Fixed and pulsed gradient diffusion methods in low-field core analysis

Evaluation of the Influence of Hypolipidemic Medication on Albino Wistar Rats' Bone Tissue by NMR Diffusiometry

Introduction: The ongoing concern of the medical profession regarding chronic medication is related to increasing patient adherence and compliance to treatment and reducing medication side effects. In this respect, drugs represented by fixed-dose combinations of active substances within the same tablet have emerged. Such a principle can be extrapolated by following the potential beneficial effects that a chronic medication can have on chronic pathologies affecting different systems. Materials and Methods: The study included 48 female Albino Wistar rats, aged 16-18 months, which were divided into two groups: ovariectomized and non-ovariectomized rats. One batch of 12 non-ovariectomized rats received no treatment, becoming a control batch (NOVX-M). The ovariectomized (OVX) group was divided into 3 batches of 12 rats each: no treatment, control (OVX-M), fenofibrate-treated (OVX-F) and statin-treated (OVX-S) rats. At 12 weeks after ovariectomy, a femoral fracture occurred in the right hind limb of all animals included in the experiment To reveal the changes, at intervals of 2, 4, 6 and 8 weeks post-fracture, the proximal part of the femur was evaluated by NMR diffusiometry, which allows random motion of proton molecules expressed by self-diffusion coefficients, D, thus allowing analysis of the size and complexity of microscopic order cavities within biological structures, such as pores inside bones. Results: The effects of hypolipidemic medication in the absence of estrogen were evidenced, proving the beneficial effect that fenofibrate can have in preserving healthy tissue exposed to osteoporotic risk during the menopausal period. The effects of lipid-lowering medication are also influenced by the duration of administration. Conclusions: Osteoporosis and heart disease are two chronic pathologies that affect mainly female population in the second half of life, and proving the dual therapeutic potential of lipid-lowering medication may also have positive effects by increasing adherence and compliance to treatment.

Improved data efficiency for NMR diffusion-relaxation processing

Two dimensional diffusion and transverse (T₂) NMR relaxation measurements are effective for a variety of research and industrial processes. Conversion of the measurements into a D-T₂ map is performed using an inverse integral transformation. A difficulty with D-T₂ estimation from data acquired without pulsed field gradients (using, for example, the inherent static field gradient of a single-sided magnet) is that the diffusion and relaxation kernels are coupled. One commonly used solution is to introduce a time offset to enable the kernels to be decoupled, but this has the undesirable results of causing some of the data, and a large proportion of the signal energy, to become unusable. This paper presents two methods of processing the data that do not require this wastage. Both methods are based on insights that arise from considering the linear operator that describes the forwards integral transformation. One method involves data compression, while the other method is an application (that we call FLINT) of the fast iterative soft thresholding algorithm. Both methods are able to use all of the available data. The paper demonstrates the improved accuracy that results from these methods on simulated data, as well as the improved discovery of important features on measured data.

Multidimensional dynamic NMR correlations in sedimentary rock cores at different liquid saturations

In Nuclear Magnetic Resonance (NMR) spin echo measurements of confined liquids, the dynamic behaviour of liquid molecules are influenced by diffusion (D), translational displacement of molecules in internal gradients (G₀), and transverse surface relaxation (T₂). In this study, an experimental approach that enables characterisation of water and oil in rock core materials is presented. The approach is based on three-dimensional D-DG₀²-T₂ correlations, but the main focus is on the two-dimensional parts that involve DG₀²-T₂ and D-∣G₀∣. In order to evaluate potential signal loss that can be introduced when going from a two-dimensional to a three-dimensional experiment, D-T₂,DG₀²-T₂ and D-∣G₀∣ correlations derived from subsets of data obtained in the D-DG₀²-T₂ experiment are compared to directly obtained D-T₂ and DG₀²-T₂ correlations. The results show that when diffusion encoding is included in a multi-dimensional correlation experiment, it may lead to a significant loss of signals from liquids with relatively high diffusivity and which is located close to the mineral surface. Furthermore, a negative correlation between D and ∣G₀∣ is observed for the confined liquids in all the saturation states. Such correlations have not been measured previously, and they results in a more detailed description of the local distribution of the confined liquids. In particular, at significantly high water saturations, the surviving signal from water is found at lower values of internal gradients compared to the main part of the oil signal, indicating that this water is located further away from the surface compared to the oil. The study shows that the impact from heterogeneity in pore geometry and surface properties on the individual liquids is described in more detail in DG₀²-T₂ and D-∣G₀∣ correlations compared toD-T₂ correlations, but that potential signal loss during diffusion encoding intervals should be monitored and verified.

Characterising oil and water in porous media using correlations between internal magnetic gradient and transverse relaxation time

A method for characterising water and oil in a rock core plug using correlations between diffusion decay in internal magnetic gradient and transverse relaxation time (DG₀²-T₂) is presented. The method is evaluated at different saturation levels and is compared with the measurement of correlations between diffusion and transverse relaxation time (D-T₂). It is shown how signals from water and oil can be separated based on their difference in diffusion decay in internal gradients. The obtained results show that the impact from heterogeneity in pore geometry and mineralogy on the individual liquids is revealed in more detail in DG₀²-T₂ correlations compared to the more established D-T₂ correlations. Measurements of DG₀²-T₂ correlations should be included in the toolbox of NMR experiments performed in the laboratory analysis of rock core plugs, and could then potentially lead to more detailed estimations of saturation levels and surface wettability properties.

Downhole Applications of Magnetic Sensors

In this paper we present a review of the application of two types of magnetic sensors—fluxgate magnetometers and nuclear magnetic resonance (NMR) sensors—in the oil/gas industry. These magnetic sensors play a critical role in drilling wells safely, accurately and efficiently into a target reservoir zone by providing directional data of the well and acquiring information about the surrounding geological formations. Research into magnetic sensors for oil/gas drilling has not been explored by researchers to the same extent as other applications, such as biomedical, magnetic storage and automotive/aerospace applications. Therefore, this paper aims to serve as an opportunity for researchers to truly understand how magnetic sensors can be used in a downhole environment and to provide fertile ground for research and development in this area. A look ahead, discussing other magnetic sensor technologies that can potentially be used in the oil/gas industry is presented, and what is still needed in order deploy them in the field is also addressed.

Viscoelastic polymer flows and elastic turbulence in three-dimensional porous structures

Viscoelastic polymer solutions flowing through reservoir rocks have been found to improve oil displacement efficiency when the aqueous-phase shear-rate exceeds a critical value. A possible mechanism for this enhanced recovery is elastic turbulence that causes breakup and mobilization of trapped oil ganglia. Here, we apply nuclear magnetic resonance (NMR) pulsed field gradient (PFG) diffusion measurements in a novel way to detect increased motion of disconnected oil ganglia. The data are acquired directly from a three-dimensional (3D) opaque porous structure (sandstone) when viscoelastic fluctuations are expected to be present in the continuous phase. The measured increase in motion of trapped ganglia provides unequivocal evidence of fluctuations in the flowing phase in a fully complex 3D system. This work provides direct evidence of elastic turbulence in a realistic reservoir rock - a measurement that cannot be readily achieved by conventional laboratory methods. We support the NMR data with optical microscopy studies of fluctuating ganglia in simple two-dimensional (2D) microfluidic networks, with consistent apparent rheological behaviour of the aqueous phase, to provide conclusive evidence of elastic turbulence in the 3D structure and hence validate the proposed flow-fluctuation mechanism for enhanced oil recovery.

Characterising oil and water in porous media using decay due to diffusion in the internal field

In the method Decay due to Diffusion in the Internal Field (DDIF), the diffusion behaviour of water molecules in the internal magnetic field makes it possible to determine a distribution of pore sizes in a sample. The DDIF experiment can also be extended to a DDIF-Carr-Purcell-Meiboom-Gill (DDIF-CPMG) experiment to measure correlations between the pore size and the transverse relaxation time, T2. In this study we have for the first time applied the DDIF experiment and the DDIF-CPMG experiment to porous materials saturated with both water and oil. Because of the large difference in diffusion rates between water and oil molecules, the DDIF experiment will act as a filter for the signal from oil, and we are left with the DDIF-signal from water only. This has been verified in model systems consisting of glass beads immersed in separate layers of water and oil, and in a sandstone sample saturated with water and oil. The results show that the DDIF and DDIF-CPMG experiments enable the determination of the confining geometry of the water phase, and how this geometry is correlated to T2. Data obtained in the sandstone sample saturated with water and oil also show that with the exception of the smallest pores there is no clear correlation between pore size and the relaxation time of water.

Real-time oil-saturation monitoring in rock cores with low-field NMR

Nuclear magnetic resonance (NMR) provides a powerful suite of tools for studying oil in reservoir core plugs at the laboratory scale. Low-field magnets are preferred for well-log calibration and to minimize magnetic-susceptibility-induced internal gradients in the porous medium. We demonstrate that careful data processing, combined with prior knowledge of the sample properties, enables real-time acquisition and interpretation of saturation state (relative amount of oil and water in the pores of a rock). Robust discrimination of oil and brine is achieved with diffusion weighting. We use this real-time analysis to monitor the forced displacement of oil from porous materials (sintered glass beads and sandstones) and to generate capillary desaturation curves. The real-time output enables in situ modification of the flood protocol and accurate control of the saturation state prior to the acquisition of standard NMR core analysis data, such as diffusion-relaxation correlations. Although applications to oil recovery and core analysis are demonstrated, the implementation highlights the general practicality of low-field NMR as an inline sensor for real-time industrial process control.

Measuring diffusion-relaxation correlation maps using non-uniform field gradients of single-sided NMR devices

Single-sided NMR systems are becoming a relevant tool in industry and laboratory environments due to their low cost, low maintenance and capacity to evaluate quantity and quality of hydrogen based materials. The performance of such devices has improved significantly over the last decade, providing increased field homogeneity, field strength and even controlled static field gradients. For a class of these devices, the configuration of the permanent magnets provides a linear variation of the magnetic field and can be used in diffusion measurements. However, magnet design depends directly on its application and, according to the purpose, the field homogeneity may significantly be compromised. This may prevent the determination of diffusion properties of fluids based on the natural inhomogeneity of the field using known techniques. This work introduces a new approach that extends the applicability of diffusion-editing CPMG experiments to NMR devices with highly inhomogeneous magnetic fields, which do not vary linearly in space. Herein, we propose a method to determine a custom diffusion kernel based on the gradient distribution, which can be seen as a signature of each NMR device. This new diffusion kernel is then utilised in the 2D inverse Laplace transform (2D ILT) in order to determine diffusion-relaxation correlation maps of homogeneous multi-phasic fluids. The experiments were performed using NMR MObile Lateral Explore (MOLE), which is a single-sided NMR device designed to maximise the volume at the sweet spot with enhanced depth penetration.

Contributed review: nuclear magnetic resonance core analysis at 0.3 T

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.

Two-dimensional diffusion time correlation experiment using a single direction gradient

The time dependence of the diffusion coefficient is a well known property of porous media and commonly obtained by pulsed field gradient (PFG) NMR. In practical materials, its analysis can be complicated by the presence of a broad pore size distribution and multiple fluid phases with different diffusion coefficients. We propose a two-dimensional Diffusion Time Correlation experiment (DTC), which utilizes the double-PFG with a single-direction gradient to yield a two-dimensional correlation function of the diffusion coefficient for two different diffusion times. This correlation map separates out restricted diffusion from the bulk diffusion process and we demonstrate this on a plant and bulk water sample. In its development, we show that the d-PFG should then be thought of as correlating two apparent diffusion coefficients measured by two overlapping gradient waveforms.

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.

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.

An improved approach to calibrating high magnetic field gradients for pulsed field gradient experiments

Probes capable of generating short high intensity pulsed magnetic field gradients are commonly used in diffusion studies of systems with very short T(2). Traditional methods of calibrating magnetic field gradients present unique challenges at ultrahigh field strengths and are often inapplicable. Currently the most accurate method of determining magnetic gradient strength is to use the known diffusion coefficient of a standard sample and determine gradient strength from the echo attenuation plot of a diffusion experiment, however, there are problems with finding suitable standards for high intensity gradients. Here, we show that molecules containing at least two receptive nuclei (i.e. one with high and one with low gyromagnetic ratios) are excellent systems for calibrating high intensity gradients.

Porous media characterization by PFG and IMFG NMR

Fully and partially filled with tridecane quartz sand was studied by different NMR techniques. The set of NMR experiments was carried out to obtain information about porous media geometry and fluid localization in it in case of partially filled porous space. The study was done using three NMR approaches: pulse field gradient NMR (PFG NMR), DDif experiment and tau-scanning experiment. The possibility to use all three approaches to study porous media properties even at the high resonance frequency is shown together with complementarity of the given by them information. Thus, first two approaches give information about porous sizes and geometry, at the same time tau-scanning experiment allows us to obtain information about distribution of internal magnetic field gradients in the porous space and draw conclusions about fluid localization in it.

Low magnetic fields for flow propagators in permeable rocks

Pulsed field gradient NMR flow propagators for water flow in Bentheimer sandstone are measured at low fields (1H resonance 2 MHz), using both unipolar and bipolar variants of the pulsed gradient method. We compare with propagators measured at high fields (1H resonance 85 MHz). We show that (i) measured flow propagators appear to be equivalent, in this rock, and (ii) the lower signal to noise ratio at low fields is not a serious limitation. By comparing different pulse sequences, we study the effects of the internal gradients on the propagator measurement at 2 MHz, which for certain rocks may persist even at low fields.

Relationship between susceptibility induced field inhomogeneities, restricted diffusion, and relaxation in sedimentary rocks

Low field relaxation and diffusion measurements have become essential tools to study the pore space of sedimentary rocks with important practical applications in the field of well logging and hydrocarbon extractions. Even at Larmor frequencies below 2 MHz, diffusion measurements are often affected noticeably by internal field inhomogeneities. These field inhomogeneities are induced by susceptibility contrast between the rock and the fluid and are evident in most sandstones. Using sets of two-dimensional diffusion-relaxation measurements in applied and internal gradients, we study in detail the correlation between the field inhomogeneities, restricted diffusion, and relaxation time in three rocks of different susceptibility. We find that in the sandstone cores, the field inhomogeneities in large pores can be described by a local gradient that scales inversely with relaxation time above 250 ms. At shorter relaxation times, the extracted internal gradients deviate from this scaling relationship and we observe a dependence on diffusion time. This demonstrates that in this case, the internal field has structure on a length scale of a few microns.