J. Phys. II France
Volume 5, Numéro 3, March 1995
Page(s) 465 - 482
DOI: 10.1051/jp2:1995133
J. Phys. II France 5 (1995) 465-482

Permeability of a Single Fracture; Validity of the Reynolds Equation

V.V. Mourzenko, J.-F. Thovert and P.M. Adler

LPTM/CNRS, Asterama 2, Avenue du Téléport, 86360 Chasseneuil du Poitou, France

(Received 17 October 1994, received in final form 1 December 1994, accepted 7 December 1994)

Single fractures are generated by statistical methods and described by a probability density of the profile heights and a spatial covariance function which is either Gaussian or self-affine. The results of numerical simulations based on both 2D Reynolds and 3D Stokes equations are presented. Total fluxes predicted by these equations for the same fractures are given and discussed. The difference between predictions of both models is analysed for the range of correlation lengths and apertures of real fractures, and it is found that the total fluxes for the same fractures may differ more than two times. When the local distance between the surfaces is used, the Reynolds equation provides much better results.

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