Mass Transfer
471
a.
Show that:
Do*ff Pg ~ H oCo^
5t
RT(c*0 - c
0)
0
)
Dog is the diffusion coefficient of 0
2
in the inlet gas, pg is the concentration of 0
2
in the inlet gas,
Co
is the equilibrium concentration of 0
2
in the liquid, and
S,
is the wall thickness of the silicone
tubing.
b.
Plot
k/
versus in a system where
S ~
0*35 mm, the head space pressure is 1 atm, and the pressure in
the inlet gas is 2 atm. The temperature is 30 °C.
D0
= 0.2 10"* m
3
s
'1
and c0* (1 atm, 30 °C ) = 1.16
mmoles L'1.
c.
State
kj
as a function of the inlet gas pressure and the temperature, when the head space pressure is
1
atm.
d.
For a given length
l
and inner diameter
d„
of the tube, calculate the effect of the wall thickness on
the volumetric surface area
a.
The porosity of the tubing is e.
e.
For / = 1 m,
di =
1 mm and s = 0.40, calculate
k&
for a bioreactor in which the inlet gas is pure 0
2
with a pressure of 2 atm and a temperature of 30 °C. The head space pressure is kept constant at 1
atm, and the dissolved 0
2
concentration is measured to be 0.6 mmol L 1.
f.
From experiments at different agitation speeds, you observe that
kft
increases with the agitation
speed. How do you explain this observation?
Problem 10.3. Mass transfer in a pilot plant bioreactor
Data for determination of
kfi.
by the 85Kr method are given in the following table:
Vj fwnri
P3
fWl
kta
th-11
1.0
3000
951
0.2
3000
688
0.1
3000
598
0.05
3000
525
1.0
5000
1358
1.0
1000
440
1.0
500
268
A pilot plant bioreactor with a height-to-diameter ratio of 3:1 is equipped with two standard Rushton
turbines. The bioreactor is filled with 1 m
3
of sterile medium. The aeration rate is 1 wm, and with a total
power dissipation of 3000 W the degree of filling is 69.5% and the gas holdup is measured to be 10%. The
temperature is 30 °C, and the head space pressure is 1 atm.
a.
Calculate the superficial gas velocity
us,
the mean bubble rise velocity
ub,
and the average residence
time of gas bubbles
tb.
b.
Under the assumption that the medium is coalescing, calculate
kp
using the correlation of Eq.
(10.27) with k = 0.026,
a =
0.5, and P - 0.4. From measurements in the exhaust gas and the
dissolved oxygen concentration during a fermentation experiment, you suspect that the calculated
k/a
value is too low. You therefore decide to examine the system more carefully. Using the S5Kr
method to determine
k&
you observe the effect of variations in vs and
Pg
when the bioreactor is
filled with sterile medium. The results of the study are listed in Table 1.
Estimate the parameters for the correlation in Eq. (10.27) using these data. How do you explain that
the measured
k/a
is significantly higher than the value calculated from the literature correlation?