Non-linear statistical modeling and optimization of the electro-Fenton process for tramadol removal from aqueous media

Advanced statistical models incorporating quadratic, cubic, and interaction terms were developed to predict and optimize the electro-Fenton (EF) process for tramadol (TRA) degradation and mineralization in aqueous media. The influence of key operational parameters, including Fe²⁺ concentration, current density, reaction time, and initial contaminant concentration, was systematically analyzed to capture complex, non-linear interactions governing the EF process. The models were calibrated and validated using experimental data, and they demonstrate 100 % TRA degradation within 12 min. and a 94.3 % reduction in chemical oxygen demand (COD) after 6 h. under optimal conditions. These data provided a robust foundation for predictively modeling the degradation kinetics and mineralization efficiency. The degradation model (R 2 =0.8825) effectively described TRA removal kinetics, accounting for saturation effects and parameter interactions to enhance predictive accuracy under varying conditions. The mineralization model (R 2 =0.9266) accurately represented COD reduction over time, demonstrating the critical role of current density and Fe²⁺ concentration. Additionally, the Instantaneous Current Efficiency (ICE) model (R 2 =0.9815) optimized operational conditions by enhancing pollutant removal efficiency while reducing energy losses associated with parasitic reactions. This study highlights the potential of advanced statistical modeling to enhance the efficiency, scalability, and industrial applicability of the EF process for pharmaceutical contaminant removal. The proposed modeling framework could be extended to optimize the treatment of other emerging contaminants, supporting the large-scale deployment of EF technology in wastewater treatment.