A Lattice Boltzmann Method for Coupled Fluid Flow, Solute Transport, and Chemical Reaction

In this chapter we present a lattice Boltzmann method (LBM) for modeling coupled fluid flow, solute transport, and chemical reaction at a fundamental scale where the flow is governed by continuum fluid equations. Our numerical model accounts for multiple processes, including fluid flow, diffusion and advection of species, ion-exchange and mineral precipitation/dissolution reactions, as well as the evolution of pore geometry due to dissolution/precipitation. Homogeneous reactions are described either kinetically or through local equilibrium mass action relations. Heterogeneous reactions are incorporated into the LBM through boundary conditions imposed at the mineral surface. The LBM can provide detailed information on local fields, such as fluid velocities, solute concentrations, mineral compositions and amounts, as well as the evolution of pore geometry due to chemical reactions. Simulation examples include flow in a channel coupled with different reactions (linear kinetics for a single component, nonlinear kinetics for multi-components, and ion exchange reaction with constant Kd), crystal growth from supersaturated solution, and injection of CO₂ into a limestone rock.

Keywords: Lattice Boltzmann method, fluid flow, reactive solute transport, homogeneous reaction, heterogeneous reaction, dissolution, precipitation, sorption, physicochemical transport and interfacial processes, porous media, evolution of pore geometry, pore scale, continuum scale.