EXPERIMENTAL STUDY’ OF RESIDENCE T I M E DISTRIBUTION IN A MULTISTAGE FLUIDIZED BED D A V I D W O L F ’
A N D W I L L I A M
Department of Chemical Engineering, Technion-Israel
R E S N I C K Institute of Technology, H a i f a , Israel
Residence time distribution of solids in single and multicompartment fluidized beds was investigated as a function of solids and gas flow rates. Two types of baffles were investigated-perforated plates and plates equipped with a downcomer. The residence time distribution was represented by the F function and was determined experimentally with the aid of a pulse of magnetic tracer. The residence time distribution f - f
for a single stage was represented by F ( t ) = 1 - e-’ (7 for) F ( t ) 2 0. The two parameters, 7 and E, varied as would b e expected from the physical behavior of the system. The results obtained for multistage operation could be calculated by the use of the values obtained for 7 and E from single-stage data.
important design advantages are available if a reaction can be carried out in a fluidized system. Easy reaction control is afforded by the rapid heat transfer and uniform temperatures that are characteristic of such systems. T h e large surface-to-volume ratio of the solids medium and the ease or transferring a large volume of solid are additional possible advantages. A high degree of solids mixing is attained which, dependent on the type of reaction, may be an advantage. If consecutive reactions occur or if the solid is one of the reactants? good mixing can be a disadvantage and piston flow of the solids would be desirable. Most of the previous work reported in the literature shows that peifect or near-perfect mixing of solids takes place in a fluidized bed. Singer, Todd? and Guinn ( 3 ) showed that the catalyst in a commercial catalytic cracker could be considered as perfectly mixed. Overcashier, Todd, and Olney (2) showed that the solids mixing behavior in a five-compartment baffled fluidized bed was similar to that expected for three perfect mixing stages in series. Tailby and Cocquerel ( 4 ) showed that the aspect ratio, solids flow rate, and fluidized gas rate had important effects on the tendency to plug flow in a 3l/*inch diameter fluidized bed. T h e purpose of this work was to investigate the solids residence time distribution in single- and multiple-compartment fluidized beds as a function of solids and gas flow rate and of type of baffle. T h e data obtained were also to be used to test the author’s hypothesis (.5) that residence time data for real systems could be represented by ASY
M’chemical .
F(t) = 1 - e
-?(y)
(1)
for F ( t ) 2 0 where F ( t ) , following the nomenclature adopted by Danckwerts (7), represents the fraction of material that spends less than time t in the system, 0 is the average residence time, and 7 and e are measures of mixing efficiency and system phase shift.
Experimental
In all the work reported here the fluidization was carried out in a Perspex column of 140-mm. inside diameter. The column was composed of sections 22 cm. long, each section corresponding to one compartment. A maximum of five compartments could be assembled in series. The solids flow was countercurrent to the fluidizing medium. Air, the fluidizing medium, was supplied by a Sutorbilt blower and metered by a rotameter. Sand was the solid medium. Its size distribution is shown in Table I and the average diameter was 0.28 mm. Rate of sand flow was regulated by an orifice in the input line. Orifice diameters from 5 to 10 mm. were used, dependent on the desired flow rate. Two types of baffles were used. One was a perforated plate 138 mm. in diameter and 10 m m . thick. T h e perforations were 3.5 m m . in diameter and there were 38, 71, 104, or 137 per plate. T h e corresponding free spaces were 2.44, 4.56, 6.68, and 8.81% of the total cross-sectional area, respectively. I n this type of plate the sand and air passed through the same openings. The other type of plate was equipped with downcomers for the solid medium. T h e perforations in this plate, 126 in number, were 2 mm. in diameter and served only for passage of air. T h e lower part of the column was conical and equipped with a plug valve and 3/4-inch quick-connect coupling in the sanddischarge line. During the experiment, sample bottles were connected to this coupling in order to collect the sand for analysis.
Table I. Screen Site M e s h U . S. Standard
35 35-40 40-45 45-50 50-60 60-70 70-100 100-200 200
Size Distribution of Sand Av. Diameter of T w o Consecutiw 7,. Weight Screens, M m . Fraction of Sand 0.500 0 0.460 3.2 0.385 9.8 36.6 0.323 0.273 37.1 0.230 3.7 0.179 7.9 0.111 1.7 0 100 ~
Present address, McGill University, Montreal, Quebec, Canada VOL. 4
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IJ I.I
I
I.o
0.S
01 4 7 ~
CONVLVNQ PI
(u
Figure 3. plates
u
10
IO
31
4.0
4.0
SO
e
With With With With
0
'CONICAL
2.1
Correlation between g and 8 for perforated
X A
Figure 1.
LO
3 8 holes, Expt. 1, 2, 5 71 holes, Expt. 6 , 7, 8 1 0 4 holes, Expt. 9, 10, 1 1 1 3 7 holes, Expt. 12, 1 8
SEAL
Injector
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b
Figure 4. plates
1 I
2
I a
I
I
4
I
e Correlation between 7 and 8 for perforated Experlmentr 19 to 2 4
-
8ANO FLOW RATE, 4/min; sm!
Figure 5. Operating range of fluidized bed with perforated plates t /e
Figure 2. Graphical representation of In[l - F ( t ) ] as a function of f / 8 for various plates Perforated plates
A X V
78
l&EC
With With With With With
3 8 holes, Expt. 5 71 holes, Expt. 6 1 0 4 holes, Expt. 9 1 3 7 holes, Expt. 17 downcomer, Expt. 2 4
FUNDAMENTALS
A. B. C.
0 3
A
* X
@
0
+
rn
0
Operating zone Accumulation zone Depletion zone One plate with 3 8 holes One plate with 71 holes One plate with 1 0 4 holes One plate with 1 3 7 holes Two plates with 1 3 7 holes Three plates with 3 8 holes Three plates with 71 holes Three plates with 1 0 4 holes Three plates with 1 3 7 holes Five plates with 1 3 7 holes
wne
Figure 6. plates
t/2
F(t) function for multistage systems with perforated 0
A X
Expt. 17; Expt. 25; Expt. 30; Expt. 31;
n = 1 n = 2 n = 3 n = 5
T h e residence time distribution was determined by measuring the column response 1.0 a pulse of tracer material. A springloaded piston, as illustrated in Figure 1, containing the tracer was attached to the top flange of the column. The tracer could be charged in less than 1 second as a pulse a t the beginning of the experiment. T h e tracer used was a “magnetic sand,” actually magnetite coated with a polymer material so that the density of the combination was equal to that of the sand. The fluidizing characteristics of the magnetic sand were checked in separate experiments and found to be identical to those of the sand. I n addition, no segregation was noted in batch fluidization experiments. ‘4fter steady-state flow of sand and air had been established through the column, the pulse of tracer was added and, simultaneously, all the sand leaving the column was collected in sample bottles over timed intervals. At the end of the experiment the sand feed was stopped and the sand in the column was discharged, collected, and weighed in order to determine the column holdup. The rate of sand flow was calculated by dividing the total weight of sand collected during the sampling period by the total sampling time. T h e average residence time was calculated as the ratio of the holdup to the average sand rate. The magnetic tracer was separated from the sand in the sample bottles, with the aid of a magnetic separator, and its concentration relative to the sand determined. T h e analysis was corrected for the amount of natural magnetic material in the original sand. Values of F ( t ) as a function of time were easily calculated from the data in this form. Experimental results in Table I1 (deposited with American Documentation Institute) represent the experimental data and derived results. Single-Stage Results
Straight lines resulted when the calculated values of F ( t ) were plotted as In [l - F ( t ) ]us. t / O . Several such plots are sholvn in Figure 2. Values of 7 and e / e were calculated from the slope and the value of‘the abscissa corresponding to F ( t ) = 0. These results support the authors’ contention that residence time data for real systems can be represented by Equation 1. As has been demonstrated (5), this equation results for a number of plausible flow models that include perfect mixing, plug flow. dead space? short-circuiting, etc., and combinations of these models. T r u e model making, however, is a n almost impossible task because of the complexity of the flow regime. Although a theoretical model may represent the experimental
e
Figure 7. F ( t ) function for two stages, perforated plates
___ 0
= 1, e / e = 0 = 0.79,e/O = 0.05 Experimental results, Expt. 2 5 r)
data very accurately, it may not represent the true physical picture. These considerations should be borne in mind in the discussion that follows. The two parameters, 7 and e: that define the residence time data obtained can be considered to be measures of mixing efficiency and phase shift, respectively, of the system. For the case of perfect mixing 7 is equal to unity and for pure plug flow 7 tends to infinity. The presence of dead space in part of a system which otherwise is perfectly mixed would result in 7 assuming a value greater than unity. whereas short-circuiting of part of the feed to a perfectly mixed volume would result in values less than unity and in an anticipatory response of the system-i.e., C/O would assume a negative value. Plug flow would result in a system lag and e / O would then be positive. T h e values obtained for 7 are plotted as a function of the average residence time in Figure 3 for the perforated plate and in Figure 4 for the plate equipped with a downcomer. Factor r) decreases with an increase in average residence time for the perforated plate, whereas for the plate equipped with a downcomer it increases, reaching a value of 1 a t the higher residence times. Because the holes in the perforated plate served for passage of sand as well as air, the flow rates of the sand and air can be varied independently only over relatively small ranges. T h e operating range of the perforated plates is shown in Figure 5. An increase in average solids residence time was arrived at. in general, by increasing column holdup and decreasing solid flow rate which, in turn, necessitated a n increase in air rate. A model could be postulated that would include perfect mixing and plug flow with short-circuiting of part of the feed to the exit. The increased turbulence resulting from the increased air rate would be expected to reduce the tendency to plug flow, thereby lowering the value of r ) . With this simple model it would also be necessary, in order for r) to assume a value less than 1, that short-circuiting increase with increasing turbulence, a factor which visual inspection of small-diameter fluidized beds would indicate as possible. An inspection of the data also shows that, in general, C / O also drops as the residence time increases, which would indicate a decrease in the tendency VOL. 4
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r/ae
Figure
8.
F ( t ) function for three stages, perforated plates - = I , €10 = o --- 7 = 0.78,€10 0.03 0 Experimental results, Expt. 30
,
to plug flow and an increase in tendency to short-circuiting as described above. Pursuing again the simple possible model of perfect mixing, plug flow and short-circuiting for the case of the plate equipped with a downcomer, it is to be noted that 7 never reached a value greater than 1. T h e possibility of substantial plug flow can, therefore, be ruled out. T h e fact that e/O did not assume positive values would also indicate that plug flow was not obtained to any great extent. For this case? the fluidizing air velocity was maintained constant and the average residence time varied by varying either the sand flow rate or the holdup. At the high flow rate, corresponding to short residence time, it could be argued that part of the sand feed was unable to blend into the bulk of the bed before it was swept to the downcomer to leave the system. This would explain the apparent tendency to an increase in short-circuiting, with a decrease in average residence time. Again, a n inspection of the data shows that the tendency of E/O to decrease with a decrease in 0 supports this explanation. Multistage Results
T h e influence of multistage operation on the residence time distribution is as would be expected from theoretical consideration-namely. as the number of stages increases the residence time distribution approaches that to be expected for true plug flow. This trend is shown clearly in Figure 6, in which the experimental values for F ( t ) obtained for I , 2, 3, and 5 stages in series are plotted against t/nO. If one assumes that the values of 7 and e are equal for each of n identical stages. the F function will be
2[7
exp
(n - I ) !
[ (ty)] -7
(2)
F ( t ) >, 0
T o test this multistage model, values of 7 were picked off Figures 3 and 4 a t the residence time corresponding to the
t/se
Figure
9.
F ( t ) function for five stages, perforated plates
-
___ 0
0
0.1
I,€10 = o 7 = 0.9,€10 = 0.1 =
Experimental results, Expt. 31
1.0
1.1
2.0
td
t/P e
Figure 10. F ( t ) function for two stages, downcomer plates
___ 0
80
7 = 1 , €10 = 0 7 = 0.98,e l 0 = 0 Experimental results, Expt. 26
l&EC FUNDAMENTALS
average residence time per stage used experimentally in the multistage runs. Values of E,’O were obtained in a similar manner from single-stage data, and \vere then used in Equation 2 to predict the F function in the multistage system. T h e results are shown in Figures 7 to 9 for perforated plate multistage operation and in Figure 10 for a two-stage unit with downcomer plates. I n all figures the solid curve represents the F function to be expected for the case of perfect mixing in each stage, the dashed line represents the performance to be expected from a multistage unit based on single-stage values for 7 and e ’ 0 . and the circles represent the experimental results. T h e agreement between the experimental and predicted results is striking. In an earlier paper (5),the experimental results reported by Overcashier, Todd. and Olney (2) for residence-time distribution in a multistage fluidized bed were treated by the same procedure. An equally good agreement was obtained between the experimental results and the expected multistage behavior based on single-stage data. Conclusion
T h e residence time distribution for the solids in a fluidized bed can b? represented by a n F ( t ) function as defined in Equation l . T h e two parameters, 7 and e. vary \\ith the several variables investigated in a manner that ivould be expected
from a kno\vledge of the physical behavior of the system. I n addition. it has been sholvn with the aid of the experimental results obtained from midtistage operation that the multistage behavior can be predicted by Equation 2 by the use of values for q and c obtained from single-stage units. Ac knowledgment
1-he authors thank D. Kohn and M. Vida, who prepared the magnetic tracer.
literature Cited (1) Danckwerts, P. V., Chem. E n g . Sci. 2, 1 (1953). (2) Overcashier, R . H., Todd, D. B.:Olney, K. B., A.1.Ch.E. J . 5 , 54 (1959). (3) Siyger, E., Todd, D. B., Guinn, V. P., Znd. En,?. Chem. 49, 11
(1927). (4) Tailby, R. S.,Cocquerel, M. A. T., Trans. Znst. Chem. E n g . 39, 195 (1960). ( 5 ) \Volf, D., Resnick, LV., ISD. ENG. CHEM.FUNDAMENTALS 2, 287 (1963). RECF,IVED for review August 26, 1963 ACCEPTED November 17, 1964 Based on work done in partial fulfillment of the requirements for the D. Sc. degree of the Technion-Israel Institute of Technology. Material supplementary to this article has been deposited as Document No. 8217 with the AD1 Auxiliary Publications Project: Photoduplication Service, Library of Congress, ib’ashington 25, D. C. A copy may be secured by citing the document number and by remitting $3.25 for photoprints or $1.25 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
Nomenclature
F i t ) = rrsidence time function n = number of stage!: in series t = time = s)-stem phase shift ij = coefficient of exponent 0 = average residence time
HYDRODYNAMIC STABILITY OF A FLUIDIZED BED R0 BE RT L
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Shell Chemical Co., Torrance, Calzf.
By examining the equations for unsteady motions of solid particles and fluid through a bed of uniform solids concentration it is found that, owing to the inertia of the solid and fluid, a small disturbance in the mixture density will grow exponentially as it’moves upward’ through the bed. A uniform density distribution is therefore unstable and a fluidized bed cannot be expected to be free of small irregularities, which may grow into “bubbles.” The rate of growth of the waves of solids concentration depends on the wavelength of the disturbance, on the void fraction, and on the mean fluidizing velocity. The growth rate is generally greater the shorter the wavelength, but growth of the shortest waves is inhibited by the bed’s resistance to shear. As a result, there is a wave that grows faster than any other; its wavelength is presumably related to the initial size of the “bubbles” that form spontaneously a t all points in the bed.
a fluid flows upward against gravity through a bed of discrete solid particles, the bed is said to be “fluidized” when the fluid supports the particles a n d they move freely, being separated from contact with each other except for occasional collisions. Lnder these conditions, the free space between the particles in the fluid bed is greater than it is in the settled or consolidated condition? the weight of the particles being born by the drag forces and the pressure gradient in the fluid rather than by particle-to-particle contact. T h e mixture of solid plus fluid becomes as mobile as a true fluid. Experiment shoivs, however, that a uniform dispersion of the solid particles through the fluid is not stable under all circumstances. Especially when the fluid is a gas, the uniformity of fluidization is often poor with pockets o r bubbles of gas forming spontaneously a n d rising to the surface of the bed like vapor bubbles in a boiling liquid. I t is commonly supposed that the gas in these bubbles does not come into close contact with suspended particles as frequently as does the gas that flows upward through the “emulsion” phase surrounding the bubbles. As a result, the efficiency of a heterogeneous HEN
catalytic chemical reaction in a fluidized reactor is poorer than that in a fixed bed of the same particles. \%’hen a liquid is used as a fluidizing medium, however, the “bubbles” of solid-free liquid seem to appear less frequently in the bed, or a t least they are not so obvious to the observer. This apparently smoother, so-called “particulate” fluidization is very desirable in industrial chemical reactors. a n d many empirical studies have sought ways of producing it with gassolid mixtures. These studies have shown that, Lvhile marked differences exist in fluidization quality between various powders. all gas-solid systems seem to have a n inherent instability that produces large bubbles when the column of solid is sufficiently high. This investigation studies the causes of the primary instability from a fluid mechanical point of view. It is supposed that the fluid and solid motions that may lead ultimately to segregation of two “phases,” one containing more and the other less solid. a r e governed by the equations connecting stresses and momenta a n d by mass balances, just as for homogeneous fluids. By ivriting these equations for small disturbances-- i.r.. small VOL. 4
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