The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses

To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for hydraulic tests in the experiments. According to the experimental results of the relationships between the hydraulic gradient and the flow rate, it is demonstrated that the Forchheimer's equation can offer a good description of the non-Darcy flow in rough fractures. In addition, the coefficients A and B in Forchheimer's equation are sensitive to the fracture geometric characteristics, and their values also increase as the confining stress rises, mainly owing to the reduction of the hydraulic aperture and the heterogeneous distribution of the interconnected void areas with the confining stress rising. Then, the surface and interior geometric properties of rough fractures were quantitatively characterized with the peak asperity height ξ and the box-counting fractal dimension D of the heterogeneous distribution of the interconnected void areas, respectively. Furthermore, an empirical relationship between the fractal dimension D and the fracture apertures was constructed according to the experimental results. Lastly, a quantitative model was proposed to represent the relationship between the fracture geometric characteristics and the non-Darcy coefficient β. This model was further used to link the non-linear coefficient B of Forchheimer's equation and the critical Reynold number Re_c with the fracture geometric characteristics. The proposed models were validated by the experimental data and would be helpful to characterize the non-Darcy flow behavior in rough fractures under various confining stresses.