Matrix-fracture exchange in a fractured porous medium: stochastic upscaling

Moussa Kfoury; Rachid Ababou; Benoit Nœtinger; Michel Quintard

doi:10.1016/j.crme.2004.04.001

Matrix-fracture exchange in a fractured porous medium: stochastic upscaling

Presented by: Michel Combarnous

Moussa Kfoury ^1,² ; Rachid Ababou ²; Benoit Nœtinger ¹; Michel Quintard ²

¹ Institut français du pétrole, 1 et 4, avenue de Bois-Préau, 92852 Rueil Malmaison cedex, France
² Institut de mécanique des fluides de Toulouse, allée du Professeur Camille Soula, 31400 Toulouse, France

Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 679-686.

Abstract
Résumé

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.

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.

Received: 2003-11-27
Accepted: 2004-04-06
Published online: 2004-06-01

DOI: 10.1016/j.crme.2004.04.001

Keywords: Porous media, Upscaling, Fractures, Dual porosity, Exchange coefficient, Homogenization, Stochastic approach
Mots-clés : Milieux poreux, Changement d'échelle, Fractures, Double porosité, Coefficient d'échange, Homogénéisation, Approche stochastique

Author's affiliations:

Moussa Kfoury ^{1, 2}; Rachid Ababou ²; Benoit Nœtinger ¹; Michel Quintard ²

¹ Institut français du pétrole, 1 et 4, avenue de Bois-Préau, 92852 Rueil Malmaison cedex, France
² Institut de mécanique des fluides de Toulouse, allée du Professeur Camille Soula, 31400 Toulouse, France

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     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},
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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/

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