# 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

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topAmara, 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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- F. Maubeuge, M. Didek, E. Arquis, O. Bertrand and J.-P. Caltagirone, Mother: A model for interpreting thermometrics. SPE 28588 (1994).
- D.Y. Peng and D.B. Robinson, A new two-constant equation of state. Ind. Eng. Chem. Fundam.15 (1976) 59–64.
- 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
- 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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