Homogenization of a one-dimensional model for compressible miscible flow in porous media

Catherine Choquet

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 2, page 399-414
  • ISSN: 0392-4041

Abstract

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We discuss the homogenization of a one-dimensional model problem describing the motion of a compressible miscible flow in porous media. The flow is governed by a nonlinear system of parabolic type coupling the pressure and the concentration. Using the technique of renormalized solutions for parabolic equations and a compensated compactness argument, we prove the stability of the homogenization process.

How to cite

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Choquet, Catherine. "Homogenization of a one-dimensional model for compressible miscible flow in porous media." Bollettino dell'Unione Matematica Italiana 6-B.2 (2003): 399-414. <http://eudml.org/doc/195051>.

@article{Choquet2003,
abstract = {We discuss the homogenization of a one-dimensional model problem describing the motion of a compressible miscible flow in porous media. The flow is governed by a nonlinear system of parabolic type coupling the pressure and the concentration. Using the technique of renormalized solutions for parabolic equations and a compensated compactness argument, we prove the stability of the homogenization process.},
author = {Choquet, Catherine},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {399-414},
publisher = {Unione Matematica Italiana},
title = {Homogenization of a one-dimensional model for compressible miscible flow in porous media},
url = {http://eudml.org/doc/195051},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Choquet, Catherine
TI - Homogenization of a one-dimensional model for compressible miscible flow in porous media
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/6//
PB - Unione Matematica Italiana
VL - 6-B
IS - 2
SP - 399
EP - 414
AB - We discuss the homogenization of a one-dimensional model problem describing the motion of a compressible miscible flow in porous media. The flow is governed by a nonlinear system of parabolic type coupling the pressure and the concentration. Using the technique of renormalized solutions for parabolic equations and a compensated compactness argument, we prove the stability of the homogenization process.
LA - eng
UR - http://eudml.org/doc/195051
ER -

References

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  1. AMIRAT, Y.- HAMDACHE, K.- ZIANI, A., Homogénéisation d'un modèle d'écoulements miscibles en milieu poreux, Asymptotic Anal., 3 (1990), 77-89. Zbl0702.35213MR1043964
  2. AMIRAT, Y.- HAMDACHE, K.- ZIANI, A., Homogenization of a model of compressible miscible flow in porous media, Boll. Un. Mat. Ital. B (7), 5 (1991), 463-487. Zbl0727.76093MR1111133
  3. AMIRAT, Y.- ZIANI, A., Global weak solutions for a parabolic system modeling a one-dimensional miscible flow in porous media, J. Math. Anal. Appl., 220 (1998), 697-718. Zbl0911.35063MR1614944
  4. BOURGEAT, A.- MIKELIĆ, A., Homogenization of two-phase immiscible flows in a one-dimensional porous medium, Asymptotic Anal., 9 (1994), 359-380. Zbl0814.35103MR1301170
  5. DOUGLAS, J. JR.- ROBERTS, J. E., Numerical methods for a model of compressible miscible displacement in porous media, Math. Comp., 41 (1983), 441-469. Zbl0537.76062MR717695
  6. KOVAL, E. J., A method for predicting the performance of unstable miscible displacements in heterogeneous media, SPEJ trans. AIME, 228 (1963), 145-154. 
  7. LIONS, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod/Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  8. MURAT, F., Compacité par compensation, Ann. Scuola Norm. Sup. Pisa (4), 5 (1978), 489-507. Zbl0399.46022MR506997
  9. MURAT, F., Soluciones renormalizadas de EDP elipticas no lineales, Prépublication du Laboratoire d'Analyse Numérique, Université de Paris 6, 93023, 1993. 
  10. PEACEMAN, D. W., Fundamentals of Numerical Reservoir Simulation, Elsevier, 1977. 
  11. SCHEIDEGER, A. E., The Physics of Flow through Porous Media, Univ. Toronto Press, 1974. Zbl0095.22402

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