This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of threedimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively-based on upscaled parameters such as surface area, solid volume, and effective reaction rate-and qualitatively-based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.
Numerical studies of fracture dissolution are frequently based on two‐dimensional models, where the fracture geometry is represented by an aperture field h(x,y). However, it is known that such models can break down when the spatial variations in aperture are rapid or large in amplitude; for example, in a rough fracture or when instabilities in the dissolution front develop into pronounced channels (or wormholes). Here we report a finite‐volume implementation of a three‐dimensional reactive transport model using the OpenFOAM® toolkit. Extensions to the OpenFOAM source code have been developed which displace and then relax the mesh in response to variations in the surface concentration; up to 100‐fold increases in fracture aperture are possible without remeshing. Our code has simulated field‐scale fractures with physical dimensions of about 10 m. We report simulations of smooth fractures, with small, well‐controlled perturbations in fracture aperture introduced at the inlet. This allows for systematic convergence studies and for detailed comparisons with results from a two‐dimensional model. Initially, the fracture aperture develops similarly in both models, but as local inhomogeneities develop the results start to diverge. We investigate numerically the onset of instabilities in the dissolution of fractures with small random variations in the initial aperture field. Our results show that elliptical cross sections, which are characteristic of karstic conduits, can develop very rapidly, on time scales of 10–20 years in calcite rocks.
The
morphological evolution of micron-sized calcite crystals dissolved
in static acidic solutions, with and without dissolved Pb2+ ions, was imaged using transmission X-ray microscopy (TXM). The
area-normalized dissolution rates measured by TXM increased with time
in both Pb-free and Pb-rich solutions but with distinct morphological
evolution. Calcite reacted in Pb-free solutions exhibited rounding
at corners and edges with faster dissolution at acute corners/edges
than obtuse corners/edges. Numerical simulations indicate that this
is controlled primarily by solution mass transport that is faster
near the acute corners/edges. In comparison, dissolution of calcite
in Pb-rich solutions was 50% slower than that in Pb-free solutions
and exhibited less rounding at corners. Faces of the calcite rhombs
exhibited increased surface roughness and the subsequent development
of surface micropyramids that formed preferentially near the acute
edges of the calcite rhombs. Spatially resolved dissolution rates
reveal that pyramid formation is associated with reduced dissolution
rates near the pyramid apex. The results demonstrate the role of impurity
metal ions in controlling the dissolution rate and the associated
complexities in the morphological evolution of dissolving mineral
surfaces.
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