R P

A Pg

Heat capacity of dry air Heat capacity of water vapor Heat capacity of the dry solids Heat capacity of liquid water Universal gas constant Air pressure within the bioreactor Enthalpy of vaporization of water Density of the gas phase in the bed

8.31x10

70225 J mol-1

1.3x1047

283356 J mol-1

8.366 x 106 J kg-biomass-1

0.3 kg-water kg-biomass-1

1006 J kg-1 °C-1 1880 J kg-1 °C-1 2500 J kg-1 °C-1 4184 J kg-1 °C-1 8.314 J mol-1 °C-1 760 mm Hgb 2.414 x 106 J kg-water-1 1.14 kg-dry-air m-3 c a The program converts all variables and parameters to a consistent set of units. Note that where "biomass" is mentioned within the units, this represents dry biomass. b Needed for the calculation of the air water activity and used in the calculation of the solids/gas heat transfer coefficient.

The model predicts that growth will be different at different heights within the bioreactor (Fig. 25.3(b)). This is due to the fact that the conditions for growth at different heights are different. Figure 25.3(c) shows the temporal substrate temperature profiles at various different heights while Fig. 25.3(d) shows the temporal substrate water activity profiles at these heights. The values of ¡uFT and ¡upw are shown in Fig. 25.3(e) and Fig. 25.3(f), respectively. These fractional specific growth rates indicate the relative effects of temperature and water activity in limiting growth. During the fermentation, both the temperature and the water activity significantly affect growth, as indicated by deviations of the fractional specific growth rates below 1.0. The tendency is for the temperature-limitation to occur first, followed by water-limitation as the bed reaches low water activities. For example, temperature limitation dominates before 20 h (Fig. 25.3(e)) while water limitation dominates at 20 h, immediately before the first mixing and water replenishment event (Fig. 25.3(f)).

Figures 25.3(c) and 25.3(d) also indicate that temperature limitations will be greater near the air outlet, that is, at the top of the bed, while water limitations will be greater in the mid sections of the bed.

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