Normal-stress dependence of fracture hydraulic properties including two-phase flow properties

A systematic approach has been developed for determining relationships between normal stress and fracture hydraulic properties, including two-phase flow properties. The development of a relationship between stress and fracture permeability (or fracture aperture and fracture closure) is based on a two-part Hooke’s model (TPHM) that captures heterogeneous elastic-deformation processes at a macroscopic scale by conceptualizing the rock mass (or a fracture) into two parts with different mechanical properties. The developed relationship was verified using a number of datasets in the literature for fracture closure versus stress, and satisfactory agreements were obtained. TPHM was previously shown to be able to accurately represent testing data for porous media as well. Based on the consideration that fracture–aperture distributions under different normal stresses can be represented by truncated-Gaussian distributions, closed-form constitutive relationships were developed between capillary pressure, relative permeability and saturation, for deformable horizontal fractures. The usefulness of these relationships was demonstrated by their consistency with a laboratory dataset.