Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures

摘要

This study focuses on experimental evaluation of the Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. Water flow tests through twelve granite fracture samples with different roughness were conducted in a triaxial cell under confining stresses varying from 1.0 MPa to 30.0 MPa. A total of 2280 experimental data in the form of pressure gradient versus discharge were collected. Three representative types of nonlinear flow behaviors induced by inertial effect, fracture dilation and solid water interaction, respectively, were observed. Regression analyses of the experimental data show that the Forchheimer equation adequately describes the non-Darcy flow behavior induced by significant inertial effect. Based on the experimental observations, two empirical equations were proposed for parametric expression of the Forchheimer's nonlinear coefficient, one as a power function of hydraulic aperture and the other dependent on both hydraulic aperture and peak asperity of the fracture surface. A new criterion was presented for assessing the applicability of Darcy's law, which relies on the ratio of discharge or pressure gradient predicted by the Forchheimer's law incorporated with the single-parameter equation to that predicted by the Darcy's law. A sensitivity analysis was performed using the double-parameter equation for examining the dependence of the Forchheimer's nonlinear coefficient on peak asperity, demonstrating the importance of incorporating the fracture roughness in the development of non-Darcy flow models. The experimental results and the proposed models are useful for understanding and numerical modeling of the nonlinear flow behaviors in fractured aquifers. (C) 2015 Elsevier B.V. All rights reserved.