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.

Fractures are ubiquitous in geological systems. As reactive fluid flow through a fracture, dissolution of the fracture walls may occur, thus altering the fracture aperture and increasing permeability. It has been recognized that gravity plays an important role in dissolving vertical fractures due to buoyancy‐driven convection. However, the role of gravity in dissolving horizontal fractures is not well understood. Here, we combine microfluidics/Hele‐Shaw experiments and a numerical method to study how the interplay of buoyancy‐driven convection and forced convection controls dissolution dynamics and permeability increase in horizontal fractures. We first develop the micro‐continuum approach by incorporating the gravitational effects, and then, we perform experiments to validate our method, confirming that the method can well capture gravitational effects on dissolution. Through 3D simulations, we find that buoyancy‐driven convection breaks the symmetry of dissolution on the upper and lower surfaces. We employ a symmetry index to identify three dissolution regimes. As the importance of gravity increases (Ri increases), the dissolution regime shifts from forced convection to mixed convection and to natural (or buoyancy‐driven) convection. We establish a link between these dissolution regimes and permeability evolution. In the forced convection or natural convection regimes, the permeability nearly remains unchanged for various Ri. However, in the mixed convection regime, permeability increase is suppressed by the gravitational effects; the underlying mechanism is that the solid phase tends to dissolve near the fracture inlet due to gravitational instability. This work improves our understanding of the gravitational effects on dissolution regimes and permeability evolution in horizontal fractures.

Rock fractures are ubiquitous in the crust of the Earth. Because of their high permeability, fractures usually provide the main pathways for fluid flow and control fluid migration in geological systems (Igonin et al., 2021). When the flowing fluid is reactive, the dissolution of minerals within fracture walls would expand the fracture aperture and form distinct dissolution patterns. These dissolution patterns determine how the dissolved region develops and how the permeability increases (Roded et al., 2018;Wang & Cardenas, 2017). Understanding and quantifying the dissolution patterns in rough fractures is fundamental to many natural settings and engineering applications, including the evolution of karst hydrology (

The dissolution dynamics of rough channels is a fundamental process occurring in the widening of fracture channels (cavity evolution) (

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