Packed Glass Beads Research Articles

MAG-PGSTE: A new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin–echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212–300 and <106 μm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168–173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324–329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177–183; P. Galvosas, F. Stallmach, J. Kärger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164–173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikroporösen Materialien, Ph.D. Thesis, Universität Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003) sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252–266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 μm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.

Complex conductivity of water-saturated packs of glass beads

The low-frequency conductivity response of water-saturated packs of glass beads reflects a combination of two processes. One process corresponds to the polarization of the mineral/water interface coating the surface of the grains. The other process corresponds to the Maxwell–Wagner polarization associated with accumulation of the electrical charges in the pore space of the composite medium. A model of low-frequency conductivity dispersion is proposed. This model is connected to a triple-layer model of electrochemical processes occurring at the surface of silica. This model accounts for the partition of the counterions between the Stern and the diffuse layers. The polarization of the mineral/water interface is modeled by the electrochemical polarization model of Schurr for a spherical grain. We take into account also the DC surface conductivity contribution of protons of the sorbed water and the contribution of the diffuse layer. At the scale of a macroscopic representative elementary volume of the porous material, the electrochemical polarization of a single grain is convoluted with the grain size distribution of the porous material. Finally, the Maxwell–Wagner polarization is modeled using the complex conductivity of a granular porous medium obtained from the differential effective medium theory. The predictions of this model agree well with experimental data of spectral induced polarization. Two peaks are observed at low frequencies in the spectrum of the phase. The first peak corresponds to the distribution of the size of the beads and the second peak is due to the roughness of the grains.

Contaminant sequestration in karstic aquifers: Experiments and quantification

A karstic aquifer typically has significant secondary porosity consisting of an interconnected system of caves or conduits. Conduit‐borne contaminants can enter the contiguous limestone matrix, remain inside for a longer time than in the conduit, and subsequently be flushed out. This retention or sequestration can significantly influence the fate of contaminants within the aquifer and alter the shape of the breakthrough curve. The mechanisms involved in sequestration have been identified and quantified by analysis of the breakthrough curves generated by a set of laboratory experiments in which a conduit, porous limestone matrix, and conservative contaminant were simulated by a porous‐walled pipe, chamber of closely packed glass beads, and salt, respectively. Experiments were conducted with both active and passive transfer of water between conduit and matrix, simulating differing hydrogeologic regimes. In active transfer the primary control parameter is the volume of water transferred; sequestration is primarily due to advection with the effects of diffusion and dispersion being minimal. In passive transfer the control parameters are the conduit Reynolds number and the duration that contaminant resides in the conduit; sequestration is caused by the combined effects of the conduit pressure drop, pressure variation due to bedform, and diffusion. Active and passive transfer can be unified by analyzing the ratio of the scale of pressure variation to the conduit length. In accordance with the resolved mechanisms a variety of models have been constructed to recover solute distributions in the matrix and to regenerate breakthrough curves. These analyses and models provide a potential approach to investigate contaminant migration in karstic aquifers.

Multi-scale Optical Analyses of Dynamic Gas Saturation During Air Sparging into Glass Beads

A multi-scale optical imaging technique was developed allowing for the 2D observation of two phase flow in porous media at two different scales simultaneously: Using two coupled cameras, a 2D flow cell (0.5 × 0.5m2) is recorded entirely at the bench scale and at the pore scale with a spatial resolution of 0.5 and 0.01 mm, respectively. The technique is applied to study channelized gas flow in saturated glass beads. We analyze the phase distribution at the pore scale and derive a pixel-based method for the measurement of saturation at the larger scale. This method assumes linearity between the mean reflected light intensity and the local gas saturation if averaging is performed over representative areas (REV). The REV depends on the irregularity of the local pore structure and has a lower limit at the correlation length of the porous medium (somewhat above the size of the glass beads) and an upper limit which correlates with the width of gas channels. These limits could be quantified through optical analysis. The optical approach to estimate phase saturations was validated by gravimetric analysis where a characteristic ratio between the optically observed flow cell wall and the saturation within the bulk material was identified, which corresponds to the expectation based on geometrical considerations of the glass bead packing. Considering a transient flow experiment the optical method is demonstrated to be able to quantify the temporal evolution of the residual and the convective gas phase. We conclude that the new technique provides a valuable tool to improve our quantitative understanding of multiphase phenomena across different scales.

Permeability analysis in bisized porous media: Wall effect between particles of different size

Summary The permeability of binary packings of glass beads with different size ratio – 13.3, 20, and 26.7, was investigated. In the Kozeny–Carman equation, the dependence of the tortuosity τ on the mixture porosity e ( x D ) was described according to τ = 1/ e n for different volume fraction of large particles in the mixture, x D . Obtained data on packing permeability shows that the parameter n is a function of the volume fraction and particle size ratio, with values between 0.5 and 0.4. This can be explained by the wall effect resulting from the arrangement of the small particles occurring near the large particle surface. A model taking in account this effect was suggested that can be useful in the characterization of transport phenomena in granular beds as well as in engineering applications.

Liquid flow texture analysis in trickle bed reactors using high-resolution gamma ray tomography

Abstract Trickle bed reactor performance and safety may suffer from radial and axial liquid maldistribution and thus from non-uniform utilization of the catalyst packing. Therefore, experimental analysis and fluid dynamic simulation of liquid–gas flow in trickle bed reactors is an important topic in chemical engineering. In the present study for the first time a truly high-resolution gamma ray tomography technique was applied to the quantitative analysis of the liquid flow texture in a laboratory cold flow trickle bed reactor of 90 mm diameter. The objective of this study was to present the comparative analysis of the liquid flow dynamics for two different initial liquid distributions and two different types of reactor configurations. Thus, the hydrodynamic behavior of a glass bead packing was compared to a porous Al2O3 catalyst particle packing using inlet flow from a commercial spray nozzle (uniform initial liquid distribution) and inlet flow from a central point source (strongly non-uniform initial liquid distribution), respectively. The column was operated in downflow mode at a gas flow rate of 180 L h−1 and at liquid flow rates of 15 and 25 L h−1.

Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers

Laboratory experiments are performed to understand the controlling parameters of the electrical field associated with the seepage of water through a porous material. We use seven glass bead packs with varying mean grain size in an effort to obtain a standard material for the investigation of these electrical potentials. The mean grain size of these samples is in the range 56–3000 μm. We use pure NaCl electrolytes with conductivity in the range 10−4 to 10−1 S m−1 at 25°C. The flow conditions cover viscous and inertial laminar flow conditions but not turbulent flow. In the relationship between the streaming potential coupling coefficient and the grain size, three distinct domains are defined by the values of two dimensionless numbers, the Dukhin and the Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity of the grains (due to conduction in the electrical double layer coating the surface of the grains) and the pore water electrical conductivity. At high Dukhin numbers (≫1) and low Reynolds numbers (≪1), the magnitude of the streaming potential coupling coefficient decreases with the increase of the Dukhin number and depends on the mean grain diameter (and therefore permeability) of the medium. At low Dukhin and Reynolds numbers (≪1), the streaming potential coupling coefficient becomes independent of the microstructure and is given by the well‐known Helmholtz‐Smoluchowski equation widely used in the literature. At high Reynolds numbers, the magnitude of the streaming potential coupling coefficient decreases with the increase of the Reynolds number in agreement with a new model developed in this paper. A numerical application is made illustrating the relation between the self‐potential signal and the intensity of seepage through a leakage in an embankment.

Comment on “Permeability prediction from MICP and NMR data using an electrokinetic approach” (

Glover et al. (2006) present a supposedly new permeability model that they call the RGPZ model. This model relates permeability to the mean grain size of a porous medium and the electric formation factor. They compare the prediction of this model with the predictions made with four other models—the Kozeny-Carman, Berg, Swanson, and van Baaren models (see Kozeny, 1927; Berg, 1970; Swanson, 1981; and van Baaren, 1979)—on different sets of permeability data covering glass bead packs and samples with various lithologies. This comparison reveals the improved accuracy of the RGPZ model compared with the four other models. The RGPZ model furthermore is used to interpret downhole measurements using the T 2 spectrum resulting from nuclear magnetic resonance (NMR) measurements.

Representative Elementary Volume Analysis of Sands Using X-Ray Computed Tomography

Abstract The concept of a representative elementary volume (REV) provides an effective means of developing macroscopic measures in the description of granular materials. However, due to the difficulties associated with the measurement and characterization of granular microstructure the existence and size of an REV has remained largely conjectural. This study presents a systematic method to examine the characteristics of the REV using X-ray computed tomography images. The 3-D images of spherical glass beads, Silica sand, and Ottawa sand have been characterized using advanced image processing techniques. An interactive computer program is developed to study porosity variation within a sphere with increasing radius from the images of these materials. The porosity variation of Silica sand and Ottawa sand showed three characteristic regions: an initial fluctuation region due to microscopic variations, a constant plateau region, and a region with a monotonic increase/decrease due to heterogeneity. The homogenous medium of glass beads did not show the last region. The results show that for a random packing of spherical glass beads the REV is about two to three times of the identical average diameter. The radius for Silica sand composed mainly of elongated particles is between 5 to 11 times of d50 and for Ottawa sand composed mainly of subrounded particles is between 9 to 16 times of d50.

Rapid surface-to-volume ratio and tortuosity measurement using Difftrain

Analysis of diffusion measurements as a function of observation time ( Δ), to calculate surface-to-volume ratios ( S/ V) and tortuosities ( κ), is a useful tool in the characterisation of porous media using NMR. However, using conventional pulsed field gradient (PFG) measurements, this requires long total experiment times (typically hours). Here, we show how the rapid diffusion measurement pulse sequence, Difftrain, can be used to provide the required experimental data much more rapidly (typically within minutes) with a consequential reduction in total experiment time of typically over an order of magnitude. Several novel modifications to the Difftrain pulse sequence are also presented to tailor it to this particular application; these include a variable delay between echoes (to ensure optimal echo position with respect to Δ) and a variable tip angle for the refocusing pulse (to ensure optimal use of available signal). Difftrain is applied to measure both S/ V and κ for a model glass bead pack; excellent agreement is found with both a conventional PFG measurement and with a bulk gravimetric measurement of S/ V.

Effects of shear fracture on in-depth profile modification of weak gels

Two sand packs were filled with fine glass beads and quartz sand respectively. The characteristics of crosslinked polymer flowing through the sand packs as well as the influence of shear fracture of porous media on the indepth profile modification of the weak gel generated from the crosslinked polymer were investigated. The results indicated that under the dynamic condition crosslinking reaction happened in both sand packs, and the weak gels in these two cases became small gel particles after water flooding. The differences were: the dynamic gelation time in the quartz sand pack was longer than that in the glass bead pack. Residual resistance factor (FRR) caused by the weak gel in the quartz sand pack was smaller that that in the glass bead pack. The weak gel became gel particles after being scoured by subsequent flood water. A weak gel with uniform apparent viscosity and sealing characteristics was generated in every part of the glass bead pack, which could not only move deeply into the sand pack but also seal the high capacity channels again when it reached the deep part. The weak gel performed in-depth profile modification in the glass bead pack, while in the quartz sand pack, the weak gel was concentrated with 100cm from the entrance of the sand pack. When propelled by the subsequent flood water, the weak gel could move towards the deep part of the sand pack but then became tiny gel particles and could not effectively seal the high capacity channels there. The in-depth profile modification of the weak gel was very weak in the quartz sand pack. It was the shear fracture of porous media that mainly affected the properties and weakened the in-depth profile modification of the weak gel.

Simulation of random packing of polydisperse particles

An optimization based model is develop to simulate random packings of polydisperse particles to mimic porous media systems. The model simulates systems with properties that map back to physically measured quantities. Input parameter include density functions of radius and coordination number. The simulated packings by incorporating physically based properties of glass bead packings obtained from 3D computed tomography images. [Display omitted]

Direct microscopic observation of particle deposition in porous media: Role of the secondary energy minimum

A flow-cell has been constructed where micrometer-sized particles flow horizontally through a single layer of packed glass beads. Deposition is viewed through a fluorescent microscope with phase contrast capabilities. This allows the visualization of particle deposition in porous media in real time and provides insight into phenomena such as secondary minimum deposition of particles and microbial pathogens during physicochemical filtration. At low ionic strengths (1–3 mM), no deposition was observed on the collector beads. As the monovalent salt concentration was raised to moderate ionic strengths (10–30 mM), the particles became trapped in the secondary minimum and translated along the glass bead surface, accumulating near the rear of the spherical collectors. At high ionic strength (100 mM), no calculated electrostatic energy barrier to deposition exists and particles deposited over the entire surface of the spherical collector. It is concluded that deposition in the secondary energy minimum is an important removal mechanism for micrometer-sized particles in flow through granular porous media.

Deviation of linear relation between streaming potential and pore fluid pressure difference in granular material at relatively high Reynolds numbers

Abstract We conducted streaming potential measurements on the packing of glass beads, and investigated the deviation of streaming potential from the Helmholtz-Smoluchowski (H-S) equation. The H-S equation was originally derived on the assumption of laminar flows. Studies using a capillary have shown that the H-S equation is valid for turbulent flows in so far as the viscous sublayer is thicker than the electrical double layer and the entrance effect is negligible. Although the streaming potential in porous media has been reported to deviate from the H-S equation for turbulent flows, its mechanism is still poorly understood. We measured the fluid flux and the streaming potential as a function of the pore fluid pressure difference. The fluid flux begins to deviate from Darcy’s law at Reynolds number &gt;3, and the streaming potential begins to deviate from the linear relation at larger Reynolds numbers. When the flow is fast, the fluid inertia separates the boundary layer from the solid surface and induces the counter flows. The fluid in the counter-flow region is separated from the circulating fluid, and ions there cannot contribute to the convection current. We think that this results in a lower streaming potential than expected from the H-S equation.

Visualization of particle behavior within a porous medium: Mechanisms for particle filtration and retardation during downward transport

A technique for visualizing particle transport in the interior of a porous medium is presented. The technique, which includes the construction of a translucent medium and the use of laser‐induced fluorescence for particle tracking, was used to examine the behavior of a dilute suspension of negatively charged, micron‐sized particles in the interior of uniform glass bead packs during one‐dimensional, downward flow. Particle behavior as a function of pore fluid velocity and bead surface roughness was observed at both the macroscopic and microscopic levels. Experimental results show that particle filtration occurred only at solid‐solid contact points (contact filtration) in smooth bead packs, while particle filtration occurred at the top of bead surfaces (surface filtration) as well as at solid‐solid contact points in rough bead packs. Particle contact filtration was the result of physical straining at solid‐solid contact points, while surface filtration was the result of particles interlocking on surface asperities. In both smooth and rough bead packs the filtration capacity of the medium decreased with the pore fluid velocity. In smooth bead packs the filtration capacity was approximately invariant with transport distance, while in the rough bead packs the filtration capacity showed a decrease with transport distance. This decrease was attributed to the early surface filtration of larger particles as a result of gravitational sedimentation. The accumulation of reversibly attached particles was observed even when particle pore fluid concentrations were stable.

Predicting macroscopic transport properties using microscopic image data

We consider eight data sets obtained from synchrotron computed microtomographic experiments performed on natural and synthetic sandstones at the GSECARS 13‐BM beam line at the Advanced Photon Source. Four data sets were collected on glass bead packs sintered to differing bulk densities; each of these data sets contains just over 225 million voxels (661 × 661 × 517), with voxel resolution of 3.34 μm. The other four data sets were collected from a single sample of natural sandstone. For the natural sandstone, three data sets were collected from different subvolumes within the sample, with these three data sets identical in size and resolution to those acquired for the sintered glass bead packs. A fourth data set was collected for one of the same subvolumes but at twice the resolution; this data set contains just over 1.6 billion voxels (1327 × 1327 × 920), with voxel resolution of 1.67 μm. Following processing to extract binary descriptions of the two‐phase (solid and pore) structure, the image data are analyzed to calculate porosity and specific surface area. The binarized image data are applied directly in massively parallel numerical simulations of single‐phase fluid flow performed using the lattice Boltzmann method; development of novel boundary conditions to facilitate efficient handling of these very large data sets is also described. The permeabilities predicted from 1 to 3 mm3 image volumes characterized at a length scale of ∼1.7–3.4 μm are compared to experimental measurements of intrinsic permeability performed at bench conditions on standard core‐sized samples (25.4 mm in diameter × 50.8 mm in length, or ∼26 cm3). The macroscopic permeability computed from the image data agree remarkably well with the experimentally measured bulk permeability over several orders of magnitude range in permeability and equate to over 4 orders of magnitude scale‐up. The results provide insight on the representative volume and length scales necessary to characterize geometrically complex porous media and predict fluid transport properties at the macroscale.

Effect of glass bead packing on the fibrillation of liquid‐crystalline polymer in polycarbonate

AbstractPolycarbonate (PC) was melt blended with small amount of liquid‐crystalline polymer (LCP) and various contents of glass beads (GB) having different diameters. The rheological measurements indicated that the GB addition increased the viscosity ratio and seemed unfavorable to the LCP fibrillation. However, the morphological observation showed that the LCP fibrillation was promoted by the GB addition and varied with the GB packing. With the increased GB packing by increasing the GB content and/or decreasing the GB diameter, LCP deformed from spheres and ellipsoids into stretched ellipsoids at lower shear rates and into long fibrils at higher shear rates. Although higher content of smaller GB jammed into the larger LCP droplets and inhibited the LCP fibrillation, very long LCP fibrils formed at higher shear rates at a high enough packing of GB. The relationship between GB packing and LCP fibrillation revealed two kinds of hydrodynamic effects of GB promoting the LCP fibrillation: at lower GB packing, the shear flow was enhanced by the high local shear between GB, in quantity; and for a high enough GB packing, the shear flow was changed, in quality, into elongational flow, which was more effective for the LCP fibrillation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1020–1030, 2006

Experimental Conditions Favoring the Formation of Fluid Banks during Counter-Current Flow in Porous Media

The purpose of this study is to investigate factors that affect the formation of fluid banks during gravity-driven counter-current flow in porous media. To our knowledge, development of a fluid bank has been observed in only one previous counter-current flow experiment, although there are some hints of fluid banks in other experiments. We have undertaken experimental and simulation studies to confirm the presence of such banks and to delineate factors which enhance or inhibit their formation. Experiments were performed using glass bead packs and X-ray Computed Tomography to monitor saturation distribution as a function of time. The simulation approach considers saturation history at every point in the sample, defining conditions at each time point from hysteresis in capillary pressure and relative permeability. The model proved to reproduce experimental observations accurately. The experiments and associated model show that a minimal vertical sample height is needed for the development of a fluid bank. In addition, round sample boundaries and higher average nonwetting phase saturation tend to prevent the formation of a bank. The validated model can improve our ability to predict and optimize counter-current flow processes, both in the laboratory and in the field (e.g. exploration and hydrocarbon extraction).

Dynamics of shallow impact cratering

We present data for the time dependence of wooden spheres penetrating into a loose noncohesive packing of glass beads. The stopping time is a factor of 3 longer than the time d/v0 needed to travel the total penetration distance d at the impact speed v0. The acceleration decreases monotonically throughout the impact. These kinematics are modeled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.

Quadrupolar relaxation of hyperpolarized krypton-83 as a probe for surfaces

This work reports the first systematic study of relaxation experienced by the hyperpolarized (hp) noble gas isotope 83Kr ( I = 9 / 2 ) in contact with surfaces. The spin-lattice relaxation of 83Kr is found to depend strongly on the chemical composition of the surfaces in the vicinity of the gas. This effect is caused by quadrupolar interactions during brief periods of surface adsorption that are the dominating source of longitudinal spin relaxation in the 83Kr atoms. Simple model systems of closest packed glass beads with uniform but variable bead sizes are used for the relaxation measurements. The observed relaxation rates depend strongly on the chemical treatment of the glass surfaces and on the surface to volume ratio. Hp 83Kr NMR relaxation measurements of porous polymers with pore sizes of 70–250 μm demonstrate the potential use of this new technique for material sciences applications.