Electrical Capacitance Volume Tomography Imaging of Three

13 Jul 2012 - The solids holdup in the annulus near the top wall area in the bend is higher than that in other locations of the annulus. At a higher s...
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Electrical Capacitance Volume Tomography Imaging of ThreeDimensional Flow Structures and Solids Concentration Distributions in a Riser and a Bend of a Gas−Solid Circulating Fluidized Bed Fei Wang, Qussai Marashdeh, Aining Wang, and Liang-Shih Fan* William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States ABSTRACT: Electrical capacitance volume tomography (ECVT) is a newly developed imaging technique that can quantify three-dimensional (3D) multiphase flows in a complex, geometric flow field. In this study, the 3D phase distribution images inside a gas−solid circulating fluidized bed (CFB) are obtained using ECVT. Specifically, measurements are made at a riser section and a 90° bend-shape riser exit section of the CFB. Inside the vertical riser, a symmetric core−annulus structure with a low solids holdup in the riser center along with a high solids holdup near the riser wall is observed. The average volume solids holdup and the thickness of the annulus decrease with the superficial gas velocity. A core−annulus flow structure is formed both in the vertical and horizontal parts of the bend. The annulus structure is noncentro-symmetric in the horizontal part of the bend. The solids holdup in the annulus near the top wall area in the bend is higher than that in other locations of the annulus. At a higher superficial gas velocity in the riser, the centrifugal acceleration increases due to high solids velocity in the bend, and more solids are separated to the outside of the bend from the main stream. A “reversed-S” shape solids holdup distribution along the diagonal line is also observed. The solids holdup increases and then decreases from the outer corner to the center of the bend, which indicates that a relatively dilute region is formed near the outer corner of the bend.

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INTRODUCTION The use of a circulating fluidized bed (CFB) in industry spans a wide range of applications such as fluid catalytic cracking processes and coal combustion. Operating variables for a CFB include both the gas flow rate and the solids flow rate. Flow properties can be determined by different combinations of these two variables.1 The riser, inside of which a suspended gas−solid flow takes place, is a key part of a CFB system. Its hydrodynamics have been studied extensively in the literature.2 Computational fluid dynamics (CFD) has been widely used to investigate the riser flow properties such as solids holdup, velocity distribution for gas and solid phases and mixing process, and regime transition,3−10 scaling,11 and the interphase mass transfer process.12 Experiments have also been performed to identify two significant flow structures for gas−solid flow in a CFB riser; the axial solids dense−dilute transition flow and radial core−annulus flow.13−15 Following these findings, results have been reported on the mixing and clustering properties of particles inside a CFB,16−19 phase holdup and bubble behaviors20−22 and CFB configuration effects.23−28 Verification of CFD simulations, however, continues to require comprehensive experimental data, particularly the 3D data and the data from other sections of the CFB system than the riser. Of interest is the flow in the bended riser exit section, which plays an important role in the hydrodynamic behavior of the riser. Numerous results have been published concerning this role. Harris et al. presented a thorough review of the exit effect on the riser axial solids concentration profile,29 and Chan et al. provided a comprehensive summary of the influences of riser exit geometry.30 In general, there are two kinds of riser exits: smooth and abrupt. Smooth exits are smoothly curved and are used for large solids fluxes operation. An abrupt exit usually has © 2012 American Chemical Society

an angular bend that is sometimes combined with an extension above the outlet of the riser. Some major previous observations of the exit effects are that of Martin et al., where they found that the blind Tee elbow could increase the solids holdup in the top region of the riser because the abrupt exit can “reflect” some particles back to the riser.31 By using an optical fiber probe, Zhou et al.32 also observed that the voidage profiles were asymmetric at the top of the riser and the voidage on the opposite side was higher than the exit side because of the exit effect. They also noticed that location of the peak particle velocity moved toward the exit side, and the thickness of the annular wall layer was thinner on the exit side than the opposite side.33 It was found that particles can accumulate in the tube between the riser exit and cyclone entrance, producing a dune.34 It has been noticed that if the dune is established, some of the particles would regularly fall back into the riser and contribute to the solids reflux, and there were also complex secondary flows inside the exit bend.35 Mei et al. also studied the riser with an abrupt exit and found that there was a downward flow in the top zone of the riser near the exit. They also found that the solids reflected by the abrupt geometry travel downward along the riser wall before joining the main flow back upward.36 Chan et al.30 directly measured the particle motion and particle occupancy in different riser exit geometries using positron emission particle tracking (PEPT) and found that an abrupt exit causes particles to be ejected out of the gas flow, forming a reflux region in the upper part of the riser. Received: Revised: Accepted: Published: 10968

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A detailed understanding of multiphase flow behavior inside a CFB requires a 3D technique capable of visualizing the flow field in real-time. Electrical capacitance volume tomography (ECVT) is a newly developed technique that can provide such measurements.37−39 In ECVT, a set of noninvasive capacitance sensors are placed around a measurement section of the flow field. Sensors interact with each other collecting real-time measurements that can be related back to phase concentrations in the section. The technique is based on reconstructed volume images from capacitance signals acquired from sensors with inherent 3D features. The attractiveness of the technique is in its low profile sensors, fast imaging speed, and scalability to different section sizes, low operating cost, and safety. Moreover, the flexibility of ECVT sensors enable them to be designed around virtually any geometry, rendering them suitable to be used for measurement of solid flows in exit regions of the

CFB.39 The feasibility of the ECVT technique for volume imaging of multiphase flows has been demonstrated through its implementation on flow sections of various shapes and sizes.39 ECVT sensors have a wide range of applicability in the shape or size of a process column. The largest known column to which ECVT sensors were applied was 60 in. in diameter, and the smallest was 1 in. in diameter. Sizes outside this range can also be accommodated. As to metal columns, capacitance sensors were placed inside a stainless-steel reactor column and separated by a ceramic layer from the flow in one recent application that involved a chemical looping reactor system. ECVT sensors can be applied to metallic columns following similar arrangements to the example mentioned here. In this study, an advanced ECVT sensor system is designed and used for imaging gas−solid flows in complex geometries. Sensors are developed for imaging 3D gas−solid flows in both the riser and the 90° bend at the exit region of a CFB. The flow structures in the riser and the bend are analyzed based on quantitative ECVT images. The volumetric solids holdup in the riser and the bend in the CFB are obtained for various superficial gas velocities. The results are compared with earlier studies of exit flow dynamics.

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EXPERIMENTAL STUDIES Experimental Setup. A 0.05 m ID gas−solid CFB is used in this study. Figure 1 is a schematic diagram of the CFB system. The CFB unit, made of Plexiglas, consists of a 0.05 m ID riser with a height of 2.6 m, a 90° bend, a cyclone, a standpipe/ downer, an L-shape nonmechanical valve and a porous distributor. The FCC particles (Geldart group A), with a mean diameter of 60 μm and a particle density of 1400 kg/m3, and air are used as the fluidized particles and fluidizing gas, respectively. A porous plate with a pore size of 20 μm and a fractional free area of 60% is used as the distributor for the CFB riser. The gas flow rate in the riser is monitored by a flow meter in the main gas line. Another flow meter is used to control the aeration gas flow rate at the bottom of the downer to provide a different solids flux in the CFB. A bend and cylindrical ECVT sensors are mounted at the exit region and at the riser in the CFB, respectively. Figure 2 is a photo of the experimental gas− solid CFB mounted with the ECVT bend and the cylindrical

Figure 1. Schematic diagram of the 0.05 m ID gas−solid CFB mounted with ECVT sensors.

Figure 2. Photograph of the 0.05 m ID gas−solid CFB mounted with ECVT sensors: (a) CFB; (b) ECVT bend sensor; (c) ECVT riser sensor. 10969

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sensors. The 3D neural network multicriterion optimization image reconstruction technique (3-D-NN-MOIRT) is used for

image reconstruction; the details of the reconstruction algorithm are illustrated elsewhere.37 Electrical Capacitance Volume Tomography. Recent developments have focused on ECVT sensor design, with 3D features, for detecting capacitance variations due to permittivity perturbations in the imaging volume. For imaging complex geometries using ECVT, sensor design is the main element of the imaging system to define the volume under interrogation. In this work, two ECVT sensors are designed to image flows in the riser and the transition region in the right-angle bend. The design of the cylindrical sensor is aimed at establishing an electrically varied field around the riser by arranging 12 electrodes in 3 layers as depicted in Figure 3a. The capacitance measurements are obtained between each plate at every layer, and all other plates of the cylindrical sensor to image the flow in

Figure 3. Configuration of the ECVT sensors in the CFB: (a) cylindrical sensor; (b) bend sensor.

Figure 4. Time-averaged solids holdup distribution in the riser at Gs = 21.6 kg/(m2 s): Ug = (a) 0.97; (b) 1.16; (c) 1.36; (d) 1.55; (e) 1.75; (f) 1.94 m/s.

Figure 5. Time-averaged solids volume holdup in the riser at Gs = 21.6 kg/(m2 s). 10970

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Figure 6. Fluctuations of the volume averaged solids holdup in the riser at Gs = 21.6 kg/(m2 s).

of the bend by arranging 12 electrodes in 2 layers perpendicular to each other as depicted in Figure 3b. The electric field concentration distribution inside the imaging domain will be formed when different sender plates are activated. Volumes illuminated by electric field refer to regions of sensitivity. As a plate is activated with a positive voltage, volume encapsulating voxels that will introduce the biggest change in capacitance signal are related directly to the strength of electric field in those voxels. In a typical capacitance measurement, sender and receiver plates are engaged to acquire capacitance signals that reflect phase distributions in the imaging domain. The sensitivity of a particular pair of plates to changes in phase distributions is related to electric field distribution of each plate pair. The capacitance sensitivity of a pair

Figure 7. Standard deviation of the volume solids holdup fluctuation in the riser.

the riser. The design of the bend sensor is also aimed at establishing an electrically varied field at and around the corner

Figure 8. Radial profiles of the time-averaged solids holdup in the riser at Gs = 21.6 kg/(m2 s): Ug = (a) 0.97; (b) 1.16; (c) 1.36; (d) 1.55; (e) 1.75; (f) 1.94 m/s. 10971

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of plates would depend on a combination of electric field distribution of both plates. It is the collective sensitivity of all independent plate measurements that is used to reconstruct a volume image of the flow. While the plates at each layer are used to image the flow entering and exiting the bend, it is the interaction between plates in both layers that most reveals the flow dynamics in the region where the flow changes direction. The ECVT sensor design is developed intuitively and confirmed by computer simulations.40 Simulations in this case confirmed the sensitivity distribution is focused at and around the bend corner. The acquisition frequency is 80 Hz and the reconstruction resolution is 20 × 20 × 20 for the 3D reconstructed images of all tests. The 3-D ECVT straight

sensor images the riser flow between 415 and 515 mm above the distributor. The horizontal and vertical dimensions of a voxel in the riser sensor are 2.5 and 5.0 mm, respectively. Both the axial and vertical dimensions of a voxel in the bend senor are 5.0 mm.

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RESULTS AND DISCUSSION Solids Holdup Distribution in the Riser. A cylindrical sensor is used for imaging real-time 3D gas−solid flows in the riser of the CFB. The volumetric solids holdup distribution in the sensor section of the riser at varying superficial gas velocity and solids flux is obtained. The instantaneous 3D dynamic gas−solid flow structures in the riser are analyzed based on quantitative ECVT images. Figure 4 shows the time-averaged solids holdup distribution in the test region of the riser with

Figure 9. Configuration of the slices for the plots of the tomographic images in the bend: (a) vertical slices; (b) horizontal slices.

Figure 12. Time-averaged solids holdup distribution in the axial plane of the bend.

Figure 10. Solids holdup distribution in the bend of the CFB riser at Ug = 1.36 m/s and Gs = 21.2 kg/(m2 s): (a) vertical slices; (b) horizontal slices.

Figure 11. Solids holdup distribution in the bend of the CFB riser at Ug = 1.16 m/s and Gs = 21.2 kg/(m2 s): (a) vertical slices; (b) horizontal slices. 10972

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average volume solids holdup decreases with Ug. The core− annulus−wall structure at the bottom of a 0.1 mm ID CFB riser was observed using two-dimensional electrical capacitance tomography.41 A symmetric core−annulus structure with a low solids holdup in the core area and a high solids holdup in the annulus area in the riser is observed. The thickness of the annulus and solids holdup in the annulus near the wall decrease with Ug. Figure 6 shows fluctuations of the volume averaged solids holdup in the riser at Gs = 21.6 kg/(m2 s). Figure 7 shows the standard deviation of the volume solids holdup fluctuation in the riser at Gs = 21.6 kg/(m2 s), which is consistent with observations by 2D ECT.42 The standard deviation of the volume solids holdup fluctuation in the riser decreases with superficial gas velocity. Figure 8 shows radial profiles of the time-averaged solids holdup in the riser at Gs = 21.6 kg/(m2 s). The core−annulus profile can be observed quantitatively. Solids Holdup Distribution in the Bend. The bendsensor is used for imaging real-time 3D gas−solid flows at the exit region of the CFB riser. The volumetric solids holdup distribution in the exit region of the CFB riser at varying superficial gas velocity is probed. The 3D solids holdup distributions in the bend of the riser are illustrated by slices in the volume image cut through the bend vertically and horizontally. The configurations of the vertical and horizontal slices are given in Figure 9. The six vertical slices in Figures 11 and 12 correspond to slices located 1, 2.5, 4, 6, 7.5, and 9 cm from the outer wall of the riser. As to horizontal cuts, they correspond to 4.5, 5, 5.5, and 6 cm from the bottom of the exit section. The exit section is defined as 10 cm from the top left corner of the riser in both the vertical and horizontal direction. Figure 10 shows the solids holdup distribution in the bend of the riser with Ug of 1.36 m/s and Gs of 21.2 kg/(m2 s). The images indicate that a core−annulus flow structure is formed in both the vertical and horizontal parts of the bend. The solids holdup in the core region is relatively low compared to that in the annulus region. The annulus structure is noncentrosymmetric in the horizontal part of the bend. The solids holdup in the annulus near the top wall area in the bend is higher than that in other locations of the annulus. The asymmetry is due to the following reasons: (1) back mixing and reflection of solids

superficial gas velocity, Ug, from 0.97 to 1.94 m/s and a solids flux, Gs, of 21.6 kg/m2 s within 10 s. Blue and red colors represent 0 and 0.6 for solids holdup, respectively. The subimage on the left in each image is the solids concentration distribution in the X−Z (X, Y: two horizontal directions; Z: direction of the axis of the riser) whereas the right subimage represents the solids concentration distribution at the top, middle, and bottom cross-sectional planes of the test region of the riser. Figure 5 shows the time-averaged volume solids holdup in the riser at Gs = 21.6 kg/(m2 s). The experimental results indicate that the

Figure 13. Quantitative time-averaged solids holdup distribution in the axial plane of the bend at Gs = 21.2 kg/(m2 s): (a) top wall area of the horizontal section; (b) outer wall of the vertical section; (c) inner wall of the vertical section.

Figure 14. Gas and solids flows in a 90° bend. Reprinted with permission from the work of Harris et al.29 Copyright Wiley 2003. 10973

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Figure 11 shows the 3D solids holdup distribution in the bend of the riser with Ug of 1.16 m/s and Gs of 21.2 kg/(m2 s). The comparison between Figures 11 and 12 indicates that the solids holdup near the top wall area in the bend increases with the superficial gas velocity. Figure 12 depicts the time-averaged solids holdup distribution in the 2D axial plane of the bend with Gs of 21.2 kg/(m2 s). It can be clearly seen that there is a densephase zone near the top wall area and the density increases as Ug increases. It can also be observed that there are some solids near the inner top side wall of the vertical riser. This is because the solids on the horizontal dune keep falling back to the riser introducing a dense-phase area near the inner corner. This result is consistent with the observation of Van der Meer et al.35 Figure 13 shows quantitative time-averaged solids holdup distributions near the top wall area of the horizontal section, outer wall of the vertical section, and inner wall of the vertical section of the bend with Gs of 21.2 kg/(m2 s). The experimental results in Figure 13 indicate that the solids holdup at these three locations increases with the superficial gas velocity. The mechanism of the gas and solids flows in the 90° bend is shown in Figure 14. As shown in the figure, solids move to the outside wall area from the main stream in the bend due to a high solids velocity at a high superficial gas velocity. An explanation is based on the Froude number (Fr) effects43the gravitational acceleration in the radial direction and the centrifugal acceleration (Up2/R) of a particle following a curved path in the riser exit are in balance, where Up and R are the particle velocity and mean radius of the curved path in the bend, respectively. Solids with a higher Fr, defined as Fr = Up2/(gR), would move to the outside of the bed.29 At a higher superficial gas velocity in the riser, the centrifugal acceleration increases due to high solids velocity in the bend, and more solids are separated to the outside of the bend from the main stream. Figure 15 shows radial profiles of the time-averaged solids holdup in the bend. The radial profiles of the time-averaged solids holdup in the bend indicate that solids holdup near the wall area is higher than that in the core area and solids holdup near the outer wall is higher than that in the inner wall. A “reversed-S” shape solids holdup distribution along the diagonal line is observed from Figure 15b. Solids holdup increases and then decreases from the outer corner to the center of the bend which indicates that a “relatively dilute” region is formed near the outer corner of the bend. This can be explained by the rectangular shape of this bend. The gas velocity is not completely parallel to the wall at the exit of vertical riser, so the tracks of most of the particles are not vertical but tilted to the horizontal cyclone entrance; so in the inner part of the corner, there are fewer particles.

Figure 15. Radial profiles of the time-averaged solids holdup in the bend: (a) horizontal line; (b) diagonal line; (c) vertical line.

from the upper wall of the horizontal duct; (2) solids in the bend are difficult to entrain with the gas flow due to an abrupt turn of the gas stream in the bend; (3) a zone with low gas velocities at the upper corner of the bend is formed, which creates a dense-phase area. The images also indicate that a solids “dune” is formed, at the bottom of the horizontal section of the bend. The sedimentation of solids in the horizontal duct is due to the following reasons: (1) the velocity of the main gas stream is not high enough to carry all the solids horizontally to the cyclone, and hence the sedimentation of solids; (2) after an abrupt turn in the bend, the gas moves toward the top of the horizontal duct in the bend, which forms a zone with relatively low gas flow rate at the bottom of the horizontal duct. Another observation is that the dune is not symmetric to the axis of the horizontal tube. One reason is that the cyclone will affect the inlet gas flow field, which creates a velocity difference between the two sides of the horizontal wall.

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CONCLUDING REMARKS An advanced ECVT sensor system is designed for real-time, 3D imaging of gas−solid flows in a riser and a 90° bend at the exit region of a CFB. The instantaneous 3D dynamic gas−solid flow structures in the riser and the bend are analyzed based on quantitative ECVT images. A symmetric core−annulus structure in the riser is observed. It is found that the thickness of the annulus and solids holdup in the annulus near the wall of the riser decrease with Ug. A core−annulus flow structure is formed both in the vertical and horizontal parts of the bend. The annulus structure is noncentro-symmetric in the horizontal part of the bend. The solids holdup in the annulus near the top wall area in the bend is higher than that in other locations of the 10974

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annulus. A solids “dune” is observed by ECVT at the bottom of the horizontal duct of the bend. The asymmetric dune indicates that the cyclone may affect the gas flow field in the horizontal tube. Some particles are also observed to be falling back at the edge of the dune. The solids holdup near the top wall area of the horizontal section and near the outer wall area of the vertical section is found to increase with the superficial gas velocity. The same phenomenon is observed near the inner wall of the vertical section of the bend. At a higher superficial gas velocity in the riser, the centrifugal acceleration increases due to the high solids velocity in the bend, and more solids are separated to the outside of the bend from the main stream. A reversed-S shape solids holdup distribution along the diagonal line is observed. The solids holdup increases and then decreases from the outer corner to the center of the bend, which indicates that a “relatively dilute” region is formed near the outer corner of the bend.

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(7) Andrews, A. T.; Loezos, P. N.; Sundaresan, S. Coarse-grid simulation of gas− particle flows in vertical risers. Ind. Eng. Chem. Res. 2005, 44, 6022−6037. (8) Jiradilok, V.; Gidaspow, D.; Damronglerd, S.; Koves, W. J.; Mostofi, R. Kinetic theory based CFD simulation of turbulent fluidization of FCC particles in a riser. Chem. Eng. Sci. 2006, 61, 5544−5559. (9) Almuttahar, A.; Taghipour, F. Computational fluid dynamics of high density circulating fluidized bed riser: study of modeling parameters. Powder Technol. 2008, 185, 11−23. (10) Armstrong, L. M.; Luo, K. H.; Gu, S. Two-dimensional and three-dimensional computational studies of hydrodynamics in the transition from bubbling to circulating fluidised bed. Chem. Eng. J. 2010, 160, 239−248. (11) Zhang, N.; Lu, B.; Wang, W.; Li, J. 3D CFD simulation of hydrodynamics of a 150 MWe circulating fluidized bed boiler. Chem. Eng. J. 2010, 162, 821−828. (12) Jiradilok, V.; Gidaspow, D.; Breault, R. W. Computation of gas and solid dispersion coefficients in turbulent risers and bubbling beds. Chem. Eng. Sci. 2007, 62, 3397−3409. (13) Rhodes, M. J.; Zhou, S.; Hirama, T.; Cheng, H. Effects of operating conditions on longitudinal solids mixing in a circulating fluidized bed riser. AIChE J. 1991, 37, 1450−1458. (14) Horio, M.; Grace, J. R.; Avidan, A. A.; Knowlton, T. M. Circulating fluidized beds; Blackie: London, U.K., 1997. (15) Smolders, K.; Baeyens, J. Gas fluidized beds operating at high velocities: a critical review of occurring regimes. Powder Technol. 2001, 119, 269−291. (16) Kunii, D.; Levenspiel, O. Fluidization Engineering; ButterworthHeinemann Press: Boston, 1991. (17) Schlichthaerle, P.; Werther, J. Solids mixing in the bottom zone of a circulating fluidized bed. Powder Technol. 2001, 120, 21−33. (18) Harris, A T.; Davidson, J. F.; Thorpe, R. B. The prediction of particle cluster properties in the near wall region of a vertical riser. Powder Technol. 2002, 127, 128−143. (19) Breault, R. W.; Guenther, C. P. Mass transfer in the core-annular and fast fluidization flow regimes of a CFB. Powder Technol. 2009, 190, 385−389. (20) Tang, C.; Heindel, T. J. Estimating gas holdup via pressure difference measurements in a cocurrent bubble column. Int. J. Multiphase Flow 2006, 32, 850−863. (21) Yang, G. Q.; Du, B.; Fan, L.-S. Bubble formation and dynamics in gas−liquid−solid fluidization-a review. Chem. Eng. Sci. 2007, 62, 2− 27. (22) Cheng, S.; Hirahara, D.; Tanaka, Y.; Gondai, Y.; Zhang, B.; Matsumoto, T.; Morita, K.; Fukuda, K.; Yamano, H.; Suzuki, T.; Tobita, Y. Experimental investigation of bubbling in particle beds with high solid holdup. Exp. Therm. Fluid Sci. 2011, 35, 405−415. (23) Pugsley, T. S.; Milne, B. J.; Berruti, F. An innovative nonmechanical solids feeder for high solids mass fluxes in circulating fluidized bed risers. Powder Technol. 1996, 88, 123−131. (24) Cheng, Y.; Wei, F.; Yang, G.; Jin, Y. Inlet and outlet effects on flow patterns in gas−solid risers. Powder Technol. 1998, 98, 151−156. (25) Gupta, S. K.; Berruti, F. Evaluation of the gas−solid suspension density in CFB risers with exit effects. Powder Technol. 2000, 108, 21− 31. (26) Lackermeier, U.; Werther, J. Flow phenomena in the exit zone of a circulating fluidized bed. Chem. Eng. Process 2002, 41, 771−783. (27) Kim, S. W.; Kirbas, G.; Bi, H.; Lim, C. J.; Grace, J. R. Flow behavior and regime transition in a high-density circulating fluidized bed riser. Chem. Eng. Sci. 2004, 59, 3955−3963. (28) Kim, J. S.; Tachino, R.; Tsutsumi, A. Effects of solids feeder and riser exit configuration on establishing high density circulating fluidized beds. Powder Technol. 2008, 187, 37−45. (29) Harris, A. T.; Davidson, J. F.; Thorpe, R. B. Influence of exit geometry in circulating fluidized-bed risers. AIChE J. 2003, 49, 52−64. (30) Chan, C. W.; Brems, A.; Mahmoudi, S.; Baeyens, J.; Seville, J.; Parker, D.; Leadbeater, T.; Gargiuli, J. PEPT study of particle motion for different riser exit geometries. Particuology 2010, 8, 623−630.

AUTHOR INFORMATION

Corresponding Author

*Tel.: 614-688-3262. Fax: 614-292-4935. E-mail address: fan@ chbmeng.ohio-state.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of the U.S. Department of Energy DOE/NETL under Grant no. DE-NT0005654 (Federal Project Manager: Steven Seachman) and the support of the Tech4Imaging LLC are gratefully acknowledged.

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NOTATION Fr = Froude number g = gravity acceleration(m/s2) Gs = solids flux (kg/(m2 s)) ne = number of capacitance electrodes r = distance to the axis of the tube R = radius of the tube or the radius of the curved path of a particle Ug = superficial gas velocity (m/s) Up = particle velocity (m/s)

Greek Letters

εs = solids holdup

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REFERENCES

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dx.doi.org/10.1021/ie300746q | Ind. Eng. Chem. Res. 2012, 51, 10968−10976