Ind. Eng. Chem. Res. 1994,33,3267-3273
3267
Gas Flow Dispersion in Jet-SpoutedBeds. Effect of Geometric Factors and Operating Conditions Martin 01azar,*Maria J. San Jose, Francisco J. Penas, Jose M. Arandes, and Javier Bilbao Departamento de Ingenieria Quimica, Universidad del Pats Vasco, Apartado 644,48080 Bilbao, Spain
The validity of using a dispersed plug-flow model to represent the gas flow in jet-spouted beds has been proven using a large number of experimental systems. The application of the model for calculation of the dispersion coefficient in the flow direction requires the knowledge of velocity profile in the contactor. The model allows for a simplified solution (one-dimensional model) for certain angle-inlet diameter combinations: y < 33" and DdDi > 213. Under these conditions the gas-flow rate is maintained constant along each and every one of the stream tubes established in the model. The effect of both the geometric factors of the contactor (angle and gas inlet diameterhase diameter ratio) and the operating conditions (particle diameter and gas velocity at the inlet) on the dispersion coefficient has been studied. 1. Introduction
The jet-spouted bed (such as it was originally called by Markowski and Kaminski (1983))or diluted spouted bed (a name that has been suggested by Epstein (1991)) is a contact regime that is obtained by expansion of a spouted bed in exclusively conical contactors. The vigorous and individualized movement of the particles makes this regime suitable for treatment of sticky solids, which are difficult to treat when the conventional gas-solid contact methods are used. In the same way, the conical geometry of the contactor permits the uniform treatment of beds with a wide particle size distribution. These properties have been proven in the polymerization on solid acid catalysts (Bilbao et al., 1987,1989). In these polymerizations, a wide distribution of the catalyst particles increased with polymer is produced and, moreover, the particles tend to fise together, thus rendering the operation unfeasible with other contact techniques. The jet-spouted bed has also been successfully used in coal gasification (Uemaki and Tsuji, 1986, 1991; Tsuji et al., 1989) and in the treatment of wood residues (Olazar et al., 1994). In previous papers, the geometric factors and the design requirements for stability have been delimited, and the operating conditions of the jet-spouted bed have been compared with those of other gas-solid contact techniques (Olazar et al., 1992). Original correlations have also been obtained for calculation of hydrodynamic properties (San Jose et al., 1992, 1993) and of correlations for the contactor design (Olazar et al., 1993a). On the other hand, due to the high gas velocity, the jet-spouted beds have a potential interest as fastreaction reactors in which selectivity is the factor for optimization, as they allow for working with short gas residence times. The design of the jet spouted bed as a reactor requires the rigorous definition of the gas-flow pattern in order for the residence time distribution to be considered. In a previous paper (Olazar et al., 1993b) a simplified model for gas flow, which is nonexistent in the literature, that aims at simple application has been proposed. It is based on the definition of gas-flow stream tubes in such a way that they adhere to the bed geometry. The model quantifies the dispersion in the stream-tube
I&+
Figure 1. Geometric factors of the contactors.
direction by using a characteristic dispersion modulus. Nevertheless, the assumption of this simplified model of considering constant gas-flow rate along each stream tube has serious limitations under certain experimental conditions. In this paper, on the basis of the experimental study of radial and longitudinal velocity profiles in the contactor, the limitations of the simplified gas-flow model previously proposed (Olazar et al., 1993b) have been studied and a more rigorous model that takes into account the mass transfer between stream tubes has been proposed. The study of a wide number of experimental systems has allowed for determining the values of the dispersion coefficientfor jet spouted beds in a wide range of geometric factors and of operating conditions.
2. Experimental Section The unit, at pilot plant scale, has been detailed in previous papers (Olazar et al., 1992, 1993~). Five conical contactors of poly(methy1methacrylate), whose geometry is defined in Figure 1,have been used, and they are made to the following dimensions: column diameter, D, = 36 cm; conical section heights, H,= 36, 40, 45, 50, and 60 cm; their corresponding contactor angles, y = 45,39,36,33, and 28"; gas inlet diameters, D O= 3 , 4 and 5 cm.
0888-5885/94/2633-3267$o4.50/00 1994 American Chemical Society
3268 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
,
I r d
Figure 2. Experimental setup for the study with tracers.
The solids used have been glass spheres (es = 2420 kg/m3)with particle diameters, d, = 1,2, 3,4, 6, and 8 mm. The characteristics of the probe for velocity measurement have been detailed in a previous paper (San Jose et al., 1993). In synthesis it consists of a Pitot tube driven by a computer-controlled crane, which allows for establishing at will a sequence of radial and longitudinal positions to measure velocity. A minimum of 20 velocity data have been measured for each system studied. The residence time distribution of the gas flow for different radial positions has been determined from 1-F curves, which have been obtained as a response t o a tracer inlet (Hz) made in negative step. The experimental setup is shown in Figure 2. The stimulus and response signals are measured using thermal conductivity detectors of platinum filament connected to a Wheatstone bridge. The filaments are protected by a metallic mesh, and the unit does not appreciably disturb the gas flow (Olazar et al., 1993b). The detector that registers the tracer concentration at the inlet is located prior t o the screen that supports the bed of solids, a t the center of the inlet section. The position of the outlet sensor, over the bed of solids, reduces to a minimum the disturbance on the solids flow. An electrovalve allows for the control of the closing time of H2 flow so that the inlet signal is reproducible. A PCL-718 data acquisition card sends the signals to the computer where they are registered as continuous curves. The temperature of the air affects its conductivity, and it has been proven that the continuous operation provokes overheating of the bed due to friction between solid particles. It has been operated in a narrow temperature range (between 24 and 30 "C) in order to avoid this disturbance. 3. Gas-Flow Model
The geometric model was proposed in a previous paper (Olazar et al., 1993b), and although it takes as historical reference the bases of the model of Lim and Mathur (1976) for cylindrical spouted beds, it has the following advantages: (1) it takes into account the peculiar characteristics of the gas-solid contact in jetspouted beds (high and uniform bed voidage, indefinition of the annular and spout zones); (2) it is of general application as is established on the basis of the contactor geometry (which is necessary in jet spouted beds, where stability for each particular system is attained with a
Figure 3. Geometry of the gas-flowmodel. Volume elements and stream tubes.
defined geometry (Olazar et al., 1992));(3) it is applied on the basis of the measurement of gas velocity profiles in the contactor. The positions in gas flow and the stream tubes are described by tracing M arcs or isolines of e spherical radius (which define the longitudinal position) and of N straight lines or isolines of 8 angular coordinate (which define the radial position). In this way, volume elements in spherical coordinates in direct relation to the contactor geometry are delimited (Figure 3). The lines that delimit the stream tubes, of section increasing with height, are traced from the coordinates' origin. This tracing of stream tubes, from the coordinates' origin (point A), general for any geometry of cone and of inlet, also establishes a dead zone for flow (streaked zone in Figure 3, delimited by line B-C) near the contactor wall and which will be a function of inletcontactor geometry. The upper limit surface of the bed is a cap. In the jet-spouted beds the homogeneous bed takes a curved shape in the upper surface (Figure 3) such as is visually observed in the experimental systems. The mass conservation equations have been developed with the following assumptions: (1)the bed voidage is uniform in the whole bed, and there is no distinction between annular and spout zones; (2) in each stream tube, the plug flow deviation is quantified by means of an longitudinal dispersion coefficient, D, defined according to Fick's law. 3.1. One-DimensionalModel (based on the radial velocity profile at the inlet). The gas-flow rate along each one of the stream tubes is assumed t o be constant. In this way, the dispersion or any other gas-mixing mechanism between stream tubes is neglected. Taking into account the accumulation term, the mass conservation equation in a differential volume element such as that defined in Figure 4, in unsteady state, is
ac = - u . . a-c+ D at
ae
a2c+ -20 ac a@
Q ae
(1)
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3269
!
e,
l0K\ I
I Figure 4. Differential volume element.
0'
\
0.2
0.4
0.6
I
0.08
0.8
1.0
e/a
with the following initial and boundary conditions: fort 5 0:
C = 1(negative step function)
(2)
for t > 0:
at the inlet o f j stream tube (e = eo):
ac
D - = U,(C - C&)) (3)
a@ at the outlet o f j stream tube (e =
g=o ae
l 0 h
(4) '0
For the N stream tubes a set of N equations is established, whose solution will give N functions that will describe the evolution of tracer concentration along each stream tube with time. 3.2. Velocity Profiles. In Figure 5, the experimental values of the vertical component of the interstitial point velocity in the contactor, uz, (experimentally measured using the probe previously described), are shown as an example for three longitudinal positions (@* = @/@M = 0.1, 0.42, and 0.75)and different radial positions (referred t o the dimensionless radial coordinate Ola). Each plot corresponds to one contactor angle, y = 28, 36, and 45". Following the procedure detailed in a previous paper (Peiias, 1993), from the vertical component of the interstitial velocity, the radial component of the velocity a t each point in the contactor, u,, has been calculated using the continuity equation:
i a - +ruJ r ar
0.2
0.4
0.6
0.8
1.0
e/a C
P' 0.70 0
A 0.43
e/a Figure 5. Vertical component of the interstitial velocity, ur,for different longitudinal and radial positions of the contactor, for DO = 4 cm, d, = 4 mm, HO= 4 cm, and uIu, = 1: (a) y = 28"; (b) y = 33"; (c) y = 45".
au2 -= 0
+ az
with the following boundary conditions: for r = 0:
u, = 0
(6)
for r = R:
u, = 0
(7)
Once the longitudinal and radial components of the interstitial velocity are known, the modulus and direction of velocity vector a t each contactor point are defined. In Figure 6, the map of velocity vectors is shown, which have been obtained for an experimental system taken as an example. The gas flow follows a similar direction to that of the stream tubes previously postulated in the gas flow model (Figure 3). For the experimental case to which Figure 6 corresponds, it has been proven, from the numerical calculations carried out using the gas velocity values obtained, that the assumption of constant flow rate
along the stream tubes is fulfilled. Nevertheless, when the results corresponding to all the experimental systems are analyzed, it can be established that the flow rate is maintained constant along the stream tubes in the systems in which the combination angle-inlet fulfils the following conditions: y < 33" and DdDj > 213. In virtue of this result the conditions previously pointed out are critical values. For the systems in which the flow rate is not maintained constant along each stream tube, a two-dimensional model has been applied for the calculation of the dispersion coefficient. 3.3. Two-DimensionalModel (based on radial and longitudinal velocity profiles). For the systems in which the flow rate is not maintained constant along each stream tube, a new two-dimensional model has been proposed for the gas flow, which takes into account the velocity vector at each point in the contactor. By application of a general mass balance in spherical coordinates to the volume element (Figure 4)
3270 Ind. Eng. Chem. Res., Vol. 33, No. 12,1994
a E
-
I
4
0.5
-
0.0 0
i
1.0
Figure 6. Map of gas interstitial velocity vectors. System: y = 36",Do = 5 cm, d, = 4 mm, HO= 4.0 cm, H = 35.0 cm, and Q = 190 m3h.
R I rl
0.5
-& $ ( s i n 8 De 9 a0 1(8) e sin 8 Assuming the total density of the system to be constant and taking into account only the dispersion coefficient along e direction, D = D, (De = 01, the following is obtained:
0.0
0
1
2
3
4
time (s)
C
-
E4
with the initial and boundary conditions defined by eqs
I
rl
2-4.
4. Dispersion Coefficient
The equations that define the flow model, with their initial and boundary conditions (for the experimental conditions of tracer injection) have been numerically solved. In this way, the concentration-time curves are calculated a t the exit of the bed, for any radial position. To illustrate the results obtained and as an example, the 1-F curves are shown in Figure 7 for the same relative radial position (intermediate in the annular zone, 8/a = 0.5) in three contactors of different angle, with the following conditions: glass spheres of d, = 8 mm, DO= 5 cm, HO= 4.0 cm and u Iumj = 1.0. The solid lines are experimental, and the dashed lines are those calculated with the dispersion coefficient of the best fit. The dotted lines are the normalized experimental curves corresponding to the tracer a t the bed inlet. In the experimental systems in which the air-flow rate is not maintained constant along each one of the stream tubes, the application of the one-dimensional model leads to the situation illustrated in Figure 8, where it is shown that, for two different radial positions in the contactor, the experimental 1-F curve fits to the calculated 1-F curve a t each radial position with a M e r e n t value of dispersion coefficient. The consideration in these cases of the two-dimensional model, with mass
0.5
0.0
-
-
0
time (s) Figure 7. 1-F response to the tracer at the bed exit at Wa = 0.5. d, = 4 mm, DO= 4 cm, HO= 4.0 cm, and U I U W = 1.0: (a) y = 28"; (b) y = 36"; (c) y = 45".
transfer between stream tubes, makes up for this anomalous situation and shows the validity of the representation of plug-flow deviation with only one dispersion coefficient. In Figure 9 the 1-F experimental curve and the one calculated with the most suitable value of D are plotted for the same radial positions as in Figure 8, but the two-dimensional model has now been applied to represent the gas flow. The calculation of the D coefficient that best fits each experimental system has been carried out by means of the Complex method, the objective function to minimize being
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3271
- - - experimental
c4
n
-
I
H
spouted beds
.
time (s) Figure 8. Comparison of 1-F experimental response at the bed exit with the response calculated using the one-dimensional model for two radial positions a t the contactor. y = 45", d, = 4 mm, DO = 4 cm, HO= 4.0 cm, and ulu,, = 1. .......bd
Figure 10. Comparison of the dispersion coefficient values in jetspouted beds with those of other contact regimes. .r
7
M&
4
k I
20-
\
n
rl
15 0.5
-
10 -
5nn-
"'"0
1
2
3
4
5
-0
2
4
6
time (s) Figure 9. Comparison of 1-F experimental response a t the bed exit with the response calculated using the two-dimensional model for two radial positions at the contactor. y = 45", d, = 4 mm, DO = 4 cm, HO= 4.0 cm, and ulu,, = 1. N
In Figure 10, the calculated values (streaked zone) are compared with those obtained in the literature (Wen and Fan, 1975; Lim and Mathur, 1976; Nishio et al., 1992) for other gas-solid contact methods. The values of D for jet-spouted beds are plotted against gas velocity U b , corresponding to the upper section of the stagnant bed (of diameter Db). The values of D obtained are of the same order of magnitude or even lower in some cases, than those correspondingto fxed beds (Gum and Pryce, 19691, and noticeably lower than those of other contact methods. Dry and White (1989) have collected from the literature and experimentally determined high values of dispersion coefficient, between 0.2 and 3.6 m2/ s, for risers in high-velocity circulating fluidized beds of FCC catalyst. It is also concluded that the plug-flow deviation is substantially lower than that observed for conical-spouted beds (Peiias, 1993). The calculated values of D are distributed in a wide zone of Figure 10, which is a consequence of the results corresponding to a wide range of experimental conditions. With the aim of quantifylng the effect of these conditions on the dispersion coefficient value, the values
8
10
H o (cm) Figure 11. Values of (DIAF~.~') modulus vs stagnant bed height,
Ho, for different values of contactor angle, y , and of inlet diameter, DO.Lines, calculated with eq 11.Points, experimental ones (0,DO = 0.03 m;
A,
DO= 0.04 m; 0, DO= 0.05 m).
of D calculated for all the experimental systems studied have been related by nonlinear regression to the dimensionless moduli that take into account the geometric factors and the operating conditions. The equation of the best fit is (with a regression coefficient, r2 = 0.92 and a relative error lower than 10%)
In eq 11it is observed that the dispersion coefficient increases with bed height (implicitly taken into account in the upper diameter of the stagnant bed, Db), with inlet diameter, DO, with contactor angle, y , and decreases with particle diameter (taken into account in the Archimedes modulus, Ar) and with gas velocity a t the contactor inlet, u. In Figure 11,to study the effect that the geometric factors of the contactor (cone angle and inlet diameter) have on the dispersion coefficient, the values calculated using eq 11, lines, and the experimental results of ( D l Ar-0.57)modulus for d, = 4 mm have been plotted vs the stagnant bed height, Ho.Figure 11 has been calculated using the minimum jet-spouting velocity (for ulum, =1.0). Each curve corresponds t o a different
3272 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
modulus have been plotted vs stagnant bed height, Ho. The experimental values plotted correspond to glass spheres of particle diameter, d, = 4 mm and contactor angle, y = 36". The curves are plotted for three values of relative velocity, ulumj = 1.0, 1.1,and 1.2, and for three values of contactor inlet diameter, DO= 3 , 4 , and 5 cm. It is observed in Figure 13 that the modulus plotted increases, in all cases, more than proportionally with stagnant bed height, Ho.For each inlet diameter, as the relative velocity increases the increase in the modulus with HOis less pronounced. 5. Conclusions
H o (cm)
Figure 12. Values of {D4tan(y/2)l1.M)modulus vs stagnant bed for different values of inlet diameter,DO,and of particle height,Ho, diameter, d,. Lines, calculated with eq 11. Points, experimental ones (0,DO= 0.03 m; A, DO= 0.04 m; 0,DO= 0.05 m).
200
Y=36O
3-
$ & -ba
150
2
loo
\
50
0
Figure 13. Values of {D/{[tan(y/2)]1.s4Ar-0~57)} modulus vs stagfor different values of inlet diameter, Do, and nant bed height, Ho, of relative velocity ulurnj. Lines, calculated with eq 11. Points, experimental ones (0, u l u d = 1.0;A, u / u d = 1.1; 0, ulumj = 1.2).
combination of the geometric factors of the contactor. In Figure 11 the adequate fit of eq 11 is noticeable. It is observed that the dispersion coefficient increases more than proportionally with stagnant bed height. This effect is more pronounced as both the contactor angle and the inlet diameter are greater. In Figure 12, with the aim of isolating the effect of the contactor angle used on the dispersion Coefficient, the values calculated, lines, and the experimental ones for y = 36", points, of {Dl[tan(y/2)11.84}modulus have been plotted against stagnant bed height, Ho.The results in Figure 12 correspond t o the minimum jetspouting velocity (for u/u? =1.0). Each curve corresponds to a different combination of particle diameter and contactor inlet diameter. The dispersion modulus increases more than proportionally as the stagnant bed height increases and in a more pronounced way as the particle diameter reduces. On the other hand, it is noteworthy that the effect of particle diameter is more important than that of the inlet diameter. This effect is observed for all the angles studied. The effect of contactor inlet gas velocity is studied in Figure 13, in which the values calculated using eq 11 and the experimental values of {D/{[tan(y/2)]1.84Ar-0.57}}
A gas-flow model that takes into account the mass and momentum transfer between stream tubes has been proposed and proven, since the one-dimensional model proposed in a previous paper (Olazar et al., 1993b) is acceptable only for systems that simultaneously fulfill the following conditions: y < 33" and DdDi > 2f3. It has been proven that in the systems with values of y lower than 33" and with ratios between inlet diameter and base diameter, DdDi, lower than 2f3, the air velocity profile shows that there is mass transfer between the stream tubes of the flow model. The validity of the model, developed and solved in a simplified way (one-dimensional) or in a rigorous way (two-dimensional) for a wide range of geometric factors and experimental conditions, is evidence of its applicability. This dispersed plug-flow model will be of easy application in the design of a jet-spouted bed as reactor. Although it has not been considered in this paper, due to the adequate fit obtained in the experimental systems studied, the model proposed allows for incorporating other real aspects of the gas-solid contact in jet-spouted beds, such as more accurate delimitation of the dead zone in the contactor wall; better definition of the fountain geometry; consideration of velocity profiles. The consideration of these aspects in those experimental systems that require them hardly hinders the mathematical solving of the model. The plug-flow deviation in jet-spouted beds is reduced. The values of the dispersion coefficient obtained are of the same order of magnitude as those values for fured beds and are substantially lower than those corresponding to fluidized beds and cylindrical spouted beds of conical base. This good behavior of the gas flow together with the good behavior in the treatment of the solid, means great potential interest in the use of the jetspouted bed as reactor in processes in which a high transport velocity together with a reduced residence time of the gas in the reactor are required. Nomenclature Ar = Archimedes number, g d p 3 ~ t-( ~&Ip2 B C, Co = dimensionlesstracer concentration and dimensionless tracer concentration at the bed inlet D,D,,De = dispersion coefficient and longitudinal and radial dispersion coefficients, respectively, m2 s-l Db,D,,Di,DO = diameter of the upper section of the stagnant bed, of the column (or the cylindrical part of the contactor),of the contactor base, and of the gas inlet, respectively, cm DPT = differential pressure transducer d, = particle diameter, mm EST = electrical signal transducer F = response curve to a step tracer stimulus
Ind. Eng. Chem. Res., Vol. 33,No. 12, 1994 3273
H,H,,HO= heights of the
developed bed, of the conical section, and of the stagnant bed, respectively, m Q = air-flow rate, m3 h-l R = contactor radius at z height, m r, z = cylindrical coordinates
t = time, s u = air velocity, m s-1 u ~= j air velocity at the contactor inlet at the j stream tube, m s-1 uu = air velocity at the z j volume element in the j stream
tube, m s-l minimum jet-spouted bed velocity, m s-l ur, up,uQ,ug = components of air interstitial velocity in r, z, e, and 8 directions, respectively, m s-l umj=
Greek Letters a = angle defined in the geometry of the gas-flow model, Figure 3, r a d y = contactor angle, rad p = viscosity, kg m-l s-l e, 8 = spherical coordinates eo, @M = lower and upper longitudinal positions of the developed bed, m e* = dimensionless radial position, @/@M ef,es = fluid and solid densities, 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 Reador with Continuous Catalyst Circulation in the Gaseous Benzyl Alcohol Polymerization. Chem. Eng. Commun. 1989,75,121-134. Dry, R.J.; White, C. C. Gas Residence-Time Characteristics in a High-Velocity Circulating Fluidized Bed of FCC Catalyst. Powder Technol. 1989,58,17-23. Epstein, N. Introduction and Overview. Can. J. Chem. Eng. 1992, 70,833-834. Gunn, D. J.; Pryce, C. Dispersion in Packed Beds. Trans. Inst. Chem. Eng. 1969,47,341-350. Lim, C. J.; Mathur, K. B. A Flow Model for Gas Movement in Spouted Beds. AIChE J. 1976,22,674-680. Markowski, A,; Kaminski, W. Hydrodynamic Characteristics of Jet Spouted Beds. Can. J. Chem. Eng. 1983,61,377-381.
Nishio, N., Kaguei, S., Wakao, N. Parameters in a Gas-Solid Fluidized Bed Absorber by Concentration Response-Technique at Incipient Fluidization. Int. Chem. Eng. 1992,32,132-139. Olazar, M.; San Jos6, M. J.;Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Stable Operation Conditions for Gas-Solid Contact Regimes in Conical Spouted Beds. Znd. Eng. Chem. Res. 1992,31,17841792. Olazar, M.;San Jos6, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Design Factors of Conical Spouted Beds and Jet Spouted Beds. Ind. Eng. Chem. Res. 1993a,32,1245-1250. Olazar, M.; San Jos6, M. J.; Pefias, F. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. A Model for Gas Flow in Jet Spouted Beds. Can. J. Chem. Eng. 1993b,71,189-194. Olazar, M.; San Jos6, M. J.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Pressure Drop in Conical Spouted Beds. Chem. Eng. J. 1993c, 51,53-60. Olazar, M.; San Jos6, M. J.; Llamosas, R.; Bilbao, J. Hydrodynamics of Sawdust and Mixtures of Wood Residues in Conical Spouted Beds. Ind. Eng. Chem. Res. 1994,33,993-1000. PeAas, F. J. Contribuci6n al Modelado del Flujo en Spouted Beds Conicos. Aplicaci6n a1 Tratamiento de Mezclas y Estudio de la Segregacibn. Ph.D. Thesis, University of the Basque Country, Bilbao, Spain, 1993. San Jos6, M. J.; Olazar, M.; Aguayo, A. T.; Arandes, J. M.; Bilbao, J. Hydrodynamic Correlations of Conical Jet Spouted Beds. In Fluidization VI& Potter, 0.E., Nicklin, D. J., Eds.; Engineering Foundation: New York, 1992;pp 831-838. San Jos6, 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. Tsuji, T.; Shibata, T.; Yamaguchi, IL;Uemaki, 0. Mathematical Modelling of Spouted Bed Coal Gasification. Proc. Int. Conf. Coal Sci. 1989,1, 457-460. Uemaki, 0.;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. Uemaki, 0.; Tsuji, T. Coal Gasification in a Jet Spouted Bed. Proceedings of the 41st Canadian Chemical Engineering Conference; Vancouver, 1991;No. 17-1. Wen, C. Y.;Fan L. T. Models for Flow Systems and Chemical Reactors; Marcel Dekker, Inc.: New York, 1975. Received for review March 23, 1994 Revised manuscript received August 1, 1994 Accepted August 15, 1994@ Abstract published in Advance ACS Abstracts, October 15, 1994. @
