Fractional calculus as a generalized kinetic model for biochemical methane potential tests

Abstract

This study presents a fractional calculus model as a generalized kinetic model for estimating the maximum methane yield and degradation kinetics in biomethane potential (BMP) assays, a key analytical method in anaerobic digestion research and application. The fractional model outperformed common first-order kinetic models by yielding superior data fitting and properly managing substrate heterogeneity. The fractional model showed robust performance in mono-digestion, co-digestion and pre-treatment BMP assays with or without presence of large tailing or sigmoidal patterns in the BMP curve. The main advantage of the fractional model over other models is its ability to capture the complexities of the methane production process without losing model accuracy. Assessment of the mathematical model revealed that for fractional orders greater than 0.8 the Mittag-Leffler sequence could be transformed into a more computationally efficient exponential function.

Keywords: Anaerobic co-digestion; Anaerobic digestion; Fractional calculus; Modelling; Pre-treatments.