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Comptes Rendus Géoscience
Volume 341, n° 4
pages 327-338 (avril 2009)
Doi : 10.1016/j.crte.2008.11.014
Received : 20 December 2007 ;  accepted : 4 November 2008
Equivalent block transmissivity in an irregular 2D polygonal grid for one-phase flow: A sensitivity analysis
Calcul de la transmissivité de bloc en maillage polygonal irrégulier 2D pour un écoulement monophasique : une étude de sensibilité

Marco De Lucia a, b, Chantal de Fouquet a, , Vincent Lagneau a, Roberto Bruno b
a Mines ParisTech, centre de géosciences, 35, rue Saint-Honoré, 77305 Fontainebleau cedex, France 
b Università di Bologna, Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali, Via Terracini, 28, 40131 Bologna, Italy 

Corresponding author.

Upscaling is needed to transform the representation of non-additive space-dependent variables, such as permeability, from the fine grid of geostatistical simulations (to simulate small-scale spatial variability) to the coarser, generally irregular grids for hydrodynamic transport codes. A new renormalisation method is proposed, based on the geometric properties of a Voronï grid. It is compared to other classic methods by a sensitivity analysis (grid, range and sill of the variogram, random realisation of a simulation); the criterion is the flux of a tracer at the outlet. The effect of the upscaling technique on the results appears to be of second order compared to the spatial discretisation, the choice of variogram, and the realisation.

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Le changement d’échelle pour la perméabilité est incontournable, entre une simulation géostatistique sur grille fine (reproduisant la variabilité spatiale à petite distance) et le maillage plus grossier et généralement irrégulier des codes de transport. Une nouvelle méthode de renormalisation, exploitant les propriétés géométriques du maillage de Voronï, est comparée à deux méthodes classiques, par une étude de sensibilité (maillage, portée et palier du variogramme, tirage ou « réalisation » d’une simulation) suivant un critère de flux d’un traceur en sortie de perméamètre. La technique de changement d’échelle apparaît du second ordre par rapport à la discrétisation spatiale, au variogramme et à la réalisation.

The full text of this article is available in PDF format.

Keywords : Equivalent permeability, Upscaling, Finite volumes, Voronï mesh, Spatial variability, Heterogeneous medium, Flow

Mots clés : Perméabilité équivalente, Changement d’échelle, Volumes finis, Maillage de Voronï, Variabilité spatiale, Milieu hétérogène, Écoulement

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