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Ind. Eng. Chem. Res. 1999, 38, 4120-4122
Bed Voidage in Conical Sawdust Beds in the Transition Regime between Spouting and Jet Spouting Martin Olazar,* Marı´a J. San Jose´ , Roberto Aguado, Beatriz Gaisa´ n, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
From the results obtained for different geometric factors of the contactor (angle and inlet diameter) and for different operating conditions (particle size, stagnant bed height, and air velocity), the validity of a linear correlation based on the ratio between drag and gravitational forces is proven for the calculation of bed voidage in conical spouted beds when they operate in the transition between the regimes of a spouted bed and a jet-spouted bed. The parameters of this equation are calculated from the correlations previously proposed for the calculation of the bed voidage corresponding to these extreme regimes. The dependency on these parameters of the geometric factors and operating conditions has been determined. Introduction Of the characteristics of conical spouted beds, their operation versatility in a wide range of gas flow rates is noteworthy, as a stable bed is obtained between two regimes, spouted bed and jet-spouted bed, corresponding to two different levels of fluid velocity.1-3 The solid flow corresponding to these regimes is outlined in Figure 1a (spouted bed regime) and Figure 1c (jet-spouted bed regime). In applications involving the handling of solids of irregular texture (such as combustion or pyrolysis of plant biomass residues),4,5 or in catalytic polymerization where the solid is sticky and has a wide particle size distribution,6 it is advisable to operate within the transition regime (outlined in Figure 1b), in which solid flow characteristics are intermediate between those corresponding to a spouted bed and a jet-spouted bed but still maintaining the cyclic particle movement characteristic of the regime of the spouted bed and its performance. In this paper, the transition regime has been characterized by using bed voidage as a magnitude to quantify bed evolution, whose values range from 0.60 to 0.99. Bed voidage is required in gas and solid flow models and in the design of units for the aforementioned applications.
Figure 1. Solid flow outline: (a) spouted bed regime; (b) transition regime; (c) jet-spouted bed regime.
Experimental Section The study was carried out at a pilot plant unit with contactors of different geometry (angle, inlet diameter, and base diameter) (Figure 2) and in a wide range of values of stagnant bed height and air velocity (above that corresponding to minimum spouting). The equipment has been described in detail in previous papers.1-3 Several fractions of sawdust with different particle size ranges have been studied. The operating conditions are set out in Table 1.
Figure 2. Geometric factors of the contactor.
forces, FD/FG (a function of air velocity): Results The expansion of the spouted bed results in an increase in bed voidage, which follows the following relationship with the ratio of drag and gravitational * To whom correspondence should be addressed. Telephone: 34-4-46012527. Fax: 34-4-4648500. E-mail:
[email protected].
) a + b log(FD/FG)
(1)
This relationship has already been proven for the expansion of both fluidized and conventional spouted beds.2,7,8 In this paper it has been proven that eq 1 is fulfilled for the incipient states of the spouted bed and jet-
10.1021/ie990228z CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4121 Table 1. Values of Parameters a and b of Equation 1 for Different Experimental Systems
Table 2. Results of the Analysis of Variance Carried Out to Parameters a and b a
γ 25°
30°
40°
D0 (mm)
dp (mm)
H0 (cm)
a
b
a
b
a
b
6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10
0.05-0.3 0.05-0.3 0.05-0.3 0.3-0.8 0.3-0.8 0.3-0.8 0.8-2.0 0.8-2.0 0.8-2.0 0.05-0.3 0.05-0.3 0.05-0.3 0.3-0.8 0.3-0.8 0.3-0.8 0.8-2.0 0.8-2.0 0.8-2.0 0.05-0.3 0.05-0.3 0.05-0.3 0.3-0.8 0.3-0.8 0.3-0.8 0.8-2.0 0.8-2.0 0.8-2.0
5 10 15 5 10 15 5 10 15 5 10 15 5 10 15 5 10 15 5 10 15 5 10 15 5 10 15
0.779 0.809 0.831 0.899 0.939 0.968 1.027 1.079 1.117 0.764 0.791 0.812 0.878 0.915 0.942 1.001 1.048 1.083 0.754 0.778 0.798 0.863 0.898 0.924 0.981 1.026 1.059
0.246 0.262 0.273 0.246 0.263 0.275 0.246 0.264 0.277 0.237 0.253 0.263 0.237 0.253 0.265 0.236 0.253 0.266 0.229 0.246 0.256 0.220 0.246 0.257 0.229 0.246 0.257
0.801 0.834 0.859 0.925 0.969 1.002 1.057 1.115 1.156 0.784 0.815 0.838 0.902 0.944 0.974 1.029 1.082 1.121 0.773 0.801 0.823 0.887 0.926 0.954 1.009 1.059 1.095
0.252 0.269 0.280 0.252 0.270 0.283 0.251 0.271 0.285 0.242 0.259 0.270 0.242 0.260 0.272 0.241 0.260 0.273 0.235 0.252 0.263 0.235 0.252 0.264 0.233 0.251 0.264
0.839 0.878 0.906 0.970 1.023 1.060 1.110 1.177 1.226 0.820 0.857 0.884 0.946 0.995 1.030 1.079 1.141 1.187 0.807 0.842 0.867 0.928 0.974 1.008 1.056 1.115 1.158
0.261 0.280 0.292 0.261 0.282 0.296 0.260 0.283 0.299 0.252 0.270 0.282 0.251 0.271 0.285 0.249 0.271 0.286 0.244 0.263 0.274 0.244 0.263 0.276 0.242 0.262 0.276
spouted bed and throughout the transition between both regimes. Consequently, parameters a and b of eq 1 may be calculated from the values of bed voidage corresponding to the states of the incipient spouted bed, ms, and incipient jet-spouted bed, mj, that is, by solving the following set of equations:
ms ) a + b log(FD/FG)ms
(2)
mj ) a + b log(FD/FG)mj
(3)
Bed voidages ms and mj are calculated from the following correlations determined in previous papers: -3.20 0.857 (ms - 0)/(1 - ms) ) 3.40(FD/FG) 1.74 γ ms (Db/D0) (4) 1.35 1.95 (mj - 0)/(1 - mj) ) 215(FD/FG) 1.74 γ mj (Db/D0) (5)
In eqs 4 and 5, the ratio between drag and gravitational forces is calculated from
FD/FG ) (3/4)CDRe2/Ar
(6)
CD ) (24/Re)(1 + Re0.687)
(7)
where
The values of a and b obtained for all the experimental systems are set out in Table 1. It is observed that a and b take characteristic values for each contactorparticle system (that is, for given geometric factors of the contactor and particle size). Consequently, when these characteristic values of a and b are used, eq 1 allows for calculating the values of bed voidage corresponding to any bed state or expansion (any air velocity above that of minimum spouting).
variable
SS
df
MS
F
total H0 D0 dp γ residual
1.17 7.59 × 10-2 2.64 × 10-2 9.74 × 10-1 8.55 × 10-2 8.20 × 10-3
80 2 2 2 2 72
1.46 × 10-2 3.80 × 10-2 1.32 × 10-2 4.87 × 10-1 4.27 × 10-2 1.14 × 10-4
333.26 116.09 4277.60 375.16
variable
SS
df
MS
F
b total H0 D0 dp γ residual
10-2
2.15 × 1.28 × 10-2 4.47 × 10-3 1.40 × 10-5 4.06 × 10-3 1.56 × 10-4
80 2 2 2 2 72
10-4
2.69 × 6.40 × 10-3 2.24 × 10-3 6.98 × 10-6 2.03 × 10-3 2.17 × 10-6
2954.53 1032.60 3.22 935.99
As is observed in Table 1, the values of parameter a are within 0.773 (for γ ) 30°, D0 ) 10 mm, H0 ) 5 cm, 0.05 < dp < 0.3 mm) and 1.226 (for γ ) 40°, D0 ) 6 mm, H0 ) 15 cm, 0.8 < dp < 2.0 mm). Parameter b is within 0.229 (for γ ) 25°, D0 ) 10 mm, H0 ) 5 cm, any sawdust size) and 0.299 (for γ ) 40°, D0 ) 6 mm, H0 ) 15 cm, 0.8 < dp < 2.0 mm). By use of the statistical package STATGRAPHICS 5.0, the analysis of variance was carried out to separate the effects on the values of parameters a and b of both the geometric factors of the contactor and the experimental conditions. This technique allows for calculating the contribution to the total variance corresponding to each factor. Table 2 shows the results obtained for the sums of squares, degrees of freedom, and mean squares for each of the factors. When the calculated values of the F ratio (sampling distribution of Fisher) are compared to the tabulated value of F for 2 and 72 df, which is 3.05 at a 95% confidence level, it is concluded that parameter a depends mainly on the particle diameter, which is due to the different bed voidages of the stagnant bed, 0. The contactor angle and stagnant bed height also have an effect, though to a lesser extent, and the inlet diameter is the factor with least effect. Parameter b, whose value is an index of expansion difficulty or of flow rate needed for expansion, depends mainly on the stagnant bed height and to a lesser extent on both the inlet diameter and contactor angle. The particle size hardly has any effect. To show the validity of eq 1 and of the corresponding parameters a and b, the experimental values of bed voidage (points) are compared in Figure 3 to the values calculated using eq 1 (lines). Each plot corresponds to a different particle size and to three values of stagnant bed height, H0 ) 5, 10, and 15 cm, and are for the same values of geometric factors: γ ) 30°, D0 ) 10 mm. It is noteworthy that eq 1 is fulfilled in a very wide range of bed voidage, as its lower applicability limit, which corresponds to the incipient spouted bed, ms, is slightly higher than the stagnant bed voidage, 0, and that the bed voidage corresponding to the incipient jetspouted bed, mj, may be as high as 0.99. The relationship between bed voidage and gas velocity allows for calculating the parameters depending on both variables, such as the gas dispersion coefficient in the bed.9,10
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Nomenclature Ar ) Archimedes number, gdp3Fg(F - Fg)/µ2) CD ) drag coefficient Db, D0 ) upper diameter of the stagnant bed and inlet diameter, m dp ) particle diameter, mm FD/FG, (FD/FG)ms, (FD/FG)mj ) ratio between drag and gravitational forces, referred to Db F ) values of the sampling distribution of Fisher obtained as the ratio of MS for each of the factors to the residual MS df ) degrees of freedom H0 ) height of the stagnant bed, m MS ) SS/df or mean squares for each factor Re ) Reynolds number referred to Db, Fudp/µ SS ) sums of squared deviations Greek Letters , 0 ) bed voidage and loose bed voidage ms, mj ) bed voidage of minimum spouting and of minimum jet spouting γ ) contactor angle, deg µ ) viscosity, kg m-1 s-1 F, Fg ) density of the solid and of the gas, kg m-3
Literature Cited
Figure 3. Comparison of the experimental results of bed voidage (points) with those calculated using eq 1 (lines). Experimental systems: γ ) 30°; D0 ) 1 cm. (Plot a) 0.05 < dp < 0.3 mm. (Plot b) 0.3 < dp < 0.8 mm. (Plot c) 0.8 < dp < 2.0 mm.
Acknowledgment This work was carried out with the financial support of the Ministry of Education and Culture of the Spanish Government (Project QUI98-1105) and of the University of the Basque Country (Project G34-98).
(1) Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes. J. M.; Bilbao, J. Stable Operation Conditions for Gas-Solid Contact Regimes in Conical Spouted Beds. Ind. Eng. Chem. Res. 1992, 31, 1784. (2) San Jose´, M. J.; Olazar, M.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Expansion of Spouted Beds in Conical Contactors. Chem. Eng. J. 1993, 51, 45. (3) Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Pressure Drop in Conical Spouted Beds. Chem. Eng. J. 1993, 51, 53. (4) Olazar, M.; San Jose´, M. J.; LLamosas, R.; Bilbao, J. Hydrodynamics of Sawdust and Mixtures of Wood Residues in Conical Spouted Beds. Ind. Eng. Chem. Res. 1994, 33, 993. (5) Aguado, R.; Gaisa´n, B.; San Jose´, M. J.; Olazar, M.; Bilbao, J. Combustio´n de Serrı´n y Residuos Agroforestales en Spouted Beds Co´nicos. In Proceedings of the II European Conference on Fluidization. Olazar, M., San Jose´, M. J., Eds.; University of the Basque Country: Bilbao, Spain, 1997; p 395. (6) 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. (7) Richardson, J. F.; Zaki, W. N., Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng. 1954, 32, 35. (8) Kmiec, A. Expansion of Solid-Liquid Spouted Beds. Chem. Eng. J. 1975, 10, 219. (9) San Jose´, M. J.; Olazar, M.; Pen˜as, F. J.; Arandes, J. M.; Bilbao, J. Correlation for Calculation of the Gas Dispersion Coefficient in Conical Spouted Beds. Chem. Eng. Sci. 1995, 50, 2161. (10) Olazar, M.; San Jose´, M. J.; Pen˜as, F. J.; Arandes, J. M.; Bilbao, J. Gas Flow Dispersion in Jet Spouted Beds. Effect of Geometric Factors and Operating Conditions. Ind. Eng. Chem. Res. 1994, 33, 3267.
Received for review March 29, 1999 Revised manuscript received July 23, 1999 Accepted August 5, 1999 IE990228Z
