(264e) 3D Simulations of Fracture Dissolution Using the Openfoam Toolkit

Although fractures take up only a small
fraction (1-2%) of the available pore space in rocks they account for
the majority of the subsurface transport of minerals and
contaminants. Water percolating through carbonate formations will
tend to dissolve the surrounding rock, due to the acidity of the
dissolved CO₂. The feedback between the flow of reactant
and the increase in permeability due to dissolution of the fracture
faces gives rise to a number of interesting and important questions,
relating to oil and gas recovery, sequestration, dam stability and
the development of caves.

Numerical models of fracture
dissolution typically take averages of the flow and reactant
concentration across the fracture aperture, giving rise to simplified
field equations that can be readily solved on a one or
two-dimensional grid. However, fracture dissolution is inherently
unstable and highly localized flow paths or wormholes develop [1].
Figure 1 shows a developing wormhole from an initially flat fracture,
with a small region of enhanced aperture near the center of the
inlet. As the wormhole grows the aperture-averaging approximation
breaks down. To study the later development of wormholes, the effects
of inertia and turbulence, and the competition between different flow
paths a fully three-dimensional model is desirable. Here we report
some preliminary developments using the OpenFOAM [2] toolkit.

The simulations solve the
Stokes equation for flow in the fracture (although it is
straightforward to include fluid inertia) and the
convection-diffusion equation for the reactant transport. Reactions
at the fracture surfaces are modeled by linear or power-law kinetics
and the rates of dissolution computed. The dissolution flux is then
used to modify the positions of the surfaces. The additional
libraries and modifications to the OpenFOAM source needed to perform
these simulations will be outlined. The major difficulty is
preserving sufficient mesh quality as the fracture opens; to
accomplish this we have implemented a customized source code to relax
the mesh on the fracture surfaces.

Results for uniformly
dissolving fractures show an excellent agreement between 2D and 3D
models. At the same time first we find that the quality of the mesh
and the implementation of the boundary conditions are extremely
important for the resulting solution. At the meeting we will present
the results of ongoing simulations of more complex fracture systems.

[1] Szymczak and A. J. C.
Ladd. The initial stages of
cave formation: Beyond the one-dimensional paradigm,
Earth Planet. Sci. Lett., 2011,
301, 424-432.

[2]
http://www.openfoam.com/