Mathematical modeling, analysis, and simulation of the dynamics of anaerobic digestion of biomass waste in discontinuous operation

In this paper, a new model of the anaerobic digestion of biomass waste in discontinuous operation is developed. It takes into account all its stages and is analyzed, and validated with data from related literature. It aims at better predicting the production of biogas. The methodology formulation of the new model is based, on the one hand, on the principles of energy conversion processes, the application of physicochemical laws, and the conservation of matter, and on the other hand, on the characteristics of the existing models which allow an optimal conversion. As results and conclusion, we demonstrate, through mathematical analysis, some experimental observations, namely the existence, uniqueness, positivity, and boundedness of the solutions of the new model. The validation tests of the model show that the dynamics of its solutions are in agreement with the experimental data of the literature. Stability in the production of biogas is observed from the 35th day. The results of these tests also make it possible to have and understand the evolution of variables that are not taken into account in the literature.