Lubrication Theory Analysis of the Permeability of Rough-Walled Fracturesby R.W. Zimmerman, Lawrence Berkeley Lab, Berkeley, United States,
S. Kumar, Lawrence Berkeley Lab, Berkeley, United States,
G. S. Bodvarsson, Lawrence Berkeley Lab, Berkeley, United States,
Abstract: Lubrication theory is used to study the permeability of rough-walled rock fractures. Two idealized models of a fracture, in which the roughness follows a sinusoidal or a sawtooth variation, are studied in detail. The results are similar to those found previously from numerical analysis of fractures with random aperture distributions, in that the ratio of the hydraulic aperture depends mainly on the mean and the standard deviation of the aperture distribution. Higher-order approximations to the Navier-Stokes equations are then studied, and it is concluded that the validity of the lubrication approximation requires the fracture walls to be smooth over lengths on the order of one standard deviation of the aperture.
Subject Headings: Cracking | Navier-Stokes equations | Hydraulic fracturing | Approximation methods | Water resources | Permeability (material) | Rocks | Hydraulic roughness
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