Mathematical Modeling Approaches for Aerobic Digestion Processes in Food Industry Waste Management: A Critical 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. In recent years, increasing pressure for sustainable waste management, circular bioeconomy strategies, and process intensification in the food industry has accelerated the development of mathematical tools for describing complex biological treatment systems, making a critical synthesis of available modeling approaches particularly timely. 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, including numerical rigidity, parametric non-identifiability, and idealized assumptions that underestimate spatial gradients and stochastic fluctuations, are examined. In continuous systems, coupled substrate–biomass–oxygen dynamics, washout phenomena, and extensions toward partial differential equations for representing real heterogeneity are explored. Structured models such as Activated Sludge Models (ASMs) incorporate multicomponent fractions but face parameterization challenges exacerbated by limited industrial data availability, as less than 25% of treatment plants currently employ formal modeling frameworks. Emerging paradigms include hybrid mechanistic–machine learning approaches for prediction under perturbations, multiscale modeling, and spatially explicit modeling. Unlike previous reviews that focus primarily on technological aspects of waste treatment, this study provides a critical comparison of modeling frameworks and their applicability to different food waste matrices. A classification table distributes approaches by food matrix, revealing the dominance of simple kinetics in composting and ASMs in activated sludge systems. Finally, a progressive model selection framework based on operational objectives is proposed, balancing model complexity with predictive robustness and experimental validation to support sustainable industrial adoption.