Abstract
A two-step model of the anaerobic digestion process is mathematically and numerically studied. The focus of the paper is put on the hydrolysis and methanogenesis phases when applied to the digestion of waste with a high content of solid matter: existence and stability properties of the equilibrium points are investigated. The hydrolysis step is considered a limiting step in this process using the Contois growth function for the bacteria responsible for the first degradation step. The methanogenesis step being inhibited by the product of the first reaction (which is also the substrate for the second one), and the Haldane growth rate is used for the second reaction step. The operating diagrams with respect to the dilution rate and the input substrate concentrations are established and discussed.
Highlights
Two-step models are very common in environmental engineering literature to describe engineered biological systems
The most common two-step model is used to describe the so-called ‘commensal ecological relationship’: it takes the form of a cascade of two biological reactions where one limiting substrate S1 is consumed by one microorganism/ecosystem X1 to produce S2, which serves as the main limiting substrate for a second microorganism/ecosystem X2, as schematically represented by the following reaction: published maps and institutional affilμ1 (.)
While the analysis of the general model of Anaerobic digestion (AD) initially proposed in [3] has been realized in [5], to the best of authors knowledge, a two-step model where the kinetic of the first step is modeled by generic density-dependent kinetics and the second step exhibits a Haldane-type function has never been studied in the literature
Summary
Two-step models are very common in environmental engineering literature to describe engineered biological systems. The different analyses of the class of models (1) available in the literature essentially differ on the growth rate functions used and whether a specific input for S2 is considered or not (i.e., if there is a source term S2in in the dynamic equation of S2 or not) They differ on the values (i) of the coefficient α (allowing to decouple the solid and liquid retention times) and (ii) of the mortality terms k i. While the analysis of the general model of AD initially proposed in [3] (representing acidogenesis and methanogenesis steps) has been realized in [5], to the best of authors knowledge, a two-step model where the kinetic of the first step is modeled by generic density-dependent kinetics and the second step exhibits a Haldane-type function has never been studied in the literature It is the aim of this paper to study such a generic model.
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