Mathematical Modelling of Zinc-Induced Inhibition on Fermentative Biohydrogen Production by Granular Sludge

Biohydrogen production in anaerobic granular sludge reactors has led to the development of stable microbial communities that enhance substrate conversion rates. The fermentation process of sucrose by these microbial communities is a sustainable approach to hydrogen production, making biological dark fermentation an effective method for renewable biohydrogen generation. This study analyzed biohydrogen production data from granular sludge in a packed-bed upflow reactor processing sucrose-containing wastewater at 26 °C for more than 500 days, using multiple predictive kinetic models. The biohydrogen production data were converted to natural logarithms to improve linearity and reduce variance. The Morgan–Mercer–Flodin (MMF) model, coupled with the Multi-Objective Optimization by Ratio Analysis (MOORA) approach, achieved the best statistical results among nine tested predictive models based on error functions, including the highest adjusted R² value and the lowest RMSE, AICc, BIC, and HQC values. The MMF model successfully predicted all stages of hydrogen production sigmoidal growth while also modeling zinc-induced stimulation and inhibition effects. The combination of multi-criteria analysis (MOORA) with classical error-function analyses improved model discrimination, enabling a deeper understanding of microbial growth patterns under different environmental conditions to optimize biohydrogen production systems.