Formulation and mathematical analysis of a three-step model of anaerobic digestion with inhibition by ammonia

Abstract

In this work, we are interested in the construction and mathematical analysis of a three-step anaerobic digestion model (Hydrolysis–Acidogenesis–Methanogenesis). Our aim is to investigate the qualitative properties of the system. In addition to the hypotheses used for formulating the well-known baseline two-step anaerobic model, we take into account the inhibition by ammonia together with the decay rate of acidogenic and methanogenic microorganisms, and consider the hydrolysis step to determine its effect on the growth of the methanogens. By so doing, we obtain a system of six ordinary differential equations describing the whole dynamics of the aforementioned phenomenon. As far as the mathematical analysis of this model is concerned, we first prove the existence of a unique positive and bounded global solution. Then we derive local and global stability results. The proofs of the main results rely essentially on some tools from the theory of ordinary differential equations. Finally, by performing some numerical simulations, we illustrate the theoretical results obtained and highlight the key parameters acting on the model’s behavior.