Solid Trajectories and Cycle Times in Spouted Beds - American

Ind. Eng. Chem. Res. 2004, 43, 3433-3438

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Solid Trajectories and Cycle Times in Spouted Beds Marı´a J. San Jose´ ,* Martin Olazar, Miguel A. Izquierdo, Sonia Alvarez, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain

A study has been made of the effect of both the geometric factors of the contactor (base angle and gas inlet diameter) and the experimental conditions (stagnant bed height, particle diameter, and gas velocity) on the trajectories of the particles in the three zones (spout, annulus, and interface) of spouted beds. The trajectories have been determined from the experimental results of the vertical component of the particle velocity measured by means of an optical fiber probe. Cycle time distributions have been calculated from the trajectories, and they have been compared with the experimental results obtained by monitoring colored particles using video-imaging treatment. Original correlations have been proposed for calculating the average cycle time from the geometric factors and experimental conditions. 1. Introduction Spouted beds are the focus of renewed attention for physical and chemical operations that require handling of solids for which fluidized beds have problems because of their great size, irregular texture, or sticky nature, as is the case of combustion of vegetable biomass or bituminous coal,1,2 pyrolysis of vegetable biomass,3,4 pyrolysis of waste plastics,5,6 and catalytic polymerizations.7,8 The good performance for conventional applications (drying, granulation, and coating) and for those of a more recent nature is due to the cyclic movement of particles and to the versatility in the properties related to solid circulation (such as the time required by a particle to complete a cycle and the fractions of this time spent in the spout and the annular zones). The aim to reach in the design of spouted beds for their application in operations or processes is the establishment of the optimum trajectories by acting on the experimental conditions (geometric factors of the contactor-particle system and gas velocity). Consequently, knowledge of particle circulation and of the effect of the process conditions on it is of great relevance in the application of spouted beds. Several authors have experimentally studied the trajectories of the solid,9-12 and others have proposed theoretical models for predicting these trajectories in the annular zone.12-15 From the results obtained in the studies on cycle times, the importance of experimental conditions is noteworthy. Thus, the contactor base angle,9,16 particle diameter,17,18 stagnant bed height, and gas inlet19 all influence the cycle time. Roy et al.20 determined that the average cycle time is independent of the bed level. In this paper, particle trajectories have been determined by means of the results obtained in a previous paper in which longitudinal and radial profiles of the vertical and horizontal components of the particle velocity were determined in the three zones of the spouted bed: annulus, spout, and fountain.21 This previous study was extended to a wide range of geometric factors of the contactor (base angle and gas inlet diameter) and of experimental conditions (stagnant bed * To whom correspondence should be addressed. Tel.: 3494-6015362. Fax: 34-94-6013500. E-mail: [email protected].

height, particle diameter, and gas velocity). From the trajectories, cycle time distributions have been calculated, and they have been compared with the experimental results obtained in this paper for different values of geometric factors and experimental conditions. The main contribution of this paper is the extension of the study of solid trajectories to the three zones (spout, annulus, and fountain) of the spouted bed, whereas previous studies correspond to the trajectories in the annulus.12-15 2. Experimental Section Five contactors of poly(methyl methacrylate) have been used, which have the following dimensions (geometry defined in Figure 1): column diameter Dc, 0.152 m; base diameter Di, 0.063 m (except for γb ) 180°, where Di ) Do); height of the conical section Hc, 0.168, 0.108, 0.078, 0.026, and 0 m; angle of the contactor base γb, 30, 45, 60, 120, and 180°; gas inlet diameter Do, 0.03, 0.04, and 0.05 m; stagnant bed height Ho, between 0.05 and 0.35 m. The solids studied are glass spheres (density ) 2420 kg m-3) of particle diameters 2, 3, 4, and 5 mm. Three air velocities have been used: 1.02ums, 1.2ums and 1.3ums. The minimum spouting velocity, ums, has been calculated using the equation of Mathur and Gishler.22 In a previous paper, the validity of this equation for the calculation of ums for solids of different density and shape factors has been proven in a wide range of experimental conditions (base angle, air inlet diameter, stagnant bed height, particle size, and air velocity at the inlet). The average relative error of the equation of Mathur and Gishler for predicting the values corresponding to glass spheres is 4%.23 The values of the velocity vector in the spout, annulus, and fountain have been determined from the experimental results of the vertical component of the particle velocity obtained by means of an optical fiber probe. These values and the technique used have been described in detail in a previous paper.21 The distribution of cycle times has been measured by monitoring a colored particle using an image treatment system that is composed of a camera, a video recorder, a monitor, and the computer support needed for treatment of the data obtained. The camera used is a Hitachi

10.1021/ie030668x CCC: $27.50 © 2004 American Chemical Society Published on Web 05/26/2004

3434 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004

Figure 2. Particle flow patterns in the spout and annular zones. Experimental conditions: γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums.

have been calculated for n streamtubes defined by dividing the upper surface of each zone into n annuli with the same mass flow of solid. The Stokes stream functions for each tube, ψj, are solved in cylindrical coordinates:

For the horizontal component of velocity: (1 - )Fs 1 ∂Ψj υr ) QsH r ∂z

(1)

For the vertical component of velocity: (1 - )Fs 1 ∂Ψj υz ) QsH r ∂r

(2)

Figure 1. Geometric factors of the contactor.

With the following boundary conditions: color VM-S7200E, of eight luxes, with a horizontal resolution of 625 lines, and provided with automated adjustment for shutter control and focusing. For high particle velocities, manual control was carried out in order to avoid tail filming and loss of definition. The VCR is a JVC BR-S600E super VHS with a horizontal resolution of 400 lines and with six heads, allowing for good freeze-frame images. It is provided with several playback speeds in slow motion (from 1/6 down to 1/30 of the normal speed). The time range between two successive frames is 0.04 s. The monitor used is a JVC color VM-R150E, with a horizontal resolution of 500 lines and provided with a Elographics E274 tactile screen. Communication with the computer is carried out by means of a PCL-725 card of opto-insulated inlet and eight relay outlets. The cycle time, namely, the time spent by a particle in traveling the annulus and spout and returning to the fountain, has been determined by freezing the image where the particle is seen again in the fountain after one cycle. The cycle time is calculated by counting the frames between two consecutive appearances of the particle in the fountain and taking into account that the time between two frames is 1/25 s. 3. Results 3.1. Trajectories in the Annulus and Spout. The trajectories of the particles in the annulus and spout

At the bottom of the bed (z ) 0, ro < r < ri), at the axis (z ) H + Hf, r ) 0), and at the wall (r ) rw, 0 < z < H): ψj ) 0

(3)

At the interface between the spout and the annulus:

∂Ψj )0 ∂r

(4)

Equations 1-4 are solved by means of a program written in PASCAL and using the experimental results of the vertical component of the particle velocity and the results calculated for the horizontal component (by solving the mass balances) at different radial and longitudinal positions in the bed. These results have been obtained in a previous paper at every 2 cm in the longitudinal direction and 1 cm in the radial direction.21 In this previous paper, the calculation of the horizontal velocity components and velocity vectors is explained in detail. The results of the trajectories (streamlines) and of the streamtubes between these lines in the spout and annular zones are shown in Figure 2, for an experimental system taken as an example. In the same figure, the velocity vector is also drawn. Although five streamtubes are shown in the figure, for a better visualization of the

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results, the program allows for obtaining any number of trajectories and streamtubes. Furthermore, for a better visualization, the scale of the moduli of the velocity vector in the annulus is 25 times greater than that of the spout. Moreover, in Figure 2, the borders of the spout are shown, which have been determined in a previous paper by means of an optical fiber probe.24 When Figure 2 (for γb ) 45°) is compared with that corresponding to other base angles, the importance of this angle is noteworthy. Its increase leads to an important rise in the particle velocity in the two zones of the bed. It is observed that the trajectories are almost straight lines in the cylindrical section of the bed, either when it is a small fraction of the total height, as in Figure 2 (for γb ) 45°), or when it is almost the entire bed (for γb ) 120°). Nevertheless, the incorporation of particles from the spout into the annular zone occurs, in all cases, at every longitudinal position of the annulus-spout interface. In Figure 2, it is observed that the solid descends along the annular zone following streamlines that approach the spout-annulus interface. Furthermore, the particles that descend through the annular zone following a short trajectory (near the interface) generally follow the same trend in the spout, where they follow a streamtube near the interface. In general, all of the particles in the upper half of the spout follow ascending trajectories that curve away slightly from the axis. The particles that describe a longer trajectory in the annular zone and enter the spout at the lower part of the bed (lower than the neck of the spout) follow a trajectory that approaches the axis. The experimental results of the particle velocity show that νz ) 0 when the solid crosses the spout at any value of z. The radial position for which this value is adopted corresponds to the spout-annulus interface. The base angle has a significant effect on the trajectories of the particles in the spout. For the contactor of base angle γb ) 120°, particles entering the spout in a wide stretch of the lower part of the bed are converging toward the axis. For the contactor of base angle γb ) 45° (Figure 2), this trend is followed only by particles entering the spout below the neck. This result is a consequence of the effect of the base angle on the position of the spout neck, which is located at a higher level when the base angle is greater and no neck is observed for γb ) 120°. The effect of increasing the gas velocity is similar to that of increasing the base angle because it also provokes a displacement of the spout neck toward higher levels in the bed. Thus, for a gas velocity of u ) 1.3ums, particles enter the spout in the lower part of the bed and converge toward the axis of the spout along a wider length than that in Figure 2 corresponding to u ) 1.02ums. It is also observed for u ) 1.3ums that particles ascending in the spout are moving away from the axis to a lesser extent than when the gas velocity is lower (Figure 2). 3.2. Trajectories in the Fountain. Kutluoglu et al. studied the role of the fountain in the distribution of particles on the upper surface of the annulus, and they remark the importance of this distribution in the trajectories of the particles in the whole bed and in the segregation when particles of different size are handled.25 Two zones are distinguished in the fountain:26 the core, where particles from the spout ascend, and the periphery, where the particles descend and fall onto the upper

Figure 3. Particle flow patterns in the fountain. Experimental conditions: γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums.

surface of the annular zone. The trajectories in the fountain have been calculated by solving eqs 1 and 2 together with the corresponding boundary conditions, which are as follows: eq 3 on the surface of the fountain (H < z < H + Hf, r ) rf), at the axis (H < z < H + Hf, r ) 0), and on the surface of the annular zone (z ) H, rs < r < rw); eq 4 at the core-periphery interface in the fountain (H < z < H + Hf, r ) rn). In Figure 3, the trajectories and the velocity vectors in the fountain are plotted for the same experimental system as that in Figure 2. It is observed that the particles follow the same trend in the core of the fountain as that when leaving the spout (moving away from the axis). In the particle descending zone of the fountain, the particles move away from the core, and this trend is more relevant for radial positions further away from the axis. When the results corresponding to different experimental conditions are compared, it is observed that, similarly to that commented on above for the annular and spout zones, the base angle and gas velocity have great influence on the velocity of the particles and on the height and shape of the fountain. Nevertheless, in contrast to the other zones, the importance of velocity in the fountain is greater than that of the base angle. Furthermore, when the gas velocity is increased from u ) 1.02ums (Figure 3) to u ) 1.3ums, both the height and the amplitude of the fountain increase significantly, so that for u ) 1.3ums the periphery or solid descending zone occupies all of the upper surface of the annular zone. When the angle is increased to γb ) 120°, the fountain height slightly decreases compared to that when γb ) 45° (Figure 3), whereas the effect on the amplitude of the fountain on the upper surface of the annular zone is greater, which means that particles fall onto a small region of the annular zone. Under certain experimental conditions (generally when u ) 1.02ums), the particle descent zone of the fountain does not fully cover the upper surface of the annular zone. In these situations, to calculate the trajectories and streamtubes in the annular zone and fountain, the existence of an interface between the fountain periphery and the annular zone must be taken into account. This interface, with an important radial component of the particle velocity toward the wall, has been delimited by means of an optical fiber probe (and its thickness is between 1 and 3 cm).27 Each streamtube in the interface is established by joining the streamtubes of the fountain and annular zones. As mentioned above, the same number of tubes has been established in the two zones (nine in Figure 4) and the same flow rate circulates through all of them (total flow rate/9 in Figure 4). Figure 4 shows the trajectories and streamlines in the whole bed, including this interface. The results correspond to the experimental system of Figures 2 and 3. 3.3. Cycle Time Frequency. The frequency of the cycles described by a colored particle has been deter-

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Figure 4. Particle flow patterns in the whole bed. Experimental conditions: γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums.

mined in all of the experimental systems, by means of equipment for the acquisition and treatment of video images described in the Experimental Section. The number of cycles considered in each system is always above 1000. In Figure 5, the histograms shown correspond to the experimental results of the cycle time frequency (in percent) determined for a given operation time. The results correspond to systems that differ in one of the geometric parameters of the contactor (angle and gas inlet diameter) or in one of the experimental conditions (stagnant bed height, particle diameter, and gas velocity) Graphs a-f in Figure 5 show that there is a major dispersion of cycle times for time values above those corresponding to the maximum frequency. This result is a consequence of the wide distribution of cycle times for the particles that descend in the annular zone following positions near the contactor wall and in the area below the level of the spout neck. It is noteworthy that the percentage of cycles of short duration is small, which is evidence of the efficiency of the fountain for the radial distribution of particles in the annular zone and of the fact that the particles only occasionally enter the spout in its upper part. The value of the time corresponding to the maxima of the graphs in Figure 5 is approximately the cycle time of the particles that circulate following an intermediate position in the annular zone and enter the spout at its neck. When the graphs in Figure 5 are compared, it may be concluded that the conditions that mostly affect the cycle time distribution are the geometric factors of the contactor (base angle and gas inlet diameter). It is observed that the maximum displaces to longer times as the contactor angle, the inlet diameter, and the stagnant bed height are increased. On the other hand, the maximum displaces to shorter times as the particle diameter and the gas velocity over that of minimum spouting are increased. A program has been developed in PASCAL language for calculating the cycle times and their frequencies from the aforementioned trajectories. The initial data of the program are the experimental results obtained

in previous papers and those that have been calculated by means of correlations. Thus, the input data are the geometry and characteristics of the contactor-particle system, the spout shape,24 the fountain geometry,26 and the experimental results of the vertical component of the velocity in the annular zone and at the axis.21 The calculation steps are as follows: 1. First, the vertical component of the velocity in the spout zone and the map of voidage in the bed are calculated. The correlations for these calculations have already been published.21,28 2. The horizontal component of the particle velocity at any position in the bed is determined by solving the mass conservation equations in differential volume elements.21 3. The stream function is calculated by solving eqs 1 and 2 expressed in terms of the solid velocity. 4. The frequency for each streamtube is calculated from the distribution of the solid flow rate into the annuli on the upper surface of the annular zone. 5. Because the evolution of the particle velocity along each trajectory is known, the cycle time corresponding to each streamtube is calculated. The results calculated using the program are the lines plotted in the graphs of Figure 5. The satisfactory fitting between the calculated and experimental results of cycle time is evidence that the results provided by different techniques are coherent. This applies to particle monitoring by filming (for the experimental measurement of cycle times) and to an optical fiber probe for obtaining bed properties (particle velocity and voidage) used in the calculation of trajectories. 3.4. Average Cycle Time. This average has been calculated from the distribution of cycle times:29 n

tc )

tifi∆ti ∑ i)1

(5)

fi∆ti ∑ i)1

The results of tc show that the experimental conditions of major influence are the geometric factors of the contactor. Thus, as the base angle is increased from 30° to 120°, the average cycle time increases from 3.68 to 7.64 s, and as the contactor inlet diameter is increased from 0.03 to 0.05 m, the average cycle time increases from 3.09 to 5.36 s. The results for all of the experimental systems have been fitted (with a regression coefficient of r2 ) 0.97 and a maximum relative error of 5%) to the following equations expressed in terms of the dimensionless moduli that are commonly used to characterize the hydrodynamic properties in spouted beds:

For γb e 45°: tc ) 1.13

() () ( ) () dp Dc

-0.68

Do Dc

1.70

u ums

-1.14

H Dc

-0.56

γb-0.29 (6)

For γb > 45°:

() () ( ) ()

tc ) 1.51

dp Dc

-0.68

Do Dc

1.70

u ums

-1.14

H Dc

-0.56

γb0.91 (7)

4. Conclusions Particle trajectories have been calculated in the spout, annulus, and fountain of spouted beds by using rela-

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Figure 5. Cycle time frequency. Histograms: experimental results. Lines: calculated from the trajectories. Experimental conditions: (graph a) γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums; (graph b) γb ) 120°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums; (graph c) γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.30ums; (graph d) γb ) 45°, Do ) 0.04 m, Ho ) 0.20 m, dp ) 4 mm, u ) 1.02ums; (graph e) γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, dp ) 3 mm, u ) 1.02ums; (graph f) γb ) 45°, Do ) 0.03 m, Ho ) 0.25 m, dp ) 4 mm, u ) 1.02ums.

tively basic experimental data, such as those of the vertical component of the particle velocity. The results of cycle times calculated from these trajectories are in agreement with the experimental results, which is evidence of the validity of the correlations used in the calculation of magnitudes: the voidage map, the vertical component of the particle velocity in the spout, and the horizontal component of the particle velocity in the annulus, spout, and fountain. This calculation has been possible because of the precise knowledge of the spout and fountain geometry for different geometric factors of the contactor-particle system and other operating conditions, such as the gas velocity over that of minimum spouting. Particle ascending trajectories in the spout depend on the longitudinal position of particle incorporation from the annulus into the spout, so that cycles are shorter (and the trajectories are nearer to the spoutannulus interface) as the level of particle incorporation

becomes higher. Particles move toward the axis of the contactor as they rise in the spout, except near the fountain, where they move toward the outside. Radial circulation toward the wall of the particles that fall from the fountain periphery onto the surface of the annular zone plays an important role in the particle descending trajectories in the annular zone. The correlations determined for calculating the average cycle time of the particles are evidence of the versatility of the design of spouted beds. Thus, increases in the contactor base angle and in the gas inlet diameter contribute to significantly increasing cycle times. Although this study rests on a wide experimental base, it will be interesting to extend it to contactors of larger diameter than that used (0.152 m) and to solids of different density. This latter aspect is especially interesting because new applications of spouted beds involve the treatment of solids of very diverse density

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and because the density has a relevant effect on hydrodynamics. Acknowledgment This work was carried out with the financial support of the University of the Basque Country (Project 9/UPV 00069.310-13607/2001) and of the Ministry of Science and Technology of the Spanish Government (Project PPQ2001-0780). Notation Dc, Di, Do ) diameter of the column, of the contactor base, and of the inlet, respectively, m dp ) particle diameter, m fi ) cycle time frequency H, Hf, Ho ) height of the developed bed, of the fountain, and of the stagnant bed, respectively, m QsH ) solid flow rate on the surface of the spout, kg s-1 r, z ) cylindrical coordinates, m ri, ro ) radius of the contactor base and of the gas inlet, m rf, rn, rw ) radius of the fountain, of the core, and of the contactor wall at any level z, m tc, ti ) average cycle time and cycle time corresponding to the frequency fi, s u, ums ) gas velocity and minimum spouting velocity, m s-1 Greek Letters  ) bed voidage Ψj ) Stokes stream function for streamline j γb ) contactor included base angle, rad Fs ) density of the solid, kg m-3 υr, υz ) horizontal and vertical components of the particle velocity, m s-1

Literature Cited (1) Lim, C. J.; Watkinson, A. P.; Khoe, G. K.; Low, S.; Epstein, N.; Grace, J. R. Spouted, Fluidized and Spout-Fluid Bed Combustion of Bituminous Coals. Fuel 1988, 67, 1211-1217. (2) Wang, Z.; Huang, H.; Li, H.; Wu, C.; Chen, Y.; Li, B. Pyrolysis and Combustion of Refuse-Derived Fuels in a SpoutingMoving Bed Reactor. Energy Fuels 2002, 16, 136-143. (3) Aguado, R.; Olazar, M.; San Jose´, M. J.; Aguirre, G.; Bilbao, J. Pyrolysis of Sawdust in a Conical Spouted Bed Reactor. Yields and Product Composition. Ind. Eng. Chem. Res. 2000, 39, 19251933. (4) Olazar, M.; Aguado, R.; Barona, A.; Bilbao, J. Pyrolysis of Sawdust in a Conical Spouted Bed Reactor with a HZSM-5 Catalyst. AIChE J. 2000, 46, 1025-1033. (5) Aguado, R.; Olazar, M.; Gaisa´n, B.; Prieto, R.; Bilbao, J. Kinetic Study of Polyolefins Pyrolysis in a Conical Spouted Bed Reactor. Ind. Eng. Chem. Res. 2002, 41, 4559-4566. (6) Aguado, R.; Olazar, M.; San Jose´, M. J.; Gaisa´n, B.; Bilbao, J. Wax Formation in the Pyrolysis of Polyolefins in a Conical Spouted Bed Reactor. Energy Fuels 2002, 16, 1429-1437. (7) Olazar, M.; San Jose´, M. J.; Zabala, G.; Bilbao, J. A New Reactor in Jet Spouted Bed Regime for Catalytic Polymerizations. Chem. Eng. Sci. 1994, 49, 4579-4588. (8) Olazar, M.; Arandes, J. M.; Zabala, G.; Aguayo, A. T.; Bilbao, J. Design and Simulation of a Catalytic Polymerization Reactor

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Received for review August 14, 2003 Revised manuscript received January 26, 2004 Accepted April 19, 2004 IE030668X