Heat transfer can occur between any of the three phases, the substrate bed, the headspace gases, and the bioreactor wall (Fig. 4.2). In all bioreactor types, heat can be transferred by conduction from the substrate bed to the wall. Also, there will be heat transfer by convection between the headspace gases and the bioreactor wall, the direction of this heat transfer depending on the relative temperatures of these phases. The heat and mass transfer between the bed and headspace will depend on how the bioreactor is aerated (Fig. 4.4):
• In bioreactors that are forcefully aerated, the convective flow of the air leaving the bed and entering the headspace carries energy and mass (water vapor, O2, and CO2) across the subsystem boundary. In this case the majority of water vapor leaving the bed was already in the vapor phase.
• In bioreactors where air is only circulated past the bioreactor surface, the heat and mass transfer occur by conduction and diffusion across a static gas layer at the bed surface, to the air circulating past the bed. In this case most of the O2 and CO2 will be exchanged between the inter-particle spaces and the head-space, whereas a significant amount of water may evaporate from the exposed substrate particles.
Fig. 4.4. The difference in bed-to-headspace heat and mass transfer for unaerated and forcefully aerated beds. The regions shown here correspond to areas at the surface of the bed (see the dashed boxes within the Group I and Group II bioreactors in Fig. 4.2). In the left-hand diagram the dotted line represents the boundary between the static gas phase and the flowing gases within the headspace
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