Quantitative integration of substrate‐inhibition kinetics and machine learning for reactor design in phenol–4‐chlorophenol biodegradation

Abstract The treatment of high‐strength phenol–4‐chlorophenol (4‐CP) mixtures is fundamentally limited by substrate inhibition and the lack of quantitative frameworks linking microbial kinetics to reactor design. This study addresses this critical gap by developing a unified, predictive framework integrating substrate‐inhibition kinetics, machine learning (ML), and reactor‐scale engineering. A defined four‐strain consortium achieved complete mineralization of 1000 mg L −1 phenol–4‐CP within 48 h under optimized conditions (45°C, pH 8.5, 12% inoculum), outperforming most reported systems at comparable or higher loads. System behaviour was rigorously characterized using multiple inhibition models, where the Haldane model provided the most physically consistent and statistically robust description ( R 2 = 0.9625; AIC = −100.31), yielding μ m = 0.034 h −1 , K S = 34.25 mg L −1 , and K i = 146.36 mg L −1 . Model validity was further confirmed through multi‐metric evaluation ( R 2 = 0.922, root mean square error [RMSE] = 0.018 (for μ ), mean absolute percentage error [MAPE] = 10.42%) and cross‐verification with ML models, where artificial neural network ( R 2 = 0.991) and support vector regression ( R 2 = 0.968 for biomass; 0.995 for degradation) demonstrated superior predictive capability. Critically, kinetic parameters were quantitatively translated into reactor design criteria. The volumetric degradation rate ( Q S = 26.11 mg L −1 h −1 ) predicted an oxygen uptake rate of ~60 mg L −1 h −1 , establishing engineering requirements of kLa ≥15 h −1 , P / V ≈ 0.8 W L −1 , and HRT ≥48 h for stable 500 L operation. This work advances beyond empirical modelling by establishing a direct, quantitative linkage between inhibition kinetics and reactor design, enabling predictive scale‐up under inhibitory conditions.