Scale-up of Bioprocesses
495
11.3.4. Scale-up related effects on mass transfer
The fundamentals of mass transfer were covered in Chapter 10. Here we will only point out
some specific scale dependent mass transfer phenomena, which deserve special attention. The
concern over oxygen transfer was certainly the first scale-up problem faced by the early pioneers
trying to scale-up the production of penicillin in the 1940s (Humphrey, 1998). Initially, it was a
problem to give even a crude quantitative description of the transfer rate of oxygen from the gas
phase to the liquid. Systematic studies resulted in very useful correlations of the kind discussed
in Chapter 10, i.e. that the overall value of
kia
depended on the specific power input,
P/V,
and the
superficial gas velocity,
us
by equations of the type given by Eq. (11.18)
kta
=
k,ua
s
(11.18)
Although very useful, these correlations should be used with care when estimating mass transfer
at widely different scales.
Superficial gas velocity
The correlations of the kind given by Eq. (11.18) are only valid as long as the impeller is not
flooded, i.e. totally immersed in gas. A perhaps not immediately obvious consequence of scale-
up is that the ratio between aeration rate and liquid volume may need to be changed. The aeration
rate is often specified in w
m,
or
volume o f gas per volume o f liquid per minute
(e.g. m
3
gas m
3
liquid min'1). As seen in Table 11.5, the superficial gas velocity,
us,
increases as
r 73
if the same
wm-value is maintained. If the superficial gas velocity exceeds the bubble rise velocity,
ub,
flooding will definitely occur. For a broth viscosity about 1 mPa s,
ub
can be estimated to be
about 0.2 m s"1. Already at a superficial gas velocity approaching 25-50% of the bubble rise
velocity, flooding is likely to occur. Thus, the superficial gas velocity should be kept below 0.05
m s
' 1
to safely avoid flooding for water-like broths. However,
ub
depends strongly on viscosity,
and the allowed superficial gas velocity may therefore be an order of magnitude lower for highly
viscous media.
Surface aeration
Oxygen transfer to the liquid takes place not only via dispersed bubbles, but also via the surface.
In small scale reactors (< 501), the contribution of this surface oxygen transfer may be quite
Table 11.5. Superficial velocity as a function of scale for an aeration rate of 1 wm in a cylindrical stirred
tank reactor with h/dt= 1._____________________________________________
Reactor volume (L)
Superficial gas velocity (m s'1)
10
0.006
100
0.013
1000
0.028
10000
0.063
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