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

We study, numerically, the behavior of capillary pressure (Pc) 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 Pc, can be used to qualitatively characterize fracture aperture heterogeneity. We show that the distribution of forward avalanche sizes follows a power law Nf(Sf)∝Sf−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.