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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.