Inertia Effects in High-Rate Flow Through Heterogeneous Porous Media

Authors: Fourar, M.¹; Lenormand, R.²; Karimi-Fard, M.³; Horne, R.³

Source: Transport in Porous Media, Volume 60, Number 3, September 2005 , pp. 353-370(18)

Publisher: Springer

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Abstract:

The paper deals with the effects of large scale permeability–heterogeneity on flows at high velocities through porous media. The media is made of a large number of homogeneous blocks where the flow is assumed to be governed by the Forchheimer equation with a constant inertial coefficient. By assuming the validity of the Forchheimer equation at the large scale, an effective inertial coefficient is deduced from numerical simulations. Different media are investigated: serial-layers, parallel-layers and correlated media. The numerical results show that: (i) for the serial-layers, the effective inertial coefficient is independent of the Reynolds number and decreases when the variance and the mean permeability ratio increases; (ii) for the parallel-layers and the correlated media, the effective inertial coefficient is function of the Reynolds number and increases when the variance and the mean permeability ratio increases. Theoretical relationships are proposed for the inertial coefficient as function of the Reynolds number and the characteristics of the media.

Keywords: heterogeneous porous media; flow at high-velocity; Forchheimer’s equation; effective inertial coefficient

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11242-004-6800-6

Affiliations: 1: Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, Ecole des Mines de Nancy, Parc de Saurupt, 54042, Cedex, Nancy, France, Email: fourar@mines.inpl-nancy.fr 2: Institut Français du Pétrole, 1 et 4, avenue de Bois Préau, 92852, Rueil Malmaison, Cedex, France, 3: Department of Petroleum Engineering, Stanford University, 367, Panama Street, Stanford, CA, 94305-2220, USA,

Publication date: 2005-09-01