EngFiring Process development
Solid Particles CLARK 0.MILLER1 AND A, K. LOGWiNUKZ CASE INSTITUTE OF TECHNOLOGY, CLEVELAND, OHIO
T h e purpose of this investigation was to study some of the factors governing the fluidization of solids and heat transfer i n fluidized beds of solids. A “critical mass velocity” is defined and related to the fluid and solids properties by the following equation:
C.M.V.
0.00125 Df
(pp
-
P
This mass velocity was found to be independent of weight or bed height for a given material. Heat transfer studies from a hot dense fluid bed to a vertical cool tube were carried out. Three gases and two solids were utilized. Coefficients of 40 to 200- B.t.u./(hour)(square foot)(’ F.) were encountered, and a correlation is presented. Qualitative observations of electrostatic charges encountered in a fluidized solid system are discussed. The data presented should be of assistance in the design and operation of fluidized systems, particularly where an exothermic catalytic reaction is used.
A
LTHOUGH fluidization of particles, in a sense, has been known for some time, only in recent years has it been applied t o the field of chemical engineering. During those few years the process has gained so much importance that today it is generally accepted as a unit operation of chemical engineering. The process is being applied chiefly t o the catalytic cracking of petroleum. However, it is also important in catalysis, FischerTropsch reactions, gasification of coal, drying, calcination of limestone, and transport of a variety of solids. Considerable research has been and is being conducted with fluo-solids, but only a comparatively small part has found its way into the literature. Boucher ( 2 ) reviewed this literature, but for the moat part, the articles are qualitative in nature. I n 1948 Wilhelm and Kwauk (IO)discussed fluidization of solid particles by air and water in 3and 6-inch-diameter columns. Materials ranging in density from 1.125 t o 10.79 grams per cc. and in size from 5 t o 0.3 mm. were used. Qualitative observations were reported with 100- t o 200-mesh catalyst material. Leva ( 5 ) investigated fluidization of round and sharp sands by air, carbon dioxide, and helium in 2.5- and 4-inch columns. T h e equation,
was presented with which the mass velocity corresponding t o the point of bed expansion can be calculated. Additional papers were presented during a fluidization symposium in 1948 (S), and a review of the literature on fluid dynamic8 and heat transfer was given by Leva ( 4 ) in 1950.
the fluidization studies reported here were undertaken for particles in the 60- t o 200-mesh size, using helium, carbon dioxide, air, and ethane as the fluidizing media. As the term implies, “fluidization” means that the catalyst or solid behaves as a fluid. It has many of the attributes of a fluid. Probably one of the chief advantages of the process is that fluoaolids can be transported by meam of pipes or ducts, analogous to a true liquid. As a result of this behavior many processes which had been heretofore non- or semicontinuous could be made fully continuous. Other advantages, such as improved heat transfer and temperature distribution, also resulted from the extremely turbulent nature of the fluo-solid phase. Fluidization can occur in either a dilute or a dense phase. During transport of solids the dilute phase is encountered. However, if the velocity is decreased so that the velocity of slip exceeds the gas velocity, the particles will begin t o settle out and a dense phase is built up. A low solid-to-gas ratio is implied by “dilute,” and conversely, “dense” means a relatively high ratio of solid t o fluid. T h e dense phase is the type encountered in reactors and standpipes of fluid catalytic petroleum equipment. I t appeared to be the more important in general catalytic work; hence, the studies presented in this paper were restricted to this phase. I n attempting t o plan a logical approach to the application of fluidization to various practical problems, data on the behavior or mechanics of the process were required. Initially it YTas deemed necessary to determine the important factors affecting the fluidization of solids, particularly the point a t which movement of particles becomes prevalent. The problem hence became one of de. termining the mass velocity required t o initiate movement. This mass velocity was termed “critical mass velocity” and was defined as the minimum mass velocity required to keep a bed in a fluid state or one below which fluidization will cease. I n order to make the data of greatest practical significance and of greatest ease in handling, only the readily available properties of the gas and solid were included. The particle diameter D p , the difference in particle and gas density p p - p f , gas viscosity w , gas density p i , and gravitational constant g were chosen as the properties most likely t o influence the critical mass velocity. The following expression was set up:
Using dimensional analysis the exponents were evaluated in the following manner:
$fT-IL
LaATII“L -3b&fcL - 3 c L v d L ,
Solving for M , =
DYNAMICS
I n view of the limited amount of design data in the literature at the time this work was started, particularly for small particles,
-2
01’
l ~ +.pc
l = b + c + d
Solving for T i n a similar manner,
Present address, Cleveland Industrial Research. Ino , Cleveland, Ohio. *Present address, Arthur G. McKee 8; Co , Cleveland, Ohio. 1
1=2e+d 1220
+a
--d
T-dLe T - 2 6
’
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
May 1951
in
preciable percentage of the total flow. As a result, the flow through the rotameters was discontinued.
-LegendA,B,C,DMonometors 0-Orif ice E.F Small Rotameters G 2“ Glass toiumn M Pressura Manifold
0
S - Fine Screen H - Straightening
Vanes
P ~ * , ~ Pressure , ~ -
Taw
Figure 1.
FLUIDIZATION EXPERIMENTS
The procedure employed was relatively simple. A weighed quantity of sieved material, silicon carbide, sand, aluminum oxide, or silica gel, was poured into the column and fluidized. The gas flow was decreased and the solids were permitted t o free settle. T h e bed was then ready for the fluidization experiments. When a small mass velocity of gas-air, carbon dioxide, helium, or ehhane-was permitted to flow through the prepared bed, a corresponding pressure drop occurred; the pressure drop increased linearly with gas flow (curve 1-2, Figure 2). At point 2, corresponding essentially t o
Fluidization-Pressure Drop Apparatus
Solving for L,
-2 = a
- 3(b
1221
+ e) - d + e
(C)
Solving (A):
l - d = b + c
(D)
1-d=2e
(E)
Solving (B):
+
APf =
weight of solids in column cross sectional area of column
the bed began t o expand; however, the pressure drop was no longer increasing linearly with gas flow. The increase in bed volume was small but continued until a large enough free mean path was established for fluidization t o start. At this point a break occurred in the curve, 3-4; the pressure drop decreased t o AP, and the particles became fluidized. This fluidization was in the dense phase and was termed “smooth” or “percolating” because the action somewhat resembled smooth shock waves or fronts moving u p through the material and terminating in a
Hence 2e = b c. Now using Equation C and the results of D and E, Equation C becomes: -1 = a - 3 ( b + c )
or
-1
= a
- 1- d + e
- 3e
(F)
However, it was found experimentally that a was essentially\ equal to 2; hence e from Equation F was equal t o I . Then from Equation E the value of d must equal - 1.0; consequently b c must equal 2.0. The actual values of b and c had t o be found b y trial-and-error adjustments of the experimental data.
+
FLUIDIZATION APPARATUS
Figure 1 is a schematic diagram of the fluidization apparatus. Four manometers were used; A measured the upstream pressure above the calibrated interchangeable orifice, 0; a 50-inch water manometer, B, gave the pressure drop across the orifice, and a 30-inch manometer, C, filled with water or mercury, measured the pressure drop across the bed of solid particles. The lower t a p of manometer C was placed approximately 1/32 inch above a fine screen, S; the upper tap could be placed a t any one of three indicated points in the column by use of a pressure manifold, M . Mercury manometer D was used primarily as a check on C . Because of the screen resistance, readings on D had to be greater than, b u t close t o readings on C. The column was made of a 2-inch diameter glass tube, 70 inches long. The glass had been sealed into metal supports with litharge. Three pressure taps were provided in the glass column, one just above the screen, another 20 inches above the screen, and the third 40 inches above. A fourth tap was p u t into the metal top of the column about 3 inches above the glass tube. Pressure t a p PI was made up of four pressure taps at 90” radial intervals, all leading into one common tube, which in turn led to manometer C. The fine screen S was placed at the bottom and across the entire column. The gases were obtained from constant pressure sources and, before passing into the bed of solid particles, passed through straightening vanes H consisting of a bundle of l/r-inch copper tubes. When the apparatus was first built, two small capacity rotameters, E and F , were inserted into the pressure tap lines. These rotameters were t o be used for flushing the pressure taps and for a small backflow of gas in order t o keep the pressure taps from plugging. However, when actual experimental work was begun, it was found that such small flows constituted a n ap-
1
Log. G
Figure 2.
Pressure Drop us. Mass Velocity
percolating action a t the top, simulating a n erupting volcano or coffee percolator. This action threw the central particles to the side, and is illustrated in Figure 3. Despite the so-called shock waves, there can be noted a definite pattern of motion which is circulatory from the center t o the side, b u t in general the motion is up the center and down along the sides. When the gas velocity was increased further, the material fluidized more vigorously and expanded t o occupy a greater volume. I n general, the pressure drop velocity relationship appeared as curve 5-6, Figure 2. T h e curve, however, is theoretical; actually it followed the course indicated b y 5-7. This w a ~particularly true for larger particles; a small particle may follow course 5-8 or even 5-6, although when slugging occurred, it would also deviate upward. This deviation appeared t o be caused by the wall effect of the column. During velocity increase, bubbles of fluid coalesced a t times and bubbled through the fluidized material, analogous t o a gas bubble passing through a liquid. At still greater flows of fluid these bubbles a t times stretched from one wall of t h e column
INDUSTRIAL AND ENGINEERING CHEMISTRY
1222
TABLE I. CORRELATION OF D.IT.I Gas
Air
Solid Silicon carbide
8.73 12.9 25.7 59.6
0 0 0 0
0038 0049 007 0098
0 018 0 018 0 018 0 018
0 074
0 074 0 074
198 198 198 138
P 6,340 10,400 21,700 42,500
0 074
Air
Aluminum oxide
8.15 13 33.6 85.6
0 0038 0 0049 0 007 0 0098
0 0 0 0
018 018 018 018
0 074 0 074 0 074 0 084
243 243 243 243
7,650 12,600 26,200 51,300
Air
Silicon dioxide
6.5 10.6 17.5 25.2 41.5
0.00346 0.00487 0.00632 0.00752 0.00977
0.018 0.018 0 018 0,018 0.018
0.074 0.074 0.074 0.074 0,074
165 165 165 165 165
4,630 8,950 15,100 21,300 36,100
Air
Silica gel
2.86 5.08 8.66 13.2 18.9
0.00346 0.018 0.00487 0.018 0.00632 0 018 0 00752 0 018 0.00977 0.018
0,074 0.074 0.074 0.074 0,074
Helium
Silicon carbide
Helium
0.825 1.32 2.96 7.18
70.2 70.2 70.2 70.2 70.2
0.0185 0,0102 0.0185 0.0102 0.0185 0.0102 0.0186 0.0102
198 198 198 198
694 1,140 2,370 4,650
Aluminum oxide
0.96 1.43 4.45 10.4
0 0038 0 0049 0 007 0 0098
0.0185 0.0185 0 0185 0 0185
0 0102 0 0102 0.0102 0,0102
243 243 243 243
837 1,370 2,860 5,610
Helium
Silicon dioxide
0.48 1.29 2.08 3.1 5.21
0.00346 0.00487 0.00632 0.00752 0.00977
0.0185 0.0185 0.0185 0.0185 0.0185
0,0102 0,0102 0,0102 0.0102 0,0102
165 165 165 165 165
497 982 1,650 2,330 3,960
Helium
Silica gel
0.672 1.04 1.46 2.14
0.00487 0.00632 0.00752 0.00977
0 0185 0.0102 0.0185 0.0102 0 0185 0.0102 0.0185 0,0102
CO:
Silicon carbide
23.5 48.7 108
0.0049 0.007 0.0098
0.0148 0,112 0 0148 0.112 0.0148 0.112
198 198 198
13,860 41,400 81,200
COS
Aluminum oxide
17 24.7 64.7 145
0.0038 0,0049 0.007 0.0098
0.0148 0.0148 0.0148 0.0148
0.112 0.112 0.112 0.112
243 243 243 243
14,600 24,000 50,000 98,000
CO>
Silica gel
10.1 14.9 21.9 36.5
Ethane
Silicon carbide
27 50.8 107.5
0.0049 0.007 0.0098
0,0094 0.0765 0.0094 0.0765 0.0094 0.0765
198 198 198
20,600 43,000 83,700
Ethane
Aluminum oxide
21.3 28.3 69.7 133
0.0038 0.0049 0.007 0.0098
0.0094 0.0094 0.0094 0,0094
243 243 243 213
15,200 24,300 51,900 102,000
Ethane
Silica gel
18.1 25.3 41.3
0 . 0 0 4 8 7 0.0148 0.112 0.00632 0,0148 0.112 0.00722 0.0148 0,112 0.00977 0.0148 0.112
0.0765 0.0765 0.0765 0.0765
0.00632 0.0094 0.0762 0.00752 0 , 0 0 9 4 0.0765 0.00977 0.0094 0.0765
70.2 70.2 70.2 70.2
70.2 70.2 70.2
critical mass velocity. This critical mass velocity has important significance, for below it there can be no ffuidixation. .4 plot of the critical mass velocity (corresponding t o point 0 of Figure 2) against the average particle diameter on log-log paper indicated that the mass velocity was substantially a function of the square of the particle diameter. The average particle diameter in the case of closely screened materials (such as through a 48and on a 65-mesh screen) were chosen as the geometric mean of the openings of the two screens. For a mixture of particles a weighted geometric mean was found to be satisfactory-that is,
2,080 4,110 6,950 9,800 16,600
0.0038 0.0049 0.007 0.0098
70.2 70.2 70.2 70.2
Vol. 43, No. 5
452 761 1,070 1,820
where d,,,
X
= weight fraction of closely screened
material
= geometric mean diameter of fraction
y = number of fractions
Knowing that the critical mass velocity varied with the square of the particle diameter, correlations wele tried using the equation,
+
where b c = 2, which had been derived by dimensional analysis. It was found by trial and error that when b = 0.9 and c = 1.1, a straight line with a slope of 1 resulted. Figure 4 shows a plot of the experimental points and the correlation. Foot, pound, and hour units were used throughout the correlation. The data are presented in Table I.
7,890 13,300 18,800 31,900
Percola! in@ Action
13,800 19,500 33,000 jhocklikr Waves
‘
t o the other. When this occurred, the entire bed of material above the bubble was lifted up as a unit or, more simply, as a slug. This slug would break and the solid materials would then rain down through the bubble. It was possible for several slugs t o be in existence a t one time This behavior was termed “slugging” fluidization and was accompanied by significant fluctuations of the pressure drop. K h e n the fluid flow was decreased, the upward course of a hP vs. G curve was retraced with good reproducibility until fluidization ceased. Then with further decrease in flow. permitting free settling of the bed, curve la-2a, Figure 2, was produced. I n most cases curves 1-2 and la-2a were found to be parallel. The distance, d, between the two curves was dependent upon the initial nature or settling of the original bed and was not always reproducible, except for the slope and approximate horizontal position of points 3 and 4. In all cases curve la-2a was found reproducible. If curve la-2a is extended to meet the extension of curve 5-6 at point 0, we have a point a t which fluidization would occur if there were no interparticle attraction; the mass velocity corresponding to this point was defined as the
Gas
Figure 3. Schematic Representation of Particle Movement during Fluidization
I t had further been desired t o determine the effect, if any, of the weight or height of packed column upon the critical mass velocity, so experiments using varying weights of materials but constant particle diameters were run. These experiments clearly showed that a 300% increase in weight or height of the bed did not appreciably affect the critical mass velocity. The constancy in the critical mass velocity for silicon carbide having
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1951
108
102
104
Figure 4.
106
Critical Mass Velocity
1223
These types of reactions may also require rigid constant temperature control, which may be difficult t o achieve with a stationary bed of catalyst. I n addition, some reactions form hot spots in the bed and destroy the catalyst by sintering, decomposition, volatilization of promoters, etc. Or if channeling occurs, as is readily possible in fixed beds, only part of the catalyst may be in active use; the catalyst contact time may be decreased and temperature control may prove t o be difficult and inaccurate. The fluid process alleviates many of the temperature control and heat transfer difficulties encountered in stationary beds. The dirth of heat transfer data for fluid beds encouraged the preliminary investigations reported here. I n these investigations an attempt was made t o determine some of the factors influencing the heat transfer coefficients in the fluid bed. Mickley (8) studied the heat transfer characteristics of fluid beds in 1- and 4-inch tubes, and heat was transferred t o the fluid bed either internally or externally. Glass beads were fluidized by air, and heat transfer coefficients of 10 t o 120 B.t.u./(hour)(square foot)(" F . ) were obtained. Leva (6) derived a n equation for heat transfer coefficients based on terms of characteristic fluidization variables. H e used iron catalyst and sand, and helium, air, and carbon dioxide were the fluidizing gases. Observed coefficients varied from 0.25 to 80 B.t.u./(hour)(square foot)(' F.). I n addition, heat .transfer coefficients were determined in a fluidized system under a variety of conditions by Baerg ( 1 ) . The investigations covered in this paper were carried out with silicon carbide and fused aluminum oxide, using air, carbon dioxide, and helium a t relatively low bed expansion and mass gas flow (7). HEAT TRANSFER APPARATUS
20
40
60
100
G
The apparatus is illustrated by Figure 6: The outer tube was made of standard 2-inch stainless steel pipe, fitted with a screen and a copper tube (3/a-inch outside diameter and 0.035-inch
Figure 5. Pressure Drop vs. Mass Velocity for 0.0098-Inch Silicon Carbide
. *
a n average particle diameter of 0.0098 is shown by Figure 5, in a-hich pressure drop is plotted against mass velocity on loglog paper. Other particle sizes and materials gave similar results with the exception t h a t the curves were shifted in the horizontal direction, depending upon the size and density of the particles. Neither the weight of material nor the increased height of packing were found t o affect the critical maw velocity. Consequently most of the experiments had been run for only one weight of material. However, frequent checks had been made. CONCLUSIONS. Countergravity flow of air, carbon dioxide, helium and ethane through beds of solid particles having specific gravities of 1 t o 4 were investigated. A correlation has been developed which can permit the estimation of the minimum mass velocity required to fluidize a mixture of particles or a closely screened bed of particles. The correlation included the particle size and density and the gas density and viscosity. I n addition it was found t h a t this mass velocity did not depend upon the height or weight of material in the column. HEAT TRANSFER FROM FLUID BED TO VERTICAL TUBE
Where large quantities of heat must be transferred, for example, in exothermic or endothermic chemical reactions on catalytic surfaces, the fluid-solid process may be found advantageous.
IO v
STAINLESS STEEL Figure 6.
-Y-H20
IN
Heat Transfer Apparatus F. Fluid bed M. R.
Tc.
Insulation Rheostats Thermocouples
INDUSTRIAL AND ENGINEERING CHEMISTRY
1224
wall thickness) placed in the center of the outer tube. Stainless steel tubes were welded to the copper tube a t the ends in order to minimize conduction. The fluid bed was in the annulus, and water flowed through the copper tube. The tube wall temperature was taken by two skin thermocouples placed into the tube skin and flush with the outer wall. The bed temperatures were measured with iron-constantan couples placed one quarter and three quarters up the bed. Water inlet and outlet temperatures were taken with iron-constantan couples sheathed with stainless steel and placed in the copper tube. The mater couples were placed opposite the bed and skin couples, 22 and 3/s inch apart. A11 thermocouples had previously been calibrated. The fluid bed was heated by electrical coils placed around and about 0.5 inch away from the stainless steel tube. Heat transfer coefficients were determined by placing a definite voltage across the heating coils and permitting sufficient elapse of time for steady-state conditions to be reached. Thermocouple readings were made with a Leeds & Korthrup potentiometer (Model 315775), and the quantity of heat transferred was calculated by the equation: Qo
where
=
U,AAf,,
=
90 60
240 r
100
80
60 3
O
O
The fluid film coefficient was then calculated by the equation: h, = L',At,,/AtmW
where h, = gas film coefficient Atnw = arithmetic mean temperature difference between n all and bed, O F. HEAT TRANSFER EXPERIMENTS
It was found in passing air, carbon dioxide, and helium through silicon carbide that, for a fixed mass velocity and particle size, a plot of the heat transfer coefficients against the driving force (At,,) did not give an appreciable variation in the covered experimental range of temperature differences, or temperatures (since the average cooling mater temperature remained essentially
9 us.
GU.2kj.S @.6Cl.O 0.6 Pg
iL
in which the thermal properties were obtained at the actual fluid bed temperatures (Figure 10). Results of aluminum oxide fluidized by air also fitted the above correlation. The correlation, however, was slightly displaced in the horizontal direction. The correlations for the two solids coincided when the thermal conductivities of the solids, as supplied by Norton (9),were taken into consideration. Figure 11 gives the final empirical correlation. I t must be pointed out that this final correlation is not dimensionless, and care must be exercised in the use of this expresfiion.
y I 00
Q%O Heat Transfer Coefficients us. AT
constant). Figure 7 is a typical curve illustrating the degree of variation. Therefore, as a preliminary approximation the heat transfer coefficients were assumed to be independent of the temperature in the range covered, and the coefficients for the given mass velocity and particle size were averaged. It was believed t h a t if the thermal properties (thermal conductivity, viscosity, or specific heat of the gases) influence the heat transfer coefficients, as they usually do, then their large variation in the three gases studied would be more indicative than the influence of temperature alone. For the individual gases in question, these thermal properties did not vary too greatly in the temperature range covered (150' t o 500" F.). A plot (Figure 8) of the average heat transfer coefficients against the particle diameters studied (0.0038 t o 0.0098 inch) indicated that the heat transfer coefficients \yere essentially a function of the -0.6 power of the particle diameter.
6
3
I n general, it was found that the mass velocity entered the picture to approximately the 0.2 power for the smaller particles. However, some discrepancy existed for the larger particles, Plots of average heat transfer coefficients as a function of Go.2/ D:.6 are shown by Figure 9 for helium, air, and carbon dioxide. I t was thought that, although the concentrations of the solids in the bed might be important, the variation of mass velocities covered, 6 to 200 pounds/(hour)(square feet), was not sufficient to vary the concentration sufficiently t o justify inclusion of the concentration term. However, it may well be that the solids concentration is an important factor. Since it appeared that the separation in the lines of Figure 9 for the three gases could be due t o gas properties-Le., thermal conductivity, heat capacity, and viscositj-correlations involving these variables were tried. The best straight-line relationship was obtained by plotting the actual heat transfer coefficient against the following empirical relationship :
heat transferred, €3 t.u./hour over-all heat transfer coefficient, B.t.u./(hour) (square foot)( F.) Atmo = arithmetic mean temperature difference, bed to water, F. A ~ H ~=o temperature increase of water, F. C, = specific heat of water, B.t.u./(lb.)( O F.) Qo = =
Figure 7.
9
io4- FEET Figure 8. Average Heat Transfer Coefficients Particle Diameter
(lb. HzO/hour)CPAt~,o
0
6
DP x
U,
q..
Vol. 43, No. 5
200
100
r
70
30
100
200
100
200
300
100
2M)
300
GQ2/D?
Figure 9.
Average Heat Transfer Coefficients us. Go.2/Do.6
May 1951
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
SILICON-CARBIDE
ALUMINUM OXIDE
1225
the mass velocity, particle diameter, thermal properties of the gases used, and thermal conductivity of the solids. It is believed t h a t the effect of the thermal properties of the solids may not exist a t all. Since the data presented are actually on cooling studies, and since all other data,on heat transfer in fluid beds in the literature are for heating, it was felt t h a t a critical comparison of the present correlation with the work in the literature was not justified. ELECTROSTATIC EFFECTS PREVALENT DURING FLUIDIZATION
I I IIIII 8
6
IO
20
Figure 10. Heat Transfer Gas Film Coefficients as a Function of Properties of Gas and Particle Diameter
Attempts t o measure the influence of particle size on heat transfer coefficients, when silica gel was used instead of silicon carbide or aluminum oxide gave contradictory results. With silica gel the heat transfer coefficients increased with increasing particle size, which was in opposition t o data obtained with other materials. It was found that the impugnation was due t o electro-
0-SIC
A-sic
- AIR - HELIUM
200
IO0 0
80
r
60
40
5
c
7
IO
20
Since in heat transfer studies with silica gel anomalous results were encountered, which were believed t o be attributed t o electrostatic effects, and since the build-up of electrostatic charges during fluidization was not emphasized in the literature, it was decided that it would be of interest t o make a short qualitative study of these effects and present them with substantiating photographs. A fluid system consisting of two bottles and a transport tube was used. T h e finely divided particles were s u c k e d through the transport tube from 2 one bottle into the other. When P silica gel, slightly contaminated with sqme fine alumina, was transported through the copper tube, the tube became charged; in addition, the receiving bottle also became highly charged and D,x 104-FEET r picked u p paper and dirt particles Figure 12. Average Heat Transfer Coeflying nearby. A pith ball placed ficients us. Particle near the bottle was attracted t o Diameter for Silica it, as illustrated in Figure 13. Gel Uncontaminated silica gel gave a somewhat smaller charge. T h e charge upon the copper tube section of the transport tube became so highly charged t h a t i t was easy t o obtain sparks over one inch in length. When the copper tube was sprinkled with silica gel, the particles were attracted t o it and in turn became charged. A pith ball was easily attracted by the copper tube containing the fluidized material (Figure 14). T h e particles adhering to the tube wall fell off when fluidization was stopped, and a period of time in which t h e charge dissipated itself was permitted t o elapse. A stainless steel transport tube gave results substantially less pronounced than those with the copper t,ube. It also appeared t h a t apparently a greater charge was obtained with higher particle temperatures, and t h a t the greatest charge at a fixed teniperature appeared t o be present when a fluid stream became dilute; that is, when the ratio of solids t o gas was decreased.
Figure 11. Heat Transfer Gas Film Coefficients as Function of Properties of Gas and Fluidized Solid
static charges being built up on the silica gel. T h e charged particles clung t o the tube wall and thus increased the resistance t o heat flow. Larger particles permitted more interparticle space, hence a greater area of clean heat transfer surface. T h e smaller particles coated the heat transfer surface completely. I n addition, during the course of fluidization the larger particles were more prone to being dislodged, which was not the case with t h e smaller particles. Figure 12 is a typical heat transfer coefficient plot against the particle diameter for silica gel. Heat coefficients of 40-200 B.t.u. DISCUSSION OF RESULTS. (hour)(square feet)( O F.) were obtained with a densely fluidized bed of solids, a t gas flow mass velocities which would have given coefficients of approximately 1-2 had a n empty tube been used. T h e coefficients were experimentally correlated as a function of
Figure 13. Receiving Bottle Electrostatically Charged by Fluidized Solid Particles
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
1226
Vol. 43, No. 5
6 = fraction voids (dimensionless) d,,
=
Up = g = G = h, = h,,, = k =
k’ = L = h = = AP =
X
=
G ’ f
Q = p =
7‘ =
U
=
geometric mean diameter of closely screened particles, feet average particle diameter, feet gravitational constant, feet/hour squared mass velocity, pounds/(hour)(square foot) heat transfer coefficient for gas film average gas-film heat transfer coefficient thermal conductirity, B.t.u./(hour)(square foot)( F./ foot) constant (dimensionless) length, feet particle shape factor (dimensionless) mass, pound preswre drop, pounds/square foot pressure drop at point of fluidization, pounds/square foot quantity of heat transferred, B.t.u./hour density, pounds/cubic foot time, hour over-all heat transfer coefficient, B.t.u./(hour)(square foot)( F.) viscosity, pounds/(hour)(foot) O
p =
Subscripts o = over-all .f = fluidizing fluid g = gas p = particle ACKXOW LEDGMENT
Figure 14. Copper Transport Tube Electrostatically Charged by Fluidized Solid Particles
Silicon carbide and aluminum oxide did not build up a charge in the copper tube or in the bottles to any appreciable extent, although a very slight attraction for the pith ball did exist. The difference in the behavior of the solids may be due t o different dielectric constants or, more likely, t o the nature and characteristics of the surfaces of the materials. Also, absorption of a monomolecular film (such as alumina) on the surface of the solid may alter the picture entirely. As a result of the observations it may be said that electrostatic charges can be built up within a fluid process, and may give erratic results in heat transfer or mass transfer studies. Some of the factors which may affect the magnitude of the charge may be (1) dielectric constant of the material used, (2) contact potential difference, ( 3 ) ratio of fluidized solids to gas, (4) properties of the gas, ( 5 ) temperature of the solid-fluid system, and (6) nature of the surface of the solid particles.
Thanks are due to C. F. Priitton for advice, to J. Lukes of the Diamond Alkali Co. for suggestions on the construction of the heat transfer apparatus, and to the Glenn L. Martin Co. for providing the funds which made these investigations possible. LITERATURE CITED
Baerg, A , , Klassen, J., and Gishler, P. H., “Heat Transfer in a Fluidized Solids Bed,” submitted for publication in Can. J . Research.
Boucher, D., IND. ENG.CHEM.,40, 32 (1948). IXD. ENG.CHEM.,41, 1098-250 (1949). Leva, M., Ibid., 42, 55-9 (1950). Leva, M., Grummer, &I and .,Weintraub, M., Chem. E n g . Progress, 44, 511 (1948). Leva, M., Weintraub, hl., and Grummer, M., Zbid., 45, 563 (1949). Logwinuk, A. K., thesis, Case Institute of Technology, 1948. Mlckley, H. S., and Trilling, C. -4., IND. ENG.CHEM.,41, 1135 (1949).
Norton, F. H., “Refractoiies,” Kew York, McGraw-Hill Book Co.. 1931.
Wilhelm, R. H., and Kn-auk, M., Chem. Eng. Progress, 44, 201 (1948).
NOMEBCLATURE
RECEIVED May 23, 1950. Presented before the Division of Industrial and CHEMICAL Engineering Chemistry a t t h e 117th Meeting of t h e AMERICAS SOCIETY, Detroit, Mich.
A = heat transfer area, square feet C, = specific heat a t constant pressure, B.t.u./(lb.)(” F.)
EngE;ri
Dittus-Boelter Equation for Heati ooling liquids
ng
pocess development
I
T
JOHN F. HEISS’ UNIVERSITY
HE calculation of the film coefficients of heat transfer is
necessary in the design of liquid-liquid heat exchangers. McAdams ( 2 ) recommends the following equation to be used in calculating the film coefficients for fluids having viscosities not more than twice that of water, for Reynolds numbers exceeding 2100: 1 Present address, m’estvaoo Chemical ~ Chemical Corp., South Charleston, W. Va.
i
~
i~~~d ~ ihIachlnery ~ ~ , and
AND
JAMES CQULL
OF PITTSBURGH, PITTSBURGH, PA.
h_o k
= 0.023
(F)”’” c2)0.4
(1)
This equation with consistent units may be called a modification of the Dittus-Boelter equation, where the coefficient 0.023 is such that safe design values are obtained for the film coefficient, h . The coefficients determined formerly by Dittus and Boelter ( 1 ) were 0.0243 for heating and 0.0265 for cooling, with the esponents of the Prandtl number, c , ~ / k ,respectively, 0.4 and 0.3.
