4 AL
= = = =
C
=
e
=
U
I.c
=
L, G
=
m
= = = =
surface tension as denoted by suffix viscosity of fluid as denoted by suffix function suffix referring to air-liquid mixture suffix referring to motive fluid before expansion from nozzle suffix referring to entrained fluid at entrance to diffuser suffix referring to motive fluid just after expansion from nozzle s u f h referring to secondary fluid-Le., liquid, gas at entrance to ejector suffix referring to motive fluid at nozzle outlet for air-liquid system suffix referring to initial conditions of entrained fluid for air-air system suffix referring to conditions at entrance to diffuser suffix referring to mixed motive and entrained fluids a t outlet from ejector
literature Cited (1) Flugel, G., V D I Forschungsh. 1939, p. 395. (2) Haberman, W. L., Morton, R. K., David Taylor Model Basin, Rept. 802 (1953). (3) Kaissling, F., Fortschr. Gebiete Ingenieur 14, 30 (1943).
(4) Kastner, L. J., Spooner, J. R., Proc. Inst. Mech. Engrs. 162,155 (1950). (5) Keenan, J. H., Neumann, E. P., Lustwerk, F., J . Appl. Mech. Trans. ASME 69, A317 (1947). (6) Ibid., 72, 299 (1950). (7) McClintock, F. A., Hood, J. H., J . Aeronaut. Sci. 13, 559 (1946).
( 8 ) Mitra, A. K., Guha, D. K., Roy, A. N., Indian Chem. Eng. Trans. 5 , 59 (1963). (9) Mitra, A. K., Roy, A. N., Ibid., 5, 127 (1963). (10) Nicklin, D. J., Trans. Inst. Chem. Engr. 41, 29 (1963). (11) Peebles, F. N., Garber, H. J., Chem. Eng. Progr. 49, 89 (1953). (12) Reid, W. H., Proc. Cambridze Phil. SOC.57, 415 (1961). (13) Richardson, J. F., Higson, D. J., Trans. Inst. Chem. Engr. 40,169 (1962). (14) Rosenberg, B., David Taylor Model Basin, Rept. 727 (1950). (15) Slotboom, J. G., Transactions of Ninth International Congress of Applied Mechanics, Brussels, Vol. 11, p. 37, 1957. (16) Smith, R. A., “Some Aspects of Fluid Flow,” p. 229, Edward Arnold, London, 1951. (17) Swindin, W., Proc. Chem. Eng. Group SOC.Chem. Ind. 10, 116 (1928). (18) Van Der Lingen, T. W., J . Basic Eng. Trans. ASME 82, 947 (1960). (19) White, E. T., Beardmore, R. H., Chem. Eng. Sci. 17, 351 (1962).
RECEIVED for review June 28, 1966 ACCEPTED January 18,1967
MOMENTUM TRANSFER STUDIES IN EJECTORS Correlationf o r Three- Phase (Air- Liquid-Solid) System G. S. D A V I E S , ’ A.
K. M I T R A , AND A.
N . ROY
Department of Chemical Engineering, Indian Institute of’ Technology, Kharagpur, India
Momentum transfer studies in an ejector with air as the motive fluid and slurries composed of finely divided solid particles in liquids as the entrained fluid are described. A correlation in terms of dimensionless groups relates the mass ratio of entrained slurry to motive fluid with the Reynolds number of motive fluid, geometry of the ejector, and physical properties of a solid-fluid system.
transfer studies in a n ejector for single-phase and two-phase systems have been reported ( 3 ) . This paper deals with studies in a n ejector for three-phase systems with air as the motive fluid and slurries composed of finely divided solid particles suspended in liquid as the entrained fluid. OMENTUM
Experimental Apparatus
T h e details of the ejector system and the nozzles employed have been reported ( 3 ) . T h e experimental setup shown in Figure 1 for the three-phase system is essentially that employed for the air-liquid system, except for attachments. The manometer tubes, M , are connected to a n overhead vessel, 0, containing liquid for flushing the tubes free from solids whenever necessary. Tappings are provided in the glass column, L, 6, 16, 28, and 4 0 inches above the divergent end of the Present address, Indian Institute of Technology, Madras, India.
diffuser for the purpose of taking out samples to determine the solids concentration along the vertical length of the column. Physical Properties of Materials
Solids. Solid materials used are kieselguhr, iron catalyst (for Fischer-Tropsch synthesis), coal, and quartz. T h e maTable l. Properties of Solids Displacement Mean Particle Specijc Diameter, Material Gravity Microns Kieselguhr 2.260 49.70 Iron catalyst= 3.000 50.00 Coal* 1.560 61.50 Quartz 2.754 42.35 a Iron catalyst (composition). 700 Fe: 10 Cu:6 M g 0 : 4 CaO: 3 K10:50 kieselguhr. Coal (proximate analysis. Moisture 2.501,, volatile matter 31.5%, ash 75.801,,jxed carbon 50.201,).
VOL. 6 NO. 3
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299
GAS
A
A
1
M
f
terials are powdered and sieved to pass through 150-mesh and retained on 250-mesh British Standard Sieve. T h e relevant properties of the materials are given in Table I. Densities of the solid materials have been determined by the standard specific gravity bottle method, average size of the solid particles, by the microscopic method. The liquids used are water and kerosine. Slurries. Apparent viscosities of the slurries have been determined in a specially designed rotational viscometer of the concentric cylindrical type (7). Surface tension of the slurries have been determined in a Du Nuoy tensiometer. The surface tension values are approximately the same as that of the liquid medium. In the case of catalyst-liquid slurries, the values are higher because of the dissolution of the alkali present in the catalyst. Density of the slurries have been determined by the standard density bottle method. Physical properties of the slurries are given in Table 11. Experimental Procedure
The experimental procedure for an air-slurry system is similar to that described for an air-liquid system ( 3 ) .
AIR
t Figure 1. Apparatus for study of performance of ejector gas-liquid-solid system E. E.
Connector Ejector G. Pressure g a g e H. Gas-liquid separator 1. Glass column M. Manometer 0. Overhead vessel S. Recirculation system
The nozzle is fixed at the position of optimum projection ratio, (L”/D), 1.9, and initial experiments are carried out to determine the flow conditions under which the distribution of solid particles in the liquid medium is more or less uniform along the vertical length of the glass column. The apparatus is charged with a slurry of known concentration (range 3 to 25y0 by weight), and at various air flow rates samples of slurry are withdrawn simultaneously from the four tappings and solids concentration is determined. Air flow rate in the range of 12 to 28 cu. feet per hour is found to give uniform distribution of solid particles throughout the length of the column. The experiments are performed with the five nozzles of diameters 0.803, 0.949, 1.332, 1.870, and 2.676 mm. (corresponding area ratios being 22.6, 46.2, 91.0, 172, and 247) at the various flow rates for the five different slurry systems (Table 11). The rate of slurry flow in side tube S is determined by measuring the pressure drop across tappings T I and Tz and calculating from the empirical correlation proposed by Bhattacharya and Roy (2). For the calculation of the average density of air slurry mixture, holdup determinations have been made following the procedure adopted for the air-liquid system. Correlation and Discussion
The value of the critical area ratio for an air-slurry system has been found to be 197, the same as that obtained for gas-gas and gas-liquid systems.
System
Kieselguhr-water Catalyst-water Catalyst-kerosine Coal-water Quartz-water
300
Table II. Physical Properties of Slurries at 30’ C. Apparent Surface Solids Density Viscosity Tension Concn., (PSL), (PSL)? (USL), wt. % Lb./Cu. Ft. Centipoises DyneslCm. 8.50 65.30 1 .80 69.50 13.50 67.27 2.825 1.65 77.70 63.26 3.15 67.05 3.18 10.90 73.50 5.06 23.90 49.69 1.34 4.40 1.71 34.90 53.92 13.30 59.39 2.12 25.00 63.19 1.12 4.75 1.38 67.5 64.49 9.75 68.96 2.50 24.20 4.12 63.74 1.39 67.6 15.37 68.96 2.25
IhEC PROCESS DESIGN A N D DEVELOPMENT
gPSL4 PSLUSL’
2.83 1.71 1.54 2.01 1.17 2.58 6.29 1.35 4.96 1.07 1.14 1.16 6.96
X 10-lO X 10-0 X 10-lo
x
10-0 X 10-8 X 10-lO X 10-0
X X X X X X
lo-” 1O-IO
10-0 10-lo 10-0
P A S L (av.),
Lb./Cu. Ft. 47.82 49.25 45.76 48.50 53.16 33.60 36.48 40.53 46.28 47.23 49.46 46.68 50.50
I
-
SYSTEMS 1. KIESELGUHR 2. KIESELGUHR
-
WATER WATER
I 3 40 4.40 I O 90 5. CATALYST WATER 23.90 6. CATALYST .KEROSENE 3.1 5 7. CATALYST KEROSENE f 0 . 9 0 8. CATALYST KEROSENE 23.90 9. C O A L WATER 4.15 KI C O A L WATER 9.75 14.20 I1 C O A L WATER 4.12 12. PUARTZ WATER 15.37 13 OUARTZ WATER
3. CATALYST WATER 4 CATALYST WATER
-
-
1
I
Wt. b.C. Wt.hC. Wt. hC. Wt.K Wt.hC. Wt.hC
Wbht WtCC Wb#. W t Lf. Wt.K
Wt.K
0 N O Z Z L E NO. I
A
V NOZZLE
NO. 4
NOZZ L E
NO. 5
+
IO a/2I 62
2
4
3
+ ---I---
N O Z Z L E NO* 2
0 N O Z Z L E NO. 3
5 6 7 8 9
i‘ Figure 2.
Relation between mass ratio,
I
I
I
MRsL,
2
3
4
5
6 7 89;;’
and
I
4 3 I
I
II
2 -
Id$ 9 -
a a -
= -56 = ul ul
e
I
7 6 -
QUARTLWATER
I 1 4.12 15.37
I I
6
A
I
5 4
3 -
2
IO
Figure 3.
Correlation for gas-liquid-solid system
To retain clarity, data of only two nozzles plotted
VOL. 6 NO. 3
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301
For the correlation of experimental data in the case of an air-slurry system, the method developed for an air-liquid system by dimensional analysis (3) has been applied with slight modification, due to the drag force (4)exerted on the solid particles by the liquid. This effect is usually expressed in the form of a dimensionless group ( C D Res2). I n the case of a spherical particle of diameter d p and density p s , moving down ~ viscosity p s L under the action of in a slurry of density p s and gravity, the value of the drag is CD
*
4 Res2 = -gdp3
3
PSL(PS
- PSL)
PSL2
Assuming the slurry to behave as a Newtonian liquid, the u ~ ~the 3 , combined effect of the slurry group, g p s ~ 4 / p ~ ~and drag is given by the following dimensionless group:
The modified expression for a gas-slurry system thus takes the form
Upon correlating it is found that parallel lines are obtained (Figure 2) for different slurry systems. Taking into consideration the density difference effect between the slurry density, psL, in the side tube, S, and the air-slurry mixture density, p A S L , in the glass column, L, the final correlation can be expressed as (Figure 3) :
Nomenclature = area-ratio = drag coefficient D = diameter of diffuser throat d, = diameter of nozzle = diameter of solid particle d, KsL = constant = acceleration due to gravity g L” = distance between nozzle tip and commencement of diffuser throat M = mass rate of flow of motive or entrained fluid as denoted by suffix MRsL = mass ratios for air-liquid solid systems Res = Reynolds number referring to solid particle U = velocity of fluid as denoted by suffix = density of fluid as denoted by suffix p U = surface tension as denoted by suffix = viscosity of fluid as denoted by suffix p ASL = suffix referring to air slurry mixture rn = suffix referring to motive fluid at nozzle outlet S = s u f i referring to solids SL = suffix referring to slurry AR CD
literature Cited ( 1 ) Bhattacharya, A., Roy, A. N., Anal. C h m . 27,1287 (1955). ( 2 ) Bhattacharya, A., Roy, A. N., Ind. Eng. Chem. 47,268 (1955). ( 3 ) Davies, G. S., Mitra, A. K., Roy, A. N., IND.ENG.CHEM. PROCESS DESIGN DEVELOP. 6,293 (1967). ( 4 ) Lapple, C. E., “Fluid and Particle Mechanics,” University of Delaware, Newark, Del., 1956.
RECEIVED for review June 28, 1966 ACCEPTEDJanuary 18, 1967
FLOW METHOD STUDY OF THE GAMMAIRAYINDUCED POLYMERIZATION OF ETHYLENE Intuence of Flow Rate on Polymerization
WAICHIRO KAWAKAMI, YOSHlHlKO HOSAKI, M l Y U K l HAGIWARA, S U E 0 MACHI, AND TSUTOMU KAGIYA Japan Atomic Energy Research Institute, Takasaki Radiation Chemistry Research Establishment, Takasaki, Gumma, Japan
ITH the development of the atomic power industries much w a t t e n t i o n has recently been paid to finding uses for radiation energy. A promising application of radiation is to induce chemical reactions. The polymerization of ethylene induced by y-ray is expected to become a commercial process, because the reaction has a high G value (number of ethylene molecules polymerized per 100 e.v. absorbed) (3, 8) and other advantageous features. We have undertaken a series of investigations on the y-rayinduced polymerization of ethylene. Several studies (3-7) on polymerization in a small scale batch system without agitation have been reported.
302
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
This paper demonstrates the continuous flow type of y-rayinduced polymerization of ethylene on a rather large scale. A detailed study was made to provide the technological information which is essential for the design of a full scale plant. Experimental
Gamma Radiation Facility. All irradiations were performed in the Takasaki Radiation Ciiemistry Research Establishment c o - 6 0 Radiation Facility, which has 500,000 curies of cobalt-60. These are kept a t the bottom of a canal filled with water, which provides an effective shield of 5 meters of water. Irradiations were carried out in a hot cave over the canal by lifting the sources from the bottom and placing them beside
