Mathematical Analysis of a Coupled Anaerobic Digestion and In Situ Biomethanation Model for Methane Production

In the context of renewable energy production, the anaerobic biodegradation of organic matter represents an efficient tool for methane production. However, the resulting biogas contains about 60% methane and 40% carbon dioxide, which limits its energetic value. To increase methane production, we study a coupled mathematical model that combines a three-stage anaerobic digestion process with hydrogenotrophic biomethanation and gas–liquid mass transfer. The coupled system is qualitatively analyzed, showing that the coupled model can admit twelve equilibria, and their local stability is subsequently investigated. Numerical simulations are performed to construct operating diagrams that identify the conditions leading to favorable methane production and to separate them from regions where microbial washout or bistability may occur. The results show that methane production is enhanced by suitable choices of the organic substrate, as well as acetate and hydrogen inflow concentrations, depending on the associated growth functions and the dilution rate. In bistable regions, high methane production can still be obtained under favorable initial concentrations.