Mathematical Modeling Approaches for Aerobic Digestion Processes in Food Industry Waste Management. A Review

This critical review examines the evolution of mathematical modeling approaches for aerobic digestion processes in food industry waste management, highlighting their role in operational optimization and dynamic prediction. Starting from mass conservation principles, simple kinetic models such as first-order and Monod models are analyzed. These models assume homogeneity and perfect mixing but fail to capture the heterogeneity of effluents rich in variable carbohydrates, proteins, and lipids. Structural limitations, such as numerical rigidity, parametric non-identifiability, and idealized assumptions that underestimate spatial gradients and stochastic fluctuations, are discussed. In continuous systems, coupled substrate-biomass-oxygen dynamics, washout phenomena, and extensions to partial differential equations for real heterogeneity are explored. Structured models such as ASM incorporate multicomponent fractions but face parameterization crises exacerbated by data scarcity in industrial settings, where less than 25% of plants use formal modeling. Emerging paradigms include hybrid mechanistic-machine learning approaches for prediction under perturbations, multiscale modeling , and spatially explicit modeling. A table distributes approaches by food matrix, revealing the dominance of simple kinetics in composting and ASM in activated sludge. Finally, a progressive selection framework based on operational objectives is proposed, balancing complexity with predictive robustness and experimental validation, emphasizing that sophistication must be justified to overcome barriers such as sensor costs and stochastic variability, thus promoting sustainable industrial adoption.