- Email: [email protected]
Local porosity in conical spouted beds consisting of solids of varying density
Chemical Engineering Science 60 (2005) 2017 – 2025 www.elsevier.com/locate/ces
Local porosity in conical spouted beds consisting of solids of varying density María J. San José∗ , Martin Olazar, Sonia Alvarez, Alberto Morales, Javier Bilbao Departamento de Ingeniería Química, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain Available online 29 January 2005
Abstract Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fluidization; Hydrodynamics; Particle processing; Conical spouted bed; Spouted bed; Voidage
1. Introduction The spouted bed of totally conical geometry allows for handling, in a stable way and without segregation, solids of different size, irregular texture and sticky ones. It has been successfully used in the polymerization of sub-bituminous coal (Uemaki and Tsuji, 1986) and in catalytic polymerizations (Bilbao et al.,1987; Olazar et al., 1994, 1997). Recently, this bed has been proven to have a good performance in the pyrolysis of biomass (Aguado et al.,2000; Olazar et al.,2000), of black liquor (Olazar et al.,2002) and of waste plastics (Aguado et al., 2002a,b, 2003). In addition to the features of the conventional spouted beds (cylindrical ones and those with conical bottom), such as the cyclic movement of the particles and an almost countercurrent contact between gas and solid, the conical spouted bed allows for operating stable in a wide range of gas flowrates, which may be increased almost without limit in order to increase bed turbulence (Olazar et al., 1992, 1999). ∗ Corresponding author. Tel.: +34 946 012527; fax: 34 946 013500.
E-mail address: [email protected] (M.J. San José). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.12.004
In the pyrolysis of waste plastics, the cyclic movement of the solid (characteristic of spouted beds) facilitates the homogeneous coating of the sand particles that make up the bed with the feeding plastic (Aguado et al., 2002a,b). This homogeneity is especially important in order to attain a good gas-solid heat transfer. Moreover, when gas velocities above those for minimum spouting are used, agglomeration of sticky particles in the bed is avoided. This agglomeration is the main problem of fluidized beds for this application (Arena and Mastellone, 2000; Mastellone and Arena,2002). In order to design the conical spouted bed reactor for pyrolysis of waste plastics, progress in the modelling of the gas and solid is still required. One of the difficulties for the proposal of these models is the heterogeneity of bed voidage in each of the three zones of the spouted bed (spout, annulus and fountain) (Fig. 1The volume of these zones depends on the geometric factors of the contactor (angle, inlet diameter) and on the experimental conditions (particle diameter, stagnant bed height). In a previous paper, the influence of these conditions on the geometry of the spout and fountain has been studied (San José et al., 2005).
2018
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
position in the annulus, especially in the upper half of the bed (Heertjes and Khoe, 1980). In order to quantify bed voidage in the spout, numerous experimental studies have been carried out (Mathur and Epstein, 1974; Grbavcic et al., 1976; Chandnani and Epstein, 1986; Day et al., 1987; Wu et al., 1987; Cai et al., 1992;He et al., 1994). Several authors have developed theoretical models to predict this voidage (Lefroy and Davidson, 1969; Morgan et al., 1985; Krzywanski et al., 1992). Experimental studies of bed voidage in the fountain are essential in the processes of coating and granulation, due to the importance of this zone in the radial distribution of the solid that falls onto the annular zone (Robinson and Waldie, 1979; Waldie et al., 1986). Moreover, this zone cannot be ignored in the modelling of the gas and solid flow because it means an important fraction of the total solid inventory (up to 10% in deep beds and even higher in shallow spouted beds). Furthermore, bed voidage in this zone is heterogeneous due to the fact that there are two clearly differentiated regions, the fountain core and the fountain periphery. In the core, the particles and gas move concurrently upward, whereas in the periphery the particles return to the top of the annulus countercurrently with the fluid rising from the top of the annulus. The experimental observation that the bed voidage in the core decreases with the radial position and fountain level (He et al., 1994) is in agreement with the theoretical model of Grace and Mathur (1978). A gap in these studies is the lack of results in the periphery of the fountain. Fig. 1. Scheme of the zones in the spouted bed and in the fountain and geometric factors of the contactor.
2. Experimental This paper is an extension of a previous one where the local bed voidage has been studied in the annulus and spout of conical spouted beds made up of glass beads (San José et al., 1998). Given that density is an essential parameter in hydrodynamics, in this paper the study has been extended to plastic materials of density lower than that of glass (polyethylene, polypropylene, extruded polystyrene and expanded polystyrene). The aim is the establishment of correlations of general application (for different reactor geometries and experimental conditions), which allow for determining the map of local bed voidages in the entire conical spouted bed, including the fountain. The study of bed voidage in cylindrical spouted beds has been approached in the literature ever since the development of spouted bed technology. Nevertheless, whereas the spout and the fountain have been addressed, bed voidage in the annular zone has usually been taken, for the sake of simplicity, as constant and equal to that corresponding to the loose bed (Mathur and Gishler, 1955; Madonna, 1966; Mathur and Epstein, 1974; Day et al., 1987), which in turn is taken as equal to the bed voidage of minimum fluidization with a minimum value of 0.42 for equally sized spherical particles (Epstein and Grace, 1984; Day et al., 1987). Nevertheless, there is experimental evidence that bed voidage changes with
The experimental unit was described in previous papers (San José et al., 1998; Olazar et al., 1999). The experimental work was carried out with contactors of poly(methyl methacrylate), whose geometric factors are defined in Fig. 1. The values of the geometric factors are as follows: column diameter, Dc = 0.36 m; angle, = 33◦ , 36◦ , and 45◦ ; their corresponding conical section heights, Hc = 0.50, 0.45, and 0.36 m; air inlet diameter, Do = 0.03, 0.04, and 0.05 m. The design of the inlet for system stability was described in detail in a previous paper (Olazar et al., 1992). The values of stagnant bed height were varied between 0.05 and 0.30 m. The solids used are described in Table 1 and are of varying particle diameter, density and shape factor. The probe used for voidage measurement consists of a stainless steel encasing with maximum and minimum dimensions of 3.0 and 1.5 mm, respectively, containing three optical fibres in parallel (Fig. 2). When a particle passes near the head of the probe, it reflects the light emitted by the central fibre. The reflected light is collected in succession by the two fibres located at the extremes, between which there is an effective distance of de =4.3 mm. This distance has been determined on a rotary disk of known angular velocity following the method proposed by Benkrid and Caram (1989). The probe section reduces perturbation to a
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
2019
Fig. 2. Scheme of the optical fibre probe.
Table 1 Properties of the materials used Material
(kg m−3 )
dp (mm)
o
Glass Polypropylene Extruded polystyrene Expanded polystyrene LDPE HDPE
2420 890 1030 65 923 940
3.5 3.5 3.5 3.5 3.5 3.5
0.96 0.90 0.80 0.95 0.95 0.92
0.35 0.36 0.36 0.32 0.34 0.36
minimum in the solid flow (both upward and downward). The greatest precision is obtained with a range field equal to the particle diameter. The intensity of light emission or sensitivity is regulated by means of a power meter, allowing for the range to be changed between 1 and 6 mm and, consequently, for operation with beds of different particle size within this range. The frequency of the light used is 50 Hz. The light signal is collected by photodiodes and converted into voltage (0–100 mV). The signals pass through a signal amplifier (−12 to +12 V). A 12-V light source transmits light to the emitting fibre, and a filter controls the intensity of the beam. An analogical/digital interface sends the data to the computer for processing. The intensity of the light reflected by the particles that pass in front of the fibre depends on the type or composition of the particle, on its size or size distribution, and on bed voidage. For this reason, a calibration has been carried out for each solid so that local bed voidage has been related to the probe signals, in three zones of the bed (spout, annulus and fountain). The calibration carried out for the spout is valid for the two regions of the fountain. The calibration procedure has been described in detail in a previous paper (San José et al., 1998). 3. Results Figs. 3 and 4 show the longitudinal and radial profiles, respectively, of the local bed voidage for a given experimental system (solid: extruded polystyrene; = 33◦ ; Do = 0.03 m; dp = 3.5 mm; Ho = 0.18 m; u = 1.02ums ). The value of ums has been calculated by means of the correlation proposed in a previous paper (Olazar et al., 1992). The results of Figs. 3 and 4 are clear evidence of the important differences in bed voidage depending on the position
Fig. 3. Longitudinal profile of bed voidage at different radial positions in the contactor. Material: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
Fig. 4. Radial profile of bed voidage at different longitudinal positions in the contactor. Material: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
in the bed. Consequently, in order to understand the results, the differences between the zones of the bed (spout, annulus and fountain) and the geometry of the spout and fountain must be taken into account. It is noteworthy that the spout diameter changes greatly with bed level, as is shown in Fig. 1, corresponding to the same experimental system as Figs. 3 and 4. Furthermore, this evolution depends on the experimental conditions. This aspect has been studied in a previous paper (San José et al., 2005). Consequently, with the aim of rationalizing the exposition of the results and the establishment of correlations for their calculation, the results of bed voidage must be studied separately in the different zones of the bed and special attention must be paid to certain positions within these zones, as is the
2020
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
case of the spout axis and the proximity of the contactor wall. 3.1. Bed voidage along the spout axis The evolution of bed voidage with the longitudinal position in the spout is qualitatively similar for the different materials. Thus, it is of parabolic shape and dependent on the system variables. The experimental results have been fitted to a correlation expressed as a function both of the axis bed voidage near the bottom of the contactor (at a distance z = 0.02 m, where bed voidage is measured), (0)z=0.02 , and of the bed height, H : z 2 (0) = (0)z=0.02 − E . (1) H At the bottom of the contactor there is an important solid cross-flow from the annulus into the spout, but the results of this paper show that the solid cross-flow starts at an upper position in the bed as the solid is heavier. Thus, for glass beads, the solid cross-flow into the spout takes place for z > 0.02 m and, consequently, below this position, bed voidage is unity. Nevertheless, for solids lighter than glass, the solid cross-flow into the spout is significant at the base itself, and for (0)z=0.02 has values between 0.69 and 0.84, being higher as the material is heavier. In view of these results, the following has been established:
(0)z=0.02 = 1 for g , 0.2 (0)z=0.02 = for < g . g
Fig. 5. Longitudinal profile of bed voidage at the axis of the spout for different values of stagnant bed height. Points: experimental results. Lines: calculated with Eq. (1). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, dp = 3.5 mm, u = 1.02ums .
(2) (3)
In Eq. (1) the values of the parameter E vary between 0.26 and 0.71 depending on the geometric factors of the contactor and operating conditions. By fitting the experimental results, by means of the complex method of non-linear regression (Box, 1965), the following expression is obtained: −0.12 −0.97 Db Ho u −0.71 −0.19 E = 1.20 . (4) Do Di ums Eq. (4) is the same previously proposed for glass beads (San José et al., 1998) except that the exponent of is slightly different. The fitting of the experimental results to Eq. (1) has a regression coefficient of r 2 = 0.97, with a maximum relative error of 7%. The quality of the fitting is shown in Figs. 5 and 6, where the experimental results of evolution of (0) along the longitudinal position (points) are plotted together with the values calculated by means of Eq. (1) (lines). Fig. 5 corresponds to the results of extruded polystyrene obtained for different values of stagnant bed height when the remaining experimental conditions are maintained constant. Fig. 6 corresponds to the different materials studied under given experimental conditions. As is observed in Fig. 6, the experimental results for expanded PS fit poorly to
Fig. 6. Longitudinal profile of bed voidage at the axis of the spout for different materials. Points: experimental results. Lines: calculated with Eq. (1). = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
Eq. (1), given that this equation overestimates the voidage along the spout axis. This poor fitting is explained by the small difference between the density of the expanded PS and the spouting agent, whose consequence is a very smooth and homogeneous spouted bed with a different hydrodynamics to the other materials for which Eq. (1) has been developed. 3.2. Bed voidage at the wall The lowest values of bed voidage are registered near the wall of the contactor (Fig. 4). The bed voidage at this position has been experimentally determined by placing the tip of the probe at a distance of 1 particle diameter from the internal
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
Fig. 7. Longitudinal profile of bed voidage in the proximity of the wall for different values of stagnant bed height. Points: experimental results. Lines: calculated with Eq. (5). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, dp = 3.5 mm, u = 1.02ums .
2021
Fig. 8. Longitudinal profile of bed voidage in the proximity of the wall for different materials. Points: experimental results. Lines: calculated with Eq. (5). = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
side of the contactor wall. The measurement at this distance avoids the wall effect due to the poor packing of the particles in contact with the wall. The experimental results are evidence that bed voidage along the wall decreases with the longitudinal position in the bed. These results have been fitted by non-linear regression (the regression coefficient is r 2 = 0.92, with a maximum relative error of 13%) to the following equation: H − z 0.5 (w) = o 1 + , (5) H where o is the loose bed voidage, which is the minimum value of the experimental results and is registered on the upper surface of the bed against the wall. The quality of the fitting of Eq. (5) to the experimental results is shown in Fig. 7, where the experimental results of bed voidage along the longitudinal position of the wall (points) for given conditions are shown together with those calculated with Eq. (5) (lines). These results correspond to extruded polystyrene. The experimental results and those calculated for the different materials studied are compared in Fig. 8. 3.3. Correlation for calculation of the local bed voidage in the bed By analyzing the experimental results of the voidage radial profile in the bed (Fig. 4 and results corresponding to the other systems studied), it is observed that its shape depends on the bed voidage at the axis, (0), the bed voidage at the wall, (w), and the spout radius, rs . This latter variable conditions the position of the inflection point observed in Fig. 4. The values of rs for the different experimental systems have been determined in a previous paper (San José
Fig. 9. Comparison of the experimental results of local bed voidage at different longitudinal and radial positions in the bed (points) with those calculated using Eq. (6) (lines). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
et al., 2005). The experimental results of bed voidage have been fitted by non-linear regression to the following equation, which has already been proposed in a previous paper for glass beads (San José et al., 1998):
=
(0) − (w) + (w). 1 + exp((r − rs )/27.81rs2.41 )
(6)
In Eq. (6) the bed voidage at the axis of the spout, (0), is calculated with Eq. (1) and the bed voidage at the wall, (w), with Eq. (5). The fitting of the results to Eq. (6) provides a regression coefficient of r 2 = 0.98, with a maximum relative error of 3%. The quality of the fitting is shown in Fig. 9, corresponding to a given experimental system, where
2022
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
3.5. Bed voidage in the fountain
Fig. 10. Evolution with longitudinal position of the average bed voidage in the annulus and spout for different materials. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
the points are experimental results and the lines are those calculated by means of Eq. (6). 3.4. Average bed voidage in the spout and annulus When a simplified design of conical spouted beds is carried out, the knowledge of average values of voidage at each longitudinal position is interesting. These values are calculated as follows: At the spout zone:
¯ s =
rs 0
At the annular zone:
2r dr, rs2
¯ a =
rw rs
2r dr. (rw2 − rs2 )
(7)
(8)
Fig. 10 shows the results of average bed voidage in the spout and annular zones for the three solids of different density. It is observed that the average bed voidage in the spout zone decreases significantly as solid density is lower, whereas in the annular zone the higher values of average bed voidage correspond to the material of intermediate density (extruded polystyrene). This result is attributable to the opposed effect of density and shape factor. In contrast to the results of Day et al. (1987) for cylindrical spouted beds of flat bottom, in which voidage is practically unity along a significant distance of the spout bottom, the average bed voidage in the spout is lower than unity from the contactor base itself. This difference in results is explained by the incorporation of particles from the annular zone of the spout, which in conical spouted beds takes place at the very bottom. This incorporation is caused by the conical geometry of the contactor and starts at lower levels, as the solid density is lower.
As was aforementioned, there are two zones in the fountain (Fig. 1), the core (where the solid is ascending) and the periphery (where the solid is descending and is distributed on the upper surface of the annular zone). The core may be considered as a continuation of the spout and Eqs. (1)–(4) have been obtained by including the experimental results of this zone of the fountain. The effect of solid density and shape factor on the fountain voidage is noteworthy. This is a consequence of the effect of these properties on the geometry of the fountain, which has been studied in a previous paper together with the effect of the remaining experimental conditions (San José et al., 2005). This difference in the geometry of the fountain has great incidence on the delimitation of its two regions and, consequently, on the bed voidage map. Fig. 11 shows the experimental results of radial profile of voidage in the fountain core for two materials of different density, as are glass beads (Fig. 11a) and extruded polystyrene (Fig. 11b). The remaining experimental conditions are the same for both materials. It is observed that bed voidage at the same level in the fountain core decreases radially from the axis to the core–periphery interface and that this decrease is qualitatively similar for both materials, although the maximum voidage is different, as predicted by Eq. (3). Moreover, as other authors have observed for cylindrical contactors of conical bottom (He et al., 1994; Izquierdo, 1998), bed voidage at any radial position in the core is lower as the level in the fountain is higher. When the radial profiles of voidage in the descent zone of the fountain are analysed for both solids (Fig. 12), the values of voidage are very similar in this zone of the fountain. Bed voidage increases radially in a very pronounced way in positions near the interface and then it slightly decreases at radial positions near the external surface of the fountain. For a given radial position, bed voidage increases with the fountain level near the interface, but it decreases with level near the outer surface. When the profiles of bed voidage for extruded polystyrene (Figs. 11b and 12b), = 0.80, are compared with the experimental results corresponding to low density polyethylene (Fig. 13), = 0.95, it is observed that the values of voidage are very similar. Taking into account that the height and width of the fountain increase as shape factor decreases, it is concluded that the lower the shape factor the higher the amount of solid in the fountain. Consequently, this zone is of great importance in the design of the equipment.
4. Conclusions In this paper, a correlation (Eq. (6)) is proposed for quantifying the local bed voidage in conical spouted beds. This equation is applicable to the spout and annular zones, to solids of different density, in contactors with different
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
(a)
2023
(b)
Fig. 11. Radial profiles of bed voidage in the fountain core. Graph a: glass beds. Graph b: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
(a)
(b)
Fig. 12. Radial profiles of bed voidage in the fountain periphery. Graph a: glass beds, dp = 3.5 mm. Graph b: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
(a)
(b)
Fig. 13. Radial profiles of bed voidage in a bed of low density polyethylene. Graph a: fountain core. Graph b: fountain periphery. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
geometric factors and in a wide range of operating conditions. It must be taken into account that local bed voidage depends on the voidages at the axis and wall (maximum and minimum values at each level in the bed) and on the spout
radius (which corresponds to the position of the inflection point in the radial profile of voidage). It has been determined that the bed voidage has a maximum value at the central point of the gas inlet, where it is
2024
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
unity for solids with a density similar to glass. This maximum voidage decreases as solid density is lower, which is predicted by means of Eq. (3). Bed voidage at the axis of the spout and fountain decreases with bed level, following the trend shown by Eq. (1) and depends on the experimental conditions. Nevertheless, the bed voidage at the wall, which is described by Eq. (5), only depends on bed level and solid properties (which condition loose bed voidage). Bed voidage in the fountain core decreases radially from the axis to the core-periphery interface. The bed voidage in the core at any radial position decreases as the bed level in the fountain is higher. In the descent zone of the fountain, the values of voidage are very similar for solids of different density. Thus, they sharply increase with the radial position near the interface and then they slightly decrease near the external surface of the fountain. For a given radial position, voidage increases with level. It has also been proven that shape factor does not significantly affect the values of voidage in the two regions of the fountain, which is evidence that a greater volume of the fountain caused by a decrease in shape factor has as consequence an increase of solid amount in the fountain and, consequently, of its importance in the design of the equipment.
Notation de dp Db Dc , Di , Do H , H c , Ho r, z rs , rw u, ums zf
effective distance between the two receiving fibres, m particle diameter, m bed diameter at the upper surface of the stagnant bed (Di + 2Ho tan(/2)), m diameter of the column, of the bed bottom and of the air inlet, respectively, m heights of the developed bed, of the conical section, and of the stagnant bed, respectively, m cylindrical coordinates, m spout radius and radial position of the contactor wall at level z, m velocity and minimum spouting velocity of the gas, m s−1 longitunal coordinate in the fountain, m
Greek letters
, o (0), (w) ¯ a , ¯ s , g
contactor angle, deg (rad in Eq. (4)) bed voidage and loose bed voidage bed voidage along the axis and on the bed wall average bed voidage in the annular and spout zones density of the solid and of the glass, kg m−3 shape factor
Acknowledgements 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 PPQ20010780). References Aguado, R., Olazar, M., San José, M.J., Aguirre, G., Bilbao, J., 2000. Pyrolysis of sawdust in a conical spouted bed reactor. Yields and product composition. Industrial and Engineering Chemistry Research 39, 1925–1933. Aguado, R., Olazar, M., Gaisán, B., Prieto, R., Bilbao, J., 2002a. Kinetic study of polyolefins pyrolysis in a conical spouted bed reactor. Industrial and Engineering Chemistry Research 41, 4559–4566. Aguado, R., Olazar, M., San José, M.J., Gaisán, B., Bilbao, J., 2002b. Wax formation in the pyrolysis of polyolefins in a conical spouted bed reactor. Energy and Fuels 16, 1429–1437. Aguado, R., Olazar, M., Gaisán, B., Prieto, R., Bilbao, J., 2003. Polystyrene pyrolysis in a conical spouted bed reactor. Chemical Engineering Journal 92, 91–99. Arena, U., Mastellone, M.L., 2000. Defluidization phenomena during the pyrolysis of two plastic wastes. Chemical Engineering Science 55, 2849–2960. Benkrid, A., Caram, H.S., 1989. Solid flow in the annular region of a spouted bed. A.I.Ch.E. Journal 35, 1328–1336. Bilbao, J., Olazar, M., Romero, A., Arandes, J.M., 1987. Design and operation of a jet spouted bed reactor with continuous catalyst feed in the benzyl alcohol polymerization. Industrial and Engineering Chemistry Research 26, 1297–1304. Box, M.J., 1965. A new method of constrained optimization and a comparison with other methods. Computation Journal 1, 42–52. Cai, P., Dong, X.R., Jin, Y., Yu, Z.Q., 1992. A new technique for determining the hydrodynamic characteristics of spouted beds. Canadian Journal of Chemical Engineering 70, 835–839. Chandnani, P.P., Epstein, N., 1986. Spoutability and spout destabilization of fine particles with a gas. In: Ostergaard, K., Sorensen, A. (Eds.), Fluidization, vol. V. Engineering Foundation, New York, pp. 233–240. Day, J.Y., Morgan III, M.H., Littman, H., 1987. Measurements of spout voidage distributions, particle velocities and particle circulation rates in spouted beds of coarse particles. II Experimental verification. Chemical Engineering Science 42, 1461–1470. Epstein, N., Grace, J.R., 1984. Spouting of particulate solids. In: Otten, L., Fayed, M.E. (Eds.), Handbook of Powder Science and Technology. Van Nostrand Reinhold, New York. (Chapter 11). Grace, J.R., Mathur, K.B., 1978. Height and structure of the fountain region above spouted beds. Canadian Journal of Chemical Engineering 56, 533–537. Grbavcic, Z.B., Vukovic, D.V., Zdansky, F.K., Littman, H., 1976. Fluid flow pattern, minimum spouting velocity and pressure drop in spouted beds. Canadian Journal of Chemical Engineering 54, 33–42. He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72, 229–234. Heertjes, P.M., Khoe, G.K., 1980. Advances in spouted bed technology. Chemie Ingenieur Technik 52, 333–338. Izquierdo, M.A., 1998. Characterization of bed and solid trajectories in cylindrical spouted beds. Ph.D. Thesis, University of the Basque Country, Bilbao, Spain. Krzywanski, R.S., Epstein, N., Bowen, B.D., 1992. Multi-dimensional model of a spouted bed. Canadian Journal of Chemical Engineering 70, 858–872.
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025 Lefroy, G.A., Davidson, J.F., 1969. The mechanics of spouted beds. Transactions of the Institution of Chemical Engineers 47, T120. Madonna, L.A., 1966. Void fraction variation in the spouted-bed annulus. An approximation. Industrial Engineering Chemistry, Process Design and Development 5, 47–50. Mastellone, M.L., Arena, U., 2002. Fluidized-bed pyrolysis of polyolefins wastes: predictive defluidization model. A.I.Ch.E. Journal 48, 1439– 1447. Mathur, K.B., Epstein, N., 1974. Spouted Beds. Academic Press, New York. Mathur, K.B., Gishler, P.E., 1955. A technique for contacting gases with coarse solid particles. A.I.Ch.E. Journal 1, 157–164. Morgan III, M.H., Day, J.Y., Littman, H., 1985. Spout voidage distribution, stability and particle circulation rates in spouted beds of coarse particles. 1. Theory. Chemical Engineering Science 40, 1367–1377. Olazar, M., San José, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1992. Stable operation conditions for gas-solid contact regimes in conical spouted beds. Industrial and Engineering Chemistry Research 31, 1784 –1791. Olazar, M., San José, M.J., Zabala, G., Bilbao, J., 1994. A new reactor in jet spouted bed regime for catalytic polymerizations. Chemical Engineering Science 49, 4579–4588. Olazar, M., Arandes, J.M., Zabala, G., Aguayo, A.T., Bilbao, J., 1997. Design and simulation of a catalytic polymerization reactor in dilute spouted bed regime. Industrial and Engineering Chemistry Research 36, 1637–1643. Olazar, M., San José, M.J., Aguado, R., Gaisán, B., Bilbao, J., 1999. Bed voidage in conical sawdust beds in the transition regime between spouting and jet spouting. Industrial and Engineering Chemistry Research 38, 4120–4122.
2025
Olazar, M., Aguado, R., Barona, A., Bilbao, J., 2000. Pyrolysis of sawdust in a conical spouted bed reactor with a HZSM-5 catalyst. A.I.Ch.E. Journal 46, 1025–1033. Olazar, M., Aguado, R., Sánchez, J.L., Bilbao, R., Arauzo, J., 2002. Thermal processing of straw black liquor in fluidized and spouted bed. Energy and Fuels 16, 1417–1424. Robinson, T., Waldie, B., 1979. Dependency of growth on granule size in a spouted bed granulator. Transactions of the Institution of Chemical Engineers 57, 121–127. San José, M.J., Olazar, M., Alvarez, S., Bilbao, J., 1998. Local bed voidage in conical spouted beds. Industrial and Engineering Chemistry Research 37, 2553–2558. San José, M.J., Olazar, M., Alvarez, S., Morales, A., Bilbao, J., 2005. Spout and fountain geometry in conical spouted beds consisting of solids of different density. Industrial and Engineering Chemistry Research 44 (1) 193–200. Uemaki, O., Tsuji, T., 1986. Gasification of a sub-bituminous coal in a two-stage jet spouted bed reactor. In: Ostergaard, K., Sorensen, A. (Eds.), Fluidization, vol. V. Engineering Foundation, New York, pp. 497–504. Waldie, B., Wilkinson, D., McHugh, T.G.P., 1986. Measurement of voidage in the fountain of a spouted bed. Canadian Journal of Chemical Engineering 64, 950–953. Wu, S.W.M., Lim, C.J., Epstein, N., 1987. Hydrodynamics of spouted beds at elevated temperatures. Chemical Engineering Communications 62, 251–268.
Local porosity in conical spouted beds consisting of solids of varying density María J. San José∗ , Martin Olazar, Sonia Alvarez, Alberto Morales, Javier Bilbao Departamento de Ingeniería Química, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain Available online 29 January 2005
Abstract Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fluidization; Hydrodynamics; Particle processing; Conical spouted bed; Spouted bed; Voidage
1. Introduction The spouted bed of totally conical geometry allows for handling, in a stable way and without segregation, solids of different size, irregular texture and sticky ones. It has been successfully used in the polymerization of sub-bituminous coal (Uemaki and Tsuji, 1986) and in catalytic polymerizations (Bilbao et al.,1987; Olazar et al., 1994, 1997). Recently, this bed has been proven to have a good performance in the pyrolysis of biomass (Aguado et al.,2000; Olazar et al.,2000), of black liquor (Olazar et al.,2002) and of waste plastics (Aguado et al., 2002a,b, 2003). In addition to the features of the conventional spouted beds (cylindrical ones and those with conical bottom), such as the cyclic movement of the particles and an almost countercurrent contact between gas and solid, the conical spouted bed allows for operating stable in a wide range of gas flowrates, which may be increased almost without limit in order to increase bed turbulence (Olazar et al., 1992, 1999). ∗ Corresponding author. Tel.: +34 946 012527; fax: 34 946 013500.
E-mail address: [email protected] (M.J. San José). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.12.004
In the pyrolysis of waste plastics, the cyclic movement of the solid (characteristic of spouted beds) facilitates the homogeneous coating of the sand particles that make up the bed with the feeding plastic (Aguado et al., 2002a,b). This homogeneity is especially important in order to attain a good gas-solid heat transfer. Moreover, when gas velocities above those for minimum spouting are used, agglomeration of sticky particles in the bed is avoided. This agglomeration is the main problem of fluidized beds for this application (Arena and Mastellone, 2000; Mastellone and Arena,2002). In order to design the conical spouted bed reactor for pyrolysis of waste plastics, progress in the modelling of the gas and solid is still required. One of the difficulties for the proposal of these models is the heterogeneity of bed voidage in each of the three zones of the spouted bed (spout, annulus and fountain) (Fig. 1The volume of these zones depends on the geometric factors of the contactor (angle, inlet diameter) and on the experimental conditions (particle diameter, stagnant bed height). In a previous paper, the influence of these conditions on the geometry of the spout and fountain has been studied (San José et al., 2005).
2018
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
position in the annulus, especially in the upper half of the bed (Heertjes and Khoe, 1980). In order to quantify bed voidage in the spout, numerous experimental studies have been carried out (Mathur and Epstein, 1974; Grbavcic et al., 1976; Chandnani and Epstein, 1986; Day et al., 1987; Wu et al., 1987; Cai et al., 1992;He et al., 1994). Several authors have developed theoretical models to predict this voidage (Lefroy and Davidson, 1969; Morgan et al., 1985; Krzywanski et al., 1992). Experimental studies of bed voidage in the fountain are essential in the processes of coating and granulation, due to the importance of this zone in the radial distribution of the solid that falls onto the annular zone (Robinson and Waldie, 1979; Waldie et al., 1986). Moreover, this zone cannot be ignored in the modelling of the gas and solid flow because it means an important fraction of the total solid inventory (up to 10% in deep beds and even higher in shallow spouted beds). Furthermore, bed voidage in this zone is heterogeneous due to the fact that there are two clearly differentiated regions, the fountain core and the fountain periphery. In the core, the particles and gas move concurrently upward, whereas in the periphery the particles return to the top of the annulus countercurrently with the fluid rising from the top of the annulus. The experimental observation that the bed voidage in the core decreases with the radial position and fountain level (He et al., 1994) is in agreement with the theoretical model of Grace and Mathur (1978). A gap in these studies is the lack of results in the periphery of the fountain. Fig. 1. Scheme of the zones in the spouted bed and in the fountain and geometric factors of the contactor.
2. Experimental This paper is an extension of a previous one where the local bed voidage has been studied in the annulus and spout of conical spouted beds made up of glass beads (San José et al., 1998). Given that density is an essential parameter in hydrodynamics, in this paper the study has been extended to plastic materials of density lower than that of glass (polyethylene, polypropylene, extruded polystyrene and expanded polystyrene). The aim is the establishment of correlations of general application (for different reactor geometries and experimental conditions), which allow for determining the map of local bed voidages in the entire conical spouted bed, including the fountain. The study of bed voidage in cylindrical spouted beds has been approached in the literature ever since the development of spouted bed technology. Nevertheless, whereas the spout and the fountain have been addressed, bed voidage in the annular zone has usually been taken, for the sake of simplicity, as constant and equal to that corresponding to the loose bed (Mathur and Gishler, 1955; Madonna, 1966; Mathur and Epstein, 1974; Day et al., 1987), which in turn is taken as equal to the bed voidage of minimum fluidization with a minimum value of 0.42 for equally sized spherical particles (Epstein and Grace, 1984; Day et al., 1987). Nevertheless, there is experimental evidence that bed voidage changes with
The experimental unit was described in previous papers (San José et al., 1998; Olazar et al., 1999). The experimental work was carried out with contactors of poly(methyl methacrylate), whose geometric factors are defined in Fig. 1. The values of the geometric factors are as follows: column diameter, Dc = 0.36 m; angle, = 33◦ , 36◦ , and 45◦ ; their corresponding conical section heights, Hc = 0.50, 0.45, and 0.36 m; air inlet diameter, Do = 0.03, 0.04, and 0.05 m. The design of the inlet for system stability was described in detail in a previous paper (Olazar et al., 1992). The values of stagnant bed height were varied between 0.05 and 0.30 m. The solids used are described in Table 1 and are of varying particle diameter, density and shape factor. The probe used for voidage measurement consists of a stainless steel encasing with maximum and minimum dimensions of 3.0 and 1.5 mm, respectively, containing three optical fibres in parallel (Fig. 2). When a particle passes near the head of the probe, it reflects the light emitted by the central fibre. The reflected light is collected in succession by the two fibres located at the extremes, between which there is an effective distance of de =4.3 mm. This distance has been determined on a rotary disk of known angular velocity following the method proposed by Benkrid and Caram (1989). The probe section reduces perturbation to a
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
2019
Fig. 2. Scheme of the optical fibre probe.
Table 1 Properties of the materials used Material
(kg m−3 )
dp (mm)
o
Glass Polypropylene Extruded polystyrene Expanded polystyrene LDPE HDPE
2420 890 1030 65 923 940
3.5 3.5 3.5 3.5 3.5 3.5
0.96 0.90 0.80 0.95 0.95 0.92
0.35 0.36 0.36 0.32 0.34 0.36
minimum in the solid flow (both upward and downward). The greatest precision is obtained with a range field equal to the particle diameter. The intensity of light emission or sensitivity is regulated by means of a power meter, allowing for the range to be changed between 1 and 6 mm and, consequently, for operation with beds of different particle size within this range. The frequency of the light used is 50 Hz. The light signal is collected by photodiodes and converted into voltage (0–100 mV). The signals pass through a signal amplifier (−12 to +12 V). A 12-V light source transmits light to the emitting fibre, and a filter controls the intensity of the beam. An analogical/digital interface sends the data to the computer for processing. The intensity of the light reflected by the particles that pass in front of the fibre depends on the type or composition of the particle, on its size or size distribution, and on bed voidage. For this reason, a calibration has been carried out for each solid so that local bed voidage has been related to the probe signals, in three zones of the bed (spout, annulus and fountain). The calibration carried out for the spout is valid for the two regions of the fountain. The calibration procedure has been described in detail in a previous paper (San José et al., 1998). 3. Results Figs. 3 and 4 show the longitudinal and radial profiles, respectively, of the local bed voidage for a given experimental system (solid: extruded polystyrene; = 33◦ ; Do = 0.03 m; dp = 3.5 mm; Ho = 0.18 m; u = 1.02ums ). The value of ums has been calculated by means of the correlation proposed in a previous paper (Olazar et al., 1992). The results of Figs. 3 and 4 are clear evidence of the important differences in bed voidage depending on the position
Fig. 3. Longitudinal profile of bed voidage at different radial positions in the contactor. Material: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
Fig. 4. Radial profile of bed voidage at different longitudinal positions in the contactor. Material: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
in the bed. Consequently, in order to understand the results, the differences between the zones of the bed (spout, annulus and fountain) and the geometry of the spout and fountain must be taken into account. It is noteworthy that the spout diameter changes greatly with bed level, as is shown in Fig. 1, corresponding to the same experimental system as Figs. 3 and 4. Furthermore, this evolution depends on the experimental conditions. This aspect has been studied in a previous paper (San José et al., 2005). Consequently, with the aim of rationalizing the exposition of the results and the establishment of correlations for their calculation, the results of bed voidage must be studied separately in the different zones of the bed and special attention must be paid to certain positions within these zones, as is the
2020
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
case of the spout axis and the proximity of the contactor wall. 3.1. Bed voidage along the spout axis The evolution of bed voidage with the longitudinal position in the spout is qualitatively similar for the different materials. Thus, it is of parabolic shape and dependent on the system variables. The experimental results have been fitted to a correlation expressed as a function both of the axis bed voidage near the bottom of the contactor (at a distance z = 0.02 m, where bed voidage is measured), (0)z=0.02 , and of the bed height, H : z 2 (0) = (0)z=0.02 − E . (1) H At the bottom of the contactor there is an important solid cross-flow from the annulus into the spout, but the results of this paper show that the solid cross-flow starts at an upper position in the bed as the solid is heavier. Thus, for glass beads, the solid cross-flow into the spout takes place for z > 0.02 m and, consequently, below this position, bed voidage is unity. Nevertheless, for solids lighter than glass, the solid cross-flow into the spout is significant at the base itself, and for (0)z=0.02 has values between 0.69 and 0.84, being higher as the material is heavier. In view of these results, the following has been established:
(0)z=0.02 = 1 for g , 0.2 (0)z=0.02 = for < g . g
Fig. 5. Longitudinal profile of bed voidage at the axis of the spout for different values of stagnant bed height. Points: experimental results. Lines: calculated with Eq. (1). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, dp = 3.5 mm, u = 1.02ums .
(2) (3)
In Eq. (1) the values of the parameter E vary between 0.26 and 0.71 depending on the geometric factors of the contactor and operating conditions. By fitting the experimental results, by means of the complex method of non-linear regression (Box, 1965), the following expression is obtained: −0.12 −0.97 Db Ho u −0.71 −0.19 E = 1.20 . (4) Do Di ums Eq. (4) is the same previously proposed for glass beads (San José et al., 1998) except that the exponent of is slightly different. The fitting of the experimental results to Eq. (1) has a regression coefficient of r 2 = 0.97, with a maximum relative error of 7%. The quality of the fitting is shown in Figs. 5 and 6, where the experimental results of evolution of (0) along the longitudinal position (points) are plotted together with the values calculated by means of Eq. (1) (lines). Fig. 5 corresponds to the results of extruded polystyrene obtained for different values of stagnant bed height when the remaining experimental conditions are maintained constant. Fig. 6 corresponds to the different materials studied under given experimental conditions. As is observed in Fig. 6, the experimental results for expanded PS fit poorly to
Fig. 6. Longitudinal profile of bed voidage at the axis of the spout for different materials. Points: experimental results. Lines: calculated with Eq. (1). = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
Eq. (1), given that this equation overestimates the voidage along the spout axis. This poor fitting is explained by the small difference between the density of the expanded PS and the spouting agent, whose consequence is a very smooth and homogeneous spouted bed with a different hydrodynamics to the other materials for which Eq. (1) has been developed. 3.2. Bed voidage at the wall The lowest values of bed voidage are registered near the wall of the contactor (Fig. 4). The bed voidage at this position has been experimentally determined by placing the tip of the probe at a distance of 1 particle diameter from the internal
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
Fig. 7. Longitudinal profile of bed voidage in the proximity of the wall for different values of stagnant bed height. Points: experimental results. Lines: calculated with Eq. (5). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, dp = 3.5 mm, u = 1.02ums .
2021
Fig. 8. Longitudinal profile of bed voidage in the proximity of the wall for different materials. Points: experimental results. Lines: calculated with Eq. (5). = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
side of the contactor wall. The measurement at this distance avoids the wall effect due to the poor packing of the particles in contact with the wall. The experimental results are evidence that bed voidage along the wall decreases with the longitudinal position in the bed. These results have been fitted by non-linear regression (the regression coefficient is r 2 = 0.92, with a maximum relative error of 13%) to the following equation: H − z 0.5 (w) = o 1 + , (5) H where o is the loose bed voidage, which is the minimum value of the experimental results and is registered on the upper surface of the bed against the wall. The quality of the fitting of Eq. (5) to the experimental results is shown in Fig. 7, where the experimental results of bed voidage along the longitudinal position of the wall (points) for given conditions are shown together with those calculated with Eq. (5) (lines). These results correspond to extruded polystyrene. The experimental results and those calculated for the different materials studied are compared in Fig. 8. 3.3. Correlation for calculation of the local bed voidage in the bed By analyzing the experimental results of the voidage radial profile in the bed (Fig. 4 and results corresponding to the other systems studied), it is observed that its shape depends on the bed voidage at the axis, (0), the bed voidage at the wall, (w), and the spout radius, rs . This latter variable conditions the position of the inflection point observed in Fig. 4. The values of rs for the different experimental systems have been determined in a previous paper (San José
Fig. 9. Comparison of the experimental results of local bed voidage at different longitudinal and radial positions in the bed (points) with those calculated using Eq. (6) (lines). Material: extruded polystyrene, = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
et al., 2005). The experimental results of bed voidage have been fitted by non-linear regression to the following equation, which has already been proposed in a previous paper for glass beads (San José et al., 1998):
=
(0) − (w) + (w). 1 + exp((r − rs )/27.81rs2.41 )
(6)
In Eq. (6) the bed voidage at the axis of the spout, (0), is calculated with Eq. (1) and the bed voidage at the wall, (w), with Eq. (5). The fitting of the results to Eq. (6) provides a regression coefficient of r 2 = 0.98, with a maximum relative error of 3%. The quality of the fitting is shown in Fig. 9, corresponding to a given experimental system, where
2022
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
3.5. Bed voidage in the fountain
Fig. 10. Evolution with longitudinal position of the average bed voidage in the annulus and spout for different materials. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
the points are experimental results and the lines are those calculated by means of Eq. (6). 3.4. Average bed voidage in the spout and annulus When a simplified design of conical spouted beds is carried out, the knowledge of average values of voidage at each longitudinal position is interesting. These values are calculated as follows: At the spout zone:
¯ s =
rs 0
At the annular zone:
2r dr, rs2
¯ a =
rw rs
2r dr. (rw2 − rs2 )
(7)
(8)
Fig. 10 shows the results of average bed voidage in the spout and annular zones for the three solids of different density. It is observed that the average bed voidage in the spout zone decreases significantly as solid density is lower, whereas in the annular zone the higher values of average bed voidage correspond to the material of intermediate density (extruded polystyrene). This result is attributable to the opposed effect of density and shape factor. In contrast to the results of Day et al. (1987) for cylindrical spouted beds of flat bottom, in which voidage is practically unity along a significant distance of the spout bottom, the average bed voidage in the spout is lower than unity from the contactor base itself. This difference in results is explained by the incorporation of particles from the annular zone of the spout, which in conical spouted beds takes place at the very bottom. This incorporation is caused by the conical geometry of the contactor and starts at lower levels, as the solid density is lower.
As was aforementioned, there are two zones in the fountain (Fig. 1), the core (where the solid is ascending) and the periphery (where the solid is descending and is distributed on the upper surface of the annular zone). The core may be considered as a continuation of the spout and Eqs. (1)–(4) have been obtained by including the experimental results of this zone of the fountain. The effect of solid density and shape factor on the fountain voidage is noteworthy. This is a consequence of the effect of these properties on the geometry of the fountain, which has been studied in a previous paper together with the effect of the remaining experimental conditions (San José et al., 2005). This difference in the geometry of the fountain has great incidence on the delimitation of its two regions and, consequently, on the bed voidage map. Fig. 11 shows the experimental results of radial profile of voidage in the fountain core for two materials of different density, as are glass beads (Fig. 11a) and extruded polystyrene (Fig. 11b). The remaining experimental conditions are the same for both materials. It is observed that bed voidage at the same level in the fountain core decreases radially from the axis to the core–periphery interface and that this decrease is qualitatively similar for both materials, although the maximum voidage is different, as predicted by Eq. (3). Moreover, as other authors have observed for cylindrical contactors of conical bottom (He et al., 1994; Izquierdo, 1998), bed voidage at any radial position in the core is lower as the level in the fountain is higher. When the radial profiles of voidage in the descent zone of the fountain are analysed for both solids (Fig. 12), the values of voidage are very similar in this zone of the fountain. Bed voidage increases radially in a very pronounced way in positions near the interface and then it slightly decreases at radial positions near the external surface of the fountain. For a given radial position, bed voidage increases with the fountain level near the interface, but it decreases with level near the outer surface. When the profiles of bed voidage for extruded polystyrene (Figs. 11b and 12b), = 0.80, are compared with the experimental results corresponding to low density polyethylene (Fig. 13), = 0.95, it is observed that the values of voidage are very similar. Taking into account that the height and width of the fountain increase as shape factor decreases, it is concluded that the lower the shape factor the higher the amount of solid in the fountain. Consequently, this zone is of great importance in the design of the equipment.
4. Conclusions In this paper, a correlation (Eq. (6)) is proposed for quantifying the local bed voidage in conical spouted beds. This equation is applicable to the spout and annular zones, to solids of different density, in contactors with different
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
(a)
2023
(b)
Fig. 11. Radial profiles of bed voidage in the fountain core. Graph a: glass beds. Graph b: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
(a)
(b)
Fig. 12. Radial profiles of bed voidage in the fountain periphery. Graph a: glass beds, dp = 3.5 mm. Graph b: extruded polystyrene. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
(a)
(b)
Fig. 13. Radial profiles of bed voidage in a bed of low density polyethylene. Graph a: fountain core. Graph b: fountain periphery. = 33◦ , Do = 0.03 m, Ho = 0.18 m, dp = 3.5 mm, u = 1.02ums .
geometric factors and in a wide range of operating conditions. It must be taken into account that local bed voidage depends on the voidages at the axis and wall (maximum and minimum values at each level in the bed) and on the spout
radius (which corresponds to the position of the inflection point in the radial profile of voidage). It has been determined that the bed voidage has a maximum value at the central point of the gas inlet, where it is
2024
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025
unity for solids with a density similar to glass. This maximum voidage decreases as solid density is lower, which is predicted by means of Eq. (3). Bed voidage at the axis of the spout and fountain decreases with bed level, following the trend shown by Eq. (1) and depends on the experimental conditions. Nevertheless, the bed voidage at the wall, which is described by Eq. (5), only depends on bed level and solid properties (which condition loose bed voidage). Bed voidage in the fountain core decreases radially from the axis to the core-periphery interface. The bed voidage in the core at any radial position decreases as the bed level in the fountain is higher. In the descent zone of the fountain, the values of voidage are very similar for solids of different density. Thus, they sharply increase with the radial position near the interface and then they slightly decrease near the external surface of the fountain. For a given radial position, voidage increases with level. It has also been proven that shape factor does not significantly affect the values of voidage in the two regions of the fountain, which is evidence that a greater volume of the fountain caused by a decrease in shape factor has as consequence an increase of solid amount in the fountain and, consequently, of its importance in the design of the equipment.
Notation de dp Db Dc , Di , Do H , H c , Ho r, z rs , rw u, ums zf
effective distance between the two receiving fibres, m particle diameter, m bed diameter at the upper surface of the stagnant bed (Di + 2Ho tan(/2)), m diameter of the column, of the bed bottom and of the air inlet, respectively, m heights of the developed bed, of the conical section, and of the stagnant bed, respectively, m cylindrical coordinates, m spout radius and radial position of the contactor wall at level z, m velocity and minimum spouting velocity of the gas, m s−1 longitunal coordinate in the fountain, m
Greek letters
, o (0), (w) ¯ a , ¯ s , g
contactor angle, deg (rad in Eq. (4)) bed voidage and loose bed voidage bed voidage along the axis and on the bed wall average bed voidage in the annular and spout zones density of the solid and of the glass, kg m−3 shape factor
Acknowledgements 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 PPQ20010780). References Aguado, R., Olazar, M., San José, M.J., Aguirre, G., Bilbao, J., 2000. Pyrolysis of sawdust in a conical spouted bed reactor. Yields and product composition. Industrial and Engineering Chemistry Research 39, 1925–1933. Aguado, R., Olazar, M., Gaisán, B., Prieto, R., Bilbao, J., 2002a. Kinetic study of polyolefins pyrolysis in a conical spouted bed reactor. Industrial and Engineering Chemistry Research 41, 4559–4566. Aguado, R., Olazar, M., San José, M.J., Gaisán, B., Bilbao, J., 2002b. Wax formation in the pyrolysis of polyolefins in a conical spouted bed reactor. Energy and Fuels 16, 1429–1437. Aguado, R., Olazar, M., Gaisán, B., Prieto, R., Bilbao, J., 2003. Polystyrene pyrolysis in a conical spouted bed reactor. Chemical Engineering Journal 92, 91–99. Arena, U., Mastellone, M.L., 2000. Defluidization phenomena during the pyrolysis of two plastic wastes. Chemical Engineering Science 55, 2849–2960. Benkrid, A., Caram, H.S., 1989. Solid flow in the annular region of a spouted bed. A.I.Ch.E. Journal 35, 1328–1336. Bilbao, J., Olazar, M., Romero, A., Arandes, J.M., 1987. Design and operation of a jet spouted bed reactor with continuous catalyst feed in the benzyl alcohol polymerization. Industrial and Engineering Chemistry Research 26, 1297–1304. Box, M.J., 1965. A new method of constrained optimization and a comparison with other methods. Computation Journal 1, 42–52. Cai, P., Dong, X.R., Jin, Y., Yu, Z.Q., 1992. A new technique for determining the hydrodynamic characteristics of spouted beds. Canadian Journal of Chemical Engineering 70, 835–839. Chandnani, P.P., Epstein, N., 1986. Spoutability and spout destabilization of fine particles with a gas. In: Ostergaard, K., Sorensen, A. (Eds.), Fluidization, vol. V. Engineering Foundation, New York, pp. 233–240. Day, J.Y., Morgan III, M.H., Littman, H., 1987. Measurements of spout voidage distributions, particle velocities and particle circulation rates in spouted beds of coarse particles. II Experimental verification. Chemical Engineering Science 42, 1461–1470. Epstein, N., Grace, J.R., 1984. Spouting of particulate solids. In: Otten, L., Fayed, M.E. (Eds.), Handbook of Powder Science and Technology. Van Nostrand Reinhold, New York. (Chapter 11). Grace, J.R., Mathur, K.B., 1978. Height and structure of the fountain region above spouted beds. Canadian Journal of Chemical Engineering 56, 533–537. Grbavcic, Z.B., Vukovic, D.V., Zdansky, F.K., Littman, H., 1976. Fluid flow pattern, minimum spouting velocity and pressure drop in spouted beds. Canadian Journal of Chemical Engineering 54, 33–42. He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72, 229–234. Heertjes, P.M., Khoe, G.K., 1980. Advances in spouted bed technology. Chemie Ingenieur Technik 52, 333–338. Izquierdo, M.A., 1998. Characterization of bed and solid trajectories in cylindrical spouted beds. Ph.D. Thesis, University of the Basque Country, Bilbao, Spain. Krzywanski, R.S., Epstein, N., Bowen, B.D., 1992. Multi-dimensional model of a spouted bed. Canadian Journal of Chemical Engineering 70, 858–872.
M.J. San José et al. / Chemical Engineering Science 60 (2005) 2017 – 2025 Lefroy, G.A., Davidson, J.F., 1969. The mechanics of spouted beds. Transactions of the Institution of Chemical Engineers 47, T120. Madonna, L.A., 1966. Void fraction variation in the spouted-bed annulus. An approximation. Industrial Engineering Chemistry, Process Design and Development 5, 47–50. Mastellone, M.L., Arena, U., 2002. Fluidized-bed pyrolysis of polyolefins wastes: predictive defluidization model. A.I.Ch.E. Journal 48, 1439– 1447. Mathur, K.B., Epstein, N., 1974. Spouted Beds. Academic Press, New York. Mathur, K.B., Gishler, P.E., 1955. A technique for contacting gases with coarse solid particles. A.I.Ch.E. Journal 1, 157–164. Morgan III, M.H., Day, J.Y., Littman, H., 1985. Spout voidage distribution, stability and particle circulation rates in spouted beds of coarse particles. 1. Theory. Chemical Engineering Science 40, 1367–1377. Olazar, M., San José, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1992. Stable operation conditions for gas-solid contact regimes in conical spouted beds. Industrial and Engineering Chemistry Research 31, 1784 –1791. Olazar, M., San José, M.J., Zabala, G., Bilbao, J., 1994. A new reactor in jet spouted bed regime for catalytic polymerizations. Chemical Engineering Science 49, 4579–4588. Olazar, M., Arandes, J.M., Zabala, G., Aguayo, A.T., Bilbao, J., 1997. Design and simulation of a catalytic polymerization reactor in dilute spouted bed regime. Industrial and Engineering Chemistry Research 36, 1637–1643. Olazar, M., San José, M.J., Aguado, R., Gaisán, B., Bilbao, J., 1999. Bed voidage in conical sawdust beds in the transition regime between spouting and jet spouting. Industrial and Engineering Chemistry Research 38, 4120–4122.
2025
Olazar, M., Aguado, R., Barona, A., Bilbao, J., 2000. Pyrolysis of sawdust in a conical spouted bed reactor with a HZSM-5 catalyst. A.I.Ch.E. Journal 46, 1025–1033. Olazar, M., Aguado, R., Sánchez, J.L., Bilbao, R., Arauzo, J., 2002. Thermal processing of straw black liquor in fluidized and spouted bed. Energy and Fuels 16, 1417–1424. Robinson, T., Waldie, B., 1979. Dependency of growth on granule size in a spouted bed granulator. Transactions of the Institution of Chemical Engineers 57, 121–127. San José, M.J., Olazar, M., Alvarez, S., Bilbao, J., 1998. Local bed voidage in conical spouted beds. Industrial and Engineering Chemistry Research 37, 2553–2558. San José, M.J., Olazar, M., Alvarez, S., Morales, A., Bilbao, J., 2005. Spout and fountain geometry in conical spouted beds consisting of solids of different density. Industrial and Engineering Chemistry Research 44 (1) 193–200. Uemaki, O., Tsuji, T., 1986. Gasification of a sub-bituminous coal in a two-stage jet spouted bed reactor. In: Ostergaard, K., Sorensen, A. (Eds.), Fluidization, vol. V. Engineering Foundation, New York, pp. 497–504. Waldie, B., Wilkinson, D., McHugh, T.G.P., 1986. Measurement of voidage in the fountain of a spouted bed. Canadian Journal of Chemical Engineering 64, 950–953. Wu, S.W.M., Lim, C.J., Epstein, N., 1987. Hydrodynamics of spouted beds at elevated temperatures. Chemical Engineering Communications 62, 251–268.