Upscaling pore-scale reactive transport equations using a multiscale continuum formulation

Reactive transport equations are solved at the pore scale using the lattice Boltzmann (LB) method, and the results are upscaled using volume averaging over a representative elemental volume and are fit to a multiscale continuum model. The multiscale continuum model accounts for local concentration gradients within diffusion-dominated matrix domains that are coupled to the primary continuum fluid. In general it is found that a multiscale continuum formulation is required to fit the upscaled pore-scale results. However, it is also demonstrated that in some cases, multiscale processes may be represented by a single-continuum model employing effective parameters that are not directly measurable. Provided that sufficient resolution of the pore-scale geometry can be obtained, the pore-scale model can be used to determine the most appropriate form of continuum formulation (single, dual, or multiple continua) that best fits the upscaled pore-scale simulation and, simultaneously, to provide parameters needed for constitutive relations appearing in the multiscale continuum formulation. It is suggested that a multiscale continuum approach may help explain the observed discrepancy between laboratory and field-derived reaction rates by explicitly representing distinct transport domains through separate interacting continua which could be responsible for the formation of preferential pathways. An example is presented on the basis of a multiscale, synthetic, structured porous medium describing transport of a tracer and linear reaction kinetics.