Cobalt Adsorption Kinetics in Fixed-Bed Columns: A Hybrid ANN–Yan Approach

Abstract

A hybrid predictive–mechanistic model was developed for continuous Co²⁺ removal from wastewater using fixed-bed adsorption columns packed with cellulose-derived composite adsorbents. The Artificial Neural Network (ANN) model used a feed-forward backpropagation algorithm optimised through a trial-and-error grid search to determine network topology, with an independent validation vector using early-stopping protocols to reduce overfitting. Experimental breakthrough data generated under varying influent concentrations (50–150 mg L⁻¹), flow rates (4–12 mL min⁻¹), bed heights (4–12 cm), contact times, adsorbent dosages, and adsorbent configurations were used to construct the modelling dataset. A total of 1,842 observations obtained from ten breakthrough experiments were analysed and divided into training (70%, n = 1,289) and testing (30%, n = 553) subsets. Artificial Neural Network (ANN) modelling was used to capture nonlinear relationships among operating variables, while Weibull, Yoon–Nelson, and Yan equations were evaluated for breakthrough characterisation. The ANN achieved strong predictive performance on the independent testing dataset (R² = 0.9324, RMSE = 0.2815, MAE = 0.1887), outperforming Ridge Regression, Random Forest, and Support Vector Regression benchmark models. Comparative kinetic analysis demonstrated that the Yan model provided the best representation of breakthrough behaviour, yielding R² values between 0.9931 and 0.9996 and lower error-function values than the Weibull and Yoon–Nelson models. Combining this data-driven model with the regularizing mechanistic boundaries of the Yan model demonstrates a superior predictive accuracy (R2 values approaching unity) over isolated classical kinetics. A Yan-derived kinetic correction factor was subsequently integrated with ANN predictions to account for breakthrough progression and adsorption-bed saturation. The resulting ANN–Yan hybrid framework improved predictive performance (R² = 0.9648, RMSE = 0.2141, MAE = 0.1433) while enhancing the physical interpretability of adsorption-performance prediction. Feature-importance analysis identified contact time, influent concentration, and bed height as the dominant variables influencing Co²⁺ removal efficiency. Although further validation using independent datasets and real wastewater systems is required, the proposed model provides a promising tool for adsorption modelling, process optimisation and engineering design support of cobalt-contaminated wastewater treatment systems.