The impact of pore-scale magnetic field inhomogeneity on the shape of the nuclear magnetic resonance relaxation time distribution

Abstract

Measurements of the nuclear magnetic resonance (NMR) signal’s behavior with time provide powerful noninvasive insight into the pore-scale environment. The time dependence of the NMR signal, which is a function of parameters called relaxation times, is intimately linked to the geometry of the pore space and has been used successfully to estimate pore size and permeability. The basis for the pore size and permeability estimates is that interactions occurring at the grain surface often function as the primary mechanism controlling the time dependence of the NMR signal. In this limit, called the fast diffusion limit, and when each pore can be considered to be isolated, the measured relaxation times are often interpreted as representative of pore sizes. In heterogeneous media, where the NMR signal is described by a distribution of relaxation times, the measured relaxation time distribution is often interpreted as representative of the underlying pore-size distribution. We have explored a scenario in which an additional relaxation mechanism, which arises due to magnetic field inhomogeneity across the pore space, violates the assumption that interactions occurring at the grain surface are the dominant relaxation mechanism. Using both synthetic and laboratory studies, we demonstrate that magnetic field inhomogeneity can lead to a complex relationship between the measured relaxation time distribution and the underlying pore-size distribution. Magnetic field inhomogeneity is observed to lead to a spatially heterogeneous magnetization density across the pore space requiring multiple eigenmodes to describe the evolution of the magnetization within a single pore during the NMR experiment. This results in a breakdown of the validity of the interpretation of the relaxation time distribution as representative of the underlying pore-size distribution for sediments with high magnetic susceptibility.

NMR relaxation times for soil texture estimation in the laboratory: A comparison to the laser diffraction and sieve–pipette methods

“…In materials with high magnetic susceptibility, induced magnetization associated with the magnetic particles results in inhomogeneities in the magnetic field. In this case the diffusion relaxation term is no longer negligible; laboratory and numerical studies have shown that this results in a broadening of the T 2 distribution and a shift of the T 2 distribution to shorter relaxation times (Fay, Knight, & Song, 2015; Grombacher, Fay, Nordin, & Knight, 2016; Keating & Knight, 2007). When we compare the T 2 distributions to the GSDs from the LDPSA data, we see the effect of the high magnetic susceptibility minerals most clearly at profiles 2, 3 and 4 in site 2.…”

“…These values are similar to the oil industry standard of 3 ms used to define the capillary‐bound and clay‐bound fluid in sandstones. However, the value of around 3 ms of T 2 a is not applicable to site 2 soils with high MS, which can cause relaxation to occur faster and cause the relaxation time distributions to be broader (Grombacher et al, 2016; Keating et al, 2020; Keating & Knight, 2008). The T 2 distribution of site 2 soils with high MS is not linearly proportional to the PSD as the diffusion relaxation term is no longer negligible.…”

Investigating the effect of internal gradients on static gradient nuclear magnetic resonance diffusion measurements

“…where P i is the proportion of pore fluid relaxing with the relaxation time T 2i . Surface relaxation is often assumed to be the dominant relaxation mechanism in porous materials; the contribution of bulk relaxation is assumed to be negligible, and the contribution from T 2D is assumed to be small for short t E , although this assumption may be violated in the case of large internal gradients (Grombacher et al, 2016). For most cases in which these assumptions are valid, the observed decay rate will be proportional to S∕V.…”

“…In addition to magnetic susceptibility contrasts, pore geometry also impacts the magnitude of the internal gradients; gradients increase as pore size decreases (Song, 2001). Internal gradients also vary with their proximity to the pore walls (Cho et al, 2009), with the highest localized gradients occurring near inflection points (such as sharp corners) on a pore surface (Brown and Fantazzini, 1993;Zhang et al, 2003;Grombacher et al, 2016). The background field strength controls the magnitude of internal gradients, such that measurements conducted at lower fields will be less impacted by internal gradients (Mitchell et al, 2010; see also Figure 11 in Fay et al 2015).…”

“…The magnitude of internal gradients depends on the susceptibility contrast between the solid phase and the pore fluid, and so variability in χ of the solid phase will result in different gradient magnitudes. Pore size, pore geometry, and proximity to pore walls also impact internal gradient magnitudes (Cho et al, 2009;Grombacher et al, 2016), such that even sediments with uniform χ will exhibit a distribution of internal gradient magnitudes.…”