S = total mass of dry solids in the bed (dry biomass plus dry residual substrate)
Fig. 25.2. Summary of the model of an intermittently-mixed, forcefully-aerated bioreactor (von Meien and Mitchell 2002). The variables shown in parentheses after the heading in each text box is the variable that is isolated in the differential term on the left hand side of the differential equation before the equation set is solved. Subscripts: s = solids phase, g = interparticle gas phase, sat = saturation. Also indicated are the meanings of several of the symbols representing key system variables
In the gas phase water balance (Fig. 25.2, lower left):
• the left hand side represents the temporal variation in the amount of water vapor in the air phase at a given position;
• the first term on the right hand side represents convective flow of water vapor with the gas phase;
• the second term on the right hand side represents the water exchange between the solid and gas phases.
In the gas phase energy balance (Fig. 25.2, upper left):
• the left hand side represents the temporal variation in the sensible energy of the dry air and water vapor in the air at a given position;
• the first term on the right hand side represents the convective flow of energy in the flowing moist air (i.e., mixture of water vapor and dry air);
• the second term on the right hand side represents the sensible heat exchange between the solid phase and the gas phase.
In the solid phase water balance (Fig. 25.2, middle right):
• the left hand side represents the temporal variation in the water content of the solids phase at a given position;
• the first term on the right hand side represents the metabolic production of water;
• the second term on the right hand side represents the exchange of water between the solid and gas phases.
In the solid phase energy balance (Fig. 25.2, upper right):
• The left hand side represents the temporal variation of the sensible energy within the dry solids and liquid water at a given position;
• the first term on the right hand side represents sensible energy exchange with the gas phase;
• the second term on the right hand side represents the removal of energy from the solid as the latent heat of evaporation;
• the third term on the right hand side represents the liberation of waste metabolic heat in the growth process.
The mixing period is modeled in a simple manner. A 15-minute long mixing event begins whenever the water activity of the outlet air (i.e., percentage relative humidity divided by 100%) falls below a predetermined value (awg*). This mixing completely inhibits growth during the mixing event, but growth is re-established as soon as static operation is resumed. During the mixing event, the bed temperature is brought back to the optimum temperature for growth and the water activity is brought back to its zero time value. The program calculates how much water needs to be added to reach this water activity. A volume-weighted average biomass content is used as the starting point for a new round of operation in packed-bed mode. It is calculated on the basis of the amount of biomass and dry solids in the various regions of the bioreactor at the time the mixing event is triggered.
Some of the assumptions that are made by the model are:
• there is no change in bed height as dry matter is consumed. Rather, the effect of the loss of solids is to decrease the density of the bed.
• maintenance metabolism is not significant. In other words, water and heat production and dry solids consumption occur only as a result of the production of new biomass.
The values of the various variables and parameters used in the base case simulation are shown in Tables 25.1 and 25.2. The simulations presented here are done for Aspergillus niger, using the same growth kinetic parameters as those used in Chap. 22. As in that case, it is possible to specify a combination of parameters either for an Aspergillus-type water relation or a Rhizopus-type water relation.
As in the well-mixed bioreactor model presented in Chap. 22, the isotherm determined for corn by Calgada (1998), described by Eq. (22.5), is used to calculate Wsat, the water content that the solids would have if they were in equilibrium with the gas in the void spaces. The relationship between the water content and the water activity of the solids is as described by Eqs. (19.8) and (19.9).
The coefficients for convective heat transfer and water transfer between the solid and gas phases are given by Eqs. (20.8) and (20.9), determined for the drying of corn (Calado 1993; Mancini 1996).
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