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.
Mots clés : petroleum reservoir, thermometrics, porous medium, mixed finite elements, a posteriori estimators
@article{M2AN_2005__39_2_349_0,
author = {Amara, Mohamed and Capatina-Papaghiuc, Daniela and Denel, Bertrand and Terpolilli, Peppino},
title = {Mixed finite element approximation for a coupled petroleum reservoir model},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {349--376},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/m2an:2005015},
mrnumber = {2143952},
zbl = {1130.76045},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005015/}
}
TY - JOUR AU - Amara, Mohamed AU - Capatina-Papaghiuc, Daniela AU - Denel, Bertrand AU - Terpolilli, Peppino TI - Mixed finite element approximation for a coupled petroleum reservoir model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 349 EP - 376 VL - 39 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005015/ DO - 10.1051/m2an:2005015 LA - en ID - M2AN_2005__39_2_349_0 ER -
%0 Journal Article %A Amara, Mohamed %A Capatina-Papaghiuc, Daniela %A Denel, Bertrand %A Terpolilli, Peppino %T Mixed finite element approximation for a coupled petroleum reservoir model %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 349-376 %V 39 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005015/ %R 10.1051/m2an:2005015 %G en %F M2AN_2005__39_2_349_0
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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