Density-dependent kinetics models for a simple description of complex phenomena in macroscopic mass-balance modeling of bioreactors

From experiments originally proposed by Ardity et al. [Arditi, R., Perrin, N., Saïah, H., 1991. Functional responses and heterogeneities: an experimental test with cladocerans. Oikos 60, 69-75] in the field of fundamental ecology, this paper derives conditions under which mass balance ratio-dependent kinetics models are more appropriate (in a sense to be specified in the sequel) than substrate-dependent kinetics models to macroscopically describe bioprocesses with attached biomass. From literature results, it is also suggested that the use of Contois growth functions should be preferred to substrate-dependent kinetics when macroscopically modeling an immobilized-biomass bioreactor. The “robustness” of this result, rather based on a qualitative reasoning, is investigated in simulation and a number of fundamental properties of ratio-dependent models are highlighted. Furthermore, it is shown that ratio-dependent models are well suited to describe macroscopically bioreactors where the diffusion phenomenon is obviously one of the most important limiting factor.