ANALYTICAL SOLUTIONS FOR WATER–GAS FLOW THROUGH 3D ROCK FRACTURE NETWORKS SUBJECTED TO TRIAXIAL STRESSES

Abstract

This study presented the analytical solutions for water–gas flow through three-dimensional (3D) fracture networks subjected to triaxial stresses. The relationship between fractal dimension for fracture aperture distribution subjected to triaxial stresses and that subjected to no stresses is established, and the analytical solutions for fractal dimensions for aperture distribution and the equivalent permeability of both fluid and gas phases were derived. The results show that the calculated relative permeability of water phase-saturation curves agree well with those reported in the literature, which indicates that the proposed solutions are validate. With the increment of normal stresses applied on the fracture surface, both the maximum aperture and minimum aperture decrease; however, their ratio increases first and then decreases. The fractal dimensions for fracture aperture distribution of water and gas phases with respect to saturation are axisymmetric along saturation [Formula: see text]. With the increase in saturation, the fractal dimension for fracture aperture distribution of water phase increases significantly when the saturation is less than 0.1, and then gently when the saturation is continuously increased by up to 1.0. The normal stress increased by two orders of magnitude for a larger normal stress (i.e. increased from [Formula: see text][Formula: see text]MPa to 10[Formula: see text]MPa) corresponds to smaller variations in equivalent permeability of both water and gas phases for a smaller normal stress (i.e. increased from [Formula: see text][Formula: see text]MPa to [Formula: see text][Formula: see text]MPa).