EngFnyring
Fluid Bed Flowmeter
Process development
C. F. GERALD1 DEPARTMENT OF CHEMISTRY AND C H E M I C A L ENGINEERING, UNIVERSITY OF W A S H I N G T O N , SEATTLE 5, W A S H ,
T
HE problem of metering the flow of liquids is a common one, and many types and designs of flowmeters have been proposed. The fluid bed flowmeter here described has apparently not been described before, although it may be the same in principle as outlined in a foreign patent ( 4 ) . It has the desirable features of simplicity, continuous indication of flow rate, adaptability to corrosive situations, freedom from stagnant pockets, small holdup volume, and high sensitivity without excessive pressure drop. If the rate of flow of a fluid passing upward through a bed of solid particles is above a certain minimum value required to fluidize the bed of varticles. the heirrht of bed increases with the tlow rate: The fluidized bed height is well suited to measure the flow of a liquid but gases ordinarily pass through the bed in rather large bubbles, causing the top level t o fluctuate, and hence a fluidized bed. is not adapted to accurate flow measurement of gases.
t
The assembly is fastened in place by short lengths of flexible tubing. Alternatives to the screen support, especially useful wheremetalsmust be avoided, are sharp bends or re-entrant tubes. Porous plugs of glass wool were tried with little success because they would slip in the tube because of the pressure drop across them. Sealed-in porous plates would be satisfactory. A flowmeter for use a t 150 pounds per square inch pressure was made using a Merriam manometer, with a rolled-up piece of screen material a t the bottom of the U-tube, acting as bed support. The particles were placed in the outlet leg of the manometer. Although fluidization phenomena have been studied by several investigators and various correlations have been proposed to relate bed height and fluid vel'ocity (1-8, 6 ) , none of these correlations were entirely suitable to predict calibration curves for narrow tubes of fluidized solids as used for flowmeters. Figure 2 shows typical calibration curves for the flow of water through
APPARATUS AND CALIBRATION CURVES
t Figure 1. Schematic of View Fluid Bed Flowmeter 1 Present
Figure 1 shows the type of flowmeter used in this study. The solid particles, usually of a diameter less than one-tenth that of the tube, were supported by a screen whose hole sire was nmaller than the particle diameter. I n this work, glass tubes of from 1 mm. to about 2 inches inside diameter were used, but any transparent material can be used. Even nontransparent tubes can be used, if magnetic or other evel-detecting devices are em loyed. Normally an enlargement was rovidefat the top of the tube to prevent accixental carry-over of solids. Nearly any particles of not too wide size distribution may be used; glass spheres, lead shot, Ottawa sand, and crushed granite were used in these tests. The particles used in this study had a size range of d%:l or less, and showed some evidence of size segregation by visual observation during operation. For this range of sizes, however, there was no noticeable effect due to nonequilibrium of particle size classification. This was evidenced by the absence of hysteresis effects and by the correspondence of average flow rate and average flowmeter reading in tests when the flow fluctuated. In general, the more nearly spherical particles fluidized more smoothly and gave more reproducible calibration curves. A convenient way of attaching the screen which supports the particles, for low pressure work, is to use a circular piece of screening with a diameter equal to the outer diameter of the flowmeter tubing. This piece of screen is held in position in the joint between two lengths of the flowmeter tube by a sleeve of larger size tubing that just slips over the flowmeter tube.
I
I 2oQ
I
I 400
I
I
I
100
I
1
BQQ
Flow,MI. per Minute
Figure 2. Calibration Curves for Flow of Water through Beds of Various Materials l/Z-irkch diameter tube 1. 48-to 65-meah crushed granite 2. 28- to 35-mesh glass spheres 3. 14- to $&mesh glass spherea 1. 1/16-inch glass toroids
beds of various partides in a l/rinch diameter tube, and Figure 3 shows low range data for flow of a number of liquids through a bed of 28- to %-mesh glass spheres in a tube having an inside diameter of 6 mm. The calibration curve is very nearly a linear function of the rate until the bed height about doubles, when the velocity is about four times the fluidizing velocity, but departs rather widely from linearity a t higher rates. EFFECT OF FLOWMETER T U B E VARIABLES
The height of the fluidized bed for a given liquid flow rate was found to be proportional to the quantity of solids in the tube, which is in agreement with previous investigators of fluidization. A more sensitive flow indication is secured, then, with a deeper initial bed of particles, at the expense of a longer tube being required for a given flow range, and a proportionately higher pressure drop. The sensitivity of flow measurement by the fluid bed
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INDUSTRIAL AND ENGINEERING CHEMISTRY
flowmeter is relatively constant through its range. The steeper slope at high rates is accompanied by sbme fluctuation of level and less precision of observation because of greater diffuseness of the bed interface, so that the over-all measurement sensitivity is about the same as a t low rates. This characteristic is similar to the rotameter, although for a different reason, and is in contrast to the variable sensitivity of orifice or capillary flowmeters.
larger diameter a t the top than a t the bottom. Several models using this principle have been employed, some of which allowed precise flow measurement over an 18-fold change in fluid flow rate, but the best combination of tube lengths and diameters has not been systematically investigated. Preliminary tests on tubes of annular cross section showed that noncircular tubes can also be used as flowmeters. For such annular tubes, the centering and alignment of the inner cylinder is quite critical, however. EFFECT OF PROPERTIES OF FLUID AND PARTICLES
The effects of particle size and density are less easily characterized than the flowmeter tube variables, and the effects of fluid density and viscosity act in a similar complex fashion to affect the calibration curve. It was found that, although not allowing the accurate prediction of the calibration curve, the correlation of Lewis, Gilliland, and Bauer (2)gives a fair approximation to the initial fluidization velocity, which is the lower limit of utility of a given flowmeter. Flow, M1. per Minute
Figure 3.
Low Range Data for Various Liquids through Bed of 28- to 35-Mesh Glass Spheres &mm. t u b e 1. 2-propanol
2. 3. 4. 5. 6.
Carbon tetrachloride 15% acetone-85% 2-propanol mixture Water 50% a c e t o n e 5 0 % 2-propanol Aeetone
Previous investigations of fluidization have shown that the tube diameter is without effect if the flow is expressed as superficial linear velocity. This was confirmed in these studies even though relatively small tubes were used, and the ratio of bed height to bed width was larger than in most work reported in the literature. The effects of initial bed height and tube diameter are demonstrated in Figure 4,where the ratio of bed height to initial bed height at zero flow is plotted against superficial velocity. The calibration curves for flowmeters whose cross-sectional areas differ by 60-fold, and whose initial bed heights differ by threefold are identical on this basis. Since the degree of packing of the initial bed of particles can be considerably different for these small particles, the initial bed heights used in Figure 4 were determined by a definite procedure. The bed was first fluidized and then the flow was slowly decreased to zero, avoiding sudden changes in rate and jarring of the tube. Under these conditions, the, nearly spherical particles used in this work had a voids fraction very near 0.40. Inclination of the flowmeter tube from the vertical causes changes in the bed level a t a given flow rate. This effect was not studied thoroughly, but it was noted in preliminary tests that an inclination from the vertical TABLE I. COMPARISION OF of about 5' caused the flow required for a given flowmeter reading, measured along the tube axis, to be 10% higher. This same ratio held Over the full range of the meter. The calibration of Figures 2' 37 and show that the range of flow measurement is limited Unless a Calibration curve with a serious change in slope is used. This difficulty can be overcome by use of flowmeter tubes of a
Particles 14- t o 20-mesh glass spheres 28- t o 35-mesh glass spheres 28- to 35-mesh glass spheres
U , Cm. per Minute
Figure 4. Symbol
Effects of Initial Bed Height and Tube Diameter Initial Bed Height, Cm.
Tube Diameter, Mm. 5.94 5.94 5.94 10.1 14.9
7.62
8
14.2 4.93 7.62 7.95
70
Table I lists observed and calculated initial fluidization velocities. There is a systematic deviation of the observed and calculated velocities, which is indicated by Figure 5 to be a function of the magnitude of the Reynolds number at the fluidization velocity. The experimental fluidization velocities of Table I were determined by extrapolation of the linear portion of the calibra-
OBSERVED VALUES OF SUPERFICIAL VELOCITY AT FLUIDIZATION
CALCULATED AND
Fluid Acetone Acetone 50% acetone, 50% 2-propanol 28- to 35-meah glass spheres Water 28- to 35-meah glass spheres 15% acetone. 85% 2-propanol 28- to 35-mesh glass spheres Carbon tetrachloride 28- to 35-mesh glass spheres 2-Propanol 12- t o 14-mesh lead shot Water 14- to 2O-mesh lass spheres Water 20- to 28-mesh 8ttawa sand Water
Ui, Ui, -0bsvd. Calcd." 0.79 0 . 3 4 5 126b 83 0 , 7 8 4 0 , 3 1 6 45.0b 38.5
Slope, Figure 3
D 0.100 0.050
2.554 2.554
0.050 0.050
2.554 0.783 0.532 2.554 0,996 0.836
28.9 16.0
27.8 17.4
0.400 0.568
0.050 0.050 0.050 0.128 0.100 0,071
2.554 0.782 1.15 2.554 1 ,577 0 . 9 0 6 2,554 0,782 2.07 10.79 1.0 0.90 2.554 1 . 0 0.90 2.64 1.0 0.90
12.2 8.50 5.79 363* 63 45
15.7 10.0 9.7 234 43 28
0.609 0,901 0.909
PS
P
p
01322
...
...
.,. .
a Calculated from dotted curve of Figure 5, which is the modified drag-coefficient Reynolds number correlation of Lewis, Gilliland, and Bauer. using fraction voids of 0.40. b Slight bubbling occurred in these runs.
January 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY Figure 6 shows that
D Uip ___ P
Figure 5. Comparison of Observed Initial Fluidization Velocities with Fluidization Correlation of Lewis, Gilliland, and Bauer Dashed curve indicates correlation of Lewis, Gilliland, and Bauer
tion curve back to the velocity corresponding to the measured initial bed height. Figure 5, which is a rearrangement of the modified drag coefficient versus Reynolds number correlation of Lewis, Gilliland, and Bauer, is helpful also to select a suitable tube diameter for a flowmeter design. The value of CN;. is first calculated from the properties of the fluid to be metered and the density and diameter of available pal ticles of suitable characteristics, estimating ci as 0.40 for spheres in the absence of experimental values. From the vaIue of Reynolds number indicated by Figure 5, the fluidizing velocity is calculated. The tube diameter required is one that gives the superficial fluidization velocity at the lowest desired flow rate. The particles used must be such that the resulting ratio of tube diameter to particle diameter is at least 10 to 1 to avoid irregular particle motion.
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dH
zv,the slope of the calibration curve, is lin-
darly related to the fluid viscosity. The slopes for water and carbon tetrachloride depart from this curve because of density effects. The slopes with water and carbon tetrachloride are brought essentially on the line of Figure 6 by multiplying by the ratio of ( p . - p ) for the liquid to (p. - p ) for acetode-1,Z-propanol. The particle size enters into the relation between slope and liquid properties in an important way that has not yet been determined. In order to use the fluid bed flowmeter for measurements of high flow rates and still have a meter of convenient diameter, high density particles of relatively large diameter would be required. This leads to bubble formation of the liquid passing through the bed, or when more pronounced, to slugging (6). A small amount of such irregular action-a slight bubbling-was noted with lead shot and water and in runs with acetone, even with small glass particles, indicating that low fluid viscosity is also a factor in causing bubbling action. The accuracy of measurement was not significantly affected, except that more fluctuation of the bed interface resulted. Hence slight bubble action can be tolerated in the fluid bed flowmeter, but this effect limits the maximum flow that can be measured conveniently to the order ot 25 gallons per minute. The fluid bed flowmeter is thus more of a laboratory instrument than an industrial scale flowmeter. NOMENCLATURE
D
= g = L = LS = U = Ui = c = p = pa = p =
particle diameter acceleration of gravity bed height initial bed height superficial linear fluid velocity fluidization velocity fraction voids fluid density solids true density fluid viscosity ACKNOWLEDGMENT
The work of several students in chemical engineering a t the University of Washington provided portions of the data reported. The work of Galen A. Truesdell, Jr., was especially helpful in exploring the possibilities of using fluidized beds as flowmeters. LITERATURE CITED
Ergun, S., and Orning, A. A.. IND.ENQ.CHEM..41, 1179 (1949). Lewis,W. K., Gilliland, E. R., and Bauer, W. C., Zbid., 41, 1104 (1949).
Morse, R.D.,Zbid., 41,1117 (1950). Solvay & Cie, Belg. Patent 470,557 (Jan. 10, 1947). Wilhelm, R. H., Research, 3, 159 (1950). Wilhelm. R. H., and Kwauk, M., C h a . Eng. Progress, 44, 201 (1948). RECEXVED
I.’, 0.P.
Figure 6. Empirical Correlation of Slopes of Figure 3 with Viscosity of Fluid Open circles are acetone-2-propanol mixtures with constant density
The fluid properties affect not only the point of initial fluidization, but the shape of the curve as well. The data of Figure 3, for a variety of liquids, allow the following empirical correlation of the effect of fluid properties on the slope of the straight portion of the calibration curve. The results with acetone, isopropyl alcohol, and mixtures, which form a series with nearly constant density as shown in Table I, allow correlation of viscosity effects.
January 19, 1951.
