Magnetic resonance imaging of chemical waves in porous media

Magnetic resonance imaging (MRI) provides a powerful tool for the investigation of chemical structures in optically opaque porous media, in which chemical concentration gradients can be visualized, and diffusion and flow properties are simultaneously determined. In this paper we give an overview of the MRI technique and review theory and experiments on the formation of chemical waves in a tubular packed bed reactor upon the addition of a nonlinear chemical reaction. MR images are presented of reaction-diffusion waves propagating in the three-dimensional (3D) network of channels in the reactor, and the 3D structure of stationary concentration patterns formed via the flow-distributed oscillation mechanism is demonstrated to reflect the local hydrodynamics in the packed bed. Possible future directions regarding the influence of heterogeneities on transport and reaction are discussed.     

Fractal patterns of fluid domains for displacement processes in porous media

Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.     

Magnetic resonance visualisation of single- and two-phase flow in porous media.

Three-dimensional MRI and flow visualisation data are presented for single and two-phase flow occurring within packed beds of glass spheres. The initial motivation for this work has been to understand the operation of fixed-bed reactors used in many chemical processing operations; these systems also serve as model porous media in which to investigate the effect of the structure of a pore space on the flow phenomena occurring within it. For the case of single-phase flow, maps of the liquid shear rate components are calculated from which forces on individual spheres within the bed are obtained. The velocity histogram for flow transverse to the direction of superficial flow is exponential in both negative and positive directions. This form of the velocity histogram implies an exponential form for the displacement propagator, in contrast to the Gaussian distribution obtained by pulsed gradient spin echo measurements. This difference arises because the spatially resolved velocity imaging sequence measures only the average velocity within each voxel and is insensitive to the effects of incoherent (diffusive) motion. Visualisations of air-water flow through a sphere pack are also reported and the capability of MRI to yield information on rivulet formation and surface wetting characteristics is illustrated.     

Using NMR displacement imaging to characterize electroosmotic flow in porous media.

Pulsed field gradient nuclear magnetic resonance (PFG-NMR) and NMR imaging were used to study temporal and spatial domains of an electrokinetically-driven mobile phase through open and packed segments of capillaries. Characteristics like velocity distribution and an asymptotic dispersion are contrasted to viscous flow behavior. We show that electroosmotic flow in microchannel geometries can offer a significant performance advantage over the pressure-driven flows at comparable Peclét numbers, indicating that velocity extremes in the pore space of open tubes and packed beds are drastically reduced. An inherent problem of capillary electrochromatography that we finally address is the existence of wall effects when in the general case the surface zeta-potentials of the capillary inner wall and the adsorbent particles are different. Using dynamic NMR microscopy we were able resolve this systematic velocity inequality of the flow pattern which strongly influences axial dispersion and may be responsible for long time-tails of velocity distribution in the mobile phase.     

Magnetic resonance imaging: applications of novel methods in studies of porous media.

NMR imaging is finding broad applications in nonbiological areas including the study of fluid flow and fluid ingress in porous media. The porous media include at the one end mineral rocks and various building materials through various solid plastic materials to foodstuffs at the other end of the spectrum. The fluids within these various media range from crude oil and water mixtures, and water itself, to a range of organic solvents in plastic materials. This paper is concerned with the flow and ingress of water through Bentheimer sandstone and Ninian reservoir specimens, and also in solid nylon blocks.     

Magnetic resonance in porous media: forty years on

A personal view of the field of magnetic resonance in porous media is presented in which an attempt is made to survey the current status and achievements, to highlight some of the contributions made by my group over the years and, at the end, to try and identify where further effort and growth points may be perceived. All this is done with the knowledge that the first and last sections are certain to be partial, incomplete and wrong, at least in part, and that the middle section describes work carried out by some of the many excellent students, post-doctoral researchers and other colleagues with whom it has been a pleasure to collaborate over a forty year research career.     

Three-dimensional fluid pressure mapping in porous media using magnetic resonance imaging with gas-filled liposomes

This paper presents and demonstrates a method for using magnetic resonance imaging to measure local pressure of a fluid saturating a porous medium. The method is tested both in a static system of packed silica gel and in saturated sintered glass cylinders experiencing fluid flow. The fluid used contains 3% gas in the form of 3-mum average diameter gas filled 1,2-distearoyl-sn-glycero-3-phosphocholine (C18:0, MW: 790.16) liposomes suspended in 5% glycerol and 0.5% Methyl cellulose with water. Preliminary studies at 2.35 T demonstrate relative magnetic resonance signal changes of 20% per bar in bulk fluid for an echo time T(E)=40 ms, and 6-10% in consolidated porous media for T(E)=10 ms, over the range 0.8-1.8 bar for a spatial resolution of 0.1 mm(3) and a temporal resolution of 30 s. The stability of this solution with relation to applied pressure and methods for improving sensitivity are discussed.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Magnetic resonance imaging of single- and two-phase flow in fixed-bed reactors

Magnetic resonance imaging and flow visualization techniques are increasingly used to study transport processes in chemical and biochemical reactors. Three recent case studies from our own research program are reported, each illustrating quite different applications of magnetic resonance techniques in such applications. First, two-phase flow in a trickle-bed reactor is considered. Images of the steady-state gas-liquid distribution are obtained which yield quantitative measures of liquid holdup and wetting efficiency. Second, a radiofrequency pulse sequence based on that for rapid acquisition with relaxation enhancement is used to perform ultrafast visualization of gas-liquid flow in individual channels within a ceramic monolith. Finally,¹H volume-selective nuclear magnetic resonance spectroscopy is employed to perform an in situ spatially resolved study of the extent of conversion of the liquid-phase esterification reaction of methanol and acetic acid, catalyzed by an acid catalyst (Amberlyst 15 ion exchange resin) in a fixed-bed reactor. In particular, the effect of the superficial flow rate of the feed on conversion is investigated.     

Magnetic resonance diffusion-weighted imaging: quantitative evaluation of age-related changes in healthy liver parenchyma

The purpose of this study was to verify in healthy liver parenchyma the possible influence of age on DwI-related parameters: apparent diffusion coefficient (ADC), perfusion fraction (PF), diffusion and pseudodiffusion coefficient (D and D^?). Forty healthy adult volunteers (age range 26-86 years), divided into four age groups, were prospectively submitted to a breath-hold magnetic resonance diffusion imaging (MR-DwI) (two b values, 0-300 and 0-1000 s/mm²). A smaller cohort of 16 subjects underwent a free-breath multi-b acquisition (16 b values, 0-750 s/mm²). Quantitative analysis was performed by two observers with manually defined regions of interest, on the most homogeneous portion of the right liver lobe. Individual and group statistical analysis of data was performed: ANOVA to establish differences between groups and Pearson correlation coefficient to investigate the association between DwI parameters and age. The mean, S.D. and 95% limits of agreement of ADC values for each age-defined group are reported. ANOVA showed no significant differences between group means (P always >.05). No significant correlation between subjects' age and DwI parameters was established, both in breath-hold and free-breath acquisitions, on the whole range of adopted b values. Our study conducted on healthy liver parenchyma shows that there are no significant differences in ADC, PF, D and D^? of younger or older subjects.     

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.     

Two-dimensional propagators and spatio-temporal correlations for flow in porous media: A comparative study

The two-dimensional displacement joint probability densityPΔ(X,Z) and the two-time probability density W₂(Z₁,Δ₁;Z₂,A₂) for water flowing through several porous systems have been measured by means of pulsed field-gradient nuclear magnetic resonance (PFG-NMR). The simultaneous particle displacementsX and Z perpendicular and parallel to the pressure gradient, respectively, at a given encoding time Δ are obtained from an experiment employing orthogonal magnetic field gradients. Time-correlated propagators which relate the displacement spectra at two consecutive times Δ_l, and Δ₂ with each other were derived by applying rephasing gradients in two steps. Flow through a random packing of glass beads and through natural sandstone is compared to flow through arrays of either oriented or unoriented fibers with different solid volume fractions. The dependence of the dispersion tensor D^* as a function of time is discussed and related to a characteristic length ξ_tT transverse to the flow direction. Within a certain range of Z values, displacements inX and Z are related by a power law <X²(Z)> ∝Z _γ. The spreading exponent γ is found to increase with growing orientational order in the porous system and is largest for fiber bundles being twisted with respect to the mean pressure gradient axis. The evolution of the correlation coefficient px²,z with time gives a measure for the typical correlation length of the system parallel to the flow axis, ξ_‖. Analyzing the shape ofW ₂(Z₁,Δ₁Z₂,Δ₂) allows one to investigate the loss of coherence in flow by an alternative approach. The decay of the two-time correlation coefficient,pZ ₁,Z₂, is sensitive to the change of the z-component of the particle velocity and probes a different lengthscale thanpx ₂z^.     

Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media

An optical Doppler tomography (ODT) system that permits imaging of fluid flow velocity in highly scattering media is described. ODT combines Doppler velocimetry with the high spatial resolution of low-coherence optical interferometry to measure fluid flow velocity at discrete spatial locations. Tomographic imaging of particle flow velocity within a circular conduit submerged 1 mm below the surface in a highly scattering phantom of Intralipid is demonstrated.     

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.     

Dissimilar electro-osmotic flow and ionic current recirculation patterns in porous media detected by NMR mapping experiments

Random-site percolation clusters were milled into ceramic (polar) and polystyrene (nonpolar) plates as a paradigm for porous media or complex microsystem channel networks. The pore space was filled with electrolyte solutions. Using NMR microscopy techniques, maps of the following quantities were recorded: (i) flow velocity driven by external pressure gradient, (ii) electro-osmotic flow (EOF) velocity, (iii) ionic current density in the presence of EOF, (iv) ionic current density in the absence of EOF. As far as possible, the experiments were supplemented by computational fluid dynamics simulations. It is shown that electro-osmotic flow as well as the electric current density include vortices and recirculation patterns. Remarkably, all transport patterns turned out to be dissimilar, and the occurrence and positions of vortices do not coincide in the different maps.