Kinetic and Thermodynamic Modeling of Heavy Metal Inhibition in Anaerobic Digestion Systems for Biogas Production

Abstract

Anaerobic digestion (AD) is a foundational technology for renewable biogas generation and the stabilisation of organic waste. Still, its operational efficiency is compromised by heavy-metal contamination in the multifaceted streams of garbage. The main issue is that most current inhibition tests rely solely on empirical and kinetic measures, which do not account for sudden digester collapse, energetic failure, and the ineffective recovery habitually observed under metal stress. This paper aimed at identifying and employing a coupled kinetic-thermodynamic model of heavy-metal inhibition to analyse mechanistically the effect of heavy-metal inhibition on anaerobic digestion systems to generate biogas. The methodology combined Monod-based microbial growth dynamics and metal-specific inhibition with a Gibbs free energy-based feasibility threshold, supported by numerical simulations, global sensitivity analysis, regression modelling, and stability regime categorization. The research findings indicated that heavy metals had a substantial impact on all key performance indicators (p < 0.001), and thermodynamic deviation had the most significant effect (η² = 0.71). Earlier energetic collapse was caused by cadmium and lead, whereas a loss of thermodynamic feasibility (ΔG′ ≥ ΔG_crit) was consistently observed before total failure in methane generation during progressive metal addition. Multi-metal exposure (especially Cd × Cu) was strongly synergistically inhibited (β = -0.42, p < 0.001), thereby cumulatively increasing the toxicity of Cd and Cu, whereas no such effect was observed for individual metals. In the global sensitivity analysis, the metal inhibition constant and the _critical Gibbs free energy threshold were identified as the preponderant controls of methane yield. The coupled model also significantly outperformed a kinetic-only formulation, reducing RMSE by 0.19-0.08, increasing R2 by 0.63-0.86, and improving failure-prediction accuracy, with improvements ranging from 61 to 89%. The Paper concludes that microbial kinetics of heavy-metal inhibition in AD are governed by both microbial energetic reachability and thermodynamic risk assessment, and recommends aligning biogas sampling, control, and regulation, as well as process mathematical modeling, with traditional kinetic indices and risk-based thermodynamics.