Correlations between dispersion and structure in porous media probed by nuclear magnetic resonance

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Abstract
Magnetic Resonance Imaging (MRI) and Pulsed Gradient Stimulated Echo (PGSTE) Nuclear Magnetic Resonance (NMR) experiments have been used to probe structure and dispersion in a model porous system formed from a packed bed of spherical particles. The structure of the pore space is characterized from the MRI images by determining radial distribution functions for the pore space. The PGSTE experiments yield an average displacement propagator from which the variance of the average molecular displacement and dispersion coefficient are determined at a range of times over which the flow develops. Experiments have been performed over a wide range of Péclet number and flow velocity. The behavior of the dispersion is shown to be closely related to the structure of the pore space. Dispersion transverse to the direction of superficial flow is dominated by Taylor dispersion. In the axial direction, non-Fickian effects become important, even for flow within a single pore. The axial dispersion coefficient approaches an asymptotic limit characterized by a scale length that corresponds to the pore-to-packing correlation length in the direction of flow, suggesting that the non-Fickian dispersion reaches a limiting behavior after just one mixing between streams merging from two interconnected pores.