MIXING J. HENRY RUSHTON Purdue University, Lafayeffe, Ind.
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Ill< previous review ( 3 6 ) covered the year to August 1954. During the ensuing year there have appeared a number of excellent papers of a review nature and on specific applications of mixers to heat transfer, extraction, and other operations with liquids, and also on solids mixing and on the mixing of very viscous materials.
Reviews and General Papers Bn aiticle by Rushton ( 3 5 ) called attention to the fluid mechanics aspect of mixing and the importance of flow and tnrbulence in a mixing vessel. There are short discusPions of recent published articles in the field of mixing, and how they can be applied. Different physical and chemical reactions are affected to a different extent by flow and turbulence. Techniques are now available by which the ratio of flow and turbulence resulting from mixing impeller rotation in a fluid can be controlled. Accordingly, reactions influenced by mixing should be studicd by such mixing techniques, so that the proper ratio of flow and turbulence best suited to the desired results can be evaluated. A review of the fundamentals of mixing in its many aspects as applicable to the petroleum refinery industry was prescnted a t the Fourth World Petroleum Congress by Rushton (37‘). Rushton and Mahony (38) reviewed the fundamentals of mixing as applied to extractive metallurgical processing. They suggest significant means by which mixers can be applied for improved extractions. The review article by Green referred to in the 1954 review (36)now has a more accessible reference (14). .4n article in the German literature by Reiss and Erdmenger (31) gives an excellent review of continuous process equipment for the mixing of pastes, viscous polymers, and other doughlike materials. Several of the most useful types of equipment are discnssed in detail. Mixing equipment used for the preparation of soap mixtures, detergents, and other specialties is di.qcussed in a general article (@) which describes equipment manufactured by eight companies. An excellent review on the usc of mixers in fermentation and other aeration operations on both laboratory and industrial scale has been published by Finn (8). He reviews all literature to date pertaining to biological aeration practices and summarizes the techniques bcst suited for the laboratory and large scale plant opcrations. Finn emphasizes the need to obtain data on mass transfer coefficients related to volumetric air rates and to the dissolved gas content, and the need for adequate baffling in the tanks. He recommends that air rates for flat-bIaded turbine impellers should not exceed 400 feet per hour and for paddle impcllers 70 feet per hour. These are superficial velocities based on the cross section of the container. Lyons and Parker (19) published a discussion of the turbine impeller as a mixing tool. They traced the history of turbine mixing from a reference in Agricola printed in 1556 to the presentday design and use of turbine impellers. Many of the fornis of turbines in present use are shown, and a selection chart is given to indicate the adaptation of turbines to nine different mixing operations. 552
A shoit article 011 propeller positioning (50)repeats the uellknown statements that an off-centered propeller can be used a i t h the absence of liquid swirling if the position is carefully chown. Diagrams are given for positioning a side-entering and topentering propeller. Unfortunately, the positions as explained are wrong in several aspects. Correct diagrams and specifications for such units have appeared many time? in the literature, and are now included in elementary unit operations textbooke. Heat Transfer Many liquid mixing operations are accompanied by heat liberation or absorption. Consequently, mixing impellers ale significant in promoting rapid heat transfer during mixing operations. Helical coils are the most widely used means of supplging heat-transfer surface in mixing vessels, yet only a few reliahle data have been available for heat-transfer coefficients under mixing conditions. Oldshue and Gretton (26) have published extensive data on heat-transfer coefficients with helical coils using flatbladed turbine-type mixers in the most common industrial type of use of tank, coils, baffles, and impellers. Data are correlated on the basis of dimensionless groups and they are applicable to scale-up to very large size units. The data apply to conditions of fully developed turbulence. The article by Uhl on heat transfer to viscous materials, rcviewed last year (36), is now available in a more convenient referenre (44).
Blending Van de Vusse (47‘) in a two-part article gives experimental results on the mixing of miscible liquids by means of paddles, propellers, and turbines. This is a condensation of a dissertation, reviewed last year (36). His most important conclusions mere: that the time required for blending (under turbulent conditions) is proportional to the pumping capacity of the impeller, and that mixing by a jet from a high velocity nozzle requires about four times the p o m r consumption of a paddle impeller for the saine mixing. These conclusions are completely consistent with other recent information (%)-for example, the blending of hydrocarbons in very large tanks is favored by large flow rather than by a high level of turbulence (39). His compaiison with the nozzle jet uses the data of Fossett and Prosser (11): van deVussr’s conclusioi~sgive further evidence to dispel the faulty concliisions implied by a reccnt article on jet blending ( 7 ) based on the eucellent Foseett and Prosser data. A common method of promoting blending of liquids in tanks is the use of a recirculating stream wherein the expanding jet emerging from a pipe entrains and mixes uith the surrounding liquid. In 1949 Fossett and Prosser (11) published an extensive work on the blending of gasoline n ith tetraethjdlead, and the blending of other hydrocarbon liquids. They studicd the use of nozzles in large tanks to produce very high velocity jets- for esample, a nozzle 2 inches in diameter in a tank I00 feet in diameter
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MIXING They gave performance data and shorn ed the optimum conditions for use of jet streams of such small diameter for blending. Fossett and Prosser were careful to point out that, although they worked n ith jets of small diameter, such jets were not optimum, and that greater economies could be gained the larger the jet diameter, piovided that there was sufficient velocity head to promote complete circulation in the tank. These data of Fossett and Prosser have been reworked into nomograph form by Du Pont and publiihed in a 14-installment article ( 7 ) . The last seven parts of the ar tide arc single page containing a single noniograph per page. The design of a “jct-in-tank jet-mixing system” from these data applies only for the rangrs of the Fossett and Prosqer work. The ai tide concludes that sniall diameter jet mixing is mole cconornic31 than propeller mixing. No reference is made to other previ011s information to the contrary in the literature ( I O ) . Conipaiison3 ale made with propeller mixers n hich are well-known to be more economical in the use of energy for blending in large tanks (39). I t is difficult to reconcile the Du Pont conclusions mith common industrial practice, with other data in the literature, and mith parts of the Fossett and Prosser article itsclf. The blending of crude oils for feed t o petroleum refinery units ii important to assure steady operations. The bottom sediment and water nhich collects in crude and other storage tanhs is a rccurring prohlem necessitating periodical removal and costly shiitdo\! ns unleqs steps are taken to prevent its accumulation. Both the blending of crude stocks and prevention of bottom sediment and mater can be acconiplished by side-entering propeller mixers. Comprehensive test data are given by Wilson ( Z Z ) , showing the costs of these operations, the size of mixers, and the time required to produce blending and to prevent bottom sediment and watrr For a variety of conditions it was concluded that side-entering miwrs were economically sound and provided the best means for accomplishing the desired results. This is additional confirmation of the economic advantage of side-entering propeller-type mixers for blending operations, as compared to recirculation mixing by means of high velocity jets ( 7 ) ,discussed above
Gas-liquid and liquid-liquid Mixing Finn has given a complete resume of gas-liquid mixing as applied to fermentations (8). Vermeulen and others ( 4 6 ) used a light transmission techniqiie to study the size of drops and bubbles dispersed in a liquid by means of paddle impellers in bamed tanks. They measured mean drop diameter, from whirh interfacial area can be calculated, for a number of immiscible liquid-liquid pairs and for three pairs of gas-liquids. Results showed that the drop size was a function of the interfacial tension, the density and viscosity of the liquids, and the volume fraction of the dispersed phase. The light transmission technique for drop-size rneawrement appears to be reliable and should be usrful in mixing 15 ork involving the formation of drops or biibhlep.
J. HENRY RUSHTON is professor of chemical engineering, Purdue University, and consultant to Mixing Equipment Co., Rochester, N. Y. He studied at the University of Pennsylvania (B.S. and Ph.D.). Rushton is past chairman of the ACS Division of Industrial and Engineering Chemistry and a member of the Society of Chemical Industry. H e is vice president of AIChE and the 1952 recipient of the William H. Walker Award.
March 1956
The power required to operate gas-liquid mixing impellers was studied by Oyama and Endoh (28). They give power characteristics for paddles and flat-bladed turbines for various rates of gas flow. Kafarov, Goldfarb, and Ivanova (16) published data on mixing of gas and liquid by large-area paddles. Magnusson has studied different inipeller designs to find those best adapted t o form stable emulsions (20). He compared the stability of vegetable oil and glycerol emulsions for different impellers a t known rates of power input and gave data for scaling up the results from pilot plant to large size. He found that paddletype impellers were inost useful of those tested, and when high heat tranifer coefficients are necessary together with emulsion formation, he recommends use of large blade area and relatively flat paddles of small diameter. Flynn and Treybal ( 9 ) reported on estraction of benzoic acid in a water-toluene system and a a ater-kerosine system. The extractors weie cvlindrical vessels fitted with baffle5 and with flat-bladed turbine mixing impellers. Continuous flow of fluids was maintained, and the extraction data show a perforinance of the system during flow without mixing and with mixing. Stage efficiencies were correlated on the basis of total pomcr input per volume of fluid floming. Measurements were also made for batch extraction and were related directly to the continuous flow operations. Countercurrent extractions may be performed Rith multiple mixing stages. One such arrangement, consisting of a series of smooth diskp mounted on a single vertical shaft, is rotated within a vertical cylinder separated into compartments by horizontal plates having relatively large central holes. Such units are called rotating disks contactors and ere first described in the literature by Renian in 1951. Kcnian and Olney (33) present new and extensive data on the perkormanre of this device for e q u i p nient in four sizes: 4 inches, 16 inches, 25 inches, and 6 feet 6 inches in diameter. Some data are from laboratory work using pure liquids, and some are for large scale plant operations using ordinary petroleum refinery dreams. The data show capacity and stage efficiency limits, and it is clear that this contactor is versatile and highly efficient. Comparison is made with packed colnnins and columns made up of alternate sections of mixers and coalescers. This column vrithout alternate coalescers seems t o be much preferable to those containing coalcscer sections. This confirms the conclusions of Oldshue and Rushton ( 2 7 ) for the multiple turbine miser column described several years ago.
Theoretical and Experimental Techniques Hixon and others (15) proposed the use of the “transfer unit” and “agitation number” concept for batch operations involving mass transfer. They found that time of a transfer unit multiplied by a velocity-e.g., inipeller tip velocity-gave a constant which they called the agitation number. It is proposed that such a constant can be used to predict performance in scale-up to dimensionally similar systems. Data of their own and from the literature confirmed their conclusions for a limited range of miuing conditions. Stange ( 4 5 ) discusses thr requirements for sampling of mixtures in order to evaluate the pcrformancc of mixers. He ielatcs the results of mixing experinients to the randomness of components in the sample. -4technique for measuring rate of chemical reartion during turbulent mixing through a small tube has been described by Ruhy (34). I n essence, two components are fcd to a tube, through which the reactants pass a t a high Reynolds number. ilt the end of the tube a third component is added, which reacts with one of the original reactants, thereby stopping the first reaction. Continuous flow of materials through processing units,is discussed by Ilanckwerts ( 5 ) from the standpoint of the effect of residence times and mixing on the rates of reaction. The differences betveen piston-type flow and completely mixed flow, and many intermediate situations, have an important bearing on the
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UNIT OPERATIONS REVIEW
Solids mixing receives long-needed study.
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mass transfer resulting from tho flow and turbulence within thc flow. Flow patterns adjacent to several different mixing impellers have been studied by Kraus (18) through a novel application of color photography. White light is passed through a prism and the resulting band of colors is sent t,hrough a mixing vessel a t desired positions. Photographs in color show the lines of flow because of the differences in refractive index of imniiscible fluids adjacent t o the rotating impeller.
Fluidized Beds
COURTESY MIXINO EOUIPMENT C O .
A 20-hp. mixer suspending solids in liquids for fertilizer manufacture time required to biing about certain mass and hcat transfer opcrations. Another article on the performance charactcristics of stirredtank reactors has been published by Acton and Lapidus ( I ) . They were primarily interested in the ti nnsient conditions during the startup of single and series reactors operated with inixets. Previous analyses have clearly defined the characteristics of steady-state operation of such cquipnient, but the transient conditions are important and are here analyzed. The authors pay particular attention to second-order chemical reactions. Fluids flowing in long pipelines are mixed almost exclusively by turbulence; the mixing in a plane pcrpendicular to the axis of flow is very rapid, but the mixing in the axial or longitudinal direction is slon7. The diffusion (or mixing) coefficient of gas floming in a long pipeline was measured by Davidson and others ( 6 ) and shown to be the same as that for liquids. It appears that the Schmidt group has no influence on longitudinal diffusion a t high Reynolds number flow. The problem of turbulent mixing of gases during the spread of jet flow has rrceived further attention by Pai (29). He has considered and developed both the velocity and the density distribution cocficients for turbulent exchange. The volumetric discharge of a flat-bladed mixing turbine rotating in a cylindrical tank with baWcs was studied by Sarhs and Rushton (40). A photographic technique wa9 nsed to determine the rate of travel of small tracer particles in water. Velocities, flow distributions, and total flow displaced by the inipeller 11 ere determined. Data on flow should prove to be fundamental in a thorough understanding of mixing impeller performance and
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An increasing number of chemical reactions are being conducted in beds of fluidized solids. Gases and solids are in contact and mixing of both the gases and the solids is a natural result of fluidization. Reman ( 3 2 ) has studied the effect of both gas mixing and solids mixing and gives data and correlations for such mixing. He shows the effect of both gas and solids mixing on the rate of chemical ieactions for zero-order, first-order, and second-order roactions, and gives results in terms of effective ditTusion coefficients. It is clear that the dimenfiions of a fluidized bed greatly affert mixing and that this must be taken into account in determining space velocities to be used in large scale reactors and in the scale-up from pilot plant to large scale design. A mathematical approach to internal circulation rates in fluidized beds based on the assumption of instantaneous mixing has been developed by Kat2 and 7knz ( 1 7 ) . They suggest that deviations from instantaneous mixing can be correlated with their mathematical developments and that data from existing operations shonld be compared TI ith their equations to determine deviations froin the theoretical. Heat transfer to and from hcds of solids fluidized by gas is often of low rate and may be the limiting factor in design. The gas film heat tranRfer coeffirients can be raised a t least tenfold by means of niechanical mixers, but very few data in the literature describe these operations. Reed and Fcnske (30) have reported on the use of horizontal platcs moved up and down within rectangular cross-eection fluidized beds. The mixing and agitation effect of this motion greatly increases hcat transfer corfficients and improves the fluidization characteristics throughout the bed. They give data for nickel, copper, carbon, and silica-alumina particles fluidized with air. The vibration motion of thc plates was in the neighborhood of 2000 cycles per minute with str0kt.s in the neighborhood of */*inch The article gives a good bibliography of patents and publications applying to heat transfer in fluidized beds.
Metallurgical Applications Extractive metallurgy applications have been reviewed by Rushton and Mahony (38). A series of paper appears in the proceedings of the American Institute of Mining and Metallurgical Engineers on the mixing of molten metals in arc furnaces. Induction cxrrents are used to sct up fluid motion and promote mixing. An outline of the advantages of mixing and the problems encountered in mixing in metallurgical furnaces is given by Walther (48). Details of large steel furnace induction stirrers ( 2 1 )have been given by Malmlow. Equipment is discussed in detail and data arc shown for the resisting forces which the stirrer must overcome. These are useful in design of induction stirring equipment. Mahnlow and Graham (28) describe the first induction stirrer installed in a 100-ton electric arc steel furnace in the United States. A brief description of the same stirrer is given by Graham ( 1 3 ) . A rotating
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MIXING magnetic stirrer is described by Browning and Jones (S),who give performance data showing the energy necessary to cause flow and mixing by magnetic fields. Another article on metal furnace mixing appears in the Indian literature (41). The effect of proper and improper mixing techniques is emphasized, particularly as related to slag carry-over from open-hearth to converter operations. Rapid quenching of steel and other metal products has for many years been practiced with the aid of propeller-type mixers, but no data have appeared until a recent article by the U. S. Steel Corp. (45). The basic principles of fluid flow and turbulence in quenching fluid are discussed in detail. A number of typical quenching opcrations are described and recommendations made for proper installation of propeller mixers. Recomniendcd size of impeller and power input are given. One item of considerable importance is taken for granted in the work-nanirly, that all impellers referrcd to are right-hand in operation. With this fact i n mind, all the diagrams showing the propcr and critical positioning of the propellers are correct.
Solids Mixing The mixing of solids by rotation in smooth cylinders (axis horizontal) is the subject of a paper by Weidenbaum and Ronilla (51). They conclude that the random mixing of particulate solids is best evaluated and defined by means of a chi-squaIe method. The sampling methods used to evaluate solids mixing must be clearly defined in reporting rcsults. They develop a rate equation for the mixing of solids of different sizes and densities which holds for the period of initial mixing; the length of time of mixing is an important variable. The mixing of a small amount of liquid nith a large amount of granular solids (water with dextrose and kaolinite) was studied by Michaels and Puzinaiiskas (%5),u ho found that a uniform mix could be obtained rapidly when a low critical amount of nater was present. This small amount vias that T$ hich brought the mixture to the plastic limit of the kaolinite. There appeared to be a definite optimum of water content for rapid mixiiig for each different mixture. These data are the first to appear for this little understood operation of mixing small amounts of liquids with solids. The experimental techniques should be applicable to many other solid mixing studies. The mixing of solids with small amounts of liquid or with other solids is often performed in “Afuller-type mixers.” Thew mixers are useful for a wide variety of mateiials, but there are critical limitations whenevei the mixture becomrs either too fluid or too sticky. Bullock ( 4 ) has studied this problem and gives data on perforniancr for typical applications for mixing dry and wet solids.
Miscellaneous With the advent of natural gas, replacing manufactured gas for household use, it is frequently neccssary to mix high and low pressure gas streams to produce proper blends. -4n article drscribing the use of jet compressures for continuous blending for pipelines has been written by Fl’arner (49). The growth of crystals and aggregates of crystals of potassium nitrate and ferrocyanide has been studied by Rfatusevich and others (23, 24) in small size laboratory equipment using largcarea paddles. The size of crystals and of aggregates dccreased with increasing mixer speed. One significant conclusion was that sufficient mixing should be used to prevent aggregation of crystals if it is desired to grow large single crystals, but that the impeller speed should not be too high to prevent the growth of large crystals. Baum (2) has reported on thc mixing of liquid floaing through tubes packed with solid lumps. Fowle ( 1 2 ) has described a rotating device which produces sonic and ultrasonic waves which can be used to agitate a liquid that passes through the equipment.
March 1956
Bibliography (1) Acton, F. S.,Lapidus, I,., IND. ENG.CHEIII. 47, 706 (1955). (2) Baum, V. A., Zzvest. A k a d . N a u k , U.S.S.X. 1953, p. 1317. (3) Browning, E. I€.,Jones, hl. F., Am. Znst. Mining Met. Engrs., Elec. Furnace Steel, Proc. 2, 23 (1953). (4) Bullock, H. L., Chem. Eng. P ~ o g r 51, . 243 (1955). (5) Danckwerts, P. V., I n d . Chemist 30, 102 (1954). (6) Davidson, J . F., Parquharson, D. C., others, Chem. Eno. Sci. 4 , 2 0 1 (1955). (7) Du Pont de Semours & Co., E. I.,Oil Cas J . 53, 125 (Sept. 6, 1954), 143 (Sept. 13, 1954), 111 (Sept. 27, 1954),219 (Oct. 11, 1954), 126-A. (Oct. 25, 1954), 188 (Nov. 8, 1954), 118 (Nov. 22, 1954), 95 (Nov. 29, 1954). 135 (Dee. 6, 1954), 151 (Dec. 13, 1954), 115 (Dec. 20, 1954), 123 (Jan. 3, 1955), 105 (Jan. 10, 1955), 115 (Jan. 17, 1955). ( 8 ) Finn, R. K., Bacteriol. Revs. 18, 254 (1954). (9) Flynn, A. W., Treybnl, R. E., -1.I.Ch.E. J . 1 , 325 (1955). (10) Folsom, R. G., Ferguson, C . IC., Trans. *4m. Soc. Mech. Engra. 70, 73 (1940). (11) Fossett, H., Prosser, L. E., Znst. Mech. Engrs. (London) J . 160, SO. 2 , 2 2 4 , 2 2 0 , 2 4 0 , 2 4 5(1949). (12) Fowle, -4.d.,C h e w Eng. 62, 236 (-4pril 1955). (13) Graham, Q., Am. Znst. Minin,g Met. Engrs., Elect. Furnace SteeE, Proc. 2 , 2 2 (1953). (14) Green, S. J., Tram. Znst. Chena. Engrs. (London) 31, 327-43 (1953). C‘hem.E77g.Progr. 50, 592 (1954). (15) IIixon, A. W., (16) Kafarov, V. V., Goldfarh, RI. I., Ivanova, X’. C., K h i m . Prom, 1954, p. 423. (17) Kats. S.. Zenz, F. A., Petroleum Refiner 33,203 (.\lay 1954). (18) Kraus, W., Photographie Wissenschaft3, 3 (January 1954). (19) Lyons, 1;. J., Parker, S. I[., Chem. Eng. Progr. 50, 629 (1954). (20) hlagnusson, K., Chem. Proc. Eng. 35, 276 (1954). (21) RIalmlow, E. G., A m . Inst. Mining J f e t . Engrs., EZect. Furnace Steel, Proc. 2 , 11 (1953). (22) llalmlom, E. C., Graham, Q., Iron & Steel Eng. 30, 120 (February 1953). (23) Matusevirh, L. N., Shaholin, K. S . . J . d p p l . Chern. U.S.S.R. 25,1219 (1952). (24) Rlatusevich, 1,. N., Shabolin, K. N., Priklad, H., Khim. 25, 1157 (1952). (25) Michaels, S.,Puzinauskas, V.,Chem. Eng. Progr. 50, 604 (1954). (26) Oldshue, J. Y . ,Gretton, A . T., Ibid.. 50, 615 (1954). (27) Oldshue, J. Y . ,Rushton, J. €I.,Ibid., 48, 297 (1952). (28) Oyama, Y., Endoh, H., Chem. Eng. ( J a p a n ) 19, 2 (1955). (29) I’ai, S.I.,J . A p p l . Mech. 2 2 , 4 1 (1955). (30) Reed, T. lI.,Fenske, 11. R.. IKD. ENG.CHEM.47, 275 (1955). (31) Reiss, K., Erdmenger, R., V D I Zeitschrift93, 633 (1951). (32) Reman, G. H., Cheniistry & Industry 3, 46 (1955). (33) Reman, G. I€., Olney, R.B., Chern. E n g . frog?. 51, 141 (1955). (34) Ruby, W. R., Rex. Sei. Instr. 26, 460 (1955). (35) Rushton, J. I%.,Chenz. Eng. Progr. 50, 587 (1954). (36) Rushton, J. H., IBU. EBC.CHEM.47, 582 (1955). (37) Rushton, J. H., Proc. Fourzh World Petroleum Congress, Rome, Italy, June 1955. (38) Rushton, J. H., Rlahony, L. I€., J . Metals 200, 1199 (1954). (39) Rushton, J. H., Oldshue, J. Y . , Chem. Eng. Progr. 49, 161, 267 (1953). (40) Sachs, J . P., Rushton, J. H., Ibid., 50,597 (1954). (41) Schrader, 11.. Tisvanathon, S.,Trans. Indian Znst. Metals 6 , 22 (1952). (42) Soap (e: Chem. Specialties 31, 65 (July 1955). (43) Stange, K., Chem. Ing. Tech. 26,331-7 (1954). (44) Uhl, V. W.,A m . Inst. Chena. Engrs., Symposiicm Sei-. 51, 93 (1955), S o . 17. (45) U. S. Steel Corp.. Am. Machinist 99, 143, 145. 147 (July 4), 155, 157, 159 (July 18), 129, 131 (Aug. 1, 1955). (46) Vermeulun, T., Chem. E ~ , Q Progr. . 51,85F (1955). (47) T-usse, J . G., van de, Chem. ERQ.Sci. 4 , 178 (August 1955) 209 (October 1955). L Mining M e t . Engrs., Elect. Furnace (48) Walther, 1%. F.,A ~ JInst. Steel. P ~ o c2. , 6 (1953). (49) Warner, C. K.,G a s 3 0 , 50 (1954). (50) Weber, d.P., C h e w Eng. 62,208 (January 1955). (51) Weidenbaum, S. S.,Ronilla, C. F., Chem. Eng. Progr. 51, 275 (1955). (52) m’ilson, N. J., Oil Gas J . 53,165 (Sovetnber 1954).
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