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Fig. 22.7. Predicted performance of a bioreactor 2 m high by 2 m diameter. In the left hand column the temperature of cooling water in the water jacket is maintained constant (Run 7) whereas in the right hand column it is controlled according to Eq. (22.6) with J=3 (Run 8). (a) and (d) Predicted growth (—) compared to that which would be achieved if optimal conditions were maintained throughout the fermentation (---); (b) and (e) Temperatures of the solids phase (top solid curve), the gas phase (middle solid curve), the bioreactor wall (bottom solid curve), and the cooling water (dashed curve); (c) and (f) Relative limitations of growth by temperature and water: (—) fractional specific growth rate based on temperature, /jPT; (---) fractional specific growth rate based on water activity, ¡j.WT

22.3.3 Effect of Scale and Operation on Contributions to Cooling of the Solids

It is interesting to explore the relative importance of the various mechanisms for removal of heat from the solids, and to explore how this relative importance varies under different operating conditions.

The operating conditions of runs 1, 3, 5, and 7 are such that wall cooling is not maximized, while the operating conditions of runs 2, 4, 6, and 8 maximize wall cooling and minimize evaporation. This is of course reflected in Fig. 22.8, which plots the contributions to cooling for these runs. Table 22.4 compares the contributions in percentage terms at the time of peak heat production.

An interesting question arises. If a water jacket is not practical on a large-scale bioreactor and heat removal through the bioreactor wall is negligible, how should the bioreactor be operated? This question becomes increasingly relevant as the scale of the bioreactor increases since it might be expected that it would become increasingly difficult to mix the solids. If good mixing is not assured, then a static layer of solids near the wall may be overly cooled by a water jacket and would provide an insulating layer preventing the cooling water from removing heat from a mixed region in the center.

Table 22.4. Comparison of the predicted contributions of the various mechanisms to the cooling of the solids at the time of peak heat production, for bioreactors at different scales and under different operating conditionsa

Run

Time (h)b

Growth (W)c

% to walld

% sensible to gasd

% evaporation11

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