A novel column breakthrough model for fixed-bed adsorption based on a capacity-loading framework: A semi-mechanistic framework

Accurate simulation of breakthrough behaviour in fixed-bed columns remains a critical challenge in water treatment due to the complex interplay among solute loading, mass-transfer resistance, and progressive bed saturation. In this study, a novel capacity-loading-based breakthrough model, termed the Sutherland Capacity-Loading Model (SCLM), is developed as a semi-mechanistic framework for describing column dynamics. The model is formulated by linking solute loading to an effective capacity-resistance function. This resulted in an expression that can describe the full breakthrough profile, including the initial delay, transition, and asymptotic saturation regions. Additionally, the fitted parameters are phenomenologically interpretable in terms of time scaling, resistance and loading dynamics. The SCLM was applied to experimental data for Cu(II) adsorption onto peat moss and evaluated against established models, including the Thomas, Yan, Richards and the four-parameter Hill-logistic model. The results demonstrated that the SCLM provided closer agreement with experimental data under ideal and, most notably, non-ideal conditions exhibiting asymmetry, extended tailing, and sub-unit plateau behaviour. In addition, the model estimated column adsorption capacity with values within 1% of experimental results. The model was further extended to desorption by reformulating in terms of desorption efficiency, Ed(t) , allowing the description of recovery profiles that do not attain complete desorption. This is an important advantage over standard models, which are limited to fixed sigmoidal forms. These results indicate that the SCLM can serve as a semi-mechanistic framework for modelling both adsorption and desorption, well-suited for breakthrough curve representation, parameter estimation, and comparative evaluation.