Analysis of general rate model of linear chromatography considering finite rates of the adsorption and desorption steps

This article presents semi-analytical solutions and temporal moments of the general rate model of chromatography with a focus on evaluating the effect of finite rates for the adsorption and desorption steps, typically considered to be in equilibrium. The model equations are analytically solved in the Laplace domain and numerical Laplace inversion is applied to get back solutions in the actual time domain. The expression of first four temporal moments are derived from the analytical solutions in the Laplace domain. The derived analytical solutions and moments are helpful tools to predict dynamic behaviors inside the column and to evaluate the influence of model parameters on the elution profiles, in particular the effect of finite rates of the intrinsic adsorption and desorption steps. The correctness of analytical solutions are verified through the numerical solutions of a high resolution finite volume scheme. Several case studies are considered to quantify effects of the rate constants for adsorption and desorption, axial dispersion, film mass transfer resistance, intraparticle diffusion resistance, and inlet boundary conditions on the elution profiles.