[Coefficient d'échange matrice-fracture en milieu poreux fracturé : changement d'échelle par approche stochastique]
On présente dans cette Note une approche stochastique (probabiliste) du problème d'échange matrice-fractures en milieu poreux fracturé hétérogène. On introduit l'échelle intermédiaire des sous-blocs ou « unités », lors du passage de l'échelle locale (détails des fractures) à l'échelle globale de la maille représentative du réservoir (« bloc réservoir »). Une solution probabiliste en temps continu, sans transport, avec terme d'échange purement aléatoire, est développée. Ceci permet l'homogénéisation (instantanée ou non) du problème d'échange pur. Les résultats obtenus sont une première contribution au problème plus général du passage de l'échelle des unités à l'échelle du bloc ou maille réservoir, pour un écoulement double-milieu avec échanges matrice-fracture.
We present in this Note a stochastic approach to the matrix-fracture exchange in a heterogeneous fractured porous medium. We introduce an intermediate scale, called the unit-scale, between the local-scale (fracture-scale) and the large-scale characteristic of the reservoir mesh (reservoir block). This paper focuses on the problem of upscaling fluid exchange phenomena from the unit scale to the reservoir mesh or block scale. Simplifying the Darcian flow terms enables us to obtain a probabilistic solution of the dual continuum problem, in continuous time, in the case of a purely random exchange coefficient. This is then used to develop several upscaling approaches to the fluid exchange problem, and to analyze the so-called ‘effective’ exchange coefficient. The results are a first contribution to the more general problem of upscaling multidimensional flow-exchange processes in space and time, in randomly heterogeneous dual continua.
Accepté le :
Publié le :
Mot clés : Milieux poreux, Changement d'échelle, Fractures, Double porosité, Coefficient d'échange, Homogénéisation, Approche stochastique
@article{CRMECA_2004__332_8_679_0,
author = {Moussa Kfoury and Rachid Ababou and Benoit N{\oe}tinger and Michel Quintard},
title = {Matrix-fracture exchange in a fractured porous medium: stochastic upscaling},
journal = {Comptes Rendus. M\'ecanique},
pages = {679--686},
publisher = {Elsevier},
volume = {332},
number = {8},
year = {2004},
doi = {10.1016/j.crme.2004.04.001},
language = {en},
}
TY - JOUR AU - Moussa Kfoury AU - Rachid Ababou AU - Benoit Nœtinger AU - Michel Quintard TI - Matrix-fracture exchange in a fractured porous medium: stochastic upscaling JO - Comptes Rendus. Mécanique PY - 2004 SP - 679 EP - 686 VL - 332 IS - 8 PB - Elsevier DO - 10.1016/j.crme.2004.04.001 LA - en ID - CRMECA_2004__332_8_679_0 ER -
%0 Journal Article %A Moussa Kfoury %A Rachid Ababou %A Benoit Nœtinger %A Michel Quintard %T Matrix-fracture exchange in a fractured porous medium: stochastic upscaling %J Comptes Rendus. Mécanique %D 2004 %P 679-686 %V 332 %N 8 %I Elsevier %R 10.1016/j.crme.2004.04.001 %G en %F CRMECA_2004__332_8_679_0
Moussa Kfoury; Rachid Ababou; Benoit Nœtinger; Michel Quintard. Matrix-fracture exchange in a fractured porous medium: stochastic upscaling. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 679-686. doi : 10.1016/j.crme.2004.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.04.001/
[1] The relationship of the degree of interconnection to permeability in fracture networks, J. Geophys. Res., Volume 90 (1985) no. 4, pp. 3087-3098
[2] Continuum modeling of coupled T-H-M processes in fractured rock (A. Peters et al., eds.), Computational Methods Water Resources, vol. 1, Kluwer Academic, 1994, pp. 651-658 (Chapter 6)
[3] Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches, VCH, New York, 1995
[4] Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math., Volume 24 (1960), pp. 213-240
[5] Transport in chemically and mechanically heterogeneous porous media - I: theoretical development of region averaged equations for slightly compressible single-phase flow, Adv. Water Resources, Volume 19 (1996), pp. 29-47
[6] Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems, Adv. Water Resources, Volume 24 (2001), pp. 863-876
[7] Up-scaling flow in fractured media: equivalence between the large scale averaging theory and the continuous time random walk method, Transport in Porous Media, Volume 43 (2001), pp. 581-596
[8] Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Appl. Math., Volume 21 (1985), pp. 3087-3098
[9] Pressure transient response of stochastically heterogeneous fractured reservoirs, Transport in Porous Media, Volume 11 (1993), pp. 263-280
[10] Solution of stochastic groundwater flow by infinite series, and convergence of the one-dimensional expansion, Stochastic Hydrology and Hydraulics, Volume 8 (1994), pp. 139-155
[11] Stochastic-perturbation analysis of a one-dimentional dispersion–reaction equation: effect of spatially-varying reaction rates, Transport in Porous Media, Volume 32 (1998), pp. 139-161
Cité par Sources :
Commentaires - Politique
Multi-scale study of diffusion in composite grain–pore systems based on particles random walk
Hamza Oukili; Rachid Ababou; Gérald Debenest; ...
C. R. Méca (2021)
Statistical physics and applied geosciences: some results and perspectives
Benoît Noetinger
C. R. Phys (2020)
Marco De Lucia; Chantal de Fouquet; Vincent Lagneau; ...
C. R. Géos (2009)