Mathematical study of a two-stage anaerobic model when the hydrolysis is the limiting step

Mohammed Hanaki (1) , Jérôme Harmand (2) , Zoubida Mghazli (1) , Tewfik Sari (3) , Alain Rapaport (4) , Pablo Ugalde (2)

1 Interdisciplinary Laboratory for Natural Resources and Environment
2 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]
3 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles
4 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We study mathematically and numerically a 2-step model of anaero-bic digestion process. We focus on the hydrolysis and methanogenesis phases when applied to the digestion of waste with a high content in solid matter: existence and stability properties of the equilibrium points are investigated. The hydrolysis step is considered as a limiting step in this process using the Contois growth function for the bacteria responsible for the first degradation step. The methanogenesis step being inhibited by the product of the first reaction (which is also the substrate for the second one), the Haldane growth rate is used for the second reaction step. The operating diagrams with respect to the dilution rate and the input substrate concentrations are established and discussed.

Mots clés: Anaerobic digestion; Mortality; stability analysis; operating diagram

Domaines: Systèmes dynamiques [math.DS]; Biotechnologie; Biodiversité et Ecologie

Mohammed Hanaki, Jérôme Harmand, Zoubida Mghazli, Tewfik Sari, Alain Rapaport, et al.. Mathematical study of a two-stage anaerobic model when the hydrolysis is the limiting step. 2020. ⟨hal-02531141v2⟩