On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π-criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation-optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash-out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square-wave forcing leads in practice to the extinction of the wash-out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters.