Immiscible displacements in rough-walled fractures: Competition between roughening by random aperture variations and smoothing by in-plane curvature

Phase structure during capillary displacement of fluid phases within rough-walled fractures is controlled by the competition between random aperture variability which tends to roughen the interface and in-plane curvature which tends to smooth it. We show that the phase structure and corresponding areal saturation at the end of displacement depend primarily on the ratio of two dimensionless parameters: one that controls roughening (the coefficient of variation of the aperture field, delta) and another that controls smoothing (the curvature number C, which weighs the mean influences of aperture induced and in-plane curvature). Interestingly, for C/delta above approximately 0.5, areal saturation for wetting and nonwetting invasion first diverges and then converges to create an envelope, whose width increases with delta. This nonunique behavior with respect to wettability is fundamental to capillary displacements in rough-walled fractures and is due to an asymmetry in capillary competition in wetting versus nonwetting invasions.