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

Fast spin echo MRI of reservoir core plugs with a variable field magnet

Fast Spin Echo MRI is now widely employed in biomedicine for proton density and T2 contrast imaging. Fast Spin Echo methods provide rapid data acquisition by employing multiple echoes to determine multiple k-space lines with single excitations. Due to the multi-exponential behavior of T2 in typical porous media, and the strong dependence of T2 on the details of the experiment, acquiring a proton density image with Fast Spin Echo methods requires favorable sample and acquisition parameters. In recent years, we have shown the value of pure phase encode Free Induction Decay based methods such as SPRITE. However, in a reservoir rock, a typical T2* is hundreds of µs, whereas a typical T2 is hundreds of ms. Hence, there is merit in considering spin echo-based MRI measurements such as the Fast Spin Echo for rock core plug studies. A variable field superconducting magnet was employed in this study. This is a new class of magnet for MR/MRI. These magnets have the flexibility of operation in the field range of 0.01 Tesla to 3 Tesla. This is advantageous when working with rock core plugs, as it allows one to maximize sample magnetization, by increasing the static field while controlling magnetic susceptibility mismatch effects, and thereby T2 and T2*, through reducing the static field. The magnetic fields employed in the study were 0.79, 1.5, and 3 Tesla. Measurements were undertaken on five brine-saturated reservoir rock core plugs (Bentheimer, Berea, Buff Berea, Nugget, and Wallace). The results show that Fast Spin Echo measurements are more sensitive than SPRITE methods in amenable samples and usually feature higher resolution. Quantification of saturation with Fast Spin Echo methods requires correction for T2 attenuation. The results also show that 3 Tesla is too high a static field in general for rock core MRI studies with either method. While the current study is focused on five representative reservoir rock cores, the conclusions which result are general for MRI of fluids in porous media.

Assessing spatial resolution, acquisition time and signal-to-noise ratio for commercial microimaging systems at 14.1, 17.6 and 22.3 T

This work provides a systematic comparison of the signal-to-noise ratio (SNR), spatial resolution, acquisition time and metabolite limits-of-detection for magnetic resonance microscopy and spectroscopy at three different magnetic field strengths of 14.1 T, 17.6 T and 22.3 T (the highest currently available for imaging), utilizing commercially available hardware. We find an SNR increase of a factor 5.9 going from 14.1 T to 22.3 T using 5 mm radiofrequency (saddle and birdcage) coils, which results in a 24-fold acceleration in acquisition time and deviates from the theoretically expected increase of factor 2.2 due to differences in hardware. This underlines the importance of not only the magnetic field strengths but also hardware optimization. In addition, using a home-built 1.5 mm solenoid coil, we can achieve an isotropic resolution of (5.5 µm)³ over a field-of-view of 1.58 mm × 1.05 mm × 1.05 mm with an SNR of 12:1 using 44 signal averages in 58 h 34 min acquisition time at 22.3 T. In light of these results, we discuss future perspectives for ultra-high field Magnetic Resonance Microscopy and Spectroscopy.

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.

BLIPPED (BLIpped Pure Phase EncoDing) high resolution MRI with low amplitude gradients

MRI image resolution is proportional to the maximum k-space value, i.e. the temporal integral of the magnetic field gradient. High resolution imaging usually requires high gradient amplitudes and/or long spatial encoding times. Special gradient hardware is often required for high amplitudes and fast switching. We propose a high resolution imaging sequence that employs low amplitude gradients. This method was inspired by the previously proposed PEPI (π Echo Planar Imaging) sequence, which replaced EPI gradient reversals with multiple RF refocusing pulses. It has been shown that when the refocusing RF pulse is of high quality, i.e. sufficiently close to 180°, the magnetization phase introduced by the spatial encoding magnetic field gradient can be preserved and transferred to the following echo signal without phase rewinding. This phase encoding scheme requires blipped gradients that are identical for each echo, with low and constant amplitude, providing opportunities for high resolution imaging. We now extend the sequence to 3D pure phase encoding with low amplitude gradients. The method is compared with the Hybrid-SESPI (Spin Echo Single Point Imaging) technique to demonstrate the advantages in terms of low gradient duty cycle, compensation of concomitant magnetic field effects and minimal echo spacing, which lead to superior image quality and high resolution. The 3D imaging method was then applied with a parallel plate resonator RF probe, achieving a nominal spatial resolution of 17 μm in one dimension in the 3D image, requiring a maximum gradient amplitude of only 5.8 Gauss/cm.

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.