January 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
h p / A T = pressure drop per foot of packed height, inches of water per foot V , = linear pore velocity of gas, feet per second b, s, k , n = constants pa = relative viscosity p s = relative density U, = relative surface tension ACKNOWLEDGMENT
The authors are indebted to Donald W. Deed for his helpful suggestions, and for his initiation of the entrainment studies a t the Cooper Union School of Technology. LITERATURE CITED
i*
i
(1) Am. Soc. Mech. Engrs., New York, “Fluid Meters Report,” 4th ed., 1937. (2) Bacaewski, Z., undergraduate thesis in chemical engineering, Cooper Union, 1943. (3) . . Bain. W. A.. and Hougen, 0. A,, Trans. Am. Znst. Chem. Engrs., 40,29 (1944). (4)Baker, T., Chilton, T. H., and Vernon, H. C., Ibid., 31, 296 f 1935). (5) Reiietti,’J. W., Ibid., 38,1023 (1942). (6) Boelter, L. M.K., and Kepner, R. H., IND.ENG.CHEM.,31, 426 (1939). (7) Cooper, C. M.,Christl, R. J., and Peery, L. C., Trans. Am. Inst. Chem. Ezlgrs., 37,979 (1941). ( 8 ) Elgin, J. C., and Weiss, F. B., IND. ENG.CHEM.,31,435 (1939). (9) Furnas, C.C.,and Bellinger, F., Trans. Am. Znst. Chem. Engrs., 34,251 (1938). (10) Gazley, C . , Jr., Ph.D. thesis in chemical engineering, University of Delaware, 1949. (11) Houghten, F. C., Ebin, L., and Lincoln, R. L., J. Am. SOC.Heating Ventilating Engrs., 30,139 (1924). (12)Jesser, B. W., and Elgin, J. C., Trans. Am. Inst. Chem. Engrs., 39,277 (1943). (13) Lerner, B. J., undergraduate thesis in chemical engineering, Cooper Union, 1943. (14)Lewis, W. K., Gilliland, E. R., and Batter, W. C., IND.ENG. CHEM.,41,1104 (1949).
225
(15) Lobo, W.E., Friend, L., Hasmall, F., and Zenz, F., Trans. Am. Inst. Chem. Engrs., 693 (1945). (16) Mach, E., Forsch. Gebiete Ingenieurw., 6,Forschungsheft, No. 37, 59 (1935). (17) Martinelli, R. C., Boelter, L. M. K., Taylor, T. M., Thomsen, E. G., and Morrin, E. H., Trans. Am. Soc. Mech. Engrs., 66,139 (1944). (18) Martinelli, R. C.,and Nelson, D. B., Ibid., 70,695 (1948). (19) Martinelli, R. C., Putnam, J. A., and Lockhart, R. W., Trams. Am. Inst. Chem. Engrs., 42,681 (1940). (20) Matheson, G . L.,Herbst, W. A,, and Holt, P. H., IND.ENG. CHEM.,41,1099 (1949). (21) Molstad, M. C.,Abbey, R. G., Thompson, A. R., and McKinney, J. F.,Trans. Am. Inst. Chem. Engrs., 38,387(1942). (22) O’Bannon, L. S., J . Am. SOC.Heating Ventilating Engrs., 30, 157 (1924). ENR.CHEM.,14,476 (1922). (23) Peters, W. A., IND. (24) Piret, E. L.,Mann, C. A., and Wall, T., Ibid., 32,861 (1940). (25) Rouse, H.,“Elementary Mechanics of Fluids,” pp. 322-40,New York, John Wiley & Sons, 1946. (26) Sarchet, B.R., Trans. Am. Inst. Chem E w s . , 38,283 (1942). (27) Schlaifer, S., undergraduate thesis in chemical engineering, Cooper Union, 1944. (28) S,choenborn, E. M.,and Dougherty, W. C., Trans. Am. Inst. Chem. Engrs., 40,51 (1944). (29) Scofield, R. C., paper presented at 42nd Annual Meeting, Am. Inst. Chem. Engrs., Pittsburgh, Pa.,Dec. 4,1949. (30)Sherwood, T. K.,“Absorption and Extraction,” pp. 138-55, New York, McGraw-Hill Book Co., 1937. (31) Sherwood, T.K., Shipley, G. H., and Holloway, F. A. K., IND. ENG.CHEM.,30,765 (1938). (32)Tillson, P.,S.M. thesis in chemical engineering, Massachusetts Institute of Technology, 1939. (33) White, A. M., Trans. Am. Inst. Chem. Engrs., 31,390 (1934-35). and Othmer, D. F., Zbid., 38,1067 (1942). (34) White, R. E., (35) Zena, F. A.,Ibid., 43,415 (1947). RECEIVED January 7, 1950. Presented before the Division of Industrial and Engineering Chemistry a t the 117th Meeting of the AMERICAN CHEMICAL SOCIETY, Houston, Tex. Abstract of P a r t I of a dissertation submitted b y B. J. Lerner in partial fulfillment of the requirements for the degree of doctor of philosophy at Syraouse University.
Velocities and Effective Thermal Conductivities in Packed Beds MAXIM0 MORALES, C. W. SPINN,
AND
Engfinnedering B O W S
development
J. M. SMITH
PURDUE UNIVERSITY, LAFAYETTE, IND.
r
Fluid velocities in packed beds are of primary importance in determining heat transfer and mass transfer rates. Because no data were available on the variation of these velocities with radial position, this information was obtained in a bed 2 inches in inside diameter, packed with 1/p, I/d-, and a/e-inch cyIindrica1 pellets and through which air was passed. The results indicated that, at bed depths
above 2 inches, the velocity decreased both near the tube wall and near the center, giving a maximum value at a point between the center of the tube and the wall. These conclusions, which are not in agreement with the widespread assumption that the velocity profile in packed beds is uniform, explain some problems encountered in heat and mass transfer in packed beds in this laboratory.
T
solution of the differential equations relating temperature, conversion, and position in the catalyst bed. The effective thermal conductivity has been determined experimentally by measuring temperatures in a packed bed in which no reaction takes place-that is, by passing an inert gas such as air through the catalyst bed. Under such conditions the equation relating the temperature and position in the bed takes the form
HE temperature in every part of the catalyst bed in gas-solid
catalytic reactors must be predictable if reliable design methods are to be developed for estimating the conversion. In nonadiabatic reactors the situation is particularly difficult because of radial temperature variations. It is customary to approach the problem of radial temperature gradients by introducing the concept of the effective thermal conductivity as a measure of the radial heat transfer rate in the packed bed. A knowledge of this conductivity along with certain simplifying assumptions permits
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
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LITHARGE AND
0 OIL
Figure 1.
C u t of Anemometer and Support
mental investigation is needed to gain information on true effective thermal conductivities. The purpose of this paper is t o present the results of such an investigation-namely, the study of the radial variation in velocities in packed beds under iaothermal conditions.
or
B y evaluating the slopes of t against r (radial position),
at zr
against T , and t against 5 (bed depth) curves from the experimental temperature measurements, all the derivatives in Equation l can be calculated. Bunnell and eo-workers ( 2 )and Coberly and Marshall (4)have calculated effective conductivities, K , values, in this manner by multiplying the group ( K e / c p G ) , obtained from Equation 1 by the specific heat and by a constant value of mass velocity, Go, equal to the bulk mean value based on the empty tube area. Values of K , so calculated were found (1) to be directly proportional to Go, and (2) to vary with radial position, decreasing as the tube wall is approached. The first result is not unexpected, since the direct proportionality arose from plotting a variable against itself-that
is, plotting
(3)
c,Go against Go. A more appropriate method of correlation would be t o plot the experimentally determined group (K,/cpG) against Go. The fact that the effective thermal conductivities obtained by multiplying
(3)
c,Go changed M ith radial position
indicates t h a t the assumption of a constant mass velocity (equal to Go) is open to question; for if G were constant with respect to radial position, it is difficult to explain how the K , values varied across the radius of the reactor. From these results it is apparent that true values of the effective thermal conductivity cannot be determined from temperature measurement alone, but only values of the group
(5). Also
i t is not possible t o evaluate how K , varies with mass velocity, although it is possible to measure the effect of the bulk mean mass velocity, Go, on the group
(5).
An independent experi-
EXPERIMENTAL METHODS
There are almost no published data on the radial variation of velocity for fluids floning through packed tubes. Kinney ( 1 4 ) , in calibration woik preparatory to studying velocities in a blast furnace, measured the velocities in a bed 24 inches deep of 1- to 2-inch crushed limestone particles placed in a 16-inch inside diameter tube. D a t a were not obtained near the wall, but the results indicated a minimum in the velocity a t the center of the tube, with increasing values as the distance from the center increased. Coberly and Marshall ( 4 ) state that the velocity profile in packed beds was investigated by a hot wire anemometer method and the results substantiated the usual assumption of rodlike flow. After preliminary experimental work with three methodsPitot tube; hot wire anemometer; and thin-walled cylinders of varying diameters inserted to the top of the packing to measure rates of flow over different sections of the bed-it was decided that the hot wire anemometer approach would give the most reproducible and accurate results, although careful calibration and frequent recalibration would be necessary. The mass velocity range of interest in catalytic reactors extends so low (100 pounds per hour per square foot) that a manometer used in conjunction vr.ith a Pitot tube would have to permit accurate readings of 0.0009 inch of water pressure differential. Although tilting types of micromanometers, such as those designed by Chattock (3’) and Ower ( 1 9 , 2 0 ) ,can be used for pressure differentials of this order of magnitude, they are so sensitive to exterior influences that reproducible results are difficult t o secure. The third method, involving measuring the rate of flow in separate annular spaces, was investigated experimentally and found to be unsatisfactory. Small differences in the resistance of the separate paths leading from the top of the bed to the flowmeasuring
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1951
rotameters changed the actual distribution of flow in the packed bed so much that worth-while data could not be obtained. Preliminary investigations with a small, movable, hot wire anemometer (Figure 1) were sufficiently encouraging to indicate that this method could be used to give reasonably accurate data. The instrument consisted of a small coil of platinum wire which could be moved across the major portion of the diameter of the tube. With this setup a study was made of the velocities directly above a 2-inch inside diameter tube packed with '/s-inch cylindrical particles.
227 MICA SUPPORTS PLATINUM WIRE, CIRCULAR
WOODEN FRAME
COPPER
LEADS
Figure 2. Relative Positions of Five Circular Anemometers in %Inch Diameter Pipe, left; One Anemometer Assembly, right
SCOPE OF WORK
~
Following this initial work a series of circular anemometers of various diameters (Figure 2) was used for more precise measurement of the average velocity a t a series of radial positions corresponding to the radii of the circular anemometers. The range of operating conditions covered with this second set of anemometers is as follows: Reactor tube inside diameter, inches Packing (cylindrical pellets of alumina) diameter and height, inch Air velocity, lb./(hr.) (5s. ft.) Air condition Temp., F. Pressure, inches Hg Packing bed depth, inches
2.067 >/a,
1/4,
%/a
0 t o 500 75 0 to 3 0 to IS
A number of different anemometer designs have been proposed and used (1, 6, 8, 9, 11, l b , l Y , 11-24) although these may be divided into two general classes-a constant-resistant type illustrated by King's arrangement ( 1 3 ) and a constant-current type illustrated by Morris' device (16). The movable coil anemometer shown in Figure 1 may be characterized as a constant voltage type, whereas the circular anemometers shown in Figure 2 were used as constant-current devices.
arranged so that both the packing depth and 1ocation:of the anemometers with respect to the top of the packing could be varied. The acking was supported with a 10-mesh, stainless steel screen geld in place in the tube by a friction fit. After passing the anemometer the total air rate was measured in a precision rotameter. The velocity data were sensitive to the method of packing and to the rearrangement of pellets as a result of tapping after the packing had been added to the tube. To reduce to a minimum variations introduced by these two factors, the tube was always filled by adding the packing from a funnel. The size of the hole in the bottom of the funnel could be adjusted so that the resulting pellet spray just covered the entire tube and gave a uniform depth across the diameter. All the data were obtained without tapping of the tube. The packing density was approximately 79 pounds per cubic foot for the l/s-inch pellets, 49 for the l/c-inch, and 46 for the a/s-inch pellets. CALIBRATION OF ANEMOMETERS
Several methods of calibrating anemometers have been described in the literature, such as a rotating arm of controllable speed to which is attached the instrument or a wind tunnel
EQUlPMENT
4
s
The movable coil anemometer (Figure 1) consisted of a 2-inch length of annealed platinum wire 0.005 inch in diameter, wound in inch in diameter and '/4 inch in length. the form of a helix, This coil was held in position with a brass fork designed to minimize the disturbance of the air stream and yet protect the coil against deformation. In addition to the anemometer the circuit consisted of a variable resistance and a constant resistance, both of constantan wire, and a source of constant direct current voltage. The velocity of gas passed the anemometer coil determined the current through it, and this current was measured with a precision potentiometer with leads connected across the constant resistance. The circular anemometers (Figure 2) were made of 0.005-inch platinum wire and had diameters of 0.654, 1.13, 1.46, 1.73, and 1.96 inches. These diameters were chosen so that the bulk mean velocity over the entire 2,067-inch tube could be obtained by adding the velocities indicated by each device and dividing the sum by five. Frames constructed of mica sheets were built for the five anemometers so that each one could be inserted separately in the tube. The electrical circuit was of the constant-current type and again involved voltage readings with the precision potentiometer. Each circular anemometer was built in a wooden frame (Figure 2) with a cricular hole designed to make a smooth junction with the reactor tube. At any one set of conditions, measurements were made with each of the five anemometers inserted successively in the tube. The data were taken with the circular anemometers placed 3/* inch above the top of packing. The general arrangement of the apparatus is shown in Figure 3. Air was dried in a tube filled with silica gel and then passed through the pressure regulator. The air entered a t the bottom of the 2-inch reactor tube, and the length of straight section of tube from the entrance to the packing could be varied from 3 to 18 feet. An 8-inch length of straightening vanes was permanently inserted a t the entrance to the tube. The anemometers were
f
Figure 2.
Apparatus
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Vol. 43, No. 1
An average voltage wm obtained by graphically integrating such curves in accordance with the equation
where calibration can be accomplished by comparison with a previously calibrated instrument. In this investigation it was believed desirable to calibrate the anemometers in place in the reactor tube. Accordingly, both the movable coil and the circular types were calibrated in the empty 2-inch tube over the required velocity range.
A comparison of this average voltage with the value determined from the rotameter determined a single point on the calibration curve. Repeating this process at a number of different average velocities established the calibration curve shown in Figure 4. Figure 4 was then used to relate the measured point voltage to the point velocity in the tests with packed tubes. This procedure of assuming that the relation between the average voltage and average velocity is the same as that between point values of E and u is not correct unless the relation id linear. Since the curve in Figure 4 is not exactly a straight line, this method of calibration may be subject to small errors. Inasmuch as the circular anemometers were used for the final velocity measurements, no attempt RW made to improve this method of calibration for the movable device. The velocity profile in the empty tube at a total flow rate of 0.95 cubic feet per minute (Re = 750) is shown in Figure 5. Although the length t o diameter ratio of straight pipe between the anemometer and straightening vanes ~ y a 9only 24, the profile approaches that of well developed streamline flow. Calibration of Circular Anemometers. To obtain the precise data required with the annular anemometers it was necessary to employ a different calibration procedure. For this case, an 18foot section of straight, empty tube was inserted directly downstream from the anemometers, providing a length: diameter ratio of 108. According t o the extensive data of Xikuradse ( 1 8 ) a constant velocity pattern for streamline flow is obtained after a tube length of 50 diameters. Hence the calibration method was based on the assumption of a parabolic velocity gradient a t the location of the anemometers. Since the average velocity over the whole tube was measured with the precision rotameter, this approach gave a relation between the anemometer voltage and the average velocity (average with respect t o angular
DISTANCE FROM PACKING TO ANEMOMETER = 1/8"
CITY-
ISOLBS
2.8 -
2.4I
0
,
02 04 06 08 IO DISTANCE FROM C E N T E R - INCHES
Figure 5. Velocity Traverse in Empty %-InchS t a n d a r d Pipe (Movable Anemometer) Movable Coil Anemometer. The movable coil was approximately calibrated with a 4-foot section of empty reactor-tube downstream from the anemometer position. Voltage readings were observed over two thirds of the diameter of the reactor tube a t 0.1-inch stations, To check the symmetry of the velocity profile, data were taken by inserting the anemometer from three positions (90' apart) on the circumference of the reactor tube. The observed voltages were corrected by subtracting the value corresponding to no flow and then plotted against radial position.
0'
: -.2,u-
c L I
L
-
>. 1.6
-
W
-
c 2
>
1.2
0.8
-
0.4 -
l-
o
I
~.'2
d4 DISYANCE
I
I
1
'
d6 0.8 1.0 FROM WALL- I N C H E S
1
I
12
I
1.4
1.5
Figure 6 . Effect of Increasing Total Flow Rate
January 1951
229
INDUSTRIAL AND ENGINEERING CHEMISTRY I
9.8
-
2.4
-
0.8
9.0 ' -
0.4
ki r
'6 8j >
-
I
6"
I
I I
I
I
I
I
I
I
1
1
'
1
I
I
I
'
I
I
I
-
1.9
0 0
Figure 7.
0.P
0.4 DISTANCE
0.6
FROM
1.0 W A L L , INCHES 0.8
.
1.9
1.4
-
TOTAL FLOW RATE
-
DISTANCE, PACKING TO ANEM.,= 3"
04
'
1
1
I
'
=
I
I
1.32 CFM
'
I
'
i "
1
Effect of Angular Position on Velocity Profile
position) at a distance from the center of the tube equal to the radius of the circular anemometer. Such a relation was obtained for each of the five anemometers. To minimize the effect of the anemometers themselves on the flow pattern, only one was placed in the tube a t a time, both in the calibration and test runs. This method of calibration depends not only on the assumption that a parabolic velocity distibution is obtained, but also on an accurate knowledge of the position of the separate anemometers in the tube. A knowledge of the magnitude of both these sources of error is available from a comparison of the total flow rates through the tube determined ( 1 ) from the individual anemometer readings by graphical integration and (2) from the rotameter readings. An analysis of this comparison for forty-five sets of data obtained in the packed tube and six sets in the empty tube is given in Table I. The maximum deviation for the fiftyone sets of data was 7.6% and the average deviation 2.7%. Therefore, i t is believed that the error in the reported velocities is, on the average, less than 5%. Because of the possibility of vaporization of platinum from the wire, the anemometers were recalibrated at frequent intervals. RESULTS
m
= 1.32 CFM
DISTANCE, PACKING TO ANEM,= I
2 0 i
o,4
+7
TOTAL FLOW RATE
g -
-
1.6
-
RUN 03
Movable Anemometer. The results obtained with the movable anemometer clearly show the existence of large variations (up to 200a/0) in the local velocities existing in packed beds. This is illustrated in Figure 6 where local velocities are plotted against distance from the tube wall for a series of average veloc-
TABLEI. DEVIATION BETWEEN AVERAGEVELOCITIES CALCULATED mox CIRCULAR ANEMOMETER READINGS AND MEASURED WITH ROTAMETER (Includes 45 seta of d a t a in packed tube a n d 6 sets in e m p t y tube) No. Observations ' Deviation Range, % 1 -3,OtO - 2 . 0 - 2 . o t o -1.0 3 6 - 1. o t o 0 . 0 5 0 . 0 t o 1.0 5 1 . 0 to 2.0 5 2 . 0 to 3.0 9 3.0 t o 4.0 9 4 . 0 to 5.0 5 5.0 to6.O 1 6 . 0 t o 7.0 2 7 . 0 to 8 . 0 Av. 2.7 Total %
ities, based on the empty tube area. The bed consisted of approximately 35 inches of l/rinch pellets. The variations in actual velocities within the packing are probably even more extreme than Figure 6 shows because the anemometer was located in the empty tube above the top of the bed. Although the distance from the top of the packing to the anemometer was but 1s,' inch, this small distance permits some equalization of velocities. Thus within the packing there are dead spaces where the velocity would approach zero, whereas even inch above the bed these low velocities would not exist. From the relative size of the '/cinch pellets shown in the figure, i t is evident that sometimes successive peaks and dips in the velocity profile occur a t a distance apart equal to the diameter of the pellet. However, just as frequently the successive peaks are farther apart, suggesting that grpups of pellets form more dense and less dense packing arrangements; these in turn cause channeling of the gas. This same channeling phenomenon was observed by Furnas ( 7 ) in studying packing conditions. Variations in local velocities also existed in the angular direction-that is, the velocity profile was not symmetrical. This is illustrated in Figure 7 where the results are presented for measurements made along three different radii, a t an angle of 90" to each other. The effect of distance of the anemometer above the top of the packing is indicated in Figure 8. When this distance was increased to 3 inches, the large local variations in velocity were dampened to a considerable extent, and a t the &inch position the velocity was almost uniform across the diameter. The three distinct curves a t each distance, corresponding to different diameters across the tube, show that the velocity is still not symmetrical around the tube, even at a considerable distance from the top of the bed. The degree of coincidence of the three curves a t the center of the tube is a measure of the reproducibility of the data. In Figures 7 and 8 the average velocity is 1.0 foot per second in all cases. Hence, a comparison of the three sets of curves shows the influence of the distance of the anemometer from the top of the packing. When this distance is inch, the average velocity from the anemometers readings is about 1.8 feet per second, This difference is attributed to turbulence (velocity components in ea dkection perpendicular to the axis of the tube) caused by t h e
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Vol. 43, No. 1
TABLE11. TYPICAL RESULTSWITH CIRCULARAXEMOMETERS Tabulated Figures Refer to Point Velocities (Ft./Sec.) a t Different Radii: Anemometer No. 1, 0.654 Inch; S o . 2, 1.13 Inches; No. 3 , 1.46 Inches; S o . 4, 1.73 Inches; No. 5 , 1.96 Inches .___7 Point Velocities, Feet/Second _______--Anemometer No. 7 Anemometer No. r~Anemometer ho' .--~ v e r a g eVelocitiesa 70 m, % Lb./ DeviDeviDevi(hr./sg. ft.) Ft./sec. 1 2 3 4 5 ationa 1 2 3 4 5 arion 1 2 3 4 5 ation E m p t y Tube, L/D = 108 E m p t y Tube, L / D = 24 2-Inch Bed Depth, I/s-Inch Pellets 3.15 2.45 1.75 1.02 0.350 0.0 2.64 2 . 3 8 1 . 9 5 1.28 0.432 - 0 . 8 2 1.76 2.17 2.10 1.99 0 . 7 8 474 1.75 0.11 1.48 1.86 0.0 2.26 2.03 1 . 6 6 1 . 0 7 0.380 -0.13 2.67 2.07 0.297 1.58 1 . 8 6 1.82 1.71 0.70 398 1.48 3.4 1.69 1.21 0.705 0.242 0.0 1.90 1.69 1.36 0.87 0,294 1.21 2.18 1.0 1 . 2 8 1 . 5 6 1 . 5 3 1 . 3 9 0.60 323 5.0 1.32 0.945 0.550 0.190 0.0 1 . 5 3 1 . 3 8 1 . 0 8 0 . 6 4 0.227 0.945 1.70 2.8 0.98 1.24 1.15 1.04 0.49 252 3.7 1.22 0 . 9 5 5 0.680 0.400 0 , 1 3 6 0.0 1 . 1 6 1.01 0.75 0 . 4 5 0.159 3.8 0.63 0.96 0.78 0.73 0.36 181 0.680 1.8 0.0 0 , 7 3 0 0 . 5 6 5 0.405 0 . 2 4 0 0 . 0 8 0 0 . 7 2 0.62 0.44 0 . 2 4 0.097 4.5 0.26 0.67 0.45 0.46 0.21 108 0.405 1.2 6-Inch Bed Depth, I/s-Inch Pellets 6-Inch Bed D e p t h , '/s-Inch Pellets 6-Inch Bed Depth, l/s-Inch Pellets 474 1.76 2.00 2.20 2.10 1.79 0.78 1.4 2.15 2.40 2.24 l . S 2 0.74 3.4 1 . 9 5 2 . 0 9 2 . 3 4 1.80 0.72 1.7 398 1.48 1.66 1.94 1.96 1.50 0.71 4.8 1.79 2.02 1.83 1.48 0 . 6 4 4.7 1 . 6 1 1 . 7 6 2.20 1.56 0.65 2.6 323 1.21 1.22 1.48 1.60 1.33 0.61 3.1 1 . 4 7 1 . 6 4 1.44 1 . 2 4 0 . 5 4 4.6 1.26 1.46 1.69 1.29 0.55 3.3 252 0,945 0.92 1.10 1.22 0.99 0.50 0.0 1 . 1 3 1.29 1.08 0 . 9 3 0 . 4 5 3.3 0 . 9 0 1 . 2 0 1.32 0 . 9 9 0 . 4 5 2.9 181 0.680 0.48 0.88 0.89 0.68 0.40 - 2 . 1 0.80 0.88 0 . 7 5 0 . 6 3 0 . 3 5 0.3 0 . 5 7 0 . 9 0 0 . 9 1 0 . 6 4 0 . 3 4 -1 2 108 0.405 .. .. .. .. .. . . . 0 , 5 0 0.49 0.46 0.44 0.21 3.7 0 . 2 7 0.62 0.58 0 . 4 0 0.19 1.5 6-Inch Bed Depth, '/a-Inch Pellets 6-Inch Bed Depth, 3/s-Inch Pellets 18-Inch Bed Depth, '/s-Inch Pellets 2.20 1.83 0.75 5.4 1 . 7 2 2 . 0 4 2.22 2 . 3 0 0 . 8 5 1.84 4.3 1.60 1.92 2.13 2.20 0.79 -1.1 1.75 474 0.68 4.6 1.60 5.8 1.47 1.71 1.87 1.92 0.78 1.29 1.60 1.85 1.90 0.72 -0.6 1.48 1.86 1.48 398 6.6 1.11 1 . 3 8 1 . 5 5 1 . 6 0 0 . 6 7 0.59 4.3 1.52 1.34 1.00 1.31 1.55 1.55 0.63 1.21 1.18 0.0 323 0.46 1.05 3.1 0.88 1 . 0 6 1 . 2 0 1 . 1 7 0 . 5 5 0.71 1.00 1.22 1.18 0.53 -1.8 2.9 0.88 1.12 0.945 252 0.35 - 0 . 3 0.75 0.73 0.54 0 . 7 6 0.91 0.81 0 . 4 0 0.6 0.61 0.47 0.76 0.91 0.88 0.41 0.8 0.680 181 0.22 0.47 2.5 0.26 0.46 0.65 0.50 0.25 0.44 0.35 4.7 0.405 108 a Average velocities based upon e m p t y tube cross-sectional area. 5 yo deviation between average velocity calculated f r o m anemometer readings a n d nieasured with rotameter
--
.
~
deviation between results for average velocities for the circular anemometer was only 2.7y0, indicating that turbulence effects were small. Circular Anemometers. The large local fluctuations apparent in the results for the movable anemometer mask the relation between velocity and radial position, tvhich was the main objective of the work. This 1% as the reason for changing to circular anemometers where the longer length of wire permitted measurement of an average velocity a t one radial position. Some of the data obtained with the second type anemometer are summarized in Table I1 (complete tables are on file in the School of Chemical Engineering, Purdue Cniversity). Figure 9 shows the results of reproducibility tests for the same depth of 1/8-inch pellets at two different rates of flow. The curves a t each flow rate represent the results for three different packed beds, although each bed was packed in the same way. In other words, these curves show the degree of reproducibility of packing conditions. Check runs made without repacking the bed agree exactly, so that the divergence exhibited in Figure 9 is entirely due t o the inability to reproduce packing conditions. Also, all three curves in each set give ovei-all flow rates which are in good agreement with the measured values (based on the rotameter readings). Figures 10, 11, and 12 are velocity profiles for a series of over-all flow rates and for the three packing sizes, I/g, I/*, and 3 1 8 inch. The curves for different sizes of packing are I/B INCH CYLINDERS similar; all exhibit a decrease in RIATION OF VELOCITY velocity both near the wall and near O F l L E W I T H AIR R A T E the center of the tube. The maxi0.2 0.4 0.6 0.8 1.0 mum velocity occurs a t a radial posiWALL tion of about 0.7 of the distance from R A D I A L POS I T I O N l/ro the renter to the tube wall. Figure 10
close proximity of the anemometer to the packing. IVhen the distance is increased to 3 inches and 6 inches, the curves in Figure 8 show t h a t the average velocity from the anemometer readings agrees favorably n i t h the true value, indicating negligible velocity components perpendicular to the axial direction. I t is concluded from these comparisons that if the distance betwern the anemometer and packing is too small, the velocity measurements will include the effect of turbulence, but if the distance is too large, the true velocity profile existing in the packed bed \!ill have been seriously changed, After some experimentation the compromise distance chosen for all the data taken with the circular anemometer was inch. 4 s noted earlier, the average
2 INCH 011. P I P E 61HCH BED DEPTH
1,"s
INCH
CYLINDERS
OOUCIEILI'TY
OF
1 , 1 1 _ 1 l l l l I 1 a2
0.4
06
0.8
R A D I A L POSITION-vfo
Figure 9
I O
WALL
CENTER
-
-
January 1951
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
23 1
tions exists primarily near the wall and not near the center of the tube, the variation in average values of 6 2.4 observed by Leva is most likely due to the increase in void space near the 22 wall as the ratio DJD, increases. This means that the void space near 20 the wall is greater than that near the center of the tube. The lower I 8 void space near the center would 0 cause a decrease in velocity. This W v) 1 6 effect combined with the opposing a w wall effect would lead t o a maximum a 14 in the velocity profile in agreement ILL with the results shown in Figures I le 9 to 13. The effect of variations > in void space would not be signifiIcant for the first inch or so of the gJ 1 0 packed bed but would become more W > 08 so as the bed depth increased. This a --a is evidenced by the more uniform 0 6 profile observed for the 2-inch bed depth as shown in Figure 13. Comparison with Effective Con04 IATION OF V E L O C I T Y ductivity Data. As mentioned at H C H BED DEPTH F I L E W I T H AIR R A T the beginning of this paper, it is pos0 2 02 04 0 8 0 8 10 sible to determine values of the CENTER 0 LL group (K,/c,G) from Equation 1and R A D I A L P O S I T I O N - r/r, radial and longitudinal temperature CENTER WALL Figure 12 measurements in packed beds. The R A D I A L PosiTtoN-r/r, data of Coberly and Marshall ( 4 )for Figure 11 a bulk mass velocity of 750 pounds per hour per square foot of empty tube area and several depths of Although a full explanation for the type Profile illustrated in packing are shown in Figure 14. There is considerable similarity Figures 9 to 12 Will not be attempted, it is believed that two between these curves and the velocity profiles a t high bed depths important factors influencing the results are (1) the effect of skin shown in ~i~~~~ 13. Since Hougen (io), Coberly and &farfriction a t the tube wall and (2) the variation in void space with &a]] ( 4 ) ,and Bunnell et al. ($) all found K,/c,G to be an increasradial position in the packed bed. ing function of the over-all mass velocity, Go, it seems reasonable I n streamline flow in an empty pipe the velocity decreases parabolically from the center of the tube because of wall friction. When packing is introduced, the effect of wall friction on the velocity is dampened, and near the center of the tube it is actually negligible. However, as the wall is approached this effect is important even in a packed bed and is the cause of the decreasing velocities near the wall shown in Figures 9 to 12. This influence of the tube wall in a packed bed is illustrated by Figure 13 where velocity profiles are shown a t different depths of packing a t two average velocities (1.48 and 0.95 feet per second), and for the same packing size (1,’s inch). The curve corresponding to zero bed depth (empty tube) exhibits the lowest velocity near the tube wall and the highest a t the center of the tube. As packing is added to the tube the velocity near the wall is increased; this illustrates the dampening of the wall influence until the highest values are reached for the 18-inch bed depth. Similarly, near the center of the tube the effect of the packing is to depress the velocity, so that the lowest value corresponds to the 18-inch bed depth. Figure 13 shows that the characteristic of maximum velocity occurs for ell depths of packing,, although it is not so pronounced a t the low depth of 2 inches. This maximum and subsequent decrease in velocity near the center of the tube is believed to be due to the second factor mentioned previously-that is, the 2 INCH DIA P I P E variation in void space with radial position. I n his studies of pressure drops through packed beds ( I @ , Leva found experimentally that average values of the void space, 6, for the entire 26
0
*
II
tube increased about linearly with the ratio of the diameter of the packing to that of the tube. If the pellets were packed uniformly in the bed, there would be no variation in 6 with the ratio DJD,. As the opportunity for nonuniform packing condi-
O
CENTER
oe
04
RADIAL
06
0.8
P O S I T I O N -r/ro
Figure 13
10
WALL
INDUSTRIAL AND ENGINEERING CHEMISTRY
232
Vol. 43. No. 1
to suppose such mass velocities were equal to G in the nonisothermal data for K,/c,G is equivalent t o assuming a negligible effect of temperature on the mass velocity profile. Although this may be a reasonable approximation, since the effect of temperature on the velocity would tend to be balanced by the corresponding effect on the density, experimental velocity measurements under nonisothermal conditions are needed fully to solve the problem.
DATA OF COBERLY AND MARSHALL(4)
L
CONCLUSIONS
ca
Experimental investigations with hot wire anemometers indicate that the velocity in packed beds decreases near the wall of the containing tube and also near the center. The measurements were limited to isothermal conditions. Similar variations with radial position were observed in the effective thermal conductivity group (K,/c,G). It is suggested that these variations in (KL/cpG) are the result of the nonuniform velocity profiles.
9 9
0.002
' 0
CENTER
02 04 06 08 RADIAL POSITION - '/r0
IO WALL
Figure 14. Variation of I(,/c,G with Radial Position in 5-InchDiameter Tube
ACKNOWLEDGMENT
Financial assistance for this investigation was kindly supplied by the Research Corporation, Kew York, N. Y.
to conclude that the variations in K,/c,G due to radial position illustrated in Figure 14 are a t least partially attributable to corresponding variations in local mass velocities as indicated in Figures 9 t o 13. This correlation between (K,/c,G) and velocity also is illustrated in Figure 15 which shows values of K,/c,G against radial position for different depths of packing. These results were obtained by Crenshaw, Stallings, and Schuler ( 5 ) from Equation I and temperature measurements in a 2-inch inside diameter tube packed with '/ginch pellets. Air entered the bottom of the packing a t about 400" C. and was cooled by a boiling-glycol bath surrounding the 2-inch tube. At low bed depths the value of K,/c,G is high near the center of the tube, This would be expected from the residual effects of the empty tube velocity profile, which exhibits a maximum a t the center. However, as the amount of packing increases, the velocity profiles in Figure 13 and the curves of (K,/c,G) become similar in shape, and both show maximum values a t about the same radial position. The velocity measurements were made under isothermal conditions whereas the data shown in both Figures 14 and 15 were obtained under conditions of rather large radial gradients within the packed bed. Since there is no evidence to indicate that either the velocity or mass velocity profile is independent of temperature, true values of K , cannot be computed from the K./c,G data and the isothermal velocity information. Of course Figures 9 t o 13 can be converted to a mass velocity basis because the density is constant under isothermal conditions. I-Ioaevei,
0O
I
6
m
-
1 AIR __~ MASS VELOClTY=244 LBS/HR -
4PACKING-
0 014
I / @ x 1/8 CYLINDERS (ALUMINA)
BED DEPTH-FT
0 012
LEGEND
0 0300 0 0625
I
0
I
01
Figure 15.
02
SQ - FT -
0 0
1
03 04 05 06 RADIAL POSITION - Vr-
07
08
09
IO
Variation of K,/c,G witb Radial Position
NOMENCLATURE
' F.) Dp Dt E = voltage, millivolts G = air mass velocity, lb./(hr. sq. ft.), a t any point in tube Go = air mass velocity based on cross-sectional area of emptv c,
= specific heat of air a t constant pressure, B.t.u./(lb. = diameter of packing, inches = diameter of tube, inches
tube IC. = effective thermal conductivity, B.t.u./(hr. ft. F.) r = radial distance measured from center of tube, inches = radius of tube, inches TO u = linear velocity, ft./sec. 6 = fraction void space in packed bed LITERATURE CITED
~
Bailey, A , , Reports and Memoranda of the Aeronautical Kesearch Commit,tee, Gt. Brit., S o . 777 (1922). Bunnell, D. G., Irvin, H. B., Olson, R. W., and Smith, J. M . , IND.ENQ.CHEM.,41, 1977 (1949). Chattock, A. P., Phil. Mag., Series 6, 19, 450 (1910). Coberly, C. A , , and Marshall, W. R., presented at meeting of American Institute of Chemical Engineers, Pittsburgh, Pa. (December 1949). Crenshaw, J. B., Stallings, V., and Schuler, R. W., unpublished data. Davis, A. H., Proc. Phys. Soc. (London),33, 152 (1921). Furnas, C. C., U . S. Bur.iMines Bull. 307 (1929). Gerdien, H., Ber. deut. physik. Ges., 15, 961 (1913). Gerdien, H., and Holm, R., Wiss. Verdfentl. Siemens-Konzern. 1, 107 (1920). Hougen, J., presented a t meeting of American Institute of Chemical Engineers, Pittsburgh, Pa. (December 1949). Kennelly, A. E., Wright, C. A., and Blyeveet, J. S., Trans. Am. Inst. Elec. Engrs., 28, 363 (1909). King, L. V., Proc. Roy. SOC.(London), 90A, 563; Phil. Mag., 214A, 373 (1914); J . Franklin Inst., 181, 1, 191 (1916); 183, 785 (1917). King, R. O., Engineering, 117, 136, 249 (1924). Kinney, S. P., U . S. Bur. Mines Tech. Paper, 442 (1929). Leva, hl., Chem. Eng. Progress, 43, 713 (1947). Morris, J. T., EZectrician, 69, 1056 (1912). Neil, P. B., Trans. A m . Inst. Mech. Engrs., 61, 301 (1939). Nikuradse, J., Forschungsheft. 356 (Sept.-Oct. 1932). Ower, E., Phil. Mag., Series 7 , 10, 544 (1930). Ower, E., and Johansen, F. C., Aeronautical Research Commie tee (Gt. Brit.), Repts. and Mem., 1437 (1931). Piret, E. I,., James, W., and Stacey, M . , IXD. ENG.CHEM.. 39, 1088 (1947). Simmons, F., and Bailey, A., Phil. Mag., Series 6, 3, 81 (1927). Thomas, J. S. G., Phil. Mag., Series 6, 40, 240 (1921); 43, 277, 688 (1922). Weske, J. R., NatZ. Advisory Comm. Aeronautics, Tech. Note 880 (1943); 881 (1943); 990 (1946). RECEIVED -March 23, 1950.
