Determination ofk}a by the sulphite method.
The bioreactor was filled with 10 L of water, and sulphite was added to give a concentration of 0.26 mol L
' 1
at
t =
0. The gas was turned on, and liquid samples were analyzed for sulphite concentration. The
experimental results are shown in the table below. During the experiment the dissolved oxygen
concentration can be assumed to be zero because of fast reaction. Calculate
kta
in the bioreactor and discuss
the sulphite method.
t (min)
Sulphite concentration fmMt
0
260
3
241
9
209
15
178
22
146
28
1 1 2
34
80
b.
Determination ofkta by the direct method.
We now want to determine
kp.
during a fermentation experiment, and we therefore implement an
exhaust-gas analyzer for measuring Ch and CCb. The 0 : analyzer is based on paramagnetic resonance, and
the CO, analyzer is based on infrared detection. Since the analyzers measure the partial pressures, it is
essential to dry the gas by letting it pass through a column containing Drierite (anhydrous CaS04). During
penicillin fermentation, the gas-flow rate is
1
w m (volume per volume per minute), and the working
volume is 10 L. At a certain time the Q> content in the exhaust gas is 20.63%, and the dissolved 0
2
concentration is measured to be constant at 69% of the equilibrium concentration, which is about 90% of
that in water. The gas constant is R —
0.082045 L atm mol
'1
K'1. Calculate kia during the fermentation, and
discuss the difference from the value determined by the sulphite method.
Problem 10.2. Mass transfer during fermentations with mammalian cells
Mammalian cells are shear-sensitive, and aeration is often carried out by diffusion of 0
2
across the wall of
silicone tubing placed inside the bioreactor. The inlet gas (often pure 0 2) normally has a higher pressure
than the head space pressure, which ensures a pressure drop across the wall of the silicone tubing,
k/a
for
this system depends on the pressure difference across the silicone tube wall, the temperature, and the
porosity of the silicone tubing. When very little 0
2
leaves the silicone tube through the tube wall, the 0
2
concentration is almost constant throughout the tube. It is the aim of this exercise to quantify these effects in
bioreactor with a volume of
V —
1 L.