Recent progresses in Lattice Boltzmann simulations of flow and multi-component reactive transport in porous media

Abstract

In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical tool for simulating complex fluid flows and modeling physics and chemistry in fluids. Derived from the continuum Boltzmann equation used in statistical mechanics, the LB method has the advantage of describing non-equilibrium dynamics, especially in fluid-flow applications involving interfacial dynamics and complex boundaries, without simplifying the physics. In addition, the parallel structure inherent in the LB method makes it extremely suitable for parallel computing. Because of these features, the LB method affords the most comprehensive pore-scale approach to systematically investigate fundamental issues involving flow and reactive transport in porous media. In this paper, the state of the art of this method is discussed. Specifically, a multi-component LB model for simulating reactive transport in porous media at the pore scale is presented. In the model, a set of distribution functions is introduced to simulate fluid flow and solute transport. The LB equation for flow recovers the correct pore-scale continuity and Navier-Stokes equations. The LB equations for solute transport are modified to recover advection-diffusion equations for total concentrations at the pore scale. The model takes into account advection, diffusion, homogeneous reactions among multiple aqueous species, heterogeneous reactions between the aqueous solution and minerals, as well as changes in solid and pore geometry. Homogeneous reactions are described through local equilibrium mass action relations. Mineral reactions are treated kinetically through boundary conditions at the mineral surface. Simulation examples presented include injection of carbon dioxide saturated brine into a limestone rock with pore geometry derived from a thin section, crystal formation from a supersaturated solution without flow, and crystal formation during carbon dioxide sequestration in oceanic sediments.