Lattice Boltzmann simulation of solute transport in heterogeneous porous media with conduits to estimate macroscopic continuous time random walk model parameters

Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcy's Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves.