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Roughness Control on Multiphase Flow in Rock Fractures

The roughness of rock fractures induces irregular flow passages and significantly affects the displacement front. Previous studies focus on displacement instabilities in porous media, but how roughness controls displacement patterns in rock fractures remains unclear. Here, we derive a theoretical model that describes the two transitions of drainage displacement patterns from capillary fingering to the crossover to viscous fingering as functions of roughness. The phase diagram predicted by this model exhibits excellent agreement with our experimental results, showing that increasing roughness index λb destabilizes displacement fronts. We further find that in capillary fingering regime the percentage of dissipated energy to the total external work increases from 39% to 61% as λb increases from 0.082 to 0.245. Our work elucidates the mechanism of roughness control on multiphase flow in fractures and provides a basis for developing a rigorous upscaling methodology that relates Darcy‐scale flow behavior to the local fluid displacements via energy dissipation.