Pore-Size Measurement from Eigenvalues of Magnetic Resonance Relaxation

Abstract

Nonground eigenvalues are widely disregarded in magnetic resonance relaxation measurements of porous media due to difficulties involved in their measurement, detection, and the derivation of physically meaningful parameters from them. Such nonground eigenvalues may be experimentally observed in relaxation measurements, such as the relaxation correlation of T 1 − T 2 , and yield information on the pore size and surface relaxivity of porous media without calibration through other independent measurements. Nonground eigenvalue analysis of T 1 − T 2 measurements on Berea sandstone undertaken at three static magnetic fields produces pore sizes consistent with those obtained through x-ray microtomography and SEM measurements. Similar agreement is found for a Bentheimer sandstone with a more complex pore geometry. A phase-encoding imaging variant of this method measures the imbibition confinementsize profile in Berea sandstone. It is suggested that the existence of nonground eigenmodes may be much more prevalent in simple magnetic resonance relaxation measurements than previously considered. Therefore, it is possible to measure pore size by matching numerical Brownstein-Tarr solutions with those of experiments in a wide variety of samples and magnetic resonance methods.

Bayesian Optimization With Transfer Learning: A Study on Spatial Variability of Rock Properties Using NMR Relaxometry

“…For comparison, the identified values for surface relaxivity are close to the reported ρ 2 = 8.0 μm/s for Bentheimer sandstone determined using the Bayesian MR approach by comparing the T 2 distribution and pore size distribution (Holland et al, 2013), but are smaller than the reported ρ 2 = 26 μm/s for Bentheimer sandstone Afrough et al (2021). The latter 2-3 times higher value is mainly due to the planar geometry assumed in their work, which provides less surface area per volume compared to spherical geometry.…”

“…Consequently, if the assumptions leading to Equation are violated and, for example, there is higher susceptibility contrast around a pore resulting in larger internal gradients, larger values of ρ 2 will compensate for the resultant faster relaxation (Duschl et al., 2015; Stingaciu et al., 2010). Alternate 1D and 2D NMR methods based on the Decay due to Diffusion in the Internal Field (DDIF) technique (Song et al., 2002), or similar in nature, were proposed to measure pore‐size distributions of sedimentary rock, though constant pore shape and uniform constant surface relaxivity again are limiting assumptions (Afrough et al., 2021; Liu et al., 2014; Muncaci & Ardelean, 2013; Zhang et al., 2016).…”