Ind. Eng. Chem. Res. 2004, 43, 1163-1168
1163
Fountain Geometry in Shallow Spouted Beds Martin Olazar,* Marı´a J. San Jose´ , Miguel A. Izquierdo, Sonia Alvarez, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
The effect of the operating conditions (base angle, air inlet diameter, stagnant bed height, particle diameter, and air velocity) on the fountain geometry (height and amplitude) has been studied. Likewise, particle ascending and descending zones in the fountain have been delimited. These studies have been carried out by means of an optical fiber and by an image treatment system. An equation has been proposed for the calculation of the fountain height from the vertical component of the particle velocity in the axis at the base of the fountain. The contactor base angle has a major incidence on the fountain geometry. The external diameter of the fountain and that of the core are conditioned by the diameter of the spout at the base of the fountain. The diameter of the core (or ascending zone) decreases with the fountain level for all experimental conditions. 1. Introduction The fountain is a region that is characteristic of spouted beds, whose shape is paraboloidal1,2 and where two zones are distinguished (Figure 1), a core zone where solids rise and a peripherial 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. He et al.3 determined, by means of an optical fiber, that the core initially widens, it then reaches its maximum diameter near the base of the fountain, and finally it narrowers toward the top of the fountain. This result is in contradiction to that previously obtained by Hook et al.4 using a filming procedure, in which they observed a progressive widening of the core as the level of observation in the fountain increased. 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. 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.5-7 Furthermore, the consideration of the gas-solid contact in the fountain is especially important in shallow beds, in which the fountain contributes to an important fraction of the total contact in the bed. In previous papers, significant properties of the fountain have been studied, such as the bed voidage and particle velocity.8,9 In this paper, the geometry of the fountain (height, Hf, and amplitude, Af) and the delimitation of the interface between its core and periphery (Figure 1) have been studied. The knowledge of the fountain height, to establish the total height of the contactor, has been a subject of study * To whom correspondence should be addressed. Tel.: 3494-6012527. Fax: 34-94-4648500. E-mail:
[email protected].
Figure 1. Scheme of the zones in the spouted bed and in the fountain.
since the origin of this technology, and correlations have been proposed in the literature for its calculation from the geometric factors of the contactor-particle system. The development of the correlations has been addressed through, on the one hand, theoretical bases such as force balances2,10 and, on the other hand, empirical correlations based on particular design factors determined from experimental studies. Concerning the theoretical correlations, Grace and Mathur proposed,2 on the basis of force-balance analysis, the following equation for the calculation of the fountain height, Hf (Figure 1), from the particle velocity, νsH(0), and voidage, s(H), in the spout at the bed surface level:
ν (0)2 1.46 sH
Hf ) s(H)
10.1021/ie030641d CCC: $27.50 © 2004 American Chemical Society Published on Web 01/15/2004
2g
Fs Fs - F
(1)
1164 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004
Morgan et al.10 also modified eq 1, and they proposed the following relationship between the fountain height and the solid velocity on the upper surface of the spout νsH(0):
[ ]
νsH(0) Fs 0.704 (Fs - F)g 2
Hf )
(
) ( ) 0.865
H HoM
-1
(4)
(2)
( ) () ()
-0.379
Hf π u ) H 4 C/u
o ms
After these studies, Kutluoglu et al.5 used binary mixtures of solids of different density and they found a deviation of 16% between their results and those predicted by eq 1. Liu and Lister remarked the need for considering the shape factor of the particles in the calculation of the particle velocity and bed voidage of eq 1.11 Of the studies for empirically correlating the fountain height to experimental equations, McNab and Bridgwater determined that the fountain height is approximately proportional to the gas velocity at the spout inlet (bottom of the bed), but they establish no coefficient for this relationship.12 Passos et al.13 provided different criteria according to the column diameter, Dc, for predicting the height of the fountain in dryers, as a function of the bed height up to the base of the fountain, H. These criteria are Hf ) 0.25H for Dc < 0.25 m and Hf ) 0.50H for Dc > 0.25 m. For very large beds (Dc > 0.91 m), Lim and Grace determined that, as the stagnant bed height is increased, the fountain height passes through a maximum for a given value of the ratio of the gas velocity to minimum spouting velocity, ur ) u/ums.14 Epstein and Chandnani studied the height and shape of the fountain for small particles and proved that they were very sensitive to the values of air velocity, stagnant bed height, and particle diameter,15 which is in agreement with the predictions of eqs 1 and 2. Wu et al.16 studied the effect of temperature on the height of the fountain, and they explained the decrease in the fountain height as the temperature is increased by the reduction in the momentum transfer from gas to particles. Day determined (with an average deviation of 12.4% for their experimental data) the following empirical expression that takes into account the effect on the fountain height of operating conditions and bed geometry (grouped in dimensionless moduli):17
Hf u ) 46.4 -1 Do ums
the ratio of the gas velocity to minimum spouting velocity:
Fs - F -0.892 F dp -3.49 Do -2.75 (3) Do Dc
A2.13
Day proved that the fitting of the experimental data of Grace and Mathur to eq 3 was less satisfactory (with an average deviation of 14.7%) than that to eq 1,2,17 although eq 3 is easier to apply because it is established as a function of experimental conditions and avoids the need for ascertaining the solid velocity and bed voidage. Furthermore, eq 3 suitably takes into account the aforementioned effect of experimental conditions, which have been qualitatively observed by several authors.12,15,16 Hook et al.4 proposed a pseudo-empirical equation for calculation of the relationship between the height of the fountain and that of the developed bed, as a function of
where C/o is the sum of the pressure drop in the spout and the momentum by surface area of the gas jet at the spout inlet. The calculation of this parameter requires knowledge of complex experimental data, such as the gas velocity at the base of the fountain and at the position of maximum pressure drop in the spout. Furthermore, this position and the actual value of the corresponding pressure must be known. The results concerning the application of eqs 1-4 in the literature must be taken with reservations because of the problems of the techniques used in the past for measurement of the bed properties. Thus, the existence of a radial profile of the particle velocity in the spout has been proven,9 which requires the measurement of this velocity at the axis, νsH(0), to apply eqs 1 and 2. Furthermore, important errors are introduced by the use of half-columns, in which the hydrodynamics of the spout is altered, which especially affects the measurement of the particle velocity.3 2. Experimental Section Five contactors of poly(methyl methacrylate) have been used, which have the following dimensions: column diameter Dc, 0.152 m; base diameter Di, 0.62 m (except for γb ) 180°, where Di ) Do); height of the conical section Hc, 0.168, 0.108, 0.078, 0.026, and 0 m; angle of the contactor base γb, 30, 45, 60, 120, and 180°; air inlet diameter Do, 0.03, 0.04, and 0.05 m; stagnant bed height Ho, between 0.05 and 0.35 m. The solids studied are glass spheres (density ) 2420 kg m-3) of particle diameter 2, 3, 4, and 5 mm. Three air velocities have been used: 1.02ums, 1.2ums, and 1.3ums. The minimum spouting velocity, ums, has been calculated using the equation of Mathur and Gishler.18 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 video equipment has been described in detail in a previous paper19 and is composed of a camera, a video recorder, a monitor, and the computer support needed for treatment of the data obtained. 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. The probe was described in a previous paper20 and consists of an encasing of stainless steel with maximum and minimum dimensions of 3.0 and 1.5 mm, respectively, and which contains three optical fibers in parallel. A vertical displacement device is provided for the probe. This device positions the probe in front of the contactor hole, at the level at which the measurement is to be carried out. The probe is manually placed at the radial position in the bed, through holes made in the contactor wall (every 20 mm height). Graduation of the probe allows
Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1165
for setting of the radial position in the bed within a maximum error of 1 mm. When a particle circulates near the head of the probe, it reflects the light emitted by the central fiber. The reflected light is successively collected by the two lateral fibers and sent to two analogue channels. The signals pass through a signal amplifier (-12 V + 12 V). A 12 V light source sends light to the emitting fiber, and a filter controls the intensity of the beam. An analogue/digital interface sends the data to the computer for processing. From a statistical analysis, by means of the crosscorrelation function (incorporated in MATLAB 6.0 program), only those signals with statistically significant correlation coefficients are accepted (indicating that the same particles pass in front of both fibers). These coefficients are higher than 90% in the spout zone. From the effective distance between the two receiving fibers (de ) 4.3 mm) and the delay time between the two signals, τ (time corresponding to the maximum value of the cross-correlation function), the velocity of the particle along the longitudinal direction is calculated:
νs ) de/τ
Figure 2. Effect of the stagnant bed height on the fountain height, for different values of the contactor base angle. Lines: calculated with eq 6. Points: experimental results. Experimental conditions: Do ) 0.03 m, dp ) 4 mm, and u ) 1.02ums.
(5)
This calculation procedure was repeated five times, and the average relative error was 2% in the spout zone. The results of the velocity obtained were symmetrical with respect to the axis of the spout. The intensity of the light reflected by the particles that pass in front of the fiber depends on the bed voidage, on the type or composition of the particle, and on its size and size distribution. Accordingly, a calibration has been carried out for this solid so that the local bed voidage is related to the probe signals. The calibration procedure has been previously detailed.8 The average relative error of bed voidage measurements, which have been repeated three times at each point, is 4%. 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. 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. 3. Results 3.1. Fountain Height. The validity of eqs 1-4 for the calculation of Hf has been studied by comparing the calculated and experimental results. From this comparison, the following comments are worth mentioning: (i) Equation 1 of Grace and Mathur predicts values of Hf that are significantly lower than the experimental results.2 The relative error is in the 50-65% range. (ii) On the other hand, eq 2 of Morgan et al.10 predicts values of Hf that are higher than the experimental ones, with a relative error of approximately 75%. (iii) On the basis of the criteria of Passos et al.,13 the fountain height should be approximately 20 cm, which means an overestimate of the experimental results, with a relative error in the 20-75% range. (iv) Both eq 3 of Day et al.17 and eq 4 of Hook et al.4 predict values of Hf lower than the experimental ones, with a relative error in the 30-60% range. (v) Taking into account the aforementioned errors obtained with the correlations of the literature, different correlations based on eq 1 with different combinations
Figure 3. Effect of the air velocity on the fountain height, for different values of the contactor base angle. Lines: calculated with eq 6. Points: experimental results. Experimental conditions: Do ) 0.03 m, Ho ) 0.20 m, and dp ) 4 mm.
of coefficients have been used. In the fitting, the experimental results used are those of the vertical component of the particle velocity in the axis of the spout at the base of the fountain, νsH(0), and those of bed voidage at this level, sH. These properties may also be calculated using the correlations proposed in previous papers.8,9 The result of coefficient optimization leads to the following equation:
νsH(0)2 Fs Hf ) 2g Fs - F
(6)
Equation 6 is the same as that obtained by Thorley et al.21 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. The good fitting of eq 6 to the experimental results is shown in Figures 2 and 3, which have been chosen as examples for illustrating the parametric effect and in which the points are the experimental results and the curves have been calculated by means of eq 6. As the base angle of the contactor or the stagnant bed height (Figure 2) is increased for the same value of the remaining experimental conditions, the fountain height decreases. 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
1166 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004
Figure 4. Effect of the contactor inlet diameter on the fountain amplitude, for different values of the contactor base angle. Experimental conditions: Ho ) 0.20 m, dp ) 4 mm, and u ) 1.02ums.
cylindrical section is increased, the effect of the experimental conditions on the fountain height attenuates. Consequently, for angles of 120° and 180°, the differences in the fountain heights are small. Moreover, it has been observed that, as the contactor inlet diameter is increased, the fountain height decreases. This effect attenuates as the base angle is increased because of the aforementioned effect of increasing the cylindrical fraction of the bed. As the particle diameter is increased, the fountain height decreases in all of the contactors. The effect of the particle diameter is more important than that predicted by Day et al.,17 given that in this paper the stagnant bed height is lower and, consequently, the fraction of the bed in the cylindrical section is smaller. This effect is more pronounced in the contactor of base angle γb ) 30°, where Hf decreases to 1/3 when the particle diameter, dp, increases from 3 to 5 mm. The effect of an increase in the relative velocity (gas velocity above the minimum spouting velocity) is that of linearly increasing the fountain height (Figure 3). Thus, for the contactor of γb ) 30° and for u ) 1.3ums, the fountain height is approximately 3-fold that corresponding to u ) 1.02ums. This effect attenuates as the base angle of the contactor is increased. 3.2. 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 1). The 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. 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 on the upper surface of the bed. In a previous paper, the effect of the experimental conditions on the geometry of the spout has been studied.22 It is observed that the amplitude of the fountain decreases as the base angle of the contactor is increased but increases as the contactor inlet diameter (Figure 4), the stagnant bed height, the particle diameter, and the relative air velocity are increased. 3.3. 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
Figure 5. Fountain geometries for three values of the stagnant bed height: (a) Ho ) 0.15 m; (b) Ho ) 0.20 m; (c) Ho ) 0.30 m. Experimental conditions: γb ) 45°, Do ) 0.03 m, dp ) 4 mm, and u ) 1.02ums.
shape.1,2 Nevertheless, under certain experimental conditions, it also has the shape of a spherical cap. By means of the optical fiber, the interface between the core and the periphery of the fountain has been delimited (Figure 1). 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. Figure 5 shows the geometries of the fountain and the delimitation between their two zones, for the base angle of 45° and for three values of the stagnant bed height, Ho ) 0.15, 0.20, and 0.30 m. The results correspond to the following experimental conditions: Do ) 0.03 m, dp ) 4 mm, and u ) 1.02ums. It is observed that both the fountain and the core become flatter as the stagnant bed height is increased. This trend is also observed as the particle diameter and the contactor inlet diameter are increased. The effect of increasing the air velocity above that of minimum spouting is observed by comparing Figures 5b and 6. Both correspond to a cylindrical contactor of base angle 45°, with a contactor inlet diameter of Do ) 0.03 m. The results correspond to Ho ) 0.20 m, to dp ) 4 mm, and to two air velocities, u ) 1.02ums (Figure 5b) and 1.3ums (Figure 6). The velocity increase makes both the fountain and the core become elongated (as a consequence of a greater increase in height than in amplitude), and the fountain changes its shape from spherical cap to paraboloidal. This elongation is maximum in the contactors with a base angle around 45°, for which the paraboloidal shape is common to all experimental conditions. It is observed that an increase in the air velocity provokes a lengthening of the fountain core, and this effect is more pronounced as the air velocity is increased. Consequently, for velocities above that of minimum
Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1167 H, Ho, HoM ) height of the developed bed and of the stagnant bed and the maximum spoutable height, respectively, m u, umf, ums ) velocity of gas at the contactor inlet, of minimum fluidization, and of minimum spouting and terminal velocity, respectively, m s-1 Greek Letters s(H) ) bed voidage in the spout at the base of the fountain γb ) contactor included base angle, rad F, Fs ) density of the gas and of the solid, kg m-3 τ ) delay time between the two signals, s νs, νsH(0) ) vertical component of solid velocity at any point and in the axis of the contactor at the base of the fountain, m s-1 Figure 6. Fountain geometries for u ) 1.30ums. Experimental conditions: γb ) 45°, Do ) 0.03 m, Ho ) 0.20 m, and dp ) 4 mm.
spouting, the fountain core may be considered to be made up of two consecutive sections. In the first one (zone a in Figure 6), 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 (zone b in Figure 6), the geometry of the core is similar to that corresponding to the minimum spouting velocity (Figure 5b). 4. Conclusions Equation 6 has been proven to be valid for calculating the fountain height in shallow spouted beds. This equation is that obtained by Thorley et al.21 for relating the particle velocity at the base of the fountain to the fountain height, by means of force balance, ignoring drag force. The fountain shape in shallow spouted beds is generally paraboloidal, as was observed by Mathur and Epstein1 and by Grace and Mathur,2 but has the shape of a spherical cap under certain experimental conditions. The geometry depends, to a great extent, on the experimental conditions and, in shallow spouted beds, especially on the base angle. An increase in the air velocity above that of minimum spouting produces a fountain that is made up of two consecutive sections, one near the surface of the bed where the core is a continuation of the spout and another at the top of the fountain with a geometry that is almost the same as that corresponding to the fountain for u ) ums. 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). Nomenclature A ) dimensionless modulus Af, Hf ) amplitude and height of the fountain, m Dc, Di, Do ) diameter of the column, of the bed base, and of the inlet, respectively, m de ) effective distance, m dp ) particle diameter, m g ) gravity constant, m s-2
Literature Cited (1) Mathur, K. B.; Epstein, N. Spouted Beds; Academic Press: New York, 1974. (2) Grace, J. R.; Mathur, K. B. Height and Structure of the Fountain Region above Spouted Beds. Can. J. Chem. Eng. 1978, 56, 533-537. (3) He, Y. L.; Qin, S. Z.; Lim, C. J.; Grace, J. R. Particle Velocity Profiles and Solid Flow Patterns in Spouted Beds. Can. J. Chem. Eng. 1994, 72, 561-568. (4) Hook, B. D.; Littman, H.; Morgan, M. H., III. A Priori Modelling of an Adiabatic Spouted Bed Catalytic Reactor. Can. J. Chem. Eng. 1992, 70, 966-982. (5) Kutluoglu, E.; Grace, J. R.; Murchie, K. W.; Cavanagh, P. H. Particle Segregation in Spouted Beds. Can. J. Chem. Eng. 1983, 61, 308-316. (6) Cook, H. H.; Bridgwater, J. Particle Residence Times in the Continuous Spouting of Mixtures. Can. J. Chem. Eng. 1985, 63, 326-331. (7) Rovero, G.; Piccinini, N. Discharge Composition and Concentration Profiles in a Continuously Operating Spouted Bed. Can. J. Chem. Eng. 1985, 63, 997-1000. (8) Olazar, M.; San Jose´, M. J.; Izquierdo, M. A.; Alvarez, S.; Bilbao, J. Local Bed Voidage in Spouted Beds. Ind. Eng. Chem. Res. 2001, 40, 427-433. (9) Olazar, M.; San Jose´, M. J.; Izquierdo, M. A.; Ortiz de Salazar, A.; Bilbao, J. Effect of Operating Conditions on the Solid Velocity in Spout, Annulus and Fountain of Spouted Beds. Chem Eng. Sci. 2001, 56, 3585-3594. (10) Morgan, M. H., III.; Day, J. Y.; Littman, H. Spout Voidage Distribution, Stability and Particle Circulation Rates in spouted Beds of Coarse Particles. I. Theory. Chem. Eng. Sci. 1985, 40, 1367-1377. (11) Liu, L. X.; Lister, J. D. The Effect of Particle Shape on the Spouting Properties of Non-spherical Particles. Powder Technol. 1991, 60, 59-67. (12) McNab, G. S.; Bridgwater, J. A Theory for Effective Solid Stresses in the Annulus of a Spouted Bed. Can. J. Chem. Eng. 1979, 57, 274-279. (13) Passos, M. L.; Mujumdar, A. S.; Raghavan, V. G. S. Spouted Beds for Drying: Principles and Design Considerations. In Advances in Drying; Mujundar, A. S., Ed.; Hemisphere Publishing Corp.: Bristol, PA, 1987; pp 359-396. (14) Lim, C. J.; Grace, J. R. Spouted Bed Hydrodynamics in a 0.91 m Diameter Vessel. Can. J. Chem. Eng. 1987, 65, 366372. (15) Epstein, N.; Chandnani, P. P. Gas Spouting Characteristics of Fine Particles. Chem. Eng. Sci. 1987, 42, 2977-2981. (16) Wu, S. W. M.; Lim, C. J.; Epstein, N. Hydrodynamics of Spouted Beds at Elevated Temperatures. Chem. Eng. Commun. 1987, 62, 261-268. (17) Day, J. Y. Fountain Height and Particle Circulation Rate in a Spouted Bed. Chem. Eng. Sci. 1990, 45, 2987-2990. (18) Mathur, K. B.; Gishler, P. E. A Technique for Contacting Gases with Coarse Solid Particles. AIChE J. 1955, 1, 157164.
1168 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 (19) Olazar, M.; San Jose´, M. J.; Aguado, R.; Bilbao, J. Solid Flow in Jet Spouted Beds. Ind. Eng. Chem. Res. 1996, 35, 27162724. (20) Olazar, M.; San Jose´, M. J.; LLamosas, R.; Alvarez, S.; Bilbao, J. Study of Local Properties in Conical Spouted Beds Using an Optical Fiber Probe. Ind. Eng. Chem. Res. 1995, 34, 40334039. (21) Thorley, B.; Saunby, J. B.; Mathur, K. B.; Osberg, G. L. An Analysis of Air and Solids Flow in a Spouted Wheat Bed. Can. J. Chem. Eng. 1959, 37, 184-192.
(22) San Jose´, M. J.; Olazar, M.; Izquierdo, M. A.; Bilbao, J. Spout Geometry in Shallow Spouted Beds. Ind. Eng. Chem. Res. 2001, 40, 420-426.
Received for review August 4, 2003 Revised manuscript received November 21, 2003 Accepted December 2, 2003 IE030641D
