Mass Transfer
427
Since the interfacial concentrations are not directly measurable, we specify the overall flux o f the
considered component from the gas bubble to the liquid phase as an overall mass transfer
coefficient multiplied by the driving force in the liquid phase, i.e.,
J A — K l{cA
- c A)
(10.4)
where
cA
is the saturation concentration in the bulk liquid corresponding to the bulk gas phase:
c
(10.5)
At steady state,
JAg~ JAJ=JA
and by inserting Eqs. (10.3) and (10.5) in Eq. (10.1), we find
1
_
1
J_
K, ~ H Ak s
( 10.6)
kg
is typically, considerably larger than
kt
and for gases with large values of
HA
such as oxygen and
carbon dioxide (which have a small to moderate solubility in water) the gas-phase resistance is
therefore negligible. Thus the overall mass transfer coefficient
Kt
is approximately equal to the
mass transfer coefficient in the liquid film, i.e.,
kh
Normally
kt
is used for quantification of the mass
transfer despite the fact that in practice only
Kt
can be measured.
To find the mass transfer rate of compound A per unit of reactor volume, i.e., the volumetric mass
transfer rate
q j,
we multiply the overall flux
JA
by the gas-liquid
interfacial area
per unit liquid
volume
a
(unit: m2/m3 = m'1). Thus
q‘A = J Aa
=
k}a{c*A - c A)
(10.7)
The product of the liquid mass transfer coefficient
k,
and the specific interfacial area
a
is called the
volumetric mass transfer coefficient
or most often
kfL.
Due to the difficulties in the determination of
k,
and
a
individually, their product is normally used to specify the gas-liquid mass transfer. From
Eq. (10.7), the volumetric mass transfer rate can be calculated if
k{i
and the driving force
(ca
~
c a
) are known. The influence of the operating conditions on the value of
k/a
is discussed in
the following sections.
In a well-mixed tank,
cA,
has the same value at any position in the tank, whereas the value of
cA
depends on the gas-phase concentration. Due to consumption or production, the inlet and outlet
mole fraction of A will be different. A suitable approximation for the average driving force is the
so-called logarithmic mean driving force, in which the known saturation concentrations at the inlet
and exit from the tank are used in place of the true variable
cA.
previous page 449 Bioreaction Engineering Principles, Second Edition  read online next page 451 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off