Effects of geometrical feature on Forchheimer-flow behavior through rough-walled rock fractures

In order to study the relationship between the geometrical feature and the nonlinear flow properties of rough-walled rock fractures, a numerical model based on the fractal behavior is proposed to characterize the three-dimensional geometry of rough-walled fractures. By solving the N-S (Navier-Stokes) equation directly, the effects of mean aperture, standard deviation of aperture and different fractal dimensions on the Forchheimer flow characteristics of fractures are investigated. The Forchheimer equation is validated to describe the nonlinear relationship between the flow rate and the pressure gradient. The results show that with the lower flow rate, the linear coefficient increases and the hydraulic aperture decreases with the decreasing mean aperture and increasing standard deviation of the aperture, thus the empirical relation for the hydraulic aperture, the mean aperture and the standard deviation of aperture is put forward, while the effects of the fractal dimension almost can be ignored. On the contrary, with larger flow rate, for the flow pattern changing from linear to nonlinear flow, as the mean aperture decreases and the standard deviation of aperture and the fractal dimension increase, the nonlinear coefficient increases, and the critical Reynolds number decreases, with the range of Re_c being 11.16~39.3.