Lattice Boltzmann Simulation of Solute Transport in Heterogeneous Porous Media with Conduits to Estimate Macroscopic Continuous Time Random Walk Model Parameters

We use Lattice Boltzmann models to simulate solute transport in porous media traversed by larger conduits and fit the resulting solute breakthrough curves with macroscopic Continuous Time Random Walk (CTRW) models. In this paper, the porous media are simulated using a real-numbered coefficient that partially damps the inertial components of the flow and, when the damping is large enough, leads to a Darcy’s Law solution in the porous media in contrast to the normal Navier-Stokes solution provided by the standard lattice Boltzmann model. As required in macroscopic simulation of solute transport in porous media, anisotropic dispersion is incorporated using a directiondependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard advection-dispersion equation (ADE) including moderate Reynolds number flow in conduits traversing porous media that leads to eddy mixing. As the simplest case examined, zero diffusion transport in laminar flow in a slit is fitted with the CTRW model. CTRW also fits breakthrough curves from homogeneous and heterogeneous domains for high and low Reynolds numbers. The advection-dispersion equation fails to adequately fit any of these breakthrough curves.