Mixed finite element approximation for a coupled petroleum reservoir model
Amara, Mohamed ; Capatina-Papaghiuc, Daniela ; Denel, Bertrand ; Terpolilli, Peppino1
1 Total, CST Jean Feger, Avenue Larribau, 64018 Pau Cedex, France.
ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 349-376.

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.

DOI : 10.1051/m2an:2005015
Classification : 35Q35, 65N15, 65N30, 76S05
Mots-clés : petroleum reservoir, thermometrics, porous medium, mixed finite elements, a posteriori estimators
Amara, Mohamed  ; Capatina-Papaghiuc, Daniela  ; Denel, Bertrand  ; Terpolilli, Peppino 1

1 Total, CST Jean Feger, Avenue Larribau, 64018 Pau Cedex, France. 
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Amara, Mohamed; Capatina-Papaghiuc, Daniela; Denel, Bertrand; Terpolilli, Peppino. Mixed finite element approximation for a coupled petroleum reservoir model. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 349-376. doi : 10.1051/m2an:2005015. http://www.numdam.org/articles/10.1051/m2an:2005015/

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