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.     

Hydrodynamics in two-phase flow within porous media

Ultra-fast magnetic resonance imaging techniques are used to image liquid distribution in two and three dimensions during air-water co-current down flow through a fixed bed of cylindrical porous pellets of length and diameter 3 mm, packed within a 43 mm internal diameter column in both the trickle- and pulsing-flow regimes. The data acquisition times used were 20 and 280 ms, giving 2-D and 3-D spatial resolutions of 1.4 mm x 2.8 mm and 3.75 mm x 3.75 mm x 1.87 mm, respectively. This work reports images of local pulsing events within the bed occurring during the trickle-to-pulse flow transition. The evolution of the local instabilities is studied as a function of increasing liquid velocity at constant gas velocity.     

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。     

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.     

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.     

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.     

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 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.     

Magnetic resonance for fluids in porous media at the University of Bologna

The magnetic resonance in porous media (MRPM) community is now a vast community of scientists from all over the world who recognize magnetic resonance as an instrument of choice for the characterization of pore space and of the distribution, diffusion and flow of fluids inside a vast range of different materials. The MRPM conferences are the occasions in which this community gets together, compares notes and grows. The scene was different in 1990, when this series of conferences was promoted at Bologna. I will go briefly over the history of these events, showing the role played by the University of Bologna and in particular by the intuition, ingenuity and passion of Giulio Cesare Borgia. The MRPM work at Bologna began in the mid-1980s. New correlations were found among parameters from NMR relaxation measurements and oil field parameters such as porosity, permeability to fluid flow, irreducible water saturation, residual oil saturation and pore-system surface-to-volume ratio, and fast algorithms were developed to give the different NMR parameters. Interest in valid interpretation of data led to extensive work also on the inversion of multiexponential relaxation data and the effects of inhomogeneous fields from susceptibility differences on distributions of relaxation times. In the last few years, extensive developments were made of combined magnetic resonance imaging and relaxation measurements in different fields.     

Numerical methods for multiscale transport equations and application to two-phase porous media flow

We discuss numerical methods for linear and nonlinear transport equations with multiscale velocity fields. These methods are themselves multiscaled in nature in the sense that they use macro and micro grids, multiscale test functions. We demonstrate the efficiency of these methods and apply them to two-phase flow in heterogeneous porous media.     

Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method

We present a stable numerical scheme for modelling multiphase flow in porous media, where the characteristic size of the flow domain is of the order of microns to millimetres. The numerical method is developed for efficient modelling of multiphase flow in porous media with complex interface motion and irregular solid boundaries. The Navier–Stokes equations are discretised using a finite volume approach, while the volume-of-fluid method is used to capture the location of interfaces. Capillary forces are computed using a semi-sharp surface force model, in which the transition area for capillary pressure is effectively limited to one grid block. This new formulation along with two new filtering methods, developed for correcting capillary forces, permits simulations at very low capillary numbers and avoids non-physical velocities. Capillary forces are implemented using a semi-implicit formulation, which allows larger time step sizes at low capillary numbers. We verify the accuracy and stability of the numerical method on several test cases, which indicate the potential of the method to predict multiphase flow processes.     

Acoustic wave propagation in two-phase heterogeneous porous media

The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to marine sediments with various physical parameters.     

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.     

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.     

Magnetic resonance imaging study of complex fluid flow in porous media: flow patterns and quantitative saturation profiling of amphiphilic fracturing fluid displacement in sandstone cores

Magnetic resonance imaging is used to follow the removal process of a visco-elastic surfactant (VES) fracturing fluid in Bentheimer sandstone cores at typical reservoir temperatures (T=333 K). Two displacing fluids were investigated, a Gadolinium doped water phase (1M NaCl solution), and a Gadolinium doped hydrocarbon phase (Mineral Spirits). In addition to flow characteristics obtained by conventional core-flooding, i.e., the macroscopically averaged volumetric flow rates and differential pressures, we have also measured the saturation profiles and characteristic displacement patterns during all stages of the removal process. To acquire these data we have used quantitative one-dimensional chemically specific profiling along with fast two-dimensional imaging experiments while flooding Bentheimer sandstone cores in situ in the spectrometer. Our results show that both displacement processes (complex fluid displaced by water or hydrocarbon phase) are dominated by the large viscosity contrasts present. However, distinct differences were found between the displacement characteristics of water and hydrocarbon, which confirmed the sensitivity of the complex fracturing fluid to the displacing fluid.     

Magnetic susceptibility contrast induced field gradients in porous media.

Using a two-component composite theory, we compute the internal field gradient of a periodic porous medium induced by the magnetic susceptibility contrasts. The magnetization of such a system is computed by using the diffusion eigenstates in Fourier representation. We show that the volume averaged field gradient, when used in the formula for free diffusion, significantly overestimates the magnetization decay rate. We also establish bounds for such a periodic system within which the Gaussian approximation is valid for diffusion of spins in the pore space.