Mesoscopic modeling of flow and dispersion phenomena in fractured solids

The problem of hydrodynamic dispersion in porous media is considered and numerical predictions of the mixing degree in a single intersection are provided. The flow field in the intersection and adjacent pores or fractures is calculated using a lattice Boltzmann model for single phase flow. A particle-tracking scheme is used, subsequently, that monitors the migration of solute particles in the area of the intersection taking into account the local flow field and a Brownian field. Mixing is quantified in terms of the probability of solute transfer across the junction into the opposite fracture. To circumvent the problem of large computational times for cases of fast flow compared to diffusion, a lattice Boltzmann advection–diffusion model is used, that offers significant savings on computational time without sacrificing accuracy. It is shown that the solute dispersion in a fracture network is a strong function of the Reynolds number, even if the Peclet number remains constant, due to the extensive recirculation areas that may develop in regions close to the junction.