Impact of Confining Stress on Capillary Pressure Behavior During Drainage Through Rough Fractures

We study, numerically, the behavior of capillary pressure (P_c) during slow immiscible displacement in a rough fracture as a function of the degree of fracture aperture heterogeneity that results from two distinct mechanisms: normal confining stress and fracture surface correlation. We generate synthetic self-affine rough fractures at different correlation scales, solve the elastic contact problem to model the effect of confining stress, and simulate slow immiscible displacement of a wetting fluid by a nonwetting one using a modified invasion percolation model that accounts for in-plane curvature of the fluid-fluid interface. Our modeling results indicate that the power spectral density, S(f), of P_c, can be used to qualitatively characterize fracture aperture heterogeneity. We show that the distribution of forward avalanche sizes follows a power law N_f(S_f) ∝ S_f^−α, with exponent α=2, in agreement with previously reported values for porous media and equal to the expected theoretical exponent for a self-organized criticality process.