On the Role of Gravity in Dissolving Horizontal Fractures

Abstract

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.

Buoyancy-Driven Dissolution Instability in a Horizontal Hele-Shaw Cell

“…The relation ε f + ε s = 1 is valid in a control volume, where ε s is the volume fraction of the solid space. Subsequently, Hu et al 31 developed the modeling approach by incorporating gravitational effects, which is suitable for modeling dissolution processes involving buoyancy-driven convection. Note that the Darcy scale deals with average behavior, while the pore scale refers to the microscopic scale that finely describes physicochemical processes.…”

“…The Boussinesq approximation assumes that we can ignore the effects of density change on the inertial term (left side of eq 1), the gradient pressure term, and the diffusion-like viscosity and only consider the influence of density variation on the buoyancy force term. 31,33,51,52 Some work has indicated that the Boussinesq approximation is valid when the relative density difference is not larger than 10%. 33,51,52 In this work, the maximum relative density difference between inflowing unsaturated and saturated NaCl solutions is 10%.…”

“…At the pore scale, the local density of the fluid near the solid–liquid interface would increase due to the solubility of dissolved minerals. Even though this local relative density difference is 0.1% in a gravity field, buoyancy-driven convection may have a non-negligible effect on the dissolution dynamics . The dissolution dynamics depend not only on the Pe and Da numbers but also on the Richardson number Ri and Rayleigh number Ra .…”

“…Even though this local relative density difference is 0.1% in a gravity field, buoyancy-driven convection may have a non-negligible effect on the dissolution dynamics. 31 The dissolution dynamics depend not only on the Pe and Da numbers but also on the Richardson number Ri and Rayleigh number Ra. Here, Ri represents the relative impact of buoyancy-driven convection to forced convection and Ra quantifies the relative impact of buoyancy-driven convection to diffusion.…”

“…2,31,40,42,43 The buoyancy-driven convection under various flow-rate conditions can produce various dissolution morphologies like parallel stripes, parallel grooves, and dissolution hotspots. 31,36,39,44 Hu et al 31 identified three dissolution regimes by the critical Richardson number (Ri), indicating that gravitational effects cannot be ignored for horizontal fractures when Ri > 10. Under these circumstances, gravitational effects suppress the increase of permeability and the development of wormholes by enhancing the dissolution on the upper wall near the horizontal fracture inlet.…”