494
Chapter 11
Example 11.3. Estimation of typical cooling requirements.
We will here consider approximate cooling requirements for two stirred tank reactors; one of size 100 L,
and the other of size 50 m\ Both reactors should be able to handle an aerobic process with a cell density
of 20 g DW L
/ 1
at a specific growth rate of 0.2 h *. The overall reaction can be regarded as simply
production of biomass according to
- C H 20 - Y „ 0 2 - Y S„NH) + Y ^ C H ,,0 osN„2 + YicC 0 2 +Y4„H20
(1)
The two major sources of
heat generation in the bioreactor are the metabolic heat evolution and the
dissipated stirring power. The cooling capacity of the reactor should thus exceed the sum of these two
heat sources. The metabolic heat evolution for an aerobic process will depend on the cell density, x, and
the specific oxygen uptake rate, r0. As shown in Chapter 4, a reasonable approximation of the metabolic
heat evolution,
Qmeli
can be obtained by the simple relation
^ - = 460 103rox
(2)
V
where (if maintenance oxygen requirements are neglected)
ro =
(
3
)
For a value of
Ysx
= 0.56 C-mol/C-mol in Eq. (1), we get
Yxo =
0.735 moI/C-mol. By combining Eqs. (2)
and (3) we thus get
= 460-10i •0.735-0.2-0.813-1000 = 15270 w m ,
V
3600
A typical value for the stirring power input is 1
kW m'3. The total cooling requirement is thus
approximately 16 kW m
'3
for both reactors, or from Eq. (11.12)
u hea t =
(5)
By assuming that 50% of the total surface area from Table 11.3 is available for cooling, we get the
following requirements for the product of the heat transfer coefficient and the temperature difference
across the wall:
UmAT>
2566 W m
2
for V = 0.1 m
3
and
UHEAT>
20360 W m
’ 2
for V = 50 m
3
With an assumed maximum value of
AT of
about 20 K, this gives the requirement
UHE >
1067 W m
'2
K
1
for the larger reactor. Internal cooling coils may be considered to ensure a
sufficient cooling in this case._________________________________________________________