A fractal permeability model for 2D complex tortuous fractured porous media

The complex fracture networks are of significance to petroleum production in unconventional reservoirs, but effectively predicting its permeability is challenging due to the complex distribution and geometry of fracture networks. This paper proposes a new permeability model for 2D complex tortuous fractured porous media based on fractal theory, and two important characteristics of fractures, i.e. branching and tortuosity are considered in the developed permeability model. In this paper, the fractured porous media is assumed to be made up of a bundle of tortuous fractal-like tree fracture networks. First, the modified cubic law for describing flow rate in a fracture with fractal distribution of tortuosity is derived. Secondly, the fractal-like tree fracture network is used to represent the distribution of complex fracture networks, and then flow rate in a tortuous fractal-like tree fracture network is derived. After that, with the assumption of the fractal scaling law between fracture number and fracture apertures, the total flow rate in a bundle of tortuous fractal-like tree fracture networks is given and then the analytical expression for permeability of 2D complex tortuous fractured porous media is derived. Finally, the model reliability is verified with a case study and the key parameters influencing permeability of 2D fracture porous media are investigated with sensitivity study. The research results show that the fractal dimension of aperture distribution D-f, tortuosity fractal dimension D-T, branch level m and fracture length ratio gamma have significant influence on fracture network permeability; the effects of branch angle theta and the straight length of the zero-level fracture l(0) on fracture network permeability are insignificant.