Advanced Mathematical Modeling of Hydrogen and Methane Production in a Two-Stage Anaerobic Co-Digestion System

This study introduces a novel mathematical model characterizing the anaerobic co-digestion of wheat straw and waste algal biomass for hydrogen and methane production, implemented in a two-stage bioreactor system. Co-digestion can be a tool to increase biogas production utilizing difficult-to-digest organic waste by introducing easily degradable substrates. Two continuous operational regimes, with organic loading rates of 50 g/L and 33 g/L, were employed to generate the experimental datasets for model parameterization and validation, respectively. Parameter identification was achieved through dynamic experimentation, utilizing three distinct optimization algorithms: the deterministic active-set method (A-S) and the metaheuristics–genetic algorithm (GA), coyote optimization algorithm (COA), and marine predator algorithm (MPA). We assessed the predictive capability of the developed mathematical models using an independent dataset. The models demonstrated good agreement with the experimental data across all measured process variables. Notably, the MPA exhibited superior data fitting accuracy, as quantitatively confirmed by the objective function value, compared to GA, COA, and the A-S algorithm.