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By R. R. Vandervoort

The creep behavior of Nb(Cb), Ta, Mo, and W was determined under conditions of constant atomic dif-fzisivity, constant stress to elastic modulus ratio, and nearly equivalent grain size, and the steady-state creep rates obtained from these tests were correlated with calculated stacking fault energies for the metals. These results, in conjunction with similar data for several fccMetals,13 suggest that stacking fault energy may influence the creep strength ofbcc metals. The interrelationship between steady-state creep rate, subgrain size, and stacking fault energy was examined. It was found that the subgrain size for a given creep stress, increased as stacking fault energy increased, but that this relationship did not cormpletely account for the effect of stacking fault energy on creep rate. The crystallography and energetics of stacking fault formation in bcc metals has been discussed by a num-ber of authors,1-5 and impurity stabilized stacking faults on (112) planes have been observed in Nb,6,7 w,8,9 Fe,] and V" by transmission electron microscopy. However, a crucial question is whether or not stack-ing faults influence the mechanical strength of bcc metals. Potentially, stacking faults could increase strength by reducing the mobility of the partial dis-locations bounding the fault, by acting as barriers to slip dislocations, and by retarding the climb of dislo-cations during high-temperature deformation. The objective of this study was to seek a correlation be-tween creep strength and stacking fault energy for several bcc metals; namely, Nb, Ta, Mo, and W. The creep behavior of most polycrystalline metals and alloys at high temperatures and moderate stresses can be described by the following relation:11,12 im=Af(s) where i, = minimum creep rate, A = constant, j(s) = a function involving metallurgical structure, a = applied stress, E = average elastic modulus at the test tempera-ture, w = constant (equal to 5 for most pure metals), D = diffusion coefficient. One factor in the structure function F(s) which sig- R. R. VANDERVOORT, Member AlME is Research Metallurgist, Process and Materials Development Division, Chemistry Department, Lawrence Radiation Laboratory, University of California, Livermore, Calif. Manuscript submitted February 28, 1969. IMD nificantly affects the creep resistance of fcc metals is stacking fault energy, and creep rate has been shown to vary directly with stacking fault energy to the 3.5 power." In the latter investigation, four fcc metals of widely different stacking fault energies (Ag, Cu, Ni, and Al) were creep tested at a constant stress to modulus ratio of 1.21 x 10-4, at a constant diffusivity of 2.7 x 10-12 sq cm per sec, and at nearly equivalent grain sizes of about 0.7 mm. The creep data were then correlated with stacking fault energies. In the present study, a similar procedure was followed. All materials used in this work were consolidated by powder metallurgy techniques. Impurity contents in the as-received materials are listed in Table I. Chemical analyses showed that no measurable contamination of the test specimens occurred during pretest annealing treatments or creep testing. Specimens with a gage section 0.75 by 0.125 by 0.050 in. were creep tested in tension in a vacuum of less than 10-9 torr. Deformation at temperature was measured by tracking fiducial marks on the gage section of the specimen with an optical comparator. Optical deformation measurements also permitted observation of the macroscopic characteristics of the deformation Table I. Typical Specimen Impurity Content, ppm Nb Ta Mo W C 45 10 155 6 O 185 30 4 10 N 30 6 3 2 H 5 I 1 <1 als 3 10 2 15 Ca <5 I3 5 Cr 5 <3 10 <5 Cu 10 50 2 15 Fc 10 10 150 35 Ni 2 150 20 <5 Si <I0 1 3 <10 Ta 100 Ti 10 8 1 Zi 15 50 1 3 Table II. Test Conditions for Constant Stress-Modulus Ratio of 6 X 10.&apos; and Constant Diffusivity of 2.7 X 10-12 sq cm per see, and Grain Size Values for the Given Pretest Annealing Treatments Literature references Pretest Annealing for E and D Treatment Stress, Temperature, ___"&apos;Values__ Grain Tempera-Metal psi "C E D Size, mm ture, .C Time hr Nb 745 1525 14 15 to 17 0.83 1650 I Ta 1220 1770 18 19.20 O.91 1800 I Mo 1975 1630 18 21 0.77 2200 I W 2140 2265 18 22 040 2400 5

Jan 1, 1970

LUTHER B. EAMES, Pueblo, Colo. (written discussion*).-In reading Mr. North&apos;s interesting paper, several points have been noted that appear to warrant discussion. With a feed all through 20 mesh, I feel inclined to question the use of steel balls as large as 2 in. in a tube mill. I have seen balls as small as-3/4 in. used for the dry grinding of cement clinker, and surely many more points of contact would result from smaller balls. This would seem to be desirable in a mill as short as 6 ft. The heavy load in the classifiers would also indicate a high proportion of returned pulp. I hope that some discussion by Mr. North -and others may develop this point. The flow sheet on page 1181 shows the solution returning from the dam valued at 40 c. per ton being added to the last decantation tank. Theoretically, this solution should not be added to that of a lower value. As I calculate it, if this solution were added to tank X the solution finally discharged from tank Z would be reduced in value by nearly 4 c. per ton.

Jan 10, 1919

By Henry E. Wood

Cleveland Meeting, October, 1912.) IN my opinion, the concentration of minerals by flotation is the most interesting problem in ore-dressing, and will command eventually far more consideration than it has at present. For many ores it furnishes a complete method of concentration absolutely independent of specific gravity, and thus simplifies the milling of many difficult combinations. Not having to recognize the influence of specific gravity, we are also able to dispense with some of the complications resulting from classifying-conditions. Where flotation cannot be used for a complete separation of the minerals from the gangue, it will be found, in nearly all cases, to save those portions which are generally lost by reason of their fine state of division. For this reason, it should be looked upon mainly as an aid to general concentration, although there are many ores so well adapted to flotation that more than 90 per cent. of the valuable metals can be recovered from them in one operation by this process. In presenting the results of my investigations in. flotation, I have endeavored to theorize as little as possible. That side of the subject has been extensively discussed by others. My earliest work with flotation was done in 1895, when I used various oils, grease, soap, etc., with results that were remarkable. I did not realize then that with water alone equally good separations could be made. Up to 1906, my endeavors were confined to attempts to keep the concentrates on the tables well wetted and away from exposure to the air. In common with others, I observed that when there was any obstruction in. the wash-water on the table of sufficient size to divert the water to either side, the concentrates collected, and, on exposure to the air, would promptly float away. This convinced me that the sulphides were all good " swimmers," and that if,

Nov 1, 1912

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By J. E. Tobey

THERE are a lot of good things about this great industry of ours. Let us stop commiserating and consider some of the things that are right in this business. Coal is number one in the basic material industries. Our civilization owes more to it than to any other basic commodity. We are literally immersed in the benefactions of coal. In cur man-made world it is indispensable and we are constantly surrounded by objects, materials, and services which owe their existence to coal. Practically all the important materials, such as iron, steel, brick, cement, lime, rubber, glass, cotton, and wood have felt its magic touch.

Jan 1, 1939

By Arthur C. Spencer

(Glen Summit Meeting, June, 1911.) THREE great deposits of iron-ore, in Camaguey and Oriente Provinces, Cuba, are well known to me through careful field-examinations executed in the years 1901 and 1907. In 1901 I visited the Cubitas iron-ore district, which lies about 12 miles distant from the city of Camaguey in a northerly direction, and the Mayari district, which includes the Sierra Nipe, lying opposite Nipe bay on the north side of Oriente Province. In 1907 I again visited the Cubitas district, and also made a sojourn of several days in the Moa district, where the extensive deposits of iron-ore were observed and studied. The observations of 1901 were made under the auspices of the then Military Governor of Cuba; Gen. Leonard Wood, and my conclusions concerning the value of these deposits were incorporated in a report.1 The examination of certain denouncements of iron-ore in the Moa district in 1907 was made in behalf of iron-masters operating in the United States, to whom I reported the existence of large amounts of easily-workable limonitic iron-ore, properly designated " brown iron-ore " in the terminology now current among iron-ore producers in the United States. In 1908 I published a paper entitled Three Deposits of Iron Ore in Cuba, outlining the occurrence and origin of the surficial ores existing in the Cubitas, Mayari, and Moa districts.2 . 1 A Geological Reconnoissance of Cuba, by C. Willard Hayes, T. Wayland Vaughan and Arthur C. Spencer, printed as a part of the report of the Military Governor of Cuba for the year 1901, vol. i. 2 Bulletin No. 390, U. S. Geological Survey, pp. 318 to 329 (1908).

Mar 1, 1911

The world&apos;s largest steam-driven mine hoist, built by Nordberg Manufacturing Co. a half century ago, has become a major tourist attraction in Michigan&apos;s Upper Peninsula. The hoist, designed by company founder Bruno V. Nordberg, is located in the Quincy Mine Number Two, just north of Hancock. Nordberg began construction of the mammoth machine before World War I, but delayed completion until after the war. The hoist became operational in 1920 and continued running until the mine was shut down in 1931.

Jan 9, 1968

Executive.. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS. ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANEWAY, Jr., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L, YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library. JAMES F. KEMP, Chairman. JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALES. C. HUMPHREYS 4 BRADLEY STOUGHTON.

Jan 7, 1913

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Jan 1, 1907

By M. C. LAKE

THE industrial development of the United States has been stimulated by the presence of high-grade iron ore in the Lake Superior district. These great deposits have been susceptible to economical extraction and are conveniently located for cheap lake vessel transportation to the great consuming centers. The district furnishes from 80 to 85 per cent of the iron ore annually consumed in the United States, and a full understanding of the available supply of this great commodity is so important that it is well to consider whether or not the industrial supremacy and national independence attained as a result of the abundance of cheap ore are permanent. The enormous deposits of high-grade ore available in the Lake Superior district have been the foundation upon which the vast industrial structure of the steel and allied industries has been built. It is extremely important to the country as a whole, and especially to those States and communities now dependent on Lake Superior ore for their prosperity, that their industries shall retain the particular advantages with which they are now endowed, and that a generous supply of high-grade raw material be available for their consumption at a satisfactory cost. The steel industry is so basic and fundamental that any fluctuation in the cost of its finished products as determined by the supply and cost of the raw materials involved in its manufacture will necessarily affect the business of a wide variety of industries which are dependent on it.

Jan 1, 1926

By A. J. Shaler, J. Prieto Isaza, John Wulff

TANTALUM metal has a number of unique properties which give it widespread application in modern technology and in research. In electronic apparatus involving high temperatures in vacuo some of the refractory metals become brittle. Tantalum retains its ductility at elevated temperatures, and this property, together with its low vapor pressure and its ability to absorb gases, make it important in this field. Its chemical inertness in the presence of acids, halogens, and other corrosive media, makes it useful in chemical apparatus and in neuro and orthopedic surgical applications. As an addition to tungsten carbide in steel-cutting grades of cemented-carbide tools, the carbides of tantalum and of its sister element columbium have found considerable use. The present-day method1 of manufacturing tantalum is to sinter a powder compact of the metal in vacuo. Because tantalum- columbium alloys are difficult to work and since tantalum ores almost always contain columbium, the two metals must be separated chemically, the products of the separation being generally in the form of potassium tantalum fluoride and potassium columbium oxyfluoride. These salts are used in fused-salt electrolytic baths from which coarse metallic powder is deposited as a sponge at the cathode. Finer powder can be made from the coarse product or from tantalum scrap by first submitting it to an embrittling heat treatment in hydrogen and then crushing it. The fine hydrogen- containing powder may subsequently be degassed in vacuo at a high temperature. Prompted by the success of others2,3 in the magnesium reduction of titanium and zirconium halides, one of the authors under- took4 an investigation of the thermo- chemistry of the reaction between solid magnesium and gaseous tantalum penta-chloride, a subject which had not previously been studied. He found that the heat of formation of tantalum pentachloride is approximately 364,250 cal per mol at temperatures lower than the melting point of magnesium. A value of 83 units was found for the standard entropy at these temperatures. With these values, it was shown that magnesium and tantalum pentachloride are capable of reacting exothermically at temperatures less than the melting point of magnesium, and that no great violence is to be expected when these substances are heated together. The exothermic nature of the reaction indicated that the process should be efficient and should not require much externally applied energy. Tantalum pentachloride is not commonlv made commercially, and any process using it therefore involves the subsidiary problem of producing and handling this substance. A series of experiments was carried out in which dried chlorine saturated with carbon tetrachloride was passed over heated tantalum, either in the metallic state or combined

Jan 1, 1947

By P. D. I. Honeyman

DURING 1938 many copper companies again felt the economic pinch and smelter operations were often on a reduced basis which some- times resulted in intermittent operations and complete shutdowns. During the last half of the year production was stepped up and smelting operations resumed a more normal appearance. One of the present-day trends in reverberatory sme1ting is definitely toward high-tonnage operations. i\ t the Phelps Dodge Corporation&apos;s Douglas plant, the reconstructed 107 by 26- ft. reverberatory furnaces are operated at the rate of 1000 tons of solid charge per day. The arch, all of silica brick; is sufficiently high above the bath to give

Jan 1, 1939

By GUY B. HUNNER

THOSE magnetite ore bodies comprising the Clifton Mines are situated in the south central part of St. Lawrence County, New York, on the western slope of the Adirondack Mountains. The topography is made up of gently rolling hills densely wooded with second-growth maple, birch, and hemlock. Drainage is north and west to the St. Lawrence River.

Jan 1, 1943

By C. R. Wohrman

A MELT of pure electrolytic iron with about 0.4 per cent. sulfur and 7 per cent. manganese was prepared in connection with a study of inclusions in iron. The alloy darkened rapidly when etched with a 10 per cent. alcoholic solution of nitric acid, and microscopic examination revealed the presence of a semimartensitic, semi-Widmanstättian structure (Figs. 1 and 2) closely resembling the structures found by Benedicks in his artificially prepared "meteoric iron." 1 The structures found by Benedicks were readily explained by the presence in his alloy of the two well known iron-nickel solid solutions, taenite and kamacite, and of their eutectoid (?) aggregate, plessite. By analogy, one would infer the existence of similar phases in the iron-manganese alloy just described, such as inference being strengthened by the similarity displayed in many ways by nickel and manganese in their effects on iron. IRON-MANGANESE ALLOTS ARE REGARDED AS HOMOGENEOUS Heterogeneity of iron-manganese alloys has not been recognized heretofore, judging from the data of standard metallographic books and those of original papers. In fact, iron and manganese are quite generally regarded as completely miscible in the solid state. Dr. Rosenhain,2 for example, writes: Alloys of group (a), of which those of gold-silver, iron-manganese, and copper-nickel are examples, when allowed to crystallize sufficiently slowly to attain their condition of final equilibrium, present a microstructure exactly similar to that of a pure metal-the homogeneous character of the molten solution is in that case so completely maintained that the microscope cannot detect the presence of any second constituent.

Jan 1, 1927

By J. V. Vogel

Jan 1, 1969

By Jay J. Burns

TWO zinc concentrating mills are operated by the St. Joseph Lead Co. in St. Lawrence County, N. Y. The Edwards mill is operating at present only sixteen hours a day treating 400 tons daily. The metallurgy at Edwards presents no unusual problems therefore this discussion is mainly limited to the metallurgy of the Balmat ore. The Balmat mill has a capacity of 1,250 tons per day and the operating crew consists of three shift bosses each with five millmen per shift. Two crusher operators work on each of two shifts and one cleanup man on day shift. The repair crew is made up of a foreman and three repairmen, one of the repairmen being capable of taking over any operating job in the mill from shift boss down. Each millman is capable of handling the next job in line and several men in the yard crew are broken into handling the start-off job in the mill so that temporary shortages of men do not cause extensive overtime. Sphalerite, pyrite, and galena, the principal ore minerals, occur in a gangue of calcite, dolomite, and silicates, especially diopside, plus tremo-

Jan 1, 1947

By T. K. Perkins, W. W. Krech

Jan 1, 1969

By W. S. Steele

Vermiculite is a nonmetallic mineral of the mica family, probably related to biotite mica. Its occurrence has been noted at numerous places in the United States and in some foreign countries, but it can be said that vermiculite is of only moderately wide distribution. A laboratory and field survey of over 60 deposits in the United States by F. 1;. Schundler & Co., of Joliet, Ill., indicates that the purest deposit represented in this survey is on the property of the Zonolite Company at Libby, Montana The Zonolite Company is commercially active and the vermiculite it produces is sold as Zonolite. Hereafter, in this report, the word "Zonolite " will be used to designate the vermiculite produced by the Zonolite Company. Values given herein to Zonolite are peculiar to the vermiculite produced from the Zonolite Company&apos;s deposits. References to " vermicullite," are to he interpreted as covering the broad field covered by the Schundler survey. Composition and Characteristics of Vermiculite Vermiculite is an aluminum-nmgnesium silicate. The following typical analysis is published by the United States Bureau of Standards: silica, 41 per cent; iron oxide, 7; aluminum oxide, 18; magnesium oxide, 21; calcium oxide, 1; alkalis (sodium and potassium), 1; moisture, 11. Vermiculite breaks down into platelike formation in crushing and grinding operations. Its cleavage is basal. Crude, screened, dry Zonolit,e weighs between 80 and 90 Ib. per cubic foot; its specific gravity is 2.8 and its specific heat is approximately 2. The fusion point of Zonolit&apos;e is 2462" F. Crude vermiculite contains between 7 and 9 per cent of chemically combined moisture. The instantaneous introduction of crude Zonolite into an expansion furnace at a temperature of between 1800" and 2000" F. transforms the combined moisture into steam, which in an effort to liberate itself forces all explosive expansion of the platelike crude material

Jan 1, 1934

By William Fink

Two of the aluminum-alloy systems previously studied-the alumi-num-titanium and the aluminum-chromium-exhibit a peritectic reaction at the extreme aluminum end of the diagram. Preliminary work indi-cated that the aluminum-zirconium and certain other aluminum systems were similar in this respect. The present paper, the twentieth of a series from the Aluminum Research Laboratories, reports the results of a recent investigation of equilibrium relations in aluminum-zirconium alloys of high purity, which confirm the preliminary observations. PREVIOUS INVESTIGATIONS There has been only one investigation of the aluminum end of the aluminum-zirconium system. Sykes1 prepared and studied alloys containing 0 to 70 per cent Zr. The lowering of the freezing point of aluminum by the addition of zirconium was found to be very little, if any (less than 2°C.). He placed the solid solubility of zirconium in aluminum at room temperature between 0.57 and 0.97 per cent. A few other investigators have attempted to determine the com-position of the intermetallic compounds occurring in this system. Hönigschmid2 obtained the compound ZrAl3 as a by-product during the preparation of ZrSi2. He made no attempt to prepare other aluminum-zir-conium compounds. Weiss and Newmann3 prepared an alloy by heating aluminum with a double fluoride of potassium and zirconium. When this alloy was treated consecutively with caustic soda and hydrochloric acid, there was a residue, which contained approximately 72 per cent Zr and 28 per cent Al (Zr3Al4). Marden and Rich4 prepared an alloy in the same way, treated it with caustic soda, and obtained a residue of silver-white crystals, which contained 70 per cent Zr and 30 per cent Al (Zr3Al4).

Jan 1, 1939

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.&apos;," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".&apos;"&apos;, &apos;" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"&apos; have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.&apos; The final expression presented by Starling and Ellingto&apos;n is: i&apos;. (micropoise) -- /t,, exp rX(7&apos;) p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) &apos; &apos; &apos; X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay&apos;s method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967