Analytical and Numerical Solutions of Dynamic Models for Liquid Chromatography Systems

Abstract

This dissertation presents solutions of general rate models (GRMs) of non-reactive and reactive liquid chromatography with a focus on evaluating the effect of finite rates for the adsorption and desorption steps, typically considered to be in equilibrium. Such slow rates of adsorption-desorption steps influence the column efficiency and elution shapes. The model equations are partial differential equations accounting for convection, dispersion, mass transfer resistances, and/or reaction kinetics coupled with algebraic and ordinary differential equations for describing adsorption-desorption on the stationary phase. Mostly in liquid chromatography operations, the injected sample is diluted or of small volume, justifying the use of linear models for process simulation. In this study, the Laplace trans formation is applied for deriving analytical solutions of the linear model equations. To get back solutions in the original time domain, numerical Laplace inversion formula is applied. Analytical solutions are further used for deriving the Laplace domain expressions of the first four temporal moments. In some applications, mixture samples are concentrated and have large volumes, necessitating the use of nonlinear models which are not solvable analyt ically. A high resolution finite volume scheme is applied for the numerical approximation of nonlinear GRM considering core-shell particles. Several test problems are considered to compute influences of the rate constants for adsorption and desorption, axial dispersion, intraparticle diffusion resistance, film mass transfer resistance, core-radius fraction and in let boundary conditions on the elution profiles. The developed analytical and numerical solutions are helpful tools to predict dynamic behaviors inside the column and to evalu ate the influence of model parameters on the elution profiles, in particular the effects of finite rates of the intrinsic adsorption and desorption steps. They provide useful tools for sensitivity analysis, process optimization and for parameters estimation from experiments.