Analysis of anaerobic digestion model with two serial interconnected chemostats

TL;DR

This paper provides a detailed mathematical analysis of a two-step anaerobic digestion model with two serial chemostats, revealing complex stability behaviors and multiple equilibria depending on operational parameters.

Contribution

It introduces a reduced four-dimensional model from an eight-dimensional system and characterizes all steady states and their stability conditions.

Findings

Multiple steady states with up to fifteen equilibria identified.

Conditions for stability and existence of equilibria derived.

Rich dynamic behaviors including bistability and tristability analyzed.

Abstract

In this paper, we study a well known two-step anaerobic digestion model in a configuration of two chemostats in series. This model is an eight-dimensional system of ordinary differential equations. Since the reaction system has a cascade structure, we show that the eight-order 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 steady states of the model where there can be more than fifteen equilibria with a non-monotonic growth rate. Then, the necessary and sufficient conditions of existence and local stability of all steady states 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 analyzed theoretically to describe the asymptotic behavior of the process according to the four control parameters. There can be seventy regions with rich behavior where the system may exhibit bistability or tristability with the coexistence of both microbial species in the two bioreactors.