Mathematical analysis of an anaerobic co‐digestion model with preference function and mortality

Abstract

Anaerobic co‐digestion is defined as the simultaneous anaerobic digestion of two or more substrates. Mixing several substrates has many advantages. In particular, it can increase biogas production. In our work, we built a mathematical model to describe the anaerobic co‐digestion of two substrates, with preference and mortality of bacteria in closed mode. The existence and boundedness of positive solutions are investigated. We show that trajectories converge toward a global attractor which is composed of an infinite number of non‐hyperbolic equilibria. The choice of growth functions, for both bacteria, can completely change the performance of the process. Numerical tests are presented to illustrate the theoretical analysis. They allow the prediction of the quantities of the initial mixture for a better biogas production.