Obtaining true transverse relaxation time distributions in high-field NMR measurements of saturated porous media: Removing the influence of internal gradients

Structural integrity and healing efficiency study of micro-capsule based composite materials via 1H NMR relaxometry

In this work we present a novel approach utilizing nuclear magnetic resonance (NMR) relaxometry to assess the structural stability of microcapsules employed as self-healing agents in advanced aerospace composites both in ambient and harsh environmental conditions. We successfully correlate the amount of the encapsulated self-healing agent with the signal intensity and confirm non-destructively the quantity of the encapsulated self-healing agent mass for the first time in the literature using ¹H NMR spin-spin relaxation techniques on urea-formaldehyde (UF) microcapsules of different diameters containing an epoxy healing agent. The amount of self-healing agent is shown to increase by reducing the capsule diameter; however, the reduced shell mass renders the capsules more fragile and prone to failure. Most notably, via NMR experiments conducted during thermal cycling simulating flight conditions, we demonstrate that the microcapsule integrity under thermal fatigue varies according to their size. Especially we experimentally verify that the microcapsules with the most sensitive shells are the 147 nm and 133 nm diameter microcapsules, which are the most commonly used in self-healing systems. Finally, we were able to retrieve the same results using a portable NMR spectrometer developed in-house for in situ microcapsule testing, thus demonstrating the potential of NMR relaxometry as a powerful non-destructive evaluation tool for the microcapsule production line.

NMR Relaxation Modelling in Porous Media with Dual-Scale-Resolved Internal Magnetic Fields

A pore-scale forward modelling approach for NMR relaxation responses of sandstones incorporating their dual-scale nature is presented. The approach utilises X-ray micro-CT images to capture inter-granular porosity and scanning electron microscopy images to reconstruct clay regions via a resolved clay micro-structure model. A key to calculating the NMR response with resolved clay micro-structure is the development of a dual-scale internal magnetic field calculation. This is achieved by a separation of near- and far-field effects in a dipole approximation of the internal field with periodic clay micro-structures, the latter of which take local clay pocket porosity into account. Tri-linear interpolation of the micro-CT image before calculation of the internal magnetic field further reduces errors in the transition regions between coarse- and fine-scale structure, with final discretisation level matching the fine-scale clay micro-structure model across the whole domain. The method is validated against direct calculations of model media at full resolution and applied to Bentheimer sandstone. Measured and simulated NMR $$T_2$$ T 2 relaxation responses, including relaxation time distribution shape, are in excellent agreement and distributions of internal magnetic field gradients at the highest spatial resolution as well as diffusion-averaged effective gradients are reported.

Combination of MRI and SEM to Assess Changes in the Chemical Properties and Permeability of Porous Media due to Barite Precipitation

The understanding of the dissolution and precipitation of minerals and its impact on the transport of fluids in porous media is essential for various subsurface applications, including shale gas production using hydraulic fracturing (“fracking”), CO2 sequestration, or geothermal energy extraction. In this work, we conducted a flow through column experiment to investigate the effect of barite precipitation following the dissolution of celestine and consequential permeability changes. These processes were assessed by a combination of 3D non-invasive magnetic resonance imaging, scanning electron microscopy, and conventional permeability measurements. The formation of barite overgrowths on the surface of celestine manifested in a reduced transverse relaxation time due to its higher magnetic susceptibility compared to the original celestine. Two empirical nuclear magnetic resonance (NMR) porosity–permeability relations could successfully predict the observed changes in permeability by the change in the transverse relaxation times and porosity. Based on the observation that the advancement of the reaction front follows the square root of time, and micro-continuum reactive transport modelling of the solid/fluid interface, it can be inferred that the mineral overgrowth is porous and allows the diffusion of solutes, thus affecting the mineral reactivity in the system. Our current investigation indicates that the porosity of the newly formed precipitate and consequently its diffusion properties depend on the supersaturation in solution that prevails during precipitation.

A fluid specific dimension of confinement as a measure of wettability in porous media

The wettability of a reservoir rock is among the most important factors influencing oil recovery. This study presents how the application of a modified CPMG pulse sequence can determine the wettability of porous samples containing oil and water in the same pore network. This method can be applied as an average of the signal over the entire sample as well as with spatial resolution using slice selection. Correlations between dephasing in internal gradients (G₀²D) and the spectral linewidth (Δν) were used to calculate a fluid specific dimension of confinement (DOC) distribution for oil and water separately during forced displacement experiments performed inside the bore of an NMR spectrometer. Two samples, one water-wet and one oil-wet, were investigated. Data averaged over the entire sample show oil and water distribution at endpoint saturations (S_w=1,S_w,i and S_or) while spatially resolved data show which pores are initially occupied by the displacing fluid as well as the displacing efficiency. Both the data averaged over the entire sample and the spatially resolved data can, by itself, indicate wettability. As opposed to relaxation times as an indirect indication of wettability, the DOC distributions provide a direct fluid dimension, which more carefully describes the distribution of oil and water in the pore network.

Investigating pore geometry in heterogeneous porous samples using spatially resolved G0-Δχapp and G0-Δν correlations

This study presents a two-dimensional NMR pulse sequence for obtaining spatially resolved correlations between magnetic susceptibility induced internal gradients (G₀), and both the apparent difference in magnetic susceptibility (Δχ_app) and spectral frequency (Δν). G₀-Δχ_app correlations were utilized to generate spatially resolved pore size distributions, while the G₀-Δν correlations were used to additionally evaluate sample heterogeneity. The spatially resolved measurements were performed on a water saturated heterogeneous porous sample which contains one layer of 5-50 μm glass spheres (top layer) and one layer of 140-165 μm glass spheres (bottom layer). The slice selection was validated by applying the pulse sequence on a liquid mineral oil and water sample as well as on the porous sample. The resulting spatially resolved pore size distributions show very good agreement with results from our previously published non slice selective pulse sequence in the 140-165 μm glass spheres and good agreement in the 5-50 μm glass spheres. The G₀-Δν correlations correctly indicate a slightly higher degree of heterogeneity in the 5-50 μm glass spheres compared to the 140-165 μm glass spheres.

Effect of paramagnetic species on T1, T2 and T1/T2 NMR relaxation times of liquids in porous CuSO4/Al2O3

This work explores the effect of paramagnetic ions deposited on solid surfaces on T₁, T₂ and T₁/T₂ relaxation times.

Effect of magnetic pore surface coating on the NMR relaxation and diffusion signal in quartz sand

Magnetic impurities are ubiquitous in natural porous media such as sand and soil. They generate internal magnetic field gradients because of increased magnetic susceptibility differences between solid and liquid phase in the pore space and because of the presence of magnetic centers. These internal gradients accelerate NMR relaxation rates and thus might limit the possibility of pore space characterization using NMR. In this study, we investigate the effects of coating the surface of natural sands by the antiferromagnetic iron oxyhydroxide goethite on NMR relaxation and diffusion properties. We found a non-quadratic dependence of the relaxation time distributions on the echo time indicating that the relaxation experiments were not performed in the fast diffusion limit, while the weak dependence on the external magnetic field strength is explained by the preponderance of the surface relaxation over the effect of diffusion in internal gradients. The surface to volume ratio of the pore space, determined by NMR diffusimetry ((S/V)_NMR ) remains approximately constant, whereas the same quantity, determined from gas adsorption ((S/V)_BET ) increases proportional to the coating density. This is because gas adsorption measures surface roughness on sub-nanometer scale, whereas NMR diffusimetry averages over structures smaller than few microns. This has consequences for the calculation of the surface relaxivities. The usage of the (S/V)_NMR leads to constant values, whereas the usage of (S/V)_BET leads to apparently decreasing relaxivities with increasing coating, which is unrealistic. Copyright © 2016 John Wiley & Sons, Ltd.

Direct correlation of internal gradients and pore size distributions with low field NMR

Internal magnetic field gradients Gint, which arise from the magnetic susceptibility difference Δχ between solid matrix and fluid in porous media relate to the pore geometry. However, this relationship is complex and not well understood. Here we correlate internal-gradient distributions to pore-size distributions directly to examine internal gradients in detail at low field NMR. The pore-size distributions were obtained by the method of Decay due to Diffusion in the Internal Field (DDIF), and the internal-gradient distributions were measured with the Carr-Purcell-Meiboom-Gill (CPMG) method. The internal-gradient-pore-size distributions correlation maps were obtained for water in packs of glass beads with different diameter and in a sandstone sample. The relationship between internal gradients and pore structure is analyzed in detail by considering the restricted diffusion of fluids in porous samples. For each case diffusion regimes are assigned by plotting normalized CPMG data and comparing the diffusion lengths, the dephasing lengths and pore diameters. In the free-diffusion limit, the correlation maps reveal the true relationship between pore structure and internal gradients so that Δχ can be approximated from the correlation maps. This limit is met most easily at low field. It provides information about porous media, which is expected to benefit the oil industry, in particular NMR well logging.

11-interval PFG pulse sequence for improved measurement of fast velocities of fluids with high diffusivity in systems with short T2(∗)

Magnetic resonance (MR) was used to measure SF6 gas velocities in beds filled with particles of 1.1 mm and 0.5 mm in diameter. Four pulse sequences were tested: a traditional spin echo pulse sequence, the 9-interval and 13-interval pulse sequence of Cotts et al. (1989) and a newly developed 11-interval pulse sequence. All pulse sequences measured gas velocity accurately in the region above the particles at the highest velocities that could be achieved (up to 0.1 ms(-1)). The spin echo pulse sequence was unable to measure gas velocity accurately in the bed of particles, due to effects of background gradients, diffusivity and acceleration in flow around particles. The 9- and 13-interval pulse sequence measured gas velocity accurately at low flow rates through the particles (expected velocity <0.06 ms(-1)), but could not measure velocity accurately at higher flow rates. The newly developed 11-interval pulse sequence was more accurate than the 9- and 13-interval pulse sequences at higher flow rates, but for velocities in excess of 0.1 ms(-1) the measured velocity was lower than the expected velocity. The increased accuracy arose from the smaller echo time that the new pulse sequence enabled, reducing selective attenuation of signal from faster moving nuclei.

A multi-dimensional experiment for characterization of pore structure heterogeneity using NMR

In a liquid saturated porous sample the spatial inhomogeneous internal magnetic field in general depends on the strength of the static magnetic field, the differences in magnetic susceptibilities, but also on the geometry of the porous network. To thoroughly investigate how the internal field can be used to determine various properties of the porous structure, we present a novel multi-dimensional NMR experiment that enables us to measure several dynamic correlations in one experiment, and where all of the correlations involve the internal magnetic field and its dependence on the geometry of the porous network. (Correlations: internal gradient - pore size, internal gradient - magnetic susceptibility difference, internal gradient - longitudinal relaxation, longitudinal relaxation - magnetic susceptibility difference.) It is always a spatial average of the internal magnetic field, or one of the related properties, that is measured, which is important to take into consideration when analyzing the obtained results. We demonstrate how these correlations can be an indicator for pore structure heterogeneity, and focus in particular on how the effect from spatial averaging can be evaluated and taken into account in the different cases.

Dehydration of AlPO4-34 studied by variable-temperature NMR, XRD and first-principles calculations

Complementary techniques elucidate water–framework interactions in different states of dehydration, two of which have not been observed before.

Gint2D-T2 correlation NMR of porous media

The internal magnetic field gradient induced in porous media by magnetic susceptibility differences at material interfaces impacts diffusion measurements in particular at high magnetic field and can be used to probe the pore structure. Insight about the relationship between pore space and internal gradient G(int) can be obtained from 2D Laplace NMR experiments. When measuring distributions of transverse relaxation times T(2) in fluid filled porous media, relaxation and diffusion in internal gradients arise simultaneously and data are often interpreted with the assumption that one or the other parameter be constant throughout the sample. To examine this assumption we measure correlations of the distributions of G(int)(2)D and T(2) by 2D Laplace NMR for three different kinds of samples, glass beads with different bead diameters saturated with water, glass beads filled with oil and water, and a wet mortar sample. For the first two samples the cases where either the internal gradient or diffusion dominates were examined separately in order to better understand the relationship between G(int) and D. These results are useful for assessing the impact of internal gradients and diffusion in unknown samples, such as the mortar sample. The experiments were performed at different magnetic field strengths corresponding to 300 MHz and 700 MHz (1)H Larmor frequency to identify the impact of the magnetic field on the internal gradient. Subsequently, spatially resolved Gint(2)D-T(2) maps were obtained to study the sample heterogeneity.

Diffusion-assisted selective dynamical recoupling: a new approach to measure background gradients in magnetic resonance

Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling (SDR) [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out "intrinsic" T1 and T2 weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the system's composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.

Superstatistics model for T₂ distribution in NMR experiments on porous media

We propose analytical functions for T2 distribution to describe transverse relaxation in high- and low-fields NMR experiments on porous media. The method is based on a superstatistics theory, and allows to find the mean and standard deviation of T2, directly from measurements. It is an alternative to multiexponential models for data decay inversion in NMR experiments. We exemplify the method with q-exponential functions and χ(2)-distributions to describe, respectively, data decay and T2 distribution on high-field experiments of fully water saturated glass microspheres bed packs, sedimentary rocks from outcrop and noisy low-field experiment on rocks. The method is general and can also be applied to biological systems.

Spatially resolved D-T(2) correlation NMR of porous media

Within the past decade, 2D Laplace nuclear magnetic resonance (NMR) has been developed to analyze pore geometry and diffusion of fluids in porous media on the micrometer scale. Many objects like rocks and concrete are heterogeneous on the macroscopic scale, and an integral analysis of microscopic properties provides volume-averaged information. Magnetic resonance imaging (MRI) resolves this spatial average on the contrast scale set by the particular MRI technique. Desirable contrast parameters for studies of fluid transport in porous media derive from the pore-size distribution and the pore connectivity. These microscopic parameters are accessed by 1D and 2D Laplace NMR techniques. It is therefore desirable to combine MRI and 2D Laplace NMR to image functional information on fluid transport in porous media. Because 2D Laplace resolved MRI demands excessive measuring time, this study investigates the possibility to restrict the 2D Laplace analysis to the sum signals from low-resolution pixels, which correspond to pixels of similar amplitude in high-resolution images. In this exploratory study spatially resolved D-T2 correlation maps from glass beads and mortar are analyzed. Regions of similar contrast are first identified in high-resolution images to locate corresponding pixels in low-resolution images generated with D-T2 resolved MRI for subsequent pixel summation to improve the signal-to-noise ratio of contrast-specific D-T2 maps. This method is expected to contribute valuable information on correlated sample heterogeneity from the macroscopic and the microscopic scales in various types of porous materials including building materials and rock.

Evaporation kinetics in swollen porous polymeric networks

NMR is a fast, nondestructive, and noninvasive technique that can provide information about the pore structure of macroporous polymer beads and the dynamics of liquids confined in them. In this work, we describe the study of the pore structure of the macroporous polymer of ethylene glycol dimethacrylate and 2-hydroxyethyl methacrylate [poly(EGDMA-co-HEMA)] in the dry but also in the swollen state by measuring relaxation times of liquids contained in the polymer network. The results show that the pore architecture differs from the dry to the soaked state. The behavior of polar liquids during evaporation and deswelling dynamics is monitored and described. An internal migration of water from the swollen polymer mesh into expanding pores takes place. With this procedure it is possible to obtain information about the microscopic morphology behavior of the matrix during evaporation and deswelling. This information is of great interest with the aspect of possible and future applications for these types of materials.

Rapid measurements of heterogeneity in sandstones using low-field nuclear magnetic resonance

Sandstone rocks can contain microscopic variations in composition that complicate interpretation of nuclear magnetic resonance (NMR) relaxation time measurements. In this work, methods for assessing the degree of sample heterogeneity are demonstrated in three sandstones. A two-dimensional T1-Δχapp correlation (where Δχapp is the apparent solid/liquid magnetic susceptibility contrast) reveals the microscopic heterogeneity in composition, whilst a spatially resolved T1 profile reveals the macroscopic structural heterogeneity. To perform these measurements efficiently, a rapid measure of longitudinal T1 relaxation time has been implemented on a low-field NMR spectrometer with a magnetic field strength B0=0.3 T. The "double-shot" T1 pulse sequence is appropriate for analysis of porous materials in general. Example relaxation time distributions are presented for doped water phantoms to validate the method. The acquisition time of the double-shot T1 sequence is equivalent to the single-shot Carr-Purcell Meiboom-Gill (CPMG) sequence used routinely in petrophysics to measure transverse T2 relaxation. Rapid T1 measurements enable practical studies of core plugs at magnetic field strengths previously considered inappropriate, as T1 is independent of molecular diffusion through pore-scale (internal) magnetic field gradients.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Updated methodology for nuclear magnetic resonance characterization of shales

Unconventional petroleum resources, particularly in shales, are expected to play an increasingly important role in the world's energy portfolio in the coming years. Nuclear magnetic resonance (NMR), particularly at low-field, provides important information in the evaluation of shale resources. Most of the low-field NMR analyses performed on shale samples rely heavily on standard T1 and T2 measurements. We present a new approach using solid echoes in the measurement of T1 and T1-T2 correlations that addresses some of the challenges encountered when making NMR measurements on shale samples compared to conventional reservoir rocks. Combining these techniques with standard T1 and T2 measurements provides a more complete assessment of the hydrogen-bearing constituents (e.g., bitumen, kerogen, clay-bound water) in shale samples. These methods are applied to immature and pyrolyzed oil shale samples to examine the solid and highly viscous organic phases present during the petroleum generation process. The solid echo measurements produce additional signal in the oil shale samples compared to the standard methodologies, indicating the presence of components undergoing homonuclear dipolar coupling. The results presented here include the first low-field NMR measurements performed on kerogen as well as detailed NMR analysis of highly viscous thermally generated bitumen present in pyrolyzed oil shale.

Two-dimensional T2 distribution mapping in rock core plugs with optimal k-space sampling

Spin-echo single point imaging has been employed for 1D T(2) distribution mapping, but a simple extension to 2D is challenging since the time increase is n fold, where n is the number of pixels in the second dimension. Nevertheless 2D T(2) mapping in fluid saturated rock core plugs is highly desirable because the bedding plane structure in rocks often results in different pore properties within the sample. The acquisition time can be improved by undersampling k-space. The cylindrical shape of rock core plugs yields well defined intensity distributions in k-space that may be efficiently determined by new k-space sampling patterns that are developed in this work. These patterns acquire 22.2% and 11.7% of the k-space data points. Companion density images may be employed, in a keyhole imaging sense, to improve image quality. T(2) weighted images are fit to extract T(2) distributions, pixel by pixel, employing an inverse Laplace transform. Images reconstructed with compressed sensing, with similar acceleration factors, are also presented. The results show that restricted k-space sampling, in this application, provides high quality results.

Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D(app) and effective transverse relaxation time T(2,eff) to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D(app)-T(2,eff) correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D-T(2) pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T(2) samples in general.