Supercritical water oxidation is an innovative and very efficient process to treat hazardous organic waste. In order to better understand the complex physic phenomena involved in this process, and to design more efficient reactors or to insure future efficient scale-up, a simulation with the Computational Fluid Dynamics software FLUENT was carried out for a simple tubular reactor. The turbulent non-reactive flow is well-represented using the $\kappa-\epsilon$ model. Nevertheless, the $\kappa-\epsilon$ model gives better results when a source term is added to take into account the chemical reaction. Two approaches are used to model the reaction rate: an Arrhenius law and the Eddy Dissipation Concept (EDC) generally used to describe combustion reactions. The results of this simulation using Arrhenius law, are in good agreement with experimental data although a simple thermohydraulic model was used. Moreover, the sensitiveness to the inlet temperature has been demonstrated. It influences the reaction start-up and the shape of the measured wall temperature peak. Equally, the simulated temperature profiles using Eddy Dissipation Concept model are in good agreement with experimental ones. Hence, the two approaches give similar results. Nevertheless, the EDC model predicts more precisely the thermal peak location at the reactor wall.