A simple liquid state 1H NMR measurement to directly determine the surface hydroxyl density of porous silica.

Silica is widely used in industrial applications and its performance is partially decided by its surface hydroxyl density αOH. Here we report a quick, simple liquid 1H NMR method to determine αOH using a benchtop 1H NMR spectrometer. The results show excellent agreement with the literature with an αOH range from 4.16 to 6.56 OH per nm2.

Characterizing pore-scale structure-flow correlations in sedimentary rocks using magnetic resonance imaging.

Quantitative, three-dimensional (3D) spatially resolved magnetic resonance flow imaging (flow MRI) methods are presented to characterize structure-flow correlations in a 4-mm-diameter plug of Ketton limestone rock using undersampled k- and q-space data acquisition methods combined with compressed sensing (CS) data reconstruction techniques. The acquired MRI data are coregistered with an X-ray microcomputed tomography (µCT) image of the same rock sample, allowing direct correlation of the structural features of the rock with local fluid transport characteristics. First, 3D velocity maps acquired at 35 µm isotropic spatial resolution showed that the flow was highly heterogeneous, with ∼10% of the pores carrying more than 50% of the flow. Structure-flow correlations were found between the local flow velocities through pores and the size and topology (coordination number) associated with these pores. These data show consistent trends with analogous data acquired for flow through a packing of 4-mm-diameter spheres, which may be due to the microstructure of Ketton rock being a consolidation of approximately spherical grains. Using two-dimensional and 3D visualization of coregistered µCT images and velocity maps, complex pore-scale flow patterns were identified. Second, 3D spatially resolved propagators were acquired at 94 µm isotropic spatial resolution. Flow dispersion within the rock was examined by analyzing each of the 331 776 local propagators as a function of observation time. Again, the heterogeneity of flow within the rock was shown. Quantification of the mean and standard deviation of each of the local propagators showed enhanced mixing occurring within the pore space at longer observation times. These spatially resolved measurements also enable investigation of the length scale of a representative elementary volume. It is shown that for a 4-mm-diameter plug this length scale is not reached.

Identification of sampling patterns for high-resolution compressed sensing MRI of porous materials: 'learning' from X-ray microcomputed tomography data.

There exists a strong motivation to increase the spatial resolution of magnetic resonance imaging (MRI) acquisitions so that MRI can be used as a microscopy technique in the study of porous materials. This work introduces a method for identifying novel data sampling patterns to achieve undersampling schemes for compressed sensing MRI (CS-MRI) acquisitions, enabling 3D spatial resolutions of 17.6 µm to be achieved. A data-driven learning approach is used to derive k-space undersampling schemes for 3D MRI acquisitions from 3D X-ray microcomputed tomography (µCT) datasets acquired at a higher spatial resolution than can be acquired using MRI. The performance of the new sampling approach was compared to other, well-established sampling strategies using simulated MRI data obtained from high-resolution µCT images of rock core plugs. These simulations were performed for a range of different k-space sampling fractions (0.125-0.375) using images of Ketton limestone. The method was then extended to consideration of imaging Estaillades limestone and Fontainebleau sandstone. The results show that the new sampling approach performs as well as or better than conventional variable density sampling and without need for time-consuming parameter optimisation. Further, a bespoke sampling pattern is produced for each rock type. The novel undersampling strategy was employed to acquire 3D magnetic resonance images of a Ketton limestone rock at spatial resolutions of 35 and 17.6 µm. The ability of the k-space sampling scheme produced using the new approach in enabling reconstruction of the pore space characteristics of the rock was then demonstrated by benchmarking against the pore space statistics obtained from high-resolution µCT data. The MRI data acquired at 17.6 µm resolution gave excellent agreement with the pore size distribution obtained from the X-ray microcomputed tomography dataset, while the pore coordination number distribution obtained from the MRI data was slightly skewed to lower coordination numbers. This approach provides a method of producing a k-space undersampling pattern for MRI acquisition at a spatial resolution for which a fully sampled acquisition at that spatial resolution would be impractically long. The approach can be easily extended to other CS-MRI techniques, such as spatially resolved flow and relaxation time mapping. LAY DESCRIPTION: Magnetic resonance imaging (MRI) is widely used to study the microstructure of, and fluid transport phenomena in porous media relevant for engineering applications. A major application is the study of water and hydrocarbon transport in porous sedimentary rocks, which typically have pore sizes smaller than 100 µm. The spatial resolution of routine MRI acquisitions, however, is limited to several hundred µm due to the relatively low sensitivity of the magnetic resonance method. Therefore, there exists a strong motivation to increase the spatial resolution of MRI by one to two orders of magnitude to be able to study these rocks at a pore scale. This work reports the initial step towards achieving this. Three-dimensional images of rock pore structure are acquired at both 35 and 17.6 µm spatial resolution. In ongoing work, these methods are now being incorporated into magnetic resonance velocity imaging methods, thereby enabling imaging of both pore structure and hydrodynamics at these much higher spatial resolutions than were hitherto possible. Although X-ray microcomputed tomography (µCT) produces high spatial resolution images, it is far more limited in being able to spatially map transport processes (i.e. flow) in porous media. This work reports a strategy for accelerating the image acquisition time such that sufficient signal-to-noise ratio (SNR) is achieved to increase the spatial resolution, that is, the voxel size within which there is sufficient SNR within the resulting image. To achieve this, a technique known as compressed sensing is used which exploits undersampling of the acquired data relative to the standard fully sampled image. In MRI, data are acquired in so-called k-space and Fourier transformed to yield the real space image. The challenge, when undersampling, is to optimise the specific points in k-space that are acquired because these will influence the quality of the resulting image. This work reports a straightforward, robust strategy for identifying the optimal sets of k-space points to acquire. The method introduced uses simulated MRI images calculated from high-resolution µCT images of the rocks of interest, from which optimised MRI sampling patterns are obtained. The method does not require any optimisation of parameters for its implementation, which is a significant advantage compared to other strategies. Moreover, we show that the pore space characteristics of the acquired MRI images are in excellent agreement with the same characteristics obtained from a high-resolution µCT image.

Insights into adsorption behaviour of binary liquid mixtures in porous media using fast field cycling NMR.

Fast field cycling, FFC, NMR relaxometry experiments are reported in the frequency range of 10 kHz-40 MHz to characterise the adsorption behaviour of cyclohexane:THF (non-polar:polar) and THF:methanol (polar:polar) binary liquid mixtures adsorbed on a γ-alumina surface of catalytic interest. Laplace inversion of the relaxation rate data is employed to identify the chemical species in the binary mixture. In both systems studied, the more polar molecule preferentially interacts with the surface compared to the co-imbibed species. The relaxation rate data were analysed to explore the relative influences of surface dynamics and surface accessibility on the observed relaxation rates. For both binary systems, the change in relaxation behaviour with composition is interpreted as a change in the surface accessibility of each species caused by a micro-phase separation at the pore surface.

Optimising sampling patterns for bi-exponentially decaying signals.

A recently reported method, based on the Cramér-Rao Lower Bound theory, for optimising sampling patterns for a wide range of nuclear magnetic resonance (NMR) experiments is applied to the problem of optimising sampling patterns for bi-exponentially decaying signals. Sampling patterns are optimised by minimizing the percentage error in estimating the most difficult to estimate parameter of the bi-exponential model, termed the objective function. The predictions of the method are demonstrated in application to pulsed field gradient NMR data recorded for the two-component diffusion of a binary mixture of methane/ethane in a zeolite. It is shown that the proposed method identifies an optimal sampling pattern with the predicted objective function being within 10% of that calculated from the experiment dataset. The method is used to advise on the number of sampled points and the noise level needed to resolve two-component systems characterised by a range of ratios of populations and diffusion coefficients. It is subsequently illustrated how the method can be used to reduce the experiment acquisition time while still being able to resolve a given two-component system.

Accelerating the estimation of 3D spatially resolved T2 distributions.

Obtaining quantitative, 3D spatially-resolved T2 distributions (T2 maps) from magnetic resonance data is of importance in both medical and porous media applications. Due to the long acquisition time, there is considerable interest in accelerating the experiments by applying undersampling schemes during the acquisition and developing reconstruction techniques for obtaining the 3D T2 maps from the undersampled data. A multi-echo spin echo pulse sequence is used in this work to acquire the undersampled data according to two different sampling patterns: a conventional coherent sampling pattern where the same set of lines in k-space is sampled for all equally-spaced echoes in the echo train, and a proposed incoherent sampling pattern where an independent set of k-space lines is sampled for each echo. The conventional reconstruction technique of total variation regularization is compared to the more recent techniques of nuclear norm regularization and Nuclear Total Generalized Variation (NTGV) regularization. It is shown that best reconstructions are obtained when the data acquired using an incoherent sampling scheme are processed using NTGV regularization. Using an incoherent sampling pattern and NTGV regularization as the reconstruction technique, quantitative results are obtained at sampling percentages as low as 3.1% of k-space, corresponding to a 32-fold decrease in the acquisition time, compared to a fully sampled dataset.

Optimising magnetic resonance sampling patterns for parametric characterisation.

Sampling strategies are often central to experimental design. Choosing efficiently which data to acquire can improve the estimation of parameters and reduce the acquisition time. This work is focused on designing optimal sampling patterns for Nuclear Magnetic Resonance (NMR) applications, illustrated with respect to the best estimate of the parameters characterising a lognormal distribution. Lognormal distributions are commonly used as fitting models for distributions of spin-lattice relaxation time constants, spin-spin relaxation time constants and diffusion coefficients. A method for optimising the choice of points to be sampled is presented which is based on the Cramér-Rao Lower Bound (CRLB) theory. The method's capabilities are demonstrated experimentally by applying it to the problem of estimating the emulsion droplet size distribution from a pulsed field gradient (PFG) NMR diffusion experiment. A difference of <5% is observed between the predictions of CRLB theory and the PFG NMR experimental results. It is shown that CLRB theory is stable down to signal-to-noise ratios of ∼10. A sensitivity analysis for the CRLB theory is also performed. The method of optimizing sampling patterns is easily adapted to distributions other than lognormal and to other aspects of experimental design; case studies of optimising the sampling scheme for a fixed acquisition time and determining the potential for reduction in acquisition time for a fixed parameter estimation accuracy are presented. The experimental acquisition time is typically reduced by a factor of 3 using the proposed method compared to a constant gradient increment approach that would usually be used.

In Situ Chemically-Selective Monitoring of Multiphase Displacement Processes in a Carbonate Rock Using 3D Magnetic Resonance Imaging.

Accurate monitoring of multiphase displacement processes is essential for the development, validation and benchmarking of numerical models used for reservoir simulation and for asset characterization. Here we demonstrate the first application of a chemically-selective 3D magnetic resonance imaging (MRI) technique which provides high-temporal resolution, quantitative, spatially resolved information of oil and water saturations during a dynamic imbibition core flood experiment in an Estaillades carbonate rock. Firstly, the relative saturations of dodecane ( S o ) and water ( S w ) , as determined from the MRI measurements, have been benchmarked against those obtained from nuclear magnetic resonance (NMR) spectroscopy and volumetric analysis of the core flood effluent. Excellent agreement between both the NMR and MRI determinations of S o and S w was obtained. These values were in agreement to 4 and 9% of the values determined by volumetric analysis, with absolute errors in the measurement of saturation determined by NMR and MRI being 0.04 or less over the range of relative saturations investigated. The chemically-selective 3D MRI method was subsequently applied to monitor the displacement of dodecane in the core plug sample by water under continuous flow conditions at an interstitial velocity of 1.27 × 10 - 6 m s - 1 ( 0.4 ft day - 1 ) . During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of 0.31 mm × 0.39 mm × 0.39 mm were acquired on a timescale of 16 min per image. Using this technique the spatial and temporal dynamics of the displacement process have been monitored. This MRI technique will provide insights to structure-transport relationships associated with multiphase displacement processes in complex porous materials, such as those encountered in petrophysics research.

Validation of a low field Rheo-NMR instrument and application to shear-induced migration of suspended non-colloidal particles in Couette flow.

Nuclear magnetic resonance rheology (Rheo-NMR) is a valuable tool for studying the transport of suspended non-colloidal particles, important in many commercial processes. The Rheo-NMR imaging technique directly and quantitatively measures fluid displacement as a function of radial position. However, the high field magnets typically used in these experiments are unsuitable for the industrial environment and significantly hinder the measurement of shear stress. We introduce a low field Rheo-NMR instrument (1H resonance frequency of 10.7MHz), which is portable and suitable as a process monitoring tool. This system is applied to the measurement of steady-state velocity profiles of a Newtonian carrier fluid suspending neutrally-buoyant non-colloidal particles at a range of concentrations. The large particle size (diameter >200µm) in the system studied requires a wide-gap Couette geometry and the local rheology was expected to be controlled by shear-induced particle migration. The low-field results are validated against high field Rheo-NMR measurements of consistent samples at matched shear rates. Additionally, it is demonstrated that existing models for particle migration fail to adequately describe the solid volume fractions measured in these systems, highlighting the need for improvement. The low field implementation of Rheo-NMR is complementary to shear stress rheology, such that the two techniques could be combined in a single instrument.

Retaining both discrete and smooth features in 1D and 2D NMR relaxation and diffusion experiments.

A new method of regularization of 1D and 2D NMR relaxation and diffusion experiments is proposed and a robust algorithm for its implementation is introduced. The new form of regularization, termed the Modified Total Generalized Variation (MTGV) regularization, offers a compromise between distinguishing discrete and smooth features in the reconstructed distributions. The method is compared to the conventional method of Tikhonov regularization and the recently proposed method of L1 regularization, when applied to simulated data of 1D spin-lattice relaxation, T1, 1D spin-spin relaxation, T2, and 2D T1-T2 NMR experiments. A range of simulated distributions composed of two lognormally distributed peaks were studied. The distributions differed with regard to the variance of the peaks, which were designed to investigate a range of distributions containing only discrete, only smooth or both features in the same distribution. Three different signal-to-noise ratios were studied: 2000, 200 and 20. A new metric is proposed to compare the distributions reconstructed from the different regularization methods with the true distributions. The metric is designed to penalise reconstructed distributions which show artefact peaks. Based on this metric, MTGV regularization performs better than Tikhonov and L1 regularization in all cases except when the distribution is known to only comprise of discrete peaks, in which case L1 regularization is slightly more accurate than MTGV regularization.

Obtaining sparse distributions in 2D inverse problems.

The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxation-relaxation, T1-T2, and diffusion-relaxation, D-T2, correlation experiments in NMR, which have found widespread applications in a number of areas including probing surface interactions in catalysis and characterizing fluid composition and pore structures in rocks. We introduce a robust algorithm for solving the L1 regularization problem and provide a guide to implementing it, including the choice of the amount of regularization used and the assignment of error estimates. We then show experimentally that L1 regularization has significant advantages over both the Non-Negative Least Squares (NNLS) algorithm and Tikhonov regularization. It is shown that the L1 regularization algorithm stably recovers a distribution at a signal to noise ratio<20 and that it resolves relaxation time constants and diffusion coefficients differing by as little as 10%. The enhanced resolving capability is used to measure the inter and intra particle concentrations of a mixture of hexane and dodecane present within porous silica beads immersed within a bulk liquid phase; neither NNLS nor Tikhonov regularization are able to provide this resolution. This experimental study shows that the approach enables discrimination between different chemical species when direct spectroscopic discrimination is impossible, and hence measurement of chemical composition within porous media, such as catalysts or rocks, is possible while still being stable to high levels of noise.

Do group 1 metal salts form deep eutectic solvents?

Mixtures of metal salts such as ZnCl2, AlCl3 and CrCl3·6H2O form eutectic mixtures with complexing agents, such as urea. The aim of this research was to see if alkali metal salts also formed eutectics in the same way. It is shown that only a limited number of sodium salts form homogeneous liquids at ambient temperatures and then only with glycerol. None of these mixtures showed eutectic behaviour but the liquids showed the physical properties similar to the group of mixtures classified as deep eutectic solvents. This study focussed on four sodium salts: NaBr, NaOAc, NaOAc·3H2O and Na2B4O7·10H2O. The ionic conductivity and viscosity of these salts with glycerol were studied, and it was found that unlike previous studies of quaternary ammonium salts with glycerol, where the salt decreased the viscosity, most of the sodium salts increased the viscosity. This suggests that sodium salts have a structure making effect on glycerol. This phenomenon is probably due to the high charge density of Na+, which coordinates to the glycerol. 1H and 23Na NMR diffusion and relaxation methods have been used to understand the molecular dynamics in the glycerol-salt mixtures, and probe the effect of water on some of these systems. The results reveal a complex dynamic behaviour of the different species within these liquids. Generally, the translational dynamics of the 1H species, probed by means of PFG NMR diffusion coefficients, is in line with the viscosity of these liquids. However, 1H and 23Na T1 relaxation measurements suggest that the Na-containing species also play a crucial role in the structure of the liquids.

Accelerating flow propagator measurements for the investigation of reactive transport in porous media.

NMR propagator measurements are widely used for identifying the distribution of molecular displacements over a given observation time, characterising a flowing system. However, where high q-space resolution is required, the experiments are time consuming and therefore unsuited to the study of dynamic systems. Here, it is shown that with an appropriately sampled subset of the q-space points in a high-resolution flow propagator measurement, one can quickly and robustly reconstruct the fully sampled propagator through interpolation of the acquired raw data. It was found that exponentially sampling ∼4% of the original data-points allowed a reconstruction with the deviation from the fully sampled propagator below the noise level, in this case reducing the required experimental time from ∼2.8h to <7min. As a demonstration, this approach is applied to observe the temporal evolution of the reactive flow of acid through an Estaillades rock core plug. It is shown that 'wormhole' formation in the rock core plug provides a channel for liquid flow such that the remaining pore space is by-passed, thereby causing the flow velocity of the liquid in the remaining part of the plug to become stagnant. The propagator measurements are supported by both 1D profiles and 2D imaging data. Such insights are of importance in understanding well acidisation and CO2 sequestration processes.

Fast imaging of laboratory core floods using 3D compressed sensing RARE MRI.

Three-dimensional (3D) imaging of the fluid distributions within the rock is essential to enable the unambiguous interpretation of core flooding data. Magnetic resonance imaging (MRI) has been widely used to image fluid saturation in rock cores; however, conventional acquisition strategies are typically too slow to capture the dynamic nature of the displacement processes that are of interest. Using Compressed Sensing (CS), it is possible to reconstruct a near-perfect image from significantly fewer measurements than was previously thought necessary, and this can result in a significant reduction in the image acquisition times. In the present study, a method using the Rapid Acquisition with Relaxation Enhancement (RARE) pulse sequence with CS to provide 3D images of the fluid saturation in rock core samples during laboratory core floods is demonstrated. An objective method using image quality metrics for the determination of the most suitable regularisation functional to be used in the CS reconstructions is reported. It is shown that for the present application, Total Variation outperforms the Haar and Daubechies3 wavelet families in terms of the agreement of their respective CS reconstructions with a fully-sampled reference image. Using the CS-RARE approach, 3D images of the fluid saturation in the rock core have been acquired in 16min. The CS-RARE technique has been applied to image the residual water saturation in the rock during a water-water displacement core flood. With a flow rate corresponding to an interstitial velocity of vi=1.89±0.03ftday(-1), 0.1 pore volumes were injected over the course of each image acquisition, a four-fold reduction when compared to a fully-sampled RARE acquisition. Finally, the 3D CS-RARE technique has been used to image the drainage of dodecane into the water-saturated rock in which the dynamics of the coalescence of discrete clusters of the non-wetting phase are clearly observed. The enhancement in the temporal resolution that has been achieved using the CS-RARE approach enables dynamic transport processes pertinent to laboratory core floods to be investigated in 3D on a time-scale and with a spatial resolution that, until now, has not been possible.

Gravitational collapse of depletion-induced colloidal gels.

We study the ageing and ultimate gravitational collapse of colloidal gels in which the interparticle attraction is induced by non-adsorbing polymers via the depletion effect. The gels are formed through arrested spinodal decomposition, whereby the dense phase arrests into an attractive glass. We map the experimental state diagram onto a theoretical one obtained from computer simulations and theoretical calculations. Discrepancies between the experimental and simulated gel regions in the state diagram can be explained by the particle size and density dependence of the boundary below which the gel is not strong enough to resist gravitational stress. Visual observations show that gravitational collapse of the gels falls into two distinct regimes as the colloid and polymer concentrations are varied, with gels at low colloid concentrations showing the onset of rapid collapse after a delay time. Magnetic resonance imaging (MRI) was used to provide quantitative, spatio-temporally resolved measurements of the solid volume fraction in these rapidly collapsing gels. We find that during the delay time, a dense region builds up at the top of the sample. The rapid collapse is initiated when the gel structure is no longer able to support this dense layer.

Determining adsorbate configuration on alumina surfaces with (13)C nuclear magnetic resonance relaxation time analysis.

Relative strengths of surface interaction for individual carbon atoms in acyclic and cyclic hydrocarbons adsorbed on alumina surfaces are determined using chemically resolved (13)C nuclear magnetic resonance (NMR) T1 relaxation times. The ratio of relaxation times for the adsorbed atoms T1,ads to the bulk liquid relaxation time T1,bulk provides an indication of the mobility of the atom. Hence a low T1,ads/T1,bulk ratio indicates a stronger surface interaction. The carbon atoms associated with unsaturated bonds in the molecules are seen to exhibit a larger reduction in T1 on adsorption relative to the aliphatic carbons, consistent with adsorption occurring through the carbon-carbon multiple bonds. The relaxation data are interpreted in terms of proximity of individual carbon atoms to the alumina surface and adsorption conformations are inferred. Furthermore, variations of interaction strength and molecular configuration have been explored as a function of adsorbate coverage, temperature, surface pre-treatment, and in the presence of co-adsorbates. This relaxation time analysis is appropriate for studying the behaviour of hydrocarbons adsorbed on a wide range of catalyst support and supported-metal catalyst surfaces, and offers the potential to explore such systems under realistic operating conditions when multiple chemical components are present at the surface.

Characterising the rheology of non-Newtonian fluids using PFG-NMR and cumulant analysis.

Conventional rheological characterisation using nuclear magnetic resonance (NMR) typically utilises spatially-resolved measurements of velocity. We propose a new approach to rheometry using pulsed field gradient (PFG) NMR which readily extends the application of MR rheometry to single-axis gradient hardware. The quantitative use of flow propagators in this application is challenging because of the introduction of artefacts during Fourier transform, which arise when realistic sampling strategies are limited by experimental and hardware constraints and when particular spatial and temporal resolution are required. The method outlined in this paper involves the cumulant analysis of the acquisition data directly, thereby preventing the introduction of artefacts and reducing data acquisition times. A model-dependent approach is developed to enable the pipe-flow characterisation of fluids demonstrating non-Newtonian power-law rheology, involving the use of an analytical expression describing the flow propagator in terms of the flow behaviour index. The sensitivity of this approach was investigated and found to be robust to the signal-to-noise ratio (SNR) and number of acquired data points, enabling an increase in temporal resolution defined by the SNR. Validation of the simulated results was provided by an experimental case study on shear-thinning aqueous xanthan gum solutions, whose rheology could be accurately characterised using a power-law model across the experimental shear rate range of 1-100 s(-1). The flow behaviour indices calculated using this approach were observed to be within 8% of those obtained using spatially-resolved velocity imaging and within 5% of conventional rheometry. Furthermore, it was shown that the number of points sampled could be reduced by a factor of 32, when compared to the acquisition of a volume-averaged flow propagator with 128 gradient increments, without negatively influencing the accuracy of the characterisation, reducing the acquisition time to only 3% of its original value.

Nuclear magnetic resonance measurements of velocity distributions in an ultrasonically vibrated granular bed.

We report the results of nuclear magnetic resonance imaging experiments on granular beds of mustard grains fluidized by vertical vibration at ultrasonic frequencies. The variation of both granular temperature and packing fraction with height was measured within the three-dimensional cell for a range of vibration frequencies, amplitudes and numbers of grains. Small increases in vibration frequency were found--contrary to the predictions of classical 'hard-sphere' expressions for the energy flux through a vibrating boundary--to result in dramatic reductions in granular temperature. Numerical simulations of the grain-wall interactions, using experimentally determined Hertzian contact stiffness coefficients, showed that energy flux drops significantly as the vibration period approaches the grain-wall contact time. The experiments thus demonstrate the need for new models for 'soft-sphere' boundary conditions at ultrasonic frequencies.

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.

Measurement of the true transverse nuclear magnetic resonance relaxation in the presence of field gradients.

A measure of the nuclear spin transverse relaxation time T2, as determined using the nuclear magnetic resonance Carr-Purcell Meiboom-Gill (CPMG) experiment, provides unique information characterizing the microstructure of porous media which are themselves ubiquitous across fields of petrophysics, biophysics, and chemical engineering. However, the CPMG measurement is sensitive to diffusion in large magnetic field gradients. Under such conditions an effective relaxation time T2,eff is observed instead, described by a combination of relaxation and diffusion exponents. The relaxation exponent always varies as nte (where n is the number, and te is the temporal separation, of spin echoes). The diffusion exponent varies as nte (k), where 1 < k ≤ 3, although the exact analytic form is often unknown. Here we present a general approach to separating the influence of relaxation and diffusion by utilizing a composite diffusion exponent. Any T2,eff component with a power of k > 1 is removed to provide a measure of the true T2 relaxation time distribution from CPMG data acquired in the presence of a strong background gradient. We apply the technique to discriminate between the effects of relaxation and diffusion in porous media using catalysts and rocks as examples. The method is generally applicable to any CPMG measurements conducted in the presence of a static magnetic field gradient.