Simulation of dissolution in porous media in three dimensions with lattice Boltzmann, finite-volume, and surface-rescaling methods.

ABSTRACT

We present a pore-scale dissolution model for the simulation of reactive transport in complex porous media such as those encountered in carbon-storage injection processes. We couple a lattice Boltzmann model for flow calculation with a finite-volume method for solving chemical transport equations, and allow the computational grid to change as mineral surfaces are dissolved according to first-order reaction kinetics. We appraise this scheme for use with high Péclet number flows in three-dimensional geometries and show how the popular first-order convection scheme is affected by severe numerical diffusion when grid Péclet numbers exceed unity, and confirm that this can be overcome relatively easily by using a second-order method in conjunction with a flux-limiter function. We then propose a surface rescaling method which uses parabolic elements to counteract errors in surface area exposed by the Cartesian grid and avoid the use of more complex embedded surface methods when surface reaction kinetics are incorporated. Finally, we compute dissolution in an image of a real porous limestone rock sample injected with HCl for different Péclet numbers and obtain dissolution patterns in concordance with theory and experimental observation. A low injection flow rate was shown to lead to erosion of the pore space concentrated at the face of the rock, whereas a high flow rate leads to wormhole formation.