Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 231
Minimum Fluidization Velocities of Lime and Limestone Particles Jaroslav Pata and Mlloslav Hartman* lnstitute of Chemical Process Fundarnenfals, Czechoslovak Academy of Sciences, 165 02 Prague, Czechoslovakia
Minimum fluidization velocities of a bed of limestone and its calcine that holds its potential for commercial desulfurization of flue gas were determined. Using air, experiments were carried out in an 85-mm i.d. column with particles of average size ranging from 1.Oto 8.1 X l o v 4 m. The minimum fluidization velocities of a bed in the same size region were determined from a plot of pressure drops vs. velocity of air at room temperature. The experimental results were compared to the values computed from equations given by Ergun (1952), Kunii and Levenspiel (1969), Leva (1959), Johnson (1949),and from simplified equations published by Wen and Yu (1965), Miller and Logwinuk (1951), and Todes (1957). The Ergun equation was used to predict the minimum fluidization velocity of beds of lime and sulfated lime particles fluidized by flue gas at 850 'C. The needed voidage and particle sphericity of limestone and lime were determined by separate experiments.
Introduction The necessity to reduce the emission of sulfur dioxide released by combustion of sulfur-containing coals has led to extensive research on removal of this pollutant from flue gases. There are numerous approaches to this problem; one of them is the use of a fluidized bed of lime. Efficient desulfurization can be achieved in a fluidized bed operating at about 850-900 "C (Hartman and Coughlin, 1976). Under these conditions finely ground limestone decomposes almost immediately into lime and subsequently reacts with sulfur dioxide and excess oxygen present to give solid calcium sulfate (Hartman, 1975). The weight of particles of limestone thus decreases rapidly at the beginning, owing to calcination, and then gradually increases as the sulfation reaction proceeds. One of the important parameters in the design of such fluidized bed reactors is the minimum fluidization velocity. Although different correlations and equations make it possible to compute this value, the most reliable way is to determine it by experiment. The aim of this work is to provide these and other characteristic data for the fluidized bed of limestone and lime particles. Experimental Section Apparatus. The experimental setup is shown in Figure 1. A known volume of the material was charged into the glass column (1)of inside diameter D k = 8.6 X m and height H k = 0.9 m. The column was equipped with a gas plate distributor (4) of free area cp = 1%and orifice diameter d o = 1.6 X m and with a fluidizing grid (3) of free area cp = 1%,d o = 1.0 X m. The distance between these plates was 3.0 X m. A ring with a height of 1.5 X m (2) was situated above the fluidizing grid. There was a perimeter slot 1.0 X m high in the ring for measurements of the pressure close above the fluidizing grid. Pressure drop across the bed was measured by means of manometer (5), and the pressure below the fluidizing grid. by manometer (6). Incidentally elutriated particles were acumulated in the fabric filter (7). The velocity of air dried in the dryer (9) was checked by rotameter (8). Materials Used. The present work was conducted with the limestone ST tested in our previous kinetic studies (Hartman, 1975, 1976). This limestone is a crystalline high-grade mineral containing 53.7% CaO. The chemical composition and density of limestone is shown in Table I. The hand-picked stones, which contained no visible inclusions, were crushed and sieved. The fractions investigated in this study comprised six size ranges: 0.09 to 0.16 mm ((1, = 0.13 mm), 0.18 to 0.25 mm (d, = 0.21 mm), 0.25 to0.40 mm (d, 0019-7882/78/1117-0231$01.00/0
= 0.31 mm), 0.315 to 0.630 mm (d, = 0.47 mm), 0.50 to 1.00 mm (d, = 0.65 mm), and 0.5 to 1.25 mm (d, = 0.81 mm). The lime was prepared by thermal decomposition of the screened fractions of limestone maintained for 4 h at 900 "C in an electric furnace and then kept in an airtight container. The average particle diameters of both materials were evaluated from the sieve analysis and computed according to the relation (Reboux, 1954)
1_
Xi
dp-=G
(1)
The results are given in Table I1 and indicate that the average particle size was slightly lowered during calcination. Air, the density and viscosity of which differ only slightly from combustion gases, dried in dryer (9) at a temperature of 20 f 2 "C was used as fluidizing medium.
Results and Discussion Minimum Fluidization Voidage. Knowledge of minimum fluidization voidage is essential for predicting the onset of fluidization. Since no increase of the bed height of either lime or limestone particles was observed at the minimum fluidization velocity, the procedure suggested by Leva (1959) was used. The author reported that for most solids a close approximation can be obtained by substituting the value tmf for the value ,e obtained by pouring the solids carefully from one container into another. Vrlues obtained in such a way may be a few percent higher than those obtained from the actual experimental behavior of the bed. These higher values should yield slightly more conservative values of minimum fluidization velocity. The minimum fluidization voidage was thus determined by weighing a 500-cm3 volume of particles obtained under the conditions mentioned above. The values of emf were calculated according to the relation
and results for all 12 fractions of lime and limestone particles tested are shown in Figure 2. The values of minimum fluidization voidage for lime are 17-21% lower than those for limestone within the whole range of particle size. This decrease of voidage of the poured bed may be caused by rounding of sharp edges of the particles during calcination. However, this rounding was not distinct under the microscopic observation. The measured values of bed voidage tp were compared with those published for sand and sharp sand (Leva, 1959).Voidage
0 1978 American Chemical Society
232
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3,1978
Table I. Chemical Composition of Limestone ST and Density of Lime and Limestone ST Component
Table 11. Mean Particle Diameters Fractionld, X lo4 m
Content (%bywt)
CaO MgO Si02
53.70 0.68 2.15
Limestone Lime
1
2
3
4
5
6
1.3
2.1 2.1
3.1 2.8
4.7
6.5 6.0
8.1 8.0
1.0
4.4
0.54
A1203
Fez03 Weight loss on calcination Density of limestone, kg/m3 Density of lime, kg/m3
0.47 42.60 2660 1600
A v e r o g e p o r t i c l e diameter doX
?Okm
Figure 3. Variation of particle sphericity of limestone and lime with average particle diameter. Curve 1,limestone; curve 2, lime.
I Figure 1. Experimental setup: 1, column; 2, ring; 3, fluidizing grid; 4, gas plate distributor; 5, manometer; 6, manometer; 7, fabric filter;
8, rotameter; 9, dryer; 10, valve; 11,valve.
..
060 r i b-
oiot
1
I 2
4
A v e r a g e p a r t i c l e diameter, dp
X
1 6 104m
8
Figure 4. Comparison of measured particle sphericitiesof limestone: determined from bulk density of bed, 0 ;pressure drop, (D; minimum fluidization velocity, 0 .
1
5 Averoge p a i ! : c ' e d,ome:er,
8
d;%
Io'r~
Figure 2. Variation of minimum fluidization voidage of limestone. and lime bed with average particle diameter. Curve 1,limestone;curve 2, lime.
of the bed of limestone in range d, = 1.2-5.0 X m is close to the value for sharp sand, tp = 0.57-0.48. Voidage of the bed of lime is practically the same as that of the bed of sand, E , = 0.47-0.42. Particle Sphericity. Particle sphericity was determined by a method based on the procedure reported by Brown et al. (1950),according to which the voidage of a static poured bed of particles is related to their sphericity. The plot for dense packing was used for determination of a particle sphericity as recommended by Foust et al. (1965) for evaluation of minimum fluidization velocity. The results for particles of
different size are given in Figure 3. It is of interest to note that the values of sphericity $ of the lime are 16-44% higher than those of the limestone due to their different voidage. In order to verify the obtained values, sphericity of limestone particles was determined in two other ways. Using the Ergun equation ( 5 ) (see Table VI), sphericity was evaluated from minimum fluidization velocity found by experiment. The third method applied in this work is based on pressure drop measuring of the static bed. According to this method the particle sphericity can be calculated by
'( =
1 5 0 / ~ ~ L-( 1C ) ~ U C ) O . ~ d,2gc3Sp
(3)
provided Re < 10. Pressure drop was measured by means of a pair of probes immersed in the particle bed. The probes were similar to those used by Blickle and Ormos (1973) in their study of fluidization bed voidage. The probes consisted of two m 0.d. Each tube had two orifices of glass tubes of 8.0 x 1.0 X 10-3 m i.d. in its wall. The mutual shift of tubes was 5.0 X m. The pressure differences were read on a manometer
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 50
Table 111. Mean Sphericities of Lime and Limestone Particles Mean value of iL evaluated from tp Ap umf
Material Limestone Lime
0.55 0.74
0.55 -
[
I
233
I 1
1
Average sphericity
0.56 0.79
0.55 0.77
Table IV. Measured Values of Minimum Fluidization Velocities of Limestone
d p X 104m umf X 10'
1.3 3.0
2.1 5.0
3.1 8.0
4.7 15.0
6.5 28.0
8.1 37.0
3.0
5.0 4.0
8.0 8.0
14.0
32.0
36.0
15.0
30.0
38.0
14.7
28.0 28.0 28.0 29.0
m/s
a m f X 10'
3.0
4.7
8.0
6 Superficial gas velocity
20
uG x d n / s
Figure 5. Typical plots of pressure drop against gas velocity. Curve 1,limestone, d, = 4.7 x m; curve 2, lime, d, = 4.4 x 1 0 -m; ~ HO = 0.50k.
37.0
m/s Table V. Measured Values of Minimum Fluidization Velocities of Lime
d,, X 104m umfXlo2 m/s
amfX 10'
1.0 0.9
2.1 2.1
2.8 3.4
4.4 6.0
6.0 16.0
8.0 21.0
0.9 1.0
2.2
6.4 6.4
22.0 22.0
0.9
2.2
3.5 3.6 3.7 3.6
17.4
2.2
6.3
16.7
21.7
m/s filled with distilled water. Good reproducibility of the particle sphericity was shown by repeated measurements with new charges. The maximum relative deviations of the values obtained with individual fractions were in one case approximately 6%, and in others near 3%. In spite of this relatively good reproducibility, the values measured showed considerable scatter, similar to those calculated from the minimum fluidization velocity. Particle sphericities of the limestone particles obtained by all three methods are shown and compared in Figure 4. Although the results obtained by these methods are considerably scattered, the deviation from the calculated average value = 0.55 (for limestone) was below 10%in almost all cases. The dependence of the sphericity on the particle diameter evaluated from t, was not definitely confirmed by the other two
+
methods. Owing to this fact, the calculated average value of particle sphericity, given in Table 111,seems to be a well suited and convenient parameter for calculation of umfin the whole region of sizes. Minimum Fluidization Velocity. Minimum fluidization velocity was determined experimentally under air flow in the setup shown in Figure 1.The dependence of pressure drop on air flow was measured with the air velocity gradually reduced from a well fluidized state. Minimum fluidization velocity was then appointed from the plot of pressure drop vs. the velocity of air. Measurement was made at LIDk ratios between 0.5 and 2. As an example, the plots of pressure drops of limestone and lime beds are shown in Figure 5. Minimum fluidization velocity found for measured fractions of lime and limestone are presented in Tables IV and V and m/s for the limestone parthey vary from 3.0 to 37.0 X m. Corresponding values of u,f ticles of d, = 1.3-8.1 X for the lime particles range from 0.9 to 21.7 X lo-* m/s. Many papers suggesting a number of equations for prediction of minimum fluidization velocity have been published. To compare the experimental values with theoretical predictions, several equations recommended by Leva (1959), Kunii and Levenspiel (1969), and Davidson and Harrison (1971) were employed. The equations used are given in Table VI. All of these equations were developed originally for a monodisperse bed of spherical particles and, therefore, the product of average particle diameter and particle sphericity
Table VI. Eauations Used to Predict the Minimum Fluidization Velocitv Range of applicability
Equation 1 - emf Rem? Ga = 150 -Remf+ 1.75 emf3
emf3
Not limited
Small particles Remf< 20 Large particles Remf> 1000
No. of equation
Author
5
Ergun (1952)
6
Kunii and Levenspiel (1969)
6
Kunii and Levenspiel (1969)
7
Leva (1959)
8
Johnson (1949)
9
Johnson (1949)
234
Ind. Eng. Chem. Process Des. Dev.. Vol. 17, No. 3, 1978
Table VII. Simplified Equations Used to Predict the Minimum Fluidization Velocity
(
+
Remf= 33.12 0.0408 dpPF(PS
No. of equation
Range of applicability
Equation
- pF)g)0'50 - 33.7
PF2
Author
Not limited
10
Wen and Yu (1965)
Re < 20 Small particles
10
Wen and Yu (1965)
Not limited
I1
Todes (1957)
Not limited
12
Miller and Logwinuk (1951)
Averoge p o r t l c l o dtarneter, r i p % 104m
Average p a r t i c l e dlorne'er,
d,
X
104W
Figure 6. Comparison of measured and computed values of minimum fluidization velocities of limestone: 0 ,experimentaldata points; curve 1,eq 6; curve 2, eq 5; curve 3, eq 7 ; curve 4, eq 8 and 9.
Figure 7. Comparison of measured and computed values of minimum fluidization velocities of lime: 0 , experimental data points; curve 1, eq 6; curve 2, eq 5; curve 3, eq 7; curve 4, eq 8 and 9.
has been substituted into these equations instead of particle diameter. Difficulties in determining minimum fluidization voidage and particle sphericity made some authors (Wen and Yu, 1965; Miller and Logwinuk, 1951; Todes and Goroskhov, 1957) simplify the equations already derived or develop new relations in which these factors would be eliminated. Such simplified equations were also applied in this work and are given in Table VII. The experimental minimum fluidization velocity of limestone and lime and values predicted by eq 5-9 are plotted in Figures 6 and 7 . Minimum fluidization voidage and particle sphericity given in Figures 2 and 3 were used in the computations. Of the equations presented in Table VI, the Ergun equation ( 5 ) demonstrated the best agreement between measured and computed minimum fluidization velocities. The maximum deviation for limestone was 6, = -43.3%; for lime, 6,, = -44.4%. Mean deviations for all sets of measured particle fractions were b = f17.7% for limestone and b = 416.7% for lime.
The agreement between theoretical predictions and experimental values was somewhat improved when average values of sphericity $ = 0.55 for limestone and $ = 0.77 for lime were used in computations. The computed results and their comparison with measured values are shown in Table VI11 for limestone and in Table X for lime. The Ergun equation ( 5 ) now showed better agreement and their maximum deviations decreased to 6,, = -33.3% for = +36.4% for lime. Mean deviations limestone and to 6,, decreased to 8 = 414.5% for limestone and 6 = 415.1% for lime. The results computed from simplified equations summarized in Table VI1 and deviations from values measured are shown for limestone in Table IX; for lime, in Table XI. Very good agreement is shown in the case of Todes' eq 11. Maxi= mum deviations from experimental results were 6,, -43.3% for limestone and , , ,a = -33.3% for lime. Mean deviations were b = f13.3% for limestone and b = f22.3% for lime. These values were in some cases even better than those predicted by the Ergun equation which is remarkable with
+
Table VIII. Computed Minimum Fluidization Velocities of Limestone emf (0.56 - 0.50); = 0.55 dpx 104 m
1.3 2.1 3.1 4.7 6.5 8.1
Ergun (1952) x 102 m/s % 2.0 4.4 9.4 17.6 26.8 37.9
Mean rel. dev.
-33.3 -6.4 +17.5 +19.7 -7.6 +2.4 f14.5
Computed values and relative deviation from umf Kunii (1969) Leva (1959) x 10' m/s % x lo2 m/s % 2.0 4.4 9.6 18.9 30.9 47.9
-33.3 -6.4 +20.0 +28.6 +6.6 +29.5 f20.7
1.5
-50.0
3.3
-29.8 -10.0 -3.4 -20.3 -3.0
7.2
14.2 23.1 35.9
-19.2
Johnson (1949)
x lo2 m/s
%
1.9 4.0 8.7 16.5 25.7 39.9
-36.7 -14.9 +8.8
+12.2 -11.4 +7.8
f15.3
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
235
Table IX. Computed Minimum Fluidization Velocities of Limestone. Simplified Equations Computed values and relative deviation from u,f
d, x 104 m
x
1.3
102
Wen (1965) m/s
3.1 4.7 6.5 8.1
%
1.7 4.1 8.3 16.6 27.2 36.7
-43.3 -12.8 +3.8 +12.9 -6.2 -0.8
-19.1 +2.5 +21.8 +6.6 +15.7
Mean rel. dev.
Miller (1951)
x IO2 m/s
-50.0
1.5 3.8 8.2 17.9 30.9 42.8
2.1
Todes (1957) YO
f19.3
x IO2m/s
%
1.4 3.7
-53.3 -21.3 +1.3 +25.9 +22.1 $48.7
8.1
18.5 35.4 55.0
f13.3
f28.8
+
Table X. Computed Minimum Fluidization Velocities of Lime c,f (0.48 - 0.39); = 0.77
d, x 104 m
X
Ergun (1952) IOz m/n 96 0.8 3.0 3.5 7.0 12.6 20.7
1.0 2.1 2.8
4.4 6.0 8.0
Mean rel. dev.
X
-11.1
+36.4 -2.8 +11.1
-24.6 -4.6
Computed values and relative deviation from umf Kunii (1969) Leva (1959) INL m/s 96 X loz m/n o/o 0.8 3.0 3.5 7.3 13.6 24.1
-11.1
f15.1
0.6 2.3 2.7
+36.4 -2.8 +15.9 -18.6
10.2
+11.1
18.1
5.5
Computed values and relative deviation from umf Wen (1965) Todes (1957) Miller (1951) x 104 x io^ x 102 x 102 m m/s % m/s % m/s %
d,
%
0.6 2.4 2.4 4.5 8.3 14.8
-25.0 +4.6 -25.0 -12.7 -38.9 -16.6
f16.0
Table XI. Computed Minimum Fluidization Velocities of Lime. Simdified Eauations
Johnson (1949) X 1 W m/s
-25.0 +9.1 -33.3 -28.6 -50.3 -31.8
f20.0
f29.3
2.8,
I
I -1
/
24F
~~
1.0 2.1 2.8
4.4 6.0 8.0
0.5 2.3 4.1 9.8 17.2 27.7
Mean rel. dev.
-44.4 +4.5 +13.9 +55.6 +3.0 +27.6 f24.8
0.6 2.5 4.3 9.5 15.8 24.2
-33.3 +13.6 +19.4 +50.8 -5.4 +11.5 f22.3
0.5
2.3 4.2 10.3 19.1 33.9
-44.4 +4.5 +16.7 C63.5 +14.4 +56.2 f33.3
1 D I
14,
0
I 02
L
04
F ~ O C : I O P'onversion O~
respect to its simplicity. As mentioned above, the temperature for efficient removal of sulfur dioxide from flue gas is close to 850 O C (Hartman and Coughlin, 1976). Experimental measurements demonstrated that the density of reacting particles of lime changed considerably during the sulfation reaction, because of large differences in molar volumes of calcium oxide and calcium sulfate. Results for different limestones and data of Borgwardt and Harvey (1972) are plotted in Figure 8. The maximum on the curve determined from the Borgwardt experiments corresponds to filling of the original pore volume formed by decomposition of calcium carbonate. As the reaction proceeds, the particles begin to expand to some extent and their density is lowered. A minimum fluidization velocity has been computed by the Ergun equation which yielded the best predicted values for lime at room temperatures, using the following parameters: (1) temperature, 850 "C; (2) composition of flue gas (% by volume): water, 12.5; carbon dioxide, 10.0; oxygen, 3.5; nitrogen, 74.0; (3) density of flue gas, 0.309 kg/m3; (4) P a s; (5) density of particles, viscosity of flue gas, 4.45 X 1600 kg/m3 (lime) and 2660 kg/m3 (sulfated lime); (6) average particle diameters (d, X lo4 m) and minimum fluidization voidages (emf) respectively: 1.0, 0.48; 2.0, 0.44; 3.0, 0.42; 4.0, 0.41; 5.0, 0.40; 6.0,0.40; 7.0,0.40; 8.0,0.40; (7) particle sphericity, 0.77. The computed dependence of minimum fluidization ve-
06 X
Figure 8. Variation of density of reacting lime particles with conversion: data of Borgwardt and Harvey (1972), 0 ;data of Hartman (1975):limestone VI, Q; CD, 8 ;MO, 8 ;CI, @; PI, 0.
locity on particle diameter of lime and sulfated lime is shown in Figure 9. The area between these two curves shows roughly the extent of minimum fluidization velocities of differently sulfated particles of lime. Flue gas velocities required to fluidize even the heaviest particles in the bed are shown in the upper curve. This curve can thus be considered as the lower fluidization limit of a mixture of lime particles partially converted into calcium sulfate.
Summary and Conclusions The minimum fluidization velocities of air vary from 3.0 to 37.0 X m/s for high-grade limestone particles of average m. The minimum fluidsize ranging from 1.0 to 8.1 X ization velocities for particles of lime increase in accordance m/s. The average value with their size from 0.9 to 21.7 X of particle sphericity provided by any of three methods used is convenient for the evaluation of minimum fluidization velocity. The sphericity of limestone particles which averages 0.55 is substantially increased by the process of calcination to a mean value of 0.77. The experimental minimum fluidization velocities were
236 Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 I
Ap = pressure drop, m of water = superficial gas velocity in empty column, m/s u,f = superficial gas velocity required for minimum fluidization, m/s amf = average superficial velocity required for minimum fluidization, m/s V, = volume of poured bed, m3 w p = weight of poured bed, kg X = conversion of lime to sulfated lime (mol of CaS04/mol of (Cas04 CaO)) UG
+
Aderase p o r t l c e d i o w e t e i
dp Y 104m
Figure 9. Minimum f l u i d i z a t i o n velocity o f l i m e a n d sulfated l i m e particles predicted by the E r g u n equation ( 5 ) as a function o f particle size: curve 1, lime, X = 0; curve 2, sulfated lime, X = 0.5; f l u i d i z i n g medium, flue gas a t 850 "C.
compared with predictions of seven equations. The Ergun ( 5 ) and Todes (11)equations showed the best agreement of the equations employed. The mean relative deviation of the former equation was 6 = &17.7% for limestone and 6 = +16.7% for lime. On the average, the simplified equation of Todes fitted the experimental values with an accuracy 8 *13.3% for limestone and 6 = &22.3% for lime. The said equations seem to be the most suitable for the evaluation of minimum fluidization velocity of partially reacted particles under conditions of practical interest.
Acknowledgment The authors wish to thank J. Rathousky, Head of The Institute of Chemical Process Fundamentals, for the interest he has shown in this work. Nomenclature 4, = particle (surface mean) diameter, m d, = average particle diameter over the narrow size range, m a', = orifice diameter, m Dk = inside diameter of the column, m g = gravitational acceleration, m/s2 G,f = fluid mass velocity for minimum fluidization, kg/m2 S
H o = initial height of the bed, m Hk = height of the column, m L = mutal shift of tubes, m
Dimensionless Groups Re = u G d p p F / M F , particle Reynolds number / p ~ , Reynolds number a t minimum Remf = ~ ~ p d , p ~ particle fluidization velocity Ga = g d p 3 p F * ( p S - PF)//.LF*, Galilei number Ar = g d p 3 p p ( p s - P F ) / M F ~Archimedes , number Greek Symbols 6 = relative deviation ((ucomp - U,,~)/U,,~) , , ,a = maximum relative deviation 8 = mean relative deviation t = bed voidage fraction tmf = bed voidage fraction a t minimum fluidization e , = bed voidage fraction of a poured bed p = free areaof plate $ = particle sphericity p~ = fluid air density, kg/m3 p s = solids density, kg/m3 p~ = fluid (air) viscosity, P a s
Literature Cited Blickle, T., Ormos, Z., Hung. J. lnd. Chem., 1, 31 (1973). Borgwardt, R. H., Harvey, R. D., Environ. Sci. Techno/., 6, 350 (1972). Brown, G. G., "Unit Operations", Wiley, New York, N.Y., 1950. Davidson, J. F., Harrison, C. D., "Fluidization" Academic Press, London,
1971. Ergun, S., Chem. Eng. Prog., 46, 69 (1952). Foust, A. S., Wenzel, L. A,, Clump, C. W., Maus, L., Andersen, L. B., "Principles of Unit Operations", Wiiey, New York, N.Y., 1965. Hartman, M., Collect. Czech. Chem. Commun., 40, 1466 (1975). Hartman, M., Coughlin, R . W., AlChEJ., 22, 490(1976). Hartman, M., Int. Chem. Eng., 16 (l),66 (1976). Johnson, E., Inst. Gas Eng. (London),Rept. 1949-50,Publ. No. 378/179(cited in Leva, 1959). Kunii, D.. Levenspiel, O., "Fluidization Engineering", Wiley, New York, N.Y.,
1969. Leva, M., "Fluidization", McGraw-Hill, New York, N.Y., 1959, Miller, C. 0.. Logwinuk, A. K., Ind. Eng. Chem., 43,1220 (1951). Reboux, P., "Phenomenes de fluidisation", Association Francaise de Fluidisation, Paris, 1954. Syromjatnikov, N. I,, Volkov, V. F., "Fluidized bed", (in Russian), Metallurgizdat, Sverdlovsk, 1959. Todes, 0. M.,Goroskhov, V. D., "Proceedings of the USSR Symposium on Processes with Fluidized Beds" (in Russian), Gostechnika USSR, Moscow, 1957 (cited in Syromjatnikov et ai., 1959). Wen, C. Y., Yu, Y. H., AlChEJ., 12, 610 (1965).
Receiued for reuiero August 19, 1977 Accepted December 15,1977
