Various mathematical models have been proposed for well-mixed bioreactors. For example, Nagel et al. (2001b) developed a model for a well-mixed bioreactor that had the special feature of treating the intracellular and extracellular water in the substrate particle as distinct variables. The model was used to explore the on-line control of moisture content during a fermentation. dos Santos et al. (2004) developed a model of a well-mixed bioreactor that incorporated equations for the production and thermal denaturation of enzymes and this model was used to explore the potential for the high temperatures that are sometimes reached in SSF bioreactors to cause denaturation of the enzyme produced by the microorganism.

The model presented in this chapter is an extension of the model of dos Santos et al. (2004) in which the solids and gas phases are treated as different subsystems and the bioreactor wall is specifically recognized as a separate subsystem. No assumption is made as to which type of well-mixed bioreactor it represents. With appropriate selection of parameters, coefficients, and variables, the model should be able to represent any of the various well-mixed designs presented in Chap. 9.

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