A modified invasion percolation model for low-capillary number immiscible displacements in horizontal rough-walled fractures: Influence of local in-plane curvature

We develop and evaluate a modified invasion percolation (MIP) model for quasi-static immiscible displacement in horizontal fractures. The effects of contact angle, local aperture field geometry, and local in-plane interfacial curvature between phases are included in the calculation of invasion pressure for individual sites in a discretized aperture field. This pressure controls the choice of which site is invaded during the displacement process and hence the growth of phase saturation structure within the fracture. To focus on the influence of local in-plane curvature on phase invasion structure, we formulate a simplified nondimensional pressure equation containing a dimensionless curvature number (C) that weighs the relative importance of in-plane curvature and aperture-induced curvature. Through systematic Variation of C, we find in-plane interfacial curvature to greatly affect the phase invasion structure. As C is increased from zero, phase invasion fronts transition from highly complicated (IP results) to macroscopically smooth. In addition, measurements of fracture phase saturations and entrapped cluster statistics (number, maximum size, structural complication) show differential response between wetting and nonwetting invasion with respect to C that is independent of contact angle hysteresis. Comparison to experimental data available at this time substantiates predicted behavior.