Fixed bed reactors with a single fluid phase are widely used in the refining or petrochemical industries for reaction processes catalysed by a solid phase. The design criteria for industrial reactors are relatively well known. However, they rely on a one-dimensional writing and on the separate resolution of the equation of conservation of mass and energy, and of momentum. Thus, with complex geometries, the influence of hydrodynamics on the effectiveness of the catalyst bed cannot be taken into account. The calculation method proposed is based on the multi-dimensional writing and the simultaneous resolution of the local conservation equations. The example discussed concerns fixed-bed catalytic reactors. These reactors are distinguished by their annular geometry and the radial circulation of the feedstock. The flow is assumed to be axisymmetric. The reaction process is reflected by a simplified kinetic mechanism involving ten chemical species. Calculation of the hydrodynamic (mean velocities, pressure), thermal and mass fields (concentration of each species) serves to identify the influence of internal components in two industrial reactor geometries. The map of the quantity of coke formed and deposited on the catalyst, calculated by the model, reveals potential areas of poor operation.