The Development of Wormholes in Laboratory‐Scale Fractures: Perspectives From Three‐Dimensional Simulations

Abstract

We investigate the development of wormholes in laboratory‐scale fractures using three‐dimensional numerical simulations. Well‐controlled initial conditions, involving a small perturbation near the inlet of an otherwise flat fracture aperture field, were used to make a systematic study of the effects of flow rate and reaction rate on the aperture evolution. We find at least two characteristic wormhole shapes, which can be grouped within a phase diagram in the space of Péclet and Damköhler numbers. We investigate how this phase diagram depends on fracture geometry, specifically the length (L) and width (W) in comparison to the initial aperture (h0). This information is used to determine an effective Damköhler number that leads to a Péclet and length‐independent phase boundary between wormholes and uniform dissolution. We relate these observations to experimental studies of wormhole formation in dissolving fractures.

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

“…Codes using unstructured meshes are better able to conform to the shape of the boundary, although the mesh must be able to adapt to the changing geometry. As points on the boundary move according to the computed normal displacements (5), the mesh as a whole must be smoothed to maintain mesh quality, while simultaneously maintaining the shape of the surface [99,100].…”

“…1e). In a conforming mesh approach, a subset of the vertices lie on the fluid-solid boundaries, with a simple conservative calculation of the fluxes [99,100]. When the mineral dissolves, the boundary points move in accordance with Eq.…”

“…Further, simulation results resolve variables that are not easily available from experiments, for example concentration gradients within the pore space. Such data enables additional insights to be drawn, especially when comparison to experimental data is possible [15,66,75,96,97,99].…”

“…A central theme of pore-scale numerical investigations has been the study of the effects of pore structure and mineral heterogeneity on reaction rates [30,51,65,75]. A significant number of pore-scale modeling contributions have focused on the interactions of CO 2 -rich fluids with carbonate-rich porous media in the context of CO 2 sequestration, including the development of the reactive infiltration instabilities [35,66,75,96,99,108,119]. Microbially driven evolution of porous media, including biofilm formation, has also received broad attention [14,93,109].…”

Mineral Precipitation in Fractures: Using the Level‐Set Method to Quantify the Role of Mineral Heterogeneity on Transport Properties

“…For uniform surface mineralogy, it is relatively straightforward to convert local reaction rates into changes in fracture aperture by applying a 1-D alteration of the local domain (e.g., Andre & Rajaram, 2005;Cheung & Rajaram, 2002). However, when surface roughness increases, it is necessary to develop more rigorous approaches for tracking the fracture surface (Starchenko et al, 2016;Starchenko & Ladd, 2018;Yu & Ladd, 2010) and account for evolving reactive surface area (Molins, 2015).…”