Studies of porous media by thermally polarized gas NMR: current status

Three examples of thermally polarized gas NMR performed at New Mexico Resonance are presented to demonstrate its unique advantages in porous media studies. 1) In-vivo animal lung imaging by Kuethe et al., in which useful quality 3D images of rat lungs were obtained in 30 min. It is conjectured that comparable human lung images would take much less time to make, possibly by the ratio of body weights, a factor of several hundred. 2) The success of the lung imaging suggested other porous media as candidates for thermally polarized gas NMR. Caprihan and coworkers obtained excellent images from partially sintered ceramics and Vycor glass. Since then, Beyea has developed the technique of spatially resolved BET curves for ceramics and other nanoporous solids. In this way, surface area, pore size, and porosity, averaged over an image voxel, can be spatially resolved. This greatly aids in the characterization of such materials, especially with regards to spatial heterogeneities. 3) Finally, we describe Codd's propagator experiments on propane gas flowing through a packed bed of 300 microm beads. In order to increase signal-to-noise ratio, the flowing gas was pressurized to 170 kPa. Excellent quality propagators showing the discrete nature of the bead pack were obtained. This type of information is not available in comparable liquid studies because most spins will not diffuse far enough to sample the walls in the time available.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

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

Single-phase liquid flow in porous media such as bead packs and model fixed bed reactors has been well studied by MRI. To some extent this early work represents the necessary preliminary research to address the more challenging problem of two-phase flow of gas and liquid within these systems. In this paper, we present images of both the gas and liquid velocities during stable liquid–gas flow of water and SF₆ within a packing of 5 mm spheres contained within columns of diameter 40 and 27 mm; images being acquired using ¹H and ¹⁹F observation for the water and SF₆, respectively. Liquid and gas flow rates calculated from the velocity images are in agreement with macroscopic flow rate measurements to within 7% and 5%, respectively. In addition to the information obtained directly from these images, the ability to measure liquid and gas flow fields within the same sample environment will enable us to explore the validity of assumptions used in numerical modelling of two-phase flows.     

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter.     

NMR relaxation and pulsed field gradient study of alginate bead porous media

Experiments are presented, which correlate molecular displacement with the multi-exponential T2 relaxation times of water flowing and diffusing through an alginate bead pack. Three systems were studied comprising beads of 3, 1 or < mm in diameter. T2-resolved propagators were obtained through a combined pulsed gradient stimulated echo (PGSTE) and Carr-Purcell-Meiboom-Gill (CPMG) experiment. Fourier transformation with respect to q produces a propagator for each echo in the CPMG train. Inverse Laplace transformation of the CPMG decays for each point (Z) in the propagator produced a two-dimensional propagator. Analysis of these two-dimensional propagators provided insight into the transport and exchange behaviour of water flowing through this system. This experiment has been simulated in a model bead structure and the resulting T2 relaxation time behaviour and T2-resolved propagators were found to be in good agreement with the experimental data. We also present a theoretical analysis of the response to the combined PGSTE/CPMG sequence in the simple model case of Pouseille flow in a cylindrical capillary, where diffusion to a surface sink is assumed to be the dominant relaxation mechanism.     

Correlated displacement-T2 MRI by means of a Pulsed Field Gradient-Multi Spin Echo Method

A method for correlated displacement-T2 imaging is presented. A Pulsed Field Gradient-Multi Spin Echo (PFG-MSE) sequence is used to record T2 resolved propagators on a voxel-by-voxel basis, making it possible to perform single voxel correlated displacement-T2 analyses. In spatially heterogeneous media the method thus gives access to sub-voxel information about displacement and T2 relaxation. The sequence is demonstrated using a number of flow conducting model systems: a tube with flowing water of variable intrinsic T2's, mixing fluids of different T2's in an "X"-shaped connector, and an intact living plant. PFG-MSE can be applied to yield information about the relation between flow, pore size and exchange behavior, and can aid volume flow quantification by making it possible to correct for T2 relaxation during the displacement labeling period Delta in PFG displacement imaging methods. Correlated displacement-T2 imaging can be of special interest for a number of research subjects, such as the flow of liquids and mixtures of liquids or liquids and solids moving through microscopic conduits of different sizes (e.g., plants, porous media, bioreactors, biomats).     

Applications of controlled-flow laser-polarized xenon gas to porous and granular media study

We report initial NMR studies of continuous flow laser-polarized xenon gas, both in unrestricted tubing, and in a model porous media. The study uses Pulsed Gradient Spin Echo-based techniques in the gas-phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients. Pulsed Gradient Echo studies of continuous flow laser-polarized xenon gas in unrestricted tubing indicate clear diffraction minima resulting from a wide distribution of velocities in the flow field. The maximum velocity experienced in the flow can be calculated from this minimum, and is seen to agree with the information from the complete velocity spectrum, or motion propagator, as well as previously published images. The susceptibility of gas flows to parameters such as gas mixture content, and hence viscosity, are observed in experiments aimed at identifying clear structural features from echo attenuation plots of gas flow in porous media. Gas-phase NMR scattering, or position correlation flow-diffraction, previously clearly seen in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack is not so clear in experiments using a different gas mixture. A propagator analysis shows most gas in the sample remains close to static, while a small portion moves through a presumably near-unimpeded path at high velocities.     

Displacement propagators of brine flowing within different types of sedimentary rock

This paper explores the correlation between different microstructural characteristics of porous sedimentary rocks and the flow properties of a Newtonian infiltrating fluid. Preliminary results of displacement propagator measurements of brine solution flowing through two types of sedimentary rock cores are reported. The two types of rocks, Bentheimer and Portland, are characterized by different porosities, pore-size distributions and permeabilities. Propagators have been measured for brine flow rates of 1 and 5 ml/min. Significant differences are seen between the propagators recorded for the two rocks, and these are related to the spatial distribution of porosity within these porous media.     

Quantitative magnetic resonance flow and diffusion imaging in porous media

Quantitative flow and diffusion measurements have been made for water in model porous media, using magnetic resonance micro-imaging methods. The samples consisted of compacted glass beads of various sizes down to 1 mm diameter. Typical flow and diffusion images exhibited a spatial resolution of 117 μm × 117 μm and velocities in the range 1–2 mm/s. Comparison of volume flow rates calculated from the flow velocity maps with values measured directly yielded good agreement in all cases. There was also good agreement between the mean diffusion coefficient of water calculated from the diffusion maps and the bulk diffusion coefficient for pure water at the same temperature. In addition, the mean diffusion coefficient did not depend on the pore sizes in the bead diameter range of 1–3 mm. Our results also show that partial volume effects can be compensated by appropriate thresholding of the images prior to the final Fourier transformation in the flow-encoding dimension.     

Internal magnetic gradient fields in glass bead packs from numerical simulations and constant time diffusion spin echo measurements

Internal magnetic field gradients in water saturated glass bead packs were studied by numerical simulations and a constant time spin echo (CTSE) experiment. The CTSE is comprised of two spin echo refocusing periods where each of the two evolution periods, tau1 and tau2, is varied so that the total evolution, 2(tau1 + tau2), is held constant. The experiment is similar to that introduced by Norwood and Quilter and allows the effects of dephasing due to diffusion in a magnetic field gradient to be separated from other relaxation mechanisms. In our experiments, the magnetic susceptibility difference between the pore fluid and glass beads creates the internal field gradient. CTSE measurements were performed at 7 T (300 MHz 1H) for water saturated in 50 microm diameter glass bead pack. We find that the internal gradients in the center of the pore bodies, where free diffusion applies, is in the range of 10 to 100 G/cm. This fluid volume accounts for < or =10% of the total pore volume. From direct numerical simulations of the internal magnetic field based on a first principles calculation, we find that the major fraction, >90%, of the pore volume has internal gradients of order 500 to 5,000 G/cm. Signals from water in these large gradients is not observed in our CTSE measurements.     

Observation of molecular migration in porous media using 2D exchange spectroscopy in the inhomogeneous magnetic field

We present a new method for observing fluid diffusion in a porous medium. The method employs 2D exchange spectroscopy for molecules diffusing in the presence of local magnetic field inhomogeneities, in our case distilled water in various sized glass bead packs. Our experiment involves an acquisition and evolution time domain with the two Fourier domains corresponding to the spectral distribution of local fields. We show that exchange in the internal magnetic field can be seen in a 2D spectrum with a characteristic time on the order of that required to diffuse 0.15 sphere diameters with similar behavior found for computer simulations. The method is potentially useful for studying the internal migrations in more complicated systems such as sandstones or other porous media.     

Time-dependent velocities in porous media dispersive flow.

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

超声波对多孔介质中两相流动的影响

近年来，超声技术已被应用于采油工程中，在油井解堵，水井增注等方面发挥了重要的作用。     

Probing porous media with gas diffusion NMR.

We show that gas diffusion nuclear magnetic resonance (GD-NMR) provides a powerful technique for probing the structure of porous media. In random packs of glass beads, using both laser-polarized and thermally polarized xenon gas, we find that GD-NMR can accurately measure the pore space surface-area-to-volume ratio, S/V rho, and the tortuosity, alpha (the latter quantity being directly related to the system's transport properties). We also show that GD-NMR provides a good measure of the tortuosity of sandstone and complex carbonate rocks.     

Modelling of candle burning with a self-trimmed wick

As an example of a coupled gas-phase diffusion flame with porous media flow, a candle burning model with a porous wick is offered in this paper. The porous media analysis includes capillarity-induced liquid flow, liquid vaporisation, vapour motion and re-condensation and multi-phase heat transfer. Coupling with the gas phase flame is through the conservation of mass, momentum and energy at the wick surface. The steady state solutions obtained not only yield the flame structure but also the detailed flow pattern and saturation distributions inside the wick. One of the novel features of the present model is the capability to address the self-trimming phenomena of candle burning. The self-trimming wick length and the associated flame characteristics have been computed as a function of gravity level, wick permeability and wick diameter.     

MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow

Supercritical fluids (SCF) are useful solvents in green chemistry and oil recovery and are of great current interest in the context of carbon sequestration. Magnetic resonance techniques were applied to study near critical and supercritical dynamics for pump driven flow through a capillary and a packed bed porous media. Velocity maps and displacement propagators measure the dynamics of C(2)F(6) at pressures below, at, and above the critical pressure and at temperatures below and above the critical temperature. Displacement propagators were measured at various displacement observation times to quantify the time evolution of dynamics. In capillary flow, the critical phase transition fluid C(2)F(6) showed increased compressibility compared to the near critical gas and supercritical fluid. These flows exhibit large variations in buoyancy arising from large changes in density due to very small changes in temperature.     

多孔介质内受迫对流凝结时两相共存区的非达西模型

本文提出多孔介质内受迫对流凝结时两相共存区的二维非达西流模型。分析了蒸气在多孔介质内沿水平平板和填充国管内受迫对流凝结时两相共存区的厚度。假定局部平衡和暂先假设蒸气为理想气体，化简了能量方程。     

Optical manipulation of microspheres along a subwavelength optical wire

The propulsion of 3 microm polystyrene spheres along a subwavelength optical wire is demonstrated. Velocities in the range of 7-15 microm/s are observed. Simulations are carried out to evaluate the evanescent field at the waveguide-water suspension interface.     

Enhanced (13)C PFG NMR for the study of hydrodynamic dispersion in porous media

PFG NMR methods are frequently used as a means of probing both coherent and incoherent molecular motions of fluids contained within heterogeneous porous media. The time scale over which molecular displacements can be probed in a conventional PFG NMR experiment is limited by the relaxation characteristics of (1)H - the nucleus that is typically observed. In multiphase systems, due to its sensitivity to susceptibility gradients and interactions with surfaces,(1)H signal is frequently characterized by rapid T(1) and T(2) relaxation. In this work, a heteronuclear approach to PFG NMR is demonstrated which allows the study of molecular displacement over extended time scales (and, consequently, length scales) by exploiting the longer relaxation time of (13)C. The method presented employs the DEPT technique of polarization transfer in order to enhance both the sensitivity and efficiency of (13)C detection. This hybrid coherence transfer PFG technique has been used to acquire displacement propagators for flow through a bead pack with an observation time of up to 35 s.