Journal of Mathematical Biology

, Volume 78, Issue 4, pp 1067–1087 | Cite as

On the steady state optimization of the biogas production in a two-stage anaerobic digestion model

  • Térence Bayen
  • Pedro GajardoEmail author


In this paper, we study the optimization problem of maximizing biogas production at steady state in a two-stage anaerobic digestion model, which was initially proposed in Bernard et al. (Biotechnol Bioeng 75(4):424–438, 2001). Nominal operating points, consisting of steady states where the involved microorganisms coexist, are usually referred to as desired operational conditions, in particular for maximizing biogas production. Nevertheless, we prove that under some conditions related to input substrate concentrations and microorganism biology, characterized by their growth functions, the optimal steady state can be the extinction of one of the two species. We provide some numerical examples of this situation.


Anaerobic digestion Biotechnology Steady state analysis Equilibrium Optimization 

Mathematics Subject Classification

78A70 65K10 93A30 



This paper has benefited considerably from advice and comments by Andrés Donoso (CETAQUA, Chile) and Jérôme Harmand (INRA, France), although they should not be held responsible for any mistake. The authors are very grateful to them. We are also grateful to two anonymous reviewers for comments that greatly improved this manuscript. The first author would like to thank INRA Montpellier and the UMR MISTEA for providing a half year delegation during the academic year 2017–2018. This research benefited from the support of FONDECYT grant (Chile) N 1160567 and Proyecto Redes 150011 (Chile). The second author was also partially supported by Basal Project CMM Universidad de Chile.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IMAGUniv Montpellier, CNRSMontpellierFrance
  2. 2.MISTEA, Univ Montpellier, INRA, Montpellier SupAgroMontpellierFrance
  3. 3.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile

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