Real-Time Magnetic Resonance Imaging of Bubble Behavior and

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Thermodynamics, Transport, and Fluid Mechanics

Real-Time Magnetic Resonance Imaging of Bubble Behavior and Particle Velocity in Fluidized Beds Alexander Penn, Christopher Boyce, Thomas Kovar, Takuya Tsuji, Klaas P. Pruessmann, and Christoph R. Müller Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00932 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 28, 2018

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Real-Time Magnetic Resonance Imaging of Bubble Behavior and Particle Velocity in Fluidized Beds

Alexander Penn1,2*, Christopher M. Boyce1,3*, Thomas Kovar3, Takuya Tsuji4, Klaas P. Pruessmann2, Christoph R. Müller1*

1

Department of Mechanical and Process Engineering, ETH Zurich Institute for Biomedical Engineering, ETH Zurich and University of Zurich 3 Department of Chemical Engineering, Columbia University 4 Department of Mechanical Engineering, Osaka University 2

(*) Corresponding authors. These authors contributed equally to the work. Emails: [email protected]; [email protected]; [email protected]

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Abstract Snapshots of particle concentration and velocity fields in bubbling gas-solid fluidized beds were acquired using magnetic resonance imaging. Using a recently developed multichannel radiofrequency receiver coil in combination with fast readout techniques, adapted from medical MRI protocols, the temporal resolution was 7 ms and 18 ms for 2D images of particle concentration and velocity fields, respectively. A cylindrical bed with 190 mm diameter and 300 mm height was filled to heights of 100 mm, 150 mm and 200 mm with spherical 1 mm and 3 mm diameter particles and fluidized at ratios of superficial gas velocity to minimum fluidization velocity (U/Umf) of 1.2, 1.5, 2.0, 3.0 and 4.0. Effects of these varying parameters on the number of bubbles, bubble diameter, bed height and particle speed are investigated. It is hoped that these data sets will become important benchmarks against which computational, analytical and empirical models can be validated.



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Introduction Gas-solid fluidized beds are critical to processes in the oil and gas1, polymer production2 and pharmaceuticals3 industries as well as developing technologies relevant to carbon dioxide capture4. Despite this far-reaching importance, the physics governing fluidized beds are still poorly understood as compared to systems involving only liquids and gases or only grains, due in large part to complex instabilities such as bubbling and clustering occurring at the meso-scale. A major difficulty in developing an in-depth understanding of the underlying physics has been generating robust data sets for fluidization behavior based on experimental techniques which can probe the particle (and gas) dynamics inside these 3D opaque systems. Traditionally, three major limitations have applied to measurement techniques used to characterize fluidized beds: (1) An inability of optical techniques, such as particle image velocimetry5,6, to make measurements in the interior of 3D fluidized beds, limiting their application to pseudo2D beds with very different behavior due to wall effects. (2) An inability of tracer particle techniques, such as positron emission particle tracking7,8, to obtain flow field information on a temporally resolved level. (3) An inability of tomographic techniques, such as X-ray9,10 and electrical capacitance tomography11, to obtain flow field information beyond particle concentration. In the past decade, magnetic resonance imaging (MRI) has proven a powerful method for addressing most of these limitations. MRI has been used for time-averaged measurements of both gas12 and particle12–14 velocities and granular temperature13,14 as well as snapshots of 2D particle concentration fields with temporal resolution of ~30 ms15,16 in 3D beds. Still, until recently, MRI has been limited to only temporally unresolved measurements of particle velocity as well as beds of diameter less than 50 mm. Recent application of medical MRI techniques and 3 ACS Paragon Plus Environment

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scanners have enabled real-time 2D slice imaging of both particle concentration and velocity fields in a bed of 190 mm in diameter17. These capabilities have been used to study the effects of cohesive liquid bridging between particles on fluidization behavior18. In this paper, we seek to utilize these measurement capabilities to characterize the effects of particle size, bed height and superficial velocity on bubbling characteristics, bed height and particle velocity in 3D bubbling gas-solid fluidized beds. Experimental Fluidized Bed A cylindrical polymethyl methacrylate (PMMA) bed of inner diameter 190 mm and height 300 mm was used. A PMMA plate of thickness 10 mm with 6416 laser cut holes of diameter 0.5 mm holes was used as a distributor, with even gas distribution confirmed by imaging of bubble frequency and distribution just above the distributor. The bed was filled to unfluidized heights H0 of 100 mm, 150 mm and 200 mm with engineered particles (agar shell filled with middle chain triglyceride oil) to give MRI signal to the particles. Two types of particles were used: (a) diameter dp = 1.02 ± 0.12 mm, density ρp = 1040 kg/m3, minimum fluidization velocity Umf = 0.25 m/s, coefficient of friction of µ = 0.54 ± 0.05 and coefficient of restitution of e = 0.70 ± 0.03 (referred to hereon as 1 mm particles) and (b) diameter dp = 2.93 ± 0.04 mm, density ρp = 1040 kg/m3, Umf = 0.70 m/s, µ = 0.56 ± 0.04 and e = 0.69 ± 0.03 (referred to hereon as 3 mm particles). Both sets of particles are Group D in Geldart’s classification19. The mass of particles used at different initial bed heights is summarized in Table 1. Air at ambient conditions (density = 1.20 kg/m3; viscosity = 1.00 mPa s) was used to fluidize the bed to superficial velocities U selected such that U/Umf = 1.2, 1.5, 2.0, 3.0 and 4.0. The highest values of U/Umf were only achieved for the smallest particles and initial bed heights because the highest



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gas flow rate achievable by the compressor could only bring smaller particles to the highest values of U/Umf. Additionally, taller initial bed heights resulted in significant numbers of particles reaching the roof of the bed at high values of U/Umf, and thus the highest values of U/Umf were not tested for these taller initial bed heights. Magnetic Resonance Imaging A Philips Achieva 3T medical MRI scanner was used for MRI experiments. The body radiofrequency (r.f.) coil was used for signal excitation and a custom-built 16-channel r.f. coil fitting directly around the fluidized bed was used for signal detection17. The oil within the engineered particles provided the magnetic resonance (MR) signal. The imaging methodology used for this work is detailed by Penn et al.17. In short, multiple MRI scan acceleration techniques were combined allowing to sample data in frequency space (k-space) time-efficiently: (1) multichannel signal reception and SENSE20 reconstruction were used to sample below the Nyquist21 density, (2) Hermitian symmetry was exploited to sample only part of k-space and (3) single-shot echo planar imaging (EPI)22 pulse sequences were designed that acquire an entire MR image after a single excitation pulse. The imaging pulse sequences were adapted to the effective transversal relaxation time (T2*) of the engineered particles in order to maximize the signal-to-noise ratio (SNR) of the acquisitions. Images of both local particle concentration and local particle velocity were obtained in a slice through a vertical cross-section of the bed using EPI and phase-contrast23 EPI, respectively. The standard EPI measurements of local particle concentration had a spatial resolution of 3 mm (horizontal) × 3 mm (vertical) with a 10 mm slice. For these measurements, the temporal resolution was 7.17 ms and 600 scans were conducted to obtain dynamic information over the course of 4.3 s. The field of view was 205 mm (horizontal) × 289 mm (vertical), with the field of


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view spanning the bed diameter and starting just below the distributor. A flip angle of 15° was used. The phase-contrast EPI measurements of the local particle velocity required three signal excitations per measurement, in order to determine the particle velocity in the vertical and horizontal directions. Thus, these measurements had a repetition time of 6.06 ms between excitations but a temporal resolution of 18.18 ms. 600 scans were conducted, acquiring dynamic information over the course of 10.9 s. The spatial resolution was 3 mm (horizontal) × 5 mm (vertical) with a 10 mm slice in the third direction. The field of view and flip angle were the same as those used in the standard EPI measurements. For both EPI and phase-contrast EPI, all measurements were repeated 3 times. MRI is a technique used for decades to characterize concentration and flow in a variety of different systems. Despite this, the lack of familiarity of many researchers in the field may lead to doubts of the robustness of MRI measurements and the areas of uncertainty in the measurements. MRI has been used in the past in conjunction with pressure measurements24, electrical capacitance tomography25, positron emission particle tracking26, X-ray26 and computational modeling12,27 for cross-validation purposes in studying fluidized beds. Thus, we are confident in the validity of the MRI measurements presented here. The following considerations make us confident in the validity of the MRI measurements presented here: Both the particle density and the particle velocity measurements are based on standard MRI protocols, which have been approved for their use in clinical applications. In addition, we performed logical assessments for both the particle position and the particle velocity measurements. For the particle position measurements, we (a) confirmed that the geometry of the real system corresponds to the geometry observed in the images and (b) filled a hollow plastic sphere with the particles used in



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this study and dropped the sphere while recording its trajectory using MRI. The recorded trajectory corresponded to the trajectory predicted by Newton’s laws of motion. For the particle velocity measurements, we measured the upward vertical speed of particles in the wake region of a single gas bubble injected into an incipiently fluidized bed and confirmed that the average velocity in the wake corresponds to approximately the rising speed of the gas bubble. Potential sources of uncertainty of the MR imaging methodology used here are discussed elsewhere17,18. Image Processing MATLAB with the MRecon interface (ReconFrame 3.0, GyroTools LLC, Zurich, Switzerland) was used to process the MRI data. A threshold was used to distinguish the particleladen phase from the gas phase (bubbles and freeboard) in a binary manner. Pixels with a signal intensity greater than 12.5% of the signal intensity from the pixel with the maximum signal intensity in the image series for the specific experiment (e.g. H0 = 150 mm, U/Umf = 3.0, experiment 1) were considered as consisting of the particle-laden phase. Bed height analysis was conducted by identifying the highest point of interconnected pixels in the particle-laden phase at each frame in time; particles flung into the freeboard by bubble eruption were not included on the basis of excluding sets of interconnected pixels below a minimum size. Bubble analysis was conducted by identifying the size and centroid position of interconnected pixels in the gas phase; the freeboard was omitted from this analysis by excluding bubbles located above the bed height. The “height” of a bubble in the bed was determined by the vertical coordinate of its centroid, and the effective diameter of a bubble was determined by the diameter of a circle with the same area as that of the interconnected pixels constituting the bubble. Figure 1 provides insights into how a grayscale image of local particle concentration (a) is converted into a binary image (b) via application of a threshold, and how this binary image is used to extract information on bubble


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behavior and bed height. In this image, small bubbles are not counted due to a minimum bubble size (324 mm2) for registering, and the highest points of particle-laden phase are not counted towards bed height because they are not interconnected with the rest of the particle phase. Particle velocity data was obtained via identifying the in-plane speeds of particle-laden pixels. This data was collected over all particle-laden pixels for each image in the time series to produce probability density functions (PDFs) of particle speed as well as the average particle speeds and the standard deviation in particle speeds for each MRI measurement. Results and Discussion Images Figure 2 shows a representative time series of images of local particle concentration and local particle velocity in a vertical slice through the center of the fluidized bed. The images shown are for 1 mm particles with an initial bed height of H0 = 150 mm at (a) U/Umf = 1.2 and (b) U/Umf = 3.0. At U/Umf = 1.2, the bubbles are small as compared to the diameter of the bed and local particle speeds only approach 1 m/s close to bubbles near the top of the bed; the direction of the velocity vectors is upward surrounding bubbles, but fairly random in other parts of the bed. At U/Umf = 3.0, many bubbles with diameter comparable to that of the bed are observed with local particle speeds much faster than those seen at U/Umf = 1.2. With complex interactions between bubbles, the directions of particle velocity vectors at U/Umf = 3.0 does not follow clear trends. From comparing Figures 2 (a) and (b), it is clear that the expanded bed height is much higher at U/Umf = 3.0 than U/Umf = 1.2. All of these qualitative observations fit with what could be expected based on previous experimental observations and theory; various aspects of these differences based on fluidization velocity, particle size and initial bed height will be quantified in the following sections.



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Bed Height Figure 3 shows the bed height behavior as a function of fluidization velocity for various values of initial bed height and particle size. In Figure 3 (a), the average expanded bed height increases monotonically with fluidization velocity, as could be expected. Particle size does not seem to have a large effect on bed expansion, at least not at the low values of U/Umf we were limited to for the 3 mm particles in these experiments, owing to the maximum gas flow rate we could achieve. The ratio of H/H0 tends to be higher for smaller values of the unfluidized bed height, H0, than larger values of H0. This result is somewhat surprising, since larger bubbles could be expected to develop in deeper beds, increasing the expanded bed height. An explanation could be that more particles are flung into the freeboard of deeper beds due to the breakthrough of large bubbles, and these particles were not counted towards the expanded bed height, based on the definition given in the experimental section. Figure 3 (b) shows the standard deviation in the expanded bed height over the time series of images versus U/Umf. This standard deviation captures the oscillation in bed heights which occurs due to bed height increasing as large bubbles form and approach the bed surface and then sharply decreasing as these bubbles break through the bed surface. For both 1 mm and 3 mm particles at bed heights H0 = 100 mm and 150 mm, this standard deviation increases monotonically with U/Umf, as could be expected, since more large bubbles form with increasing U. In contrast, a slight decrease is observed in the standard deviation with increasing U/Umf for H0 = 200 mm, which is perhaps attributable to the bed height approaching the field of view for imaging in these cases. In most cases, the standard deviation increases with increasing particle size at the same value of U/Umf. This trend can be explained as follows: due to a higher value of Umf, the excess gas velocity in beds of larger particles has a higher excess gas velocity, U-Umf, at


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the same value of U/Umf, leading to slightly larger bubbles forming. With larger bubbles, the standard deviation in bed height oscillations increases. Bubble Behavior Figure 4 shows the average number of bubbles per image in the time series of images as a function of the vertical position in the bed (y) for 1 mm particles (first row) and 3 mm particles (second row) with an unfluidized bed height of 100 mm (first column), 150 mm (second column) and 200 mm (third column). Across all cases, a few clear trends can be seen: 1) The number of bubbles decreases with increasing vertical position in the bed; this trend is explained by bubbles coalescing as they rise through the bed. 2) The number of bubbles increases with increasing U/Umf, especially at higher vertical positions in the bed; this trend is explained by more gas going into bubbles at higher values of U and the expanded bed height increasing with U. 3) The number of bubbles high in the bed increases with increasing initial bed height; this trend follows from the fact that the expanded bed height increases with increasing initial bed height. 4) The number of bubbles decreases with increasing particle size from 1 mm to 3 mm; this trend can be explained by larger bubbles forming with larger particles, and thus fewer bubbles forming overall with increasing particle size. A few exceptions exist with regards to the aforementioned trends. For a few cases with low values of U/Umf, the number of bubbles increases with increasing vertical position very low in the bed. This increase is explained by the fact that bubbles of a minimum area of 324 mm2 are registered by the detection algorithm and at this low flow rate with smaller particles, bubbles must coalesce first low in the bed before they are registered. 10 ACS Paragon Plus Environment


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Figure 5 shows the average bubble diameter as a function of the vertical position in the bed (y) for 1 mm particles (first row) and 3 mm particles (second row) with an unfluidized bed height of 100 mm (first column), 150 mm (second column) and 200 mm (third column). The following trends can be seen: i.

Bubble diameter increases with increasing vertical positions in all cases, as could be expected due to bubble coalescence.

ii.

Bubble diameter increases with gas flow rate, as could be expected due to more gas going into bubbles.

iii.

Bubble diameter increases slightly with particle size, as could be expected based on previous reports in the literature28–30.

One abnormal feature of Figure 5 is that the bubble size seems to level off or to decrease slightly with increasing vertical position close to the initial bed height in a few cases. Analysis of the local particle concentration images before and after applying a threshold showed that large bubbles after were not recorded as bubbles breaking through the bed surface, as desired. However, small voids which disintegrated after one or two frames were left behind after this breakthrough and registered as bubbles. Thus, these puzzling trends high in the bed should be viewed as a flaw in the bubble detection algorithm to distinguish between a true bubble and a fleeting void left after a bubble breakthrough, rather than distinct new trends which have not been seen in prior studies. Figure 6 shows (a) the average number of bubbles per frame, (b) the average bubble diameter and (c) the average total area of all bubbles, averaged over the entire vertical cross-section of the bed. In most cases, the number of bubbles increases with increasing U/Umf at low values of U/Umf


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and then appears to asymptotically approach a maximum value at high values of U/Umf. This approach of an asymptotic value is perhaps explained by excess gas flow going into larger bubbles rather than forming more bubbles. The number of bubbles increases with bed height, as can be explained by the opportunity for more bubbles to exist simultaneously in a taller bed. The number of bubbles generally increases with decreasing particle size; this can be explained by larger bubbles forming in beds of larger particles, rather than more bubbles forming. The bubble diameter behavior in Figure 6 (b) reiterates the same trends seen in Figure 5: bubble diameter increases with increasing U/Umf and particle size. Additionally, bubble diameter increases with increasing bed height due to the fact that there is more space for large bubbles to form via coalescence in taller beds. Figure 6 (c) shows the average total area of bubbles normalized by the cross-sectional area of the vertical slice of the bed when unfluidized (Dbed∙H0) as compared to the normalized gas velocity in excess of that needed for fluidization. This plot provides an opportunity to assess the prediction of the “two-phase theory of fluidization” that all gas flow in excess of that needed for minimum fluidization forms bubbles31. According to this theory, the value should be 1.0 on this plot for all bed conditions. As shown in Figure 6 (c), the value is significantly below 1.0 for all conditions. This discrepancy can be explained via a variety of factors: a. Not all excess gas velocity goes into bubbles, but rather some of the excess gas velocity goes into an increased interstitial flow between particles, and thus the theory is not completely valid. b. Gas flow goes into bubbles smaller than those which are detected based on the minimum bubble size criteria set in registering bubbles. This can explain why the



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values are particularly low for H0 = 100 mm beds and low gas flow rates, but increase at this bed height with increasing gas flow rate. c. After bubble breakthrough, these bubbles no longer count towards the total bubble area; however, the expanded bed height is still fairly high directly after the breakthrough of a large bubble. Thus the definition of expanded bed height used is problematic for this comparison, especially with the large fluctuations in bed height which occur upon bubble breakthrough relative to the small initial bed heights used in this study. d. This analysis is based on bubble area through a central slice of the bed, while twophase theory pertains to total bubble volume throughout the entire volume of the bed. Thus, this analysis is prone to area being an insufficient analog to volume and a bias given toward bubble behavior in the center of the bed by taking a central slice. Despite the complications of reasons (b), (c) and (d), Figure 6 (c) does indicate that the twophase theory of granular flow is not completely valid and some excess gas flow goes into interstitial flow rather than entirely into bubbles. Particle Speed Figure 7 shows probability density functions (PDFs) of in-plane particle speed for particle-laden pixels from all regions of the bed with varying U/Umf at bed heights of (a) 100 mm, (b) 150 mm and (c) 200 mm. The results show that both (i) increasing U/Umf and (ii) increasing unfluidized bed height lead to a broadening of the particle speed distribution with a longer tail of particles with high speeds. These trends are attributed to increasing bed height or gas flow rate leading to an increase in the number of large, fast moving bubbles, which cause particles around them to move at faster speeds. 13 ACS Paragon Plus Environment

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It should be noted that a Maxwellian distribution of particle speeds is often assumed in deriving a kinetic theory for granular flows32, yet the speed distributions in Figure 7 do not follow a Maxwellian distribution. This difference can be explained as follows: several studies have shown that the presence of bubbles leads to an anisotropic distribution of granular temperature in the vertical component as compared to the horizontal components, since bubbles rise vertically13,33. Thus, here we are only measuring a “bubble” granular temperature33, rather than a homogeneous granular temperature. Additionally, since only in-plane speeds are measured, the speed distribution is biased toward the vertical direction, since only one horizontal component is considered. Figure 8 shows PDFs of in-plane particle speed for particle-laden pixels from all regions of the bed with U/Umf = 1.2 m/s for different initial bed heights for 1 mm and 3 mm particles. In all cases, the wider speed distributions are seen for the 3 mm particles than the 1 mm particles. This trend can be explained by the fact that larger bubbles are formed in the 3 mm particles than the 1 mm particles, as shown in Figure 6 (b). With larger bubbles rising faster, particles with thus be conveyed faster in the beds of 3 mm particles. Figure 9 provides insights into the in-plane speed of particles in particle-laden pixels across the entire vertical cross-section of the bed for 1 mm and 3 mm particles. Figure 0 (a) shows that the average particle speed increases with increasing U/Umf, as could be expected from an increasing drag force. Additionally, the average particle speed increases with increasing bed height, which can be explained by larger bubbles rising faster and thus particles surrounding larger bubbles moving faster and larger bubbles having a chance to form via coalescence in taller beds. Figure 9 (b) shows that the standard deviation of particle speeds follows the same trends as



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the average values; these trends can be explained by increased motion of particles allowing for a wider distribution in particle speeds, as also seen in the PDFs in Figures 7 and 8. Conclusions This paper demonstrates the capabilities of real-time MRI to image particle concentration and motion under different bubbling conditions in fluidized beds. These images were processed to produce data on bubble size, the number of bubbles and particle speeds, showing that all of these important parameters in fluidized bed behavior increase with increasing bed height and gas flow rate, as could be expected based on physical reasoning. A quantification of the fraction of gas flow in excess of that needed for minimum fluidization which rises in the form of bubbles indicates that not all of this gas flow goes into bubbles, as was postulated by the two-phase theory of fluidization. The quantification of several key parameters for fluidization behavior in this study provides an important dataset for determining the validity of various computational models. Supporting Information Appendix A: figures showing the effect of the choice of threshold value on the bubble diameter registered. Acknowledgments This work was supported by the Swiss National Science Foundation under grant number 200021_153290.


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References: (1)

(2) (3) (4) (5) (6)

(7)

(8) (9) (10) (11)

(12)

(13)

(14)

(15)

(16)

(17)

Arbel, A.; Huang, Z.; Rinard, I. H.; Shinnar, R.; Sapre, A. V. Dynamic and Control of Fluidized Catalytic Crackers. 1. Modeling of the Current Generation of FCC’s. Ind. Eng. Chem. Res. 1995, 34 (4), 1228–1243. Choi, K.-Y.; Harmon Ray, W. The Dynamic Behaviour of Fluidized Bed Reactors for Solid Catalysed Gas Phase Olefin Polymerization. Chem. Eng. Sci. 1985, 40 (12), 2261–2279. Muzzio, F. J.; Shinbrot, T.; Glasser, B. J. Powder Technology in the Pharmaceutical Industry: The Need to Catch up Fast. Powder Technol. 2002, 124 (1), 1–7. Abanades, J. C.; Anthony, E. J.; Lu, D. Y.; Salvador, C.; Alvarez, D. Capture of CO2 from Combustion Gases in a Fluidized Bed of CaO. AIChE J. 2004, 50 (7), 1614–1622. Westerweel, J. Fundamentals of Digital Particle Image Velocimetry. Meas. Sci. Technol. 1997, 8 (12), 1379. Müller, C. R.; Davidson, J. F.; Dennis, J. S.; Hayhurst, A. N. A Study of the Motion and Eruption of a Bubble at the Surface of a Two-Dimensional Fluidized Bed Using Particle Image Velocimetry (PIV). Ind. Eng. Chem. Res. 2007, 46 (5), 1642–1652. Parker, D. J.; Broadbent, C. J.; Fowles, P.; Hawkesworth, M. R.; McNeil, P. Positron Emission Particle Tracking-a Technique for Studying Flow within Engineering Equipment. Nucl. Instrum. Methods Phys. Res. Sect. Accel. Spectrometers Detect. Assoc. Equip. 1993, 326 (3), 592–607. Devanathan, N.; Moslemian, D.; Dudukovic, M. P. Flow Mapping in Bubble Columns Using CARPT. Chem. Eng. Sci. 1990, 45 (8), 2285–2291. Fischer, F.; Hoppe, D.; Schleicher, E.; Mattausch, G.; Flaske, H.; Bartel, R.; Hampel, U. An Ultra Fast Electron Beam X-Ray Tomography Scanner. Meas. Sci. Technol. 2008, 19 (9), 094002. Mudde, R. F. Time-Resolved X-Ray Tomography of a Fluidized Bed. Powder Technol. 2010, 199 (1), 55–59. Warsito, W.; Fan, L. S. Neural Network Based Multi-Criterion Optimization Image Reconstruction Technique for Imaging Two-and Three-Phase Flow Systems Using Electrical Capacitance Tomography. Meas. Sci. Technol. 2001, 12 (12), 2198. Boyce, C. M.; Rice, N. P.; Ozel, A.; Davidson, J. F.; Sederman, A. J.; Gladden, L. F.; Sundaresan, S.; Dennis, J. S.; Holland, D. J. Magnetic Resonance Characterization of Coupled Gas and Particle Dynamics in a Bubbling Fluidized Bed. Phys. Rev. Fluids 2016, 1 (7), 074201. Holland, D. J.; Müller, C. R.; Dennis, J. S.; Gladden, L. F.; Sederman, A. J. Spatially Resolved Measurement of Anisotropic Granular Temperature in Gas-Fluidized Beds. Powder Technol. 2008, 182 (2), 171–181. Müller, C. R.; Holland, D. J.; Sederman, A. J.; Scott, S. A.; Dennis, J. S.; Gladden, L. F. Granular Temperature: Comparison of Magnetic Resonance Measurements with Discrete Element Model Simulations. Powder Technol. 2008, 184 (2), 241–253. Müller, C. R.; Holland, D.; Davidson, J.; Dennis, J.; Gladden, L.; Hayhurst, A.; Mantle, M.; Sederman, A. Rapid Two-Dimensional Imaging of Bubbles and Slugs in a Three-Dimensional, GasSolid, Two-Phase Flow System Using Ultrafast Magnetic Resonance. Phys. Rev. E 2007, 75 (2). Müller, C. R.; Davidson, J. F.; Dennis, J. S.; Fennell, P. S.; Gladden, L. F.; Hayhurst, A. N.; Mantle, M. D.; Rees, A. C.; Sederman, A. J. Real-Time Measurement of Bubbling Phenomena in a ThreeDimensional Gas-Fluidized Bed Using Ultrafast Magnetic Resonance Imaging. Phys. Rev. Lett. 2006, 96 (15), 154504. Penn, A.; Tsuji, T.; Brunner, D. O.; Boyce, C. M.; Pruessmann, K. P.; Müller, C. R. Real-Time Probing of Granular Dynamics with Magnetic Resonance. Sci. Adv. 2017, 3 (9), e1701879.



(18) (19) (20) (21) (22) (23) (24)

(25)

(26)

(27)

(28) (29)

(30) (31) (32) (33)

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Boyce, C. M.; Penn, A.; Pruessmann, K. P.; Müller, C. R. Magnetic Resonance Imaging of Gas–Solid Fluidization with Liquid Bridging. AIChE J. 2017, n/a-n/a. Geldart, D. Types of Gas Fluidization. Powder Technol. 1973, 7 (5), 285–292. Pruessmann, K. P.; Weiger, M.; Schneidegger, M. B.; Boesiger, P. SENSE: Sensitivity Encoding for Fast MRI. Magn. Reson. Med. 1999, 42, 952–962. Nyquist, H. Certain Topics in Telegraph Transmission Theory. Trans. Am. Inst. Electr. Eng. 1928, 47 (2), 617–644. Stehling, M. K.; Turner, R.; Mansfield, P. Echo-Planar Imaging: Magnetic Resonance Imaging in a Fraction of a Second. Sci. Wash. 1991, 254 (5028), 43. Caprihan, A.; Fukushima, E. Flow Measurements by NMR. Phys. Rep. 1990, 198 (4), 195–235. Müller, C. R.; Davidson, J. F.; Dennis, J. S.; Fennell, P. S.; Gladden, L. F.; Hayhurst, A. N.; Mantle, M. D.; Rees, A. C.; Sederman, A. J. Oscillations in Gas-Fluidized Beds: Ultra-Fast Magnetic Resonance Imaging and Pressure Sensor Measurements. Powder Technol. 2007, 177 (2), 87–98. Holland, D. J.; Marashdeh, Q.; Müller, C. R.; Wang, F.; Dennis, J. S.; Fan, L.-S.; Gladden, L. F. Comparison of ECVT and MR Measurements of Voidage in a Gas-Fluidized Bed. Ind. Eng. Chem. Res. 2009, 48 (1), 172–181. Pore, M.; Ong, G. H.; Boyce, C. M.; Materazzi, M.; Gargiuli, J.; Leadbeater, T.; Sederman, A. J.; Dennis, J. S.; Holland, D. J.; Ingram, A.; et al. A Comparison of Magnetic Resonance, X-Ray and Positron Emission Particle Tracking Measurements of a Single Jet of Gas Entering a Bed of Particles. Chem. Eng. Sci. 2015, 122, 210–218. Boyce, C. M.; Holland, D. J.; Scott, S. A.; Dennis, J. S. Adapting Data Processing To Compare Model and Experiment Accurately: A Discrete Element Model and Magnetic Resonance Measurements of a 3D Cylindrical Fluidized Bed. Ind. Eng. Chem. Res. 2013, 52 (50), 18085–18094. Kato, K.; Wen, C. Y. Bubble Assemblage Model for Fluidized Bed Catalytic Reactors. Chem. Eng. Sci. 1969, 24 (8), 1351–1369. Park, W. H.; Kang, W. K.; Capes, C. E.; Osberg, G. L. The Properties of Bubbles in Fluidized Beds of Conducting Particles as Measured by an Electroresistivity Probe. Chem. Eng. Sci. 1969, 24 (5), 851–865. Yasui, G.; Johanson, L. N. Characteristics of Gas Pockets in Fluidized Beds. AIChE J. 1958, 4 (4), 445–452. Toomey, R. D.; Johnstone, H. F. Gaseous Fluidization of Solid Particles. Chem. Eng. Prog. 1952, 48 (5), 220–226. Ding, J.; Gidaspow, D. A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow. AIChE J. 1990, 36 (4), 523–538. Jung, J.; Gidaspow, D.; Gamwo, I. K. Measurement of Two Kinds of Granular Temperatures, Stresses, and Dispersion in Bubbling Beds. Ind. Eng. Chem. Res. 2005, 44 (5), 1329–1341.


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Figures:

Figure 1. (a) Grayscale snapshot image of local particle density in a central vertical slice through the fluidized bed with light colors indicating areas of high particle density and dark areas indicating low particle density. (b) Binary image produced after applying a threshold to (a); numbers indicate counting of bubbles in this frame; Ab,1 indicates the area of bubble 1 used to calculate its effective diameter; H indicates how the expanded height is calculated for this image.



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Figure 2. Time series of instantaneous maps of local particle concentration (first row) and local in-plane particle velocity (second row) across a central vertical cross-section through the bed for (a) U/Umf = 1.2 and (b) U/Umf = 3.0 with an initial bed height of H0 = 150 mm. Particle velocity maps use arrows to show the direction of the velocity vector and colors to show the magnitude.


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Figure 3. (a) Average expanded bed height (H) and (b) standard deviation in expanded bed height normalized by unfluidized bed height (H0) as a function of U/Umf for different bed heights and particle sizes.



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Figure 4. Number of bubbles per image averaged over the entire time series of images for 1 mm particles (first row) and 3 mm particles (second row) and unfluidized bed heights of 100 mm (first column), 150 mm (second column) and 200 mm (third column) as a function of the vertical position (y) of the center of the bubble.


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Figure 5. Bubble diameter normalized by bed diameter averaged over the entire time series of images for 1 mm particles (first row) and 3 mm particles (second row) and unfluidized bed heights of 100 mm (first column), 150 mm (second column) and 200 mm (third column) as a function of the vertical position (y) of the center of the bubble.



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Figure 6. (a) Number of bubbles per frame and (b) average bubble diameter averaged over the entire cross-section of the bed and (c) average total area of bubbles per frame as a function U/Umf for various particle sizes and unfluidized bed heights.


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Figure 7. Probability density functions of in-plane particle speeds over the entire cross-section of the bed for 1 mm particles with unfluidized bed heights of (a) 100 mm, (b) 150 mm and (c) 200 mm for different values of U/Umf.



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Figure 8. Probability density functions of in-plane particle speeds over the entire cross-section of the bed for unfluidized bed heights of (a) 100 mm, (b) 150 mm and (c) 200 mm for different particle sizes.


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Figure 9. (a) Average in-plane particle speed and (b) standard deviation in in-plane particle speed over the entire cross-section of the bed as a function of U/Umf for different bed heights for 1 mm and 3 mm particles.



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Table 1. Mass of particles in the bed for different initial bed heights. Particle Size (mm) 1 1 1 3 3 3

Initial Bed Height (mm) 100 150 200 100 150 200

Mass of Particles (kg) 1.823 2.710 3.564 1.828 2.716 3.570


Real-Time Magnetic Resonance Imaging of Bubble Behavior and

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