Application of the ADM–PVSDM Model for Interpreting Breakthrough Curves and Scaling Liquid-Phase Adsorption Systems Under Continuous Operation

Fixed-bed adsorption is widely employed in the scaling-up of liquid-phase adsorption processes because it offers significant operational advantages over batch systems. However, conventional approaches for scaling up adsorption columns are subject to important limitations. In this regard, the Axial Dispersion Model (ADM) coupled with the Pore Volume and Surface Diffusion Model (PVSDM) provides a framework capable of overcoming these constraints. In this study, ADM–PVSDM was applied predictively using equilibrium relationships and diffusion coefficients obtained from batch experiments. Model validity was assessed against nine experimental breakthrough curves, yielding an average deviation of 7.6% in breakthrough time. Furthermore, the model successfully predicted system behavior across a feed-flux range of 18–174 g h−1m−2. The integration of ADM–PVSDM was supported by the characterization of the Mass Transfer Zone (MTZ), which underpins the scaling approach proposed herein. The predicted breakthrough curves were also used to estimate MTZ length and velocity, which ranged from 0.97 to 8.7 cm and from 0.56 × 10−3 to 20 × 10−3 cm min−1, respectively, with mean percentage deviations of 6.4% and 7.3%. These predictions enabled the development of a methodology which is capable of scaling adsorption columns over a wide operational range while requiring substantially fewer experiments compared to conventional scaling methods. Finally, it was demonstrated that commonly used empirical models, such as the Bohart–Adams model, failed to predict breakthrough curves with sufficient accuracy, thus rendering them unsuitable for developing this scaling methodology.