Magnetic resonance velocity imaging of liquid and gas two-phase flow in packed beds

Full-Field Comparison of MRV and CFD of Gas Flow through Regular Catalytic Monolithic Structures

Understanding the influence of gas flow maldistribution in honeycombs can be beneficial for the process design in various technical applications. Although recent studies have investigated the effect of maldistribution by comparing the results of numerical simulations with experimental measurements, an exhaustive 3D full-field comparison is still lacking. Such full-field comparisons are required to identify and eliminate possible limitations of numerical and experimental tools. For that purpose, spatially resolved flow patterns were simulated by computational fluid dynamics (CFD) and measured experimentally by non-invasive NMR velocimetry (MRV). While the latter might suffer from a misinterpretation of artefacts, the reliability of CFD is linked to correctly chosen boundary conditions. Here, a full-field numerical and experimental analysis of the gas flow within catalytic honeycombs is presented. The velocity field of thermally polarized methane gas was measured in a regular 3D-printed honeycomb and a commercial monolith using an optimized MRV pulse sequence to enhance the obtained signal-to-noise ratio. A second pulse sequence was used to show local flow propagators along the axial and radial direction of the honeycomb to quantify the contribution of diffusion to mass transport. A quantitative comparison of the axially averaged convective flow as determined by MRV and CFD shows a very good matching with an agreement of ±5% and 10% for printed and commercial samples, respectively. The impact of maldistribution on the gas flow pattern can be observed in both simulation and experiments, confirming the existence of an entrance effect. Gas displacement measurements, however, revealed that diffusive interchannel transport can also contribute to maldistribution, as was shown for the commercial sample. The good agreement between the simulation and experiments underpins the reliability of both methods for studying gas hydrodynamics within opaque monolith structures.

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.

Opportunities for Characterizing Geological Flows Using Magnetic Resonance Imaging

Geological flows-from mudslides to volcanic eruptions-are often opaque and consist of multiple interacting phases. Scaled laboratory geological experiments using analog materials have often been limited to optical imaging of flow exteriors or ex situ measurements. Geological flows often include internal phase transitions and chemical reactions that are difficult to image externally. Thus, many physical mechanisms underlying geological flows remain unknown, hindering model development. We propose using magnetic resonance imaging (MRI) to enhance geosciences via non-invasive, in situ measurements of 3D flows. MRI is currently used to characterize the interior dynamics of multiphase flows, distinguishing between different chemical species as well as gas, liquid, and solid phases, while quantitatively measuring concentration, velocity, and diffusion fields. This perspective describes the potential of MRI techniques to image dynamics within scaled geological flow experiments and the potential of technique development for geological samples to be transferred to other disciplines utilizing MRI.

Functionalized multiscale visual models to unravel flow and transport physics in porous structures

The fluid flow, species transport, and chemical reactions in geological formations are the chief mechanisms in engineering the exploitation of fossil fuels and geothermal energy, the geological storage of carbon dioxide (CO₂), and the disposal of hazardous materials. Porous rock is characterized by a wide surface area, where the physicochemical fluid-solid interactions dominate the multiphase flow behavior. A variety of visual models with differences in dimensions, patterns, surface properties, and fabrication techniques have been widely utilized to simulate and directly visualize such interactions in porous media. This review discusses the six categories of visual models used in geological flow applications, including packed beds, Hele-Shaw cells, synthesized microchips (also known as microfluidic chips or micromodels), geomaterial-dominated microchips, three-dimensional (3D) microchips, and nanofluidics. For each category, critical technical points (such as surface chemistry and geometry) and practical applications are summarized. Finally, we discuss opportunities and provide a framework for the development of custom-built visual models.

Pore Scale Visualization of Drainage in 3D Porous Media by Confocal Microscopy

We visualize the dynamics of immiscible displacement of a high viscosity wetting phase by a low viscosity non-wetting phase in a three-dimensional (3D) glass bead packing using confocal microscopy. Both phases were doped with two different fluorescent dyes, which enabled visualization of both phases simultaneously and quantification of the phase volumes without the need of image subtraction operations. The transient results show details of the displacement process and how pores are invaded by the non-wetting displacing phase. The static images at the end of the displacement process reveal how the trapped ganglia volume and morphology change with capillary number. The wetting phase is trapped as pendular rings spanning one to multiple pore necks. Details of the pore scale flow of oil wet media revealed with the experimental methods presented here can lead to better fundamental understanding of the physical processes and optimized enhanced oil recovery methods, CO₂ sequestration and aquifer remediation.

Effects of motion on MRI signal decay from micron-scale particles

Transverse decay rate (R2^∗) mapping is an established method for measuring iron overload in various biological tissues. Recently, R2^∗ mapping was used to measure the mean 3D concentration distribution of micron-size particles dispersed in turbulent flows. However, some discrepancy was observed between the measured R2^∗ and the expected decay based on existing theory. The present paper examines three flow-related mechanisms that could be responsible for this discrepancy. Computational simulations were used to study the effects of relative particle-fluid motion and preferential concentration by turbulence, while the effect of enhanced proton dispersion due to turbulence was examined via the existing MRI relaxation theory. Each flow phenomenon was shown to produce a different effect on the signal-time curve, as well as the extracted R2^∗. Comparison to experimental data in a square channel flow showed that relative motion between the particles and fluid was the most likely cause of the discrepancy in the previous experiments; however, all three effects may be present in both medical and non-medical flows, and their differing effects on the MRI signal may eventually allow for their identification from MRI data.

Gas Void Fraction Measurement of Gas-Liquid Two-Phase CO2 Flow Using Laser Attenuation Technique

The carbon capture and storage (CCS) system has the potential to reduce CO₂ emissions from traditional energy industries. In order to monitor and control the CCS process, it is essential to achieve an accurate measurement of the gas void fraction in a two-phase CO₂ flow in transportation pipelines. This paper presents a novel instrumentation system based on the laser attenuation technique for the gas void fraction measurement of the two-phase CO₂ flow. The system includes an infrared laser source and a photodiode sensor array. Experiments were conducted on the horizontal and vertical test sections. Two Coriolis mass flowmeters are respectively installed on the single-phase pipelines to obtain the reference gas void fraction. The experimental results obtained show that the proposed method is effective. In the horizontal test section, the relative errors of the stratified flow are within ±8.3%, while those of the bubble flow are within ±10.6%. In the vertical test section, the proposed method performs slightly less well, with relative errors under ±12.2%. The obtained results show that the measurement system is capable of providing an accurate measurement of the gas void fraction of the two-phase CO₂ flow and a useful reference for other industrial applications.

Accessing the long-time limit in diffusion NMR: The case of singlet assisted diffusive diffraction q-space

The latest developments in the field of long-lived spin states are merged with pulsed-field gradient techniques to extend the diffusion time beyond what is currently achievable in standard q-space diffusive-diffraction studies. The method uses nearly-equivalent spin-1/2 pairs that let diffusion times of the order of many minutes to be measured allowing access to the long-time limit in cavities of macroscopic size (millimeters). A pulse sequence suitable to exploit this regime has been developed and validated with the use of numerical simulations and experiments.

MRI of chemical reactions and processes

As magnetic resonance imaging (MRI) can spatially resolve a wealth of molecular information available from nuclear magnetic resonance (NMR), it is able to non-invasively visualise the composition, properties and reactions of a broad range of spatially-heterogeneous molecular systems. Hence, MRI is increasingly finding applications in the study of chemical reactions and processes in a diverse range of environments and technologies. This article will explain the basic principles of MRI and how it can be used to visualise chemical composition and molecular properties, providing an overview of the variety of information available. Examples are drawn from the disciplines of chemistry, chemical engineering, environmental science, physics, electrochemistry and materials science. The review introduces a range of techniques used to produce image contrast, along with the chemical and molecular insight accessible through them. Methods for mapping the distribution of chemical species, using chemical shift imaging or spatially-resolved spectroscopy, are reviewed, as well as methods for visualising physical state, temperature, current density, flow velocities and molecular diffusion. Strategies for imaging materials with low signal intensity, such as those containing gases or low sensitivity nuclei, using compressed sensing, para-hydrogen or polarisation transfer, are discussed. Systems are presented which encapsulate the diversity of chemical and physical parameters observable by MRI, including one- and two-phase flow in porous media, chemical pattern formation, phase transformations and hydrodynamic (fingering) instabilities. Lastly, the emerging area of electrochemical MRI is discussed, with studies presented on the visualisation of electrochemical deposition and dissolution processes during corrosion and the operation of batteries, supercapacitors and fuel cells.

Magnetic Resonance Imaging and Velocity Mapping in Chemical Engineering Applications

This review aims to illustrate the diversity of measurements that can be made using magnetic resonance techniques, which have the potential to provide insights into chemical engineering systems that cannot readily be achieved using any other method. Perhaps the most notable advantage in using magnetic resonance methods is that both chemistry and transport can be followed in three dimensions, in optically opaque systems, and without the need for tracers to be introduced into the system. Here we focus on hydrodynamics and, in particular, applications to rheology, pipe flow, and fixed-bed and gas-solid fluidized bed reactors. With increasing development of industrially relevant sample environments and undersampling data acquisition strategies that can reduce acquisition times to <1 s, magnetic resonance is finding increasing application in chemical engineering research.

11-interval PFG pulse sequence for improved measurement of fast velocities of fluids with high diffusivity in systems with short T2(∗)

Magnetic resonance (MR) was used to measure SF6 gas velocities in beds filled with particles of 1.1 mm and 0.5 mm in diameter. Four pulse sequences were tested: a traditional spin echo pulse sequence, the 9-interval and 13-interval pulse sequence of Cotts et al. (1989) and a newly developed 11-interval pulse sequence. All pulse sequences measured gas velocity accurately in the region above the particles at the highest velocities that could be achieved (up to 0.1 ms(-1)). The spin echo pulse sequence was unable to measure gas velocity accurately in the bed of particles, due to effects of background gradients, diffusivity and acceleration in flow around particles. The 9- and 13-interval pulse sequence measured gas velocity accurately at low flow rates through the particles (expected velocity <0.06 ms(-1)), but could not measure velocity accurately at higher flow rates. The newly developed 11-interval pulse sequence was more accurate than the 9- and 13-interval pulse sequences at higher flow rates, but for velocities in excess of 0.1 ms(-1) the measured velocity was lower than the expected velocity. The increased accuracy arose from the smaller echo time that the new pulse sequence enabled, reducing selective attenuation of signal from faster moving nuclei.

X-ray digital industrial radiography (DIR) for local liquid velocity (V(LL)) measurement in trickle bed reactors (TBRs): validation of the technique

Local liquid velocity measurements in Trickle Bed Reactors (TBRs) are one of the essential components in its hydrodynamic studies. These measurements are used to effectively determine a reactor's operating condition. This study was conducted to validate a newly developed technique that combines Digital Industrial Radiography (DIR) with Particle Tracking Velocimetry (PTV) to measure the Local Liquid Velocity (V(LL)) inside TBRs. Three millimeter-sized Expanded Polystyrene (EPS) beads were used as packing material. Three validation procedures were designed to test the newly developed technique. All procedures and statistical approaches provided strong evidence that the technique can be used to measure the V(LL) within TBRs.

Study of the fluid flow characteristics in a porous medium for CO2 geological storage using MRI

The objective of this study was to understand fluid flow in porous media. Understanding of fluid flow process in porous media is important for the geological storage of CO2. The high-resolution magnetic resonance imaging (MRI) technique was used to measure fluid flow in a porous medium (glass beads BZ-02). First, the permeability was obtained from velocity images. Next, CO2-water immiscible displacement experiments using different flow rates were investigated. Three stages were obtained from the MR intensity plot. With increasing CO2 flow rate, a relatively uniform CO2 distribution and a uniform CO2 front were observed. Subsequently, the final water saturation decreased. Using core analysis methods, the CO2 velocities were obtained during the CO2-water immiscible displacement process, which were applied to evaluate the capillary dispersion rate, viscous dominated fractional flow, and gravity flow function. The capillary dispersion rate dominated the effects of capillary, which was largest at water saturations of 0.5 and 0.6. The viscous-dominant fractional flow function varied with the saturation of water. The gravity fractional flow reached peak values at the saturation of 0.6. The gravity forces played a positive role in the downward displacements because they thus tended to stabilize the displacement process, thereby producing increased breakthrough times and correspondingly high recoveries. Finally, the relative permeability was also reconstructed. The study provides useful data regarding the transport processes in the geological storage of CO2.

Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches

In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozov's discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging.

Recent advances in flow MRI

The past five years have seen exciting new developments in Flow MRI. Two-dimensional images are now routinely acquired in 100-200 ms and, in some cases, acquisition times of 5-10 ms are possible. This has been achieved not only by advances in the implementation of existing pulse sequences but also in data acquisition strategies, such as Compressed Sensing and Bayesian approaches, and technical advices in parallel imaging and signal enhancement methods. In particular, the short imaging timescales that are now achieved offer significant opportunities in the study of transient flow phenomena.

Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing

We present a method for accelerating the acquisition of phase-encoded velocity images by the use of compressed sensing (CS), a technique that exploits the observation that an under-sampled signal can be accurately reconstructed by utilising the prior knowledge that it is sparse or compressible. We present results of both simulated and experimental measurements of liquid flow through a packed bed of spherical glass beads. For this system, the best image reconstruction used a spatial finite-differences transform. The reconstruction was further improved by utilising prior knowledge of the liquid distribution within the image. Using this approach, we demonstrate that for a sampling fraction of approximately 30% of the full k-space data set, the velocity can be recovered with a relative error of 11%, which is below the visually detectable limit. Furthermore, the error in the total flow measured using the CS reconstruction is <3% for sampling fractions > or = 30%. Thus, quantitative velocity images were obtained in a third of the acquisition time required using conventional imaging. The reduction in data acquisition time can also be exploited in acquiring images at a higher spatial resolution, which increases the accuracy of the measurements by reducing errors arising from partial volume effects. To illustrate this, the CS algorithm was used to reconstruct gas-phase velocity images at a spatial resolution of 230 microm x 230 microm. Images at this spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques.