Ind. Eng. Chem. Res. 2001, 40, 4983-4989
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GENERAL RESEARCH Study on the Hydrodynamics of a Spouting-Moving Bed Zhiqi Wang, Ping Chen, Haibin Li, Chuangzhi Wu, and Yong Chen* Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, 510070 P.R. China
Baoqing Li State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan Shanxi, 030001 P.R. China
Experiments were carried out in a spouted bed with auxiliary gas introduced horizontally. Auxiliary gas introduced horizontally has an obvious effect on the minimum spouting gas velocity; the minimum spouting gas velocity decreases with increasing auxiliary gas velocity. An empirical equation for the minimum spouting velocity is modified to fit the experimental data. With an increase in the proportion of the auxiliary gas for a fixed total gas flow, the fountain height decreases, but the relative voidage in the spout decreases, which means that more particles are circulated. Comparatively, the spouting gas has a distinct effect on the particle velocity in the spouting region, but the auxiliary gas velocity affects the particle velocity in the annular region markedly. The radial profiles of relative voidage and particle velocity at different axial heights are also studied in detail. Introduction The production of municipal solid waste (MSW) and its accumulation have become important global environmental issues. Combustion, pyrolysis, or gasification offer some benefits over conventional landfill: energy can be recovered, and the quantity of waste can be reduced greatly. Studies1-4 indicated that emission of poisonous gas and heavy metals might be less by pyrolysis or gasification (with gas combustion) than by direct combustion. Refuse-derived fuels (RDF), made from combustible components of MSW, are suitable for pyrolysis or gasification for their following advantages: (1) They have a high heating value. (2) They have identical density and similar size. (3) They are easy to transport. (4) By addition of additives during the molding process, sulfur and chlorine can be removed during the thermal treatment process. A spouted bed is a kind of high-performance reactor for fluid-solid particles (dp > 1 mm) reaction. This technology has been applied to a wide variety of chemical processes such as gasification, combustion, and pyrolysis.5-7 A spout-fluid bed is a hybrid fluid-solid contacting system in which a spouting gas is introduced upward through an orifice located in the center of the bottom, accompanied by auxiliary gas from a surrounding distributor (flat or conical base). Therefore, it has the characteristics of both a spouted bed and a fluidized bed and is suitable for handling agglomerating or sticky solids. A study8 showed that the minimum operation fluid flow rate of a spouted bed is much less than that of a spout-fluid bed. Considering that a low oxygen level (less air volume) is expected for pyrolysis or * Corresponding author. Phone: 86-020-87759561. Fax: 86020-87608586. E-mail:
[email protected].
gasification of RDF, a spouted bed is preferred as the reactor. Moreover, because of the bad flowability of RDF, horizontal auxiliary gas is introduced to improve the movement of RDF particles in the spouted bed, just like a spout-fluid bed, but with no fluidization in the annulus. Thus, we call this kind of reactor a “spoutingmoving bed”. Many investigators8-12 have studied the hydrodynamic parameters of spout-fluid beds, but the introduction direction of the auxiliary gas was mostly focused on the vertical or right angle to the surface of the distributors. There is little information about a horizontally introduced auxiliary gas in a spouted bed. In this paper, the effect of a horizontal auxiliary gas on the minimum spouted velocity, fountain height, particle velocity, and relative voidage distribution without fluidization of the annulus is investigated. Experimental Equipment and Materials A cylindrical spouted bed made of Plexiglas is employed in this study, as shown in Figure 1. The bed is 190 mm in diameter and 1200 mm in height. At the bottom of the bed, there is a 60° cone-shaped distributor (146 mm in height), on which 72 holes (2 mm in diameter) are perforated horizontally. The distributor is made of carbon steel (15 mm in thickness). Because the conical distributor is 15 mm thick, the holes perforated on it are just like small horizontal tubes of 2 mm diameter. The spouting nozzle (21 mm in diameter) locates in the center of the distributor. Properties of the particulate materials studied in the experiments are summarized in Table 1. A Pv-4A particle velocity analyzer (developed by the Institute of Chemical Metallurgy, Chinese Academy of Sciences) is used to measure the particle velocity and
10.1021/ie000947+ CCC: $20.00 © 2001 American Chemical Society Published on Web 09/29/2001
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Figure 1. Schematic of a spouting-moving bed.
Figure 2. Schematic of reflection light signals of two channels. Table 1. Properties of Particulate Materials material
dp (mm)
Fp (kg/m3)
Fb (kg/m3)
Φ
millet sand RDF
2.5 1.45 5×8
1335 2410 836
755 1469 381
0.43 0.39 0.54
1.0 0.86 0.67
relative voidage. Holes are drilled at vertical intervals of 50 mm along the column wall, in which a fiber probe is placed at different radial and axis positions in the bed. Graduation of the probe allows for settling of the radial position in the bed accurately. An optical fiber probe consists of two channels of optical fibers; each channel is arranged parallel to many optical fibers that can emit and reflect light. When the particle passes vertically in front of the probe head, it reflects light emitted by the optical fibers, and the light reflection is collected by other optical fibers in the same channel. With the known separated distance and delayed time of the fibers’ collection of light signals between two channels as shown in Figure 2, the particle velocity can be computed. The particle velocity measured in this work is vertical velocity both in the spout and in the annulus. The cone-shaped distributor is 146 mm high where horizontal gas is introduced, and the smallest distance from the gas inlet to detect the particle velocity in the spout and the annulus is 163 mm, just above the cone distributor, so the particle in the annulus is considered to be a vertical move. In addition, if the light reflection density is defined as corresponding to a maximum voidage ( ) 1) when the probe is set in an empty bed and a minimum voidage ( ) 0) when the probe is set in a packed bed, the relative voidage of the
bed can also be calculated by the density of the light reflection of either channel. In this study, the sampling frequency is 7.8 kHz and 4086 data are collected at each position. A Pv-4A software can analyze the collected data automatically. It can optimize the data; if the data deviate largely, most data will be cut off until normal distribution is reached and the average error is less than 10%. The value of each point for the particle velocity and the relative voidage is an average value of the optimized data. The particle in the spout has upflow, and the particle in the annulus has downflow. The transition occurs at about 20-30 mm radial distance from the spout axis, where the software cannot give satisfied data of the particle velocity because the particle in this position has not only upflow but also downflow and other movement; the software cuts off all of the data. However, the density of reflection of the light is not affected at these positions for each channel, so the relative voidage can be given out. Results and Discussion Minimum Spouting Velocity. The minimum spouting velocity corresponds to the onset of spouting of particles in the spouted bed when particles start to be suspended and move upward in the spouting region. The minimum spouting velocity in conventional spouted beds has been extensively studied, and the well-known Mathur and Gishler13 correlation has been found to give an accurate prediction of experimental data in relatively deep beds with H/Dc G 1.3 as follows:14
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Ums )
( )( ) x d p Di Dc D c
2gH(Fp - F) F
1/3
(1)
al.15
Zhang et have studied the minimum spouting velocity of the aerated spouted bed with a conical bottom (auxiliary gas introduced vertically and with no fluidization in the annulus), and a dimensionless correlation based on the experimental data is given as
dpUmsF ) 1- µ 0.38 dp H 0.25 Dc Dc
() () () ( 2.54
Di Dc
0.33
)
0.75
F(Fp - F)gDc3) µ2
-0.54
Table 2. Comparison of Experimental Data and Calculated Values for Ums material sand
10 wt % RDF + 90 wt % sand
Rea
(2)
where 13 e Rea ) dpUaF/µ e 72. Aeration gas was not included in Ums. The minimum spouting velocity is measured by observation in this study. The point where the spout collapses and the bed pressure drop increases suddenly while the gas velocity is reduced corresponds to the minimum spouting velocity. The results of the minimum spouting velocity of different particles and their mixtures in the present experiment are displayed in Table 2. The values calculated by eq 1 (no auxiliary gas) and eq 2 are also listed. Because of RDF’s cylindrical shape, an effective spherical diameter (dp ) dpeΦ, where dpe is the equivalent sphere volume diameter) is employed. For a binary mixture of particles such as sand and RDF, the voidage is employed as the sand voidage because the RDF particles are immerged in the sand completely, and the mean diameter is used to determine the average particle size of the mixture where
∑(xi/dpi)
dp ) 1/
15 wt % RDF + 85 wt % sand
20 wt % RDF + 80 wt % sand
millet
(3)
The density of the mixture is employed as follows:
Fp )
∑xiFpi
(4)
This shows that the values calculated by eq 2 are much larger than the experimental data as shown in Table 2. Because of the absence of a correlation to predict the experimental results for Ums within a fair accuracy, the values of Ums obtained in the present experiment are correlated empirically over the shown ranges of Table 2. The following modification is made:
dpUmsF ) 1- µ 0.38 dp H 0.25 Dc Dc
() () () ( 2.54
Di Dc
0.33
)
F(Fp - F)gDc3) 2
µ
0.75
Rea-0.6 (5)
where 13 E Rea E 82. The modification of eq 2 probably is caused by different directions of auxiliary gas introduction. The values of Ums calculated by eq 5 are also shown in Table 2. The values calculated by a modified equation can better fit the experimental data than those of eq 2. As shown in Table 2, horizontal auxiliary gas has an obvious effect on the minimum spouting gas velocity; the minimum spouting gas velocity decreases with increasing auxiliary gas velocity. Spouting gas would be prevented from leaking into the annulus by the
a
Ums (m/s) eq 2 eq 5
H (mm)
Ua (m/s)
Ums(exp) (m/s)
200 200 200 200 200 200 200 200 200
0.000 0.196 0.245 0.294 0.343 0.392 0.441 0.490 0.000
0.412 0.358 0.333 0.314 0.294 0.274 0.253 0.235 0.353
0.352a 0.462 0.409 0.371 0.341 0.317 0.298 0.282 0.312a
200 200 200 200 200 200 200 200
0.196 0.245 0.294 0.343 0.392 0.441 0.490 0.000
0.299 0.279 0.270 0.260 0.245 0.230 0.216 0.392
0.441 0.390 0.354 0.326 0.303 0.285 0.269 0.310a
0.369 0.322 0.289 0.264 0.244 0.226 0.213
200 200 200 200 200 200 200 200
0.196 0.245 0.294 0.343 0.392 0.441 0.490 0.000
0.333 0.319 0.304 0.279 0.265 0.245 0.216 0.421
0.434 0.386 0.349 0.321 0.299 0.281 0.265 0.316a
0.363 0.317 0.285 0.259 0.240 0.223 0.209
200 200 200 200 200 200 200 300 300 300 300 300 300 300 300
0.196 0.245 0.294 0.343 0.392 0.441 0.490 0.000 0.196 0.245 0.294 0.343 0.392 0.441 0.490
0.363 0.343 0.314 0.299 0.279 0.270 0.265 0.588 0.520 0.490 0.451 0.421 0.387 0.363 0.343
0.432 0.383 0.347 0.319 0.297 0.278 0.263 0.572a 0.605 0.536 0.440 0.447 0.416 0.390 0.369
0.390 0.341 0.306 0.279 0.257 0.240 0.225
0.388 0.339 0.305 0.278 0.256 0.239 0.224
0.557 0.487 0.436 0.398 0.367 0.342 0.321
Calculated by eq 1.
horizontal auxiliary gas that is introduced from the conical distributor, while spouting gas flows in the conical base. However, the total minimum spouting gas velocity Umt (Umt ) Ums + Ua) is still higher than the minimum spouting velocity without auxiliary gas (Ums). From Table 2, we can also find that the results calculated by eq 1 for the first four materials without auxiliary gas do not fit the experimental data well but do fit the millet well. Reference 14 indicates that eq 1 applies only for H/Dc g 1.3, so the result calculated by eq 1 fits experimental data well only for the millet (H/ Dc ) 1.6) without auxiliary gas, but there is a large deviation for the first four materials in Table 2 (H/Dc ) 1.03). Fountain Heights. From a design point of view, it is important to know the height of the fountain in order to determine the overall height of the column required. Fountain heights are determined for the spouted bed with horizontal auxiliary gas by measuring the distance from the annular surface to the top of the fountain. The fountain heights at different spouting gas velocities with different auxiliary gas velocities are shown in Table 3. The fountain height increases with increasing spouting gas velocity whether the auxiliary gas is
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Figure 3. Radial profile of the relative voidage at different Us: millet, H ) 335 mm, Ua ) 0.19 m/s, Z ) 313 mm.
Figure 4. Radial profile of the relative voidage at different Ua: millet, H ) 335 mm, Us ) 0.59 m/s, Z ) 313 mm. Table 3. Effect of Auxiliary Gas and Spouting Gas on the Fountain Height (Bed Material: Millet; Bed Height H ) 300 mm) Ua ) 0 m/s
Ua ) 0.196 m/s
Ua ) 0.294 m/s
Ua ) 0.392 m/s
Us (m/s)
HF (mm)
Us (m/s)
HF (mm)
Us (m/s)
HF (mm)
Us (m/s)
HF (mm)
0.627 0.667 0.706 0.745 0.784 0.823
180 240 350 450 540 585
0.549 0.588 0.627 0.667 0.706 0.745
175 245 340 430 520 605
0.471 0.510 0.549 0.588 0.627 0.667
85 185 250 340 425 510
0.431 0.471 0.510 0.549 0.588 0.627
110 185 255 345 435 520
introduced or not. When the total gas velocity is kept at a constant value, the fountain height decreases as the auxiliary gas velocity is increased. Sutanto et al.9 also observed the same results when they studied the spouted bed with aeration (right angle to the conical base surface). This indicates that the spouting gas plays a dominant role for the fountain height. A lower gas velocity in the spouting region results in a lower fountain height. Voidage Distribution. Figures 3 and 4 show the effects of the spouting gas velocity and auxiliary gas velocity on the radial profiles of the relative voidage, respectively. There is a denser region in the relative voidage profiles at the interface of the annular and spouting regions. He et al.16 have also found this denser region in a spouted bed. They proposed that this was probably caused by the forces acting on the region, such as drag due to gas cross-flow, the shear stress caused by gas and upward-moving particles in the spout, and
Figure 5. Radial profile of the relative voidage at different Z: millet, H ) 335 mm, Us ) 0.59 m/s, Ua ) 0.19 m/s.
shear stress due to downward-moving particles in the annulus. The relative voidage in the spouting region increased with an increase in the spouting gas velocity or auxiliary gas velocity, which corresponds to the result of He et al.16 However, the spouting and auxiliary gas velocities have little effect on the annulus relative voidage, and this result is not similar to the conclusion of He et al.16 They found that the relative voidage in the annulus increased with an increase in the spouting gas velocity. There is a slight decreasing tendency with increasing spouting or auxiliary gas velocity, as shown in Figures 3 and 4, though it is not quite distinct. According to Epstein’s17 conclusion that increasing the spouting gas velocity actually decreases the net gas flow through the annulus, the result may be understandable in a manner. Because auxiliary gas is horizontally introduced, it is not easy to leak much gas into the annulus when increasing the auxiliary gas velocity, and it is perhaps easy for it to flow out into the spout. Other authors18 had also found that increasing spouting velocity in a jet-spouted bed had little effect on the annulus relative voidage. In a word, the effects of spouting gas velocity and auxiliary gas velocity on the annulus relative voidage are not considerable. The idea may be disputed and the results may be bewildering for most of people; therefore, gas flow in the annulus needs further accurate and detailed study. From Figures 3 and 4, we can also find that the relative voidage in the spouting region decreases as the auxiliary gas flow increased when the total gas flow is fixed, which means a greater concentration of the particles in the spouting region. This indicates that the particle mass circulation rate increases with auxiliary gas horizontal introduction. Figure 5 represents the axial profile of the bed relative voidage. Figure 5 shows that the relative voidage in the spouting region decreases as the axial distance from the inlet increases, and this result is similar to other authors’ conclusions.14,16,19 Whereas the axial height has little impact on the relative voidage in the annular region, only near the level of the bed surface does the relative voidage in the annulus increase slightly. We can find that there is little effect of the static bed height on the relative voidage in both the spouting and annular regions, as shown in Figure 6. Particle Velocity. Figures 7 and 8 illustrate radial profiles of particle velocities in the spouting and annular regions at different spouting gas velocities, respectively. As expected, the particle velocity in the spouting region increases with increasing spouting gas velocity. In the
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Figure 6. Radial profile of the relative voidage at different H: millet, Z ) 163 mm, Us ) 0.59 m/s, Ua ) 0.19 m/s.
Figure 9. Radial profile of Up in the spouting region at different Ua: millet, H ) 335 mm, Us ) 0.59 m/s, Z ) 313 mm.
Figure 7. Radial profile of Up in the spouting region at different Us: millet, H ) 335 mm, Ua ) 0.19 m/s, Z ) 313 mm.
Figure 10. Radial profile of Up in the annular region at different Ua: millet, H ) 335 mm, Us ) 0.59 m/s, Z ) 313 mm.
Figure 8. Radial profile of Up in the annular region at different Us: millet, H ) 335 mm, Ua ) 0.19 m/s, Z ) 313 mm.
annular region, however, the particle velocity does not vary markedly with increasing spouting gas velocity in this experiment. This differs slightly from the results obtained by He et al.,20 who found that the particle velocity in the annular increased with an increase in the spouting gas velocity. The difference probably arises from the fact that the particle velocity in the annulus is very slow and the variation is too little to be observed clearly in this study. The particle velocities in both the spouting region and the annular region decrease with an increase in the radial distance from the spouting axis. The experimental results support the earlier reports by He et al.20
Figures 9 and 10 show respectively the radial profiles of particle velocities in the spouting and annular regions at different auxiliary gas velocities. The particle velocity in the spouting region also increases with an increase in the auxiliary gas velocity, as shown in Figure 9. Compared with Figure 7, the extent of increasing particle velocity in the spouting region with an increase in the auxiliary gas velocity is much lower than that with an increase in the spouting gas velocity. In the annular region, the particle velocity increases with an increase in the auxiliary gas velocity visibly. From the above results, it seems that the spouting gas velocity has a distinct effect on the particle velocity in the spouting region but little effect on the particle velocity in the annular region. The auxiliary gas velocity has obvious effects on the particle velocities in both the spouting region and the annular region. Comparatively, the spouting gas velocity has more of an effect on the particle velocity in the spouting region than the auxiliary gas velocity but less of an effect on the particle velocity in the annular region than the auxiliary gas velocity. On the other hand, the auxiliary gas velocity has more of an effect on the particle velocity in the annular region than the spouting gas velocity but less of an effect on the particle velocity in the spouting region than the spouting gas velocity. Auxiliary gas is introduced horizontally in the conical base, which can accelerate the annular particle velocity moving into the spouting region. As a result, the particle velocity in the annular region increases with an increase in the auxiliary gas velocity markedly.
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Figure 11. Radial profile of Up in the spouting region at different Z: millet, H ) 335 mm, Us ) 0.59 m/s, Ua ) 0.19 m/s.
Figure 12. Radial profile of Up in the annular region at different Z: millet, H ) 335 mm, Us ) 0.59 m/s, Ua ) 0.19 m/s.
Radial profiles of the particle velocities in the spouting and annular regions at different vertical distances are given in Figures 11 and 12, respectively. In the spouting region, particles decelerate until they attain zero velocity at the top of the fountain and then fall down in the annular region. So, the particle velocity in the spouting region decreases with an increase in the vertical distance, as shown in Figure 11. As shown in Figure 12, the particle velocity in the annular region has first a decreasing tendency and then an increasing tendency with vertical height decreased from the top of the bed surface down to a level located somewhat above the conical and column junction. This result is not similar to the reports13,21 that the particle velocity in the annular region increased linearly with an increase in the vertical distance. The difference probably is due to horizontal introduction of auxiliary gas, which pushes the particles into the spouting region; therefore, the downward particles in the annulus accelerated suddenly above the conical and column junction. Effects of static bed depth on the radial profiles of the particle velocity are shown in Figures 13 and 14. From Figure 13, we can find that the static bed depth has hardly any effect on the particle velocity in the spouting region. However, a decrease of the particle velocity in the annular region with an increase of the static bed depth is found in Figure 14. The radial gradient of the particle velocity decreases with an increase in the static bed depth. Other authors22 also found that increasing the bed depth could decrease the radial gradient of the particle velocity in the annulus of a spouted bed.
Figure 13. Radial profile of Up in the spouting region at different H: millet, Us ) 0.69 m/s, Ua ) 0.19 m/s, Z ) 163 mm.
Figure 14. Radial profile of Up in the annular region at different H: millet, Us ) 0.69 m/s, Ua ) 0.19 m/s, Z ) 163 mm.
Conclusion Besides having characteristics of spouted bed and spouted-fluid bed, a spouted bed with horizontal addition of auxiliary gas results in a number of changes in some characteristics. The horizontal auxiliary gas has an obvious effect on the minimum spouting gas velocity, the minimum spouting gas velocity decreases with an increase in the horizontal auxiliary gas velocity. Equation 5 can well predict the experimental data of Ums. Umt of the spouted bed with horizontal introduction of auxiliary gas is higher than Ums of the spouted bed without auxiliary gas. With an increase in the proportion of auxiliary gas when the total gas flow is kept constant, the fountain height decreases and the relative voidage in the spout decreases, which means that more particles are circulated. It seems that the spouting velocity and auxiliary gas velocity have little effect on the relative voidage in the annulus. Auxiliary gas introduced horizontally not only affects the particle velocity in the spouting region but also markedly affects the particle velocity in the annular region. The particle velocity can be accelerated by horizontal introduction of auxiliary gas evidently. The spouting gas velocity has a distinct effect on the particle velocity in the spouting region but has little effect on the particle velocity in the annular region. Acknowledgment This work was financially supported by the National Natural Science Foundation of P.R. China (Project No.
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29876041). We acknowledge the wonderful help from Dr. H. T. Huang for his suggestion to revise the paper. Nomenclature dp ) particle diameter, m dpi ) particle diameter for each size cut, m Dc ) column diameter, m Di ) gas inlet diameter, m g ) acceleration of gravity, m/s2 H ) static bed depth, m HF ) fountain height, m xi ) weight fraction of particles Ua ) superficial gas velocity of auxiliary gas, m/s Up ) particle velocity, m/min. Us ) superficial gas velocity of the spouting gas, m/s Ums ) minimum superficial spouting velocity, m/s Umt ) total minimum superficial spouting velocity, m/s Z ) vertical distance from the gas inlet, m Greek Letters Fp ) particle density, kg/m3 Fb ) particle bulk density, kg/m3 Fpi ) particle density for each size cut, kg/m3 F ) gas density, kg/m3 ) static bed voidage Φ ) particle shape factor µ ) gas viscosity, kg‚m-1‚s-1
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(6) Arbib, H. A.; Levy, A. Combustion of low heating value fuels and wastes in the spouted bed. Can. J. Chem. Eng. 1982, 60, 528. (7) Lisboa, A. C. L.; Watkinson, A. P. Pyrolysis with partial combustion of oil shale fines in a spouted bed. Can. J. Chem. Eng. 1992, 70, 983. (8) He, Y.-L.; Lim, C. J.; Grace, J. R. Spouted bed and spoutfluid bed behavior in a column of diameter 0.91 m. Can. J. Chem. Eng. 1992, 70, 848. (9) Sutanto, W.; Epstein, N.; Grace, J. R. Hydrodynamics of spout-fluid beds. Powder Technol. 1985, 44, 205. (10) Heil, C.; Tels, M. Pressure distribution in spout-fluid bed reactors. Can. J. Chem. Eng. 1983, 63, 331. (11) Waldie, B. Separation and residence times of larger particles in a spout-fluid bed. Can. J. Chem. Eng. 1992, 70, 873. (12) Vukovic, D. V.; Hadzismajlovic, D. E.; Grabavicic, Z. B.; Garic, R. V.; Littman, H. Flow regimes for spout-fluid beds. Can. J. Chem. Eng. 1984, 62, 825. (13) Mathur, K. B.; Gishler, P. E. A technique for contacting gases with coarse solid particles. AIChE J. 1955, 1, 157. (14) Mathur, K. B.; Epstein, N. Spouted beds; Academic Press: New York, 1974. (15) Zhang, H. Q.; Xue, H. F.; Tian, Z. Y. Studies on hydrodynamics of spouted bed with aeration of annulus(II). Eng. Chem. Metall. 1993, 14, 260 (in Chinese). (16) He, Y. L.; Lim, C. J.; Grace, J. R.; Zhu, J. X.; Qin, S.-Z. Measurement of vodage profiles in spouted beds. Can. J. Chem. Eng. 1994, 72, 229. (17) Epstein, N.; Lim, D. J.; Mathur, K. B. Data and models for flow distribution and pressure drop in spouted bed. Can. J. Chem. Eng. 1978, 56, 436. (18) Uemaki, O.; Tsuji, T. Particle velocity and solids circulation rate in a jet-spouted bed. Can. J. Chem. Eng. 1992, 70, 925. (19) Grbavcic, Z. B.; Vukovic, D. V.; Zdanski, F. K.; Littman, H. Fluid flow pattern, minimum spouting velocity and pressure drop in spouted beds. Can. J. Chem. Eng. 1976, 54, 33. (20) He, Y. L.; Qin, S. Z.; Lim, C. J.; Grace, J. R. Particle velocity profiles and solid flow patterns in the spouted beds. Can. J. Chem. Eng. 1994, 72, 561. (21) Thorley, B.; Saunby, J. B.; Mathur, K. B.; Osberg, G. L. An analysis of air and solid flow in a spouted wheat bed. Can. J. Chem. Eng. 1959, 5, 184. (22) Suciu, G. C.; Patrascu, M. Particle circulation in a spouted bed. Powder Technol. 1978, 19, 109.
Received for review November 6, 2000 Accepted August 1, 2001 IE000947+
