Study of performance criteria of serial configuration of two chemostats

Manel Dali Youcef; Alain Rapaport; Tewfik Sari; Manel Dali Youcef; Alain Rapaport; Tewfik Sari

doi:10.3934/mbe.2020332

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6278-6309. doi: 10.3934/mbe.2020332

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Study of performance criteria of serial configuration of two chemostats

1.
MISTEA, Univ Montpellier, INRAE, Institut Agro, Montpellier, France
2.
ITAP, Univ Montpellier, INRAE, Institut Agro, Montpellier, France

Received: 08 May 2020 Accepted: 04 September 2020 Published: 22 September 2020

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.
- chemostat model,
- gradostat,
- steady-state,
- global stability,
- operating diagram,
- productivity,
- biogas production
Citation: Manel Dali Youcef, Alain Rapaport, Tewfik Sari. Study of performance criteria of serial configuration of two chemostats[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6278-6309. doi: 10.3934/mbe.2020332

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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.

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