Applicable range of the Reynolds equation for fluid flow in a rock fracture

Abstract

The applicability of the Reynolds equation to fluid flow in rock fractures has recently been questioned. One issue is that the Reynolds equation overestimates the transmissivity for rough fractures. Another issue is to delineate the range of fracture roughness over which the Reynolds equation is reasonably accurate. In this paper, the analysis was undertaken to examine the relationship between fracture geometry and the accuracy of the Reynolds equation. This analysis leads to identifying a criterion parameter, (b m /Λ)(A/Λ), whereb m /Λ is the ratio of mean aperture to wavelength, representing roughness, andA/Λ is the ratio of amplitude of oscillated fracture roughness to the wavelength, representing tortuosity. We found that when (b m /Λ)(A/Λ) is less than 0.01, the Reynolds equation may yield accurate transmissivity predictions.