Andrew J. Sederman

Structure-flow correlations in packed beds

Magnetic resonance imaging (MRI) volume- and velocity-measurement techniques are used to probe structure-flow correlations within the interparticle space of a packed bed of ballotini. Visualisation of the z-component of the flow velocity within six slices perpendicular to the symmetry axis of the bed permit the flow to be monitored throughout the bed. Significant heterogeneity in the flow is observed; in one slice it is found that approximately 8% of the pores carry 40% of the volume flow. High volume flow through any given pore is seen to be influenced most strongly by the local geometry of the pore space; i.e. the radial position of the pore within the bed, the radius of the pore and the relative amount of interfacial surface area adjoining neighbouring pores. In contrast, the topology of the bed plays a crucial role in determining the mean flow velocity through a given pore. Correlations are found between the flow velocity within a pore and both the local Reynolds number and coordination number associated with that pore. These results are discussed with reference to a simple pore network model.

Magnetic resonance imaging of liquid flow and pore structure within packed beds

Magnetic resonance imaging (MRI) volume- and velocity-measurement techniques are used to probe structure-flow correlations within the interparticle space of a packed bed of ballotini. Images of the three mutually orthogonal components of the velocity field are obtained in two perpendicular slices within a bed of 5 mm diameter ballotini packed within a glass column of internal diameter 4.6 cm. Comparison of flow images obtained for two beds of identical column-to-particle diameter ratio but of differing length show that velocity enhancements at the walls of the bed are greater in the shorter, more ordered, bed. A three-dimensional volume image of each bed is also obtained and analysed to partition the interparticle space into individual pores and determine the location of pore necks. Correlations between volume flow rate and the surface area of the constrictions (pore necks) within the interparticle space lie between two limiting behaviours. For pores associated with low local Reynolds number, the volume flow rate through the constrictions scales as the square of the cross-sectional area of the constriction, whereas at the extreme of high local Reynolds number pores show volume flow rates scaling with cross-sectional area.

Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces. A compressed sensing-electron tomography (CS-ET) approach.

In this paper, we apply electron tomography (ET) to the study of the three-dimensional (3D) morphology of iron oxide nanoparticles (NPs) with reactive concave surfaces. The ability to determine quantitatively the volume and shape of the NP concavity is essential for understanding the key-lock mechanism responsible for the destabilization of gold nanocrystals within the iron oxide NP concavity. We show that quantitative ET is enhanced greatly by the application of compressed sensing (CS) techniques to the tomographic reconstruction. High-fidelity tomograms using a new CS-ET algorithm reveal with clarity the concavities of the particle and enable 3D nanometrology studies to be undertaken with confidence. In addition, the robust performance of the CS-ET algorithm with undersampled data should allow rapid progress with time-resolved 3D nanoscale studies, 3D atomic resolution imaging, and cryo-tomography of nanoscale cellular structures.

Magnetic resonance imaging as a quantitative probe of gas-liquid distribution and wetting efficiency in trickle-bed reactors

Abstract The potential of magnetic resonance imaging (MRI) measurements to investigate gas and liquid distributions within a fixed-bed reactor operating in co-current downflow in the trickle-flow regime is demonstrated. Liquid holdup and wetting efficiency are studied for a range of gas (66– 356 mm / s ) and liquid (0.5– 5.8 mm / s ) superficial velocities. Two-dimensional and three-dimensional (3-D) magnetic resonance images have been acquired for flow within a packing of 5 mm diameter glass ballotini contained in a cylindrical column of internal diameter 40 mm . The images are of sufficiently high resolution to be able to characterise liquid rivulets within the bed and to detect the presence of thin water films on the surfaces of the packing elements. As expected, liquid holdup and wetting efficiency increase with increase in liquid flow rate, at a fixed gas flow rate. A transition in the holdup and wetting characteristics is observed at a liquid superficial velocity of 1.5– 2 mm / s . The number of liquid rivulets increased rapidly as the liquid superficial velocity was increased from 0.5 to 2.0 mm / s and then reached a plateau; the increase in liquid flow as the liquid flow rate was further increased was taken up in the increasing size of existing rivulets. Differences in the nature of the liquid distribution within the bed are also reported for different conditions of prewetting of the packing. Gas flow rate affected the onset of flow instabilities but not the liquid distribution. 3-D MRI data enabled the visualisation of the extent of liquid filling of individual ‘pores’ within the inter-particle space as a function of liquid flow rate, and how this depended on the ‘pore’ size. For each packing element, the fraction of the surface area that was wetted was found to correlate with the number of contact points that packing element made to other packing elements within the bed.

Single- and two-phase flow in fixed-bed reactors: MRI flow visualisation and lattice-Boltzmann simulations

Abstract Three-dimensional structural magnetic resonance imaging (MRI) and MRI velocimetry have been used to fully characterise the structure of the interparticle pore space and the single-phase flow field in a packed bed of alumina catalyst particles. Three orthogonal components of the velocity ( V x , V y and V z ) are acquired such that the fluid velocity vector is determined at a pore-scale resolution of 156 μm . The pore space has been analysed by unambiguously partitioning the pore space into individual pores. Characteristics of the individual pores are combined with the MRI velocity data to determine quantitative statistical information concerning flow through these pores. The ability of the lattice-Boltzmann simulation technique to predict the flow field visualised by MRI is also demonstrated by performing the simulation on a lattice derived directly from the MRI experimental three-dimensional image of the structure of the packed bed. A direct comparison of the MRI and lattice-Boltzmann results shows there is good agreement between the two methods. Using the pore analysis in conjunction with the velocity information, the flow field through the pore space is shown to be highly heterogeneous with 40% of the fluid flowing through only 10% of the pores. We also show that the lattice-Boltzmann data may be used to calculate average molecular displacement propagators similar to those acquired experimentally for such systems. The effect of the wall on the fluid velocity and porosity is calculated as a function of distance from the wall. Some difference between the MRI and lattice-Boltzmann results are observed close to the wall because of inertial effects in the high velocity channels which are not simulated by the lattice-Boltzmann method. Finally, we present initial results from the extension of this work to two-phase flow in packed beds. A case study of the visualisation of the extent of wetting of the packing as a function of time following start-up is presented.

Structure of packed beds probed by Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) volume-visualisation in combination with image analysis techniques are used to characterise the structure within the inter-particle space of unconsolidated and consolidated packed beds of ballotini for column-to-particle diameter ratios of 9, 14 and 19. The beds are characterised using two approaches. First, radial distributions of the voidage are calculated. The reduced radial distribution function of the void space in a plane perpendicular to the axis of the bed is also used to investigate correlated structures within the void space. For all column-to-particle diameters, the correlated structure extends up to 6.5 diameters into the packing material and is seen to increase upon consolidation. Second, the inter-particle space is segmented into individual pores, defined as a portion of the void space bounded by a solid surface and planes erected where the hydraulic radius of the void space exhibits local minima. Statistical distributions of the characteristics of these pores, such as radius, surface area, volume and coordination to other pores, are obtained. Upon consolidation, there is an increase in the number of small pores and decrease in the relative size of constrictions within the pore space. This significant change in the detailed pore structure of the bed will act along with the decrease in overall porosity also observed upon consolidation to create a structure, which will influence the characteristic hydrodynamics associated with the bed.

Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing.

We present a method for accelerating the acquisition of phase-encoded velocity images by the use of compressed sensing (CS), a technique that exploits the observation that an under-sampled signal can be accurately reconstructed by utilising the prior knowledge that it is sparse or compressible. We present results of both simulated and experimental measurements of liquid flow through a packed bed of spherical glass beads. For this system, the best image reconstruction used a spatial finite-differences transform. The reconstruction was further improved by utilising prior knowledge of the liquid distribution within the image. Using this approach, we demonstrate that for a sampling fraction of approximately 30% of the full k-space data set, the velocity can be recovered with a relative error of 11%, which is below the visually detectable limit. Furthermore, the error in the total flow measured using the CS reconstruction is <3% for sampling fractions > or = 30%. Thus, quantitative velocity images were obtained in a third of the acquisition time required using conventional imaging. The reduction in data acquisition time can also be exploited in acquiring images at a higher spatial resolution, which increases the accuracy of the measurements by reducing errors arising from partial volume effects. To illustrate this, the CS algorithm was used to reconstruct gas-phase velocity images at a spatial resolution of 230 microm x 230 microm. Images at this spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques.

In situ magnetic resonance visualisation of the spatial variation of catalytic conversion within a fixed-bed reactor

Abstract We report the first application of magnetic resonance techniques to explore the spatial variation in chemical conversion of a catalysed reaction occurring within a fixed-bed reactor. The reaction studied is the liquid-phase esterification of methanol and acetic acid, catalysed by a proton exchange (Amberlyst 15 ion exchange resin) catalyst. This esterification is considered as a generic liquid-phase reaction, for which the extent of reaction is measured non-invasively, in situ, by monitoring the 1 H chemical shift of the hydroxyl resonance associated with fluid in the inter-particle space of the bed. The paper highlights the application of one-dimensional chemical shift imaging and volume selective magnetic resonance spectroscopy techniques to measure directly and quantitatively the spatial distribution of chemical conversion within a fixed-bed of catalyst particles. In the specific case study considered here it is shown that while conversion within the bed is homogeneous under batch reaction conditions, as expected, when reaction occurs under flowing conditions fractional variations in steady-state conversion of up to ∼20% exist within transverse sections through the bed, perpendicular to the direction of superficial flow. We suggest that magnetic resonance visualisation techniques are now able to provide a quantitative tool to aid in the integrated design of catalyst and reactor.

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 SF(6) within a packing of 5mm spheres contained within columns of diameter 40 and 27 mm; images being acquired using (1)H and (19)F observation for the water and SF(6), 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.

Recent advances in Flow MRI

The past five years have seen exciting new developments in Flow MRI. Two-dimensional images are now routinely acquired in 100-200 ms and, in some cases, acquisition times of 5-10 ms are possible. This has been achieved not only by advances in the implementation of existing pulse sequences but also in data acquisition strategies, such as Compressed Sensing and Bayesian approaches, and technical advices in parallel imaging and signal enhancement methods. In particular, the short imaging timescales that are now achieved offer significant opportunities in the study of transient flow phenomena.