Mathematical Modeling Challenges Associated with Waste Anaerobic Biodegradability

Anaerobic digestion (AD) is a biological process, which, due to the multiple stages and microorganisms it involves, is complex to model. The feasibility of AD is highly dependent on the organic matter content, as well as physical and chemical factors that regulate the microbiological activity. Mathematical models are a constant challenge for the simulation and prediction of organic matter degradation and biogas production. This chapter is an overview of part of the great diversity of AD mathematical models from the stoichiometric and kinetic perspectives as well as microbiological and physicochemical points of view. The effect of waste composition and the changes in operational parameters on the AD modeling is analyzed. Stoichiometric, kinetic, and dynamic models are discussed. According to the review, it was confirmed that a wide number of researchers prefer the Buswell model, the first-order model, the modified Gompertz model, and the anaerobic digestion model (ADM) depending on available data and lab infrastructure. The literature related to AD modeling does not present a consensus regarding the use of statistical criteria, being a key factor to reflect the goodness of fit of the models. It was observed that there are still gaps in the co-digestion modeling due to the mixing effects on the kinetics of the anaerobic digestion. Current co-digestion models are derived from the experimental design to prove synergy or antagonism. Nevertheless, there is a need to predict the co-substrate synergy or antagonism with the kinetics, an aspect that is not solved at present using current models. To fill this scientific gap, an additive model is proposed.