This article is concerned with the numerical approximation of a nonlinear model describing the two-dimensional non-equilibrium transport of multi-component mixtures in a chromatographic column of cylindrical geometry. In contrast to previous studies, the work includes joint analysis of deviations from equilibrium and the possibility that radial concentration profiles can develop. The considered radial gradients are typically ignored, which can be problematic in the case of non perfect injections. The model consists of nonlinear convection-diffusion partial differential equations coupled with some differential and algebraic equations. A high resolution finite volume scheme is applied to solve the model equations numerically. The considered case studies include single-component, two-component and three-component elution on fixed (non-movable) beds of liquid chromatography. The developed numerical algorithm is an efficient tool to study the effects of mass transfer kinetics on the elution profiles. (C) 2016 Elsevier Ltd. All rights reserved.