Nuclear magnetic resonance measurement and lattice-Boltzmann simulation of the nonlocal dispersion tensor

Abstract

The nonlocal dispersion tensor D NL provides a fundamental description of velocity correlations and displacement information in a dispersive system. It is shown that pulsed gradient spin echo nuclear magnetic resonance can be used to measure this tensor, and we present here the first measurement of D NL in a complex flow by this or any other methods. These measurements are complemented by simulations based on a lattice-Boltzmann calculation of the fluid flow. For dispersive flow in a random bead pack of monosized spheres, six nonzero, independent components remain. These components have been measured at three times less than v , the time to flow one bead diameter. It is shown here that the various elements of D NL provide insights regarding the dispersive flow, which are extremely sensitive to the details of local correlations.

PGSE NMR measurement of the non-local dispersion tensor for flow in porous media

“…The code provides a way of statistically measuring the tensors we are interested in. The results between the simulated non-local dispersion in a algorithm-generated beadpack compare well with experimental measurements of a random bead pack [25] although large differences in porosities between our simulated beadpacks ð$ 0:7Þ and experimental beadpacks ð$ 0:4Þ preclude exact agreement. The simulated propagator of Fig.…”

“…9(c). These effects, and details of the simulation are discussed further in [25]. Statistical calculation of the non-local dispersion tensor is performed by calculating the contribution to the velocity auto correlation function from each tracer particle and putting this value in a bin, depending on how far the tracer particle has moved.…”

Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

“…The lattice Boltzmann code provides a way of statistically measuring the tensors we are interested in. The results between the simulated nonlocal dispersion in a algorithm-generated beadpack compare well with experimental measurements of a random bead pack [158] although large differences in porosities between our simulated beadpacks (∼ 0.7) and experimental beadpacks (∼ 0.4) preclude exact agreement. The simulated propagator of figure 5.10(c) clearly shows more slower moving particles than the experimental propagator of figure 5.9(c).…”

Propagator-resolved 2D exchange in porous media in the inhomogeneous magnetic field

“…We have built upon a computer model created by Hunter et al [16] which generates a random bead pack and uses a random walk model to simulate diffusion throughout its pore space. To create the bead pack we drop spheres one by one into a cylinder of diameter 10 bead diameters and allow the beads to reach their potential energy minimum.…”