Anisotropie Permeability of Fractured Media

Abstract

The mathematical equivalents of parallel plate openings are used to simulate real fractures dispersed in orientation, distributed in aperture, and of arbitrary spacing. With this idealization of jointed pervious rock, the discharge of each conductor is a second rank tensor proportional to the cube of aperture and to the projection of a hydraulic gradient generally parallel to no conductor. One may add components of discharge through each intersecting conductor and components of discharge through intervening pervious blocks. The reciprocal of specific surface of the fracture system like spacing serves as a weighting factor for the tensor sum, which is the anisotropic Darcy's law permeability of an equivalent continuous medium. Special cases of one, two, and three joint sets are modeled by applying Monte Carlo methodsto pair orientations of individual planes sampled from Fisher dispersions with apertures sampledfrom skewed normal distributions. Statistics of the orientation of principal axes and ofprincipal permeabilities are developed to show the relationship between joint geometry andanisotropy and to assess its variations.