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Mixed finite element approximation for a coupled petroleum reservoir model

Published online by Cambridge University Press:  15 April 2005

Mohamed Amara ,
Daniela Capatina-Papaghiuc ,
Bertrand Denel  and
Peppino Terpolilli
Mohamed Amara
Affiliation:
Université de Pau, L.M.A. CNRS-FRE 2570, Avenue de l'Université, 64000 Pau, France. mohamed.amara@univ-pau.fr; daniela.capatina-papaghiuc@univ-pau.fr; bertrand.denel@univ-pau.fr
Daniela Capatina-Papaghiuc
Affiliation:
Université de Pau, L.M.A. CNRS-FRE 2570, Avenue de l'Université, 64000 Pau, France. mohamed.amara@univ-pau.fr; daniela.capatina-papaghiuc@univ-pau.fr; bertrand.denel@univ-pau.fr
Bertrand Denel
Affiliation:
Université de Pau, L.M.A. CNRS-FRE 2570, Avenue de l'Université, 64000 Pau, France. mohamed.amara@univ-pau.fr; daniela.capatina-papaghiuc@univ-pau.fr; bertrand.denel@univ-pau.fr
Peppino Terpolilli
Affiliation:
Total, CST Jean Feger, Avenue Larribau, 64018 Pau Cedex, France. peppino.terpolilli@total.com
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Abstract

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.

Keywords

Petroleum reservoirthermometricsporous mediummixed finite elementsa posteriori estimators.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 2 , March 2005 , pp. 349 - 376
Copyright
© EDP Sciences, SMAI, 2005

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