2826
Ind. Eng. Chem. Res. 1993,32,2826-2834
Stability and Hydrodynamics of Conical Spouted Beds with Binary Mixtures Martin Olazar,. Maria J. San Josh, Francisco J. Pefias, Andr6s T. Aguayo, and Javier Bilbao Departamento de Ingenierh Qulmica, Uniuersidad del Pab Vasco, Apartado 644, 48080 Bilbao, Spain
The application of conical spouted beds with binary mixtures of glass spheres of particle diameters between 1and 8 mm, in stable operation regime and without segregation, has been studied. The effects of the contactor geometric factors (angle, inlet diameter), of the stagnant bed height, of the mixture composition, and of the gas velocity on bed stability and bed segregation have been analyzed. It has been proven that the correlations proposed in the literature for calculation of the hydrodynamics of spouted beds of cylindrical geometry are not suitable for evaluating the hydrodynamics of the operation with mixtures in conical contactors. Original equations for calculation of the minimum spouting velocity, of the maximum and stable operation pressure drop, and of the bed voidage of minimum spouting have been proposed. In these equations the Sauter mean diameter is used as the characteristic diameter of the mixture. A weighted average value of the (drag force)/(gravity force) ratio is used for calculation of the bed voidage of minimum spouting. 1. Introduction The spouted beds of conical geometry have advantages compared to fluidized beds and to other methods of gassolid contact, especially for treatment of solids with a wide particle size distribution. The conical contactors have been used successfully in reactions in which the particle size changes with residence time in the contactor, as happens in coal gasification (Tsuji et al., 1989; Uemaki and Tsuji, 1986,1991) and in catalytic polymerizations (Bilbao et al., 1987,1989). In previous papers, the hydrodynamics and the design factors for conical spouted beds have been profoundly studied (Wan-Fyong et al., 1969;Kmiec, 1983; Olazar et al., 1992, 1993a,b; San Jose et al., 1993). Nevertheless, these studies correspond only to solids of uniform size. The design of contactors that operate with particles of different size requires the knowledge of certain aspects whose study is approached in this paper: (a)the conditions and the geometric factors of the contactor that give way to stable operation with mixtures, with minimum segregation; (b) the hydrodynamics of the operation with mixtures. Future objectives that are beyond the scope of this paper but that will be necessary for the design of contactors that operate under segregation are (a) study of longitudinal and radial segregation of those systems which could be handled in stable way due to the versatility of conical contactors; and (b) the hydrodynamic study and proposal of correlations for those systems with noticeable segregation. The hydrodynamics of spouted beds with particle size distribution has previously been described, but only for cylindrical contactors of either nearly flat or conical base (Mathur and Gishler, 1955; Manurung, 1964; Smith and Reddy, 1964; Brunello et al., 1974; Uemaki et al., 1983). The conical beds have only been studied by Wang-Fyong et al. (19691, who only proposed a relationship for calculation of the minimum spouting velocity of binary mixtures. In the present paper, an attempt is made to fill the previously mentioned gaps in the area of spouted beds in conical contactors. First, the usefulness of conical contactors of different geometry to treat binary mixtures without noticeable segregation and in stable regime has been studied. Once the conditions for stable operation and without segregation have been delimited, new hy0888-588519312632-2826$04.00/0
Figure 1. Geometric factors of the contactors.
drodynamic correlationshave been obtained for calculation of the minimum spouting velocity, of the maximum pressure drop, of the pressure drop in stable spouting regime, and of the bed voidage corresponding to the minimum spouting velocity.
2. Experimental Section The equipment used, the probes for pressure andvelocity measurement, their usage, and the general conditions for the experimental work have been detailed in a previous paper (Olazar et al., 1992). The evolution of pressure drop with air velocity has been measured by means of a data acquisition system by computer with PC-Lab-718 card provided with a PCLS-711 software. The geometric factors of the contactors used (of poly(methy1 methacrylate)) are defined in Figure 1 (where the characteristic movement of the particles is outlined) and they have the following values: upper diameter of the contactor (column diameter), D, = 0.36 m; contactor base diameter, Di = 0.06 m; heights of the cone, H,= 0.36, 0.40, 0.45, 0.50 and 0.60 m; cone angles, y , corresponding to the previous heights = 45O, 39O, 36O, 33O, and 28O. With each contactor the study has been extended to three values of inlet diameter, DO = 0.03, 0.04, and 0.05 m. The solids uaed are glass spheres of diameter between 1 and 8 mm and density pa = 2420 kg/m3, and they all 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2827 Table I. Identification Numbers, Composition, and Sauter Diameters, Eq 1, of the Mixtures Studied. composn no. & = 1 d g = 2 20 33 50 60 67
1 2 3 4 5 6
80
80 67 50 40 33 20
composn no. d s = 1 d g = 7
composn
de
1.67 1.50 1.33 1.25 1.20 1.11
-
31 32 33 34 35 36
20 33 50 60 67 80
80 67 50 40 33 20
d, 3.18 2.35 1.75 1.52 1.39 1.20
61 62 63 64 65 66
20 33 50 60 67 80
80 67 50 40 33 20
4.29 3.61 3.00 2.73 2.56 2.31
no. d s = 1 d g = 3 7 20 80 8 33 67 9 50 50 10 60 40 11 67 33 12 80 20 composn
d,
2.14 1.80 1.50 1.36 1.28 1.15
-
composn
-
no. d s = 1 d g = 4 13 14 15 16 17 18
20 33 50 60 67 80
80 67 50 40 33 20
d,
2.50 2.00 1.60 1.43 1.33 1.18
composn
-
composn no. d s = 1 d g = 5 20 80 19 33 67 20 21 50 50 60 40 22 23 67 33 20 24 80 composn
no. d s = 1 d e = 8 37 20 80 38 33 67 50 39 50 40 60 40 41 67 33 42 80 20
d, 3.33 2.42 1.78 1.54 1.41 1.21
no. d s = 2 d g = 3 43 20 80 44 33 67 45 50 50 46 60 40 47 67 33 48 80 20
d, 2.73 2.58 2.40 2.31 2.25 2.14
no. d s = 2 d e - 4 20 80 49 33 67 50 50 50 51 60 40 52 67 33 53 80 20 54
67 68 69 70 71 72
4.67 3.84 3.11 2.80 2.62 2.33
73 74 75 76 77 78
5.00 4.00 3.20 2.86 2.66 2.35
79 80
20 33 50 60 67 80
80 67 50 40 33 20
20 33 50 60 67 80
80 67 50 40 33 20
81 82 83 84
20 33 50 60 67 80
80 67 50 40 33 20 ~
~
composn no. d s = 3 d g = 6 91 20 80 67 92 33 50 93 50 40 94 60 33 95 67 80 20 96 composn no. d s = 4 d g = 7 121 20 80 67 122 33 50 123 50 40 124 60 33 125 67 20 126 80
composn
-
ds 5.00 4.51 4.00 3.75 3.59 3.33
-
ds 6.09 5.61 5.09 4.83 4.66 4.38
no. d s = 3 d B = 7 97 20 80 98 33 67 50 99 50 40 100 60 33 101 67 20 102 80 composn no. d s = 4 d g = 8 127 20 80 128 33 67 129 50 50 40 130 60 131 67 33 132 80 20
composn no. 151 152 153 154 155 156 a
ds = 6 20 33 50 60 67 80
dg = 7 80 67 50 40 33 20
-
ds 5.53 4.86 4.20 3.89 3.70 3.31
-
ds 6.67 6.02 5.33 5.00 4.79 4.44
-
ds 6.00 5.16 3.46 4.00 3.78 3.43
composn no. dS-5 133 20 134 33 135 50 136 60 137 67 138 80
dB-6 80 67 50 40 33 20
no. 157 158 159 160 161 162
ds=6 20 33 50 60 67 80
-
ds 5.77 5.63 5.45 5.36 5.29 5.17
composn
dS 6.77 6.64 6.46 6.36 6.30 6.18
composn no. d s = 3 d g = 8 103 20 80 104 33 67 105 50 50 106 60 40 107 67 33 108 80 20
dB=8 80 67 50 40 33 20
composn no. d s = 4 d g - 5 109 20 80 67 110 33 50 111 50 112 60 40 33 113 67 20 114 80 composn
-
da 2.78 2.16 1.67 1.47 1.36 1.19
-
composn no. d s = 1 d B 1 6 25 20 80 26 33 67 27 50 50 28 60 40 29 67 33 30 20 80 composn
dS 7.50 7.21 6.86 6.67 6.54 6.32
3.00 2.26 1.71 1.50 1.38 1.20
-
no. d s = 2 dB= 5 55 20 80 56 33 67 57 50 50 58 60 40 59 67 43 60 80 20
da 3.85 3.34 2.86 2.63 2.49 2.27
3.75 3.60 3.43 3.33 3.27 3.16
85 86 87 88 89 90
4.41 4.10 3.75 3.57 3.46 2.34
~~
-
ds 4.76 4.62 4.44 4.35 4.28 4.17
20 33 50 60 67
80
80 67 50 40 33 20
~~~
composn no. d S = 4 d g = 6 115 20 80 116 33 67 117 50 50 118 60 40 119 67 33 120 80 20
ds
5.46 5.15 4.80 4.62 4.49 4.29
composn
-
composn no. 163 164 165 166 167 168
da
da 3.33 3.00 2.67 2.50 2.40 2.22
no. d s = 5 dB=7 ds no. d s = 5 d g = 8 139 20 80 6.48 145 20 80 67 6.18 146 33 67 140 33 141 50 50 5.83 147 50 50 142 60 40 5.65 148 60 40 33 5.22 149 67 33 143 67 20 5.31 150 80 20 144 80
-
-
dS = 7 20 33 50 60 67 80
dB = 8 80 67 50 40 33 20
d, 7.14 6.68 6.15 5.88 5.71 5.41
ds 7.78 7.64 7.47 7.37 7.30 7.18
Units: composition, wt % ; ds, dg, &, mm.
belong to group D of the Geldart classification(1973,1986). In Table I, the composition of the 168 binary mixtures used have been defined and each mixture has been identified with a number. In order to quantify the segregation, by means of the mixing index (Rowe et al., 1972), the solid sampling has been carried out by means of a probe connected to a suction pump. The probe is a vertical tube of 14-mm-i.d., which is displaced to any desired position in the contactor by a computer-controlled device (Olazar et al., 1993a). The air flow rate used has been 3% in excess of that corresponding to minimum spouting, with the aim of ensuring that the fountain does not disappear, due to the presence of the probe in any operating condition.
The optimum sampling duration was estimated between 3 and 5 s, as shorter times give way to errors inherent in withdrawal of small amounts of sample. Longer times, corresponding to considerable quantities of sample with respect to the inventory, alter the bed composition. Each sampling is repeated three times at each position in the bed, and the solids are returned to the contactor after each sampling. The differences in weight fractions of each particle size obtained from the three measurements have, in all cases, been lower than 4% of the average value, which has been taken as the representative one. Other sampling techniques have also been used: (a) sampling of layers of static bed; (b) solid trapping with a
2828 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table 11. Identification Numbers of Stable Mixtures for Different Contactor Anglee and Different Inlet Diameters mixture numbre DO,m 28' 33' 36' 39' 45' 0.03 without segregation 7-18; 49-168 7-18; 49-168 1-18;43-168 1-18; 43-168 1-18; 43-168 with segregation 19-42 19-42 1-2 19-42 19-42 0.04 without segregation 7-18;49-168 7-18; 49-168 1-18 43-168 1-18 43-168 1-18 43-168 with senegation 19-42 19-42 1-2 19-42 19-42 7-12; 15;63 7-18; 43-108; 115-168 1-18; 43-168 0.05 withouisble bed height for different mixtures. y = 36O; DO= 0.04m; X, = X, = 0.50.
the maximum stagnant spoutable bed height vs the dimensionlessvelocity parameter, u/u,, has been plotted for the the contactor angle of 36O and for the inlet diameter of 0.03 m. Each curve corresponds to one 5050 mixture, and for their representation the relationship of u, with Ho has been taken into account. In all the cases studied, it is observed that (Ho)Mdecreases with air velocity, in a more pronounced way as d R is greater. In Figure 5,the minimum stagnant spoutable bed height has been plotted vs the velocity parameter, uIum, also for the contactor angle of 36O and for DO=0.04 m. Each curve corresponds to one 5050 mixture, and for their representation the relationship of u, with HOhas been taken into account. It is observed that the minimum height increases with velocity. In Figures 4 and 5, the values of um used in the plotting are those corresponding to Sauter mean diameter of each mixture, d, defined as
-
1
ds=-
-+-
-
xS
xB
dS
dB
In order to carry out the hydrodynamic study, segregation of all the mixtures has been studied, with the aim of delimiting those mixtures that do not have any noticeable segregation, as these latter ones will be those that will subsequently be studied. In the literature, segregation studies in spouted beds have been carried out for cylindrical contactors with the aim of either determining cycle times and trajectories of the particles (Cook and Bridgwater, 1978;Robinson and Waldie, 1978; Piccinini et al., 1977;Uemaki et al., 1983;Kutluoglu et al., 1983,Ishikura et al., 1983;Cook and Bridgwater, 19851, or obtaining information for designing the inlet and the
(x)"
-
n
(3) vi2 where is the bed level from which the upper volume is equal to the the lower one, Figure 1. Equation 3 has been applied using different numbers of samples, depending on the height of the stagnant bed, but a distance of 25 mm has been established between sampling points in all the cases. In Table 11, the mixtures with which stable operation is possible are identified and, among these, those that are operated without noticeable segregation or with segregation have been distinguished. Mixtures without segregation have been considered those whose mixing indices, eq 2,are between 0.95 and 1.05. The remaining mixtures are assumed to operate with segregation and they have not been used for the hydrodynamic study that is subsequently presented. Due to its complexity, a more detailed study of segregation is beyond the scope of this paper and will be dealt with in later papers. (xB)u
=
4. Hydrodynamics 4.1. Pressure Drop Evolution with Air Velocity.
The evolution of pressure drop with air velocity of the beds composed of the different binary mixtures, once the bed has been loosened, is similar to that observed for beds of uniform particle diameter (Olazar et al., 1992). For example, the evolution of pressure drop with air velocity for the contactor of 36O,with an inlet diameter of 0.03 m and for a stagnant bed height of 0.10 m, has been plotted in Figure 6. The experimental results correspond to
2830
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
Table 111. Correlations Used in the Literature To Calculate the Minimum Spouting Velocity of Mixtures contactor geometry equation author (4) conical-cylindrical Mathur and Gishler (1955) u, = (d$Dc)(DdDc)’/3[2gHo(p. - P)/PI‘/~ U, = 7.63(tan fi)0.72(d~Dc)0.155 tan 8(H0u,&1/3 (5) conical-cylindrical Manurung (1964) conical-cylindrical Smith and Reddy (1964) = d&(p, - p)/pDcl”210.64 - 26.8(Di/Dc)21(Ho/D,)0~”’~7BD~~D~ (6) Wan-Ryong et al. (1969) (Reo), = 1.23Re)t ( H o / D o )[tan(y/2) ~ . ~ ~ 10.S2 (7) conical U, = 0.0143d~741H~582[2g(pl - P)/PI~.~ (8) conical-cylindrical Brunello et al. (1974) Uemaki et al. (1983) U, = 0.977(&/Dc)o~616(DdDc)o~z74[2gHo(p, - p)p]o.3ur (9) conical-cylindrical
- 10 : t
I
I
c d
0
4
8
12
16
u (mls)
Figure 7. Comparison of evolution of pressure drop withair velocity, of uniform particle beds of d, = 1 mm (stable) and d, = 4 mm (unstable) with evolution of pressure drop of a bed composed of 50 w t % mixture of both (mixture 15), which is stable. y = 36O;DO= 0.04 m; HO= 0.25 m.
uniform particles of d,= 1 and 4 mm and to a 50 w t % mixture of both particles (mixture 15). As can be observed in Figure 6,and in general for all the other mixtures studied, the shape of the APvs u curve for the mixture near the maximum pressure drop is intermediate between the shapes corresponding to the individual particles (a shape with a sharp profile for d,= 1 mm and a wider profile for d,= 4 mm). This fact seems to show that both particle sizes contribute to the formation of the maximum. This contribution is noticeable in the fact that the fo7mation of an incipient jet at the contactor base, with a cyclic movement of the particles, occurs for the mixture a t approximately the same velocity as for the smaller particles. The spout formation continues evolving until the bed surface is reached. On the other hand, it is observed in Figure 6that when the air velocity is decreased, the pressure drop has no maximum. This situation, with a high hysteresis in the AP vs u curve, is more pronounced for mixtures for which XBis approximately equal to 0.5. This result is different from what was previously observed for solids of uniform size (Olazar et al., 1992)where the hysteresis in the AP vs u curve was smaller. It is noteworthy that mixing different sizes favors bed stability, so that beds formed by mixtures of particles, which are unstable when they are forming beds of uniform diameter, are stable. In Figure 7,the evolution of pressure drop with air velocity has been plotted for the contactor angle of y = 36O,DO= 0.04m, and& = 0.25 m. The curves correspond to uniform particles of d, = 1 and 4 mm and to the 50 wt% mixture of both sizes (mixture 15). While the bed formed by mixture I5 is stable under the conditions studied, the beds formed by the individual particles have a very different and opposed behavior: the bed exclusively constituted by particles of d, = 1 rnm is stable, while the bed formed by particles of d,= 4 mm is unstable for air velocities above 7.5 mls, in the stretch a-b. In this bed, B proper spouting regime is not attained. It is visually observed that instead of forming the spout, the whole bed is lifted from the contactor base and there is no solids
circulation, which provokes the maximum to be unusually high in the evolution of pressure drop, as is shown in Figure 7. 4.2. Minimum Spouting Velocity. Although different correlations have been proposed for calculation of the minimum spouting velocity in conical contadors (Nikolaev and Golubev, 1964; Tsvik et al., 1967;Goltsiker, 1967; Gorshtein and Mukhlenov, 1964;Wan-Fyong et al., 1969; Kmiec, 1983;Markowski and Kaminski, 1983;Olazar et al., 19921,only Wan-Fyong et al. (1969)used mixtures of different particle sizes in the derivation of eq 7 (Table 111). The minimum spouting velocity for beds with particle size distribution, in either cylindrical or cylindrical with conical base contactors, has received more attention in the literature. In Table 111, the different equations proposed are set out. Althougheq 4 of Mathur and Gishler (1955)was developed for beds of uniform diameter or of a narrow particle diameter range, it is one of the more widely used, even for mixtures. It must be pointed out that different definitions of the mean particle size that characterize the mixture are used in the equations of Table 111. In this way, in eq 4of Mathur and Gishler (1955)the reciprocal or Sauter mean diameter is used, as recommended by Mathur and Epstein (1974) and was subsequently proven by Ishikura et al. (1982). The reciprocal mean diameter is also used in eq 5 of Manurung (1964)and in eq 9 of Uemaki et al. (1983), which was subsequently used by Synn (1986).The length surface mean diameter was used in eq 6 of Smith and Reddy (1964)and in eq 8 of Brunello et al. (1974). The values of minimum spouting velocity of mixtures that are stable and that do not have segregation of Table 11, which have been obtained starting at the condition of stable spouting and reducing the air velocity, have been fitted to the equations proposed in Table 111, using a Complex method of nonlinear regression. The fitting to eqs 5-8 is inadequate, the regression coefficients,P, being lower than 0.50. Even though eq 9 (Uemaki et al., 1983) and eq 4 (Mathur and Gishler, 1955)do not include the contactor angle, they give acceptable values (although lower than the experimental ones) for the present measurements only for the contactor angle of 45’. On the other hand, the variation of urnswith contactor inlet diameter that these equations predict is opposed to what is experimentally observed for conical beds. The best fitting corresponds to the equation of Mathur and Gishler (1955),with a regression coefficient of r2 = 0.70 and a standard error of 10% . The experimental data have also been fitted to the different equations proposed for beds of only one particle size in conical contactors, which have been gathered in previous revisions (Mathur and Epstein, 1974;Olazar et al., 1992), but in no case has the fitting been acceptable (r2 C 0.50). The experimental valueshave been fitted to the equation proposed in a previous paper for conical contactors with
Ind. Eng. Chem. Res., Vol. 32,No. 11, 1993 2831
. E
-E
14 12
-; 1 0 -8 8 3
S 6 4 2
0
0
2
6
4
8
1 0 1 2 1 4
0
urnsexperimental (m/s)
Figure 8. Comparison of the experimental values of minimum spouting velocity with values calculated using eq 10. y = 36O; (0)DO = 0.05 m; (A) DO= 0.04 m; ( 0 )DO= 0.03 m.
2
4
6 8 10 A P, experimental (kPa)
Figure 10. Comparisonof experimentalvalueaof maximum p r a m drop with values calculated wing eq 11. y = 36O; ( 0 )DO= 0.05 m; (A) DO= 0.04 m; ( 0 )DO= 0.03 m.
- , 8.5
L
E v
5
I l6
L= 8.0 Q
12
7.5
8 7.0
0
1 0
,
I
0.2
.
I
0.4
.
I
0.6
.
I
0.8
I
.
6.5 0
-1
(Re,), = 0.126Aro~SO(D~Do)1~68[tan(y/2)l-0~57 (10)
d,;
d,;
0.6
0.8
-
1
to the equation proposed for conical contactors with uniform particles in a previous paper (Olazar et al., 1993a):
uniform-size particles (Olazar et al., 1992):
a,
0.4
Figure 11. Effect of mixture composition on maximum pressure drop. y = 36O; HO= 0.25 m; DO= 0.03 m; dB = 4 mm.
Figure 9. Effect of mixture composition on minimum spouting velocity. y = 36O; HO= 0.25 m; DO= 0.03 m; d~ = 4 mm.
In the fitting of eq 10,different expressions for the characteristic diameter of the mixture have been tried: number length mean diameter, length surface mean number surface mean diameter, length diameter, volume (or mass) mean diameter or reciprocal diameter or Sauter diameter, number volume (or mass) mean diameter, d,;surface volume (or mass) mean diameter, daV. The best fitting of the experimental results corresponding to all the systems to eq 10 is obtained when the Sauter mean diameter, eq 1,is used. The values of d, for all the mixtures studied are set out in Table I. The regression coefficient of the experimental data fitting to eq 10 is r2= 0.87 and the standard error is 6%. In Figure 8 the adequacy of the fitting of the experimental data for y = 36O to eq 10 can be seen. In Figure 9, where the points are the experimentalresults and the curves have been calculated using eq 10,the effect of the mixture composition on the minimum spouting velocity is shown. The data that have been plotted as examples correspond to particular conditions: y = 36O, H,= 0.26m, DO= 0.03m, dB = 4 mm. Each curve of Figure 9 corresponds to one value of dR, that is, to dg = 411,412, and 413. The points at the extremes of the curves are the experimentalresults correspondingto the monosizespecies of each mixture. It is observed that the minimum spouting velocity increases more than proportionally with weight fraction of the larger particle size, XB.This effect is more pronounced as d~ is increased. 4.3. Maximum Pressure Drop. The values of maximum pressure drop corresponding to mixtures that are stable and without segregation (Table 11)have been fitted
0.2
XB
XLI
-A P M - 1 + 0.116(HdD0)0*60(tan( ~/2))4'80A~o.o'26 (11) U ! 3
In the fitting, using a Complex method for nonlinear regression, different expressions for the characteristic mean diameter of the mixture have been tried. The best fitting is obtained when the Sauter diameter, d,, is used. The regression coefficient is r2= 0.84,with a standard error of 8 % The good fitting between the values of maximum pressure drop calculated with eq 12 and the experimental values, for allthe inlet diameters tried and for the contactor angle of 36O,can be seen in Figure 10. In Figure 11 the evolution of the maximum pressure drop with the composition of the mixtures is shown, in a plot of APM vs The points are the experimental results, and the curves have been calculated using eq 11. The data correspond to particular conditions: y = 36O, Ho=0.25 m, DO= 0.03 m, and dg = 4 mm. Each curve of Figure 11 corresponds to a value of d R = 411,412,and 413. The points at the extremes of the curves are the experimental results corresponding to the monosize species of each mixture. It is observed that the maximum pressure drop decreases as the weight fraction of the greater particle increase. This effect is more pronounced as d~ increases. 4.4. Pressure Drop in Stable SpoutingRegime. The results of pressure drop in stable operation regime, corresponding to the mixtures without appreciable segregation, have been fitted to the equation proposed in a previous paper (Olazaret al., 1993a)for uniform particles:
.
G.
This correlation is fulfilled with a regression coefficient of r2 = 0.90 and a standard error of 8 % ,when the Sauter
2832 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 I
0.50 r
I
0.46 0.44
1 0 . 4 20
0 0
1
2
Figure 12. Comparison of experimental values of stable pressure DO= 0.05 m; drop with values calculated using eq 12. y = 36O; (0) (A)DO= 0.04 m; (0) DO= 0.03 m.
-
a .y
4.4 I
I
I 0
3 4 5 6 A Ps experimental (kPa)
0.2
0.4
0.6
0.8
- 1
xB Figure 14. Effect of mixture compositionon bed voidageof minimum spouting. y = 36'; HO= 0.25 m; DO= 0.03 m; dg = 4 mm. Points, experimental, lines, calculated by eqs 13 and 14. 0.55,
4.1
ad
4.0 3.8 3.6 3.4
3.2
1 0
0.2
0.4
0.6
0.8
-I X B
Figure 13. Effect of mixture compositionon stable pressure drop. y = 36O; HO= 0.25 m; DO= 0.03 m; d g = 4 mm.
mean diameter is taken as characteristic diameter of the mixtures. The adequacy of the fitting of the experimental results to the calculated ones is shown in Figure 12 for the contactor angle of 36'. In Figure 13, the evolution of stable pressure drop with the composition of the mixture for particular operating conditions is shown. When the weight fraction of the larger particles is increased, the bed pressure drop decreases, in a way similar to that previously observed for the maximum pressure drop. This effect is again more pronounced as d R increases. 4.5. Minimum Bed Voidage. The data of global bed voidage corresponding to the minimum spouting velocity have been fitted to the equation proposed in a previous paper for particles of uniform size (San Jose et al., 1993):
The fitting is not satisfactory with any of the possible expressions of mean diameter of the mixtures. The reason for this deviation lies in the fact that bed voidage of a mixture of particles of different size is not the one corresponding to the bed made up of particles whose uniform diameter is the characteristic mean diameter of the mixture. The experimental bed voidage of minimum spouting is lower than that corresponding to this mean diameter, due to the fact that small particles occupy part of the empty space left by big ones, an aspect that has been studied in fluidized and tapered beds (Suzuki et al., 1986; Toyohara and Kawamura, 1992). In Figure 14, the evolution of the minimum spouting bed voidage with the mixture composition has been shown for particular operating conditions as an example of the experimental results. In Figure 14, the bed voidage has experimentally a minimum value for the mixtures at a composition close to
0.35 10'
2 10.8
4 10'
107 FD'F,
Figure 15. Effect of FDIFGon em. Curve, calculated using eq 13; points, experimental values. y = 36O; (0) DO= 0.05 m; (A)DO= 0.04 DO= 0.03 m. m; (0)
XB =0.4, and eq 13 does not predict the existence of a minimum value with any of the possible definitions of mean diameter. In order to correct eq 13, by taking into account the phenomenon of different size particle packing, the ratio between the drag and the gravitational forces for the mixture, FD/FG,was defined as the contribution of the values of FDIFGcorresponding to individual values:
It is noteworthy in eq 14, that when the composition of the particles in the mixture, XI and x2, changes, the values ) ~ (FD/FG)P also change, as the minimum of ( F D / F G and spouting velocity of the mixture changes. The best fitting of the experimental results of bed voidage to eq 13, using eq 14, is obtained when the contribution of each one of the fractions for calculation of FD/FGin eq 14 is linear, that is, f ( x 1 ) = x1 and f ( 2 2 ) = x2. The regression coefficientis r2 = 0.98 and the average standard error is 5 % . It is noteworthy that when the weighted calculation Of FDIFGratio is carried out by eq 14, the existence of a minimum in the bed voidage of minimum spouting is taken into account, as is proven in Figure 14, in which the curves calculated fit the experimental points corresponding to a particular case. The adequacy of the fitting of the experimental results to those calculated using eq 13 can be observed in Figure 15 for the contactor angle of 36O, in a representation of ems vs FD/FG. The fact that the FD/FGratio is present in eq 13 shows the usefulness of this ratio to quantify the expansion of conical spouted beds when binary mixtures are used, a usefulness that has also been proven for fluidized beds and conical-cylindrical spouted beds (Kmiec,1977; 1982).
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2833
5. Conclusions The spouted bed in exclusivelyconical contactors allows for operating with binary mixtures of solids of the same density, in stable regime and without significant segregation, so this contact regime has good prospects for ita use in operations and processes that require handling of particles of different size. The limitations for stable operation with binary mixtures are not wider than those for operation with individual particles, and as happens with the operation of the latter, the limitations due to instability created are also related to different design factors, that is, to D d d , ratio, to DolDi ratio, and to contactor angle, as well as to gas velocity. Under certain operating conditions, the mixture gives way to stable spouting, even while the bed composed of individual particles is unstable. Although the mixtureswith appreciable segregationhave not been used in the hydrodynamic study, it has been proven that a great number of these mixtures can be handled under stable operation conditions, which increases the potential applicability of the contact regime studied. For the mixtures studied in this paper, a contactor of angle 45O and inlet diameter of 0.03 m is the most versatile one as it allows for working with greater bed height and with greater number of mixtures among those tried in stable regime. Once the minimum spouting velocity is exceeded, the maximum spoutable bed height decreases with increasing gas velocity. It is noteworthy that when d R < 4, binary mixtures of any composition can be treated without appreciable segregation. It has been proven that the correlations proposed in the literature for calculation of the hydrodynamics of spouted beds of cylindrical geometry are not suitable for evaluating the hydrodynamics of the operation with mixtures in conical contactors. For calculation of the minimum spouting velocity, the maximum pressure drop, and the stable operation pressure drop, the equations proposed for uniform size particles in previous papers, eqs 10, 11, and 12, respectively, are valid (Olazar et al., 1992,1993a1, when the particle size of the mixture is characterized by Sauter mean diameter. Equation 13, which has been previously proposed for uniform-size particles (San Jose et al., 1993), is valid for calculation of the minimum spouting voidage, when the FD/FGratio is calculated as the weighted average of the values of FD/FGratio for each individual particle size.
Nomenclature Ar = Archimedes number, gdP3p(p, - p)/r2 CD = drag coefficient, (24/Re)(l + 0.15Re0.687) Db, D,, Di, DO= top diameter of the stagnant bed, of the column (or upper diameter needed for the cone),of the bed bottom, and of the bed inlet, respectively, m dg, ds = particle diameter of the greater and of the smaller sphere, m d , = particle diameter, m d R = particle diameter ratio of the mixture, dg/ds d,, = number length mean diameter, C(xi/dpi2)/C(zi/dpi3), m dLs= length surface mean diameter, C(xi/dpi)/C(xi/dpi2),m d,, = number surface mean diameter, [C(zi/dpi)/C(xi/ -dPI.3)11/2, m d,, = number volume (or mass) mean diameter, [l/C(xi/ dPI.3)11/3,m
d,, = surface volume (or mass) mean diameter, &idpi), m -
ds = length volume (or mass) mean diameter or reciprocal diameter or Sauter diameter, l/C(xi/d,i), m
FD/FG = ratio between drag and gravitational forces, (3/4)Cde2/Ar H = bed height, m He,HO= height of the conical section and of the stagnant bed, m (Ho)M, (Ho), = maximum and minimum spoutablebed height, m = bed level from which the upper volume is equal to the lower one, m h, r, 0 = longitudinal, radial, and angular coordinates M = mixing index defined by eq 2 AP = bed pressure drop, Pa APM, AP, = maximum pressure drop and pressure drop of stable operation regime, Pa Re = particle Reynolds number referred to Db (Re)t, (Re,), = terminal Reynolds number and Reynolds number of minimum spouting referred to DO u = air velocity referred to Di, m s-1 urn= minimum spouting velocity at the maximum spoutable bed height, m s-l u, = minimum spouting velocity referred to Di, m s-l ( ~ 0 = ) minimum ~ spouting velocity referred to DO,m s-l V = bed volume, m3 XB = weight fraction of the particles of greater diameter at -any -point in the bed X,, X , = weight fraction of the particles of greater and smaller diameter in the bed (XB)"= weight average fraction of the particles of greater diameter in the upper volume half of the bed Greek Letters j3 = friction angle, rad eo, e
= voidage of stagnant bed and of bed
y = cone angle, rad c~
= viscosity, kg m-1 s-1
= density of the gas, density of the particle, and bulk density, respectively, kg m-3
p, p,, Pb
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Received for review February 25, 1993 Revised manuscript received June 15, 1993 Accepted June 29, 1993. e Abstract
1, 1993.
published in Advance ACS Abstracts, September
