Simulation of Pore-Scale Dispersion in Periodic Porous Media Using Smoothed Particle Hydrodynamics

A numerical model using smoothed particle hydrodynamics (SPH) for the simulation of pore-scale hydrodynamic dispersion is presented. The model is used to solve the Taylor dispersion problem and explore the characterization of dispersion as an asymptotic Fickian process. Discrete SPH particle data are analyzed using the method of moments. Simulations for pure tracer convection are used to calculate values of tortuosity and effective porosity for two-dimensional spatially periodic porous media. Tracer convection through such media cannot be described as an asymptotic Fickian-type process, even for large times, if the driving body force F is parallel to a line of media symmetry. If F is not parallel to a line of media symmetry, Fickian-type mixing is possible for tracer convection. An asymptotic Fickian approximation is valid for tracer dispersion through two-dimensional spatially periodic porous media when diffusion effects are included.