Preparative chromatography attains increasing importance for the isolation and purification of value added products in the pharmaceutical industry and in biotechnology. Besides the conventional discontinuous elution mode at present in particular the continuous simulated moving bed (SMB) process attracts increasing attention. Another continuous separation process is offered by the concept of annular chromatography (AC). However, this technique still waits for an industrial breakthrough. This is partly due to the restricted quality of the packing in the annulus. However, there is also a lack of accurate description of the development of the concentration profiles in the annulus. In particular, the contribution of band broadening in the circumferential direction was not evaluated in previous studies. In this paper a 2-D-formulation of the mass balance equations of the annular chromatograph is proposed. A numerical algorithm is developed to solve the coupled system of nonlinear convection diffusion equations in an iterative manner. The streamline diffusion method on an adaptively refined mesh is used to discretize the corresponding linear convection diffusion equations. Numerical tests show the robustness of the proposed algorithm over a large range of design parameters. Model and algorithm are used to perform parametric calculations to investigate the influence of several of the model parameters on typical performance criteria of the chromatographic separation process. Special attention is given to the influence of diffusion in the circumferential direction.