Authors: Yessmine Daoud ^1,2; Nahla Abdellatif ^3,2; Jérome Harmand ⁴

• 1 Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
• 2 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
• 3 École Nationale des Sciences de l'Informatique [Manouba]
• 4 Laboratoire de Biotechnologie de l'Environnement [Narbonne]

We investigate, in this work, the effects of hydrolysis on the behavior of the anaero- bic digestion process and the production of biogas (namely, the methane and the hydrogen). Two modelisations of the hydrolysis process are involved. We consider, first, that the microbial enzymatic activity is constant, then we take into consideration an explicit hydrolytic microbial compartiment for the substrate biodegradation. The considered models include the inhibition of acetoclastic and hy- drogenotrophic methanogens. To examine the effects of these inhibitions in presence of a hydrolysis step, we first study an inhibition-free model. We determine the steady states and give sufficient and necessary conditions for their stability. The existence and stability of the steady states are illustrated by operating diagrams. We prove that modelling the hydrolysis phase by a constant enzymatic activity affects the production of methane and hydrogen. Furthermore, introducing the hydrolytic microbial compartment makes appear new steady states and affects the stability regions. We prove that the biogas production occurs at only one of the steady states according to the operating parameters and state variables and we determine the maximal rate of biogas produced, in each case.