A mathematical model is formulated and numerically approximated to simulate reaction and separation occurring jointly in a chromatographic column. To cover realistic problems, the reversibility of the reactions and the occurrence of temperature gradients are considered. The model is formed by a system of convection-diffusion-reaction partial differential equations coupled with differential and algebraic equations. The presence of nonlinear transport dominated terms in mass and energy balance equations and stiffness of the reaction terms are the main sources of instabilities if simple numerical schemes are applied. In this work a high resolution finite volume scheme is applied to accurately solve the model equations. The numerical case studies, treating two stoichiometrically different reactions, demonstrate the degree of coupling concentration and thermal fronts. The impact of several key parameters on process performance is illustrated. The results obtained are seen as very useful to understand the velocities and shapes of concentration and thermal fronts in chromatographic reactors. They reveal potential for improving reactor performance exploiting the unavoidable non-isothermal operation. (C) 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.