|Abstract:|| A Saint-Venant-Exner model is deduced from an asymptotic analysis of the Navier-Stokes equations. The model is defined in terms of the mass transference between the static and the moving sediment layers. One of the improvements of this deduction is that the derived model accounts with an associated energy balance, a property that the classical SVE models do not have. Moreover, the model contains a modification to be incorporated to the gravitational term in order to take into account arbitrary sloping beds. Several numerical test will be presented in order to show such differences.