Mathematical modelling of the anaerobic digestion process with acidogenic and methanogenic biomasses

One of the most important sources of gas emissions is municipal solid waste. In the context of renewable energy production and greenhouse gas emission reduction, we are interested in the biogas produced by the decomposition process of organic matter under anaerobic conditions in a controlled landfill. We present a mathematical model of anaerobic digestion with acidogenic and methanogenic biomasses. Then, we analyze the model and show that an infinite number of non-hyperbolic equilibria induce an attractor. We give numerical results that highlight the impact of the mortality of acidogenic and methanogenic biomasses on biogas production.