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Ind. Eng. Chem. Res. 1996, 35, 2716-2724
GENERAL RESEARCH Solid Flow in Jet Spouted Beds Martin Olazar,* Marı´a J. San Jose´ , Roberto Aguado, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
Filming equipment combined with an image treatment program has been used to study the positions of the particles in the jet spouted bed (or dilute spouted bed in conical contactor). The properties determined were the density functions for distribution of particle trajectories and of their maximum heights in the bed and local bed voidages. The spout geometry has been determined for this regime. By extending the experimental study to systems with different values of contactor inlet diameter, stagnant bed height, and relative air velocity with respect to the minimum needed for the jet spouted bed, the effect of these variables on the properties that describe the solid flow has been analyzed. 1. Introduction Bed expansion in conical spouted beds leads to a peculiar regime called the jet spouted bed or dilute spouted bed, which has a hydrodynamic behavior different from that of spouted beds in conical contactors (Markowski and Kaminski, 1983; Epstein, 1992; Olazar et al., 1992; San Jose´ et al., 1993). The vigorous movement of the solid enables the jet spouted bed to perform well in operations conditioned by solid handling difficulty (when the solid is sticky or of irregular texture) such as bituminous coal gasification (Uemaki and Tsuji, 1986, 1991; Tsuji et al., 1989) and catalytic polymerization (Bilbao et al., 1987, 1989; Olazar et al., 1994a). The jet spouted bed has other advantages, such as its capacity for handling wide particle size distributions, small pressure drop (Olazar et al., 1993a), and high mass and heat transfer between phases. The high gas velocity (short contact time) and the capacity for handling fine solids (of the usual size for catalysts) (Olazar et al., 1995a) make it potentially interesting for use as a catalytic reactor in fast reactions in which reactor design is conditioned by selectivity. In the application as a catalytic reactor, the jet spouted bed can compete with reactors of more complex design and higher cost. In previous papers, the limits of the conditions for stable operation of the jet spouted bed (Olazar et al., 1992), the hydrodynamics (Olazar et al., 1993a; San Jose´ et al., 1993), and the design factors of the contactor (Olazar et al., 1993b) have been studied. Nevertheless, once the macroscopic studies are carried out, there are certain gaps in our understanding of solid circulation. In this way, although the characteristic cyclic movement of the spouted beds is visually observed, questions arise on the shape of the trajectories or even on the possibility of the existence of a partially mixed regime due to high gas velocity. Bed voidage profiles and the spout geometry are other interesting aspects for comprehension of the jet spouted bed. The knowledge of these aspects is needed for modeling the pattern of gas flow (Olazar et al., 1993c, 1994b) and solid flow, with the aim of designing the contactor for applications such as the aforementioned. * To whom correspondence should be addressed. Telephone: 34-4-4647700 ext. 2575. Fax: 34-4-4648500. E-mail:
[email protected].
In this paper an image treatment technique has been used in order to study particle trajectories, bed voidage profiles, and the spout geometry. 2. Experimental Section The unit at pilot plant scale has been described in previous papers (Olazar et al., 1992, 1993a,b). The blower supplies a maximum air flow of 300 Nm3/h at a pressure of 1500 mm of water column. The flow is measured by means of three rotameters, which are used in the ranges of 0.3-2.5, 2.5-25 and 30-250 Nm3/h. The air velocity is also measured by means of a vertical pressure tap, whose radial and longitudinal position can be established at will inside the contactor by an externally controlled displacement device (San Jose´ et al., 1993). The tap, of stainless steel, consists of a 4 mm OD external pipe provided with four orifices of 1 mm diameter at a distance of 1 cm from the end, which are for the measurement of static pressure. The dynamic pressure is measured by the 1/16 in. o.d. internal pipe of the tap. The pressures taken by the tap go to a fourway valve and from here to a differential pressure meter, whose 0-20 mA signal indicates the value of pressure difference, which is shown in a SIPAR DR20 regulator in a 0-100 range. The absolute error range for the dynamic pressure measurement is below 0.1 Pa and for the static pressure below 1 Pa. The data reading and processing is carried out by a TANDON 386/20 computer provided with a PC-Lab-718 data acquisition card with PCLS-70 software. The equipment for particle optical monitoring, Figure 1, is composed of a camera, a video recorder; a monitor; and the computer support needed for treatment of the data obtained. This technique is suitable both because the jet spouted bed has a high bed voidage and because it is based on filming the trajectories described by one of the particles, which has been painted in a different color. The technique allows for estimating the velocity and the trajectory of the traced particle from its positions in consecutive frames and the measurement of the time elapsed between them. The camera used is a color Hitachi VM-S7200E, of 8 luxes, with horizontal resolution of 625 lines and is provided with automated adjustment for shutter control and focusing. For high particle velocities manual
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Figure 1. Equipment for optical monitoring of particles. Figure 2. Contactor design factors and geometry of the contactor bottom.
control was carried out in order to avoid tail filming and loss of definition. The VCR is a JVC BR-S600E Super VHS with a horizontal resolution of 400 lines and with 4 heads, allowing for good freeze-frame images. It is provided with several playback speeds in slow motion (from 1/6th up to 1/30th of the normal speed). The time range between two successive frames is 0.04 s. The monitor used is a color JVC VM-R150E, with a horizontal resolution of 500 lines and provided with an Elographics E274 tactile screen. Communication with the computer is carried out by means of a PCL-725 card of an optoinsulated inlet and eight relay outlets. In order to determine the three-dimensional coordinates of a particle it is not sufficient to film just a single shot of the moving particle. The solution adopted to avoid duplicating equipment, which apart from the financial cost implies synchronization problems, has consisted of simultaneously filming, in the same frame, the real system and its image reflected in a mirror, Figure 1. The mathematical treatment for calculation of the real coordinates from the two virtual ones (direct and reflected) is complex. The computer system developed for this application (in collaboration with the company Innovation and Maintenance, SAL) (Pen˜as, 1993) has been called the Graphic Analyzer of Trajectories (GAT), and is computer controlled. The following parameters are needed for the mathematical treatment: the distance from the camera to the mirror; the complementary angle between the mirror and the focus axis; the origin of the coordinates for the contactor; the origin of the coordinates for the focal plane; the scale factors for each dimension in the monitor; the focal distance; ... . Although these parameters are measurable, in order to avoid experimental errors that are inherent to the results, a calibration has been carried out. For several real positions (x,y,z) that are known (never less than 10 points), the virtual positions (coordinates) of the direct images (Y1,Z1) and of the images reflected in the mirror (Y2,Z2) have been obtained. The parameters have been calculated from the mathematical relationship between the real and virtual coordinates by using the Complex algorithm (Pen˜as, 1993). This calibration must be carried out whenever the position of any of the components of the system (contactor, mirror or camera) is modified. The study has been carried out with a contactor angle of γ ) 45° (which has been proven to be of great versatility), using different gas inlet diameters (Do ) 30, 40, and 50 mm). The other geometric factors, Figure 2, are column diameter Dc ) 360 mm and conical section
Figure 3. Example of trajectory visualization by the Graphic Analyzer of Trajectories (GAT).
thick poly(methyl methacrylate). The solids were glass spheres of 8 mm diameter. When these large particles are used, a minimum bed voidage is reached (maximum solid flow by contactor unit volume) within the range of operating conditions of the jet spouted bed, in which the Do/dp ratio can be between 1 and 80 without stability problems (Olazar et al., 1992). The traced particle was very slightly weathered in acid and then painted black. Several stagnant bed height values, Ho, situated between 20 and 40 mm were used with relative air velocities, referring to those needed for the minimum jet spouted bed, ur ) 1.05 and 1.2. The minimum jet spouted bed velocity has been calculated for each experimental system using the following correlation:
(Reo)mj ) 6.891Ar0.35(Db/Do)1.46[tan(γ/2)]-0.53 (1) The adequacy of eq 1 has been proven in previous papers for a wide range of geometric factors of the contactor-particle system, for solids of regular texture (Olazar et al., 1992) and for fine solids and mixtures of solids of different granulometry (Olazar et al., 1994a). In Figure 2 the geometry of the contactor bottom, which has great incidence on particle trajectory, is shown in detail. In Figure 3, the trajectories visualized on the computer screen are shown for a system adopted as an example. The drawing on the left corresponds to the results of the image collected directly, and the drawing on the right corresponds to the filming of the image reflected in the mirror, which is logically smaller. The solid lines join consecutive positions of the traced
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upper part of the bed is due to the fact that the particle is out of the camera range. The filming period is approximately 1.5 min. The GAT saves the data in ASCII files. The treatment that is carried out on these data is long and complex and is summarized subsequently. With the aim of correcting possible deviations of the real position of the particles, which can be due to factors such as the contactor wall refractive index, the GAT uses a previously obtained calibration to establish positions in the contactor corresponding to the trajectories visualized in the direct image and on the image reflected in the mirror. The measurement of the real position for the calibration has been carried out by using a positioning probe whose displacement within the contactor is controlled by computer (San Jose´ et al., 1993). The possibility that the image reflected on the mirror might be partially deformed (and reduced) has been taken into account. This aspect has been studied by visualizing the vertical and horizontal displacement of a graduated ruler and it has been proven that, if a correction coefficient between the two images is used, the measurement of these displacements is the same when it is taken from the readings of either the direct image or the reflected image. The correction coefficient is constant for the calculation of the vertical and radial trajectories. The three-dimensional measurements of the trajectories have been mathematically expressed in cylindrical coordinates (height, radius, and angle). 3. Particle Trajectories 3.1. Positions of the Traced Particle. The distribution along the bed, in 20 mm ranges, of the number of positions through which the traced particles passes has been calculated. Figure 4a corresponds to the experimental system of Figure 3 (Do ) 50 mm; Ho ) 20 mm; ur ) 1.05). The results plotted correspond to the distribution along the longitudinal coordinate in the bed, z, of 1570 positions of the traced particle, and they are equal to the instantaneous visualization of the state of the particles in the bed. It is observed in Figure 4a that the number of positions gradually decreases along the longitudinal position in the bed. It must be pointed out that the measurements shown are the average of three experiments carried out under the same conditions and that the results never differed by more than 1% of the average value. An optimization study of the contactor bottom design has been carried out, which was aimed at achieving uniformity in particle distribution. This study has been carried out with different bottom angles, defined in Figure 2, γb ) 45, 60, 90, 120, 150, and 180°. Figure 4a corresponds to the results obtained for an inclination angle of the contactor bottom of γb ) 150°. For smaller values of γb the results obtained are similar, except for the minimum angle of γb ) γ ) 45°, for which the operation is unstable (Olazar et al., 1992). In contrast, the results obtained for γb ) 180° are shown in Figure 4b, which correspond to a scarcely uniform trajectory distribution in which, from a total of 2000 positions studied, 840 particle positions are within a distance of 20 mm from the contactor bottom. Consequently, as the maximum bottom angle is convenient for bed stability, an acceptable compromise for bed stability-uniformity is reached for γb ) 150°. It is noteworthy that the study of the effect of the
Figure 4. Distribution of positions of the traced particle along the bed: (a) γb ) 150°; (b) γb ) 180°.
was left unanswered when a previous study, carried out with a large number of materials, showed that, in order for the bed to be stable, Do < Di must be fulfilled (Olazar et al., 1992). From the results of discrete distribution of particle longitudinal positions, the corresponding values of the normalized density function, fz, are calculated (see Figure 5). From these results, an analysis of the effect of the operating conditions and of the design factors of the contactor on particle trajectories can be carried out. In Figure 5a, it is observed that an increase in the relative air velocity with respect to the minimum needed for the regime of dilute spouted bed from 1.05 to 1.2 gives way to bed expansion, so that the trajectories reach higher longitudinal positions. Consequently, the distribution of positions is more uniform (curve with smaller slope). The effect of inlet diameter can be observed in Figure 5b. It is observed that the larger the contactor inlet diameter is the slightly more uniform the distribution of longitudinal positions is. The effect of the stagnant bed height is observed in Figure 5c,d. For ur ) 1.05 (incipient jet spouted bed), Figure 5c, as the stagnant bed height increases, the trajectories reach higher longitudinal positions in the contactor. Nevertheless, for ur ) 1.2, Figure 5d, the position distribution curves are very similar for both values of Ho studied. Consequently, the state of the dilute spouted bed, with a velocity 20% higher than the minimum needed for the incipient jet spouted bed, is independent of the initial stagnant bed height. 3.2. Maximum Height of the Trajectories. In the spouted bed regime all the particles rise up to the
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Figure 5. Effect of the operating conditions on the density function of the distribution of positions of the traced particle along the bed: (a) effect of the relative air velocity; (b) effect of the contactor inlet diameter; (c) effect of the stagnant bed height, for ur ) 1.05; (d) effect of the stagnant bed height, for ur ) 1.2.
descend through this zone taking different paths, until they re-enter the spout zone. Cycle time distribution is determined by the bed level at which they re-enter the spout zone as they descend through the annular zone. These properties of solid flow in spouted beds of conical geometry have been studied in a previous paper (Olazar et al., 1995b) using an optical fiber probe. In the jet spouted bed all the particles descend as far as the contactor bottom, then they enter the spout zone and they are conveyed by the gas up to different bed levels. Cycle time distribution is determined by the bed level reached by the particle at the upper limit of its cycle. This property has been studied for different systems by counting the number of times the traced particle reaches the upper limit of its trajectory at a given bed level, which has been established within 15 mm ranges. In Figure 6 the number of times, Nz, that the trajectories (on the whole Nt ) 133) reach a range of bed level, zmax, have been plotted for an experimental system adopted as an example. From the results of Figure 6 and those corresponding to the other experimental systems, the density functions for the distribution of the maximum height of the trajectories, fzmax, have been calculated. The values of this function have been plotted in Figure 7 against the maximum height reached, for different experimental systems. It is observed in all the experimental systems that
Figure 6. Number of times that the trajectories (on the whole Nt ) 133) reach a range of bed level.
approximately symmetrical, although in some cases tails are observed at high bed levels. This indicates that the particles more frequently reach intermediate bed levels. The trajectories are absolutely uniform, which is a characteristic of the spouted beds, which is also true for jet spouted beds, in spite of the vigorousness of this regime. Another remarkable fact, observed by means of the image treatment system, is that when a certain particle describes a cycle very near the bottom of the contactor
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Figure 7. Density functions for the distribution of the maximum height of the trajectories.
that is, that the particle reaches a high bed level. As a consequence of this fact, the cycle distribution at low bed levels is similar to the distribution at high bed levels. In the same way, by inertia, the particles tend to describe the same cycles, which are interrupted by collisions (against the wall or between particles). Another aspect that has also been observed experimentally is that when a particle describes a long cycle, after a short one, it generally drops through the annular zone on the same side as when it entered the spout. On the other hand, when a particle describes a short cycle, after a long one, it generally drops through the annular zone opposite to where it entered the spout zone. 4. Spout Geometry In the jet spouted bed, although the solid trajectories are not as uniform as in the spouted bed (Olazar et al., 1995b), it has been proven that they are sufficiently uniform to consider the particle rising zone, or spout, to be delimited by a defined interface. Rising trajectories in the theoretical annular zone only take place incidentally. In Figure 8 the evolution with bed level, z, of the radial position, r, corresponding to the limit of the spout zone has been plotted. These results correspond to the highest point of the trajectories. Each curve corresponds to one experimental system. The position of the contactor wall has also been drawn in Figure 8. It is observed that the spout diameter substantially widens from the air inlet until it reaches a diameter between 2 and 5 times the inlet diameter. This widening is progressive up to high bed levels. The explanation of this evolution of the diameter is that as the particles rise, those that have an important radial component of velocity (describing short cycles) leave the spout and only those that circulate with an important vertical component of velocity remain in the spout. The spout geometry differs from that corresponding to the spouted bed regime, for which the widening is not progressive but the spout presents a necking at an intermediate bed level, in which there is greater incorporation of the solid
Figure 8. Effect of the operating conditions on the spout geometry. Curve 1: Do ) 30 mm, Ho ) 40 mm, ur ) 1.05. Curve 2: Do ) 30 mm, Ho ) 40 mm, ur ) 1.2. Curve 3: Do ) 30 mm, Ho ) 20 mm, ur ) 1.05. Curve 4: Do ) 30 mm, Ho ) 20 mm, ur ) 1.2. Curve 5: Do ) 50 mm, Ho ) 20 mm, ur ) 1.05. Curve 6: Do ) 50 mm, Ho ) 20 mm, ur ) 1.2.
1995b). In the jet spouted bed, a slight narrowing of the spout is only observed for the highest value of the contactor inlet diameter (curves 5 and 6 in Figure 8, corresponding to Do ) 50 mm). When the effect of the operating conditions on the spout geometry are analyzed, the gas velocity at the inlet is the variable determining the widening of the spout, as is observed in Figure 8 when curve 1 is compared with 2, curve 3 with 4, and curve 5 with 6. This observation is ratified by taking into account that an increase in the stagnant bed height implies an
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Figure 9. Results of (1 - z) vs longitudinal position in the bed.
spout widening phenomenon to be more pronounced (curve 1 compared with 3 and curve 2 with 4). The contactor inlet diameter does not affect the geometry of the spout. Comparing curve 3 with 5 and curve 4 with 6, it is observed that the spout diameter is different at the bottom of the contactor but, at heights approximately above one-fifth of the bed height, the geometry of the spout is independent of Do. 5. Local Bed Voidages 5.1. Longitudinal Distribution. The bed voidage at different bed levels, z, has been determined by counting the positions of the traced particle in each cone-trunk section of the bed within two bed levels, Nz, and from the volume of the solid, Vs, and the volume of the cone-trunk section, Vi:
z ) 1 -
Vs Nz Vi
H
(2)
∑Nz
z)0
The results of (1- z) vs longitudinal position in the bed have been plotted in Figure 9 for one of the experimental systems studied. The results correspond to a relative velocity with respect to the minimum needed for the jet spouted bed, ur ) 1.2. The results of Figure 9 are representative of those obtained for other experimental systems, because, as has been previously explained, above this relative air velocity the longitudinal distribution of bed voidage is similar for the different values of Do. Similarly, for the different values of stagnant bed height, Ho, bed voidage increases in each longitudinal position proportionally to the increase in solid inventory. For ur ) 1.05 a better homogeneity of the bed was observed as the inlet diameter was increased, as was pointed out when the distribution of particle positions was studied. 5.2. Radial Distribution. For the calculation of this property, the counting of particles within rings in the bed, corresponding to a given longitudinal position z and to a radial one r, was performed:
z,r ) 1 -
Vs Nz,r Vij
H
∑Nz
(3)
Figure 10. Number of particle positions at a given bed level for different radial positions. Experimental system: Do ) 30 mm, Ho ) 40 mm, ur ) 1.2.
As an example of the calculation steps followed to determine the values of z,r, the calculation for one of the systems studied is presented next (Do ) 30 mm; Ho ) 40 mm; ur ) 1.05). In Figure 10 the number of positions of the particle counted at a given bed level, Nz,r, is plotted along the radial position. Each one of the plots corresponds to one of the eight cone-trunk sections of the bed, of 20 mm height, into which the bed was divided.
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Figure 11. Density function for particle position distribution in the bed. Experimental system: Do ) 30 mm, Ho ) 40 mm, ur ) 1.2.
From Figure 10 the density function for position distribution (or solid population) has been calculated, Figure 11. By applying eq 3 the radial distribution of bed voidage, z,r, has been calculated for each one of the conetrunks into which the bed was divided. The results of this calculation have been plotted in Figure 12, where each plot corresponds to a cone-truck section of 20 mm height. The ranges of the radii of the spout-annulus interface, rs, and of the column wall, rw, have been indicated in each plot for the corresponding ranges of the bed height. In Figure 11 it is observed that for each bed level there is a maximum of particle positions at a given radial position of the contactor. As the bed level is higher, this maximum is less pronounced and the radial distribution of particles is more uniform. The maximum for the bed density at an intermediate ring located at the interface between the spout and the annular zone is also observed in Figure 12, where for the first 20 mm of bed length the heterogeneity of the bed voidage near the bed bottom is evident. The homogenization of the bed voidage for high bed levels is also observed. Thus, at a distance between 20 and 40 mm off the bottom, the maximum for the density flattens out and at higher levels (z > 40 mm) the bed voidage in spout radial positions is uniform. It is observed that for all the longitudinal positions in the bed, there is high bed voidage in the region of the annular zone near the wall. This peculiar result is because the fountain does not occupy the whole bed and in its upper reaches the descending particles do not touch the contactor wall. It must be pointed out that this result is a consequence of the value of the contactor angle, γ ) 45°. It is foreseeable that this heterogeneity in bed voidage will attenuate as the contactor angle decreases; in contrast, the bed homogeneity will unfortunately have lesser contactor versatility and narrower stable operation ranges (Olazar et al., 1992), which indicates the need for a more careful design. Another undesirable consequence with small angle contactors is the deterioration of the well-defined cyclic trajectories and the generation of random trajectories as particles collide against the wall and against each other, especially in the upper part of the bed where the fountain of particles begins to descend. The existence
Figure 12. Radial distribution of bed voidage for four longitudinal bed sections. Experimental system: Do ) 30 mm, Ho ) 40 mm, ur ) 1.2.
the bed for an angle of 45°, as is observed in Figure 3, where it is occasionally observed that the particles suddenly deviate their trajectory and cross the bed from one side to the other. As this deviation of the trajectories takes place in the lower part of the bed, its effect on the heterogeneity is not important for a contactor angle of 45°. The results obtained for the other experimental systems studied are qualitatively similar to the aforementioned. The difference is noteworthy between the aforementioned results and those corresponding to the
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there is a clear distinction between the bed voidage of the annular and spout zones. 6. Conclusions The technique used, based on filming and image treatment, is reproducible and suitable for obtaining extensive information on particle trajectories in the jet spouted bed regime. It has been proven that the distribution of trajectory positions in the bed is uniform for an appropriate design of the contactor inlet. The inclination of the contactor bottom with an angle of γb ) 150° is a solution to this problem. The cycles described by the particles can be considered homogeneous in spite of the vigorousness of the contact, because the trajectories mainly reach their highest position in the bed in a wide range of the contactor. The spout widens appreciably along the longitudinal position; the velocity at the contactor inlet being the main variable that determines the degree of widening. The air velocity at the contactor inlet, in excess with respect to the minimum velocity required for the jet spouted bed, proved to be the suitable control variable for obtaining the same trajectory distribution in the contactor for different stagnant bed heights. Near the contactor bottom bed density is maximum at a given radial position, which approximately coincides with the interface between the annular and the spout zones. For high bed levels this maximum disappears and the density is maximum at the axis of the fountain and minimum at the contactor wall. It has been proven that in order to reach a more uniform bed voidage the angle of the contactor, γ, must be smaller, which also increases the mixing degree due to collisions of particles against the wall and between particles, giving way to deterioration of the cyclic movement desired in spouted beds. In addition, the decrease in the angle gives way to an increase in instability for certain experimental systems. The experimental information obtained on bed voidage distribution along the longitudinal and radial positions in the bed or on the evolution of the spout diameter with bed level is very useful for establishing operating conditions leading to defined trajectories and for the design of contactors to be applied in physical operations or in chemical processes. The use of this information means a closer approximation to real solid flow and there is no need for assuming uniform bed voidage or a spout diameter equal to the inlet diameter (or a mean value for the whole bed), which are assumptions that, for reasons of simplicity, were adopted in the design of these contactors. Acknowledgment This work was carried out with financial support from the University of the Basque Country/Euskal Herriko Unibertsitatea (Project No. 069.310-EB144/92). Nomenclature Ar ) Archimedes number, gd3pF(Fs - F)/µ2 Db, Dc, Di, Do ) top diameter of the stagnant bed, of the column, of the bed bottom, and of the inlet, respectively, mm dp ) particle diameter, m fzmax ) density function for the distribution of the maximum height of the trajectories -2
H, Hc, Ho ) heights of the developed bed, of the conical section of the contactor, and of the stagnant bed, respectively, mm Nt, Nz, Nz,r ) total number of counts of the traced particle, number of counts along z longitudinal position in the bed, and number of counts in (z,r) position (Reo)mj ) Reynolds number, of minimum jet spouting referred to Do, Fumjdp/µ r, z ) cylindrical coordinates rs ) radius of the spout-annulus interface, mm rw ) radius of the columm wall, mm u ) air velocity, m s-1 umj ) minimum fluid velocity in the dilute spouted bed or jet spouted bed, m s-1 ur ) relative velocity, ratio between the air velocity and the minimum velocity needed for the regime of the dilute spouted bed Vi, Vij ) volume of i cone-trunk section of the bed and of ij volume element, m3 Vs ) volume occupied by the solid, m3 zmax ) maximum level reached by particle trajectories, mm Greek Letters , z, z,r ) bed voidage, bed voidage along z longitudinal position, and bed voidage at (z, r) position, respectively γ, γb ) angle of the contactor and of the bottom of the contactor, rad µ ) viscosity of the air, kg m-1 s-1 F, Fs ) density of the air and of the solid, kg m-3
Literature Cited Bilbao, J.; Olazar, M.; Romero, A.; Arandes, J. M. Design and Operation of a Jet Spouted Bed Reactor with Continuous Catalyst Feed in the Benzyl Alcohol Polymerization. Ind. Eng. Chem. Res. 1987, 26, 1297-1304. Bilbao, J.; Olazar, M.; Romero, A.; Arandes, J. M. Optimization of the Operation in a Reactor with Continuous Catalyst Circulation in the Gaseous Benzyl Alcohol Polymerization. Chem. Eng. Commun. 1989, 75, 121-134. Epstein, N. Introduction and Overview. Can. J. Chem. Eng. 1992, 70, 833-834. Markowski, A.; Kaminski, W. Hydrodynamic Characteristics of Jet Spouted Beds. Can. J. Chem. Eng. 1983, 61, 377-381. Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Stable Operation Conditions for Gas-Solid Contact Regimes in Conical Spouted Beds. Ind. Eng. Chem. Res. 1992, 31, 17841792. Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Pressure Drop in Conical Spouted Beds. Chem. Eng. J. 1993a, 51, 53-60. Olazar, M.; San Jose´, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Design Factors of Conical Spouted Beds and Jet Spouted Beds. Ind. Eng. Chem. Res. 1993b, 32, 1245-1250. Olazar, M.; San Jose´, M. J.; Pen˜as, F. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. A Model for Gas Flow in Jet Spouted Beds. Can. J. Chem. Eng. 1993c, 71, 189-194. Olazar, M.; San Jose´, M. J.; Zabala, G.; Bilbao, J. A New Reactor in Jet Spouted Bed Regime for Catalytic Polymerizations. Chem. Eng. Sci. 1994a, 49, 4579-4588. Olazar, M.; San Jose´, M.; Pen˜as, F. J.; Arandes, J. M.; Bilbao, J. Gas Flow Dispersion in Jet Spouted Beds. Effect of Geometric Factors and Operating Conditions. Ind. Eng. Chem. Res. 1994b, 33, 3267-3273. Olazar, M.; San Jose´, M. J.; Cepeda, E.; Ortiz de Latierro, R.; Bilbao, J. Hydrodynamics of Fine Solids in Conical Spouted Beds. In Fluidization VIII; Engineering Foundation: New York, 1995a (in press). 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. 1995b, 34, 40334039. Pen˜as, F. J. Contribution to the Model of the Flow in Spouted Conical Bed. Application to the Treatment of Mixtures and Study of the Segregation. Ph.D. Thesis, University of the Basque
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2724 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 San Jose´, M. J.; Olazar, M.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Expansion of Spouted Beds in Conical Contactors. Chem. Eng. J. 1993, 51, 45-52.
Uemaki, O.; Tsuji, T. Coal Gasification in a Jet Spouted Bed. Proceedings of the 41st Canadian Chemical Engineering Conference, Vancouver, 1991; No. 17-1.
Tsuji, T.; Shibata, T.; Yamaguchi, K.; Uemaki, O. Mathematical Modeling of Spouted Bed Coal Gasification. Proc. Int. Conf. Coal Sci. 1989, 1, 457-460.
Received for review August 10, 1995 Accepted May 20, 1996X
Uemaki, O.; Tsuji, T. Gasification of a sub-bituminous Coal in a Two-stage Jet Spouted Bed Reactor. In Fluidization V; Ostergaard, K., Sorensen, A., Eds.; Engineering Foundation: New York, 1986; pp 497-504.
IE950500E X Abstract published in Advance ACS Abstracts, July 1, 1996.
