Nuclear magnetic resonance average pore-size estimations outside the fast-diffusion regime

The pore-size distribution (PSD) of geologic materials is an important rock parameter to understand the flow of water in the subsurface. PSDs can be obtained from sieving analyses, mercury porosimetry measurements, and imaging techniques, but none of these methods is available for in situ measurements. Nuclear magnetic resonance (NMR) measurements are controlled by rock parameters such as the surface-area to pore-volume ratio. NMR is available for in situ measurements. State-of-the-art NMR relaxation time measurements need a calibration of the surface relaxivity $ρ$ to extract pore-size information. State-of-the-art NMR diffusion measurements avoid the calibration of $ρ$ but are limited to small pores. We developed an approach that estimates the average pore size without calibrating $ρ$ by means of incorporating higher order modes into the signal interpretation of NMR relaxation times. We conducted forward-modeling studies using an analytic solution for cylindrical tubes, 2D finite-element simulations to incorporate fractal pore spaces, and laboratory experiments on synthetic and natural samples. Our experimental data indicated that relaxation can occur outside the fast-diffusion regime not only for coarse-grained materials, but also for fine- to medium-grained unconsolidated sandy materials due to high surface relaxivities. We found that the rock-fluid interface’s roughness had a significant impact on the diffusion regime and led to an apparent increase in $ρ$⁠, which may cause intermediate or slow diffusion. The methodology was limited to materials with a narrow PSD and uniform distribution of $ρ$ because we assumed multiexponential decay due to diffusion in single isolated pores.