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

T2 analysis using artificial neural networks

Quantitative analysis of magnetic resonance signal lifetimes could reveal molecular scale information. However, it is non-trivial to recover the relaxation times from MR experiments in the multi-component exponential decay analysis. Constraints are required for the ill-posed problem in conventional inversion methods, which could lead to biased solutions. Artificial neural networks (ANNs) are a series of densely connected information processing nodes which cumulatively map a set of inputs to a set of outputs. They have proven to be universal approximators and powerful tools for solving complex nonlinear problems. In this work, ANNs were trained to recover T₂ relaxation times. Both the discrete T₂ spectrum and continuous T₂ distribution were considered. Increased accuracy was achieved compared to the traditional methods. The continuous spectrum peak widths, generally not reliable in the traditional approach, could be determined accurately with ANN when the signal-to-noise ratio permitted.

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.

Full-Harmonics Phasor Analysis: Unravelling Multiexponential Trends in Magnetic Resonance Imaging Data

Phasor analysis is a robust, nonfitting, method for the study of multiexponential decays in lifetime imaging data, routinely used in Fluorescence Lifetime Imaging Microscopy (FLIM) and only recently validated for Magnetic Resonance Imaging (MRI). In the established phasor approach, typically only the first Fourier harmonic is used to unravel time-domain exponential trends and their intercorrelations across image voxels. Here, we demonstrate the potential of full-harmonics (FH) phasor analysis by using all frequency-domain data points in simulations and quantitative MRI (qMRI) T₂ measurements of phantoms with bulk liquids or liquid-filled porous particles and of a human brain. We show that FH analysis, while of limited advantage in FLIM due to the correlated nature of shot noise, in MRI outperforms single-harmonic phasor in unravelling multiple physical environments and partial-volume effects otherwise undiscernible. We foresee application of FH phasor to, e.g., big-data analysis in qMRI of biological or other multiphase systems, where multiparameter fitting is unfeasible.

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.

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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{o}})$$\end{document}So) and water (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{w}})$$\end{document}Sw), 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{o}}$$\end{document}So and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{w}}$$\end{document}Sw 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.27\times 10^{-6}\,\hbox {m}\,\hbox {s}^{-1}$$\end{document}1.27×10-6ms-1 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.4\,\hbox {ft}\,\hbox {day}^{-1})$$\end{document}0.4ftday-1). During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.31\,\hbox {mm}\times 0.39\,\hbox {mm} \times 0.39\,\hbox {mm}$$\end{document}0.31mm×0.39mm×0.39mm 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.

T2 selective π Echo-Planar Imaging for porous media MRI

The π Echo Planar Imaging (PEPI) method has recently been modified to permit proton density imaging of fluids in porous media with moderate T₂ and short T₂^∗ signal components. In many applications, it is desirable to discriminate multiple T₂ components within each image voxel. T₂ selective imaging is explored in this paper through adiabatic inversion as a magnetization preparation with PEPI readout. When prior information of the sample relaxation times is known, responses of different species to broadband adiabatic inversion pulses can be predicted by Bloch equation simulation. Different relaxation components can be acquired by combining the images with and without inversion preparation pulses. T₂ weighting can be easily introduced in the PEPI sequence by shifting the spatial encoding gradients based on its spin echo nature. T₂ decay curves can be extracted for each image voxel from a series of T₂ weighted images and spatially resolved T₂ distributions can be generated. This method is reliable but slow. The two methods were implemented to image porous media samples with PEPI the common basis of spatial resolution. The results of both methods agree remarkably well.

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.

π Echo-Planar Imaging with concomitant field compensation for porous media MRI

The π Echo Planar Imaging (PEPI) method was modified to compensate for concomitant magnetic fields by waveform symmetrization. Samples with very short T2(∗) (a few hundred microseconds) and short T2 (tens of milliseconds to hundreds of milliseconds) were investigated. Echo spacings as short as 1.2 ms were achieved with the gradient pre-equalization method, enabling rapid 3D imaging of short relaxation time species with sub-millimeter resolution. The PEPI method yields superior quality images, compared to the Fast Spin Echo (FSE) method, with significantly reduced gradient duty cycle. Accelerated PEPI measurements with a variable number of centric interleaves are presented. Restricted k-space sampling was demonstrated for specific sample geometries, notably a Locharbriggs sandstone core plug, with the acquisition time further reduced. These methods generate proton density weighted images considering the echo time to sample T2 ratio. These methods are principally designed for 3D studies of fluid saturation in rock core plugs, evolving in time due to some manner of external perturbation, such as water flooding.

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.

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.

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

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

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.

Hybrid-SPRITE MRI

In a FID based frequency encoding MRI experiment the central part of k-space is not generally accessible due to the probe dead time. This portion of k-space is however crucial for image reconstruction. SPRITE (Single Point Ramped Imaging with T1 Enhancement), SPI with a linearly ramped phase encode gradient, has been employed to image short relaxation time systems for many years with great success. It is a robust imaging method in significant measure because it provides acquisition of high quality k-space origin data. We propose a new sampling scheme, termed hybrid-SPRITE, combining phase and frequency encoding to ensure high quality images with reduced acquisition times, reduced gradient duty cycle and increased sensitivity. In hybrid-SPRITE, numerous time domain points are collected to assist image reconstruction. An Inverse Non-uniform Discrete Fourier Transform (INDFT) is employed in 1D applications. A pseudo-polar grid is exploited in 2D hybrid-SPRITE for rapid and accurate image reconstruction.

Purely phase-encoded MRI of turbulent flow through a dysfunctional bileaflet mechanical heart valve

OBJECT

We have used a purely phase-encoded magnetic resonance imaging (MRI) technique, single-point ramped imaging with T1 enhancement (SPRITE), to investigate the steady, turbulent flow dynamics through a bileaflet mechanical heart valve (BMHV).

MATERIALS AND METHODS

We have measured in vitro the turbulent diffusivity and velocity downstream of the valve in two configurations (fully opened and partially opened), which mimic normal and dysfunctional operation. Our constant-time implementation of the MRI measurement is unusually robust to fast turbulent flows, and to artefacts caused by the pyrolytic carbon construction of the valve.

RESULTS

Turbulent diffusivity downstream of the normally functioning valve peaks at 1.05 × 10(-6)m(2)/s, while the turbulent diffusivity is higher downstream of the dysfunctional valve (peaking at 3.15 × 10(-6) m(2)/s) and is accompanied by a high-velocity fluid jet and re-circulating flow. The fluid jet is not along the centreline of the valve, as might be anticipated in conventional Doppler echocardiography measurements.

CONCLUSION

The nature of motion-sensitized SPRITE makes it unusually capable in turbulent flows and near to boundaries between different magnetic susceptibilities. These qualities have allowed us to compare the three-dimensional flow fields through normal and dysfunctional BMHVs.

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.

Magnetic susceptibility based magnetic resonance estimation of micro-bubble size for the vertically upward bubbly flow

The approach originally developed for the Nuclear Magnetic Resonance analysis of stable micro-bubbles is applied to studies of vertical bubbly flows. A very fast dispersion (diffusion) of water in bubbly flows extends the fast diffusion limit down to short (2-10 ms) measurement times, permitting the use of the simplified analytical expression to extract the micro-bubble size information both in bulk and spatially resolved. The observed strong bubble-induced reduction in T(2)(*) necessitates the use of very short encoding times and pure phase encoding methods to accurately measure the void fraction. There was an expected underestimation of bubble sizes at faster flow rates due to the limitations of the theory derived for small bubble sizes and non-interacting spherical bubbles (low void fractions and slow flow rates). This approach lends itself to studies of bubbly flows and cavitating media characterized by small bubble sizes and low void fractions.

Velocity field measurements in sedimentary rock cores by magnetization prepared 3D SPRITE

A time-efficient MRI method suitable for quantitative mapping of 3-D velocity fields in sedimentary rock cores, and granular samples is discussed. The method combines the 13-interval Alternating-Pulsed-Gradient Stimulated-Echo (APGSTE) scheme and three-dimensional Single Point Ramped Imaging with T(1) Enhancement (SPRITE). Collecting a few samples near the q-space origin and employing restricted k-space sampling dramatically improves the performance of the imaging method. The APGSTE-SPRITE method is illustrated through mapping of 3-D velocity field in a macroscopic bead pack and heterogeneous sandstone and limestone core plugs. The observed flow patterns are consistent with a general trend for permeability to increase with the porosity. Domains of low permeability obstruct the flow within the core volume. Water tends to flow along macroscopic zones of higher porosity and across zones of lower porosity.