T₂ distribution mapping profiles with phase-encode MRI

Volatilization behavior of diesel oil-water-glass bead system exposed to freeze-thaw cycles

Volatilization plays an important role in the attenuation and redistribution of petroleum products in contaminated porous media. However, the volatilization behavior of petroleum products exposed to freeze-thaw cycles is not well understood. In this study, we investigated the volatilization behavior of diesel oil-water-glass bead systems under different freeze-thaw cycles. Low-field nuclear magnetic resonance (LF-NMR) was used to quantitatively and spatially monitor the mass loss of the diesel oil-water-glass bead system during volatilization. The mechanism of the influence of freeze-thaw cycles on volatilization in the diesel oil-water-glass bead system was analyzed. The results show that the freeze-thaw cycles have a significant effect on the volatilization rate of diesel oil and water. As the number of freeze-thaw cycles increases, the volatilization rate of diesel oil shows an overall downward trend while the volatilization rate of water shows an overall upward trend. The volatilization loss of the liquids (both diesel oil and water) is mainly due to the volatilization loss of water, indicating that water is more volatile than diesel oil in the diesel oil-water system. The spatial distribution of the diesel oil signal monitored by LF-NMR showed that diesel oil volatilizes mainly in the upper layer of the sample, associating with the preferential volatilization loss in the large pores. The lumped parameter λ related to the characteristic volatilization length LV was introduced to characterize the volatilization rate of diesel oil and water with the increase of volatilization time. For a diesel oil-water-glass bead system exposed to freeze-thaw cycles, the 1/ LV of diesel oil decreases exponentially and rapidly with increasing volatilization time, while the 1/ LV of water decreases almost linearly and slowly with increasing volatilization time. This different dependence of 1/ LV on volatilization time leads to the individual volatilization behavior of diesel oil and water.

A parallel-plate RF probe and battery cartridge for 7Li ion battery studies

A new parallel-plate resonator for ⁷Li ion cell studies is introduced along with a removable cartridge-like electrochemical cell for lithium ion battery studies. This geometry separates the RF probe from the electrochemical cell permitting charge/discharge of the cell outside the magnet and introduces the possibility of multiplexing samples under test. The new cell has a geometry that is similar to that of a real battery, unlike the majority of cells employed for MR/MRI studies to this point. The cell, with electrodes parallel to the B₁ magnetic field of the probe, avoids RF attenuation during excitation/reception. The cell and RF probe dramatically increase the sample volume compared to traditional MR compatible battery designs. Ex situ and in situ 1D ⁷Li profiles of Li ions in the electrolyte solution of a cartridge-like cell were acquired, with a nominal resolution of 35 µm at 38 MHz. The cell and RF probe may be employed for spectroscopy, imaging and relaxation studies. We also report the results of a T₁-T₂ relaxation correlation experiment on both a pristine and fully charged cell. This study represents the first T₁-T₂ relaxation correlation experiment performed in a Li ion cell. The T₁-T₂ correlation maps suggest lithium intercalated into graphite is detected by this methodology in addition to other Li species.

Applications of magnetic resonance imaging in chemical engineering

While there are many techniques to study phenomena that occur in chemical engineering applications, magnetic resonance imaging (MRI) receives increasing scientific interest. Its non-invasive nature and wealth of parameters with the ability to generate functional images and contrast favors the use of MRI for many purposes, in particular investigations of dynamic phenomena, since it is very sensitive to motion. Recent progress in flow-MRI has led to shorter acquisition times and enabled studies of transient phenomena. Reactive systems can easily be imaged if NMR parameters such as relaxation change along the reaction coordinate. Moreover, materials and devices can be examined, such as batteries by mapping the magnetic field around them.

Spatially-resolved 1H NMR relaxation-exchange measurements in heterogeneous media

In the last decades, the ¹H NMR T₂-T₂ relaxation-exchange (REXSY) technique has become an essential tool for the molecular investigation of simple and complex fluids in heterogeneous porous solids and soft matter, where the mixing-time-evolution of cross-correlated T₂-T₂ peaks enables a quantitative study of diffusive exchange kinetics in multi-component systems. Here, we present a spatially-resolved implementation of the T₂-T₂ correlation technique, named z-T₂-T₂, based on one-dimensional spatial mapping along z using a rapid frequency-encode imaging scheme. Compared to other phase-encoding methods, the adopted MRI technique has two distinct advantages: (i) is has the same experimental duration of a standard (bulk) T₂-T₂ measurement, and (ii) it provides a high spatial resolution. The proposed z-T₂-T₂ method is first validated against bulk T₂-T₂ measurements on homogeneous phantom consisting of cyclohexane uniformly imbibed in finely-sized α-Al₂O₃ particles at a spatial resolution of 0.47 mm; thereafter, its performance is demonstrated, on a layered bed of multi-sized α-Al₂O₃ particles, for revealing spatially-dependent molecular exchange kinetics properties of intra- and inter-particle cyclohexane as a function of particle size. It is found that localised z-T₂-T₂ spectra provide well resolved cross peaks whilst such resolution is lost in standard bulk T₂-T₂ data. Future prospective applications of the method lie, in particular, in the local characterisation of mass transport phenomena in multi-component porous media, such as rock cores and heterogeneous catalysts.

Ultra-short echo time imaging with multiple echo refocusing for porous media T2 mapping

T₂ relaxation time measurement is a powerful tool to distinguish signal components in porous media. As T₂ weighting is generally achieved by spin-echo based methods, it is very challenging to capture very short T₂ relaxation time components, approximately 1 ms, with high resolution spatial encoding. It is especially challenging when T₂ relaxation times of the other signal components are not known a priori. We propose a method, combining ultrashort echo time (UTE) imaging with multiple spin echo refocusing, to generate a series of images with T₂ weighting. The T₂ decay curves for each image voxel were extracted, and multiple T₂ relaxation components were quantitatively evaluated. The method has been applied to a fast relaxation system, namely, moisture content in wood samples to differentiate cell wall (bound) water and cell cavity (lumen) water.

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.

Local T1-T2 distribution measurements in porous media

A novel slice-selective T₁-T₂ measurement is proposed to measure spatially resolved T₁-T₂ distributions. An adiabatic inversion pulse is employed for slice-selection. The slice-selective pulse is able to select a quasi-rectangular slice, on the order of 1 mm, at an arbitrary position within the sample.The method does not employ conventional selective excitation in which selective excitation is often accomplished by rotation of the longitudinal magnetization in the slice of interest into the transverse plane, but rather a subtraction based on CPMG data acquired with and without adiabatic inversion slice selection. T₁ weighting is introduced during recovery from the inversion associated with slice selection. The local T₁-T₂ distributions measured are of similar quality to bulk T₁-T₂ measurements. The new method can be employed to characterize oil-water mixtures and other fluids in porous media. The method is beneficial when a coarse spatial distribution of the components is of interest.

Local diffusion and diffusion-T2 distribution measurements in porous media

Slice-selective pulsed field gradient (PFG) and PFG-T₂ measurements are developed to measure spatially-resolved molecular diffusion and diffusion-T₂ distributions. A spatially selective adiabatic inversion pulse was employed for slice-selection. The slice-selective pulse is able to select a coarse slice, on the order of 1cm, at an arbitrary position in the sample. The new method can be employed to characterize oil-water mixtures in porous media. The new technique has an inherent sensitivity advantage over phase encoding imaging based methods due to signal being localized from a thick slice. The method will be advantageous for magnetic resonance of porous media at low field where sensitivity is problematic. Experimental CPMG data, following PFG diffusion measurement, were compromised by a transient ΔB₀(t) field offset. The off resonance effects of ΔB₀(t) were examined by simulation. The ΔB₀ offset artifact in D-T₂ distribution measurements may be avoided by employing real data, instead of magnitude data.

Monitoring oil displacement processes with k-t accelerated spin echo SPI

Magnetic resonance imaging (MRI) is a robust tool to monitor oil displacement processes in porous media. Conventional MRI measurement times can be lengthy, which hinders monitoring time-dependent displacements. Knowledge of the oil and water microscopic distribution is important because their pore scale behavior reflects the oil trapping mechanisms. The oil and water pore scale distribution is reflected in the magnetic resonance T2 signal lifetime distribution. In this work, a pure phase-encoding MRI technique, spin echo SPI (SE-SPI), was employed to monitor oil displacement during water flooding and polymer flooding. A k-t acceleration method, with low-rank matrix completion, was employed to improve the temporal resolution of the SE-SPI MRI measurements. Comparison to conventional SE-SPI T2 mapping measurements revealed that the k-t accelerated measurement was more sensitive and provided higher-quality results. It was demonstrated that the k-t acceleration decreased the average measurement time from 66.7 to 20.3 min in this work. A perfluorinated oil, containing no (1) H, and H2 O brine were employed to distinguish oil and water phases in model flooding experiments. High-quality 1D water saturation profiles were acquired from the k-t accelerated SE-SPI measurements. Spatially and temporally resolved T2 distributions were extracted from the profile data. The shift in the (1) H T2 distribution of water in the pore space to longer lifetimes during water flooding and polymer flooding is consistent with increased water content in the pore space. Copyright © 2015 John Wiley & Sons, Ltd.

Local T2 measurement employing longitudinal Hadamard encoding and adiabatic inversion pulses in porous media

Band selective adiabatic inversion radio frequency pulses were employed for multi-slice T2 distribution measurements in porous media samples. Multi-slice T2 measurement employing longitudinal Hadamard encoding has an inherent sensitivity advantage over slice-by-slice local T2 measurements. The slice selection process is rendered largely immune to B1 variation by employing hyperbolic secant adiabatic inversion pulses, which simultaneously invert spins in several well-defined slices. While Hadamard encoding is well established for local spectroscopy, the current work is the first use of Hadamard encoding for local T2 measurement.

k-t acceleration in pure phase encode MRI to monitor dynamic flooding processes in rock core plugs

Monitoring the pore system in sedimentary rocks with MRI when fluids are introduced is very important in the study of petroleum reservoirs and enhanced oil recovery. However, the lengthy acquisition time of each image, with pure phase encode MRI, limits the temporal resolution. Spatiotemporal correlations can be exploited to undersample the k-t space data. The stacked frames/profiles can be well approximated by an image matrix with rank deficiency, which can be recovered by nonlinear nuclear norm minimization. Sparsity of the x-t image can also be exploited for nonlinear reconstruction. In this work the results of a low rank matrix completion technique were compared with k-t sparse compressed sensing. These methods are demonstrated with one dimensional SPRITE imaging of a Bentheimer rock core plug and SESPI imaging of a Berea rock core plug, but can be easily extended to higher dimensionality and/or other pure phase encode measurements. These ideas will enable higher dimensionality pure phase encode MRI studies of dynamic flooding processes in low magnetic field systems.

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.

Spatially resolved measurements of mean spin-spin relaxation time constants

Magnetic Resonance measurements of the T2 distribution have become very common and they are a powerful way to probe microporous fluid bearing solids. While the structure of the T2 distribution, and changes in the structure, are often very informative, it is common to reduce the T2 distribution to a mean numeric quantity in order to provide a quantitative interpretation of the distribution. Magnetic Resonance Imaging measurements of the T2 distribution have recently been introduced, but they are time consuming, especially for 2 and 3 spatial dimensions. In this paper we explore a direct MRI measurement of the arithmetic mean of 1/T2, characterizing the distribution by using the initial slope of the spatially resolved T2 decay in a CPMG prepared Centric Scan SPRITE experiment. The methodology is explored with a test phantom sample and realistic petroleum reservoir core plug samples. The arithmetic mean of 1/T2 is related to the harmonic mean of T2. The mean obtained from the early decay is explored through measurements of uniform saturated core plug samples and by comparison to other means determined from the complete T2 distribution. Complementary data were obtained using SE-SPI T2 distribution MRI measurements. The utility of the arithmetic mean 1/T2 is explored through measurements of centrifuged core plug samples where the T2 distribution varies spatially. The harmonic mean T2 obtained from the early decay was employed to estimate the irreducible water saturation for core plug samples.

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.

B(1) mapping with a pure phase encode approach: quantitative density profiling

In MRI, it is frequently observed that naturally uniform samples do not have uniform image intensities. In many cases this non-uniform image intensity is due to an inhomogeneous B1 field. The 'principle of reciprocity' states that the received signal is proportional to the local magnitude of the applied B1 field per unit current. Inhomogeneity in the B1 field results in signal intensity variations that limit the ability of MRI to yield quantitative information. In this paper a novel method is described for mapping B1 inhomogeneities based on measurement of the B1 field employing centric-scan pure phase encode MRI measurements. The resultant B1 map may be employed to correct related non-uniformities in MR images. The new method is based on acquiring successive images with systematically incremented low flip angle excitation pulses. The local image intensity variation is proportional to B1(2), which ensures high sensitivity to B1 field variations. Pure phase encoding ensures the resultant B1 field maps are free from distortions caused by susceptibility variation, chemical shift and paramagnetic impurities. Hence, the method works well in regions of space that are not accessible to other methods such as in the vicinity of conductive metallic structures, such as the RF probe itself. Quantitative density images result when the centric scan pure phase encode measurement is corrected with a relative or absolute B1 field map. The new technique is simple, reliable and robust.

A comparison of magnetic resonance imaging methods for fluid content imaging in porous media

Quantitative measurements are important for imaging fluid content in porous media. Conventional MRI methods suffer from contrast because of relaxation times in porous media, resulting in measurements of apparent fluid content, not the true fluid content. We compare four magnetic resonance imaging methods for fluid content imaging in several water-saturated reservoir core plugs: frequency-encoded spin echo, single point ramped imaging with T1 enhancement, hybrid spin echo single point imaging (SE-SPI), and T2 mapping SE-SPI. 1-D profiles obtained with each method were compared in terms of image quality, image sensitivity, and quantification of water content. The image quality of short T2 lifetime samples suffered from blurring in hybrid SE-SPI images. Image sensitivity was the highest in the profiles obtained with frequency-encoded spin echo. The quantification of frequency-encoded spin echo, T2 mapping SE-SPI, and hybrid SE-SPI suffered in core plugs with a significant population of short T2 components because of T2 attenuation. Overall, single point ramped imaging with T1 enhancement was found to be the most general method for fluid content imaging.

Restricted k-space sampling in pure phase encode MRI of rock core plugs

In the study of rock core plugs with multidimensional MRI, the samples are of a regular cylindrical shape that yields well defined intensity distributions in reciprocal space. The high intensity k-space points are concentrated in the central region and in specific peripheral regions. A large proportion of the k-space points have signal intensities that are below the noise level. These points can be zero-filled instead of being collected experimentally. k-space sampling patterns that collect regions of high intensity signal while neglecting low intensity regions can be naturally applied to a wide variety of pure phase encoding measurements, such as T2 mapping SESPI, hybrid-SESPI and SPRITE, since all imaging dimensions can be under-sampled. With a shorter acquisition time, as fewer experimental data points are required, the RF and gradient duty cycles are reduced, while the image SNR is improved.

Spatially resolved solid-state 1H NMR for evaluation of gradient-composition polymeric libraries

Polyurethane libraries consisting of films with composition gradients of aliphatic polyisocyanate and hydroxy-terminated polyacrylate resin were characterized using methods of (1)H NMR microimaging (i.e., magnetic resonance imaging, (MRI)) and solid-state NMR. Molecular mobilities and underlying structural information were extracted as a function of the relative content of each of the two components. Routine NMR microimaging using the spin-echo sequence only allows investigations of transverse relaxation of magnetization at echo times >2 ms. A single-exponential decay was found, which is likely due to free, noncross-linked polymer chains. The mobility of these chains decreases with increasing content of the aliphatic polyisocyanate. The concept of a 1D NMR profiler is introduced as a novel modality for library screening, which allows the convenient measurement of static solid-state NMR spectra as a function of spatial location along a library sample that is repositioned in the rf coil between experiments. With this setup the complete transverse relaxation function was measured using Bloch decays and spin echoes. For all positions within the gradient-composition film, relaxation data consisted of at least three components that were attributed to a rigid highly cross-linked resin, an intermediate cross-linked but mobile constituent, and the highly mobile free polymer chains (the latter is also detectable by MRI). Analysis of this overall relaxation function measured via Bloch decays and spin echoes revealed only minor changes in the mobilities of the individual fractions. Findings with respect to the most mobile components are consistent with the results obtained by NMR microimaging. The major effect is the significant increase in the rigid-component fraction with the addition of the hydroxy-terminated polyacrylate resin.

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.

Local T2 distribution measurements with DANTE-Z slice selection

A CPMG pulse sequence incorporated with a DANTE-Z slice selection scheme for measuring spatially-resolved T(2) distributions has been presented. The DANTE-Z pulse train with sinc-modulated pulses selects a single, quasi-rectangular slice of less than 0.8 cm wide at an arbitrary position over a 6-cm long sample. The measured T(2) distributions are of almost the same quality as regular (bulk) CPMG measurements, with the lower T(2) limit being as good as c.a. 0.5 ms. The sequence can be found useful as a supplement or alternative to MRI-based techniques for T(2) mapping in short relaxation time samples (water-saturated rocks, building materials, wood, food products, rubbers, etc.), particularly when T(2) is required to be measured at only few positions along the sample and the resolution of ~1 cm is acceptable.

Two-dimensional T2 distribution mapping in porous solids with phase encode MRI

Two pure phase encode MRI sequences, CPMG-prepared SPRITE and spin-echo SPI with compressed sensing, for two-dimensional (2-D) T2 distribution mapping have been presented. The sequences are 2-D extensions of their 1-D predecessors previously described and are intended for studying processes in porous solids and other samples with short relaxation times whenever 2-D T2 maps are preferable to simple 1-D profiling. The sequences were tested on model samples and natural water-saturated rocks, in a low field MRI instrument. 2-D spin-echo SPI and CPMG-SPRITE demonstrate a similar performance, enabling measurement of T2 down to 1-2 ms. Both experiments are time consuming (up to 2-2.5 h sample dependent). As such, they can be recommended mostly for measurement during steady state conditions or when studying relatively slow dynamic processes (e.g. enhanced oil recovery, cement paste hydration, curing rubber, infiltration of paramagnetic ions).