In this study, we present laboratory experiments investigating the effect of pore size and surface relaxivity ρ2 on the nuclear magnetic resonance response of variably saturated sands that relax both within and outside the fast diffusion regime. We measured the NMR response of sands with a range of grain sizes (129 to 753 μm), which resulted in samples with different pore sizes, and a range of iron concentrations (0.07% to 0.38%), which resulted in sands with different ρ2 values. The laboratory results showed that the relation between relaxation time and water saturation depended on the regime in which relaxation occurred. For samples relaxing in the fast diffusion regime (i.e., small pores and low surface relaxivity), the relation between relaxation time and water saturation was linear; for the remaining samples, the relation between relaxation time and saturation demonstrated a power-law relationship with an exponent greater than one. In addition, we performed numerical simulations based on common pore-filling mechanisms (i.e., capillary tubes or thin films). The numerical simulations did not predict the experimental results for the relative surface relaxation versus saturation trends. We conclude that, in addition to the diffusion regime in which relaxation occurs, the shape of the relaxation time versus saturation curve depends on the pore-filling mechanism, the value of ρ2, and the pore size. The dependence of NMR relaxation on the pore-filling mechanism of saturating porous media may complicate efforts to develop a relation between relaxation time and saturation for use in characterizing unsaturated porous media.
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