Ind. Eng. Chem. Res. 1999, 38, 2491-2496
2491
Correlation on the Particle Entrainment Rate in Gas Fluidized Beds Jeong-Hoo Choi,*,† In-Yong Chang,† Do-Won Shun,‡ Chang-Keun Yi,‡ Jae-Ek Son,‡ and Sang-Done Kim§ Department of Chemical Engineering, Konkuk University, Seoul 143-701, Korea, Korea Institute of Energy Research, Taejeon 305-343, Korea, and Department of Chemical Engineering, KAIST, Taejeon 305-701, Korea
An empirical correlation, considering the temperature effect but no effects of interparticle forces, on the particle entrainment rate at the gas exit of the fluidized bed has been proposed on the basis of the comprehensive experimental data. The entrainment flux is considered to consist of a constant flux independent of freeboard height and another flux decreasing exponentially with freeboard height. The correlation successfully follows the measured trend where the entrainment rate increased after an initial decrease with increasing temperature and the minimum entrainment rate at a given temperature. The correlation also successfully describes the pressure effect showing that the entrainment rate increases with pressure. Introduction The effect of gas properties on the particle entrainment rate is an important area relating to analysis of the hydrodynamics and performance of gas fluidizedbed reactors. However, few studies have been carried out in this area over limited experimental ranges, as can be seen in reports by Choi et al.1,2 who have investigated the qualitative effect of temperature on the particle entrainment rate at the freeboard gas exit of a gas fluidized bed. According to their results, the particle entrainment rate increased, after an initial decrease, as the temperature increased. The minimum entrainment rate occurred at a certain temperature. At a constant gas velocity, nearly the same trend with temperature appeared for all particle sizes they considered. They explained the trend as resulting from decreasing gas density and increasing gas viscosity with neglecting the effect of interparticle forces. Over their experimental range, the variation of the particle entrainment rate with temperature was very similar to the variation of the particle size for which the terminal velocity was equal to the gas velocity under the given fluidizing conditions. They also found that correlations reported in the literature3-10 appeared inadequate to determine the temperature effect on the particle entrainment rate mentioned above. Those correlations have been obtained from experiments carried out at room temperature or in the narrow temperature range. Meanwhile, according to the recent report by Wouters and Geldart,11 the entrainment rate of fluidized catalytic cracking (FCC) particles decreased with an increase in temperature up to 400 °C. In their fluidized bed the interparticle forces seemed to be important as they mentioned. The purpose of this study is to propose a correlation on the particle entrainment rate including the temperature effect on the basis of previous experimental results. An empirical equation was developed by using * To whom correspondence should be addressed. Phone: 82-2-450-3073. Fax: 82-2-456-8347. E-mail: choijhoo@kkucc. konkuk.ac.kr. † Konkuk University. ‡ Korea Institute of Energy Research. § KAIST.
nonlinear regression from the comprehensive experimental data obtained with variations in column size, gas velocity, temperature, particle size, and density. To check the validity of the resulting equation, it was compared with previous equations and measured data. Derivation of Correlation Solid particles are ejected from the bed surface into the freeboard mainly by bubble eruption. In the freeboard region, solid particles either rise or fall, depending on the size of the particles and the gas velocity. The entrainment rate of particles has been shown to exponentially decrease along the freeboard.4,9 The mechanism of particle entrainment is so complicated that no generalized model is available yet, though extensive studies on the subject have been carried out theoretically. Therefore, empirical correlations are usually used over experimental ranges of their own in predicting the particle entrainment rate. This study also considered obtaining an empirical equation that used various dimensional or nondimensional parameters involving particle and fluid properties and operating conditions. To simplify the correlation on the particle entrainment flux, this study employed the following assumptions. (1) The entrainment flux of particles in size i (Ki*) at the freeboard gas exit consists of a cluster flux (Kih*) and a dispersed noncluster flux (Ki∞*) as suggested by Hazlett and Bergougnou.12 The trend of cluster flux with freeboard height is described as an exponential decrease. However, the dispersed noncluster flux remains constant with the freeboard height, which corresponds to the elutriation rate constant above the TDH (transport disengaging height). (2) The decay constant of the cluster flux decreasing exponentially as the freeboard height increases is linearly proportional to that of the axial solid holdup profile. (3) The particle entrainment rate is not affected by the configuration of the gas exit. Four relationships on the decay constant of the axial solid holdup profile have been proposed by Kunii and Levenspiel,13 Adanez et al.,14 Choi et al.,15 and Lei and Horio.16 To investigate the best correlation, those relationships have been compared with the data in Table 3 in the report by Lei and Horio.16 In normalized mean deviation, the correlation of Lei and Horio16 shows 0.199,
10.1021/ie980707i CCC: $18.00 © 1999 American Chemical Society Published on Web 04/30/1999
2492 Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 Table 1. Summary of Previous Studies Used for Present Correlation on Ki* particle
Fp (kg/m3)
dp (mm)
bed size (m)
Ht (m)
Umf (m/s)
U (m/s)
T (°C)
Gugnoni and George and Grace19 Choi et al.20
glass bead sand sand
2400 2630 2630
0.021∼0.102 0.030∼0.272 0.053∼0.71
0.91 i.d. 0.25 × 0.43 0.38 i.d.
8.6 3.0 9.1
sand sand
2598 2509
0.075∼0.425 0.075∼0.425
emery cast iron
3981 6158
0.075∼0.425 0.075∼0.425
0.1 i.d. 0.1 i.d. 0.1 i.d. 0.1 i.d. 0.1 i.d. 0.1 i.d.
2.25 1.97 1.97 1.97 1.97 1.97
0.152∼0.626 0.2∼1.2 0.38∼2.01 0.95∼2.44 0.81∼2.8 0.65∼2.3 1.0 1.5 0.8∼2.2 0.8∼2.2
ambient conditions 27, 162, 172 30, 45
Choi et al.17 Choi et al.1,2
0.003 0.015 0.11 0.086 0.09 0.028∼0.04 0.009∼0.015 0.054∼0.093 0.032∼0.043 0.039∼0.060
authors Zenz18
ambient conditions 20∼600 20∼500 20∼500 12∼600 12∼600
Table 2. Description of Symbols in Figure 1 range of variablesa authors
0.06 0.094 0.075 0.067 0.91 0.91 0.076 1.0 1.0 1.0 0.034∼2.06 0.5 0.5
Geldart et al.8 Wen and Chen9
Colakyan and Levenspiel10 a
Fp
Dt (m)
Yagi and Aochi3 Zenz and Weil4 Wen and Hashinger5 Tanaka et al.6 Merrick and Highley7
(kg/m3)
2600 940 1900 2000 2400 2400 2650 3500 860∼7850 1500 3500 2750 920∼5900
dp (mm)
U (m/s)
T (°C)
symbol
0.1 0.050 0.1 0.15 0.077∼0.428 0.1 0.1 0.15 0.15 0.037∼1.0 0.15 0.15 0.15
0.8∼1.0 0.3∼0.72 0.6∼1.32 1.2∼2.8 0.61∼2.44 1.8 0.6∼3.0 1.5∼10 6.0 7.0 6.0 1.5∼3.66 2.70
25 25 25 25 800 700∼900 25 25 25 25 25 25 25
A Bb C D Eb F G H I J K L M
Determined from the experimental range of authors. b B,E: measured values.
that of Choi et al.15 0.423, that of Kunii and Levenspiel 13 0.703, and that of Adanez et al.14 0.808. However, the correlation of Choi et al.15 has 0.303, that of Lei and Horio16 0.467, that of Kunii and Levenspiel13 0.510, and that of Adanez et al.14 271, with the data of Lei and Horio16 and Choi et al.15,17 The normalized mean deviation is defined as the sum of (|amea - acal|/amea) divided by the number of data. Meanwhile, the important thing is that the correlation of Lei and Horio16 needs the total entrainment rate to determine the decay constant. The total entrainment rate is an unknown value to determine. Therefore, the following correlation of Choi et al.15 was used to estimate the decay constant in this study. That correlation should be more suitable for this study than others because it has been correlated on the basis of the experimental data obtained from both cold and hot model fluidized beds.
adp )
(
)( ) ) ( )
dp dpFg (U - Umf) exp -11.2 + 210 Dt - dp µ
(
Fpgdp
0.725
Fg (U - Umf)2
{
24/Rep Cd ) 10/Re0.5 p 0.43
Fp - Fg Fg
-0.492
0.731
Cd-1.47 (1)
for Rep e 5.8 for 5.8 < Rep e 540 for 540 < Rep
Rep ) dpUFg/µ
×
(2)
(3)
The Umf in eq 1 is the minimum fluidizing velocity of the bed particle.
According to Choi et al.,15 the decay constant decreased with an increase of the gas velocity. However, the effect of the gas velocity decreased slightly as the temperature increased. The decay constant increased with temperature at a constant gas velocity. The effect of the temperature increased as the gas velocity increased. The correlation (eq 1) covered column diameters from 0.05 to 0.4 m, bed particle diameters from 46 to 720 µm, particle densities from 930 to 3050 kg/ m3, gas velocities from 0.3 to 6.2 m/s, and temperatures from 24 to 600 °C. The entrainment rates measured in relatively cold fluidized beds by Gugnoni and Zenz,18 George and Grace,19 and Choi et al.17,20 and in hot fluidized beds by Choi et al. 1,2 were used as experimental data. Their experiments were carried out using bubbling fluidized beds with variations in column size, gas velocity, temperature, particle size, and density. Their experimental conditions are summarized in Table 1. To provide consistency with the experimental method, the selection of entrainment data has been restricted to those measured at the abrupt gas exit of the bubbling fluidized bed with the steady-state recirculating system shown in the description by Kunii and Levenspiel.13 The column diameter (Dt) was considered as the hydraulic diameter for the fluidized bed of George and Grace.19 On the basis of more than a thousand experimental data, a nonlinear regression was conducted to improve the performance of the resulting equation describing the complex effect among variables. Effects of gravitational and hydrodynamic forces, but not any effect resulting from interparticle adhesion forces, were considered in determining the variables. Therefore, the present correlation is not proper for particle sizes when adhesion forces become significant compared with gravitational
Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 2493
and hydrodynamic forces. As a result, the following correlation was found to provide the best fit to the above experimental data with a correlation coefficient of 0.910.
Ki* ) Kih* + Ki∞*
(4a)
Kih*dp/µ ) CdRep exp(-9.12 - 0.0153a(Ht - Hb)) (4b) Ki∞*dp/µ ) Ar0.5 exp(6.92 - 2.11Fg0.303 - 13.1/Fd0.902) (4c) where
Ar ) gdp3Fg(Fp - Fg)/µ2 Fg ) gdp(Fp - Fg)
in SI unit
Fd ) CdFgU2/2
(
in SI unit
)
Umf Hmf )1- 1Hb U
(4d) (4e) (4f)
(1.06Umf+1)/1.06Umf
(5)
Ar, Fg, and Fd mean Archimedes number, the gravity force minus the buoyancy force per projection area of the particle, and the drag force acting on the particle per projection area, respectively. Ht, Hb, and Hmf are the column height from the distributor plate to the freeboard gas exit, the bed height at a fluidizing gas velocity (U), and the bed height at the minimum fluidizing state, respectively. As can be seen in eq 4c, it was considered that the dispersed noncluster flux or the elutriation rate constant above TDH (Ki∞*) increases exponentially with gas velocity, but its slope decreases with increasing gas velocity. As the drag force or gas velocity increases, the Ki∞* approaches a constant value which is determined by gas and solid properties. Equation 5 represents the bed expansion characteristics obtained in the fluidized bed of Choi et al.1,2,17 at room temperature with FCC, sand, emery, and cast iron particles. This relationship agreed reasonably well with the data obtained from beds of glass beads and coal particles by Lee21 and Lee and Kim.22 The Hmf/Hb is 1 at U ) Umf. However, it approaches zero as the gas velocity becomes large. Equation 5 covers a range of bed particle diameters of 96-1147 µm, particle densities of 1407-6158 kg/m3, minimum fluidizing velocities of 0.0043-0.495 m/s, gas velocities of 0.015-1.40 m/s, and bed voidage of 0.45-0.775. The range of bed voidage covers bubbling and turbulent fluidization regimes. Comparison of Correlation The dispersed noncluster flux or the elutriation rate constant above TDH (Ki∞*) calculated from the present correlation is compared in Figure 1 with those calculated from previous correlations3,5-10 and with data reported by Zenz and Weil4 and Merrick and Highley.7 Because of the validity of it, the previous correlation was compared in the experimental range of its own. The descriptions of the symbols used in Figure 1 are given in Table 2. The gas velocity was considered as a main variable in all correlations. In addition, the effect of temperature was examined in correlation with Merrick and Highley,7 the effect of solid density in correlation with Wen and Chen9 and Colakyan and Levenspiel,10
Figure 1. Comparison between the present correlation and previous correlations on Ki∞*. See Table 2 for symbol description.
and the effects of particle size and column diameter in correlation with Wen and Chen,9 respectively. Elutriation rate constants calculated from the correlations of Zenz and Weil4 and Merrick and Highley7 are considerably larger than those from the present correlation. On the basis of the experimental data in Table 1 in the report by Zenz and Weil4 and Table 3 in the report by Merrick and Highley,7 the present correlation showed better fit than the relationships by Zenz and Weil4 and Merrick and Highley7 for the experimental data of their own. The elutriation rate constant data reported in both studies agree reasonably well with those predicted from the present correlation, as can be seen in Figure 1. Correlations of Yagi and Aochi,3 Wen and Hashinger,5 Tanaka et al.,6 Wen and Chen,9 and Colakyan and Levenspiel10 agree reasonably well with the present correlation over the considered conditions. However, those correlations predicted a much more rapid decrease of Ki∞* than the present correlation as the gas velocity decreases relatively near the terminal velocity of the particle. This seems to result from terms of U-Ut in those correlations. The trend of the present correlation is quite similar to that of the correlation of Geldart et al.8 Both correlations are better than others in describing the trend of Ki∞* with a variation of gas velocity relatively close to the terminal velocity of the particle. The correlation of Wen and Chen9 predicted that Ki∞* increases with the column diameter up to 0.1 m. However, it leveled off for column diameters larger than
2494 Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999
Figure 2. Comparison between the elutriation rate constants reported by Colakyan and Levenspiel10 and values predicted from the present correlation. Solid density (kg/m3): (O) 920; (4) 2750; (0) 5900.
0.1 m like Colakyan and Levenspiel10 reported. Therefore, the present correlation seems to justifiably neglect the effect of column diameter at the freeboard height above the TDH. As the temperature increases from 700 to 900 °C, about a 10% decrease of the Ki∞* is predicted from the correlation of Merrick and Highley,7 but about a 10% increase of the Ki∞* from the present correlation. Both the present correlation and the correlation by Wen and Chen9 predict that Ki∞* decreases as the particle density increases, while the effect of the particle density in the present correlation appears larger than that in the correlation by Wen and Chen9 over their experimental range considered. The correlation by Colakyan and Levenspiel10 predicts an unusual trend in which the Ki∞* decreases after an initial increase as the particle density increases. However, the present correlation predicts the effect of the particle density relatively well over the experimental range of Colakyan and Levenspiel10 as can be seen in Figure 2. Figure 2 shows a comparison between Ki∞* calculated from the present correlation and that reported by Colakyan and Levenspiel.10 The values predicted from the present correlation are in reasonable agreement with measuresd Ki∞* except 10 pieces of experimental data deviating seriously in a total of 118 pieces of data. In normalized mean deviation, the correlation by Yagi and Aochi3 shows 1.03, that of Zenz and Weil4 4.21, that of Wen and Hashinger5 1.85, that of Tanaka et al.6 0.699, that of Merrick and Highley7 5.00, that of Geldart et al.8 0.539, that of Wen and Chen9 0.965, that of Colakyan and Levenspiel10 0.254, and that of the present correlation 0.513. The normalized mean deviation is defined as the sum of (|Ki∞*,mea - Ki∞*,cal|/Ki∞*,mea) divided by the number of pieces of data. As a result, it could be confirmed that the noncluster flux calculated from the present correlation is equivalent to the elutriation rate constant above TDH and the present correlation represents the effects of the considered variables reasonably well. Figure 3 shows the effect of gas velocity on the particle entrainment rate measured for various particle diameters by Choi et al.2 and the present correlation is compared with measured data in the figure. As the gas velocity increases, the particle entrainment rate increases because of an increase of the drag force acting on the particle surface, but the slope decreases. As can be seen in the figure, the present correlation described
Figure 3. Entrainment rate vs gas velocity. Dt ) 0.1 m; gas, air; P ) 101.3 kPa; dp (mm), (1, - - -) 0.091, (3, ‚‚‚) 0.128, (b, - - -) 0.181, (O, s) 0.256; symbols, data measured by Choi et al.2; lines, present correlation. (a) Solid, sand; Fp ) 2509 kg/m3; T ) 20 °C. (b) Solid, emery; Fp ) 3981 kg/m3; T ) 400 °C.
Figure 4. Comparison of entrainment rate measured by Choi et al.2 with values calculated from the present correlation with a variation of temperature. (a) Sand; U, 1.2 m/s. (b) Emery; U, 1.6 m/s. (c) Cast iron; U, 1.8 m/s. dp (mm): (O, s) 0.181, (b, - - -) 0.128, (3, ‚‚‚) 0.091; symbols, measured data; lines, present correlation.
the gas velocity effect reasonably well in both the cold and hot fluidized beds. Figure 4 depicts the effects of temperature on the particle entrainment rates measured for different particle sizes and densities by Choi et al.2 In the previous studies1,2 the measured entrainment rate increased after an initial decrease as the temperature increased. That result could be expected because of decreasing gas
Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 2495
tioned. Because the present correlation considered no interparticle forces from the beginning, it could not be expected to follow their results. As a result, when the interparticle forces were negligible, the present correlation was confirmed to be valid in predicting the particle entrainment rate at the freeboard gas exit for the following experimental range: particle diameter of 21-710 µm, particle density of 2400-6158 kg/m3, gas velocity of 0.15-2.8 m/s, temperature of 12-600 °C, pressure of 101-3200 kPa, column diameter of 0.1-0.91 m, and column height of 1.97-9.1 m. Conclusions
Figure 5. Comparison of total entrainment rates measured by Chan and Knowlton23 with values calculated from the present correlation with a variation of pressure. Pressure (kPa): (O, s) 446, (b, - - -) 1135, (3, ‚‚‚) 2169, (1, - - -) 3202; symbols, measured data; lines, present correlation.
density and increasing gas viscosity. The trend was very similar to a variation of the particle size that has the terminal velocity equal to the gas velocity. As seen in Figure 4, the present correlation is able to follow the measured trend where the minimum entrainment rate occurred with the temperature. The present correlation predicted a slight increase of the total entrainment rate in the temperature range from George and Grace19 that was between 27 and 172 °C as discussed by Choi et al.2 As a result, the present correlation is able to describe the temperature effect on the particle entrainment rate reasonably well over the experimental ranges. Figure 5 shows a comparison between total entrainment rates calculated from the present correlation and values measured in an ambient temperature and highpressure fluidized bed by Chan and Knowlton23 who investigated the pressure effect on particle entrainment up to 3200 kPa. The gas density and viscosity increase as the pressure increases. However, the effect of pressure on the gas viscosity is very small. They reported that the particle entrainment rate increased with increasing gas density and viscosity because of a decrease of the particle terminal velocity. As can be seen in the figure, the present correlation was also successful in predicting the measured total entrainment rate in a pressurized fluidized bed. This confirms that the present correlation predicts the effects of gas density and viscosity reasonably well. Because information could not be understood sufficiently, the total entrainment rate measured by Romanova et al.24 could not be compared with the present correlation. The total entrainment rate data reported by Knowlton et al.25 are much higher than those predicted from the present correlation. This probably results because their total entrainment rate was affected significantly by entrainment of fine particles formed by particle attrition. In the meantime, Wouters and Geldart11 reported that the particle entrainment rate decreased with an increase in temperature up to 400 °C. However, the present correlation predicted the particle entrainment rate increasing with temperature over their experimental conditions. The difference might be expected because of the presence of appreciable interparticle forces in their fluidized bed as they men-
An empirical correlation predicting the particle entrainment rate at the freeboard gas exit, which is able to describe the influence of temperature but considers no interparticle forces, has been proposed on the basis of the comprehensive experimental data. The present model correlation successfully represented the measured trend in which the entrainment rate increases after an initial decrease as the temperature increases, leading to a minimum entrainment rate with increasing temperature. It is also successful in predicting that the entrainment rate increases with pressure. It has been confirmed that the present correlation can be used reasonably well to predict particle entrainment rates in both cold and hot model bubbling fluidized beds. Acknowledgment The authors are grateful for the financial support of this work from the Korea Science and Engineering Foundation (Project 971-1109-061-2). Nomenclature a ) decay constant, 1/m Ar ) Archimedes number, gdp3Fg(Fp - Fg)/µ2, dimensionless Cd ) drag coefficient on the particle surface based on the superficial gas velocity, dimensionless dp ) particle diameter, m Dt ) column diameter, m Fd ) drag force on the particle per projection area, Pa Fg ) gravity force minus buoyancy force per projection area of particle, Pa g ) gravitational acceleration, 9.8 m/s2 Hb ) bed height calculated from eq 5, m Hmf ) Hb at Umf, m Ht ) column height, m Ki* ) entrainment rate of particles in size i, kg/(m2 s) Kih* ) cluster flux of entrained particles in size i, kg/(m2 s) Ki∞* ) dispersed noncluster flux of entrained particles in size i or elutriation rate constant of particles in size i above TDH, kg/(m2 s) Rep ) particle Reynolds number, dpUFg/µ, dimensionless T ) temperature, °C TDH ) transport disengaging height, distance above bed surface beyond which the entrainment rate becomes relatively unchanging, m U ) superficial gas velocity, m/s Umf ) minimum fluidizing velocity of bed particle, m/s Ut ) terminal velocity of particle, m/s Greek Letters µ ) gas viscosity, Pa s Fg ) gas density, kg/m3 Fp ) apparent particle density, kg/m3
2496 Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 Superscripts and Subscripts cal ) calculated value mea ) measured value
Literature Cited (1) Choi, J. H.; Choi, K. B.; Kim, P.; Shun D. W.; Kim, S. D. The Effect of Temperature on the Particle Entrainment Rate in a Gas Fluidized Bed. Powder Technol. 1997, 92, 127. (2) Choi, J. H.; Ryu, H. J.; Shun, D. W.; Son, J. E.; Kim, S. D. Temperature Effect on the Particle Entrainment Rate in a Gas Fluidized Bed. Ind. Eng. Chem. Res. 1998, 37, 1130. (3) Yagi, S.; Aochi, T. Elutriation of Particles from a Batch Fluidized Bed. Paper presented at the Society of Chemical Engineering of Japan Spring Meeting, 1955. (4) Zenz, F. A.; Weil, N. A. A Theoretical-Empirical Approach to the Mechanism of Particle Entrainment from Fluidized Beds. AIChE J. 1958, 4, 472. (5) Wen, C. Y.; Hashinger, R. F. Elutriation of Solid Particles from a Dense Phase Fluidized Bed. AIChE J. 1960, 6, 220. (6) Tanaka, I.; Shinohara, H.; Hirosue, H.; Tanaka, Y. Elutriation of Fines from Fluidized Bed. J. Chem. Eng. Jpn. 1972, 5, 51. (7) Merrick, D.; Highley, J. Particle size reduction and elutriation in a fluidized bed process. AIChE Symp. Ser. 1974, 70 (137), 366. (8) Geldart, D.; Cullinan, J.; Georghiades, S.; Gilvray, D.; Pope, D. J. The Effect of Fines on Entrainment from Gas Fluidized Beds. Trans. Inst. Chem. Eng. 1979, 57, 269. (9) Wen, C. Y.; Chen, L. H. Fluidized Bed Freeboard Phenomena: Entrainment and Elutriation. AIChE J. 1982, 28, 117. (10) Colakyan, M.; Levenspiel, O. Elutriation from Fluidized Beds. Powder Technol. 1984, 38, 223. (11) Wouters, I. M. F.; Geldart, D. Entrainment at High Temperatures. In Fluidization IX; Fan, L. S., Knowlton, T. M., Eds.; Engineering Foundation: New York, 1998; p 341. (12) Hazlett, J. D.; Bergougnou, M. A. Influence of Bubble Size Distribution at the Bed Surface on Entrainment Profile. Powder Technol. 1992, 70, 99. (13) Kunii, D.; Levenspiel, O. Fluidization Engineering; Butterworth-Heinemann: Boston, 1991; pp 165-210. (14) Adanez, J.; Gayan, P.; Garcia-Labiano, F.; de Diego, L. F. Axial Voidage Profiles in Fast Fluidized Beds. Powder Technol. 1994, 81, 259.
(15) Choi, J. H.; Ma, S. C.; Shun, D. W.; Son, J. E.; Kim, S. D. Effect of Temperature on the Decay Constant of the Axial Solid Holdup Profile in the Splash Region of a Gas Fluidized Bed. HWAHAK KONGHAK (Korea), 1997, 35, 300. (16) Lei, H.; Horio, M. A Comprehensive Pressure Balance Model of Circulating Fluidized Beds. J. Chem. Eng. Jpn. 1998, 31, 83. (17) Choi, J. H.; Kim, K. J.; Kim, S. D. Effect of Secondary Gas Injection on the Particle Entrainment Rate in a Gas Fluidized Bed. Powder Technol. 1997, 90, 227. (18) Gugnoni, R. J.; Zenz, F. A. Particle entrainment from bubbling fluidized beds. In Fluidization; Grace, J. R., Matsen, J. N., Eds.; Plenum Press: New York, 1980; p 501. (19) George, S. E.; Grace, J. R. Entrainment of Particles from Pilot Scale Fluidized Beds. Can. J. Chem. Eng. 1981, 59, 279. (20) Choi, J. H.; Son, J. E.; Kim, S. D. Solid Entrainment in Fluidized Bed Combustor. J. Chem. Eng. Jpn. 1989, 22, 597. (21) Lee, G. S. Pressure Fluctuations and Mixing Characteristics in Turbulent Fluidized Beds. Ph.D. Dissertation, Korea Advanced Institute of Science and Technology, Taejeon, Korea, 1990. (22) Lee, G. S.; Kim, S. D. Bed Expansion Characteristics and Transition Velocity in Turbulent Fluidized Beds. Powder Technol. 1990, 62, 207. (23) Chan, I. H.; Knowlton, T. M. The effect of pressure on entrainment from bubbling gas fluidized beds. In Fluidization; Kunii, D., Toei, R., Eds.; Engineering Foundation: New York, 1984; p 283. (24) Romanova, T. T.; et al. Effect of Temperature on Total Entrainment of Dust from a Polydispersed Fluidized Bed. Deposited Document, Viniti 5129-80; Moscow, Russia, 1980. (25) Knowlton, T. M.; Findlay, J.; Sishtla, C. Attrition and Entrainment Studies Related to Fluidized-Bed Gasifiers; Final Report for U. S. Department of Energy, Project DE-AC2185MC22061; Institute of Gas Technology: Chicago, IL, 1990.
Received for review November 9, 1998 Revised manuscript received March 18, 1999 Accepted March 19, 1999 IE980707I
