Modelling oscillatory behavior in batch fermentations

Abstract

A batch fermentation is modelled with constant and variable yield terms. It is shown that the model cannot exhibit oscillations if a constant yield term is used. Oscillations in the cell conccntration, but not in the limiting siibstrate concentration, can be simulated if ii variable yicld function of the limiting substrate is used. Conditions, for which the variable yield needs to satisfy in order to generate oscillations in the cell concentration, are discussed. The primary condition is t h a t the yield must become zero a t the same time that the specific growth rate does. Experimcntnl results exhibiting oscillatory behavior are presented and compared with the proposed model.

About biomass overyielding of mixed cultures in batch processes

“…Evidence of variable yield cultures could be deduced from observed oscillations in both continuous [11,15] or batch cultures [24,43], based on the fact that models without variable yields cannot exhibit oscillations [1,25]. Moreover, models with several species and variable yields have been also investigated in the literature but for continuous cultures [20,32] and not -at the best of author's knowledge -to characterizing overyielding in batch, as we do in the present work.…”

On the stability of periodic solutions for a product inhibition model of continuous biological reactors.

“…We observe that the yield expression Y in the form of Eq. (8) has been adopted in many articles which dealt with models of continuous fermentation processes (11,12). In fact, Crooke et al (S) argue that it is reasonable to expect that an increase in the substrate level should have a boosting effect on the cell to substrate yield at any moment in time.…”

“…As Tanner suggested in his recent work (14), part of the difficulty in scaling up is perhaps directly attributable to the neglect of such small deviations in the process of designing the large vessel. He further stated that if small irregularities in the cell growth were not just random deviation from a smoothed function, then they must be reproducible, lead to recognizable patterns, and ultimately make sense in terms of the underlying biochemical events among the growing microorganisms.Attempts along this line have been made by Lenbury et al (9,11) who showed that the yield expression must depend on both the cell and substrate levels for oscillations to occur in both the substrate and the cell concentrations.With continuous fermentation, on the other hand, oscillations in the ex-* Address reprint requests to: …”

“…Attempts along this line have been made by Lenbury et al (9,11) who showed that the yield expression must depend on both the cell and substrate levels for oscillations to occur in both the substrate and the cell concentrations.…”