INDUSTRIAL AND ENGINEERING CHEMISTRY
1104 201
1
I
1
I
I
r
1
Table V.
Stormer Viscosity of Blends of Synthetic Cracking Catalyst
I’iIie -
-
m-t. c/b Coarse (2o:nrionent 2 .j
0075 I D TUBE
I
1.2
5 .0
90
I
I
10 STORMER
Figure 1 1 .
35 65 75
I
1
11 I
Storiner I-iscosity, Grams 0.5 0.9 4.4 0.5 .. 1.2 .5.s 1:6 2.1 8.3 2 ,0 .. .. 7.0 , . 9.0 12 12 12
.-
0
C R A q U CAT
i
Blend Comrionent Eize, Micron5 46 64 111 46 156 1.56 156 111
34 I56
Coarse
A 30”I.D TUBE
VISCOSITY
Vol, 41, No. 6
1
95 100
12
0.5
46 137
__
..
0.5
1.1
..
0.8 1.3 2.0
8.0
4.5
,
I
, .
1.4
9.0
100
Table V I .
-G#
Effect of Stormer Viscosity of Solids on Tendency t o Slug
M a x i m u m Length-Diameter Ratio for Freedom f r o m Slug Flow
Fluidized
maxiinuni mtio of the length to the diameter of the bcd in which it can be fluidized without slugging. This critical lengt,h-diametcBi ratio for the various solids is determined as follows:
A bed of the solid having a settled bed length-diameter ratio of a t least 20 to 1 is subjected to a gradually increasing rate of aeration until the slugging reaches a maximum. This point is conveniently determined by observing the lowest point of origin of t’he slugs. The distance from the gas distributor plate to the Ion-est point of origin is then measured and taken as the maximum height of the bed t,hat could be fluidized wit,hout slugging under these conditions. The measured height of this section divided by the diameter of the tube is defined as the critical lengt,h-diameter ratio of the solid. As would be expected, t,he tendency for a solid to slug increases as its viscosity increases. This is shown in Figure 11 and Table VI, relating the maximum length-diameter ratio for freedom from slug flow with the viscosity of a variety of solids. Vessel diameters in the range of 0.75 t’o3 inches had no consistent effect 011the critical length-diameter ratio. This relationship serves to illustrate how theviscosity, which can be estimated from simple laboratory tests, can be used to predict conditions under which poor flow behavior would be expected.
l’ouder synthetic cracking catalyst
>ne, Alicrona
11.01, Rlasting *and
0-150 111 156 200 33 .
,
srorlner Length-Diameter __._ R a t E Viscosity, 0.75-inch 1 %inch 3-inch Shape G . , Net Wt. tube tube tube Irregular 2 12 17 9.4 Irregular 4.4 7.2 .. 6.7 6.5 12.0 3.7 Spherical 17 0 5.0 3,3 4.0 33 0 Spherical 3.3 3.4 R.ounded 142 1.7 1,7
NOMENCLATURE
particle diameter, niicrons bed diameter, inches bed height,, inches number of particles superficial air velocity, feet per second (calculitted on basis of empty vessel devoid of solid) particle density, pounds per cubic foot maximum bed density, pounds per cubic foot bed density, pounds per cubic foot bulk density, pounds per cubic foot LITERATURE CITED
(I) Dalla Valle, 3. &I,, “Micromeritics,” 2nd e d . , p. 47, New York, Pitman Publishing Corp., 1948. ( 2 ) L e v a , G r u m m e r , N u l t o n , Weintra&, Murray, a n d Pollchili. Chem. Eng. Progress, 44, No. 7, 511 (1948). (3) Leva, G r u m m e r , W e i n t r a u b , and Pollchik, Ibid., 44, No. 8, 619 (1948).
ACKNOWLEDGMENT
The writera wish to express their appreciation to R. G. Christopher for assistance with much of this work.
(4) P a r e n t , Yagol, a n d Steirser, Ibid., 43,429 (1947). (5) Wilhelm a n d Kwauk, I b i d . , 44, No. 3, 201 (1948). RECEIVED 1Iarch 12, 1929.
Characteristics of Fluidized Particles T h e flow characteristics for both batch and continuous fluidization of fine glass spheres have been investigated. T h e d a t a have been correlated by several methods which should be useful in predicting t h e performance of such units, and indicate t h a t glass spheres of small size give flow characteristics different f r o m those w i t h larger diameters.
W . K. LEWIS, E. R. GILLILAND,A N D W.C.BAUER M A S S A C H U S E T T S INSTITUTE OF T E C H N O L O G Y . C A M B R I D G E , M A S S
T
HE use of fluidized solids has developed rapidly, particularly for the catalytic cracking of petroleum. At present, i t is being considered for a. number of other chemical operations, such as synthesis of liquid hydrocarbons, production of phthalic anhydride, gasification of cod, burning of lime, and partial oxidation of hydrocarbons. In order to design units for such reactions, i t is necessary to have a clear picture of the factors necessary to obtain satisfactory operation of the fluidization unit. The data presented in this report cover both batch and continuous fluidization. I n the first case, the solid remains within
the unit with essentially no entrainment, and in the other case Lhe solid f l o w through the unit continuously. There have been a number of experimental investigatiom of the characteristics of the fluidized bed. Chambers (8) and Kalker (9) studied the fluidization of clay with air in units 1 inoh in diameter with large ratios of length to diameter. Walker also employed hydrogen and carbon dioxide as the fluidizing gas. Their results demonstrated that satisfactory fluidization could be obtained with 200-mesh clay, and they concluded (1) that the pressure drop under fluidized conditions was essentially
June 1949
110s
INDUSTRIAL AND ENGINEERING CHEMISTRY
n
equlvalent t o the weight of the powder; (2) that the slip velocityLe., the average superficial gas velocity minus the average solid velocity-was relatively independent of the velocities or the feed rates; (3) t h a t the slip velocity was essentially independent of the gas density-Le., approximately the same slip velocity was obtained with hydrogen, air, and carbon dioxide; and (4) that the slip velocities were much higher than the predicted free-falling velocities for single particles. On the basis of these results, they pictured each particle flowing relative to the gas in streamline motion which would explain the lack of a gas density effect. To account for the high slip velocities, it was assumed that some effect equivalent to agglomeration hsd taken place
STATIC PRESSURE
C5
TAP TEMPERATURE TWO ROTAMETERS
IN PARALLEL THREE ROTAMETERS
,
L,
i I li%
IN
P
TEST SECTION I O FEET OF I //4 INCH I. D BRASS TUE/NG
@ ,
. SLfOE VALVE
AIR AIR
DIFFEREN TlAL
MA NOME TERS
@--.
SCREEN
Figure 2.
Apparatus for Continuous Fluidization APPARATUS AND PROCEDURE
@
@
STATIC PRESSURE TAP TEMPERA TURE
Figure 1.
SEC TION
Apparatus for Batch Fluidization
Conners and Fuchs (3) and Rotzler (8) confirmed Walker’s oonolusions relative to the effect of the density of the gas by utilizing air a t pressures from 0.1 atmosphere to 80 pounds per square inch gage. Hettich and Kean (6) studied the fluidization of iron ore with air under conditions of downflow of the solids and both upflow and downflow of the gas. They also found that the slip velocity was independent of the absolute velocity. Their slip velocities were higher than those obtained by Walker using clay, and this was attributed to the higher ‘density of iron ore. Wilhelm and Kwauk ( 1 1 ) and Leva and eo-workers ( 7 ) have presented data on batch fluidization for a variety of systems. The density and viscosity effects found by these investigators agreed with those reported by Walker. I n addition, their data indicate good agreement between pressure drop and the weight of the solid within the unit. However, slip velocities were less than those predicted by free-falling velocity correlations, whereas Walker’s were greater. Friend (4) has presented limited data on fine particles, indicating that the slip velocities are greater than those t h a t would be predicted. Thus, there are both differences and agreements among the results of the various investigators, and this program was undertaken to clarify some of these points. Because of the fundamental differences in the batch and continuous fluidization, the data for these two methods of operation are considered separately here.
Apparatus. BATCH. Two tubes of Lucite 2.5 and 4.5 inches in inside diameter and 50 inches in length were used in this investigation. A schematic diagram of the larger tube is shown in Figure 1. Static pressures relative t o atmospheric pressure were read from vertical manometers connected t o pressure taps located immediately below and above the supporting screen and at distances of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, and 4.0 feet above the screen. The supporting screen consisted of a 200-mesh bronze screen soldered to a disk of perforated brass (24 perforations per inch and 0.021 inch in diameter). The pressure drop across the screen was found to be negligible within the range of air rates employed. Calibrated rotameters served t o meter the flow of air. With minor modifications the smaller tube was used to obtain data for the fluidization of solids with water, in which case calibrated orifices were used to meter the flow of water. CO~YTINUOUS. The apparatus used for the continuous transport of solids is shown in Figure 2. The vertical test section consisted of a 10-foot length of brass tubing 1.25 inches in inside diameter. Static pressure readings were obtained from five taps located 1, 3, 5, 7, and 9 feet from the bottom of the section. The top of the tube opened directly into the modified cyclone which was fitted with a baffle plate to induce the necessary swirling motion t o the solid particles, which then dropped through the diverting valve t o the solid feed standpipe. The rate of solid recirculation was controlled either by the air pressure drop maintained across the funnel constriction at the bottom of the standpi e (high rates) or by throttling the 30-mm. stopcock below the Znnel (low rates). Materials. Most of the data have been obtained with narrow, constant-diameter fractions or with known mixtures of Scotchlite glass beads. The characteristics of the various narrow fractions and of the other miscellaneous particles used are shown in Table I. The average diameters of the Scotchlite beads were determined both from photomicrographs and from micrometer measurements. For all sizes at least fifty beads were measured to establish the average diameter. The absolute densities were calculated from the water displacement of a known weight of the particles.
INDUSTRIAL AND ENGINEERING CHEMISTRY Table 1.
Vol. 41, No. 6
Physical Characteristics of Particles AV.
o A
Bcotohlite4 No. 6
Av. Diameter, Inch 0.0224
Diameter Deviation,
No. 7
0.0178
6
No. 9
0.0112
7
No. 11
0.0061
2 M - I N C H TUBE 41/2-/NCH TUBE
+ ELECTROSTATIC EFFECTS
PRESENT 2 1/2 INCH TUBE
No. 13 No. 15 Aerocat microspheresb Puffed rice
a
b
0.28
7
7 6 20 60-150mesh , ,
.
Absolute Particle Density, Lb./Cu. F 147 150
152 154 155 155 62('?)
Equivalent spherical diameter calculated from weight of 500 particles and absolute density
Of
0m0061-'nch
Spheres with Air
Operating procedure, BATCH,For a given weight of solid in the unit and a given gas rate the static pressures a t the various points in the bed, the maximum and miniinuin bed levels, and the general character of the fluidization were recorded. For all the constant-diameter fractions as well as for the known mixtures, data were also obtained for the pressure drops through fixed beds of the solids. With water fluidization the procedure was essentially the same except that no fluctuation in bed level was encountered. CONTINUOUS.The solid feed rate was determined by shunting the stream of recirculated soh& Jvith the diverting valve into the feed rate receiver and weighing the amount of solid collected over a measured period of time. For each run, the gas rate and the static pressures over the test section were also recorded. To determine the boundary between steady and unsteady operation-i,e,, smooth transport and slugging-the solid rate was fixed and the gas rate was decreased gradually until the slugging point wm reached. For all other runs, the gas rate was fixed and the data were recorded a t Various feed rates. gas rate The pressure employed drop was through foundthe to empty be negligible. tube at the maximum
respectively. If the pressure drop is equal to the weight of powder, a horizontal line equal to the value of 1 on the ordinate should be obtained. The data show considerable deviation from this line, and in some cases she\> excess pressure drops as great as ZOyo. The values below 1 presumably correspond to conditions under which all the particles in the unit are not supported by the gas. The valucs greater than I must be an indication of a frictional drag on the walls of the unit. Although it is obvious that frictional forces on the \\-all are present, i t has been usually assumed that these are small relative to the pressure drop necessary to support the powder. The force correspondirlg to the excess pressure drop as shown on Figures 3 and 4 is much greater than would be expected from gas friction alone at the velocities employed and must, therefore, indicate a force of the solid pap On the On Figure 3 in some cases the agreement between thc pressure drop and the weight of the solid is much better than in others; from an inspection of the data, it appears that the chief factor is the ratio of length to diameter, L Q I D T . Thus, for the case of LQIDTequal to 2.6 the pressure drop ratio is only slightly greater than 1, but there is a progressive increase in excess pressure drop as the L ~ / D ratio ~ increases. s u c h a trend is ,lot surprising, for an increase in LQ/DTincreases the tendency for slugging of the solids which would probably give Iargc forces 011 the mall. Two curves are given for an LQ/DT ratio equal to 9.8. The upper CUrve \?,as under conditions in which electrostatic effects were large and there was a layer of the solid adhering to
RESULTS A N D DISCUSSION O F RESULTS
Batch Fluidization. In the case of batch fluidization, the experimental data obtained are basically the amount of solid in the unit, average superficial gas velocity, pressure as a function of the bed height, visual observation of bed level, and appearance of the fluidization. In order to obtain an insight into the phenomena involved, the data are presented in several different nays. Tables I1 to VIII give the original data from which the curves were plotted. One of the conclusions of previous investigators has been that the pressure drop over the unit is equivalent t o the weight of the solid it contains. In order to make this comparison, the data obtained in thc experimental work are presented in Figures 3 and 4 as the experimental pressure drop, divided by the pressure drop based on the weight of the powder present, as a function of the Reynolds number, DPVopr/p,, where D, is the particle diameter, and VO,pf, and p f are the superficial velocity, density, and viscosity of the fluid,
6.2
Minnesota Mining and Manufactuiing Company. American Cyanamid Companj.
-
Rep
Figure 3* Batch
0.0040 0.0016 100-mesh
R
Diameter Measured by Photomicrographs and micrometer Photomicrographs and micrometer Photomicrographs and micrometer Photomicrographs Photomicrographs Photomicrographs Screening
Figure 4.
Batch Fluidization of Glass Spheres with Air D p = inches
I N D U S T R I A L - A N D EN G I N E E R I N G C H E M I S T R Y
June 1949
V, -SUPERFICIAL AIR VELOCITY - F T / S E C .
BOL
j
I
1 I I
Figure 5.
1
Dp
MIXTURE
j
1
1
DT
0Oll2'-50 %
BOXED POINTS AT e * I REPRESENT CALCULATED FREE-FALLING VELOCITIES
I
Relation of Fraction Voids t o Velocity for Batch Fluidization of Glass Spheres w i t h Air
1.0
g v)
e
2
c)
2 3
1107
A representative portion of the data obtained in the batch fluidization work is shown in Figure 5. The fraction voids value for this plot was obtained by plotting the average static pressure against the height of the unit for a given run and extrapolating the line, which in most cases was linear, to the discharge pressure. The bed height determined in this manner was used to calculate the average, fraction voids, eT. At low velocities the fraction voids is small, corresponding essentially to the voids in a fixed bed. As the velocity is increased the voids increase and on the logarithmic plots employed a linear relationship is obtained. For the large glass spheres these straight lines extrapolate to a value for the velocity, a t a fraction voids equal t o 1, that is close to the free-falling velocity predicted for single spheres. However, for the glass spheres of smaller size the curve extrapolates to a velocity severalfold the predicted value. D a t a for a mixture of constant-diameter fractions of glass spheres are included in Figure 5. I n predicting the free-falling velocity, i t was found that an average diameter equal to 1
8
Wi
A CONSTANT DIAMETER GLASS SPHERES WITH WATER-HINDERED SETTLING
-&
\o"
0.I 0.I
IO
(+Lp Figure 6.
Correlation for Batch Fluidization of Glass Spheres w i t h Air and W a t e r
Wa +z2+ & + ...
Wz
gave satisfactory agreement, where w is the weight fraction and d the particle diameter of the fraction. The data for the runs giving curves of the type of Figure 5, which extrapolate to the free-falling velocity of a sphere, can be correlated on a basis similar to the friction factor plots employed for free-falling spheres (IO). I n this case the friction factor, f ~is, defined as
the walls. When the same svstem was treated with a solution to minimize the effects of static, the results given for the lower where g = acceleration of gravity, D, = particle diameter, curve were obtained. Ps = solid density, Vo = superficial velocity, p, = fluid density, The conclusion that the pressure drop is essentially equal to the and p f = fluid weight of the powder would appear to be satisfactory for units For the Stokes' law region the friction factor is equal to with small LQ/DTratios but is likely to be in considerable error for large values or for cases having large static effects. This -2- h conclusion is based on batch fluidization experiments in which PIVOD~ the fluidized bulk density of the solid was relatively high, and slugging action would not be expected t o be significant with low bed density. Table I I . Hindered Settling of Glass Spheres in Water Figure 4 is similar t o Figure 3. in which different Settling Batch sizes-of glass spheres were fluidized at the same Velocity, Temp., Weight Run LQ/DTratio. I n this case the particles of small No. Run Constsnts Ft./Seo. e F. Grams' CT Rep fF 112.2 0.960 1.52 H-2 Apparatus. standard 1000-ml. 0.0297 69.5 31.3 diameter, which gave good fluidization-i.e., no 140.2 0.950 1 . 6 7 72.9 graduate, 2.375 inch i.d. Total 0.0300 24.5 slugging-show only a small excess pressure drop 69.0 volume of stoppered graduate 0.0294 168.3 0.940 1 . 4 7 32.0 0.930 1 . 3 4 6 8 . 0 1140ml. Dp,O.OOBlinch 0.0287 196.3 35.3 whereas those with large diameters, which gave 6 8 . 0 224.4 0 . 9 2 0 1 . 2 9 0.0278 37.9 6 8 . 0 280.4 0.900 1.23 0.0265 41.7 slugging oonditions, give much larger wall effects. 0.0244 6 7 . 0 364.6 0 . 8 7 0 1.15 50.5 The data would indicate that under conditions 69.0 0.0215 4 4 8 . 7 0.840 1 . 0 8 61.3 69.5 0.0192 532.8 0.810 0.975 75.8 of good fluidization the pressure drop is essentially 0.0166 6 8 . 0 616.9 0.780 0.777 105 0.0142 6 9 . 5 701.1 0.750 0.717 140 equivalent to the weight of the solid, but that con0.0118 6 8 . 0 785.2 0 . 7 2 0 0.549 211 ditions such as slugging can result in appreciable 6 8 . 0 8 6 9 . 4 0 . 6 9 0 0.453 0.0098 308 0.0080 67.0 456 9 5 3 . 5 0.660 0.373 discrepancies. Thus the pressure drop is a satis0.0063 6 9 . 0 1037.6 0.630 0.317 705 0.0053 6 8 . 0 1121.8 0.600 0.244 1060 factory method of estimating the solid content or 0,0039 6 8 . 0 1205.8 0.570 0.189 1780 the bed density in the first case, but i t would give H-3 Apparatus as above. Total vol- 0.0219 92.5 100.0 0.966 0.909 44.1 high values for the second case except a t the lowest 92.8 ume of stoppered graduate 1211 0.0176 3 0 0 . 0 0.900 0.736 68.3 0.0142 9 1 . 4 ml. Dp, 0.0040 inch 4 5 0 . 0 0.851 0.548 105 fluidization velocities. 0.0111 86.0 172 600.0 0.801 0.430 312 0.00824 8 6 . 0 750.0 0.752 0.319 One of the methods that has been used to cor0.00603 84.2 900.0 0.702 0.228 582 relate hindered-settling data has been a plot of frac0.00434 8 4 . 7 1050.0 0.652 0.165 1120 tion voids as a function of the superficial velocity.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1108 1000
0
MfXED SIZES OF G L A S S SPHERES WITH AIR FLUIDIZAT1ON
--. e"
-L se
Q-w
& n PI 0
It was found t h a t these data could be correlated on a single line by plotting the fraction voids as a function of the ratio of the friction factor for a single sphere to the experimental friction factor, both calculated a t the same Reynolds number. This relationship is shon-n in Figure 6. This line does not inrludr the data for the smallest spheres in the 2.5-inch tube or for the small
Vol. 41, No. 6
and intermediate sizes in the tube of larger diamotcr, which extrapolated to velocities higher than the free-falling values. For hindered settling, various investigators have been ablc to correlate their results for different systems by multiplying the friction factor by the fraction voids t o a power. Figure 6 indicates such a relationship, for which the power of the fraction voids is 4.65. The friction factor multiplied by the fraction voids to 4.65 power is plotted in Figure 7 as a function of the Reynolds number. The data cover the fluidization of conetantdiameter glass spheres with air and wat,er, the fluidiza.tion of kno-ivn mixtures wit'h air, and the hindcrcd settling of glass spheres in water. All the data fall very close to the line for freefalling spheres and a t low Reynolds numbers this line agrees closely u-it'h Stokes' law. Some of the batch data do not agree with the correlations of Figures 6 and 7 . I n all cases these systems had low ratios (less than 0.003) of particle to tube diameters, and they gave good fluidization. It is surprising t h a t the data for slugging conditions are correlated so well by these figures. These correlations make i t possible t,o predict characterist,ios of batch fluidization. For example, with Figure 7 , if the gas velocity is set for a given particle size and density, it is possible to calculate the value of the Reynolds number and of the friction factor. From the plot the fraction voids and the actual bed dcnsit'y can then be predicted. Over most of the regions given in Figure 7, the ordinate can be expressed as essentially a reciprocal relationship of the Reynolds number. I n this region the corrclation would indicate that thc fluidizing velocity required is directly proportional t o the diameter of the particle squared ; to the difference in solid and fluid density, which in the case of gas fluidization would be essentially solid density; and t o the fraction voids to the 1.65 power. The fluidizing velocity would
1.0 8
6
2
2
0.01 0 01
4
6
8
O /
2
4
6
8
lo
v,= I v o - v a ) Figure 8.
Batch Fluidization of Glass Spheres w i t h Air
4
6
8
100
June 1949
be inversely proportional to the first power of the fluid viscosity. A t t h e h i g h e r v a l u e s of t h e R e y n o l d s number where the slope of the curve d e c r e a s e s , t h e velocity required for fluidization would be proportional to the diameter to a power between 1.0 and 2.0 and to the density of the solids to a power less than 1; and inversely proportional to a fractional power of the viscosity a n d the density of the fluid. I n this region, turbulence is becoming a factor and the support of the particle is no longer due to simple viscous drag. The straight-line portion of the curve agrees with the conclusions found b y Walker-Le., the velocity of the fluid by the solid is e s s e n t i a l l y independent of the fluid density and inversely proportional to the v i s c o s i t y . It also agrees with the observation that t h e n e c e s s a r y velocity for fluidization is proportional to the density of the solid. Because the fluidizing velocity is nearly independent of gas density, the same linear gas velocity is required under vacuum and a t high pressure to give the corresponding fluidization of a given solid. However, this would not be true at very high pressure First, high pressure would increase the density of the fluidizing g a s a n d w o u l d cause an i n c r e a s e i n t h e R e y n o l d s number. Eventually this increased density would increase the Reynolds number beyond the straightline region and the fluidizing velocity would then become some inverse function of the gas density. Secondly, a t very high pressures the factor involving the difference between the density of the solid and the density of the fluid would no longer be equal to the density of the solid-Le., the density of the fluid would b e c o m e h i g h enough to exert a significant b u o y a n t effect upon the solid. The same data for batch fluidization have been correlated in still another manner. I n observing the fluidized
INDUSTRIAL AND ENGINEERING CHEMISTRY Table 111.
Run h-0.
Run Constants
1109
Batch Fluidization of Glass Spheres in Air
vo
8
Ft./Sec.
Bed Height, L , Inches Extrapolated PI, pressure, Lb./Sq. Min. Max. LP Ft.
Rep
fB
fF
222 102 69.7 62.6 53.1
....
-Dp
5-25 Tube diameter 2.5inches LQ 10.6inches VQ 0,886ft./sec.
L-13 Tube diameter 4.5inches Batch wt. 12.41lb. LQ 15 4 inches YQ 0.837ft./sec. eQ 0.4037
5-14 Tube diameter 2.8inches Batch wt. 6.33lb. LQ 25 inches Vg 0.60 ft./seo. eg 0.4068
S-24 Tube diameter 2.5inches LQ 11.35inches V Q 0,61ft./sec.
....
0.175 0.395 0.585 0,655 0.784 1.60 1.44 1.27 1.17 1.11 1.06 0 993 0.933 0 I982 1.08 1.17 1.28 1.39 1.52 1.72 1.89 2.05 2.24 2.42 2.55 2.88 3.25 0.869 0,899 0.937 0.984 1.06 1.19 1.39 1.62 1.76 1.84
.... . .
....
.....
33196 33.43 31.51 31.02 30.6 29.79 29.16
......
......
...... ...... ...... ...... ......... ......... . . . . . . . . . . . . . . . . .
......... ......... .........
......... . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
......... . . . . . . . . . .........
-Dp
0,0847 0.168 0.321 0.390 0.200 0.299 0.400 0.521 1.193 0,939 0.881 0,823 0,800 0.780 0.723 0.654 0.763 0.818 0.871 1.13 1.46 1.66 1.88 2.09 2.33 2 53
24.24 24.24 24 24 24.24 24,90 24.90 24.90 24.90 29.0 39.0 27.0 31.0 26.5 30.0 26.25 28.5 26.40 28.25 26.00 27.25 25,SO 26.75 11.44 11.65 11.80 12.40 11.95 12.80 12.10 13.55 13.20 16.60 14.50 20.60 15.CO 23.15 16.50 25.60 15.50 29.50 17.5 32.5 18.5 35.2
0.109 0.213 0.384 0.514 1.045 0,992 0.879 0.787 0 713 1.33 1.16
23.75 23,75 23.75 23.75 27.5 32.5 26.7 31.2 26.0 29.0 25.0 26.5 24.5 25.5 29.0 39.0 28.5 35.0
0,0306 0,0539 0 0942 0.1645 0.0364 0.0541 0.0926 0.1366
15.10 15.10 15.10 15.10 15.65 15.65 15.65 15.65
.... ....
=
....
....
....
... .... ....
29.70 27.96 27.24 26.82 26.76 26.22 25.92
110.1 ..... 110.1 ..... 110.2 ..... 110.3 ..... 110.6 ..... 110.9 . . . 112.7 ..... 113.4 ..... 114.4 . . . . 114.8 ..... 0.0178Inch32.32 0.770 62 35 I 52 121.6 2.92 148.0 3.54 61.43 1.81 93.30 2.72 124.6 3 63 162.5 4.74 219.8 10.92 201.3 8.60 198 1 8.06 193.0 7.53 192.0 7.32 190.6 6.86 188.3 6.62
..... ....
..
....
..... .....
.... . . . ....
..... ..... .... .. ... ... ...... .....
. . .
....
.... .... ....
...... ...... ...... ...
...... ...... ...... ...... ...... ......
......
......
...... ...... ...... ..... ...... ......
......
...... ......
......
....
....
.... ....
61.4 76.0 97.5 115 128
141 160
.... .... .... ....
.... .... .... .... ....
....
....
.... ... ....
....
....
....
.... ....
.... ....
.... ....
.... ---.I
706 347 184 152 235 159 119 91.
....
.... ....
.... ....
....
.... .... ... , . . .... .... ....
.... ....
.... .... ....
.... .... .... .
.
I
.
....
....
....
....
88.2 142 162 185 196 218 240
....
. . . .
I
.
.
...
.... .... .... .... ....
.... ....
CT
1,-2
Tube diameter 4.6 inchrr Batch wt. 19.47Ib. LQ 23.75inches V Q 0.58ft./sec. EQ
0.4063
8-10 Tube diameter 2 , 5 inches Ratch wt. 4 lb.
0.4074 32.02 0.981 0.4074 61.89 1.92 3.46 0.4074 114.0 4.63 0.4074 150.6 0.493 184.9 9.41 0.496 182.5 8.93 7.91 0.458 182.5 7.09 0.445 178.2 6.42 0.430 177.6 0.621 187.4 12.0 0.491 185.8 10.4
-Dp
440 223 127 93.
....
..... ..... ..... ..... .....
119 132 168 210 256 73.6 96.7
....
=
. . . ... ...
3010 1700 1030 5520 2050 1450 8270 5280
...
....
.... ....
.... .... ....
.... .... .... ....
...
.... .... ....
LP
S-11 Tube diameter 2.5 inches Batch wt. 6.33lb. LQ 25.0inches VQ 0.26ft./seC. eQ 0.4137
0,278 0.300 0.333 0,369 0.407 0,433 0.497 0.578
25.25 25.55 26 10 26.5 27.0 27.2 28.2 29.2 30.0 0.656 0.868 34
25.50 25.95 26.70 27.5 28.7 29.4 31.7 34.7 37.2 43
25.2 25.56 26.2 26.6 27.2 27.7 28.9 30.1 31.1 33.7
184.9 186.3 188.0 190.1 192.3 193.8 197.6 203.3 208.4 212.8
1.58 1.70 1.89 2.09 2.31 2.46 2.82 3.28 3.72 4.93
...... ...... ......
......
......
.. .. .. .. .. ..
......
1070 919 745 609 500 442 336 248 192 110
(Continued on p a g e 1110)
1110 bed i t is noted t h a t a t constant gas velocity there is considerable variation in the height of the bed and, therefore, the average density or the average fraction voids.
INDUSTRIAL AND ENGINEERING CHEMISTRY Table 1 I I .
of Glass Spheres i n Air
Batch Fluidization
(Continued)
Bed Height, L,Inches Run
No.
Run Constants
vi
Extrapressure, polated Lb./Sq. PI, 8
Ft./aec.
Min.
LP
Max.
Dp
7
Consider a bed under fluidized condition; as the gas velocity is decreased the bed height decreases and the fluctuation in height also decreases until a point is reached at mhich the bed appears essentially quiescent. I n this state the volume of the solid i s greater than t h a t with no fluidizing gas, but the solid docs not appear t o have any significant turbulent motion. As the velocity is increased the bed expands and the action becomes turbulent. I n the quiescent state the characteristic of the bed is very similar t o quicksandi.e., each particle is separated from the surrounding particles by a film of fluid-but the fluid velocities are not sufficient t o impart any significant turbulent motion t o the particles. However, in this state the bed will behave like a fluid and will yield t o any external force. As the velocity of the fluid is increased and the bed expands, visually the effect is regions of relatively low solid density and regions of high solid density, and the regions of low solid density tend t o rise through the bed more or less like bubbles. The wholephenornenon appears similar t o the bubbiing of a gas through a liquid. Wilhelm and Kwauk have reported a similar observation. For this reason, experiments were made in both of the batch units bubbling air through water, and the results are reported with the solid fluidization data.
Vol. 41, No. 6
=
Ft. Rep 0.0112 Inch (Contd.)-
IB 7
_____ 8-7
S-13
Tube diameter 2.5:incheu
Batch wt. 8 . 0 0 lb.
Lg 29.75 inches V Q 0.025 ft./sec. cQ 0.3856
8-22
Tube diametei2.5 ixxhcs L g 10.5 inches V Q 0 , 0 9 3 ft./sec.
The data for batch fluidL-7 Tube diameter 4.5 inchev ization are shown on Figure Batch wt. 20 lb. 8 as the incremental fraction Lg 24.2 inches V g 0.085 ft./sec. voids, €3,as a function of the e g 0.4162 incremental velocity, V E . The incremental fraction voids and the incremental velocity are the incremes over and above the values that were obtained with the quiescent bed, respectively. The incremental fraction voids is based upon the maximum height of bed obtained with a given gas velocity and is equal t o 1-LO/&,,, where LQ is the bed height in the quiescent state and Lmaxis t h e maximum fluidized bed height. The data €or a single diameter of particles appear to give a single line on this plot which is relatively independent of the
0,0200 0,0330 0,0430 0,0570 0,0223 0.0314 0.0422 0.0577 0.657 0.597 0.538 0.481 0.392 0.320 0.250 0.181 0.108 0.0968 0.112 0.153 0.215 0.490 0,0970 0.121 0.135 0.170 0.195 0.250 0.358 0,388 0.100 0.125 0.135 0.150 0.165 0.183 0.207 0.246 0.277 0.324 0.376 0.556 0.693 0.851 1.02 1.15 1.26 1.41 1.78 0.096 0.112 0.131 0.150 0.178 0.212 0.256 0.286 0.345 0.401 0.491 0.616 1.047 0 994 0.926 0.728 0.688 0.615 0.561 0.488 0.434 0.390 0.328 0.298 0.254 ~
0.846 0.510 0.389 0.290 0.683 0.416 0.304 0,233
...... ......
.... ....
....
.... .. _. .... ioi'
....
124 153 192 ...... 288 433 ...... 709 . . . . . . 1350 3790 ...... 4810 3570 . . . . . . 1920 . . . . . . 977 . . . . . . 187 . . . . . . 4700 . . . . . . 3030 ...... 2410 . . . . . . 1530 . . . . . . 1170 _ . . _ . . 709 ..... 345 ...... 294
...... ......
......
...... ...... 31.60 32.2 32.7 33.7 35.0 36.0 39.5 40.0 10.40 10.65 10.70 10.75 IO. 80 11.00 11.20 11.4 11.6 11.8 12.0 13.0 13.7 14.5 15.0 16.0
32.05 32.9 33.3 34.9 36.3 39.25 44.5 48.5 10.65 10.85 11.00 11.15 11.30 11.55 12.00 12.5 12.8 13.5 14.1 17.5 19.5 22.2 23.0 25.0 26.4 27.5 32.0
... ...
20.0
24.20 24.35 24.65 24.90 25.10 26.5
. .~
~~. ... ... . (
,
~
~
16.5 16.0 16.0 15.0 15.0 14.7 14.5 14.0 13.7 13.5 13.2 13.2 13.0
1
24.45 24.70 25.05 25.50 26.20 26.9 27.9 28.6 30.3 31.8 34.1 37.4 21.5 20.5 20.0 18.0 18.0 17.5 16.0 15.7 16.2 15.0 14.2 14.0 14.5
31.68 32.28 32.54 34.00 34.92 37.56 41.28 43.56
234.7 237.5 237.5 240.2 241.9 245.4 249.9 251.4
0.305 0,380 0.426 0.534 0.613 0.786 1.13 1.22
....
....
... ... ....
...
..... ..... ..... .....
.... ....
.... ....
..
, . .
..". .... , . ~ . .... .... .... .... ._.. .... .... .,..
....
.... .. ....
.,..
.,..
....
~ . .
.... ;,.. . I . .
.*.. 0.415 0.418 0.421 0.426 0.437 0.443 0.445 0.461 0.477 0.484 0,514 0.528 0.587 0.573 0.577 0.581 0.534 0.536 0.534 0,513 0.534 0.530 0.493
....
....
178.9 178.8 179.6 180.2 181.6 182.2 183.1 184.0 183.2 185.4 188.1 190.4 90.8 90.8 90.8 89.2 89.5 89.6 89.9 89.6 89.5 89.2 89.8 90.2 89.3
.....
..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....
. . I . .
....
.......... ..........
.......... . . . . . . . . . .
..........
.......... . . . . . .
......... ......... ......... ......... ......... ...... ...
.........
.......... .......... .......... .......... ..........
0.291 0.339 0.397 0,454 0.539 0.642 ...... ...... 0.775 ...... 0.860 1.04 ...... 1.21 ...... 1.49 ...... 1.86 3.21 ..... ...... 3.05 ..... 2.84 ...... 2.23 ...... 2.11 ...... 1.88 1.72 ...... ...... 1.50 1.33 ...... 1.19 ...... I .01 0.913 0.779 (Concluded on page
..
o . . .
i . . , . .
....
.... .... .... .... .... .... ....
.... . . I .
....
.... ....
.... ..
.... .... .... ....
....
.... .... ....
....
....
i111)
tube diameter and the LQ/I)2>ratio. However, there is a very significant difference between the values given by the different
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
1111
action of the Darticles that are included on Figure 8. Bed Height, L,Inches The large particles tend to Extragive slugging and the appolated pressure, Lb. bq. vo Run pearance of large bubbles of Ft./ie;ec. Min. Max. LP Run Constants No. Rep fB fP gas. For the runs given in D p 0.004 Inch Figure 10, the fluidization LP .... 0.0119 23.75 .... 62.05 0.0302 16 600 5-19 Tube diameter 2.5 inches was much more uniform and 0.0175 23.75 .... 90.08 0,0444 10;900 .... Batch wt. 6.33 lb. the bubbles are small. 8460 .... 23.75 . . . . 119.5 0.0583 0.0230 Lg 24 inches 6:695 .... 23.75 . . . . 158.7 0.0299 0.0758 Vg 0,014 ft./seo. Fixed Bed. I n utilizing ...... 96.7 0.562 33.5 41.5 35.52 1.17 192.0 eg 0.4012 ...... 105 34.0 41.5 34.38 0.540 1.13 193.0 the correlation given in Fig...... 114 34.0 0.517 190.6 41.0 34.38 1.08 .. .. .. .. .. .. 131 33.0 39.5 34.38 0.482 191.6 1.01 ures 8, 9, and 10, i t is neces160 0.436 190.0 32.7 38.5 34.38 0.911 sary to have values for the ...... 192 0,399 188.9 0.834 32.2 37.0 32.28 31.0 ...... 238 35.5 32.10 0.358 0.749 188.6 total fraction voids and the ...... 661 0.215 28.0 30.2 28.80 186.1 0.449 . . . . . . 841 0.190 185.4 27.7 29.2 27.72 0.398 velocity under the quiescent 0.175 27.5 28.7 27.36 ...... 991 185.1 0.367 .. .. .. .. .... 1300 27.0 28.0 26.94 0.153 184.8 0,320 “quicksand” state, EQ and 1820 26.25 27.25 26.76 0.130 184.4 0.271 VQ, respectively. It is be...... 3350 0.0952 25.75 26.25 25.92 182.6 0.199 lieved that the most satisfactory method of obtaining 31.7 0.426 227.5 0.0611 31.5 0.107 .......... 5-20 Tube diameter 2 . 5 inches 0.0833 31.7 32.5 0.439 228.9 . . . . . . . . . . 0.174 Batch wt. 8.00 lb. these is by experimental 0.114 32.7 33.7 0.447 . . . . . . . . . . Lg 31.4 inches 231.3 0.239 0.151 33.0 34.7 0.455 233.3 . . . . . . . . . . 0.316 V g 0.050 ft./sec. techniques employed in this 0.188 34.0 36.2 0.466 235.3 0.393 . . . . . . . . . . eQ 0.4216 35.5 37.5 0.469 237.3 0.217 .. .. .. .. .. .. .. .. .. .. 0.454 work-i.e., determining the 0.215 36.0 38.2 0.488 237.2 0.449 height of the bed as a func0.325 38.7 43.0 0.535 240.6 0.680 .......... tion of gas velocity and extra0.0160 22.00 .... 77.06 0.0337 11.500 .... L-3 Tube diameter 4 . 5 inches 22.00 0.0220 .... 141.6 113.8 0.0463 Batch wt. 18.66 lb. 8,970 .... polating back to the qui22.00 0.0280 .... 0.0589 Lg 22.25 inches 6,900 .... 22.00 0.0350 5,370 .... 0.0736 Vg 0.050 ft./seo. 171.4 escent condition. However, 0:5;13 174.9 29.0 38.0 ....... 0.688 1.38 eg 0.4114 this procedure necessitates 0.532 174.8 28.0 35.5 0.570 . . . . . . . 1.14 0.541 172.7 28.0 34.0 0.494 ....... 0.989 actual experimental work 27.0 32.0 0.443 0.544 171.1 0.887 27.1 30.5 0.382 0.518 170.7 . . . . . . . . . . 0.765 and, in order to eliminate this 26.0 30.0 0.641 0.320 0.512 170.8 .......... step, studies were made on 0.520 0.260 0.506 170.6 25.0 28.0 .......... 0.228 24.5 27.0 0.456 0.498 170.1 .......... fixed beds of the fine par0.468 169.1 24.00 25.25 0.336 0.168 .......... 0.214 0.448 167.8 23.50 24.00 .......... 0.107 ticles in order to determine whether this condition could be calculated from the properties of the system. Figure 11 presents fixed bed data, for a single size of the glass particle sizes. The line representing the experimental data for bubbling air through water is shown on Figure 8. When spheres, as the pressure drop per unit length as a function of the plotted on this basis i t gives general agreement with the solid superficial gas velocity. The four curves shown are for different fluidization data. On the left-hand side the lines have a slope fraction voids, and these differences were obtained for the same of essentially 1; the lower lines correspond to the larger particles size particle by jarring the bed to give different degrees of packing. in which appreciable slugging was encountered] while the upper The pressure drop per unit of length is very sensitive to small changes in the fraction voids and this factor has been reported lines correspond t o the smaller diameters. At higher velocities by a number of previous investigators. Carman ( 1 ) correlated the data break away from the linear relationship and extrapolate data on the pressure drop in packed beds as a function of the approximately t o the condition obtained at high fraction voids with continuous fluidization. Experimentally i t was found velocity and found that the voids correction suggested by Koaeny t h a t the data presented in Figure 8 could be correlated by using the particle diameter to the 0.5 power (Figure 9). All the data fall close t o the line drawn, with the exception of the particles with a diameter of 0.0061 inch in the 2.5-inch diameter tube. The data for the particles of very small size and for the lightweight materials such as Aerocat microspheres and puffed rice d o not plot satisfactorily with the other data. The experimental points for these materials are shown in Figure 10 and, although the appearance of the curves is similar to that of Figure 8, the slope is less than 1 and at high velocities there is in some cases a n apparent division into two branches. The extrapolation of these data t o a value of e~ = 1 gives velocities much higher than those calculated for free settling of spheres of the same diameter, but the extrapolated values are in reasonable agreement with the continuous fluidization data. This graph also contains data for the “fluidization” of water. The quiescent height was taken as the height of the water at no gas flow and the incremental fraction voids was determined by observing the increase in the height of the water. The incremental velocity was the superficial velocity. 0 065 The data for water agree well with the data on the smaller size ( p 5 cvo- V d particles. Figure 9. Correlation for Batch Fluid ration of I n observing these tests it was noted that the motion of the Glass Spheres small and light-weight particles is gonsiderably different from the D p = inoher
Table 111.
Batch Fluidization of Glass Spheres in Air (Concluded)
- 2.
INDUSTRfAL AND ENGINEERING CHEMISTRY
1112
Vol. 41, No. 6
velocity on a logarithmic basis and the slope of the line is approximately 0 5. For hatches of solids containing mixtures of various diameters, an average diameter calculated in the manner suggested for Figure 5 gives satisfactory agreement. This weight fraction avcrage diameter was also employed by Carman in correlating his work on fixed beds. All the data on the fixed beds can be represented on a friction factor type oi plot corrected by the Kozeny factor. The data in this form are given in Figure 15. The Corrected friction factor is an inverse function of the Reynolds number over the entire range investigated. Thus the product of the friction factor and the voids correction is equal to 77 divided by the Reynolds number. The equation for this linc is consistent with the results of Figures 13 and 14 in that it indicates that the velocity is dircctly proportional to the diameter of the particles squared and to the first power of the pressure drop per unit of length. Figure 10.
Batch Fluidization of Light-Weight and Very Small Particles and of Water
--
01
02
03
04
05
06 07
.oa .OS.IO
Vo - SUPERFICIAL AIR VELOCITY-FJ/SEC
V, -SUPERFICIAL AIR VELOCITY-FT/SEC
Figure 11.
Air Pressure Drop through Fixed Beds of 0.0061-Inch Glass Spheres
(6) was satisfactory. This correct,ion involves the cube of the fraction voids divided by the square of 1 minus the fraction voids. The data of Figure 11 are shown in Figure 12 corrected on this basis to a fraction voids of 0.40. There is excellent agreement. Figure 13 is similar to Figure 12 but includes the data for five different sizes of glass spheres. I n each case the IZozeny correction was employed and the data were all put on a basis of 0.40 fraction voids. I n most cases the agreement is good. There is some scattering of the points for the particles of lower diameter, but even in this case the agreement is reasonable. The data of Figure 13 are cross-plotted in Figure 14 in order t o determine the diameter function. For a given value P / L the diameter correlates well with the superficial gas
__
Figure 12.
V,
Figure 13.
Data of Figure 11 Corrected with Koreny Function, V / ( 1 ET)^
-
- SUPERFICIAL
AJR V E L O C I T Y - F T / S E C
Air Pressure Drop through Fixed Beds of Glass Spheres
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
Figure 14. Relation between Particle Diameter and Velocity i n Fixed Beds of Glass Spheres
Rep =
Figure 15. K
c $
1113
OPVopt 7
Correlation for Fluid Flow through Fixed Beds of Glass Spheres
8 7
A
error. This discrepancy results from the fact t h a t mixtures of particles were correlated on the basis of a n average particle diameter, and a bed of uniform-diameter spheres equal to this average would have a n appreciably higher fraction voids than would the mixture of particles, as in the latter case there is the possibility that the smaller particles will fit into the voids of the larger particles. I n this latter case, i t is recommended t h a t Figure 15 be employed, using for E Q a fraction voids experimentally determined for loose packing of the solid mixture in question. In this manner, i t is possible to calculate a velocity t h a t oorresponds closely to the velocity, VQ,in a quiescent state, and, in other cases, this can be used as a simple approximation. In using these methods for the quiescent condition, the pressure drop per unit length for Figure 15 is taken equal t o the weight
- DENOTET BOUNDARY LlM/TS FOR SrEADY OPERATION
I
9 0
9
0
4
8
12
16
20
24
88
32
36
40
R - SOLID FEED RATE : LB. / S O FT-SEC
Figure
16.
Continuous Fluidization Glass Spheres
of
0.0016-Inch
Carman and Leva have employed similar correlations. The constant in the case of Carman's work with glass and steel spheres was 85 and in the case of Leva's work with "round sand" was 100. It is believed t h a t the differences in the constant are due to a shape factor for the particles. Figure 15 is a correlation of the friction factor as a function of the Reynolds number for conditions of fixed bed operation, and Figure 7 is a correlation of the friction factor as a function of the Reynolds number for fluidized conditions. I n these two correlations, the main variables are the velocity, particle diameter, pressure drop per unit length, and fraction voids. I n predicting the quiescent state, i t should be possible to utilize either relation. Either alone is usually not sufficient, because the designer would have only the diameter of the particles and the pressure drop per unit length, assumed in this case to be equal to the weight of the solid. Both correlations would still have velocity and fraction voids as unknowns. By employing the two correlations simultaneously i t is possible to solve for both factors. This method was found t o work satisfactorily for constantdiameter fractions of the glass spheres. For mixtures of different particle sizes i t gave fraction voids t h a t were appreciably in
R
Figure
17.
- SOL/D FEED
RATE
'
LB.
/ S Q FT-SEC
Continuous Fluidization Glass Spheres
of
0.004-Inch
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1114
Table IV. SO.
S-26
Batch Fluidization of Miscellaneous Solids w i t h Air
Bed Height, L , Inches Ft./Sec. Min. Max. 0.036 9.40 9.55 0,048 9.45 9.65 0.060 9.50 9.75 0.123 9 . 9 5 10.35 0.171 10.20 10.65 0,275 10.65 11.15 0.358 11.1 11.7 0.464 . . 12.6 0,648 14.5 11.25 11.30 0.045 0.054 11.35 11.50 0.102 11.75 12.00 0.139 12.00 12.50 0,174 12.40 12.80 0.212 12.50 13.15 0.253 12.60 13.55 0,302 14.1 13.0 0.358 14.6 13.7 0.432 15.6 14.0 0.515 16.3 14.5 0.589 17.0 14.5
vo,
Rum Run Constants Glass spheres Dp 0.0016 inch Tube diameter 2.5 inches LQ 9.26 inches VQ 0.005 ft./sec.
Run
P1
Lb./Sh. Ft.
.... ....
Aerocat microspheres Tube diameter 2 . 5 inches Lg 11.20 inches VQ 0.028 ft./SeC.
Table
V.
Ft./Sec. 0.668 0.762 0.842 0.960 1.12
Min.
L-16
Aerocat microspheres Tube diameter 4 5 inches Batch wt. 3.72 lb. LQ 11.2 inches Vg 0.028 ft./sec.
0.0668 0,0877 0.126 0,185 0.244 0.367 0.518 0.687 0.911
11.40 11.45 11.6 12.0
L-17
Puffed rice Tube diameter 4 . 5 inches LQ 15.1 inches VQ 1.58 f t . / S R C .
Batch Fluidization w i t h Air of Mixtures of Spherical Glass Particles
PI,Lb./ Sq. Ft. 114.6 172.8 195.6 220.4 138.3 28.49 76.75 136.6 190.6 186.9 189.0 190.4 191.6 193.2 198.1 202.7 201.9 214.9 71.08 100.6 126.6 184.1 60.67 104.3 144.9 181.7 229.9 227.0 224.7 220.1 218.9 217.1 216.6 213.6 210.8 72.16 109.2 155.3 182.9 42.13 62.97 91.77 121.5 173.3 105.0 205.1 204.1 203.4 201.9 201 0 199.9 32.45 21.60
12193 12.63 12.63 13.65 14.00 13.40 13.55 13.60 13.90 13.90 14.50 14.4 15.9 ... 18.1 . , . 20.5 . . 23.7 27.0 ... 30.5 . . . 33.2
51.76 76.22 106.9 106.7 105.0 107.2 107.6 107.8 108.3 108.3 108.F, 108.3 109.9 109.9
__
Kun No.
Run Constants S-ID Dp(av.) 0.0149 inch 0.0224 inch, 50% 0.0112 inch, 50% PB(av.) 149.5 lb./cu. Et. Tube diameter 2 . 5 inches Batch wt. 6.33 lb. LQ 24.6 inches VQ 0.30 ft./seO. €Q 0.394
3-18
s-21
L-la
D p ( a y . ) 0.008 inch 0.0224 inch 20% 0.0112 inch'ZO% 0.0061 inch' 60% PS(av.) 152.2 lb'./cu,ft. Tube diameter, 2 . 5 inchep Batch wt. 7 . 0 lb.
Dp(av.) 0.006 inch 0.0112 inch, 50% 0.0040 inch 6 0 % P s ( a v . ),153.5 lL./cu. ft. Tube diameter 2 . 5 inches Batch wt. 6.65 lb.
Dp(av.) 0.0078 inch 0.0224 inch, 16.7T' 0.0178 inch. 16.7%; 0.0112 inch, 25.0% 0 0061 inch, 16 G% 0 0040 inch, 25.0% Ps(av.) 153 Ib./cu. ft. Tube diameter 4 . 5 inchpa Batch wt. 12 lb. Lg 13.23 inches VQ 0.085 ft./sec. eQ 0.3554
VO
Ft./S& 0.174 0.262 0.299 0.794 0.216 0.0528 0.141 0.286 0.357 0.409 0.431 0.453 0.577 0.488 0.528 0.560 0.603 0.703 0.0270 0.0384 0.0478 0.0687 0.0263 0.0454 0.0605 0,0773 0,599 0.555 0.494 0.403 0.330 0.286 0.253 0.215 0.191 0.0133 0,0202 0.0281 0.0329 0.0117 0.0160 0.0232 0.0304 0,0474 0.414 0.372 0.323 0.267 0.219 0.175 0.141 0.0170 0.0116
....
0.0269 0.0406 0,0582 0.163 0.115 0.146 0.247 0.381 0.510 0.708 0.921 1.18 1.44 1.72
...
I . .
~
I
.
.
....
Rep 1.35 2.02 2.31 6.12 1.66 0.408 1.09 1.98 2.76 3.16 3.32 3.49 3.68 3.76 4.07 4.25 4.57 5.33
0.110 0.157 0.195 0.280 0.107 0.185 0.247 0.315 2.44 2.26 2.01 1.64 1.34 1.17 1.03 0.879 0.777 0.0410 0.0623 0 0867 0.101 0.0360 0.0493 0 0715 0 0937 0.146 1.28 1.15 0.997 0 825 0.677 0 541 0.435 0.0660 0.0450
....
0.104 0.158 0.226 ,
.. ,
,..
... , ,
Bed Height, L , Inches PI, Max. Lb./Sq. Ft. .. . 18.0 .. 18.75 .. 19.75 . . 21.3 ,. , 23.5 ....
R u n Constants Aerocat microspheres Tube diameter 2.6 inches LQ 11.20 inches VQ 0.028 ft./SeC.
~
Bed Height, L , Inches -, Extrapolated Min. 31ax. pressure 23.40 ... 23.40 ... 23.40 28.5 36.0 30.0 23.40 24.19 24.19 24.19 24.19 ... 24.9 25.2 25.0 25.2 25.0 25.5 25.3 26.0 25.5 25.8 25.6 26.5 26.1 25.6 26.8 26.5 26.0 28.0 26.5 26.5 28.8 27.5 26.7 29.7 27.0 32.5 28.4 25.10 26.10 ,.. 25 10 25.10 25.68 25 68 26.68 25.68 ... 35.5 47.5 38.2 35.2 45.0 37.9 36.3 34 5 42.2 34.0 33.0 39.0 32.5 32.0 35.5 31.6 30.5 33.2 29.8 29.5 32.2 29.2 29.0 30.2 28 25 29.25 28.68 22.44 ... 22.74 22.74 22.74 24.03 24.03 24.03 24.03 . , 24.03 33: 4 33.5 39.0 32.5 38.0 33.1 32.0 31.5 35.7 30.0 34.0 30.6 28.5 31.2 29.3 27.8 27.5 29.2 26.75 27.75 2 6 . 8 12.63 12.63
Ve,
No. 5-30
..
s-30
Vol. 41, No. 6
,
., . . .. , . . ... ... ....
. . .,
f" n
fF
606 339 294
,,
~.402 ..
1330 410 271 194
....
..., .. .. , . .,
".
ii8 .. . . .. 56; 51 464 445
,... , . . .
...,
6640 4670 3760 2B6O 7130 3230 2530 1940
..., .. .
. .. . .. ,
,
., . . ..,, .... ..., . ~. ,
22,600 15,000 11,100 9,500 16,000 12,900 9,060 7,040 4,110
. .
.... 14,900 29,700
1o;ioo 6,560 4,320
21
., ~,
iii4 191 242 362 541 719 920 1270 1620
255 315 420 615 912 1430 2210
2.09 1.94 1.83 1.78 1.69
..
...
...
.. .. ..
... . .. . ..
... ,
.. ."
11.55 11.90 12.1 12.7 13 .O 13.8 14.2 15.4 16.7 22.7 21.0 19.5 18.3 16.9
31.67 31.93 32.35 32.61 32.76 32.76 32.92 32.92 33.23 ..,.
.... .... ..., ....
of solid per unit area per unit length, and this would be equal t o the absolute density of the solid multiplied by 1 minus the fraction voids. Thus the pressure drop per unit length can be replaced in these correlations by that factor. On the basis of the work that has been presented, there are two methods of predicting the operating conditions in a fluidized bed. Assume t h a t a given solid is t o be fluidized with a given fluid; thus, the diameter or diameter distribution, the absolute density of the solid, and the physical properties of the solid would be known. I n the case of the correlation given in Figure 7, i t would then be possible t o calculate the fraction voids and, therefore, the fluidized density of the solid at any superficial velocity desired. The alternative procedure would be t o employ Figures 7 and 15 simultaneously t o obtain the fraction voids and velocity corresponding t o the quiescent state, which would then he utilized with Figure 9 to estimate the fraction voids as a function of the fluidizing velocity.
In both cases, the greatest error will be involved with the solids of sinall particle size, but the second procedure gives more satisfactory results in such cases than the first, and it is believed to be preferable l o the other procBedure. Continuous Fluidization. I n the case of continuous fluidization, the action is different, because both pomder and gas arc being continuously transported through the unit. I n such expcriments, it was found that with a given gas velocity a fairly wide range of solid feed rates could be utilized and that the concentration of the solid obtained in the fluidized bed was a function of this feed rate. However, as the solid feed rate was increased for a given gas velocity, a condition n a s reached a t which unsteady operation was obtained. 'Instead of obtaining a steady-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
June 1949
b 6
3
k
T " $ 2 0
e
4
Figure
18.
12
16
- SOLID FEED
R
Continuous
eo z4 ca 32 36 RATE : LE. /SQ. FT-SEC.
of
Fluidization
Glass Spheres
40
0.0112-Inch
1115
state condition, the solid concentration in the fluidizing unit continually increased until the bed was of very high density. There would then be a sudden surge which would blow most of this solid out of the unit and the cycle would be repeated. Figures 16, 17, and 18 show the data plotted as the average solid density, p B , within the fluidized bed as a function of the solid feed rate, R, pounds per square foot per second, for different superficial gas velocities. The approximate boundaries of the steady and unsteady operation are shown. I n the steady-state region the experimental conditions could be maintained for a long time without any significant variations. I n general, the concentration of solid within the unit is roughly proportional to the solid feed rate a t a given gas velocity, and the density for a given solid feed rate decreases with increasing fluid velocity. In all cases, the bulk densities obtained for a given solid are lower than those for batch fluidization. Another method of presenting the same data is shown in Figure 19, in which the linear velocity of the gas is plotted against the solid feed rate for the limiting conditions. As the solid feed rate is decreased, the density in the bed decreases, and i t might be expected that the data would extrapolate back to essentially the free-falling velocity. For the two particles of larger size, this is approximately true but in the case of the small particles the data indicate an extrapolated velocity higher than the freefalling velocity. This same condition is apparent in Figures 20, 21, and 22, in which the slip velocity is plotted as a function of the solid feed rate, and data for various linear gas velocities are shown. I n calculating the slir, velocities, i t is necessary to have a value for the average velocity of the solid. For the data presented in these figures and used elsewhere in this article, the average velocity of the solid, V8, has been calculated by dividing the solid feed rate by the density of the solid within the fluidized bed. I n most cases there is a considerable scattering of the data, largely due to the fact %hat the method of calculating the slip velocity is sensitive. For a given particle size, there does not appear to be any general trend over the region investigated; this indicates that slip velocity is essentially independent of gas velocity and solid feed rate. This observation was previously made by Walker and other investigators. When these slip velocities are compared with the predicted free-falling velocities, it is found that the agreement is good 36 for the larger particles b u t that the smaller particles I
4
0
-
I6
I2
8
R
24
ce
/ S O FT
- SEC.
co
SOLID FEED RATE : LE.
32
have much higher values than those predicted. This is in agreement with the data obtained in batch fluidisation. This result is shown graphically in Figure 23, in which the slip calculated on the basis of the experimental results divided by the predicted slip is plotted against the particle diameter. For particles of diameters of 0.01
Boundary Conditions for Steady-State Continuous Fluidization of Glass Spheres
Figure 19.
6
6
5
-
4
k\ k
6
k
$ 3
-
4
1y
10
I
L
"
3 d
2
2
3
II
s
I 0
32 o
4
a
12
16
20
24
za
I 3c
3s
4
0
Figure 20.
Continuous Fluidization Glass Spheres
of 0.0016-Inch
6
4
R-SOLID frm RAE : LB. / S Q . F T -SEC.
R
Figure 21.
I2
I6
20
- SOLID FEED RATE
24
26
32
36
40
:LE. / S Q . F7: /SEC.
Continubus Fluidization of 0.004-Inch Glass Spheres
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1116 Table VI.
Run
B u n Constants
So.
6-31 Tube diameter 2 . 5 inches L g 12.85 inches Temp. 85’ F.
6-32
Tube diameter 2 . 5 inches LQ 24.90 inchec, Temp. 85’ F.
Table VII. Run
No. 7-C
R u n Constants D p 0.0178 inch DT 2 . 5 inches i’s 157 lh./cu. it. Ratch wt. 2 lb.
L,
b iFed ght,
Vu, Ft./Sec.
Inches, Max.
Run
0.597 0.372 0.205 0.166 0.112 0.0560 0.0443 0.0368 0,0289 0.0240 0.0117 1.09 0.935 0.752 0.630 2.76 2.49 2.22 1.91 1.60 1.39 1.08
17.25 16.25 15.00 14.75 14.40 13.65 13.40 13.30 13.20 13.10 12.95 19.B 19.0 18.0 17.5 27.0 25.5 24.5 23.5 22.2 21.n 20.25
L-19
1.58 1.33 1.11 0.945 0.793 0.694 0.583 0.465 0.306 0.191 0.0980 0.0320 0.0140 0.0070
40.5 39.2 37.5 36.0 35.5 34.5 32.5 31.5 29.5 28.0 26.75 25.50 25.15 25.00
R u n Constants
No.
L-20
Tube diameter inches L g 10.45 inches Temp. 94’ F.
Tube diameter inches Lg 23.03 inches Temp. 94’ F.
4.5
4.6
Ft./Sec. 0,0112 0,0155 0.0226 0.0308 0,0383
0,0689 0,0837 0,0935 0.101 0,00799 0,0156 0,0313 0,0466 0,0490 0,0619 0.00156 0,00277 0.00386 0.00523 0,00769 0,0104 0,0133 0,0184 0.0187
U p 0.0112 inch
0 2 ’ 2 . 5 inches #,Y 152 ib./cu. f t . Batch WL. 2 lb.
11-C U p 0.0061 inch DT 2 . 5 inches ps 153 lh./cu. f t Batch wt. 2 lh.
Vo,
Inches, Max.
0.0140 0.0280 0.0450 0.0630 O.OS60 0.120 0.169 0.226 0.277 0.384
10.65 10.90 11.05 11.25 11.45 11.73 12.25 12.50 13.25 14.50
0.503 0.623 0.768 0.949 1.10 1.21
15.50 16.25 16.75 17.25 17.75 18.60
0.0120 0.0240 0.0520 0.0820
23.30 23.45 24.00 24.50 25.20 26.10 26 85 27.30 29.25 30.75 32.0 34.0 35.2
0.121
NOMENCLATURE
D, DT
diamet,er of particle diameter of tube friction factor for fixed bed,
fs
= = =
j , ~
4(dimensionless). 2 (7 = friction factor for fluidized bed,
jb
=
v;
%?’(d
‘ C.
eT
17.0 18.0 17.5 16.0 15.8 l5,3 15.2 15.2 15.1 15.1 15.0 17.9 17.0 17.9 18.1 18.1 17.0 21.0 20.2 19.8 19.8 18.8 18.6 18.5 18.1 18.1
0.432 0.487 0.528 0.574 0.614 0.850 0.715 0.745 0,794 0.817 0,845 0.503 0.607 0,724 0.812 0.814 0,889 0,447 0,517 0,556 0.599 0.626 0,703 0,750 0.824 0.830
U-V,=84/
L,
Ft./Soc.
0.167 0.222 0.248 0.394 0.533 0.703 0.963 1.07
Batch Fluidization w i t h Water Vu. Temp.,
0,0458 0,0624
9-D
inch or greater the value of the ratio is essentially 1, indicating that the calculated and predicted velocities are eesentially equal. However, with the sinall particles-for example, 0.0016inch diameter-the calculated velocity ie almost seven times t h a t predicted. The relationship given by Figure 23 should be useful in predicting the performance for continuous and steady fluidization. The ratio given by thie plot plus the assumption t h a t the slip velocity is constant for particles of uniform diamet,er allows the solid density in the unit t o be estimated as a function of t,he feed rates,
Batch Fluidization, Water w i t h Air Height, Bed
Vol. 41, Ne. 6
9
I,,,,
Kelr
. f ,
769 1.41 404 2.01 190 2.89 103 3.76 66.4 4.73 5.57 46.1 24.8 7.52 20.4 8.30 13.8 10.1 11.0 11.3 9 . 5 5 11.8 0 . 652 901 235 1.25 58.6 2.56 26.5 3.82 24.0 4.02 4.94 15.0 13,000 0.0719 4 130 0.130 ‘2:130 0.180 1,160 0.244 0.350 534 0.489 294 0.59s 180 0.819 93.5 90.5 0.833
Lp Lg
R Re, VE VQ
V, Vu PI’
(dimensionless) 3VtPj friction factor for single freefalling spheres (dimensionless)
acceleration of gravity maximum fluidized bed height, = extrapolated pressure = bed height under quiescent quicksand condiLionp = solid feed rate, lh./sq. ft.-sec. = Reynolds number of part,icle,DpT’gpJpf (dimensionless) = incremental gas velocity, I’o - V Q !feet per second = superficial gas velocity under quiescent quicksa,nd conditions, feet. per second = average solid velocity, R / ~ B feet , per second = average superficial fluid sTelocitg, feet per second = ovei,-all pressure drop, pounds per square foot = =
fT/SEC
I I ~1 ~
~
0 1
0
2
4
6
R
Figure 22.
- SOL/D
8
IO
FEED RATE
I2
,
14
LE
16
I8
20
/ S Q FT - S K
Continuous Fluidization of 0.0112-Inch Glass Spheres
22
I
0 0/
0 001
1
0 05
Dp ,INCH Figure 23. Effect of Particle Diameter i n Continuous Fluidization of Glass Spheres
I N D U S T R I A L A N D EN G I N E E R I N G C H E M I S T R Y
June 1949
Table VIII.
Vo, ft./sec.
3 92 5.5u 6 85 4.11 5.80 6.55 6.99 6.99 6.95 6.95 6.95 5.99 3.99 6.09
5.99 8.29 8.29 8.29 8.29 8.29
13.6 13.6 13.6 13.6 13.6 13.6 10.8 10.8 10.8 10.8 10.8 8.11 8.11 8.11
Continuous Fluidization w i t h Air of Glass Spheres
Run (3-7, Dp 0,0016 InchB , €2, Slip, lb./sq. Ib./ ft./sec. ft./scc. ru. f t . 1 02 2.56 5.81 2.04 4.75 5.18 5.93 4.88 3.54 2.26 1.20 4.90 3.04 2.28 0.75 4.37 3.76 3.05 2.22 1.22
1.98 8.91 23.3 3.93 13.2 19.2 25.2 20.7 16.1 10.7 5.88 19.3 11.9 5.74 2.90 26.4 22.8 17.8 13.0 6.41
1.98 2.49 2.84 2.18 3.02 2.84 2.72 2.73 2.42 2.24 2.07 2.06 2.09 3.48 2.05 3.62 2.93 3.09 2.66 2.86
Vo, Ft./Sec. 8.11 8.11 .?.?I J , a1
5.51 5.51 7.90 7 87 7,5,5 7.08 5.58 5.11 7.01 5.48 5.56
VO Ft./S)ec. 9.67 .oh 9.26 8.84 8.24 Slip, 8.01 ft./sec. 8.16 3.1 7.57 13.42 2.9 13.42 4.2 13.42 5.6 13,42 5.6 5 .2 10 88 10.88 4.1 10.88 4.6 10.88 4.2 4.5 8.41 4.5 8.41 3.7 8.41 4.0 8.41 4.2 8.41
D, 0,0040 I n c h __
PB, Ib./ cu. f t .
2,56 1.42 5.04 3.99 2,99 1.24 9.71 9.19 8.98 9.71 8.51 1.36 7.49 3.51 6.02
R,
lb./sq. Slip, ft./sec. ft./sec. 11.4 3.7 3.7 6.29 4.2 6.74 5.57 4.1 3.9 4.95 3.3 2.72 4.6 32.4 4.6 30.1 26.4 4 6 19.9 .5 0 5.36 4.9 1.88 3.7 4.2 20.9 4.09 4.3 7.51 4.3 I
Run C-8,
D p 0.0112 Inch PB.
cA!L. 15.3 15.7 16.5
19.8 6.39 14.0 5.66 5.19 3.89 2.94 2.09 9.57 9.47 5.26 3 24 1.13 3 00 8.94 12 4 14 8
R,
Ib./sq. ft./sec. 27.0 20.7 19.0 12.1 1.88 5.18 1.67 27.0 20.8 16.1 11.3 26.3 18.7 12.8 10.1 1.63 2.43 3.39 4.40 8.57
l P / L = pressure drop per unit length, Ib./sq. ft.-ft. = incremental fraction voids, 1 - LQ/L,,, (dimensionless) = total fraction voids under quiescent quicksand condie~ tions (dimensionless) = average total fraction voids (dimensionless) (T = viscosity of fluid = average solid concentration, pounds per cubic foot OB pf = density of fluid = absolute solid density, pounds per cubic foot PS BE
Run C-6 ( C o n l d . ) ,
--
111’1
Slip, ft./sec
7.91 7.95 7.65 7.63 7.72 7.79 7.28 8.22 8.07 7.94 7.99 8.13 8.38 8.45 7.76 6.97 7.60 8.03 8.06 7.83
LITERATURE CITED
(1) Carman, P. C., Trans. I n s t . Chem. Engrs. (London), 15, 150
(1937). (2) Chambers, J. M., S.M. thesis in chemical engineering, Massa-
chusetts Institute of Technology, 1939. (3) Conners, J. A., and Fuchs, W. J., S.M. thesis in chemical engineering, Massachusetts Institute of Technology, 1944. (4) Friend, L., Chem. Eng. Progress, 44, No. 3, 218 (1948): (discussion on paper of Wilhelm and Kwauk) ( 5 ) Hettich, B. V., and Kean, A. M., Jr., S.M.thesis in chemical engineering, Massachusetts Institute of Technology. 1943. (6) Koseny, J., Ber. W i e n Akad., 136a, 271 (1927). (7) Leva, M., Grummer, M., Weintraub, M., and Pollchik, M., Chem. Eng. Progress, 44, No. 7, 511 (1948). (8) Rotzler, R. W., S.M. thesis in chemical engineering, Massachusetts Institute of Technology, 1940. (9) Walker, S. W., Ibid., 1940. (10) Walker, W. H., Lewis, W. K., McAdams, W. H., and Gilliland, E. R., “Principles of Chemical Engineering,” 3rd ed.. p. 296, New York, McGraw-Hill Book Co., 1937. (1 1) Wilhelm, R. H., and Kwauk, M., Chem. Eng. Progress. 44, No. 3, 201 (1948).
.
RECBIVFJD January 19, 1949.
Fluidization of Granular Solids Fluid Mechanics and Quality A t t e m p t s t o correlate published data on fluid flow i n fluidized-solid beds have resulted in a n improved understanding of t h e mechanism of fluidization. Observed differences between fluid flow i n fixed and fluidized beds are explained in terms of t h e flocculation of small particles, kinetic energy losses from turbulent motion of large particles, and t h e inherent instability of gas-fluidized systems. T h e dependence of fluidized-solid reactor performance upon quality of fluidization (uniformity of t h e dispersion of fluid and particles) is emphasized.
ROLL1 N D.MORSE, E N G I N E E R I N G
RESEARCH LABORATORY,
E. I . D U P O N T D E N E M O U R S & C O M P A N Y , I N C . , W I L M I N G T O N . DEL.
T
HE present high cost of buildings and equipment makes imperative design of new reaction equipment to secure maximum conversion and yield. The factors that must be controlled in order to secure such good performance are reasonably well understood for fixed-bed reactors. Even temperature distribution is amenable t o calculation if sufficient data are available. The situation in the boiling bed reactor is more complex because of the boiling action. Conversion, defined as the fraction of a specified feed material that reacts, measures the over-all, effect of all the reactions that take place. Yield, defined as the fraction converted into specified products, when compared with conversion, measures the balance between desirable and undesirable reactions. I n many reaction systems a complex network of parallel and consecutive reactions
is possible, so that optimum performance requires consideration of many factors. One of the most important factors is that of Uniformity of treatment, for a by-product once formed because of a deviation from optimum conditions cannot normally be recovered by a subsequent opposite deviation. The result is t h a t in such complex systems (and they constitute the majority of systems in practice) any deviation from the optimum conditions causes a lowering of reactor performance. The fluidized-solid bed has been acclaimed as a reaction bed where uniform reaction conditions are secured. -4ctually, however, the irregular boiling action makes conditions in the boiling bed less uniform in many respects than in the fixed bed. The main advantage still is the one originally claimed-the great reduction in the duration of hot spots because of the mixing.
