Mixed finite element approximation for a coupled petroleum reservoir model

Mohamed Amara; Daniela Capatina-Papaghiuc; Bertrand Denel; Peppino Terpolilli[1]

  • [1] Total, CST Jean Feger, Avenue Larribau, 64018 Pau Cedex, France.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • 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 - Modélisation Mathématique et Analyse Numérique 39.2 (2005): 349-376. <http://eudml.org/doc/245119>.

@article{Amara2005,
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.},
affiliation = {Total, CST Jean Feger, Avenue Larribau, 64018 Pau Cedex, France.},
author = {Amara, Mohamed, Capatina-Papaghiuc, Daniela, Denel, Bertrand, Terpolilli, Peppino},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {petroleum reservoir; thermometrics; porous medium; mixed finite elements; a posteriori estimators},
language = {eng},
number = {2},
pages = {349-376},
publisher = {EDP-Sciences},
title = {Mixed finite element approximation for a coupled petroleum reservoir model},
url = {http://eudml.org/doc/245119},
volume = {39},
year = {2005},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2005
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/245119
ER -

References

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  1. [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. [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) (http://lma.univ-pau.fr/publis/publis.php). Zbl1134.76466
  3. [3] G. Bourdarot, Well testing: Interpretation methods. Editions Technip, Paris (1998). 
  4. [4] S. Brenner and R. Scott, The mathematical theory of Finite Element Methods. Springer Verlag, New York (1994). Zbl0804.65101MR1278258
  5. [5] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag, New York (1991). Zbl0788.73002MR1115205
  6. [6] G. Chavent and J.E. Roberts, A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems. Adv. Water Resources 14 (1991) 329–348. 
  7. [7] P.G. Ciarlet, The finite element method for elliptic problems error analysis. North Holland, Amsterdam (1978). Zbl0383.65058MR520174
  8. [8] R.E. Ewing, J. Wang and S.L. Weekes, On the simulation of multicomponent gas flow in porous media. Appl. Numer. Math. 31 (1999) 405–427. Zbl0940.76033
  9. [9] P. Grisvard, Elliptic problems on non-smooth domains. Pitman, Boston (1985). Zbl0695.35060
  10. [10] F. Maubeuge, M. Didek, E. Arquis, O. Bertrand and J.-P. Caltagirone, Mother: A model for interpreting thermometrics. SPE 28588 (1994). 
  11. [11] D.Y. Peng and D.B. Robinson, A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15 (1976) 59–64. Zbl0332.20008
  12. [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. Zbl0875.65090
  13. [13] R. Verfürth and D. Braess, A posteriori error estimator for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431–2444. Zbl0866.65071

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