436
Chapter 10
Assuming that the average bubble diameter is given by Eq. (10.23), we may obtain a correlation for
the specific interfacial area by using Eqs. (10.15) and (10.17):
a
a
k * * * { v t )
(10.25)
In this correlation the gas holdup,
e,
appears [not necessarily as a proportionality factor, since
k
may
be a function of
£,
according to Eq. (10.24)]. The gas holdup depends on the operating conditions,
e.g., the dissipated energy and the gas flow rate, and normally an empirical correlation is applied for
the gas holdup resulting in a correlation such as Eq. (10.26) for the specific interfacial area
(Moo-Young and Blanch, 1981).
a, = ku.
( p
1 g
y,
(10.26)
us
is the
superficial gas velocity
(the gas flow rate divided by the cross-sectional area of the tank.
Unit: m s'1). The parameters for this correlation are listed in Table 10.2 for both a coalescing and a
noncoalescing medium. Theoretically,
P
should be equal to 0.4, but for a noncoalescing medium
the dissipated energy influences the gas holdup, and
P
therefore becomes larger.
Example 10.3. Bubble size and specific interfacial area in an agitated vessel
We now consider aeration of a small pilot-plant bioreactor (total volume 41 L) by mechanical agitation
(Pedersen
et ai).
Some of the data for the tank are summarized in Table 10.3.
Table 10.2 Parameter values for the correlation in Eo. (10.26).
Coalescing
Noncoalescine
k
55
15
a
0.5
0.3
0.4
0.7
Table 10.3 Data for a sparged, mechanically mixed pilot plant bioreactor.
Svmbol
Parameter
Value
d0
Orifice diameter*
10‘3m
dj
Tank diameter
0.267 m
Vi
Liquid volume
25 L
Vg
Gas flow rate
25 L min 1
__
Power inmit
75 W
“The sparger is equipped with 10 orifices.
We first consider a system with water and air at 25 °C, i.e.,
P, = 997 kg m'3
Pg= 1.285 kgm'3