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

Integrating Pore-Scale Flow MRI and X-ray μCT for Validation of Numerical Flow Simulations in Porous Sedimentary Rocks

Single-phase fluid flow velocity maps in Ketton and Estaillades carbonate rock core plugs are computed at a pore scale, using the lattice Boltzmann method (LBM) simulations performed directly on three-dimensional (3D) X-ray micro-computed tomography (µCT) images (≤ 7 µm spatial resolution) of the core plugs. The simulations are then benchmarked on a voxel-by-voxel and pore-by-pore basis to quantitative, 3D spatially resolved magnetic resonance imaging (MRI) flow velocity maps, acquired at 35 µm isotropic spatial resolution for flow of water through the same rock samples. Co-registration of the 3D experimental and simulated velocity maps and coarse-graining of the simulation to the same resolution as the experimental data allowed the data to be directly compared. First, the results are demonstrated for Ketton limestone rock, for which good qualitative and quantitative agreement was found between the simulated and experimental velocity maps. The flow-carrying microstructural features in Ketton rock are mostly larger than the spatial resolution of the µCT images, so that the segmented images are an adequate representation of the pore space. Second, the flow data are presented for Estaillades limestone, which presents a more heterogeneous case with microstructural features below the spatial resolution of the µCT images. Still, many of the complex flow patterns were qualitatively reproduced by the LBM simulation in this rock, although in some pores, noticeable differences between the LBM and MRI velocity maps were observed. It was shown that 80% of the flow (fractional summed z-velocities within pores) in the Estaillades rock sample is carried by just 10% of the number of macropores, which is an indication of the high structural heterogeneity of the rock; in the more homogeneous Ketton rock, 50% of the flow is carried by 10% of the macropores. By analysing the 3D MRI velocity map, it was found that approximately one-third of the total flow rate through the Estaillades rock is carried by microporosity—a porosity that is not captured at the spatial resolution of the µCT image.

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.

Gas and Liquid Phase Imaging of Foam Flow Using Pure Phase Encode Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is a non-invasive and non-optical measurement technique, which makes it a promising method for studying delicate and opaque samples, such as foam. Another key benefit of MRI is its sensitivity to different nuclei in a sample. The research presented in this article focuses on the use of MRI to measure density and velocity of foam as it passes through a pipe constriction. The foam was created by bubbling fluorinated gas through an aqueous solution. This allowed for the liquid and gas phases to be measured separately by probing the 1H and 19F behavior of the same foam. Density images and velocity maps of the gas and liquid phases of foam flowing through a pipe constriction are presented. In addition, results of computational fluid dynamics simulations of foam flow in the pipe constriction are compared with experimental results.

Velocity mapping of fast flows using a linearly ramped gradient waveform

We report a new pure phase encoding measurement for velocity mapping. Velocity-sensitization is achieved using a repeating, linearly ramped gradient waveform instead of rectangular bipolar pulsed field gradients. This approach reduces eddy current effects and results in the sample experiencing a gradient waveform that more closely matches the ideal input. Errors in k-space mapping and calculated velocity values are reduced when contrasted with the previous measurement method. Velocity maps were acquired of high-speed (c. 6 m/s) water flow through a pipe constriction. The application of linearly ramped gradient waveforms to non-velocity-encoded imaging measurements is discussed.

Accuracy of phase-contrast velocimetry in systems with skewed intravoxel velocity distributions

Phase contrast velocimetry (PCV) has been widely used to investigate flow properties in numerous systems. Several authors have reported errors in velocity measurements and have speculated on the sources, which have ranged from eddy current effects to acceleration artefacts. An often overlooked assumption in the theory of PCV, which may not be met in complex or unsteady flows, is that the intravoxel displacement distributions (propagators) are symmetric. Here, the effect of the higher moments of the displacement distribution (variance, skewness and kurtosis) on the accuracy of PCV is investigated experimentally and theoretically. Phase and propagator measurements are performed on tailored intravoxel distributions, achieved using a simple phantom combined with a single large voxel. Asymmetric distributions (Skewness ≠ 0) are shown to generate important phase measurement errors that lead to significant velocimetry errors. Simulations of the phase of the spin vector sum, based on experimentally measured propagators, are shown to quantitatively reproduce the relationship between measured phase and experimental parameters. These allow relating the observed velocimetry errors to a discrepancy between the average phase of intravoxel spins considered in PCV theory and the vector phase actually measured by a PFG experiment. A theoretical expression is derived for PCV velocimetry errors as a function of the moments of the displacement distribution. Positively skewed distributions result in an underestimation of the true mean velocity, while negatively skewed distributions result in an overestimation. The magnitude of these errors is shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution.

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.

Accurate phase-shift velocimetry in rock

Spatially resolved Pulsed Field Gradient (PFG) velocimetry techniques can provide precious information concerning flow through opaque systems, including rocks. This velocimetry data is used to enhance flow models in a wide range of systems, from oil behaviour in reservoir rocks to contaminant transport in aquifers. Phase-shift velocimetry is the fastest way to produce velocity maps but critical issues have been reported when studying flow through rocks and porous media, leading to inaccurate results. Combining PFG measurements for flow through Bentheimer sandstone with simulations, we demonstrate that asymmetries in the molecular displacement distributions within each voxel are the main source of phase-shift velocimetry errors. We show that when flow-related average molecular displacements are negligible compared to self-diffusion ones, symmetric displacement distributions can be obtained while phase measurement noise is minimised. We elaborate a complete method for the production of accurate phase-shift velocimetry maps in rocks and low porosity media and demonstrate its validity for a range of flow rates. This development of accurate phase-shift velocimetry now enables more rapid and accurate velocity analysis, potentially helping to inform both industrial applications and theoretical models.

Magnetic Resonance Imaging measurements of a water spray upstream and downstream of a spray nozzle exit orifice

Sprays are dynamic collections of droplets dispersed in a gas, with many industrial and agricultural applications. Quantitative characterization is essential for understanding processes of spray formation and dynamics. There exists a wide range of measurement techniques to characterize sprays, from direct imaging to phase Doppler interferometry to X-rays, which provide detailed information on spray characteristics in the "far-nozzle" region (≫10 diameters of the nozzle). However, traditional methods are limited in their ability to characterize the "near-nozzle" region where the fluid may be inside the nozzle, optically dense, or incompletely atomized. Magnetic Resonance Imaging (MRI) presents potential as a non-invasive technique that is capable of measuring optically inaccessible fluid in a quantitative fashion. In this work, MRI measurements of the spray generated by ceramic flat-fan nozzles were performed. A wide range of flow speeds in the system (0.2 to >25m/s) necessitated short encoding times. A 3D Conical SPRITE and motion-sensitized 3D Conical SPRITE were employed. The signal from water inside the nozzle was well-characterized, both via proton density and velocity measurements. The signal outside the nozzle, in the near-nozzle region, was detectable, corresponding to the expected flat-fan spray pattern up to 3mm away. The results demonstrate the potential of MRI for measuring spray characteristics in areas inaccessible by other methods.

Measurement with microscopic MRI and simulation of flow in different aneurysm models

PURPOSE

The impact and the development of aneurysms depend to a significant degree on the exchange of liquid between the regular vessel and the pathological extension. A better understanding of this process will lead to improved prediction capabilities. The aim of the current study was to investigate fluid-exchange in aneurysm models of different complexities by combining microscopic magnetic resonance measurements with numerical simulations. In order to evaluate the accuracy and applicability of these methods, the fluid-exchange process between the unaltered vessel lumen and the aneurysm phantoms was analyzed quantitatively using high spatial resolution.

METHODS

Magnetic resonance flow imaging was used to visualize fluid-exchange in two different models produced with a 3D printer. One model of an aneurysm was based on histological findings. The flow distribution in the different models was measured on a microscopic scale using time of flight magnetic resonance imaging. The whole experiment was simulated using fast graphics processing unit-based numerical simulations. The obtained simulation results were compared qualitatively and quantitatively with the magnetic resonance imaging measurements, taking into account flow and spin-lattice relaxation.

RESULTS

The results of both presented methods compared well for the used aneurysm models and the chosen flow distributions. The results from the fluid-exchange analysis showed comparable characteristics concerning measurement and simulation. Similar symmetry behavior was observed. Based on these results, the amount of fluid-exchange was calculated. Depending on the geometry of the models, 7% to 45% of the liquid was exchanged per second.

CONCLUSIONS

The result of the numerical simulations coincides well with the experimentally determined velocity field. The rate of fluid-exchange between vessel and aneurysm was well-predicted. Hence, the results obtained by simulation could be validated by the experiment. The observed deviations can be caused by the noise in the measurement and by the limited resolution of the simulation. The resulting differences are small enough to allow reliable predictions of the flow distribution in vessels with stents and for pulsed blood flow.

New opportunities for quantitative and time efficient 3D MRI of liquid and solid electrochemical cell components: Sectoral Fast Spin Echo and SPRITE

The ability to image electrochemical processes in situ using nuclear magnetic resonance imaging (MRI) offers exciting possibilities for understanding and optimizing materials in batteries, fuel cells and supercapacitors. In these applications, however, the quality of the MRI measurement is inherently limited by the presence of conductive elements in the cell or device. To overcome related difficulties, optimal methodologies have to be employed. We show that time-efficient three dimensional (3D) imaging of liquid and solid lithium battery components can be performed by Sectoral Fast Spin Echo and Single Point Imaging with T1 Enhancement (SPRITE), respectively. The former method is based on the generalized phase encoding concept employed in clinical MRI, which we have adapted and optimized for materials science and electrochemistry applications. Hard radio frequency pulses, short echo spacing and centrically ordered sectoral phase encoding ensure accurate and time-efficient full volume imaging. Mapping of density, diffusivity and relaxation time constants in metal-containing liquid electrolytes is demonstrated. 1, 2 and 3D SPRITE approaches show strong potential for rapid high resolution (7)Li MRI of lithium electrode components.

High-resolution MRI velocimetry compared with numerical simulations

Alterations of the blood flow are associated with various cardiovascular diseases. Precise knowledge of the velocity distribution is therefore important for understanding these diseases and predicting the effect of different medical intervention schemes. The goal of this work is to estimate the precision with which the velocity field can be measured and predicted by studying two simple model geometries with NMR micro imaging and computational fluid dynamics. For these initial experiments, we use water as an ideal test medium. The phantoms consist of tubes simulating a straight blood vessel and a step between two tubes of different diameters, which can be seen as a minimal model of the situation behind a stenosis. For both models, we compare the experimental data with the numerical prediction, using the experimental boundary conditions. For the simpler model, we also compare the data to the analytical solution. As an additional validation, we determine the divergence of the velocity field and verify that it vanishes within the experimental uncertainties. We discuss the resulting precision of the simulation and the outlook for extending this approach to the analysis of specific cases of arteriovascular problems.

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.