The system modeled is a traditional packed-bed bioreactor, as shown in Fig. 24.1. It is assumed that the bioreactor is sufficiently wide such that heat transfer to the side walls is negligible, and therefore only heat transfer in the axial direction is included in the equations.
Note that this model is relatively limited. It is aimed only at predicting temperatures within the bed. It does not aim to describe what happens with water in the bed. As such, it is only useful for processes in which the substrate can undergo large decreases in water content with only minor changes in water activity, such that growth is never water-limited. In any case, such substrates must be used if strict packed-bed operation is to be used, that is, with absolutely no mixing events. Such a substrate is nutrient impregnated hemp, used by Weber et al. (1999).
dz air flow direction axial convection, with a simplified manner of estimating evaporation, assuming the air remains saturated as the temperature increases
"storage of energy" due to temperature
conduction heat generation from growth, with growth following the logistic equation i V \
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