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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) proportional to S-f(-alpha), with exponent alpha = 2, in agreement with previously reported values for porous media and equal to the expected theoretical exponent for a self-organized criticality process.