Operability of continuous bioprocesses: Static behavior of a large class of unstructured models

The complete static behavior of a large class of unstructured models of con tinuous bioprocesses is classified using elementary concepts of the singula rity theory and continuation techniques. The class consists of models for w hich the cell growth rate is proportional to the rate of utilization of lim iting substrate while the kinetics of cell growth, utilization of limiting substrate and synthesis of the desired non-biomass product are allowed to a ssume general forms of substrate and product. This class of models was used extensively in the literature to model fermentation processes. Global anal ytical conditions are derived that allow the construction of a practical pi cture in the multidimensional parameter space delineating the different sta tic behavior these models can predict, including unique steady states, coex istence of wash-out conditions with non-trivial steady states and multistab ility resulting from hysteresis. These general results are applied to a num ber of experimentally validated models of fermentation processes, and allow the study of the effect of kinetic and operating parameters on the stabili ty characteristics of these models. Practical criteria are also derived for the safe operation of the bioprocesses.