Relating nuclear magnetic resonance relaxation time distributions to void-size distributions for unconsolidated sand packs

Nuclear magnetic resonance (NMR) is used in near-surface geophysics to understand the pore-scale properties of geologic material. The interpretation of NMR data in geologic material assumes that the NMR relaxation time distribution (T-2-distribution) is a linear transformation of the void-size distribution (VSD). This interpretation assumes fast diffusion and can be violated for materials with high surface relaxivity and/or large pores. We compared T(2-)distributions to VSDs using grain-size distributions (GSDs) as a proxy for VSDs. Measurements were collected on water-saturated sand packs with a range of grain sizes and surface relaxivities, such that some samples were expected to violate the fast diffusion assumption. Samples were prepared from silica sand with three different average grain sizes and were coated with the iron-oxide mineral hematite to vary the surface relaxivity. We found analytically that outside the fast diffusion regime, the T2-distributions are broader than in the fast diffusion regime, which could lead to misinterpretation of NMR data. The experimental results showed that the T-2-distributions were not linear transformations of the GSDs. The GSDs were a single peak independent of the hematite coating. The T-2-distributions were broader than the measured GSDs, and the center of the distribution depended on the coating. Using an equation that does not assume fast diffusion to transform the T-2-distributions to NMR-estimated VSDs resulted in distributions that were centered on a single radius. However, our attempts to recover the VSDs, as estimated from laser particle size analysis, were unsuccessful; the NMR-estimated VSDs were broader and yielded average pore radii that were much smaller than expected. We found that our approach was useful for determining relative VSDs from T-2-distributions; however, future research is needed to develop a method for calibrating the NMR-estimated VSDs for unconsolidated sands.