A permeability model for the fractal tree-like fracture network with self-affine surface roughness in shale gas reservoirs

Abstract

The complex natural fracture network with self-affine rough surface and branching characteristics significantly impacts the gas transport in shale gas reservoirs. However, its effects on the permeability have not been studied so far. This study proposes an analytical permeability model for the fractal tree-like fracture network with self-affine surface roughness and branching characteristics. Firstly, the self-affine rough profiles of fracture surface are generated at different fractal dimensions by the Weierstrass–Mandelbrot function and a rough fractal tree-like fracture network is constructed with these surface profiles and branching characteristics. Then, an analytical permeability model is proposed to consider the effects of fracture surface roughness and tree-like branching characteristics on gas flow. This analytical model is verified by numerical simulations. Finally, the velocity distribution of the fracture network and the sensitivity of its structure parameters are analyzed. It is found that eddy flow is more easily formed on rougher fracture surfaces with larger fractal dimension when their fracture aperture is at millimeter scale. The eddy flow disappears when the fracture aperture is at micron scale. Bigger gas flow resistance and more energy loss are observed for smaller fracture aperture and rougher fracture surface. The gas velocity in rough fractures decreases by 60% at micron scale, but decreases by 50% at millimeter scale. Gas flow resistance also increases with the increase of branch angle, branch level and length ratio, but decreases with aperture ratio. As a result, permeability decreases with fractal dimension, branch angle, branch level and length ratio, but increases with aperture ratio.