Mixed finite element approximation for a coupled petroleum reservoir model

Mohamed Amara; Daniela Capatina-Papaghiuc; Bertrand Denel; Peppino Terpolilli

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 2, page 349-376
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Amara, Mohamed, et al. "Mixed finite element approximation for a coupled petroleum reservoir model." ESAIM: Mathematical Modelling and Numerical Analysis 39.2 (2010): 349-376. <http://eudml.org/doc/194265>.

@article{Amara2010,
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. },
author = {Amara, Mohamed, Capatina-Papaghiuc, Daniela, Denel, Bertrand, Terpolilli, Peppino},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Petroleum reservoir; thermometrics; porous medium; mixed finite elements; a posteriori estimators.},
language = {eng},
month = {3},
number = {2},
pages = {349-376},
publisher = {EDP Sciences},
title = {Mixed finite element approximation for a coupled petroleum reservoir model},
url = {http://eudml.org/doc/194265},
volume = {39},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 2
SP - 349
EP - 376
AB - 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.
LA - eng
KW - Petroleum reservoir; thermometrics; porous medium; mixed finite elements; a posteriori estimators.
UR - http://eudml.org/doc/194265
ER -

References

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  1. C. Abchir, Modélisation des écoulements dans les réservoirs souterrains avec prise en compte des interactions puits/réservoir. Thèse de doctorat, Université de Saint-Etienne (1992).  
  2. M. Amara, D. Capatina, B. Denel and P. Terpolilli, Modelling, analysis and numerical approximation of flow with heat transfer in a petroleum reservoir, Preprint No. 0415, Université de Pau (2004) ().  URIhttp://lma.univ-pau.fr/publis/publis.php
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  9. P. Grisvard, Elliptic problems on non-smooth domains. Pitman, Boston (1985).  
  10. F. Maubeuge, M. Didek, E. Arquis, O. Bertrand and J.-P. Caltagirone, Mother: A model for interpreting thermometrics. SPE 28588 (1994).  
  11. D.Y. Peng and D.B. Robinson, A new two-constant equation of state. Ind. Eng. Chem. Fundam.15 (1976) 59–64.  
  12. J.E. Roberts and J.-M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical Analysis Vol. II. North Holland, Amsterdam (1991) 523–639.  
  13. R. Verfürth and D. Braess, A posteriori error estimator for the Raviart-Thomas element. SIAM J. Numer. Anal.33 (1996) 2431–2444.  

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