Mixed finite element approximation for a coupled petroleum reservoir model
Université de Pau, L.M.A. CNRS-FRE 2570, Avenue de
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In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature. The discrete problem thus obtained is well-posed and a posteriori error estimates are also established. Numerical tests are presented validating the developed code.
Mathematics Subject Classification: 35Q35 / 65N15 / 65N30 / 76S05
Key words: Petroleum reservoir / thermometrics / porous medium / mixed finite elements / a posteriori estimators.
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