Machine learning-based breakthrough prediction and mechanistic model comparison for Rhodamine B removal using biomass-derived activated carbon

Textile effluents containing Rhodamine B (RhB) are persistent pollutants that impart strong colour, reduce light penetration and pose toxicity risks. In this study, activated carbon prepared from Spathodea campanulata pods was evaluated for continuous RhB removal in a fixed-bed column. Column runs were carried out at pH 4 with varying bed height (Z = 1, 2 and 3 cm), influent dye concentration (C₀ = 40, 60 and 80 mg/L) and volumetric flow (Q = 4, 5 and 6 mL/min). Breakthrough analysis showed that Z = 2 cm, C₀ = 60 mg/L and Q = 5 mL/min constituted a practical operating condition, giving an equilibrium capacity of 344.10 mg/g. Adams-Bohart, Thomas, Yoon-Nelson and Clark models reproduced the C/C₀ profiles with coefficient of determination (R²) in the range 0.9160–0.9879 and yielded parameters that showed coherent trends with the operating conditions studied. The bed depth service time (BDST) model related service time to bed height for different breakthrough limits (C/C₀ = 0.2, 0.3 and 0.4). Further, seven machine learning algorithms were trained to predict C/C₀ from Z, C₀, Q and time, among which CatBoost showed the best predictive performance, with a test R² of 0.999 and a root-mean-square error of 0.011. Feature importance, Shapley-based interpretation and partial dependence analysis identified time as the dominant predictor, followed by Z, with C₀ and Q acting as secondary modifiers. The integrated use of fixed-bed models, BDST design and interpretable machine learning provides design-relevant guidance for RhB removal using S. campanulata pod-derived activated carbon.