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 Slip, 8.24 ft./sec. 8.01 8.16 3.1 7.57 13.42 2.9 13.42 4.2 13.42 5.6 5.6 13,42 5 .2 10 88 4.1 10.88 4.6 10.88 4.2 10.88 8.41 4.5 8.41 4.5 3.7 8.41 8.41 4.0 8.41 4.2
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 6.29 3.7 4.2 6.74 5.57 4.1 4.95 3.9 2.72 3.3 32.4 4.6 30.1 4.6 4 6 26.4 .5 0 19.9 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.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1118
Vol. 41, No. 6
QUALITY OF FLUIDIZATION
Quality of fluidization is defined to mean the uniformity of particle dispersion and the uniformity of gas velocity in a boiling bed. The more uniform are these factors, the higher is the quality of fluidization. The water-fluidized beds of sand approach perfect quality. The bed t h a t slugs or channels badly is at the other extreme of quality. The bed in which the gas pockets remain small and well distributed, with a steady, even, over-all boiling of the bed, is intermediate in uniformity, but perhaps optimum in the balance between uniformity and the requirement of mixing and boiling in order t o control temperature. Most materials fluidized with gases observed by the author appear t o be a t the low end of the quality range. I n most fluidized beds the treatment is far from uniform, and the quality is correspondingly affected. At least three effects are possible because of the nonuniform treatment. (1) The time of contact of t h e gas in the pockets is less than t h a t of t h e gas within the clumps. ( 2 ) T h e amount of particle surface available t o the gas is much more in the clumps than in the pockets. And (3), when several types of reaction are possible, the gas t h a t passes initially through pockets can react differently than the gas t h a t has adequate contact surface initially available. Because a boiling bed is produced by agitation of the particles in a rising fluid stream, i t should be possible to describe its action quantitatively by the usual parameters of fluid flow, such as pressure drop, length of flow path, cross section of path, amount of contact surface and its roughness, fluid velocity, density, and viscosity, with the addition of factors t o take into account the special characteristics of the small moving particles. Fortunately, a large amount of basic work has been done in connection with the flow of liquids through fixed beds.
(4)
For nonspherical particles, he introduced the factor following manner:
Inspection will show t h a t
+$
in the
may be defined as
+3 --5% qb8 is, therefore, unity for a sphere, and because a sphere has minimum specific surface, is less than unity for all other shapes. Carman's table of the values of + 8 for various materials is reproduced as Table I.
Table I . Material Sand, average Flint sand Flint sand Ottawa sand Sand Sand
Cork
Pulveriaed coal Natural coal dust Flue dust Flue dust Mica Fusain
Values of Nature of Grain
0
. .. . .
Jagged.
0.75 .65
~
Jagged flakes, Nearly spherical Angular Rounded
.....~._.. " . . . .. . .. .. . .
. ..
0.43
0.95
0.70-0.78 0.83 0.69
Up t o 3/8 inch Fused, aggregates Fused, spherical Flakes
0.28 0.38
~
..........
FLUID FLOW I N A FIXED BED
Of the large volume of work on fluid flow in fixed beds (1-3; 5-10, I S , 15, 16), t h a t by Carman ( 4 ) has been found most useful for application t o the fluidized bed. Carman reviewed the work of Blake ( I ) , Kozeny (7), and others, demonstrated the general applicability of Blake's method of dimensional analysis, and, for the special case of streamline Row, its reduction to the form which Kozeny derived independently from permeability measurements. Carman assembled the available data, demonstrating how well most of the data correlate.
Carman's correlating curve is drawn on most of the attached figures. Several more useful forms of Carman's equation are:
1. For the streamline flow region, where
(7:
Blake's equation is: 2.
For the turbulent flow region, where -\'R~,C
> 100
Carman's correlation of the d a t a shoffed t h a t for streamline fl 0vi
Kozeny had arrived a t this same equation, starting with the assumption t h a t the granular bed is equivalent to a group of parallel, similar channels, such t h a t the total internal surface and the total internal volume are equal to the particle surface and the pore volume, respectively, in the bed itself. H e assumed further t h a t the tortuous passage is longer than the depth of the bed, and the channel velocitv correspondingly higher than if a straight vertical channel existed. For the region of turbulent floiv, 6 ( G / p a > loo), Carman found that
For spheres, Carman transformed sptlcific surface to particle diameter by the use of the following geometrical relationship:
I n the correlations for spherical particles, the only serious deviations found by Carman were for large lead shot at high Reynolds numbers, where the pressure drops were about twice those expected. This deviation is not surprising, because the Blake dimensional-analysis correlation was not intended t o apply for large values of the Reynolds number. However, the curve correlates with the data for wire spirals and Berl saddles, which are not only nonspherical but also of different orders of size and porosity. For rings, on the other hand, the correlating curve starts in coincidence with Carman's general curve, but with increase of Reynolds number does not drop as rapidly, indicating a higher pressure drop for the rings (or hollow particles) than for solid particles a t the same Reynolds number. Carman ascribed this effect to the eddy currents and dead spaces within the rings.
June 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY DESCRIPTION OF THE BOILING BED
Consider a bed of granular particles through which a stream of gas is slowly flowing upward. Friction produces a pressure drop which increases with velocit in a manner expressed by the Carman-Kozeny fixed-bed correztion. Finally, as the velocity is increased, a point is reached where the pressure drop becomes equal to the sum of the weight of the bed per unit of cross-sectional area plus the friction of the bed against the walls. When this point is reached, one of two things may happen: either the bed expands and assumes a more open arrangement, so t h a t the gas can flow without the pressure drop exceeding the unit bed weight, or the entire bed is lifted by the gas stream and rises like a piston. This alternative occurs with materials that are not free-flowing and can, therefore, form an arch from wall to wall. I n the majority of cases the arch will break away, and the underside will fall down in clumps, or aggregates. If the clumps fall so as t o form a n open stable channel of sufficient size, most of the gas will flow through this channel, and although the bed has expanded its expansion will be far from uniform. With a further increase in gas velocity, the pores and channels enlarge and the particles become more widely separated. For free-flowing materials the pore spaces eventually become so large that no stable arrangement can exist, and the particles vibrate or circulate locally, in a semistable arrangement; this is the point at which fluidization begins, forming the quiescent fluidized bed. Another increment of velocity results in over-all circulation of the bed, often with transient gas streams flowing upward in channels t h a t contain relatively few particles and with clumps of particles flowing downward. T h e type of fluidization described above has been called “aggregative” by Wilhelm and Kwauk ( 1 7 ) . A variant of aggregative fluidization is the phenomenon known as slugging. I n vessels of small diameter many materials show a tendency t o slug when fluidized-that is, the gas pocket grows until its diameter is equal to t h a t of t h e vessel, and then i t pushes ahead of itself a slug of the material. During this time the underside of the arch is continuously breaking away, the various-sized pieces falling out until the slug decomposes entirely and the gas pocket moves u p by flow of its contents past the falling clumps. When a liquid instead of a gas is used t o fluidize a material, t h e individual particles remain comparatively well dispersed throughout the fluid. T h e fluid rises at relatively uniform velocity throughout the cross section. The turbulence is primarily finegrained and local, showing much less general circulation of the bed than in the previous cases. This type of fluidization Wilhelm and Kwauk have termed “particulate.” The basic difference between the above-mentioned gas- and liquid-fluidized beds is one of degree of segregation of the particles from the fluid. The other differences observed are believed t o arise from the difference in degree of segregation. A highly segregated bed contains comparatively long channels and large clumps of only slightly separated particles. The fluid rushing through the channels tears particles from the lower clumps and deposits the particles at subsequent low-velocity pockets or a t the surface of the bed. The upper clumps descend as the lower ones are torn apart, thereby completing t h e circulation path of the bed. I n the bed of slight segregation, on the other hand, t h e channels are small, short, and well distributed throughout the bed; the particles in the surrounding clumps are separated from one another to such a n extent t h a t the path of flow through the clumps is not much higher in resistance than the path through the channels; therefore, the fluid flow is more uniformly distributed, the range of velocities is much smaller, and the particle circulation is primarily local. These differences are of degree only-both situations commonly occur simultaneously, but in the case of aggregative fluidization the first situation predominates, and in the case of particulate fluidization the latter situation predominates. Both situations can be referred t o a common basis, the degree of segregation. The degree of segregation is the result of a dynamic balance between two tendencies: (1) the segregation tendency, or rate of separation of fluid from particles, and ( 2 ) the re-
1119
mixing tendency, or rate of gravity flow of particles into fluid pockets. T h e remixing tendency is a function of the so-called “freeflow” quality of the particles, and would be expected t o be related t o their angle of repose. Further work is required t o relate these properties. The segregation tendency is inherent in any fluidized bed, and varies with t h e properties of the fluid and particles and the shape of t h e containing vessel. A bed of free-flowing particles, with a high segregation rate, will exhibit predominantly aggregative fluidization, but with a low segregation rate will exhibit mainly particulate fluidization. T h e rate of segregation is a fluid flow problem and can be related t o the physical properties of the components by application of the Carman-Kozeny correlation to t h e segregation taking place between two small adjacent zones in a fluidized bed.
It will be assumed t h a t the rate of segregation is small enough t o fall in the viscous flow range, thereby permitting the use of Equation 7:
(7) in which c3 is the fraction of voids in the flow path from zone t o zone and L1 is the length of this flow path. For the present purpose, evaluation of e3 and LI is unnecessary. A p can be related t o the differing concentrations of particles above the two zones and reduced algebraically t o the following form: Ap =
L/(Ps- P F ) ( E Z - €1)
(11)
in which Lf is the height of fluidized bed above the two zones under consideration, and €1 and €2 are the fractions void in the columns above the two zones. Substituting this expression in Equation 7 , the following form is obtained:
From this equation several useful conclusions can be drawn: The segregation tendency is inherent in any fluidized bed qnd is self-accelerating. This conclusion is drawn from the dependence of uo on € 2 - e l . As segregation proceeds, €2 increases and el decreases; consequently their difference increases also, and thereby the segregation rate, U O ,increases. The limit is reached if becomes 1.0 and € 1 becomes the voidage of the settled bed; when this situation exists, stable channels pass through a stagnant bed, and segregation has proceeded t o completion. This situation normally occurs only with materials which are not “fluent.” The segregation rate is greatest at the bottom of the bed, as IL@ is proportional to Lf. As a corollary, deeper beds exhibit greater segregation and correspondingly poorer quality of fluidization. Liquid-fluidized beds have much smaller segregation rates than gas-fluidized beds, because of the roughly 50-fold higher viscosity and the smaller density difference. This is believed to be the principal reason for particulate fluidization in Wilhelm and Kwauk’s water-fluidized beds and aggregative fluidization of the air-fluidized beds. High-density articles have correspondingly high segregation rates. As a corofiary, decreasing the effective particle density by using hollow or vesicular particles, or by using porous flow, should decrease the segregation rate. The smaller the particle, the larger is its specific surface, and consequently, the smaller its segregation rate. Unfortunately, decrease of particle size is often accompanied by decrease in the fluency of a powder, which may offset the advantage of lower segregation rate. GENERALIZED FLUID FLOW I N A FLUIDIZED-SOLID BED
Quantitative information on fluid flow in the fluidized-solid bed is scarce. T h e only extensive published investigations are those by Wilhelm arid Kwauk ( 1?), Leva and associates ( 11, 1d ) , and Parent, Yagol, and Steiner (14). Work of Leva. Leva worked with round and with sharp sands in the range of 0.002- to 0.015-inch diameter (270 t o 35 mesh) us-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1120
MODIFIED R E Y N O L D S N J M E E R
Figure 1.
=
m
P
-
(1-6)~
As all the other terms on the right-hand side are assumed to be constant, m = 1.0 if the fluidized bed folloivs Carman’s equation. Leva correlated his data on the basis of Equation 3 7 and conclusions must, therefore, originate with it. Leva found that m v a s as large as 4.5 for bhe smallest particles (0.002 inch), decreasing gradually as particle size increased, and did not reach 1.0 until the particle size reached 0.016 inch, the largest size studied. Inspection of Equation 17 indicates that values for na above 1.0 require correspondingly higher values for velocity than would be required by Carman’s equation. From this fact and his data, Leva concludes that the smaller particles require an extra amount of energy for fluidization. H e terms the ratio of this “extra energy” t,o the total energy supplied the “fluidization efficiency” and correlates i t with particle size. Fluidization efficiency is then zero when no extra energy is required over t h a t calculated from Carman’s equation and increases as exponent m increases. Leva’s term “fluidization eficiency’’ may be misleading, as the most efficient operation would be that in which no energy is required in excess of that indicated by Carman’s equation. A better term might be “deviation factor,” signifying the deviation from Carman’s equation and defined as the difference between the actual velocity and that called for by Equation 8, divided by the actual velocity. Work of Wilhelm and Kwauk. In a comprehensive investigation, Wilhelm and Kwaulr (17‘) studied the fluidization characteristics of sand, glass beads, lead shot, crushed stone, and Socony cat,alyst beads, over a particle size range of 0.011 t o 0.21 inch. Columns of 3- and 6-inch diameter were used. (Column size and drpt,h of bed were found to beunimportant.) In addition t o air, water T ~ Salso used as a fluidizing medium. I n correlating their data, ITilhelm and Kwauk chose to use four dimensionless groups. us shown by the following equations:
6G
Fluidized Beds
Leva, and Wilhelm and Kwauk data
MODIFIED R E Y N O L D S
Figure 2.
NUMBER
-8%
( 1 - 6 )P
‘60 NU
,TI..
__= - DpG Ir
Re,C
(1 -
€)/4#J,
(18)
Leva’s U n i f o r m Round Sands
ing 2.5- and 4-inch columns. His sands were studied as narrov size cuts and also as mixtures of widely distributrd sizes. His gases were air, carbon dioxide, and helium. Various bed depths were used. Leva’s correlation vas based on Calman’s equation for laminar flow, modified by assuming a constant pressure drop for the fluidized bed, and rearranged in the following steps:
For the fluidized bed, L !vas replaced by Lj.
or
Vol. 41, No. 6
The term K a p is essent,ially the product of a friction factor and the square of a Reynolds number. By choosing this combination of functions, the velocity or flow rate term is eliminated. The friction factor and Reynolds number as defined by Wilhelm itnd Kwauk are identical with the corresponding terms used by Carman, except that ITilhelrn and Kwauk left out all voidage terms and shape factors. K a p is the same as K a p ,wit,h the weight of the bed per unit of bed area substituted for the pressure drop. The effect of voids is later included as parametric curves in plots of Kap and Kap against the Reynolds number. PF is related to Wilhelm and Kwauk noted t,hat, ( P s - P F ) 2G2 the drag coefficient, the only difference being the numerical factorwhich in the drag coefficient is 4 / 3 instead of 1/2. In their experiments on fluidization lvith water, available drag coefficient relationships mere used to calculate the points for 100% voids on the curve of Xap os. Reynolds number. Wilhelm and Kwauk noted an important difference between fluidization with water and fluidization with air. I n the former
reference to Figures 2 to 4 shows. In all cases except the largest particles, the data fall on straight lines with a considerably larger negative slope than the Carman-Kozeny line (slope = - 1 a t low Reynolds numbers). I n Figure 2 the data for uniformly sized round sands are presented and, in Figure 3, for uniformly sized
The minor differences may well be due to wrongly assumed values (0.70 for sharp sands, 0.82 for uniform for the shape factors, and mixed sizes of round sands). Nearly all the data obtained by Leva indicate lower friction factors than for the corresponding fixed bed of the same voidage. In other words, the pressure drop through the fluidized bed is smaller than through the corresponding fixed bed at the same gas velocity; put another way, at equal pressu’re drops more gas would flow through the fluidized bed. Leva’s explanation of this phenomenon was that fluidization of the bed requires extra energy above t h a t required in the fixed bed; however, this appears to be in direct opposition t o the ob-
“, 0“
-
100
0
V I -
8, N
4 0-
A
M O o i F i E o REYNOLDS NUMBER.=.=
Figure5
pa
Comparison of Size M i x t u r e s w i t h Uniform Sizes
served lower friction factor for Leva’s fluidized bed of very smaU particles. A better explanation is believed to be t h a t flocculation of the very small particles, because of the surface forces present, causes these particles t o act not as individuals but as agglomerates of large size. Use of a larger particle size in calculating the coordinates of the points would increase both the friction factor and the Reynolds number, moving the points up and to the right -that is, toward general agreement with Carman’s curve. The
INDUSTRIAL AND ENGINEERING CHEMISTRY
1122
Vol. 41, No. 6
fluidization of extremely fine, widely sized, precipitated silicas to '/g inch in diameter) such as Santocel. Large agglomerates are easily visible through the column walls. Inasmuch as the surface forces t h a t are presumed to cause the flocculation tendency probably vary from material t o material, the d a t a which Leva has secured must be considered specific to the materials studied. It may be that other equally fine materials on which the surface forces are much less will show close agreement with the Carman-Kozeny relationship. The data of Wilhelm and Kwauk (17) have also been recalculated and the results compared with the Carman-Kozeny correlation. The comparisons are presented in several groups.
MODIFIED REYNOLDS NUMBER
Figure 6.
i
''
'Sp TZ
( I - E )P
Fluidization w i t h Water
Wllhelm and Kwauk data
fact t h a t Leva's data for the larger particles are in better a g r e e ment with Carman's curve is confirmatory evidence, for i t is known that flocculation for a given material varies inversely with particle size. The steeper slope of Leva's data on very small particles may be explained in the following manner: The flocculated particles form a porous agglomerate, which in fixed or only slightly expanded beds acts much the same as the individual particles, the friction factor points agreeing Kith Carman's curve. As the gas velocity and bed expansion increase, the agglomerates are separated more and more from one another, and the paths for gas flow are primarily around the agglomerates, rather than through them. Consequently, the agglomerate effective diameter rather than the diameter of its individual particles becomes increasingly important in calculating friction factor and Reynolds numbers. Therefore, when individual particle diameters are used, the departure from Carman's curve accordingly increases as the gas velocity increases. T h e effective diameter of the agglomerate is probably less than its physical dimension, for its porosity is involved i n its effectiveness. If extremely porous, some gas passes directly through the agglomerate, making it effectively smaller. Inspection of the plots of Leva's data (Figures 2 to 5 ) indicates that a n effective diameter two t o three times the individual particle diameter will serve t o bring into line with Carman's equation those points which deviate most widely. Direct visual evidence of flocculation has been observed in the 1000
)I"-
%
. . . . . .
...
..___.
...... . .
e
g
..--T
'
.
:oc ?--
4
-.
......
,----
.
-
-
10
-
Ill
CARMAN-KOZENY*
N
IO
100
1000
M O D I F I E D R E Y N O L D S N U M B E R Gm*
(I-€
Figure 7.
10,000
Fluidization w i t h Air
Wilhelm and Kwauk data
6G
)P P .a
BEDSBEFORE F L U I D I Z I T I O S . I n the first group are all the LT-ilhelm-Kwauk data for the beds before fluidization-that is, fixed beds. These data for both air flow and water flow are plotted in Figure 8. Generally good agreement with the Carman-Kozeny line is evident. However, all the d a t a for air-flow fall slightly above the curve, while the majority of the data for water flow fall slightly below the curve. There is no obvious reason for this slight discrepancy. F L U I D I Z 4 T I O N WITH ~ ~ A T E R .I n the second group (Figure 6) are the Wilhelm-Kwauk data for fluidization with water. The slopes are the same as the Carman-Kozeny curve, but the best line for the Kilhelm-Kwauk data would fall slightly lower, the disagreement being slightly larger than in the previously mentioned fixed-bed correlation (Figure 8 ) . FLUIDIZATION WITH AIR. I n the third group are the TVilhelmKwauk data for fluidization with air. These data are the basis for the fluidized-beds line on Figure 1, which also includes Leva's data. I n Figure 7 the Wilhelm-Iiwauk data for air fluidization at high Reynolds numbers have been plotted; this time, however, the curves for each of the materials have been drawn in for comparison with the Carman-Kozeny curve. It is evident that some additional factor is now involved, for there is a complete lack of correlation. The curves show near the left-hand end a n increase of friction factor Kith Reynolds number, followed by a flattening out and then a decrease of friction factor with further increase in Reynolds number. I n the gas-fluidized beds t h a t Wilhelm and Kwauk studied, the large Reynolds numbers were secured only with relatively large or heavy particles. Both the Wilhelm and Kwauk observations and those of the author indicate a difference between the fluidization of beds of such large or heavy particles, and the fluidization of small or lowdensity particles. The difference in appearance is much the same as the difference between what W'ilhelm and Kwauk call aggregative fluidization with gases and what they call particulate fluidization with liquids. Parent, Yagol, and Steiner (14) confirm this observation about the difference of fluidization between large and small particles. T h e explanation here proposed for the deviations from the Carman-Kozeny relationship at high Reynolds numbers is based on t h e previously outlined mechanism of fluidization and the consequently inherent segregation tendency of the fluidized bed. Beds of -large or h e w y particles fluidized with gas are inherently extremely unstable, with a strong tendency to segregate. This segregation tendency results in the formation of a nonuniform bed which contains strong rising currents of expanded solid and strong descending currents of concentrated solid. Some of these currents are localized; others extend over the entire bed. The particles being elevated in these currents absorb from the gas stream the required kinetic energy, which is eventually lost by collisions among particles and against the walls. T h e order of magnitude of the loss in kinetic energy of the particles and its effect on the bed circu100,000 lation may be estimated as follows: Assume a fluidized bed, 1 foot high and 1 square foot in cross section of particles which show a fluidization curve like those on Figure 7, with a n ordinate, Zf', of 7 a t a Reynolds number of 200
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
MODIFIED REYNOLDS
Figure 8.
Fixed Beds
Wllhelm and Kwauk
and a linear su erficial gas velocity of 1 foot per second. The ordinate for the Earman-Kozeny line is about 2.6. Such a bed if of sand, might have an expanded bed density of about 80 pounds per cubic foot, equivalent to a pressure drop of 80 pounds per square foot for the 1-foot height. The pressure drop equivalent to the kinetic energy of the particles would be A~K.E= . 80 X
’q
= 50 lb./sq.ft.
The power consumption would be A ~ K . EAPO . = 50 X 1 X 1 = 50 ft.-lb./sec.
If this energy be presumed to elevate the particles from the bottom t o the t o of the bed (which from visual observations is not unreasonable7 a distance of 1 foot, turnover rate will be 50 pounds per second, equivalent to 50/80 = 0.63 times per second. The few items of Wilhelm and Kwauk data for fluidization at low Reynolds numbers do not show these large friction factor deviations. P a r t of this lack of deviation may be due t o some flocculation tendency, b u t their data are mainly a t Reynolds numbers a t or above those a t which Leva’s data indicate no more flocculation. A more logical reason is that in this Reynolds number region (the higher end of the “streamline flow” region) the large magnitude of the “viscous” forces as compared with the “inertia” forces obscures the losses of particle kinetic energy in the fluidized bed. In the region of high Reynolds numbers, the viscous forces are much lower and the inertia forces are much larger; the portion of energy used in accelerating the particles, therefore, is much more significant. SUMMARY
The quantitative data of Leva et al. for the fluidization of fine sand particles in gases, with modified Reynolds numbers below 10, show negative deviations from the Carman-Kozeny fixed-bed correlation. These deviations are explainable by the flocculation or clustering which has been observed.to occur with fine particles. T h e quantitative data of Wilhelm and Kwauk extending from modified Reynolds numbers of 10 (streamline flow) to 10,000 (turbulent flow) show increasingly large positive deviations for the rough, nonuniform, “aggregative” fluidization secured with gases. These deviations are interpreted as evidence of the large amounts of energy transferred from the fluid stream into kinetic energy of the turbulently moving particles and then dissipated by collisions. The absence of these positive deviations for the smooth, “particulate” fluidization secured with water at similar high Reynolds numbers correlates well with the observation that in such beds there is only local circulation of the particles, and consequently only small kinetic energy losses by particle collisions. Positive deviations from the Carman-Kozeny correlation are, ‘therefore, evidence of nonuniform dispersion of fluid and particles-that is, of poor quality of fluidization-and steps taken t o reduce the magnitude of these deviations would be expected t o improve the quality of fluidization. Through its effect on conversion and yield, high quality of fluidization is important in obtaining the best performance of fluidized-solid reactors. ACKNOWLEDGMENT
The assistance of C. H. Winter, Jr., and C. E. Lapple in formulating the concepts of fluidization used in this paper is gratefully acknowledged. NOMENCLATURE
A A p
= cross-sectional area of bed, square feet = surface area of the average particle of diameter, D,, square feet = diameter of sphere of the same volume as that of the DP particle feet = modified $'arming friction factor f’ = conversion factor, 32.17 (ft.) (lb.)/(lb. force) (sec.)2 so = local acceleration due to gravity, ft./(sec.)2 7! = superficial mass velocity (based on gross cross-sectional area of empty tube), lb./(sec.) (sq. ft.) k, IC‘ = empirical correlation factors, dimensionless K A ~ = Wilhelm and Kwauk’s correlating factor based on friction factor in granular beds, dimensionless K A ~ = Wilhelm and Kwauk’s correlating factor based on drag coefficient, dimensionless L = height of settled bed (or len t h of pipe), feet = height of fluidized bed, feet ?for the segregation tend4 ency, the height above the zones under consideration) La = height of hypothetical bed containing no voids, feet L1 = length of the flow path between segregating zones, feet m = exponent on $/(l - E) in Leva’s fluidization correlation, dimensionless n = exponent on Reynolds number to correlate with friction factor, dimensionless Nv = expansion ration = expanded bed volume settled bed volume
-
(1 - € 0 ) / ( 1 E) Reynolds number = &DpG/p(1 - E), dimensionless Reynolds number = DPG/p,dimensionless =
A mechanism of fluidization is hypothesized, based on the simple packed bed t o which has been added a further variable, freedom of movement of the particles because their weight is supported in an expanded bed by a fluid stream. The following phenomena derive from the existence of this variable: The particles can change their degree of flocculation in response to surface or other attractive forces. The particles can be moved around by the drag of the fluid streams and by their own weight. It was demonstrated qualitatively that this ability results in an inherently unstable expanded bed, the fluid tending to segregate from the payticles by flowing in channels or pockets, thereby promoting nonuniformity and turbulence. This tendency would be expected t o increase with difference in density between particle and fluid, and to decrease with increase in the specific surface of the solid and with increase in the fluid viscosity.
1123
pressure drop, pounds per square foot pressure drop equivalent to the kinetic energy lost by particle collisions, pounds per square foot surface area of particles per unit volume of packed space, square feet per cubic foot surface area per unit packed space of spheres of equal volume, square feet per cubic foot superficial velocity of fluid through the bed, feet per second volume of the average particle of diameter D,, cubic fA””” oot
= fraction of voids in the bed of particles, dimensionless
€
=
EO
E,I
and
€2
fraction of voids in the settled bed
= average fractions of voidage in columns above two
neighboring zones, 1and 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
1124
average fraction of voidagr in thr path of fluid srgregating from zone 1 t o zone 2 fluid viscositv. absolutr. lb. mass ’(ft.)isec.) “a function bf” Carman’s shape factor for securing the specific surface of nonsuherical oarticles. enuals (~.3 6 ~ ) ’3’ Vn2j 3 , A , by Leva (8) fluid density, lb. niass//cu. ft. true (not hulk) particle density, lb. niassjcu. ft. I
_
I
L I T E R A T U R E CITED
Blake, F. C., Trans. Am. Inst. Chem. Engrs., 14, 415 (1922) Brownell, L. E., arid Katz. D . L., Chem. Eng. Progress, 43, 537-48 (1947).
Burke, S.P . , wid P l u n i n w . IT. R . , I m . Ex:. C m x , 20, (1928).
Cnrman, I?. C., 7’rana. f i i s t . (‘hem, Brig.
(1,ondon).
1196
15, Pa1.t 1 .
15O-iiB (1937,.
Vol. 41, No. 6
( 6 ) Chilton, T. El., and Colhuin, A. P., IXD.ENG.CHEW,23, 8, 9139 (1931). Furnas, C. C., Bur. U i n e s Bull. 307 (1929). Koeeny, Ber. Wien A k a d . , 136a, 271 (1927). Leva, M . , Chem. Eng. Progress, 43, 649-54 (1947). Leva, M., and Grummer, M.. Ibid.. 43, 633-8 (1947). Ibid., 43, 713 (1947). Leva, M., Grummer, M., et al.. Ibid., 44, 511 (1948). Ibid., 44, 619 (1948). Oman. A. O., and Watson, X. M., S a t l . Petivleum S e i u s , 36, 44, Sect. 2, R795-802 (Nov. 1, 1944). (14) Parent, J . D., Yagol, S . .and Steinel, C . S., Chem. Eng. [’?ogress, 43, 429-37 (19473” (15) Rose, H. E., I n s t . Mech. Eng. Proc., 153, War Emergency Issue SO. 5 . 141-61 (194S’I. J . Applied Phys., 11, 761-5 (16) Sullivan,’ R.R., and Hertel. K. L.. (1940); 12, 503-8 (1941); 13, 725--30 (1942). (17) Wilhelm, R. H., and Kwauk. >I.. Chem. Eng. Progress, 44, 2011s (1948). R X C E I V L DFebruary 7 . 1944
Mass an
Transfer
T h i s paper deals w i t h mass t r a n s f e r between a n upward s t r e a m of l i q u i d and solid particles i n consolidated a n d in expanded, fluidized beds. T h e solid particles in question were 2 - n a p h t h o l a n d t h e l i q u i d was water. It is believed t h a t t h e mass t r a n s f e r results are applicable equally well t o heat t r a n s f e r u n d e r s i m i l a r physical circumstances. Mass transfer i s a componemt m e c h a n i s m in l i q u i d phase c a t a l y t i c processes, in leaching a n d adsorption operations, and in exchange processes such as occur in resin columns. T h e experimental t e c h n i q u e involved p a r t i a l dissolution of spherical and flake-shaped particles of d i f f i c u l t l y soluble 2 - n a p h t h o l in a r i s i n g stream of water. A precise anal y t i c a l t e c h n i q u e was developed f o r measuring t h e s m a l l concentrations o f 2 - n a p h t h o l in t h e e x i t s t r e a m i n v o l v i n g dye f o r m a t i o n a n d c o l o r i m e t r i c analysis. T h e measured variables were water flow rate, e x i t concentration, water temperature, p a r t i c l e a n d bed characteristics, a n d pressure drop. F r o m these d a t a c o r r e l a t i n g variables i n c l u d -
i n g J factor, Reynolds n u m b e r , f r i c t i o n factor, a n d d r a g coefficient were interrelated. T h e range of experimentat a n d correlative variables is: particleshape, modified spheres a n d flakes; p a r t i c l e size, 3/16, and i n c h modified spheres, 8- t o I O - and 14- t o 18-mesh flakes (UsS. standard sieves) a n d mixed sizes; Reynolds n u m b e r , 14 t o 1755 in fixed beds; degree o f expansion in fluidized beds, 36q6 voids in consolidated state t o i n f i n i t e expansion as represented b y a single suspended particle; S c h m i d t group, 1200 t o 1500; bed diameter, 4 inches; a n d consolidated bed depth, 5 t o 24 inches. T h e correlated results concerning mass t r a n s f e r a n d f r i c t i o n in fixed and fluidized beds are discussed a n d compared. T h e i m p o r t a n c e o f f r a c t i o n void a n d t h e effect of n o n u n i f o r m i t y o f flow p a t t e r n as u n i f y i n g relationships f o r mass t r a n s f e r in fixed a n d f l u i d ized bed a n d f o r single particles are discussed. Mass transfer per unit pressure d r o p in fixed a n d fluidized beds is also considered.
LEROY K. MC=GUNEIANDRICHARD W. WILMELM PRINCETON UNIVERSITY, PRINCETON, N
NOKG the many types of industrial processes that involve the interaction of solid particles with gas or liquid streams are catalytic reactions and catalyst regeneration, adsorption operations, exchange processes as in water treatment, and drying and dissolving or subliming. I n most cases the bed of solids is ‘,fixed” or confined in a n immobile state within a particular apparatus. I n a n increasing number of cases, the solids are not held immobile by mechanical restraints but are free t o move if the forces caused by a flowing stream 19ithin the bed so dictate. A bed of solids utilized in this unrestrained condition is properly called a fluidized bed, inasmuch as the solid phase behaves as a pseudoliquid and solids may be withdrawn from and added t o the main body of the fluidized mass through pipes and valves much in the manner of a true liquid. I n either fixed or fluidized beds, mass transfer rate data are required for design purposes, particularly in processes in which external mass transfer is the prime rate variable. Mass transfer 1 Present address, E. I. du Pont de Nrmours & Wilmington, Del
Company, Ino.,
J.
may also be a n important fraction of the over-all resistance offered by several mechanisms in series or parallel, as can be the case in catalytic reactions. Mass transfer rates between gases and solid particles have been the subject of several publications. Gamson. Thodos, and Hougen (S),Wilke and Hougen (9),and Hurt (4)studied mass transfer between fixed beds of granular solids and floming gases. Resnick and W i i t e ( 6 ) studied mass transfer between both fixed arid fluidized beds of solids and flowing gases. In each case experimental conditione Twre such that the process of mass transfer was steady state, or nearly so. Hougen and co-workers measured the rate of evaporation of water from wet porous granules during the constant rate drying period. Resnick, White, and H u r t measured the evaporation of naphthalene particles into various gases. KO previous work has been reported for mass transfer between liquids and beds of solid particles. The present paper presents the results of experiments on the rate of solution of 2-naphthol particles in watei \?lien in fixed
