Mathematical analysis of an anaerobic digestion model for biogas production from solid waste

Municipal solid waste is one of the most significant sources of gas emissions. In a context of renewable energy production and greenhouse gas emission reduction, we focus on the amount of biogas produced by the anaerobic digestion of organic matter in a controlled landfill environment. We present a mathematical model describing this process from a microbiological and biochemical point of view, including the dynamics of the methane and carbon dioxide produced. A qualitative analysis of the dynamic system shows the existence of an infinite number of non-hyperbolic equilibria inducing an attractor that has been identified. Through numerical tests, we explore how the non-connectivity of the attractor resulting from the choice of growth functions can entirely transform the performance of the process, and highlight critical initial stock values that influence the amount of biogas produced.