Ind. Eng. Chem. Res. 1990,29, 1785-1792
1785
Ph.D. Dissertation, University of Amsterdam, The Netherlands, 1982. Wigmans, T.; Goebel, J. C.; Moulijn, J. A. The Influence of Pretreatment conditions on the Activity and Stability of Sodium and Potassium Catalysts in Carbon-steam Reactions. Carbon 1983, 21 (3), 295-301. Wood, B. J.; Sancier, K. M. The Mechanism of the Catalytic Gasification of Coal Char, A Critical Review. Final Report, SRI International, DOE Contract DE-AC21-80MC14953, 1984. Yuh, S. L.; Wolf, E. E. Kinetics and FTIR Studies of the Sodium Catalyzed Steam Gasification. Fuel 1984, 63, 1604.
Shadman, F.; Sams, D. A.; Punjak, W. A. Significance of the Reduction of Alkali Carbonate in Catalytic Carbon Gasification. Fuel 1987,66 (12), 1658-1663. Spiro, C. L.; McKee, D. W.; Kosky, P. G.; Lamby, E. J.; Maylotte, D. H. Significant Parameters in the Catalyzed C 0 2 Gasification of Coal Chars. Fuel 1983,62 (3), 323-330. Van Heiningen, A. R. P.; Li, J.; Fallafollita, J. Canadian Patent Applicaton 583,409, Nov 17, 1988. Walker, P. L., Jr.; Rusinko, F., Jr.; Austin, L. G. Gas Reactions of Carbon. Advances in Catalysis; Academic: New York, 1959; Vol. 11, pp 133-221. Wen, W.-Y. Mechanisms of Alkali Metal Catalysis in the Gasification of Coal, Char, or Graphite. Catal. Rev.-Sci. Eng. 1980,22 (l), 1-30. Wigmans, T. Catalytic Gasification of Carbon; A Mechanistic Study.
Received for review December 12, 1989 Revised manuscript received April 18, 1990 Accepted May 5, 1990
Hydrodynamics and Mixing of Solids in a Recirculating Fluidized Bed D. Corleen Chesonis and George E. Klinzing Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Yatish T. Shah* and Carlos G. Dassori College of Engineering and Applied Sciences, The University of Tulsa, Tulsa, Oklahoma 74104
Voidage and mixing of solids were measured in a 10-cm-diameter, 6.2-m-tall recirculating fluidized bed column. T h e solids were alumina with a n average particle size of 120 pm, a wide particle size distribution, and a density of 3460 kg/m3. For mixing of solids, CaC12 impregnated on alumina as a tracer and the carbon-alumina system were examined. T h e experimental measurements were carried out in the ranges of gas velocities from 3.5 to 4.5 m/s, solid recycle rates from 7 to 11kg/(m2.s), column inventories from 19 to 24 kg, and average riser voidages from 0.879 to 0.938. The experimental data for the solid fraction were correlated well (mean deviation 26.9%) with a n expression similar t o Kwauk e t a1.k model. Mixing of solids in the riser was well correlated assuming a dilute core region, a wall region with a high concentration of solids, and interchange of solids between these two regions. The mixing model contained two parameters; the mass-exchange coefficient It, between the core and wall regions and the effective average residence time for the solids in the return leg, tPp T h e experimental data obtained in this study were well correlated by the mass-exchange coefficient, It,, whose value varied between 0.02 and 0.04 s-l. In general, It, decreases with the average residence time of solids in the riser and t increases with the solid recirculation rate. In the range of experimental measurements examinei in this study, a high degree of backmixing of solids was observed.
Introduction In recent years, a recirculating fluidized bed in which gas circulates an appropriate amount of solid particles at a velocity much higher than their natural settling velocity has found an increasing number of practical applications. This type of fluidized bed is quite different from the conventional bubbling fluidized bed because of the absence of bubbles in the gas phase. The first detailed experimental work on this subject was published by Lewis et al. (1949). More recently, various attempts have been made to correlate the average voidage as a function of gas and solid flow rates (Yerushalmi et al., 1978; Li et al., 1982; Avidan and Yerushalmi, 1982; Malladi et al., 1982). This voidage is averaged over the entire volume of the bed. However, over the last few years, several investigators (Kwauk et al., 1986; Yang, 1988; Schnitzlein and Weinskin, 1988; Yoshida and Mineo, 1989) have shown that existence of a voidage distribution along the bed axis. In general, the recirculating fluidized bed can be divided into two main regions, a dense region a t the bottom and a dilute region at the top, with a transition region in between. Yang (1988) also considers an acceleration region
* Author t o whom correspondence should be addressed. 0888-5885/90/2629-1785~02.50/0
at the entrance to the bed. Fluidization properties of the two main regions are functions of gas velocity, solid rate, solid inventory, bed diameter, and properties of the solid and the gas. The dense phase shows a large degree of backmixing in the solid phase (Yang, 1988; Schnitzlein and Weinstein, 1988). The dilute phase, leaner in content of solids, approaches plug flow in the solid phase. The objective of the present work is to investigate the hydrodynamics and mixing of solids in a recirculating fluidized bed. Experimental data are obtained for the solid content along th8 bed axis as functions of gas and solid flow rates and particle size. The degree of mixing of solids in a recirculating fluidized bed is evaluated by using the transient response analysis. The transient response data are correlated with a model for the mixing of solids for the recirculating fluidized bed. Experimental Apparatus and Procedure Voidage measurements and circulation tests of solids were conducted in a 10-cm-diameter and 6.2-m-tall recirculating fluidized bed. Figure 1 shows a sketch of the system. The column was made of Plexiglas and had eight ports, 19 mm in diameter, at intervals of about 0.8 m. Five of these ports could be used for sampling, while the other three and any of the sample ports that were not used in 0 1990 American Chemical Society
1786 Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990
f
II
k l Z n - - - - c f
8-1
Exhaust _t
t -’
-p
1
6
”
~ 5” - -&-
#
€”+ I
245”
-
.
I
18”
4”
I ;
f 7”
CY CLONE
236’
TPACSR IXJECTOR
-L r
-
220.
-
189‘
-
158.
60” S e c t i o n a: ( I n t o Paper)
- 127” -
458
96”
- 65”
from Humidifier
Air
4 5O
3 1 4 - d1.wt.r suaplinp porrr and pressure u p r
IY I
Figure 1. Schematic diagram of the experimental setup.
a particular test were fitted with purged pressure taps. The column was fluidized with air, which entered through a Plexiglas plate, 5 mm thick, with 1.6-mm diameter holes drilled a t 6-mm intervals. Fluidized air was supplied by a compressor through a regulator and a 2.5-cm-diameter line. Rotameters measured and controlled the air flow, which was pretreated to maintain the relative humidity at 60%, limiting electrostatic charging. Entrained solids were captured and returned by a cyclone and baghouse. Solids from the baghouse were fed into the leg leaving the
cyclone, where a series of valves measured and controlled the circulation rate of the solids. The return lines of the solids were 5 cm in diameter and entered the bed 5 cm above the grid. The bed material was alumina with an average particle size of 120 pm, and the particle size distribution is shown in Figure 2. The tracer was alumina impregnated with CaCl, through the incipient wetness technique (Connell and Dumesic, 1986). A solution of approximately 30% CaCl, in water was added to alumina in a ratio of about
Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990 1787 10
I
0.2
z
0
100
200
300
Dp (microns)
Figure 2. Alumina particle size distribution.
[LVE v ROTAMETER
y=; SAMPLE JAR
Figure 3. Schematic diagram of the sampling probe.
0.6 mL of solution/g of solid. The slurry was mixed and allowed to sit overnight. It was then dried under vacuum a t about 130 "C and screened to -50 mesh to remove agglomerates. As shown in Figure 2, the tracer retained a particle size distribution quite close to that of the bed material; its average particle size was 127 pm. Calcium concentrations in the bed sample were determined by atomic absorption with an accuracy of f0.02 wt % Ca. The tracer contained 4-7'37 calcium, so an amount of tracer equal to about 2% of the bed inventory gave sufficient accuracy in the analysis. The accuracy in the overall tracer concentration measurement was f 5 % . The particle size was measured by Microtrac and the particle density by a helium-air pycnometer. Tracer solids were injected from a pressurized feed chamber into the bottom of the column, 23 cm above the grid. After the tracer was injected, bed samples were taken versus time to develop a residence time distribution. The probe was inserted into different lengths to obtain radial profiles, and samples were taken a t five different heights above the grid. The sampler, similar to the one described by van Breugel et al. (1969), is shown in Figure 3. The probe was 13-mm diameter and consisted of two concentric tubes that could be purged with air, which was controlled by valves and rotameters. The tip of the probe was bent to provide directionality to the sampling and the outer tube was purged to prevent accumulation of solids a t the entrance. The sample entered the inner 6-mm-diameter tube and then passed through a small cyclone to capture the solids. The procedures for each run was to start purge air to the pressure taps and sampling probe, adjust the fluidi-
zation air to run conditions, and then fill the column with solids. The bed was fluidized at run conditions for at least an hour before measurements were begun to allow the particle size distribution to reach an equilibrium as fines in the feed material left the system. After the sampling probe was set to the desired radial position and orientation, tracer solids were charged to the feed chamber, which was then pressurized with air to a pressure greater than that of the bed. The feed valve was opened and closed to inject the tracer, requiring 10-15 s to complete the injection. The purge to the inner sample tube was shut off, and the sampling valve was opened. After the desired time, the sampling valve was closed and the purge restored. The sample was weighed and analyzed for particle size and tracer concentration. The probe was then moved to another radial position or orientation. To move the probe to another sampling port, the fluidization air was shut off and the bed was allowed to slump. A t least 15 min was allowed between the restart and the next test to be certain that the system had reached steady state. Subsequent tracer injections were made to the existing bed rather than recharging with fresh alumina. This process continued until the calcium content of the bed became too high to distinguish the increase from further tracer injections. Although the column inventory should have increased with the injections, there was sufficient loss of fines during the experiments that the final inventories were nearly the same as the initial inventories. The calculated tracer concentrations corresponded well to sampling results, implying that the fines that left the column had the same composition as the bed. In some tests, die was added to the tracer material to all visual observation of the mixing process. Injected solids mixed quickly in the bottom portion of the column, confirming the high degree of backmixing associated with the dense region of the recirculating fluidized bed. Most of the tracer appeared to be held in the dense region for perhaps a minute as it mixed into the bed material there and was diluted by fresh material entering from the return leg. The tracer gradually escaped into the dilute zone in the top of the column, but most of the tracer reaching this region seemed to have been considerably diluted. Some runs were done by injecting coke (carbon) particles into the alumina bed. As shown later, this system also gave a similar mixing pattern. The experimental program included measurements of pressure drop and residence time distribution versus gas velocity and solid recycle rate. The fluidization characteristics of the alumina were evaluated prior to the tracer tests by varying the gas velocity and solid recycle rate while monitoring the bed pressure drop. The recirculating bed regime was mapped out, and appropriate operating conditions were chosen. These conditions were gas velocity in the range 3.5-4.5 m/s and 66-100% solid return valve opening. The transition from bubbling or turbulent fluidization to recirculating fluidization was not as clear with this material as is often reported in the literature (Avidan and Yerushalmi, 1982). This is a consequence of the wide particle size distribution, since some particles can be transported out of the column even at low gas velocities. As the gas velocity increases, the amount of entrained material slowly increases as larger and larger particles can be transported. The grid, designed for high gas velocity, would not allow operation at velocities below about 2.0 m/s. At gas velocities between 2.0 and 2.5 m/s, the column was characterized as a slugging fluidized bed with large gas slugs rising through the solids, which had a well-defined
1788 Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990
82 experimental points 0 0 0 0
17 16 1s 14
m
'
0
0.02
004
,,'- I I
,4
9""
m
m6.
0.06
0.08
01
0.12
0.14
0.16
0.18
0.2
Solid Fraction(measured)
Superficial Gas Velccity (misec)
Figure 4. Alumina transport velocity
Figure 5. Solid fraction correlation.
bed height. Little entrainment of the solids occurred. A t gas velocities above about 2.5 m/s, entrainment increased, but the backmixing of solids in the lower part of the column became so intense that it was difficult to be certain when the gas velocity was high enough to transport all of the material. This backmixing was characterized by solids flowing downward at the wall and a gas/solid suspension moving upward in the center of the column. This pattern would be interrupted by the appearance of voids, pockets of gas which spanned the column. In contrast to the slugging bed regime, where the gas slugs retained their integrity as they moved up the column, these voids would appear and disintegrate rapidly and randomly. As the gas velocity increased further, the voids became smaller, less common, and less well defined. An effective transport velocity was determined by measuring the time required to empty the column after closing the return valve of the solids. When these data are plotted as shown in Figure 4 and extrapolated to l/time = 0, a velocity that would empty the column at an infinite time is determined. This velocity was defined as the effective transport velocity and was equal to 2.8 m/s for the alumina used in this study. Alternatively, at a run condition of 3.5 m/s, all of the alumina would be transported out of the column in 8 min.
dilute phases, respectively, zi is the point of inflection of the voidage profile, and zo is a characteristic length. zi can be evaluated from the integrated form of eq 1, once the average voidage (5) is known. This average voidage can be obtained from the relation
Analysis of the Voidage Distribution The solid distribution within the bed showed two main regions: a dense-phase region at the bottom and dilutephase region at the top. This kind of voidage profile is typical of recirculating fluidized beds (Kwauk et al., 1986; Schnitzlein and Weinstein, 1988; Yang, 1988). A theoretical prediction of the solid distribution within the bed presents various problems. However, Kwauk et al. (1986) and Yang (1988) have proposed models that contain various empirical parameters. The complexity of the gas-olid flow makes the development of a predictive model very unlikely. The geometrical configuration of the junction between the return led and the riser, for instance, has a key effect on the solid holdup a t the bottom of the bed (Yang, 1988). The performance of the cyclone and the inventory in the slow bed also play a role in the system. Due to the numerous hydrodynamic parameters and large uncertainty in their predictions, a simple approach was followed. Kwauk et al.'s model is particularly suitable for this purpose. In this model, the experimental data for the solid distribution were correlated by using the expression
where t, and
t*
are asymptotic voidages of the dense and
-
-E -- 6 , t*
- t,
1 + exp(zi/ziJ
- - l n1 [
L/zo
1
+ exp[(zi - L)/z,]
where L is the height of the bed. Kwauk et al. (1986) suggested that t, and t * can be correlated as 1 - t, = a1
[
18Re,, + ~ ~ e , , ' . 6 8 7
where
Ar = d , 3 p d p , - P J / P '
(7)
in meters) can be correlated to c* - ea by using the relation (Kwauk et al., 1986) 20 = 7 1 exp[-ydt* - ea)] (8) As shown in Figure 5, an overall mean relative deviation of *26.9% was obtained when eq 2, along with eqs 3-8, was used to predict solid fraction (1- E) profiles for the present set of data. A summary of the experimental data outlined in this figure is given in Table I. For the values of the parameters cy1 = 0.25 and cy2 = 0.004, PI = -0.38 and p2 = -0.001, and y1 = 500 and y2 = 45, a typical comparison between the predicted and the measured voidage profiles is shown in Figure 6. As shown, the measured and predicted profiles agree well with each other. It must be remarked that the values of the parameters in the Kwauk et al. model are different from the ones obtained in the present study. This may be partly due to the differences in the system configuration and the solid materials used in these two studies.
t o(expressed
Transient Response Analysis for Mixing of Solids In the present analysis, a recirculating fluidized bed loop is represented by a mixing model shown in Figure 7 . In
Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990 1789 059
,
1
//
0%
3
09
0 89 0.88
4
;t;/ ,
0
2
6
4
Axial Position (m) Figure 6. Void fraction profile according to eq 2.
this case, we introduced a solid tracer into the flowing solid, without altering its hydrodynamic pattern. The transient response of this tracer can be modeled as follows: The mass balances for the solid tracer in the core and wall regions can be expressed in dimensionless forms as
and
eC,
aCw k
-
- C,) 72d7-aZ+ -(Cc r
=0
(10)
Two initial conditions for eqs 9 and 10 are C,(Z,O) = C,(Z,O) = 0
(11)
with boundary conditions
C,(~,T)= Cw(1,7)
(12)
Table I. Summary of Experimentally Measured Concentrations of Solids versus Height above Grid 70 solids at z = 1.02 m 6 8 8 14 z = 2.44 m 11 11 10 13 z = 3.23 m 5 6 7 8 z = 4.02 m 2 3 3 4 z = 4.80 m 1 2 2 2 z = 5.59 m 1 1 2 2 gas velocity, m/s 4.6 4.6 4.6 3.7 6 6 6 9 rate of solids, kg/(m2.s) % solids at z = 0.44 m 6 z = 1.85 m 13 z = 3.23 m 6 z = 4.02 m 4 z = 4.80 m 2 z = 5.59 m 2 gas velocity, m/s 4.7 rate of solids, kg/(m2.s) 7 % solids a t z = 0.44 m 0 16 z = 1.46 m 13 15 z = 2.84 m 9 12 z = 4.02 m 5 4 z = 4.80 m 2 2 z = 5.59 m 2 2 gas velocity, m/s 4.7 3.7 8 8 rate of solids, kg/(m2.s) % solids at z = 0.44 m 17 z = 1.46 m 14 z = 2.44 m 13 z = 3.23 m 8 z = 4.02 m 5 z = 5.20 m 2 gas velocity, m/s 3.8 rate of solids, kg/(m2.s) 6 % solids at z = 0.44 m 8 10 17 14 18 z = 1.46 m 13 14 18 14 14 z = 2.44 m 14 16 15 15 12 z = 3.23 m 9 8 8 9 6 z = 4.02 m 6 5 6 4 4 z = 4.80 m 3 2 3 4 2 z = 5.95 m 2 2 1 2 2 gas velocity, m/s 3.7 3.6 3.3 4.2 4.9 rate of solids, kg/(mgs) 6 7 9 9 14
32 13 12 5 3 2 1
5.1 27
G,
Figure 7. Schematic diagram of the mixing model.
In addition, three other relationships are established by mass balances in the riser: Tp
= tp/fr
(22)
C&t) is a factor that accounts for the inlet pulse of the tracer. Co is determined by the condition of complete mixing a t long times:
e, = C, = 1
for 7 (23) (C)is the equilibrium concentration of tracer, and fr is the mean residence time in the loop (tr = Si,/[(aD2/4)G,]), where Si, is the solid inventory (in kilograms). ~1
G, = f,(l- t,)ug, - f,(l - ~,)u,P, fc
+ fw = 1
(1 - cc)fc+ (1 - tw)fw = 1 - z
(24) (25) (26)
where 7 is the average voidage of the riser. From eqs 24-26, one can obtain f,,f,, and t,, provided u,, u,, and c, are known. The solid velocity in the wall region is assumed to be its terminal velocity ut, and it is calculated by using an
1790 Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990 Table 11. Physical and Transport Parameters for the System p = 1.8 X kg/(m.s) d, = 120 pm (alumina) L = 6.2 m p s = 3460 kg/m3 (alumina) d, = 168 pm (carbon) pf = 1.8 kg/m3 ps = 2000 kg/m3 (carbon) D, = 10cm
expression provided by Klinzing (1981). The minimum fluidization voidage can be calculated by using the expression (Wen and Yu, 1966)
Remf= (33.72 + 0.0408Ga)1/2- 33.7
(27)
where
Remf =
P
= ue(1 - 0.68d,0.92p$5pf4.2Dc4'54)
(31)
where all parameters are in SI units, D, is the diameter of the core region, and ug is the linear air velocity. D, is obtained by making a mass balance over the cross-sectional area of the column as (32) Values of the various parameters p,, pf, p, etc., used in the present study are summarized in Table 11. A solution to eqs 9-13 can be obtained by using the Laplace transform as
L(CJ = 4 s ) exp[(w + P)ZI + B(s) exp[(w - p)zI L(C,) = A ( s ) [ 1 + p)z]
l + r
+ w +p)
( T ~ S
l + r
+ ~ ( s ) [1 + +TIS
1
(33)
+ w - p)
where = k/2r(l
+ r)
(35)
E = (1 + 2r)y
0
=
(1-
l + r --(TIS
k
exp(w
l + r
- 71)s
(37)
+y
+ 2[ss + y
(38) (39)
2)1/2
exp(w - p - 7,s) l + r
+ w - p)
+ p - rPs)
(36)
+ 72)
-(TI
(7*
p = (7*'s2
B(s) = co l + r
1 2
=
T*
1
-
l + r
l + r
71s
+w -p
71s
+w +p
1+
l + r
-(TIS
k
-
v,,= Vr(l - E )
+w +p) (40)
(42)
Then, the volume of solids in the return leg is
V ~ =I
S i n / P s - Vsr
(43)
Finally, t , is obtained from (44)
-Ps
4
We are assuming here that the average solid content in the riser can be used to characterize the overall mixing of solids. Any additional improvements of the model should be supported by extensive measurements of particle velocities within the riser, which are presently not available. We define the effective residence time in the return leg as t,, = ft,
exp[(w +
(34) y
- -
Results a n d Discussion The model presented above was used to fit the experimental data obtained in this study. The model contains two parameters; the mass-exchange coefficient, k,, and the average residence time for the solids in the return leg, t,, implying that the tracer profiles in the riser are influenced by the hydrodynamics in the return leg. The parameter t, can be computed from data, by first calculating the volume of solids in the riser, V,,, as
UmfdpPf
-
The solid velocity in the core region can be computed from the modified Hinkle correlation (Klinzing, 1981): U,
Equations 40 and 41 are inverted numerically by using a routine (DINLAP) from the IMSL library. The present model for the riser has different asymptotic behaviors depending on the values of k and r. As k a,the flow pattern approaches that of piston flow, while as k 0 the system behaves as a delayed recycle model. As r a,the flow pattern approaches that of a completely stirred tank, and as r 0, the limiting model is that of piston flow with stagnancy.
f I1
(45)
The factor f takes into account the possible dead volume and channeling in the return leg. These would occur primarily in the cyclone and the horizontal section leading to it and in the section between the return leg and the sample port value. In the present study, for various operating conditions, the return leg concentration varied between 20% and 30% below equilibrium concentration. The experimental data also suggest that this factor increases with the solid circulate rate for a given solid inventory. This implies that when more solid is circulating through the loop, less channeling occurs. In the present study, the parameter f varied between 0.39 and 0.98. Data analysis for the carbon-alumina system was done using average particle diameter and density for the mixture. For the ranges of gas velocity from 3.5 to 4.5 m/s, solid recycle rate from 7 to 11kg/(m2-s),column inventory from 19 to 23 kg, and average riser voidage from 0.879 to 0.938, comparisons between experimental and theoretical residence time distributions in the column for both the calcium tracer and the carbon-alumina system are illustrated in Figures 8-11. The results are described for various axial positions and for the column center and wall region in some cases. As shown, all the results were well correlated for values of the mean exchange parameter k, between 0.02 and 0.04 s-l. This exchange parameter is dependent on the average residence time of solids in the
Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990 1791 ,
13
1
1.4
6
g
w U
-25
0.8
- Model Prediction
-
06
3
Experimental Data
+
-
OJ
-
0.6 0.5
v1
0.4
0.3
-
02 01
'-
0
2
0.2
-
0 , 0
6
4
-
Core Region
F =0.879 &=0.040 sec-'
tr=4.48min tp=l .52min
0.1-
J
I
0
-
% .
E
F=0.902
07
.-0
03
6
1.1
1 0.9 -
v1
.-
1.3-
1.2 -.
1
20
IO
Time(minutes)
30
40
Time(minutes) Figure 10. Carbon-alumina system. z = 0.87 above grid, core region.
16
__ Model Prediction
I4
1.3
Experimental Data
u VI
5
Core Region
9
-
02
z=2.84m %= 1 1kgld sec uK=3.6m/sec h=0.025sec-l
01
f=0.98 . -
08
03
o ! o
2
4
8
6
Time(minutes) Calcium tracer concentration versus time. z = 2.84 m Figure 8. above grid; (a, top) wall region; (b, bottom) core region. 13
U
8y
09
08
I
Wall Region
Experimental Data
01 01
F=0.916
-
0.6
.g
0.5 0.4
-
6
0.3
-
E
0.2
-
E
Core Region F =0.879 Sh=24 kg
Gs=9kg/m2sec
0.1
0 , 0
30
20
10
Time(minutes) Figure 11. Carbon-alumina system. z = 5.20 above grid, core region.
k,, s-l __ Model Prediction
6
g
-
Table 111. Summary of k, and fValues Obtained from Experimental Data (Calcium Tracer)
1
03
O.* 0.7
m
l
-
u2
b-0.020sec
-1
t~2.68min
0.030 0.020 0.025 0.025 0.025 0.020 0.025 0.020
f 0.984 0.66 0.67 0.70 0.98 0.48 0.57 0.39
G,, kg/(m2.s) 11 8 3 10 11 6 9
7
fr, min
t,, min
ui, m/s
Sh, kg
4.4 6.1 5.4 4.9 4.4 7.1 4.7 7.0
1.32 1.81 1.61 1.38 1.28 2.90 1.78 2.68
3.6 3.7 3.6 3.6 3.6 4.5 4.5 4.5
23 23 23 23 23 20 20 23
0 0
2
4
Time(minutes) Figure 9. Calcium tracer concentration versus time. z = 5.2 m above grid, wall region.
riser. For a given solid inventory, the larger the residence time, the small the value of k,; i.e., lowering solid spacial velocity reduces the rate of mass exchange between the core and wall regions (see Table 111). It is also likely that both k, and f a r e functions of gas velocity and solid inventory. Unfortunately, in the range of variables examined in this study, this effect is not discernible. As shown in Figures 8-11, the tracer concentration in the riser achieves equilibrium in less than 3 min and the average residence time in the loop is of the order of 5 min. This result indicates that not all the solids in the return leg are equally recirculated. The very high degree of mixing in the riser probably allows the correlation of the entire set of data by a narrow range of values of the parameter k,. The mixing model illustrated in Figure 7 thus
adequately represents mixing characteristics in the riser for the range of operating conditions examined in this study. Although recirculating fluidized beds have always been characterized as having considerable backmixing of solids, the speed at which the tracer concentration reached equilibrium was surprising. This rapid mixing will be important in any reaction where the solid reactivity changes as the reaction proceeds. Examples of these changes would be coking of catalyst particles or sintering of reactant particles. Acknowledgment
The support of the Aluminum Company of America for D. C. Chesonis is gratefully acknowledged. Nomenclature Ar = Archimedes number, eq 7 C, = tracer concentration in core region, kgtr/mgsolid
1792 Ind. Eng. Chem. Res., Vol. 29, No. 9, 1990
6, = tracer concentration in wall region, kgtr/m3,01id
C, = dimensionless value of C, C, = dimensionless value of C, ( C ) = equilibrium tracer concentration, kgt,/m3,01id Co = impulse coefficient d, = particle diameter, m D, = core region diameter, m
D = riser diameter, m f = factor defined in eq 45 f, = volumetric core fraction of the riser f, = volumetric wall region fraction of the riser, m3wdlrepion/
m31eactor g = acceleration of gravity, m/sz Ga = Galileo number, eq 29 G, = recycle rate of solids, kg/(m2.s) G, = internal recirculation rate of solids, kg/(m2.s) H ( t - t,) = Heaviside function k , = mass-exchange coefficient, m3801id/(m3r.s) k = parameter defined in eq 18 L y riser length, m = Laplace transformation off r = parameter refined in eq 21 Remf = Reynolds number for minimum fluidization, eq 27 Resa = Reynolds number defined in eq 5 Re,* = Reynolds number defined in eq 6 S = Laplace transform variable Si, = inventory of solids, kg t = time, s fr = mean residence time for the loop t , = mean residence time for return leg, s tPf = effective mean residence time for return leg, s ud = solid velocity, m/s u = linear air velocity, m/s u i = superficial gas velocity, m3air/(m*,-s) ut = terminal velocity of solids, m/s v, = solid velocity in core region, m/s u, = solid velocity in wall region, m/s VI = volume of riser, m3 V I ,= volume of solids in return leg, m3 V,, = volume of solids in riser, m3 x = axial position, m z = dimensionless axial position zi = point of inflection of voidage profile, m zo = characteristic length, m Greek Characters
= parameter defined in eq 3 = parameter defined in eq 4 = parameter defined in eq 3 Pz = parameter defined in eq 4 y1 = parameter defined in eq 8 y 2 = parameter defined in eq 8
cyI
cxz
6(t) = t
ta t*
delta function
= voidage = asymptotic voidage of dense region = asymptotic voidage of lean region
c,
= voidage in core region, m3air/m3core
emf = voidage at minimum fluidization t, = voidage in wall region, m3air/m3wdl region z = average voidage in riser = air viscosity, kg/(m.s) = parameter defined in eq 36 p = parameter defined in eq 39 p f = air density, kg/m3 p, = solid density, kg/m3 r = dimensionless time T*
= parameter defined in eq 37
r1 = parameter defined in eq 19 r2 = parameter defined in eq 20 rp = parameter defined in eq 22 o = parameter defined in eq 38
Literature Cited Avidan, A. A.; Yerushalmi, J. Bed Expansion in High Velocity Fluidization. Powder Technol. 1982, 32, 223-232. Connell, G.; Dumesic, J. A. Acidic Properties of Binary Oxide Catalysts. J. Catal. 1986, 102, 216-233. Klinzing, G. E. Gas-Solid Transport; McGraw-Hill: New York, 1981; pp 60-61. Klinzing, G. E.; Mathur, M. P. The Behaviour of the Slip Velocity and its Relationship in Pneumatic Conveying. AIChE Symp. Ser. 1984,80 (NO. 2341, 24-31. Kwauk, M.; Ningde, W.; Youchu, L.; Bingyu, C.; Zhiyuan, S. Fast Fluidization a t ICM. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon Press: New York, 1986; Part 1,pp 3342. Lewis, W. K.; Gilliland, E. R.; Bauer, W. C. Characteristics of Fluidized Particles. Ind. Eng. Chem. 1949, 41, 1104-1117. Li, Y.; Chen, B.; Wang, F.; Wang, Y. Fast Fluidization. In Fluidization Science and Technology; Kwauk, M., Kunii, D., Eds.; Gordon and Breach Science: New York, 1982; Chapter 6. Malladi, M.; Otero-Schipper, P. H.; Krambeck, F. J. An Analysis of Gas-Solid Transport in Small and Large Diameter Riser Reactors. Presented a t AIChE National Meeting, Los Angeles, CA, 1982. Schnitzlein, M. G.; Weinstein, H. Flow Characterization in High Velocity Fluidized Beds Using Pressure Fluctuations. Chem. Eng. S C ~1988, . 43, 2605-2614. van Breugel, J. W.; Stein, J. J. M.; de Vries, R. J. Isokinetic Sampling in Dense Gas-Solid Stream. Proc. Inst. Mech. Eng. 1969,184 (Pt. k),18-23. Wen, C. Y.; Yu, Y. H. Generalized Method for predicting the Minimum Fluidization Velocity. AIChE J . 1966, 12, 610-612. Yang, W. C. A Model for the Dynamics of a Circulating Fluidized Bed Loop. Presented a t the Second International Conference on Circulating Fluidized Beds, Compiegne, France, 1988. Yerushalmi, J.; Cankurt, N. T.; Geldart, D.; Liss, B. Flow Regimes in Vertical Gas-Solid Contact Systems. AIChE Symp. Ser. 1978, 74 (NO.176), 1-24. Yoshida, K.; Mineo, H. High Velocity Fluidization. In Transport in Fluidized Particle Systems; Doraiswamy, L. K.. Mazumdar, A. S., Eds.; Elsevier Science: Amsterdam, The Netherlands, 1989; pp 241-252. Received f o r review November 20, 1989 Revised manuscript received May 9, 1990 Accepted May 30, 1990
