Phenomena Occurring Within the Substrate

Several mass- and energy-related phenomena occur within the substrate bed. The phenomena listed here are for a static substrate bed treated as a single pseudo-homogeneous phase. The situation in which the air and solid phases in the bed are treated as separate phases is covered in Sect. 4.3.3.

Metabolic heat production. The bed is the site of microbial growth, and therefore the site of metabolic heat production.

Conduction. This occurs in response to temperature gradients, with energy flowing from warmer regions to cooler regions. Depending on the bioreactor, significant temperature gradients may exist in none, one, two, or three dimensions. This conduction occurs at different rates through the solid and air phases, so typically it is useful to consider the bed as though it were a single phase with the average properties of the air and the solid (a mass-weighted average). Conduction is usually of minor importance if the bed is forcefully aerated or mixed.

Diffusion. The gas phase components (O2, CO2, and water vapor) will diffuse within the inter-particle spaces in response to any concentration gradients. Typically the contribution of diffusion to the transfer of mass across the substrate bed is only important in Group I bioreactors (tray-type bioreactors).

Convective heat transfer. This occurs if the bed is forcefully aerated. As the air moves through the bed, energy is transferred to it from the solid phase, increasing the temperature and therefore the energy of the air. Since the air is moving through the bed, it carries the energy away from the site of production, and this represents a bulk flow of energy through the bed. Note that convective heat transfer in an unmixed bed leads to the establishment of axial temperature gradients, as explained in Fig. 4.3.

Fig. 4.2. Macroscale heat and mass transfer phenomena within and between the various subsystems in the bioreactor. Key: (H) headspace; (W) wall; (B) bed; (1) Liberation of waste metabolic heat during growth and maintenance; (2) Entry of mass and energy in the inlet air; (3) Exit of mass and energy in the outlet air; (4) Conduction and diffusion within the bed (makes a negligible contribution in mixed beds); (5) Convective flow of energy and mass within the bed due to aeration; (6) Solids flow due to mixing; (7) Heat transfer from bed to wall; (8) Heat conduction within bioreactor wall; (9) Heat transfer from wall to surroundings; (10) Mass and energy transfer from the bed to the headspace (see Fig. 4.4 for more details about the exchange that occurs in the boxed area); (11) Air flow within the headspace; (12) Heat transfer from wall to headspace. Note that in the case of Group I (tray-type) bioreactors, the focus is on an individual tray

Fig. 4.2. Macroscale heat and mass transfer phenomena within and between the various subsystems in the bioreactor. Key: (H) headspace; (W) wall; (B) bed; (1) Liberation of waste metabolic heat during growth and maintenance; (2) Entry of mass and energy in the inlet air; (3) Exit of mass and energy in the outlet air; (4) Conduction and diffusion within the bed (makes a negligible contribution in mixed beds); (5) Convective flow of energy and mass within the bed due to aeration; (6) Solids flow due to mixing; (7) Heat transfer from bed to wall; (8) Heat conduction within bioreactor wall; (9) Heat transfer from wall to surroundings; (10) Mass and energy transfer from the bed to the headspace (see Fig. 4.4 for more details about the exchange that occurs in the boxed area); (11) Air flow within the headspace; (12) Heat transfer from wall to headspace. Note that in the case of Group I (tray-type) bioreactors, the focus is on an individual tray

direction of flow of saturated air saturated air

Tsoiid slightly higher than Tarriving-air

^ heat transfer to air

Tsoiid slightly higher than Tarriving-air

^ heat transfer to air air slightly warmer air increasingly warmer

the air humidity increases since water is continually evaporated from the solid as the air passes along the bed saturation curve the air humidity increases since water is continually evaporated from the solid as the air passes along the bed saturation curve

The air at a given position is almost saturated the outlet air holds more water than the inlet air (the bed is drying!)

The air at a given position is almost saturated the outlet air holds more water than the inlet air (the bed is drying!)

position

Fig. 4.3. Consequences of convective flow of air through a static bed in which an exothermic reaction is occurring in the solid phase. It is assumed the column is fed with saturated air, at a relatively low superficial velocity. (a) Mechanism by which axial temperature gradients are established; (b) Axial temperature gradient (which may not be perfectly linear); (c) Consequences of the axial temperature gradient for evaporation

Evaporation. Water evaporates from the solid into the air phase, removing energy from the solid phase in the form of the enthalpy of vaporization. The degree of evaporation depends on the saturation of the air, but even if saturated air is used to aerate a bioreactor, if the air temperature increases while the air is within the bed, the water-carrying capacity of the air increases (Fig. 4.3(c)). When the bed is treated as a single pseudo-homogeneous phase, evaporation represents a change of phase within the subsystem and not transfer between subsystems.

Convective mass transfer. As the air flows through a forcefully aerated bed it carries water vapor, O2, and CO2 with it, representing bulk flows of these components. The importance of natural convection currents in contributing to heat and mass transfer within beds that are not forcefully aerated has not been investigated.

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