Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition

Abstract

Three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis are described by a system of differential equations modelling the interaction of microbial populations in a chemostat. The microbes consume and/or produce simple substrates, alcohols and fatty acids, acetic acid, and hydrogen. Acetogenic bacteria and hydrogenotrophic methanogens interact through syntrophy. The model also includes the inhibition of acetoclastic and hydrogenotrophic methanogens due to sensitivity to varying pH-levels. To examine the effects of these interactions and inhibitions, we first study an inhibition-free model and obtain results for global stability using differential inequalities together with conservation laws. For the model with inhibition, we derive conditions for existence, local stability, and bistability of equilibria and present a global stability result. A case study illustrates the effects of inhibition on the regions of stability. Inhibition introduces regions of bistability and stabilizes some equilibria.

Optimal biogas production in a model for anaerobic digestion

“…Following the derivation in [29] with the additional inclusion of microbial death rates, we obtained the following system of differential equationṡ…”

“…The complexity of this model makes a qualitative analysis very challenging. Several simplified models have been proposed such as [4,5,8,10,14,22,28,29]. These simpler models have a structure similar to ADM1 but focus on different subprocesses of anaerobic digestion.…”

“…In Sect. 2, we present the model from [29] (including microbial death rates), prove that it is well posed, and identify the equilibria. In Sect.…”

“…The present study builds on the analysis of the model derived in [29] and combines many of the features of the models considered in [3,10] and [8]. The focus is on trying to understand how to choose operating parameters in order to prevent failure of the reactor while at the same time obtaining optimal biogas production.…”

“…Intuitively, one might think that it is always the coexistence (interior) equilibrium, the one for which all classes of microorganisms survive, that results in optimal biogas production. In [29], it was suggested that the reactor dilution rate and the concentration of the nutrient in the reactor inflow should be chosen so that an equilibrium corresponding to the coexistence of all microorganisms is stable to ensure robust biogas production. However, in this study, we show that exclusion of one of the classes of microorganisms can instead result in higher biogas production.…”