A Diagnostic Procedure for Identifying Isotherm Models in Liquid Chromatography

Liquid chromatography is a pivotal purification process widely used in pharmaceutical development and manufacturing. Efficient optimal design and control of the process rely heavily on mechanistic models such as the lumped pore diffusion model (POR) and the Equilibrium Dispersion Model (EDM), both popular choices owing to their simplicity and good accuracy for a wide range of applications. However, the choice of the functional form of the isotherm models, which describe the component adsorption equilibria, strongly affects the predictions of the chromatography model. While traditional isotherms perform well for simple compounds (e.g., small molecules), they often fall short for more complex separations (e.g., peptides), thus resulting in process-model mismatch, even following rigorous parameter estimation. As a remedy to this, recent advances have introduced hybrid models that integrate data-driven elements to improve the predictive accuracy, although at the cost of loss of process insight, low interpretability, and increased complexity. To address the process-model mismatch in chromatography, we have proposed a model diagnostic procedure, adapted from a diagnostic framework in kinetic models, based on a Lagrange multiplier test, to refine isotherm models that initially underfit. The procedure is demonstrated by three in-silico case studies, showing improved accuracy against experimental data without having to resort to black-box models, thus providing models that retain physical insight.