Equivalent Permeability of Fractured Media Incorporating Tortuosity and Nonlinear Flow

Abstract

Permeability of fractured media plays an important role in many hydrogeologic applications. In this study, we propose an approach to quantify the equivalent permeability of fractal fractured media along with the fracture length direction, and both the laminar flow and nonlinear flow are considered according to the fracture features and critical Reynolds number. The analytical expression for equivalent permeability of fractured media is derived, which depends on fractal fracture properties and the applied conditions. The new approach is applicable for any Newtonian fluid. The effects of fractal dimension for aperture and length, maximum fracture aperture, ratio of minimum to maximum aperture, critical Reynolds number and pressure head loss across the fractures are explored and discussed. The fractal dimension for fracture aperture is positively correlated with the porosity of porous media, and a clear power-law correlation between the equivalent permeability and porosity can be observed in the results. The maximum aperture and the ratio of minimum to maximum aperture control the size of fracture apertures, and the increase in both parameters leads to high permeability. The larger fractal dimension for length causes more tortuous fractures, which reduce the equivalent permeability. A higher critical Reynolds number leads to a larger equivalent permeability. A larger pressure head loss results in a smaller equivalent permeability.