Effects of roughness and aperture on mesoscopic and macroscopic flow characteristics in rock fractures

Macroscopic nonlinear flow, which is closely related to mesoscopic flow structures such as vortices, is an important property of fluid flow and solute transport in rock fractures with a high pressure gradient. Both mesoscopic flow structure and macroscopic nonlinear flow of rock fractures are affected by fracture roughness and aperture. Therefore, the macroscopic seepage process in fractures is studied numerically by directly solving the Navier–Stokes equation. The results demonstrate that the Forchheimer equation can be used to describe the relationship between flow rate and pressure gradient of rough fractures with different apertures. The linear and nonlinear coefficients of the Forchheimer equation increase with fracture roughness and decrease with fracture aperture. Empirical formulas between the linear coefficient, the nonlinear coefficient, the fracture roughness and aperture are established. When the roughness is equal to zero, the empirical formulas can degenerate into conventional cubic law. In additions, the distribution characteristics of the mesoscopic flow structure in rough fractures are also investigated. The results show that the area and kinetic energy distribution characteristics of the mesoscopic flow structure in fractures with different roughness and apertures are similar. The frequency characteristics of the area and kinetic energy of the mesoscopic flow structure in fractures can be fitted with negative exponential and logarithmic normal functions, respectively. The effect of fracture roughness on area and kinetic energy distribution characteristics is significant, but the effect of aperture can be ignored. Empirical formulas between fracture roughness and mesoscopic flow structure characteristics are established for the first time.