Abstract
This paper deals with thorough analysis of serial configurations of two chemostats. We establish an in-depth mathematical study of all possible steady states, and we compare the performances of the two serial interconnected chemostats with the performances of a single one. The comparison is evaluated under three different criteria. We analyze, at steady state, the minimization of the output substrate concentration, the productivity of the biomass and the biogas flow rate. We determine specific conditions, which depend on the biological parameters, the operating parameters of the model and the distribution of the total volume. These necessary and sufficient conditions provide the most efficient serial configuration of two chemostats versus one. Complementarily, this mainly helps to discern when it is not advisable to use the serial configuration instead of a simple chemostat, depending on: the considered criterion, the operating parameters fixed by the operator and the distribution of the volumes into the two tanks.
Highlights
The chemostat device was invented concomitantly by Monod [1] and Novick & Szilard [2] in 1950
This model is used for industrial applications with continuously-fed bioreactors such as wastewater treatment, see for instance [8], in physical reality, industrial applications which use large bioreactors hardly satisfy the assumption of the perfect mixed media
The output substrate concentration, the productivity of the biomass and the biogas flow rate are respectively treated in Sections 3.1, 3.2 and 3.3
Summary
The chemostat device was invented concomitantly by Monod [1] and Novick & Szilard [2] in 1950. Of growth functions and the various criteria is missing in the literature, which is the aim of the present work It is well known [4, 6] that, for the simple chemostat, the output concentration at steady steady S out is independent of the input concentration S in, provided that there is no washout, see (2.5). The output substrate concentration, the productivity of the biomass and the biogas flow rate are respectively treated in Sections 3.1, 3.2 and 3.3. Appendixes B and C contain respectively the proofs related to the output substrate concentration, the productivity of the biomass and the biogas flow rate. Appendix D contains proofs related to some of technical results of the paper
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