A simple liquid state 1H NMR measurement to directly determine the surface hydroxyl density of porous silica.

Silica is widely used in industrial applications and its performance is partially decided by its surface hydroxyl density αOH. Here we report a quick, simple liquid 1H NMR method to determine αOH using a benchtop 1H NMR spectrometer. The results show excellent agreement with the literature with an αOH range from 4.16 to 6.56 OH per nm2.

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.

Identification of sampling patterns for high-resolution compressed sensing MRI of porous materials: 'learning' from X-ray microcomputed tomography data.

There exists a strong motivation to increase the spatial resolution of magnetic resonance imaging (MRI) acquisitions so that MRI can be used as a microscopy technique in the study of porous materials. This work introduces a method for identifying novel data sampling patterns to achieve undersampling schemes for compressed sensing MRI (CS-MRI) acquisitions, enabling 3D spatial resolutions of 17.6 µm to be achieved. A data-driven learning approach is used to derive k-space undersampling schemes for 3D MRI acquisitions from 3D X-ray microcomputed tomography (µCT) datasets acquired at a higher spatial resolution than can be acquired using MRI. The performance of the new sampling approach was compared to other, well-established sampling strategies using simulated MRI data obtained from high-resolution µCT images of rock core plugs. These simulations were performed for a range of different k-space sampling fractions (0.125-0.375) using images of Ketton limestone. The method was then extended to consideration of imaging Estaillades limestone and Fontainebleau sandstone. The results show that the new sampling approach performs as well as or better than conventional variable density sampling and without need for time-consuming parameter optimisation. Further, a bespoke sampling pattern is produced for each rock type. The novel undersampling strategy was employed to acquire 3D magnetic resonance images of a Ketton limestone rock at spatial resolutions of 35 and 17.6 µm. The ability of the k-space sampling scheme produced using the new approach in enabling reconstruction of the pore space characteristics of the rock was then demonstrated by benchmarking against the pore space statistics obtained from high-resolution µCT data. The MRI data acquired at 17.6 µm resolution gave excellent agreement with the pore size distribution obtained from the X-ray microcomputed tomography dataset, while the pore coordination number distribution obtained from the MRI data was slightly skewed to lower coordination numbers. This approach provides a method of producing a k-space undersampling pattern for MRI acquisition at a spatial resolution for which a fully sampled acquisition at that spatial resolution would be impractically long. The approach can be easily extended to other CS-MRI techniques, such as spatially resolved flow and relaxation time mapping. LAY DESCRIPTION: Magnetic resonance imaging (MRI) is widely used to study the microstructure of, and fluid transport phenomena in porous media relevant for engineering applications. A major application is the study of water and hydrocarbon transport in porous sedimentary rocks, which typically have pore sizes smaller than 100 µm. The spatial resolution of routine MRI acquisitions, however, is limited to several hundred µm due to the relatively low sensitivity of the magnetic resonance method. Therefore, there exists a strong motivation to increase the spatial resolution of MRI by one to two orders of magnitude to be able to study these rocks at a pore scale. This work reports the initial step towards achieving this. Three-dimensional images of rock pore structure are acquired at both 35 and 17.6 µm spatial resolution. In ongoing work, these methods are now being incorporated into magnetic resonance velocity imaging methods, thereby enabling imaging of both pore structure and hydrodynamics at these much higher spatial resolutions than were hitherto possible. Although X-ray microcomputed tomography (µCT) produces high spatial resolution images, it is far more limited in being able to spatially map transport processes (i.e. flow) in porous media. This work reports a strategy for accelerating the image acquisition time such that sufficient signal-to-noise ratio (SNR) is achieved to increase the spatial resolution, that is, the voxel size within which there is sufficient SNR within the resulting image. To achieve this, a technique known as compressed sensing is used which exploits undersampling of the acquired data relative to the standard fully sampled image. In MRI, data are acquired in so-called k-space and Fourier transformed to yield the real space image. The challenge, when undersampling, is to optimise the specific points in k-space that are acquired because these will influence the quality of the resulting image. This work reports a straightforward, robust strategy for identifying the optimal sets of k-space points to acquire. The method introduced uses simulated MRI images calculated from high-resolution µCT images of the rocks of interest, from which optimised MRI sampling patterns are obtained. The method does not require any optimisation of parameters for its implementation, which is a significant advantage compared to other strategies. Moreover, we show that the pore space characteristics of the acquired MRI images are in excellent agreement with the same characteristics obtained from a high-resolution µCT image.

Optimising sampling patterns for bi-exponentially decaying signals.

A recently reported method, based on the Cramér-Rao Lower Bound theory, for optimising sampling patterns for a wide range of nuclear magnetic resonance (NMR) experiments is applied to the problem of optimising sampling patterns for bi-exponentially decaying signals. Sampling patterns are optimised by minimizing the percentage error in estimating the most difficult to estimate parameter of the bi-exponential model, termed the objective function. The predictions of the method are demonstrated in application to pulsed field gradient NMR data recorded for the two-component diffusion of a binary mixture of methane/ethane in a zeolite. It is shown that the proposed method identifies an optimal sampling pattern with the predicted objective function being within 10% of that calculated from the experiment dataset. The method is used to advise on the number of sampled points and the noise level needed to resolve two-component systems characterised by a range of ratios of populations and diffusion coefficients. It is subsequently illustrated how the method can be used to reduce the experiment acquisition time while still being able to resolve a given two-component system.

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 ( S o ) and water ( S w ) , 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 S o and S w 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 1.27 × 10 - 6 m s - 1 ( 0.4 ft day - 1 ) . During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of 0.31 mm × 0.39 mm × 0.39 mm 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.

Do group 1 metal salts form deep eutectic solvents?

Mixtures of metal salts such as ZnCl2, AlCl3 and CrCl3·6H2O form eutectic mixtures with complexing agents, such as urea. The aim of this research was to see if alkali metal salts also formed eutectics in the same way. It is shown that only a limited number of sodium salts form homogeneous liquids at ambient temperatures and then only with glycerol. None of these mixtures showed eutectic behaviour but the liquids showed the physical properties similar to the group of mixtures classified as deep eutectic solvents. This study focussed on four sodium salts: NaBr, NaOAc, NaOAc·3H2O and Na2B4O7·10H2O. The ionic conductivity and viscosity of these salts with glycerol were studied, and it was found that unlike previous studies of quaternary ammonium salts with glycerol, where the salt decreased the viscosity, most of the sodium salts increased the viscosity. This suggests that sodium salts have a structure making effect on glycerol. This phenomenon is probably due to the high charge density of Na+, which coordinates to the glycerol. 1H and 23Na NMR diffusion and relaxation methods have been used to understand the molecular dynamics in the glycerol-salt mixtures, and probe the effect of water on some of these systems. The results reveal a complex dynamic behaviour of the different species within these liquids. Generally, the translational dynamics of the 1H species, probed by means of PFG NMR diffusion coefficients, is in line with the viscosity of these liquids. However, 1H and 23Na T1 relaxation measurements suggest that the Na-containing species also play a crucial role in the structure of the liquids.

Accelerating flow propagator measurements for the investigation of reactive transport in porous media.

NMR propagator measurements are widely used for identifying the distribution of molecular displacements over a given observation time, characterising a flowing system. However, where high q-space resolution is required, the experiments are time consuming and therefore unsuited to the study of dynamic systems. Here, it is shown that with an appropriately sampled subset of the q-space points in a high-resolution flow propagator measurement, one can quickly and robustly reconstruct the fully sampled propagator through interpolation of the acquired raw data. It was found that exponentially sampling ∼4% of the original data-points allowed a reconstruction with the deviation from the fully sampled propagator below the noise level, in this case reducing the required experimental time from ∼2.8h to <7min. As a demonstration, this approach is applied to observe the temporal evolution of the reactive flow of acid through an Estaillades rock core plug. It is shown that 'wormhole' formation in the rock core plug provides a channel for liquid flow such that the remaining pore space is by-passed, thereby causing the flow velocity of the liquid in the remaining part of the plug to become stagnant. The propagator measurements are supported by both 1D profiles and 2D imaging data. Such insights are of importance in understanding well acidisation and CO2 sequestration processes.

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.

Rapid sphere sizing using a Bayesian analysis of reciprocal space imaging data.

Dispersed systems are important in many applications in a wide range of industries such as the petroleum, pharmaceutical and food industries. Therefore the ability to control and non-invasively measure the physical properties of these systems, such as the dispersed phase size distribution, is of significant interest, in particular for concentrated systems, where microscopy or scattering techniques may not apply or with very limited output quality. In this paper we show how reciprocal space data acquired using both 1D magnetic resonance imaging (MRI) and 2D X-ray micro-tomographic (X-ray µCT) data can be analysed, using a Bayesian statistical model, to extract the sphere size distribution (SSD) from model sphere systems and dispersed food foam samples. Glass spheres-in-xanthan gels were used as model samples with sphere diameters (D) in the range of 45µm⩽D⩽850µm. The results show that the SSD was successfully estimated from both the NMR and X-ray µCT with a good degree of accuracy for the entire range of glass spheres in times as short as two seconds. After validating the technique using model samples, the Bayesian sphere sizing method was successfully applied to air/water foam samples generated using a microfluidics apparatus with 160µm⩽D⩽400µm. The effect of different experimental parameters such as the standard deviation of the bubble size distribution and the volume fraction of the dispersed phase is discussed.

Nuclear magnetic resonance measurements of velocity distributions in an ultrasonically vibrated granular bed.

We report the results of nuclear magnetic resonance imaging experiments on granular beds of mustard grains fluidized by vertical vibration at ultrasonic frequencies. The variation of both granular temperature and packing fraction with height was measured within the three-dimensional cell for a range of vibration frequencies, amplitudes and numbers of grains. Small increases in vibration frequency were found--contrary to the predictions of classical 'hard-sphere' expressions for the energy flux through a vibrating boundary--to result in dramatic reductions in granular temperature. Numerical simulations of the grain-wall interactions, using experimentally determined Hertzian contact stiffness coefficients, showed that energy flux drops significantly as the vibration period approaches the grain-wall contact time. The experiments thus demonstrate the need for new models for 'soft-sphere' boundary conditions at ultrasonic frequencies.

Monitoring bacterially induced calcite precipitation in porous media using magnetic resonance imaging and flow measurements.

A range of nuclear magnetic resonance (NMR) techniques are employed to provide novel, non-invasive measurements of both the structure and transport properties of porous media following a biologically mediated calcite precipitation reaction. Both a model glass bead pack and a sandstone rock core were considered. Structure was probed using magnetic resonance imaging (MRI) via a combination of quantitative one-dimensional profiles and three-dimensional images, applied before and after the formation of calcite in order to characterise the spatial distribution of the precipitate. It was shown through modification and variations of the calcite precipitation treatment that differences in the calcite fill would occur but all methods were successful in partially blocking the different porous media. Precipitation was seen to occur predominantly at the inlet of the bead pack, whereas precipitation occurred almost uniformly along the sandstone core. Transport properties are quantified using pulse field gradient (PFG) NMR measurements which provide probability distributions of molecular displacement over a set observation time (propagators), supplementing conventional permeability measurements. Propagators quantify the local effect of calcite formation on system hydrodynamics and the extent of stagnant region formation. Collectively, the combination of NMR measurements utilised here provides a toolkit for determining the efficacy of a biological-precipitation reaction for partially blocking porous materials.

Quantitative magnetic resonance micro-imaging methods for pharmaceutical research.

The use of magnetic resonance imaging (MRI) as a tool in pharmaceutical research is now well established and the current literature covers a multitude of different pharmaceutically relevant research areas. This review focuses on the use of quantitative magnetic resonance micro-imaging techniques and how they have been exploited to extract information that is of direct relevance to the pharmaceutical industry. The article is divided into two main areas. The first half outlines the theoretical aspects of magnetic resonance and deals with basic magnetic resonance theory, the effects of nuclear spin-lattice (T(1)), spin-spin (T(2)) relaxation and molecular diffusion upon image quantitation, and discusses the applications of rapid magnetic resonance imaging techniques. In addition to the theory, the review aims to provide some practical guidelines for the pharmaceutical researcher with an interest in MRI as to which MRI pulse sequences/protocols should be used and when. The second half of the article reviews the recent advances and developments that have appeared in the literature concerning the use of quantitative micro-imaging methods to pharmaceutically relevant research.

Structure and dynamics of 1-ethyl-3-methylimidazolium acetate via molecular dynamics and neutron diffraction.

The liquid state structure of the ionic liquid, 1-ethyl-3-methylimidazolium acetate ([C(2)mim][OAc]), an excellent nonderivitizing solvent for cellulosic biomass, has been investigated at 323 K by molecular dynamics (MD) simulation and by neutron diffraction using the SANDALS diffractometer at ISIS to provide experimental differential neutron scattering cross sections from H/D isotopically substituted materials. Ion-ion radial distribution functions both calculated from MD and derived from the empirical potential structure refinement (EPSR) model to the experimental data show the alternating shell structure of anions around the cation, as anticipated. Spatial probability distributions reveal the main anion-to-cation features as in-plane interactions of anions with the three imidazolium ring hydrogens and cation-cation planar stacking above/below the imidazolium rings. Interestingly, the presence of the polarized hydrogen-bond acceptor (HBA) anion (acetate) leads to an increase in anion-anion tail-tail structuring within each anion shell, an indicator of the onset of hydrophobic regions within the anion regions of the liquid. MD simulations show the importance of scaling of the effective ionic charges in the basic simulation approach to accurately reproduce both the observed experimental neutron scattering cross sections and ion self-diffusion coefficients.

Quantitative ultra-fast MRI of HPMC swelling and dissolution.

For the first time quantitative Rapid Acquisition with Relaxation Enhancement (RARE) based ultra-fast two-dimensional magnetic resonance imaging has been used to follow the dissolution of hydroxypropylmethyl cellulose (HPMC) in water. Quantitative maps of absolute water concentration, spin-spin relaxation times and water self-diffusion coefficient are obtained at a spatial resolution of 469 microm in less than 3 min each. These maps allow the dynamic development of the medium release rate HPMC/water system to be followed. It is demonstrated that the evolution of the gel layer and, in particular, the gradient in water concentration across it, is significantly different when comparing the quantitative RARE sequence with a standard (nonquantitative) implementation of RARE. The total gel thickness in the axial direction grows faster than that in the radial direction and that the dry core initially expands anisotropically. Additionally, while HPMC absorbs a large amount of water during the dissolution process, the concentration gradient of water within the gel layer is relatively small. For the first time MRI evidence is presented for a transition swollen glassy layer which resides between the outer edge of the dry tablet core and the inner edge of the gel layer.

Magnetic resonance imaging and X-ray microtomography studies of a gel-forming tablet formulation.

The capabilities of two methods for investigating tablet swelling are investigated, based on a study of a model gel-forming system. Results from magnetic resonance imaging (MRI) were compared with results from a novel application of X-ray microtomography (XmicroT) to track the movements of embedded glass microsphere tracers as the model tablets swelled. MRI provided information concerning the movement of hydration fronts into the tablets and the composition of the swollen gel layer, which formed at the tablet surface and progressively thickened with time. Conversely, XmicroT revealed significant axial expansion within the tablet core, at short times and ahead of the hydration fronts, where there was insufficient water to be observed by MRI (estimated to be around 15% by weight for the system used here). Thus, MRI and XmicroT may be regarded as complementary methods for studying the hydration and swelling behaviour of tablets.

Time-of-flight variant to image mixing of granular media in a 3D fluidized bed.

This paper describes a variant of time-of-flight magnetic resonance (MR) imaging that provides a method of measuring the inherent mixing in a fluidized bed without the introduction of tracer particles. The modifications to conventional time-of-flight imaging enable the measurement of the axial mixing of a precisely controlled initial particle distribution, thereby providing measurements suitable for a direct comparison with models of solids mixing in granular systems. The imaging sequence is applied to characterize mixing, over time scales of 25-1000 ms, in a gas-fluidized bed of Myosotis seed particles; mixing over short timescales, inaccessible using conventional tracer techniques, is studied using this technique. The mixing pattern determined by this pulse sequence is used in conjunction with MR velocity images of the motion of the particles to provide new insight into the mechanism of solids mixing in granular systems.

Rapid two-dimensional imaging of bubbles and slugs in a three-dimensional, gas-solid, two-phase flow system using ultrafast magnetic resonance.

Ultrafast magnetic resonance has been applied to measure the geometry of bubbles and slugs in a three-dimensional gas-solid two-phase flow. A bed of particles of diameter 0.5 mm were fluidized with gas velocities in the range of 0.08-0.26 m/s. Bubbles were imaged in transverse as well as vertical planes with an acquisition time of down to 25 ms and a spatial resolution down to 1.7 mm. Owing to the ultrafast character of these measurements, it is not only possible to evaluate correlations, e.g., for the bubble diameter, but also evaluate models of complex hydrodynamic phenomena, such as the splitting and coalescence of bubbles.

Real-time measurement of bubbling phenomena in a three-dimensional gas-fluidized bed using ultrafast magnetic resonance imaging.

Ultrafast magnetic resonance imaging has been applied for the first time to measure simultaneously both the rise velocities and coalescence of bubbles, and the dynamics of the solid phase in a gas-solid two-phase flow. Here, we consider the hydrodynamics within a gas-fluidized bed of particles of diameter 0.5 mm contained within a column of internal diameter 50 mm; gas velocities in the range of 0.18-0.54 m/s were studied. The data are of sufficient temporal and spatial resolution that bubble size and the evolution of bubble size and velocity following coalescence events are determined.

Quantitative magnetic resonance imaging of urea and lysozyme in protein chromatography.

Magnetic resonance imaging (MRI) techniques have been implemented to enable quantitative imaging of protein and urea within a 5 ml HiTrap size-exclusion chromatography desalting column, without introduction of contrast agents. One-, two- and three-dimensional images of urea injected at concentrations of 2, 4, 6 and 8 M were acquired. One-dimensional profiles of lysozyme at concentrations between 5 and 25 mg ml(-1) were also obtained. All data were accurate to within +/- 15% when compared to the known amount injected. Quantitative MRI elution profiles of both urea and lysozyme were then obtained in real-time during a desalting separation.

In situ magnetic resonance measurement of conversion, hydrodynamics and mass transfer during single- and two-phase flow in fixed-bed reactors.

In recent years there has been increasing interest in applying magnetic resonance (MR) techniques in areas of engineering and chemical technology. The science that underpins many of these applications is the physics and chemistry of transport and reaction processes in porous materials. Key to the exploitation of MR methods will be our ability to demonstrate that MR yields information that cannot be obtained using conventional measurement techniques in engineering research. This article describes two case studies that highlight the power of MR to give new insights to chemical engineers. First, we demonstrate the application of MR techniques to explore both mass transfer and chemical conversion in situ within a fixed bed of catalyst, and we then use these data to identify the rate-controlling step of the chemical conversion. Second, we implement a rapid imaging technique to study the stability of the gas-liquid distribution in the low- and high-interaction two-phase flow regimes in a trickle-bed reactor.