22.2.1 The System, Equations, and Assumptions
The system modeled is shown in Fig. 22.1. The bioreactor is cylindrical, with diameter D and height HB, and its sides are water-jacketed. The model is presented in summary form in Fig. 22.2.
Growth occurs according to the logistic equation in terms of the total amount of biomass in the bioreactor (X, kg). In this equation, the specific growth rate constant is affected by the temperature and water activity of the solid. To describe the effect of temperature, the "double Arrhenius equation" (Eq. (16.13)) is used to calculate a fractional growth rate nFT (i.e., ¡uT/^opt):
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