Spout and Fountain Geometry in Conical Spouted Beds Consisting of

The effect of the geometric factors of the contactor and of the operating conditions on the geometry of the spout and fountain has been studied by mea...
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Ind. Eng. Chem. Res. 2005, 44, 193-200

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Spout and Fountain Geometry in Conical Spouted Beds Consisting of Solids of Varying Density Marı´a J. San Jose´ ,* Martin Olazar, Sonia Alvarez, Alberto Morales, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain

The effect of the geometric factors of the contactor and of the operating conditions on the geometry of the spout and fountain has been studied by means of an optical fiber probe. In the fountain, the core or solid ascending zone and the periphery or solid descending zone have been delimited. The materials studied are glass beads and different plastics (polyethylene, polypropylene, and polystyrene, both extruded and expanded). A correlation proposed for the calculation of the average spout diameter in cylindrical spouted beds of a conical base has been proven to be valid for these materials of low density. New correlations are proposed for the calculation of the height and width of the fountain. 1. Introduction Different modifications of the original spouted bed (cylindrical with a conical base) are proposed in the literature with the aim of improving its performance. These modifications mainly concern the geometry of the contactor and/or the gas inlet to the bed. Given the advanced knowledge of their hydrodynamics and applications, the spouted beds of the rectangular section, also with a rectangular gas inlet,1,2 the conical spouted beds,3-9 and the spout-fluid bed,10-16 which combines the advantages of the spouted bed and of the bubbling fluidized bed, are worth mentioning. Spouted beds with a fully conical geometry combine the features of the cylindrical spouted beds (such as the capacity for handling coarse particles, small pressure drop, cyclic movement of the particles, and so on) with those inherent to their geometry, such as stable operation in a wide range of gas flow rates.3,4,17 This versatility in the gas flow rate allows for the handling of particles of irregular texture, fine particles, and those with a wide size distribution and sticky solids, whose treatment is difficult using other gas-solid contact regimes.6,18-20 Moreover, operation can be carried out with short gas residence times (as low as milliseconds) in the dilute spouted bed.21,22 The interest of these features of the conical spouted beds has been proven in such reactions as pyrolysis and gasification of sub-bituminous coals,23,24 pyrolysis and gasification of sawdust and other vegetable biomass materials,25,26 pyrolysis of waste plastics,27 and catalytic polymerizations.20,22 In all of these reactions, there is a wide particle size distribution and particles are sticky, which provokes defluidization of bubbling fluidized beds, which is the more developed technology for the vaporization of waste materials. Moreover, the short residence time of the pyrolysis primary products allows for maximization of their yield, which is interesting for the production of waxes and for minimization of the generation of polyaromatics in the pyrolysis of polyolefins.28 Conical spouted beds have a low segregation, which allows for use of catalysts in situ in these reactions of * To whom correspondence should be addressed. Tel.: 3494-6015362. Fax: 34-94-6013500. E-mail: [email protected].

pyrolysis of waste materials in order to improve the distribution of products and, consequently, to increase their commercial interest.22,29 This property is also interesting for handling lime, without segregation in the retention of SOx in the gasification of coal. Thus, solids (such as calcium oxide or dolomites) may be used in situ for adsorption or as reactants, to retain chlorhydric acid in the pyrolysis of poly(vinyl chloride). The design of equipment for industrial application of conical spouted beds requires a better knowledge of bed properties. Among these properties, the geometries of the spout and of the fountain are especially relevant for the development of gas and solid flow models. These properties have already been studied in the conical spouted beds made up of glass beads.30 The aim of this paper is to further the knowledge of these properties for beds made up of low-density materials. This study is especially interesting for the design of reactors for the pyrolysis of waste plastics. 2. Experimental Section The experimental unit used is described in previous papers and allows for operation with contactors of different geometry.3-5 The blower supplies a maximum air flow rate of 300 N m3 h-1 at a pressure of 1500 mm of the water column. The flow rate is measured by means of two mass flowmeters 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 flowmeter 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 flowmeter 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. 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

10.1021/ie040137o CCC: $30.25 © 2005 American Chemical Society Published on Web 11/20/2004

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Figure 1. Geometric factors of the contactors. Table 1. Properties of the Materials Used material

F (kg m-3)

dp (mm)

φ

o

PP extruded PS extruded PS extruded PS expanded PS LDPE HDPE

890 1030 1030 1030 65 923 940

3.5 3.5 2.0 1.0 3.5 3.5 3.5

0.90 0.80 0.80 0.80 0.95 0.95 0.92

0.36 0.36 0.35 0.34 0.32 0.34 0.36

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. Five conical contactors made of poly(methyl methacrylate) have been used. Figure 1 shows the geometric factors of these contactors, whose dimensions are as follows: column diameter, Dc, 0.36 m; contactor angle, γ, 28, 33, 36, 39, and 45°; height of the conical section, Hc, 0.60, 0.50, 0.45, 0.42, and 0.36 m; gas inlet diameter, Do, 0.03, 0,04, and 0.05 m. The solids used are high-density polyethylene (HDPE), polypropylene (PP), and two types of polystyrene (PS), extruded and expanded PS. Table 1 shows the properties of these materials, which have been used as supplied by Dow Chemical. The different particle sizes of the extruded PS (1.0, 2.0, and 3.5 mm) 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 values of sphericity have been estimated by means of the Ergun equation and are those that best fit the data of the frictional pressure drop at several flow velocities. The measurement principle by means of the optical fiber probe is based on the collection of the light reflected by the bed particles (Figure 2). The light collected is amplified and sent to photodiodes, where it is converted

Figure 2. Arrangement of the three optical fibers in the probe.

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. Particles passing at a distance greater than the field range from the tip of the probe are not registered. With a change in the intensity of light emitted (of 50 Hz of frequency), the field range is adjusted in order to cater to a specific particle diameter, which allows for attainment of a signal of maximum clarity. The field range may be varied from 1 to 8 mm, which allows for the study of beds with particle sizes within this range. The maximum solid angle of the field range is 64°. The interface between the spout and the annulus is delimited by the differences in the signals of the optical probe (Figure 3). When the tip of the probe is in the annulus, the corresponding signal is formed by wide peaks, which is a consequence of the fact that particles are in contact and slowly moving downward. A displacement device is provided for the probe, and grooves marked on the probe allow for setting of the radial position in the bed. When the probe is radially displaced and its head reaches the spout, the signal changes sharply and is formed by narrow and pronounced peaks, which are a consequence of the individual particles rising at high velocity through the spout (Figure 3). These measurements have been carried out at 20 mm intervals of the bed level and at 2.5 mm intervals for radial positions of the probe. In this way, the interface between the annulus and the spout is delimited with an experimental error of (1.25 mm. The clarity of the peaks in the signal obtained in the spout zone allows for counting of the number of particles rising within a time range, given that each peak corresponds to one particle. The delimitation of the two zones of the fountain, the core or particle ascending zone and the periphery or particle descending zone, is carried out in the same way as the delimitation of the spout and annulus, that is, on the basis of the different signals when the probe is radially displaced. In the former case, the differences in the signals are not as pronounced as those in the latter case. For the measurement of the fountain geometry (height and width), a device for filming and image treatment has been used. It consists of a camera (Hitachi VM-

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Figure 3. Signals of the optical fiber probe in the annulus and spout.

S7200E of eight luxes with a horizontal resolution of 625 lines), a video recorder (JVC BR-S600E super VHS with a horizontal resolution of 400 lines), a monitor (JVC VM-R150E with a horizontal resolution of 500 lines and a tactile screen Elographics 274), and the software application for data acquisition (by means of a card PLC-725) and their subsequent treatment. 3. Results 3.1. Spout Diameter. After the first trial of Volpicelli et al.31 for finding a relationship of the spout diameter with the bed level in cylindrical spouted beds, several theoretical expressions have been deduced.32-36 In the design of these contactors, empirical or semiempirical expressions have been used for the calculation of the average spout diameter.31-33,37,39-45 The geometry of the spout in conical spouted beds for the different experimental systems studied is similar to that of Figure 3, which corresponds to extruded PS and to certain experimental conditions (γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums). The value of the minimum spouting velocity has been determined using a previously proposed correlation of Olazar et al.,3 in which the validity for materials of low density has already been proven.46 In Figure 3, it is observed that the spout has a pronounced neck near the contactor inlet and then progressively expands up to the fountain. This spout shape for beds made up of plastics is similar to that already determined, using the same technique, for single-sized beds of glass beads of particle diameters from 1 to 8 mm in conical spouted beds30 and in cylindrical ones with a conical base.45 This geometry of the spout confirms the partial results found in the literature for conical spouted beds. Thus, Mukhlenov

Figure 4. Effect of the contactor angle on the evolution of the spout diameter with the bed level. Solid: extruded PS, Do ) 0.03 m, Ho ) 0.18 m, dp ) 3.5 mm, and u ) 1.02ums.

and Gorshtein47 observed a contraction of the spout at an intermediate level of the bed, and Gol’tsiker48 determined a significant expansion of the spout after the neck. The results of Figures 4-8 illustrate the effect of the geometric factors of the contactor and of the operating conditions on the longitudinal profile of the spout diameter throughout the bed. All of the results correspond to extruded PS and are an example of the results obtained. The results obtained for the other materials are qualitatively similar. In Figure 4, it is observed that an increase in the contactor angle from 33 to 36° does not affect the evolution of the spout diameter up to the neck. The size of the neck is similar for both angles. Nevertheless, for 45°, the neck is more pronounced and is located at lower levels in the bed. Likewise, when the angle is increased,

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Figure 5. Effect of the gas inlet diameter on the evolution of the spout diameter with the bed level. Solid: extruded PS, γ ) 33°, Ho ) 0.18 m, 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. Solid: extruded PS, γ ) 33°, Do ) 0.03 m, dp ) 3.5 mm, and u ) 1.02ums.

Figure 7. Effect of the particle diameter on the evolution of the spout diameter with the bed level. Solid: extruded PS, γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums.

the subsequent expansion of the spout above the neck is more pronounced. When the contactor inlet diameter is increased, the spout diameter obviously increases (Figure 5). Nevertheless, the ratio of the neck diameter to the inlet diameter remains almost constant for any inlet diameter. It is also observed that when the inlet diameter is increased, the neck appears at a slightly higher level in the bed. An increase in the stagnant bed height (Figure 6), particle diameter (Figure 7), and air velocity over that corresponding to the minimum (Figure 8) causes both

Figure 8. Effect of the gas velocity on the evolution of the spout diameter with the bed level. Solid: extruded PS, γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and dp ) 3.5 mm.

Figure 9. Evolution of the spout diameter with the bed level for different materials: γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums.

the displacement of the neck to higher levels in the bed and the neck to be more pronounced. Above the neck, the spout diameter enlarges as the particle diameter is increased and, particularly, when the air velocity is raised. Scant attention should be paid to the effect of the solid density. This effect is illustrated in Figure 9, where the evolution of the spout diameter with the bed level is shown for the different materials studied. The results correspond to the same experimental conditions as those shown above. It is shown that, as the solid density is increased, the spout diameter significantly increases, the neck is more pronounced, and its position displaces toward higher levels in the bed. It is noteworthy that the solid density effect of increasing the spout diameter is more pronounced as the stagnant bed height is increased, as is observed by comparing the results of Figure 9, corresponding to Ho ) 0.15 m, with those of Figure 10, corresponding to Ho ) 0.23 m, with the remaining operating conditions staying the same. In view of the difficulty for obtaining a correlation for the calculation of the spout diameter evolution with the bed level, the following correlation is proposed for the calculation of the average spout diameter.

Ds ) 0.52G0.16Do0.41γ-1.19Db0.80ur0.80

(1)

Equation 1 is that corresponding to the best fitting of the experimental results (with a regression coefficient r2 ) 0.95 and a relative error lower than 5%). This equation is very similar (except that it is does not

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Figure 10. Evolution of the spout diameter with the bed level for different materials: γ ) 33°, Do ) 0.03 m, Ho ) 0.23 m, and u ) 1.02ums.

Figure 12. Effect of the particle diameter on the geometry of the fountain. Solid: glass beads, γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums.

Figure 11. Effect of the contactor angle on the geometry of the fountain. Solid: glass beads, Do ) 0.03 m, Ho ) 0.18 m, dp ) 4 mm, and u ) 1.02ums.

include the diameter of the cylindrical section) to that proposed by San Jose´ et al.45 for shallow cylindrical spouted beds, which in turn is a modification of the equations proposed by Mc Nab40 and Bridgwater and Mathur33 for cylindrical spouted beds. The data of Ds used for obtaining eq 1 have been calculated from the volume of the spout, Vs, whose values are obtained from the experimental results of Ds vs z according to rs

Vs )

H

π

∑0 ∑0 ∆z(2π)r] ) 4(Ds)2H [∆r

(2)

3.2. Geometry and Zones of the Fountain. The interface between the particle ascending and descending zones in the fountain has been determined by means of an optical probe, as was described in the Experimental Section (Figure 2). The core of the fountain has the same height as the fountain itself, and its maximum width is that corresponding to the spout on the upper surface of the bed (at the base of the fountain). By means of the equipment for filming and image treatment described above, the external geometry of the fountain (specifically height and width) is obtained. The results obtained for all of the experimental systems show that the cross-sectional area of the fountain core decreases with its level. This result agrees with that obtained for cylindrical contactors of a conical base.45 In the case of our experimental systems, the external shape of the fountain changes, according to the operating conditions, from the paraboloidal shape (high and

Figure 13. Effect of the gas velocity on the geometry of the fountain. Solid: glass beads, γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and dp ) 4 mm.

longish) described by Mathur and Epstein49 and by Grace and Mathur50 to a spherical cap (low and rounded). As an example of the results, those corresponding to the same material (glass) are shown in Figures 11-13, where Figure 11 displays the effect of the contactor angle, Figure 12 that of the particle size, and Figure 13 that of the air velocity. As is observed in Figure 11, the contactor angle has a small influence on the fountain height but has a strong influence on the fountain width. In fact, the greater the angle, the wider the fountain. This result, whereby the width of the fountain is not related to its height, is a consequence of the conical geometry of the contactor and

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Figure 16. Comparison of the fountain height results calculated with eq 3 (lines) with the experimental ones (points): Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums. Figure 14. Effect of the material density on the geometry of the fountain: γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums.

Figure 17. Comparison of the fountain width results calculated with eq 4 (lines) with the experimental ones (points): Do ) 0.03 m, Ho ) 0.18 m, and u ) 1.02ums.

Figure 15. Effect of the particle shape on the geometry of the fountain: γ ) 33°, Do ) 0.03 m, Ho ) 0.18 m, dp ) 3.5 mm, and u ) 1.02ums.

of the effect studied above of the operating conditions on the width of the spout on the upper surface of the bed. Thus, as is observed in Figure 12, when the particle diameter is increased, the fountain decreases but its width is hardly affected. When the air velocity is increased (Figure 13), both the height and the width increase, which is evidence of the importance of this parameter in order to modify the solid distribution in the fountain and, consequently, the global solid flow pattern in the bed. The effect of the solid density is shown in Figure 14, where the fountain geometries for glass (F ) 2429 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. The effect of the particle shape on the geometry of the fountain is also noteworthy. In Figure 15, 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 almost double, whereas its width is slightly smaller. The experimental results of the fountain height have been fitted by means of the Complex method for nonlinear regression to the following equation as a function of the contactor angle, dimensionless moduli characteristic of the contactor-particle system, solid density, and particle shape (regression coefficient r2 ) 0.96 and a relative error lower than 5%):

Hf ) 1.01 × 10-2γ-0.14

() () ( ) ( ) Do Di

-1.14

dp Do

-0.83

u ums

Ho Di

-0.52

4.80

F-0.12φ-1.45 (3)

The good fitting of the experimental results to eq 3 is shown in Figure 16, where the effect of the contactor angle on the fountain height is shown as an example. The lines have been calculated using eq 3, and the points are experimental results. These results correspond to the different materials studied and to the same value of the remaining operating conditions (Do ) 0.03 m, Ho ) 0.18 m, dp ) 3.5 mm, and u ) 1.02ums).

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The experimental results of the fountain width have been fitted to the following equation:

Af ) 0.47γ0.85

() () ( ) ( ) Do Di

0.29

dp Do

0.43

Ho Di

0.69

u ums

2.20

F-0.21φ1.22 (4)

The validity of eq 4 is revealed by Figure 17, where the effect of the contactor angle on the fountain width is shown for the materials studied. The lines have been calculated by means of eq 4, and the points are experimental. These results correspond to the same experimental conditions (Do ) 0.03 m, Ho ) 0.18 m, dp ) 4 mm, and u ) 1.02ums).

r, z ) cylindrical coordinates, m rs ) spout radius, m u, ums ) velocity and minimum spouting velocity of the gas, m s-1 ur ) relative velocity of the gas referred to the minimum spouting velocity Vs ) spout volume, m3 Greek Letters o ) voidage of the static bed φ ) sphericity γ ) contactor angle, deg (rad in eqs 3 and 4) F ) solid density, kg m-3 Fb ) density of the loose bed, kg m-3

Literature Cited 4. Conclusions The geometric factors of the contactor and the operating conditions (including density) have a major influence on the geometries of the spout and of the fountain and on the two zones of the fountain (core and periphery). As the solid density is increased, the spout diameter significantly increases, the neck is more pronounced, and its position displaces toward higher levels in the bed. This solid density effect of increasing the spout diameter is more pronounced as the stagnant bed height is increased. The operating conditions also have a major influence on the geometry of the spout. The width of the fountain is not related to its height because of the effect of the operating conditions on the width of the spout on the upper surface of the bed. This effect of the operating conditions has been quantified by means of eq 3 for height calculation and of eq 4 for width calculation. The results are evidence of the importance of the air velocity as a variable that modifies the solid distribution in the fountain and, consequently, the global solid flow pattern in the bed. The important effect of the particle shape on the geometry of the fountain has been proven, so that when the particle sphericity is decreased, the height of the fountain increases, whereas the width decreases slightly. Acknowledgment This work was carried out with the financial support of the University of the Basque Country (Project 9/UPV 00069.310-13607/2001) and of the Ministry of Science and Technology of the Spanish Government (Project PPQ2001-0780). Note Added after ASAP Publication. This article was released ASAP on November 20, 2004, with incorrect information in columns 3-5 of Table 1. The correct version was posted on November 29, 2004. Notation Af, Hf ) width and height of the fountain, m Db ) upper diameter of the stagnant bed, m Dc, Di, Do, Ds ) diameters of the column, of the bed bottom, of the inlet, and of the spout, respectively, m Ds ) average spout diameter, m dp ) particle diameter, mm G ) fluid mass flow rate per unit of the upper cross section of the stagnant bed, at the minimum spouting condition, kg m-2 s-1 H, Hc, Ho ) heights of the developed bed, of the conical section, and of the stagnant bed, respectively, m

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Received for review April 29, 2004 Revised manuscript received September 28, 2004 Accepted September 28, 2004 IE040137O