Heat capacity of dry air Heat capacity of water vapor Heat capacity of liquid water Heat capacity of the bioreactor wall Heat capacity of the dry matter Universal gas constant Bed/wall heat transfer coefficient Wall/surroundings heat transfer coefficient Bed/wall contact area Bed/headspace contact area Headspace/wall contact area Wall/surroundings contact area Mass transfer coefficient for evaporation Value of W the substrate bed would have if it were in equilibrium with the headspace Overall density of the solid bed (wet basis) Overall pressure within the bioreactor Enthalpy of vaporization of water Density of the air phase

8.31x10 70225 J mol-1 1.3x1047 283356 J mol-1

1006 J kg-1 °C-1 1880 J kg-1 °C-1 4184 J kg-1 °C-1 420 J kg-1 °C-1 1000 J kg-1 °C-1 8.314 J mol-1 °C-1 W m-2 °C-1 (Eq. (20.3))

m2 (geometric principles) m2 (geometric principles)

m2 (geometric principles)

(geometric principles) kg-dry-solids s-1 m-2. (Eq. (23.1)) kg-water kg-dry-solids-1 (Eq. (19.9)) 387 kg-wet-solids m-3 760 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.

c Used in the calculation of the headspace gas mass (G, kg) and to calculate the mass flow rate of air (F, kg-dry-air s-1) from the value input as vvm.

The base case simulation conditions are similar to those used by Stuart et al. (1999). A simulation done with n = 1 is similar to their static fermentation while a simulation done with n = 10 is similar to their rolled fermentations. The predictions of the model about the magnitude and timing of the peak bed temperatures and about headspace gas temperatures at the time of the peak bed temperature are similar to experimental results obtained by Stuart et al. (1999) (Table 23.3).

The model predicts that, during static operation (i.e., with n = 1), the wall temperature will be several degrees higher than the headspace temperature, such that the headspace air receives energy not only by direct transfer of heat from the bed, but also by the more indirect route of bed to wall to headspace (Fig. 23.5(a)). For agitated operation (i.e., with n = 10), the model predicts that the headspace temperature will be slightly higher than the drum wall temperature (Fig. 23.5(c)).

Table 23.3. Comparison of experimental and predicted peak bed temperatures and of the experimental and predicted headspace temperatures at the time of the peak bed temperature

Experimental (time reached) Model prediction

Stuart et al. (1999) (time reached)

static operation (n = 1 in model)

headspace temperature 38.6°C (28 h) 37.8°C (32 h)

headspace temperature 44.0°C (36 h) 43.8°C (32 h)

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