Scale-up of Bioprocesses
493
s?
II
^ $-
(11.15)
(11.16)
-/
As size increases, cooling often becomes a larger problem than oxygen transfer. This is due to
the fact that the ratio between surface area and volume is inversely proportional to the length
scale of the reactor, if scale up is made with a conserved aspect ratio (cf Table 11.4). Since the
metabolic heat production grows linearly with volume, it is necessary to increase the heat
transfer capacity either by increasing the temperature difference across the wall, or by increasing
the heat transfer coefficient. The cooling water is normally available at around 10-15 °C, and this
temperature cannot be easily or cheaply lowered. The internal heat transfer coefficient,
or,,
can be
increased by increasing the stirrer rate, as seen from Eq (11.14). However,
at
is only a weak
function of the stirring power,
P.
From Eq (11.14) and (11.8) it can be estimated that or, oc
P015.
A doubling of the power input thus only increases the heat transfer by approximately 10%.
Furthermore, the increased power dissipation due to mixing also need to be transfered. In
practice, it is therefore necessary to complement the external wall cooling with internal coils
above a certain reactor size (see Example 11.3).
A correlation for calculation of heat transfer coefficients for internal coils will necessarily be
more complicated, since the flow pattern in the tank is influenced by the added internal
structures. An approximate correlation is given by Oldshue and Gretton (1954):
4
0.17 R e f7
Pr037
dt
(11.17)
where the left hand side of Eq (11.17) is in fact a Nusselt number based on the diameter of the
cooling tubes,
dcoii.
A word of caution is that internal coils may influence the flow pattern in a
non-desirable way, which could give stagnant zones close to the reactor wall for non-Newtonian
media (Kelly and Humphrey, 1998). Furthermore, the desire to obtain a good mixing may be in
conflict with the desire to obtain a good heat transfer. Axial flow impellers, e.g. fluid foil
impeller, which are good for mixing, may be less suitable for good heat transfer to internal coils
(Oldshue, 1989).
Table 11.4. Ratio of total outer surface area to volume for geometrically similar cylindrical reactors (ht:dt
= D
-------------------------- ,-------------------------------------
Reactor volume (m )
Surface area/ volume (m )
0.001
55.5
0.1
11.9
1
5.5
50
1.5
100
1.2
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