Fountain Geometry of Beds Consisting of Plastic Wastes in Shallow

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Ind. Eng. Chem. Res. 2008, 47, 6228–6238

GENERAL RESEARCH Fountain Geometry of Beds Consisting of Plastic Wastes in Shallow Spouted Beds María J. San Jose´,* Sonia Alvarez, Alberto Morales, Martin Olazar, and Javier Bilbao Departamento de Ingeniería Química, Facultad de Ciencia y Tecnología, UniVersidad del Paiıs Vasco, Aptdo 644, 48080 Bilbao, Spain

The fountain is especially important in the design of spouted beds for the treatment of plastic wastes. The height and structure of the fountain in shallow spouted beds have been determined by means of an optical fiber as well as by an image treatment system. The effect of the operating variables on the fountain geometry (height and amplitude) has been analyzed by carrying out the operation with different values of the geometric factors of the contactor (base angle and gas inlet diameter) and of the operating conditions (stagnant bed height, particle diameter, particle density, particle shape, and air velocity). The materials studied are different plastic wastes (polyethylene, polypropylene, and polystyrene, both extruded and expanded). In the fountain, the core or solid ascending zone and the periphery or solid descending zone have been delimited. The experimental results prove the validity for plastic materials of the equation proven previously for prediction of the height of the fountain in cylindrical spouted beds of a conical base for glass spheres. An original equation has been proposed for prediction of the amplitude of the fountain in cylindrical spouted beds of a conical base for materials of varying density and shape. Introduction The growing consumption of plastic materials in the past decades justifies the increasing interest in plastic wastes recycling. The advantages of the conical spouted beds over fluidized beds causes this contact method to be especially suitable for the thermal treatment of plastics,1 where spouted bed technology plays a notorious role in the pyrolysis process.2 The fountain allows for a better distribution of plastic solids in the bed, therefore the possibility of a more homogeneous plastics pyrolysis reaction, and in thermal treatment contributes to avoid defluidization caused by sticky plastics agglomeration.2 Advancement in the design of spouted beds requires the establishment of theoretical models that define the solid flow in the contactor. The knowledge of solid flow in the fountain is required in order to relate the solid flow in the spout and annulus and to assemble, by means of correlations, the quantitative description of solid flow in the three bed zones of the spouted bed (spout zone, annular zone, and fountain). Furthermore, the role of the fountain in the distribution of the solid in the upper surface of the annulus makes it of vital importance in the segregation phenomena in the mixtures treatment. In addition, the consideration of the gas-solid contact in the fountain is especially important in shallow spouted beds, in which the fountain contributes to an important fraction of the total contact in the bed. The knowledge of the fountain height, the maximum height value at the axis, is important in the design of spouted beds, to establish the total height of the contactor. The fountain height has been determined experimentally by several authors, in conventional spouted beds3–13 and in conical spouted beds.14,15 Furthermore, correlations have been proposed in the literature for its calculation from the geometric factors of the contactorparticle system. The development of the correlations has been addressed through, on the one hand, theoretical bases such as * To whom correspondence should be addressed. Tel.: 34 94 6015362. Fax: 34 94 6013500. E-mail: [email protected].

force balances16,17 and, on the other hand, empirical correlations based on particular design factors determined from experimental studies.18–20 In previous papers, the fountain geometry has been studied in cylindrical spouted beds with uniform beds consisting of glass spheres of different particle size11 and in conical spouted beds with uniform beds consisting of materials of different density.15 In this paper, the geometry of the fountain (height, Hf, and amplitude, Af) and the delimitation of the interface between its core and periphery in uniform beds consisting of materials of different density and sphericity have been studied. Experimental Section The experimental unit used is described in previous papers and allows for operation with contactors of different geometry.21–23 The blower supplies a maximum air flow rate of 300 N m3 h-1 at a pressure of 15 kPa. The flow rate is measured by means of two mass flow meters in the ranges of 50-300 and 0-100 m3 h-1, 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-1) by acting on a motor valve that reroutes the remaining air to the outside. When the flow required is lower than 50 m3 h-1, it crosses the first mass flow meter and is regulated by the second one placed in series, which also acts on another motor valve that regulates the desired flow rate. The accuracy of this control is 0.5% of the measured flow rate. Five contactors of poly(methyl methacrylate) have been used, which have the following dimensions (geometry defined in Figure 1): column diameter, Dc, 0.36 m; contactor angle, γb, between 30 and 120°; height of the conical section, Hc, from 0.168 to 0.026 m; gas inlet diameter, Do, in the range of 0.03-0.05 m. Table 1 summarizes the geometric factors of the contactors. The solids used are glass spheres, high-density polyethylene (HDPE), polypropylene (PP), and two types of polystyrene (PS),

10.1021/ie071340x CCC: $40.75  2008 American Chemical Society Published on Web 07/25/2008

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Figure 2. Evolution of the pressure drop with air velocity for different values of the stagnant bed height. Experimental conditions: γb ) 45°; Do ) 0.03 m; HDPE of dp ) 3.5 mm; u ) 1.02 ums.

Figure 1. Geometric factors of the contactors. Table 1. Geometric Factors of the Contactor Poly(methyl methacrylate) and Operating Conditions factor or condition

symbol

value

column diameter contactor angle height of the conical section gas inlet diameter stagnant bed height gas velocity

Dc (m) γb (deg) Hc (m) Do (m) Ho (m) u (m/s)

0.152 30, 45, 60, and 120 0.168, 0.108, 0.078, and 0.026 0.03, 0.04, and 0.05 between 0.05 and 0.35 1.02, 1.20, and 1.30 ums

Table 2. Properties of the Materials material

Fs (kg/m3)

dp (mm)

φ

εo

glass spheres 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

extruded and expanded.11 Table 2 shows the properties of these materials, which have been used as supplied by Dow Chemical. The different particle sizes of the extruded PS have been obtained by means of a grinding mill (Fritzch Pulverizette 15). The stagnant bed heights studied are in the range between 0.05 and 0.35 m. The minimum spouting velocity (ums) in spouted beds has been calculated with the equation proposed by San Jose´ et al.24 for contactors with a base angle of γb < 60° and with the equation proposed by Mathur and Gishler25 for contactors with a base angle of γb g 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.26 for contactors of base angle γb g 60° and Do/Dc g 1/5 for materials of different particle diameter, density, and shape. The measurement of the bed pressure drop is sent to a differential pressure transducer (Siemens Teleperm), which quantifies these measurements within the 0-100% range. This transducer sends the 4-20 mA signal to a data logger (Alhborn Almeno 2290-8), which is connected to a computer, where the data are registered and processed by means of the software AMR-Control. This software also registers and processes the air velocity data, which allows for the acquisition of continuous curves of pressure drop vs air velocity.15,27

Figure 3. Scheme of the image treatment system.

To illustrate the different regimes and the determination of the experimental values of the minimum spouting velocity, in Figure 2 the results of the evolution of pressure drop in the bed with air velocity, for one spouted bed (contactor geometry: γb ) 45°; Do ) 0.03 m) and for a bed consisting of HDPE of 3.5 mm of particle diameter and for different values of the stagnant bed height, are shown as an example. The evolution of pressure drop by decreasing gas flow is plotted in dotted line. The geometric places of the conditions that delimit the beginning of the spouting are plotted in stroke line. This diagram is similar to that of a conical spouted beds reactor21 and peculiar of conical spouted-bed expansion for uniform beds23 and for mixtures.28 After the state of the fixed bed, the velocity becomes the value corresponding to the maximum pressure drop. After this, the pressure drop decreases sharply to the value of the stable pressure drop. As it is observed, the maximum pressure drop obtained by decreasing the gas velocity is much lower than that measured by increasing the air flow; therefore the hysteresis is noticeable. In addition, the hysteresis is more pronounced in cylindrical spouted beds than that observed in the same experimental conditions in conical spouted beds.21 The velocity corresponding to the beginning of the spouted bed regime is the minimum spouting velocity. The experimental value of this velocity is determined from the values of pressure drop by

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Figure 4. Example of trajectory visualization by the graphic analyzer of trajectories (GAT).

Figure 5. Scheme of the equipment used and the arrangement of the optical fiber probe.

decreasing slowly the gas flow as the point when the pressure drop levels off,1 because this velocity is more accurate and reproducible than the one obtained by increasing the gas flow. The external geometry of the fountain has been determined by means of a technique based on video equipment. This geometry has been subsequently verified by comparison with another technique based on an optical fiber. The measurement principle by means of the optical fiber probe is based on the collection of the light reflected by the bed particles (Figure 3). The light collected is amplified and sent to photodiodes, where it is converted to voltage (0-100 mV). These elements are installed in a unit that also contains the light source (12 V) for the emitting fiber and the filter for controlling the intensity of the beam. Data analysis and treatment are carried out by means of computer programs for signal treatment. The probe consists of a 3 × 1.5 mm encasing containing three optical fibers arranged in parallel, of which the central one is the one emitting light. The shape of the probe and its small section avoid disturbances in the solid flow. Each time a particle passes in front of the probe head, it reflects light emitted by the central one. The light reflected is collected in succession by the two lateral fibers. The video equipment, Figure 5, has been described in detail in a previous paper28 and is composed of a camera, a video recorder,

a monitor, and the computer support needed for treatment of the data obtained. The computer system developed for this application (in collaboration with the company Innovation and Maintenance, SAL) has been called Graphic Analyzer of Trajectories (GAT) and is computer controlled. The sequence of images corresponding to each experimental system is recorded with a data logger. This technique is based on filming the trajectories described by one of the particles. The height and amplitude of the fountain have been obtained point to point, with the video tape in pause position, by touching the tactile screen to mark the fountain height and amplitude in that moment. The video recorder is provided with several playback speeds in slow motion (from 1/6th up to 1/30th of the normal speed). The frame rate between two consecutive images is 25 fps; therefore the time interval between two images is 0.04 s. The filming period is approximately 30 s. The equipment calibration has been described in a previous paper.29 The average and standard deviation of these values have been mathematically calculated. The fountain geometry has been obtained drawing the boundary from the maximum values of the height reached by the particles in their trajectories. As an example, in Figure 4 the picture corresponding to the experimental system γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, extruded PS of dp ) 3.5 mm, and u ) 1.02 ums is shown. In this figure, particle trajectories are shown and the fountain boundary is drawn in continuous lines. In addition, the interface fountain core-periphery zone obtained by means of the optical fiber probe has been drawn in dotted lines. The properties at the base of the fountain required for applying the correlations (vertical component of particle velocity at the axis and bed voidage) and the delimitation of core and periphery zones of the fountain have been obtained by means of the optical fiber probe. This technique has also been used to confirm the measurements obtained with the other technique based on video imaging treatment, Figure 5. The probe was described in previous papers.30–34 In Figure 5, 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

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Figure 6. Signals of the optical fiber probe in the fountain. Table 3. Experimental Values of the Height and Amplitude of the Fountain for the Different Experimental Systems material

dp (mm)

Fs(kg/m3)

φ

γ (deg)

Do (m)

Ho (m)

u/ums

Hf (m)

Af (m)

expanded PS

3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 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 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5

65 65 65 65 65 65 923 923 923 923 923 923 923 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 1030 2420 2420 2420 2420 2420 2420 2420

0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 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 1 1 1 1 1 1 1

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

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.04 0.05 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.15 0.20 0.25 0.30 0.20 0.20 0.15 0.20 0.25 0.30 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.15 0.25 0.30 0.20 0.20 0.20 0.20 0.20 0.15 0.20 0.25 0.30 0.20 0.20 0.20

1.02 1.02 1.02 1.10 1.20 1.30 1.02 1.02 1.02 1.02 1.10 1.20 1.30 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.10 1.20 1.30 1.02 1.02 1.02 1.02 1.10 1.20 1.30

0.041 0.038 0.035 0.049 0.064 0.081 0.036 0.034 0.028 0.024 0.048 0.060 0.073 0.130 0.081 0.073 0.057 0.048 0.035 0.065 0.050 0.043 0.043 0.035 0.084 0.112 0.151 0.025 0.024 0.021 0.015 0.039 0.054 0.070

0.106 0.125 0.146 0.144 0.152 0.152 0.102 0.120 0.137 0.148 0.124 0.152 0.152 0.062 0.079 0.098 0.114 0.091 0.075 0.088 0.128 0.139 0.126 0.140 0.124 0.146 0.152 0.101 0.109 0.128 0.139 0.124 0.143 0.152

LDPE

extruded PS

glass spheres

on the probe allow the radial position in the bed to be set. The measurements have been performed 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. The delimitation of the external surface of the fountain and of the interface between the core and the periphery is carried out on the basis of the different signals between these zones, Figure 6. The probe gives no signal when there is no solid. Furthermore, the ascending zone (fountain core) and descending

zone (periphery) are distinguishable because the corresponding delay times are positive and negative, respectively. Results Fountain Shape and Delimitation of the Core and Periphery Zones in the Fountain. The external shape of the fountain depends on the experimental conditions and is generally of paraboloidal shape.16,34 Nevertheless, under certain experimental conditions, it also has the shape of a spherical cap.

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Figure 7. Scheme of the zones in the spouted bed and in the fountain.

In the fountain, two zones are distinguished (Figure 7), a core zone where solids rise and a peripheral zone where the particles descend toward the annulus of the bed. Whereas in the former zone the gas-solid contact is concurrent, in the latter it is countercurrent, and this difference is important from the point of view of solid flow. Despite the importance of this aspect, the interface between the core and periphery zones has hardly been studied. The interface between the core and the periphery of the fountain has been delimited (Figure 7) by means of the optical fiber. The results obtained, for all of the experimental systems studied, show that the cross-sectional area of the fountain core decreases with its level. These results agree with that obtained by He et al.5 by means of an optical fiber, who determined that the core initially widens, it then reaches its maximum diameter near the base of the fountain, and finally it narrower toward the top of the fountain. The geometries of the fountain and the delimitation between their two zones are shown in Figures 8–14. The core of the fountain has the same height as the fountain itself, and its maximum diameter (at the base of the fountain) is conditioned by the diameter of the spout zone on the upper surface of the bed. The diameter of the core (or ascending zone) decreases with the fountain level for all experimental conditions. In Figure 8, the effect of the base angle is analyzed for four values of the base angle, γb ) 30, 45, 60, and 120°. As is observed, as the base angle increases, the fountain height decreases. The amplitude of the fountain increases as the base angle is decreased from 30 to 120°. The effect of increasing stagnant bed height is shown in Figure 9 for the base angle of 45°. The fountain becomes smaller and wider as the stagnant bed height increases. This result, whereby the width of the fountain is not related to its height, is a consequence of the effect studied of the operating conditions

Figure 8. Effect of the base angle on the geometry of the fountain. Experimental conditions: γb ) 30, 45 60, and 120°; Do ) 0.03 m; Ho ) 0.20 m; extruded PS of dp ) 3.5 mm; u ) 1.02 ums.

on the width of the spout on the upper surface of the bed.36–38 This trend is also observed as the gas inlet diameter is increased, Figure 10, for three values of the gas inlet diameter. As it is observed in Figure 11, the particle diameter has a great influence on the fountain height, as well as on the fountain width. When the particle diameter is increased, the decreasing of the fountain height is very pronounced; nevertheless the width increases slightly. The effect of air velocity on fountain geometry is also noteworthy. The velocity increase above that of minimum spouting, Figure 12, makes the fountain become elongated. This result agrees with Wang et al.39 who found, for beds consisting of grain particles in spouted beds, that the fountain height

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Figure 10. Effect of the gas inlet diameter on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03, 0.04, and 0.05 m; Ho ) 0.20 m; extruded PS of dp ) 3.5 mm; u ) 1.02 ums. Figure 9. Effect of the stagnant bed height on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.15, 0.20, and 0.30 m; extruded PS of dp ) 3.5 mm; u ) 1.02 ums.

increased linearly with increasing spouting air velocity. For velocities above that of minimum spouting, the fountain core may be considered to be made up of two consecutive sections. In the first section (zone a in Figure 12b,c), the fountain core may be considered a continuation of the spout, where the diameter is almost equal to that of the spout on the upper surface of the bed. In the second section (zone b in Figure 12b,c), the geometry of the core is similar to that corresponding to the minimum spouting velocity (in Figure 12a). The effect of the solid density is shown in Figure 13, where the fountain geometries and the delimitation between their two zones, for glass spheres (F ) 2420 kg m-3) and expanded PS (F ) 65 kg m-3) are compared. The decrease in the solid density gives way to a higher fountain and, consequently, to a longer core. Moreover, the fountain is also wider. Furthermore, the fountain changes its shape from spherical cap to paraboloidal. The effect of the particle shape on the geometry of the fountain is analyzed in Figure 14, where the geometries of the fountain are compared under the same experimental conditions for two materials of similar density, but different particle shape. The upper graph corresponds to low-density polyethylene (LDPE; F ) 923 kg m-3; φ ) 0.95) and the lower graph to extruded polystyrene (PS; F ) 1030 kg m-3; φ ) 0.80). As is observed, when sphericity is decreased from 0.95 to 0.80, the fountain height is higher, whereas its width is slightly smaller.

This result is in agreement with those of Liu and Litster,9 for beds consisting of agricultural seeds in a 150 mm diameter cylindrical column with a 60° conical base, and with those of He et al.,5 for uniform beds consisting of different materials (glass beads, sand, steel shot, and polystyrene) in a cylindrical spouted bed of conical base, who reported that fountain height is very sensitive to particle shape and that it is higher for nonspherical particles. Fountain Height. The fountain height is the longitudinal position reached by the solid at the axis of the contactor. The experimental values of the fountain height have been determined by the equipment of particle optical monitoring, as it has been explained in the Experimental Section. In Figure 15, the experimental values of the height corresponds to one sequence of 750 images, in an experimental system (γb ) 45°, Do ) 0.03 m, Ho) 0.20 m, extruded polystyrene of dp ) 3.5 mm, and u ) 1.02 ums) as an example, have been plotted with the time. The average fountain height for this experimental system was 0.057 m, and the standard deviation was 0.011 m. The averages values of the experimental results of the fountain height measured in uniform beds consisting of solids of different density and sphericity (Table 2) for different geometric factors of the contactor and operating conditions (Table 1) are summarized in Table 3. These experimental results prove the validity of eq 1, obtained by Thorley et al.40 when they related the particle velocity at the base of the fountain to the fountain height by means of force balance; introducing the approximation that the drag force is small compared to gravity. This equation has

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Figure 11. Effect of the particle diameter on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; extruded PS of dp ) 1.0, 2.0, and 3.5 mm; u ) 1.02 ums.

been proven previously by Olazar et al.11 for uniform beds consisting of glass spheres. Hf )

υsH(0)2 Fs 2g Fs - F

(1)

The good fitting of the experimental results to eq 1 is shown in Figure 16 and Figure 17 with a maximum error of 5%, where the effect of the stagnant bed height, of the solid properties and of gas velocity on the fountain height is shown as an example. The lines have been calculated using eq 1, and the points are experimental results.

Figure 12. Effect of the gas velocity on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; extruded PS of dp ) 3.5 mm; u ) 1.02 ums, 1.20 ums, and 1.30 ums.

As the stagnant bed height is increased for the same value of the remaining experimental conditions, the fountain height decreases, Figure 16 and Figure 17. This result is a consequence of the fact that the fraction of the bed in the cylindrical section is increased. Thus, as the fraction of the bed in the cylindrical

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Figure 13. Effect of the solid density on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; glass spheres and expanded PS of dp ) 3.5 mm; u ) 1.02 ums.

Figure 15. Experimental fountain height values vs time. Experimental conditions: γb ) 45°; Do ) 0.03 m; extruded PS of dp ) 3.5 mm; u ) 1.02 ums.

Figure 14. Effect of the particle shape on the geometry of the fountain. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; LDPE and extruded PS of dp ) 3.5 mm; u ) 1.02 ums.

section is increased, the effect of the experimental conditions on the fountain height attenuates. As the particle density is increased, the fountain height decreases in all of the contactors, Figure 16a. These results correspond to the different materials studied and to the same value of the remaining operating conditions (Do ) 0.03 m, dp ) 3.5 mm, and u) 1.02 ums). The effect of the particle shape is illustrated in Figure 16b. It is shown that the smaller the sphericity, the higher the fountain. The effect of an increase in the relative velocity (gas velocity above the minimum spouting velocity) is an increasing of the fountain height, Figure 17. Thus, for the contactor of γb ) 45° with beds of extruded polystyrene and for u ) 1.30 ums, the fountain height is more than two times greater than that corresponding to u ) 1.02 ums. This increase is more important as the solid density increases, Figure 17a, and as the particle sphericity is decreased, Figure 17b. The effect of the solid density and sphericity on the fountain height is less pronounced in cylindrical spouted beds than in conical spouted beds (San Jose´ et al.15).

Figure 16. Effect of the stagnant bed height on the average fountain height. Lines: calculated with eq 1. Points: experimental results. Experimental conditions: γb ) 45°; Do ) 0.03 m; dp ) 3.5 mm; u ) 1.02 ums. (a) Glass spheres and expanded PS. (b) LDPE and extruded PS.

Amplitude of the Fountain. The amplitude of the fountain, Af, is the maximum diameter of the periphery of the fountain measured on the upper surface of the bed, Figure 7. The averages of experimental values of the amplitude of the fountain are shown in Table 3. It has been observed that the results of the amplitude of the fountain are affected by the experimental conditions in the same way that they affect the spout diameter

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Figure 17. Effect of the gas velocity on the average fountain height. Lines: calculated with eq 1. Points: experimental results. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; dp ) 3.5 mm; u ) 1.02 ums, 1.20 ums, and 1.30 ums. (a) Glass spheres and expanded PS. (b) LDPE and extruded PS.

on the upper surface of the bed. These results are explained because the amplitude of the fountain, due to its position, is a direct consequence of the magnitude of the spout diameter on the surface of the bed. In previous papers, the effect of the experimental conditions on the geometry of the spout has been studied in shallow spouted beds for beds consisting of glass spheres34 and for beds consisting of solids of different density and shape.36 The effect the stagnant bed height on the fountain amplitude is illustrated in Figure 18 for the different materials studied. As observed, the fountain is wider as the stagnant bed height increases. Scant attention should be paid to the effect of the gas velocity on the fountain amplitude, Figure 19. It is shown that as the gas velocity is increased, the fountain width significantly increases, and for some cases this width would be greater than the column diameter, Dc. From the point view of the design of spouted beds, the fountain width should be smaller than or equal to column diameter in order that particles do not collide with the contactor wall. In addition, it is observed that the amplitude of the fountain decreases as the particle density increases, Figure 18a and Figure 19a, as well as the particle sphericity decreases, Figure 18a and Figure 19b, and as the base angle of the contactor is increased, but increases as the stagnant bed height, the contactor inlet diameter, and the particle diameter are increased. The experimental results of the fountain width have been fitted to the following equation, where the geometric factors of the contactor and operating conditions are grouped in dimensionless modulus. The parameters of best fitting have been determined by a program written in Matlab by minimizing an error objective

Figure 18. Effect of the stagnant bed height on the average fountain width. Lines: calculated with eq 1. Points: experimental results. Experimental conditions: γb ) 45°; Do ) 0.03 m; dp ) 3.5 mm; u ) 1.02 ums. (a) Glass spheres and expanded PS. (b) LDPE and extruded PS.

function. This has been defined as the ratio between the sum of squares of the differences between experimental and calculated values and the number of degrees of freedom. Af ) 0.35γ-0.49

( ) () ( ) ( ) Do Di

0.41

dp Di

0.49

Ho Di

0.68

u ums

1.20

Fs-0.04φ0.30 (2)

The validity of eq 2 is shown in Figures 18 and 19, where the effect of the contactor angle and the gas velocity on the fountain width are plotted for the materials studied. The lines have been calculated by means of eq 2, and the points are experimental. The effect of the solid density and sphericity on the fountain width is less pronounced in cylindrical spouted beds than in conical spouted beds (San Jose´ et al.15). The adequacy of the equation proposed is shown in Figure 20, in which the calculated and experimental values of yields are shown. As it is observed, the fitting is excellent, which is also evidenced by the low value obtained for the objective function (3.3 × 10-4). Conclusions The geometry of the fountain in shallow spouted beds depends, to a great extent, on the experimental conditions and on the solid properties. The fountain shape in shallow spouted beds consisting of low-density materials is generally paraboloidal, as was observed by Mathur and Epstein33 and by Grace and Mathur16 but has the shape of a spherical cap under certain experimental conditions as well as for glass spheres.11 The decrease in the solid density changes the fountain shape from

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amplitude increases and under some experimental conditions the fountain would be wider than the column diameter. Generally, it is advisable for the design not to reach the condition of u ) 1.20 ums to ensure not to exceed the Dc for low densities (plastic materials) and u ) 1.30 ums for high densities (glass spheres). The decreasing in the solid density increases the fountain height and makes the fountain core become elongated as well as produce a greater fountain amplitude. A decrease in the solid sphericity gives way to a higher fountain height, whereas its width is smaller. The equation proposed by Thorley et al.40 has been proven to be valid for calculating the fountain height in shallow spouted beds for uniform beds consisting of low-density materials as well as for uniform beds consisting of glass spheres.11 This equation relates the particle velocity at the base of the fountain to the fountain height, by means of force balance, ignoring drag force. The effect of the geometric factors and operating conditions on the fountain width has been quantified by means of eq 2. Acknowledgment This work was carried out with the financial support of the Ministry of Industry of the Basque Government (Project SPE06IKA02 and Project DIPE 07/09). Nomenclature Figure 19. Effect of the gas velocity on the average fountain width. Lines: calculated with eq 1. Points: experimental results. Experimental conditions: γb ) 45°; Do ) 0.03 m; Ho ) 0.20 m; dp ) 3.5 mm; u ) 1.02 ums, 1.20 ums, and 1.30 ums. (a) Glass spheres and expanded PS. (b) LDPE and extruded PS.

Af ) amplitude of the fountain (m) Dc ) diameter of the column (m) Di ) diameter of the bed base (m) Do ) diameter of the inlet (m) dp ) particle diameter (m) g ) gravity constant (m s-2) Hc ) height of the conical section (m) Hf ) height of the fountain (m) Ho ) height of the stagnant bed (m) r ) radial coordinate (m) z ) longitudinal coordinate (m) u ) velocity of the gas (m s-1) ums ) minimum spouting velocity of the gase (m s-1) Greek Letters εo ) voidage of the static bed. φ ) sphericity. γb ) angle of the conical base of the contactor (deg, rad in eq 1) Fs ) density of the solid (kg m-3) νsH(0) ) vertical component of solid velocity in the axis of the contactor at the base of the fountain (m s-1)

Figure 20. Comparison of experimental values of the fountain width with values calculated using eq 2.

spherical cap to paraboloidal. Nevertheless, the effect of the solid sphericity on the fountain shape is almost negligible. In the fountain, two zones are distinguished: the core or solid ascending zone and the periphery or solid descending zone. The core of the fountain has the same height as the fountain itself, and its maximum diameter (at the base of the fountain) is conditioned by the diameter of the spout zone on the upper surface of the bed. The diameter of the core (or ascending zone) decreases with the fountain level for all experimental conditions. The effect of the gas velocity on the fountain geometry is the most important, followed by particle diameter, particle density, stagnant bed height, gas inlet diameter, particle sphericity, and base angle. As gas velocity is increased, the fountain

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ReceiVed for reView October 4, 2007 ReVised manuscript receiVed May 7, 2008 Accepted May 30, 2008 IE071340X