Spout Geometry in Shallow Spouted Beds with Solids of Different

Spout diameter has been measured in shallow spouted beds by means of an optical fiber probe, for different geometric factors of the contactor (base an...
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Ind. Eng. Chem. Res. 2005, 44, 8393-8400

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Spout Geometry in Shallow Spouted Beds with Solids of Different Density and Different Sphericity Marı´a J. San Jose´ ,* Sonia Alvarez, Alvaro Ortiz de Salazar, Martin Olazar, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain

Spout diameter has been measured in shallow spouted beds by means of an optical fiber probe, for different geometric factors of the contactor (base angle and gas inlet diameter) and under different experimental conditions (stagnant bed height, gas velocity, particle density, particle size, and particle shape). The study has been performed with glass beads and low-density solids (high and low-density polyethylene, polypropylene, and extruded and expanded polystyrene). A correlation that is valid to predict the average spout diameter in cylindrical spouted beds for beds composed of solids of different density, size, and shape has been developed that is in agreement with the experimental data. This equation is interesting for the proposal of real models for gas-solid flow. 1. Introduction The design of equipment for industrial application of spouted beds requires a knowledge of the bed properties. Among these properties, the geometry of the spout is especially relevant for the development of gas- and solidflow models. The spout geometry in spouted beds has been studied by several authors in the literature in conical spouted beds,1-4 in spouted beds of rectangular section,5 in spout-fluid beds,6 and in cylindrical spouted beds,7-18 because of the fact that it is a key factor for understanding the dynamics of the spouted bed. Although the experimental results in cylindrical spouted beds in the literature vary, a general observation is the fact that the evolution of the spout diameter with the bed level is only important at the gas inlet zone in the bed.9,11,13,14,16 Despite the fact that some researchers have tried to calculate theoretically the evolution of the spout diameter with the bed level,10,11,19-22 most of the mathematical models proposed for spouted beds suppose that the diameter of the spout-annular interface is not dependent on the longitudinal position along the bed.11,23-25 Usually, an average value of the diameter is taken, which is estimated from semiempirical or theoretical correlations. These correlations are a function of column diameter, fluid velocity, particle size or density, and stagnant bed height.8-11,13,14,19,26-29 In this paper, the study of the spout geometry in beds composed of materials with densities lower than the density of the glass beds has been performed in cylindrical spouted beds. A correlation for the calculation of the average spout diameter in spouted beds for uniform beds that are composed of solids of different density, size, and shape, which takes into account the effect of the angle of the base and of the inlet diameter, has been proposed, based on that of San Jose´ et al.18 for uniform beds that are composed of glass spheres. 2. Experimental Section The experimental unit design at pilot plant scale has been described in detail in previous papers.30-32 The * To whom correspondence should be addressed. Tel.: 3494-6015362. Fax: 34-94-6013500. E-mail: [email protected].

blower supplies a maximum air flow rate of 300 Nm3/h at a pressure of 15 kPa. The flow rate is measured by means of two mass flow meters in the ranges of 50300 and 0-100 m3/h, with both being controlled by a computer. The blower supplies a constant flow rate, and the first mass flow meter controls the air flow that enters the contactor (in the range of 50-300 m3/h) by acting on a motor valve that diverts the remaining air to the outside. When the flow required is 60° and a ratio between the inlet diameter and the column diameter of Do/Dc < 1/5 and with the equation proposed by Olazar et al.37 for contactors of base angle γb > 60° and Do/Dc > 1/5 for materials of different particle diameter, density, and shape.

10.1021/ie050447m CCC: $30.25 © 2005 American Chemical Society Published on Web 09/29/2005

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Figure 1. Geometric factors of the contactors. Table 1. Properties of the Materials materiala

Fs (kg/m3)

dp (mm)

φ

o

glass beads PP extruded PS extruded PS extruded PS expanded PS LDPE HDPE

2420 890 1030 1030 1030 65 923 940

3.5 3.5 3.5 2.0 1.0 3.5 3.5 3.5

1 0.90 0.80 0.80 0.80 0.95 0.95 0.92

0.35 0.36 0.36 0.35 0.34 0.32 0.34 0.36

a PP ) polypropylene; PS ) polystyrene; LDPE ) low-density polyethylene; and HDPE ) high-density polyethylene.

Figure 3. Signals of the optical fiber probe in the annular and spout zones of the bed. Parameters were as follows: γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, and extruded PS of dp ) 3.5 mm and u ) 1.02ums.

annular zone, the corresponding signal is formed by wide peaks, because of the fact that the particles are in contact and are moving at a low velocity. When the tip of the probe reaches the spout zone, the signal registered, which is formed by narrow and pronounced peaks, is that which corresponds to individual particles moving at high velocity. The radial position of the annular zone/ spout zone interface corresponds to the point where the signal changes from one to the other. The measurements have been performed at 20-mm intervals of bed level and at 2.5-mm intervals for radial positions of the probe tip. The delimitation of the interface between the spout zone and the annular zone has an experimental error of (1.25 mm. 3. Results Figure 2. Scheme of the equipment used and the arrangement of the optical fiber probe.

The technique for measurement of spout diameter consists of an optical fiber probe and has already been used for the study of local properties of spouted beds.3,4,17,18,38-44 The probe used for spout geometry measurement has been detailed in these previous papers. In Figure 2, a diagram of the equipment used and the arrangement of the optical fiber probe in the contactor are shown. A vertical displacement device positions the probe in front of the contactor hole, at the level at which the measurement is to be performed. The probe is placed in a radial position in the bed, through holes made in the contactor wall (at 20-mm intervals). Grooves that are marked on the probe allow the radial position in the bed to be set. The delimitation of the interface between the spout zone and the annular zone has been performed as shown in Figure 3, using the differences in the signals of the optical fiber probe. When the tip of the probe is in the

3.1. Geometry of the Spout. The general shape of the spout geometry is shown in Figure 3, which corresponds to a system that has been adopted as an example (γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; u ) 1.02ums with extruded PS that has a particle diameter of dp ) 3.5 mm). Qualitatively, the shape of the spout zone is similar in all the systems studied and has a pronounced expansion near the inlet of the contactor, which is followed by a neck and then expands toward the fountain. This spout geometry for uniform beds that consist of low-density solids is similar to that obtained in cylindrical spouted beds for uniform beds that are composed of spherical glass beads, by San Jose´ et al.18 In addition, this spout geometry has been obtained in conical spouted beds for uniform beds that consist of spherical glass beads by Olazar et al.3 and for uniform beds that consist of low-density solids by San Jose´ et al.4 The spout shape in Figure 3 has certain similarities with those of the cylindrical spouted beds observed by Mathur and Epstein12 but with the peculiarity that the

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Figure 4. Effect of the base angle γb on the evolution of the spout diameter with the bed level. Parameters were as follows: Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, and extruded PS of dp ) 3.5 mm and u ) 1.02ums.

expansion near the contactor inlet and toward the fountain is more pronounced. 3.2. Effect of the Geometric Factors and Operating Conditions on the Spout Geometry. The effect of the geometric factors of the contactor (base angle and inlet diameter) and operating conditions (stagnant bed height and gas velocity above that corresponding to the minimum spouting) on the spout geometry is shown in Figures 4-7. In Figure 4, the effect of the base angle on the evolution of spout diameter with bed level is plotted for beds that are composed of extruded PS. For base angles of 30°-60°, the spout has a neck at an intermediate level, independent of the base angle. The effect of the base angle on the initial widening of the spout in the lower section of the bed, as well as on the subsequent widening in the upper section, is not very important, although these widening are slightly greater for the base angle of 45°. For base angles of 120°-180°, the initial widening is smaller than that corresponding to smaller angles and the spout does not have a neck. The effect of the gas inlet diameter is analyzed in Figure 5. As observed in Figure 5a, as this diameter is increased, the spout diameter increases and the neck of the spout appears at slightly higher bed levels. Nevertheless, the relative neck of the spout (the ratio of the neck diameter to the inlet diameter, Ds/Do) appears at slightly higher bed levels and the final widening is less, mainly at higher bed levels (see Figure 5b). As the stagnant bed height increases (Figure 6), the initial widening of the spout in the lower section of the bed, as well as the widening of the spout after the neck, are higher. The neck of the spout appears at a slightly higher bed level and it is less pronounced for the greatest stagnant bed height. This effect is more pronounced than the observed in conical spouted beds (Olazar et al.,3 San Jose´ et al.4). For bed levels higher than the neck, the widening of the spout becomes greater as the stagnant bed height is increased. For the highest stagnant bed height, the spout neck is very slight; therefore, for beds where Ho/Do > 10, the neck is not very important. When the gas velocity is increased above that which corresponds to the minimum spouting (Figure 7), the widening of the spout at the inlet zone is slightly more pronounced, whereas the neck is less pronounced and appears at high bed levels.

Figure 5. Effect of the gas inlet diameter on (a) the evolution of the spout diameter with the bed level and (b) the evolution of the ratio of the neck diameter to the inlet diameter with the bed level. Parameters were as follows: γb ) 45°, Dc ) 0.152 m, Ho ) 0.20 m, and extruded PS of dp ) 3.5 mm, and u ) 1.02ums.

Figure 6. Effect of the stagnant bed height on the evolution of the spout diameter with the bed level. Parameters were as follows: γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, extruded PS of dp ) 3.5 mm, and u ) 1.02ums.

Even though the effect of the base angle and stagnant bed height on the spout diameter is similar to the observed in cylindrical spouted beds for beds that are composed of spherical glass beads (San Jose´ et al.18), the effect of gas velocity is more pronounced than that observed in cylindrical spouted beds for beds that are composed of spherical glass beads (San Jose´ et al.18) and in conical spouted beds for uniform beds that are composed of solids of different density and sphericity (Olazar et al.,3 San Jose´ et al.4). 3.3. Effect of Solid Properties on Spout Geometry. In Figures 8-12, the effect of solid properties (particle diameter, particle density, and particle shape) on the spout geometry is shown. As is observed in Figure

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Figure 7. Effect of the gas velocity on the evolution of the spout diameter with the bed level. Parameters were as follows: γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m and extruded PS of dp ) 3.5 mm.

Figure 8. Effect of particle diameter on the evolution of the spout diameter with the bed level. Parameters were as follows: γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, u ) 1.02ums and extruded PS.

8, which corresponds to beds of extruded PS, as the particle diameter is increased, the initial widening of the spout is slightly greater, the neck of the spout appears at slightly higher bed levels, and the posterior widening of the spout is more pronounced. When the solid density is increased (Figures 9 and 10), it is observed that the initial widening of the spout is higher, the neck of the spout is more pronounced, and it appears at higher bed levels. In fact, for uniform beds that consist of expanded PS, the narrowing is almost unnoticeable. The effect of particle shape on spout geometry for solids of similar density is shown in Figures 11 and 12. As the particle sphericity is increased, the spout diameter is slightly wider and the neck of the spout appears at slightly higher bed levels. 3.4. Average Spout Diameter. In the literature, for deep beds, the evolution of the spout geometry with the bed level is almost independent of the longitudinal position along the bed, so it is assuming a slight widening of the spout at the inlet zone and a constant diameter at higher bed levels. Nevertheless, in cylindrical spouted beds and in conical spouted beds, the variation of the spout with the bed level is very important, because it affects a large fraction of the bed volume and has an influence on gas and solid flow. In cylindrical spouted beds, as well as in conical spouted beds, the geometry of the spout is very sensitive to operating conditions, especially to the geometric

Figure 9. Effect of particle density on the spout geometry, given parameter values of γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, dp ) 3.5 mm and u ) 1.02ums: (a) glass beads, Fs ) 2420 kg/m3; (b) LDPE, Fs ) 923 kg/m3; and (c) expanded PS, Fs ) 65 kg/m3.

Figure 10. Effect of particle density on the evolution of the spout diameter with the bed level, given parameter values of γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, dp ) 3.5 mm, and u ) 1.02ums: (0) glass beads, Fs ) 2420 kg/m3; (4) LDPE, Fs ) 923 kg/m3; and (O) expanded PS, Fs ) 65 kg/m3.

factors of the contactor inlet (angle of the contactor and inlet diameter) and solid properties (density, size, and shape of the solid particles), which are not taken into account in the correlations proposed for calculation of the average spout diameter.8-11,13,14,19,26-28 The experimental values of the average spout diameter (Ds) in cylindrical spouted beds for uniform beds

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Ds ) 1.89

(

)( )

G0.49Dc0.68 Do Dc F 0.24 b

0.76

γb-0.15

(1)

with a regression coefficient of r2 ) 0.98. This equation takes into account the ratio diameter of the gas inlet/ diameter of the column (Do/Dc), the density of the loose bed (Fb), and the angle of the base (γb), which characterize the hydrodynamics of conical spouted beds. The experimental data of average spout diameter, Ds, in cylindrical spouted beds for all of the experimental systems studied has been calculated based on the volume of the spout (Vs), which has been calculated from the data of evolution of spout radius (rs) with bed level (z), by means of the following equation: rs

Vs )

Figure 11. Effect of the particle shape on the spout geometry, given parameter values of γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, dp ) 3.5 mm, and u ) 1.02ums: (a) LDPE, φ ) 0.95; (b) HDPE, φ ) 0.92; (c) polypropylene (PP), φ ) 0.90 and (d) extruded PS, φ ) 0.80.

H

π

∑0 [∆r∑0 ∆z2πr] ) 4(Ds)2H

(2)

As an example of the suitability of the experimental results for eq 1, the results obtained with this equation are compared in Table 2 with the experimental values of average spout diameter. The greatest error observed in Table 2 corresponds to a small particle diameter. As observed in Table 2, when the stagnant bed height is increased, the average spout diameter increases. This effect agrees with the equation of McNab;27 however, the empirical equation of Abdelrazek26 and the experimental values of average spout diameter of Zanoelo et al.29 indicate the opposite effect. The increase in gas velocity leads to an increase in the average spout diameter. This result is in agreement with previous studies in the literature.8-10,27,29 As the particle diameter increases, the average spout diameter increases. This result agrees with the effect reported by Lefroy and Davidson11 and is opposite to that of Zanoelo et al.29 The effect of increasing particle density gives an increase in the average spout diameter. This effect disagrees with the equation of Mikhailik9 and also with the results of Zanoelo et al.,29 who reported that the influence of solid density is negligible. The increasing in gas inlet diameter and particle sphericity gives an increase in the average spout diameter, whereas as the base angle γb increases, the average spout diameter Ds decreases. In Figure 13, the spout diameter Ds, the average spout diameter Ds, the gas inlet diameter Do, and the base

Figure 12. Effect of particle shape on the evolution of the spout diameter with the bed level, given parameter values of γb ) 45°, Dc ) 0.152 m, Do ) 0.03 m, Ho ) 0.20 m, dp ) 3.5 mm, and u ) 1.02ums: (0) LDPE, φ ) 0.95; (4) HDPE, φ ) 0.92; (O) PP, φ ) 0.90; and (9) extruded PS, φ ) 0.80.

that are composed of solids of different density, size, and shape have been fitted to the following equation, based upon that proposed by San Jose´ et al.18 for uniform beds that are composed of glass spheres, which, in turn, was a modification of the equations proposed by Bridgwater and Mathur19 and McNab,27 using the complex algorithm of optimization of Box:45

Figure 13. Diagram defining the spout diameter (Ds), average spout diameter (Ds), gas inlet diameter (Do), and base diameter (Di) (Do ) 0.03 m; Ho ) 0.20 m; extruded PS of dp ) 3.5 mm and u ) 1.02ums): (a) cylindrical spouted bed of conical base γb ) 45°, (b) conical spouted bed with γ ) 45°.

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Table 2. Experimental Values and Those Calculated Using Eq 1 of Average Spout Diameter for the Different Experimental Systems Ds(m) dp (mm)

Fs (kg/m3)

φ

γ (deg)

Do (m)

Ho (m)

u/ums

calcd

exptl

error

1.02 1.02 1.02 1.02

0.0402 0.0382 0.0352 0.0315

0.0346 0.0347 0.0345 0.0310

0.0056 0.0035 0.0007 0.0005

0.20 0.20 0.20

1.02 1.02 1.02

0.0386 0.0361 0.0315

0.0375 0.0362 0.0319

0.0011 -0.0001 -0.0004

0.20 0.20 0.20

1.02 1.02 1.02

0.0412 0.0392 0.0313

0.0393 0.0395 0.0323

0.0019 -0.0003 -0.0010

3.5 3.5 3.5 3.5

65 65 65 65

0.95 0.95 0.95 0.95

30 45 60 120

Expanded PS 0.03 0.20 0.03 0.20 0.03 0.20 0.03 0.20

3.5 3.5 3.5

890 890 890

0.90 0.90 0.90

45 60 180

0.03 0.03 0.03

3.5 3.5 3.5

923 923 923

0.95 0.95 0.95

30 45 180

0.03 0.03 0.03

3.5 3.5 3.5

940 940 940

0.92 0.92 0.92

45 60 120

0.03 0.03 0.03

0.20 0.20 0.20

1.02 1.02 1.02

0.0389 0.0359 0.0328

0.0383 0.0361 0.0332

0.0009 -0.0002 -0.0004

3.5 1.0 2.0 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5

1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030

0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80

30 45 45 45 45 45 45 45 45 45 45 60 120 180

Extruded PS 0.03 0.20 0.03 0.20 0.03 0.20 0.03 0.15 0.03 0.20 0.03 0.20 0.03 0.20 0.03 0.25 0.03 0.30 0.04 0.20 0.05 0.20 0.03 0.20 0.03 0.20 0.03 0.20

1.02 1.02 1.02 1.02 1.02 1.20 1.30 1.02 1.02 1.02 1.02 1.02 1.02 1.02

0.0379 0.0251 0.0317 0.0338 0.0370 0.0404 0.0420 0.0392 0.0409 0.0482 0.0591 0.0353 0.0325 0.0316

0.0365 0.0324 0.0339 0.0340 0.0368 0.0409 0.0428 0.0404 0.0448 0.0468 0.0568 0.0358 0.0328 0.0320

0.0014 -0.0073 -0.0022 -0.0002 0.0002 -0.0005 -0.0008 -0.0012 -0.0039 0.0014 0.0023 -0.0005 -0.0003 -0.0004

3.5 3.5 3.5

2420 2420 2420

1 1 1

30 45 120

Glass Spheres 0.03 0.20 0.03 0.20 0.03 0.20

1.02 1.02 1.02

0.0421 0.0403 0.0354

0.0393 0.0394 0.0350

0.0028 0.0009 0.0004

PP

LDPE

HDPE

diameter Di have been plotted in a cylindrical spouted bed of conical base and in a conical spouted bed, to compare the average spout diameter Ds. For a gas inlet diameter smaller than the base diameter (Do < Di), the value of Ds is between that of Do and Di, both in cylindrical spouted beds of conical base and in conical spouted beds. As observed in Figure 13a, in cylindrical spouted beds, the value of Ds is more similar to the gas inlet diameter Do, whereas in conical spouted beds (Figure 13b), the value of Ds is more similar to that of Di. 4. Conclusions The optical probe used and the program for signal treatment are suitable for determining the spout geometry of cylindrical spouted beds, as well as in conical spouted beds in a wide range of geometric factors and operating conditions. The spout geometry in cylindrical spouted beds is similar in all of the systems studied. Generally, it presents an initial widening in the lower section of the bed near the inlet of the contactor, and the spout has a neck at an intermediate bed level and a posterior widening in the upper section of the bed toward the top of the bed, as well as in conical spouted beds. In cylindrical spouted beds, it has been proven that the spout geometry is more sensitive to the geometric factors

and operating conditions than in conical spouted beds. The effect of the gas inlet diameter on the spout geometry is the most pronounced, followed by particle density, the stagnant bed height, and the gas velocity above that corresponding to the minimum spouting. The effect of the gas velocity above the minimum spouting velocity increases as particle density decreases. A correlation for calculation of the average spout diameter (Ds) in cylindrical spouted beds valid for uniform beds that are composed of solids of different density, size, and shape has been proposed based on that of San Jose´ et al.18 for uniform beds that are composed of glass spheres. This equation takes into account the ratio diameter of the gas inlet/diameter of the column (Do/Dc), the angle of the base (γb), and the gas velocity above that corresponding to the minimum spouting (u/ums). In cylindrical spouted beds, the value of Ds is between that of the gas inlet diameter (Do) and the base diameter (Di), and it is more similar to Do. Acknowledgment This work was carried out with the financial support of the University of the Basque Country (Project 9/UPV 00069.310-13607/2001). Nomenclature Dc ) diameter of the column (m) Di ) diameter of the bed base (m)

Ind. Eng. Chem. Res., Vol. 44, No. 22, 2005 8399 Do ) diameter of the gas inlet (m) Ds ) spout diameter (m) Ds ) average spout diameter (m) dp ) particle diameter (m) G ) fluid mass flow rate, relative to the column diameter Dc (kg m-2 s-1) H ) height of the developed bed (m) Ho ) height of the stagnant bed (m) r ) radial coordinate (m) z ) longitudinal coordinate (m) u ) velocity of gas (m/s) ums ) velocity of minimum spouting (m/s) rs ) radius of the spout (m) Vs ) spout volume (m3) Greek Letters φ ) sphericity γ ) contactor angle (deg) γb ) angle of the conical base of the contactor (deg) (rad in eq 1) Fb ) density of the loose bed (kg/m3) Fs ) density of the solid (kg/m3)

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Received for review April 14, 2005 Revised manuscript received July 1, 2005 Accepted July 13, 2005 IE050447M