Analysis and numerical investigation of two dynamic models for liquid chromatography

Abstract

This paper presents the analytical and numerical investigations of two established models for simulating liquid chromatographic processes namely the equilibrium dispersive and lumped kinetic models. The models are analyzed using Dirichlet and Robin boundary conditions. The Laplace transformation is applied to solve these models analytically for single component adsorption under linear conditions. Statistical moments of step responses are calculated and compared with the numerical predictions for both types of boundary conditions. The discontinuous Galerkin finite element method is proposed to numerically approximate the more general lumped kinetic model. The scheme achieves high order accuracy on coarse grids, resolves sharp discontinuities, and avoids numerical diffusion and dispersion. For validation, the results of the suggested method are compared with some flux-limiting finite volume schemes available in the literature. A good agreement of the numerical and analytical solutions for simplified cases verifies the robustness and accuracy of the proposed method. The method is also capable to solve chromatographic models also for non-linear and competitive adsorption equilibrium isotherms.