In this paper, we are interested in the modelling and the finite elementapproximation of a petroleum reservoir, in axisymmetric form. The flow in theporous medium is governed by the Darcy-Forchheimer equation coupled with arather exhaustive energy equation. The semi-discretized problem is put under amixed variational formulation, whose approximation is achieved by means ofconservative Raviart-Thomas elements for the fluxes and of piecewise constantelements for the pressure and the temperature. The discrete problem thusobtained is well-posed and a posteriori error estimates are also established.Numerical tests are presented validating the developed code.