Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three-dimensional (3-D) mass distribution for boundary nodes only when the number of external (inward-pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3-D body-centered-cubic lattices are presented for Poiseuille flow, porous-plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two-dimensional (2-D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3-D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3-D low-Reynolds-number flow.

The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions.

Pore-scale simulations of monodisperse sphere packing and fluid flow in cylinders have reproduced heterogeneities in packing density and velocity previously observed in experiment. Simulations of tracer dispersion demonstrate that these heterogeneities enhance hydrodynamic dispersion, and that the degree of enhancement is related to the cylinder radius, R. The time scale for asymptotic dispersion in a packed cylinder is proportional to R2/D̂T, where D̂T represents an average rate of spreading transverse to the direction of flow. A generalization of the Taylor–Aris model of dispersion in a tube provides qualitative predictions of the long-time dispersion behavior in packed cylinders.