Analysis of Anaerobic Digestion Model With Two Serial Interconnected Chemostats

In this paper, we study a well-known two-step anaerobic digestion model in a configuration of two chemostats in series. The model is an eight-dimensional system of ordinary differential equations. Since the reaction system has a cascade structure, the model can be reduced to a four-dimensional one. Using general growth rates, we provide an in-depth mathematical analysis of the asymptotic behavior of the system. First, we determine all the equilibria of the model where there can be fifteen equilibria with a nonmonotonic growth rate. Then, the necessary and sufficient conditions of existence and local stability of all equilibria are established according to the operating parameters: the dilution rate, the input concentrations of the two nutrients, and the distribution of the total process volume considered. The operating diagrams are then theoretically analyzed to describe the asymptotic behavior of the process according to the four control parameters. The system exhibits a rich behavior with bistability, tri-stability, and the possibility of coexistence of the two microbial species in the two bioreactors.