Aperture Field Anisotropy Control on Immiscible Displacement Patterns in Rough Fractures

Two-phase flow displacement in rock fractures is crucial for various subsurface mass transfer processes and engineering applications. In fractures, the displacement of a less viscous fluid by a more viscous one (i.e., viscosity ratio M > 1) involves viscous forces help stabilizing the displacement front in presence of capillary pressure fluctuations. Although previous studies have reported displacement patterns in isotropic fractures, the impact of anisotropic fractures on displacement patterns has not been systematically examined. In this study, we conducted flow-rate-controlled drainage experiments to examine how anisotropic aperture fields affect displacement patterns. We observed the transition of displacement patterns from capillary fingering (CF) to crossover zone (CZ) to compact displacement pattern (CD) based on variations in transverse pore-filling event (TPFE) frequency, which characterizes the competition between capillary and viscous forces. Increasing aperture correlation length in the transverse direction leads to increased TPFE frequency at a low flow rate, destabilizing displacement front. While the increasing aperture correlation length in longitudinal direction suppressed TPFE frequency, stabilizing displacement front. Therefore, the critical capillary number (Ca_CF-CZ), which indicates the onset of the CF-CZ transition, decreases as the aperture field varies from transversely to longitudinally correlated. At high flow rates, TPFEs almost disappeared, indicating that anisotropy did not affect CZ-CD transition (Ca_CZ-CD). Furthermore, we modified theoretical models of Ca_CF-CZ and Ca_CZ-CD by incorporating the aperture anisotropy factor, achieving a good fit with the experimental data. This study demonstrates the critical role of aperture field anisotropy in controlling two-phase displacement patterns and provides a theoretical framework for predicting multiphase flow behavior in natural fractures.