Nuclear magnetic resonance (NMR) offers a powerful toolbox for petrophysical analysis of reservoir rocks. Laboratory measurements are often performed at low frequency (2 MHz) to provide consistent spin physics to downhole logging tools. The popular single-shot Carr-Purcell-Meiboom-Gill (CPMG) sequence for measuring the transverse T-2 relaxation time is sensitive to local magnetic field inhomogeneities (internal gradients) that scale with resonance frequency. For T-2 analysis of conventional formations, low-field magnets are considered mandatory. Recently, there has been renewed interest in operating at higher frequency (> 20 MHz) to provide sensitivity to solid- like components in shale formations (kerogen, bitumen, structural water). The longitudinal T-1 relaxation time is insensitive to internal gradients, but slow to measure with the traditional inversion-recovery pulse sequence. Here, a modified fast double-shot T-1 pulse sequence is applied to conventional rock formations, allowing these samples to be studied reliably at high magnetic fields. Representative porosity and permeability values are recovered for a selection of brine-saturated sandstone and carbonate core plugs. This double-shot T-1 measurement is readily implementable on commercial NMR hardware appropriate for laboratory or rigsite deployment.

Nuclear magnetic resonance measurements of spin relaxation are used in studies of liquid-saturated porous media where multidimensional relaxation correlations probe interpore diffusion and other transport processes. However, the magnetic susceptibility contrast between the solid and liquid results in pore-scale field inhomogeneities that influence all measurements of transverse ${T}_{2}$ relaxation time. In a previous publication we conjectured that experimentally observed exchange phenomena can correspond to intrapore diffusion between localized volumes of coherent magnetization generated by these internal gradients, rather than interpore diffusion. Here, we use a finite-element method to explore the decay of magnetization in a single pore (interstice between spheres) for the Carr-Purcell-Meiboom-Gill and two-dimensional ${T}_{2}\text{\ensuremath{-}}{T}_{2}$ exchange experiments. These simulations permit direct visualization of the time-dependent distribution of magnetization in the pore. The chosen grain size and susceptibility contrast are matched to values for Bentheimer sandstone, allowing for a comparison of simulated and experimental results. Despite the simplicity of the model pore geometry, the salient features of the magnetization decay observed experimentally are reproduced in simulation. We demonstrate that intrapore magnetization transfer can explain observations of diffusive exchange in porous materials characterized by a monomodal pore size distribution and large internal gradients.

Two-dimensional nuclear magnetic resonance measurements are ubiquitous in the literature, with correlations of longitudinal T-1 and transverse T-2 relaxation times used extensively to characterize porous media. Decomposition of the signal acquired in the time domain to a pseudocontinuous distribution of relaxation times is achieved using numerical inversion. A popular technique to generate a stable solution to this ill-posed problem in the presence of noise is Tikhonov regularization with a non-negativity constraint imposed on the output. However, coupling of the longitudinal and transverse eigenfunctions can generate eigenvalue pairs with apparent T-2 > T-1 and negative amplitude. Such apparent signal components are encountered in the classic example of BrownsteinTarr "slow" diffusion in an isolated pore, and in weakly coupled pores governed by different relaxation rates. We show that when negative-amplitude components comprise >= 1% of the total signal, the solution achieved by non-negative Tikhonov regularization is sufficiently distorted to prevent robust interpretation. We demonstrate two alternative inversion methods that recover the negative-amplitude components: (1) half-bound Tikhonov regularization assigns a negative amplitude to any peak with apparent T-2 > T-1, and (2) the optimization problem is expressed as a l(2) regression with l(1) penalization and a solution estimated using a primal-dual algorithm without constraint on the output sign. These methods are applicable to T-1-T-2 experiments on porous materials characterized by a hierarchy of length scales, such as biological cells, cement, and limestone.

Determination of petrophysical parameters from surface measurements of drill cuttings, rather than well logs, has long been a subject of interest in the petroleum industry. Analysis of cuttings is presently included in mud logging workflows, although the methods employed tend to be labor-intensive and inefficient with an emphasis on qualitative lithological and mineralogical descriptors. Nuclear magnetic resonance (NMR) has the potential to deliver rapid formation evaluation at the rig site for near-real-time completion decisions. Despite numerous efforts to demonstrate NMR cuttings analysis, dating back to the 1980s, the technique has yet to achieve commercial success. We suggest this failure is due not to the physics of the measurement, which is understood, but rather to inadequate sample preparation. By centrifuging brine-saturated cuttings from conventional formations under a per-fluorinated oil, and using multinuclear NMR to measure liquid volumes, we obtain accurate porosity and permeability values independent of other measurements. Our robust workflow removes the inconsistencies associated with manual sample preparation. We present two case studies and the important requirements for handling actual drill cuttings.

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.

Time-domain NMR, in one and higher dimensionalities, makes routine use of inversion algorithms to generate results called \T2-distributions' or joint distributions in two (or higher) dimensions of other NMR parameters, T1, diffusivity D, pore size a, etc. These are frequently referred to as \Inverse Laplace Transforms' although the standard inversion of the Laplace Transform long-established in many textbooks of mathematical physics does not perform (and cannot perform) the calculation of such distributions. The operations performed in the estimation of a \T2-distribution' are the estimation of solutions to a Fredholm Integral Equation (of the First Kind), a different and more general object whose discretization results in a standard problem in linear algebra, albeit suffering from well-known problems of ill-conditioning and computational limits for large problem sizes. The Fredholm Integral Equation is not restricted to exponential kernels; the same solution algorithms can be used with kernels of completely different form. On the other hand, (true) Inverse Laplace Transforms, treated analytically, can be of real utility in solving the diffusion problems highly relevant in the subject of NMR in porous media.

Nuclear magnetic resonance provides a toolbox of non-invasive methods for measuring fluid transport through industrially relevant porous materials. Process optimization with magnetic resonance is largely a subject of academic interest, although in a few notable cases magnetic resonance has been accepted as a routine tool for industrial control. One example is the petroleum industry, where measurements of molecular self-diffusion and spin relaxation times have provided a wealth of information to improve oil exploration and recovery in subsurface reservoirs. In this chapter, examples are drawn from the petroleum industry, including well-logging tool measurements and laboratory analysis of fluid–rock interactions, to highlight the significance of magnetic resonance in the industrial environment.

We review the theory and operation of digital filters in modern nuclear magnetic resonance (NMR) spectrometers with fully digital receivers. Custom digital filters tailored for particular experimental requirements offer substantial improvements in signal-to-noise ratio (SNR), sensitivity, pulse sequence timing, and rejection of heteronuclear contamination. Pass-band filters are designed and applied in the frequency domain. In high-field imaging and spectroscopy, the impact of the filter is straight forward to visualize. However, low-field NMR data acquired on bench-top magnets are typically analyzed in the time-domain where the influence of a frequency-domain filter is not obvious and largely overlooked by end-users. We provide practical guidance on the design and implementation of digital filters for bench-top NMR applications, with examples of data acquired at 2.4 and 12.9 MHz. We discuss the compromise between speed (filter settling time) and noise rejection, and consider the special case of F-19 signal contamination in H-1 measurements. We suggest filter designs for narrow-line liquid samples, broad-line samples, and imaging.

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 (NMR) provides a powerful toolbox for petrophysical characterization of reservoir core plugs and fluids in the laboratory. Previously, there has been considerable focus on low field magnet technology for well log calibration. Now there is renewed interest in the study of reservoir samples using stronger magnets to complement these standard NMR measurements. Here, the capabilities of an imaging magnet with a field strength of 0.3 T (corresponding to 12.9 MHz for proton) are reviewed in the context of reservoir core analysis. Quantitative estimates of porosity (saturation) and pore size distributions are obtained under favorable conditions (e.g., in carbonates), with the added advantage of multidimensional imaging, detection of lower gyromagnetic ratio nuclei, and short probe recovery times that make the system suitable for shale studies. Intermediate field instruments provide quantitative porosity maps of rock plugs that cannot be obtained using high field medical scanners due to the field-dependent susceptibility contrast in the porous medium. Example data are presented that highlight the potential applications of an intermediate field imaging instrument as a complement to low field instruments in core analysis and for materials science studies in general.

Accurate interfacial tension data for fluid systems such as hydrocarbons and water is essential to many applications such as reservoir oil and gas recovery predictions. Conventional interfacial tension measurement techniques typically use optical images to analyze droplet shapes but require that the continuous-phase fluid be optically transparent and that the fluids are not refractive index matched. Magnetic resonance images obtain contrast between fluids using other mechanisms such as magnetic relaxation weighting, so systems that are impossible to measure with optical methods may be analyzed. In this article, we present high-field (9.4 T) MRI images of various droplets analyzed with axisymmetric drop shape analysis. The resultant interfacial tension data show good agreement with literature data. The method is subsequently demonstrated using both opaque continuous phases and refractive-index-matched fluids. We conclude with a brief consideration of the potential to extrapolate the methodology to lower magnetic fields (0.3 T), featuring more accessible hardware; although droplet imaging is possible, resolution and stability do not currently permit accurate interfacial tension measurements.

Nuclear magnetic resonance (NMR) relaxation times are shown to provide a unique probe of adsorbate-adsorbent interactions in liquid-saturated porous materials. A short theoretical analysis is presented, which shows that the ratio of the longitudinal to transverse relaxation times (T1/T2) is related to an adsorbate-adsorbent interaction energy, and we introduce a quantitative metric esurf (based on the relaxation time ratio) characterising the strength of this surface interaction. We then consider the interaction of water with a range of oxide surfaces (TiO2 anatase, TiO2 rutile, γ-Al2O3, SiO2, θ-Al2O3 and ZrO2) and show that esurf correlates with the strongest adsorption sites present, as determined by temperature programmed desorption (TPD). Thus we demonstrate that NMR relaxation measurements have a direct physical interpretation in terms of the characterisation of activation energy of desorption from the surface. Further, for a series of chemically similar solid materials, in this case a range of oxide materials, for which at least two calibration values are obtainable by TPD, the esurf parameter yields a direct estimate of the maximum activation energy of desorption from the surface. The results suggest that T1/T2 measurements may become a useful addition to the methods available to characterise liquid-phase adsorption in porous materials. The particular motivation for this work is to characterise adsorbate-surface interactions in liquid-phase catalysis.

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.

A comparison of advective displacement probability distributions (flow propagators) obtained by nuclear magnetic resonance (NMR) experiment with both lattice Boltzmann (LB) and pore network (PN) simulations is presented. Here, we apply all three methods to the exact same sample for the first time: we consider water transport in a Bentheimer sandstone. The LB and PN simulations are based on X-ray micro-tomography (XMT) images of a small rock sample; the NMR experiments are conducted on a much larger rock core-plug from which the small rock sample originated. Despite the limited size of the simulation domains, good agreement is achieved between all three sets of results, verified quantitatively by comparison of the low order moments of the flow propagators. We are concerned primarily with validating the simulations at high liquid flow rates (>10 ml min(-1)) in high permeability sandstone, ultimately for future application to geological carbon sequestration studies. Under these conditions the LB simulation is found, as expected, to be more robust than the PN model due primarily to the reduced requirement to manually tune the simulation lattice to match the petro-physical properties of the rock. (C) 2013 Elsevier Ltd. All rights reserved.

In recent work, it was reported that changes in solvent composition, precisely the addition of water, significantly inhibits the catalytic activity of Au/TiO2 catalyst in the aerobic oxidation of 1,4-butanediol in methanol due to changes in diffusion and adsorption properties of the reactant. In order to understand whether the inhibition mechanism of water on diol oxidation in methanol is generally valid, the solvent effect on the aerobic catalytic oxidation of 1,3-propanediol and its two methyl-substituted homologues, 2-methyl-1,3-propanediol and 2,2-dimethyl-1,3-propanediol, over a Au/TiO2 catalyst has been studied here using conventional catalytic reaction monitoring in combination with pulsed-field gradient nuclear magnetic resonance (PFG-NMR) diffusion and NMR relaxation time measurements. Diol conversion is significantly lower when water is present in the initial diol/methanol mixture. A reactivity trend within the group of diols was also observed. Combined NMR diffusion and relaxation time measurements suggest that molecular diffusion and, in particular, the relative strength of diol adsorption, are important factors in determining the conversion. These results highlight NMR diffusion and relaxation techniques as novel, non-invasive characterisation tools for catalytic materials, which complement conventional reaction data.

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.

The potential for tailored synthesis of porous materials using catalytic degradation of block copolymers has been shown, employing an adaptable one-pot method. Carefully selected solvent systems help to control the pore size and molecular weight of the product. In the degradation of PS-PB-PS, 2nd Generation Grubbs' catalyst creates scissions in the PB carbon-carbon double bonds resulting in the formation of a porous structure. Critically, methanol is used to maintain the integrity of the polymeric structure during this etching. Catalyst deactivation effected by methanol can be limited through using an excess of 1-hexene; thereby introducing a competitive metathesis process. Altering the ratio of the co-solvents employed further controls the degradation of PS-PB-PS and hence the resulting pore structures.

We present a modified set of recommendations for the use of paramagnetic doping agents in nuclear magnetic resonance (NMR) piloting operations of oil recovery. On occasion, manganese has been used to provide transverse T-2 relaxation time contrast in NMR well logs. Aqueous fluid-phase doping agents may become important in future piloting operations, where accurate predictions of the doping agent behavior under adverse conditions are critical. Previously, chelated manganese-EDTA was recommended for use in clay-based drilling muds and sandstones to prevent surface adsorption, whereas (unchelated) manganese was recommended for use in clay-free carbonates due to the economic advantage of the simpler formulation and weak temperature dependence. Here we review the mechanisms of paramagnetic relaxation contrast and then present examples from a case study of laboratory-scale NMR measurements of crude-oil recovery from a microporous limestone. Based on our observations, we amend the previous recommendations. When the use of paramagnetic doping agents is not advisable, alternative methods for introducing fluid-phase contrast are available. Heavy-water substitution is a practical solution at the laboratory-scale and in single-well pilots.

Magnetic resonance imaging (MRI) is a well-known technique in medical diagnosis and materials science. In the more specialized arena of laboratory-scale petrophysical rock core analysis, the role of MRI has undergone a substantial change in focus over the last three decades. Initially, alongside the continual drive to exploit higher magnetic field strengths in MRI applications for medicine and chemistry, the same trend was followed in core analysis. However, the spatial resolution achievable in heterogeneous porous media is inherently limited due to the magnetic susceptibility contrast between solid and fluid. As a result, imaging resolution at the length-scale of typical pore diameters is not practical and so MRI of core-plugs has often been viewed as an inappropriate use of expensive magnetic resonance facilities. Recently, there has been a paradigm shift in the use of MRI in laboratory-scale core analysis. The focus is now on acquiring data in the laboratory that are directly comparable to data obtained from magnetic resonance well-logging tools (i.e., a common physics of measurement). To maintain consistency with well-logging instrumentation, it is desirable to measure distributions of transverse (T-2) relaxation time the industry-standard metric in well-logging at the laboratory-scale. These T-2 distributions can be spatially resolved over the length of a core-plug. The use of low-field magnets in the laboratory environment is optimal for core analysis not only because the magnetic field strength is closer to that of well-logging tools, but also because the magnetic susceptibility contrast is minimized, allowing the acquisition of quantitative image voxel (or pixel) intensities that are directly scalable to liquid volume. Beyond simple determination of macroscopic rock heterogeneity, it is possible to utilize the spatial resolution for monitoring forced displacement of oil by water or chemical agents, determining capillary pressure curves, and estimating wettability. The history of MRI in petrophysics is reviewed and future directions considered, including advanced data processing techniques such as compressed sensing reconstruction and Bayesian inference analysis of under-sampled data. Although this review focuses on rock core analysis, the techniques described are applicable in a wider context to porous media in general, such as cements, soils, ceramics, and catalytic materials. (c) 2013 Elsevier B.V. All rights reserved.