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By D. I. Bardos, A. M. Bardos, Paul A. Beck

The approximate effective silicon radii in ternary Laves phase alloys with transition elements and silicon were found to range between 1.16 and 1.21A, i.e., considerably smaller than the atomic radius calculated for elemental silicon. The atomic radii were found to increase with the size of the transition element atoms in the structure. It has been noted by Aronsson1 that silicon in solid solution in iron, cobalt, and nickel has an effective CN 12 atomic radius of approximately 1.20Å, a value very much smaller than the CN 12 radius of 1.34Å derived from the interatomic distances in elemental silicon.7 The unusually short metal-silicon interatomic distances in transition element monosilicides and disilicides have been also pointed out by various investigators.1 A similar tendency was observed by Nevitt in Cr3O type silicides.2 Recent work on Laves phases in ternary systems of silicon with transition elements4"8 suggested that extensive Laves phase fields may occur in such systems.8 It has been pointed out by Laves7 that the MgCu2 and MgZn2 type structures lend themselves particularly well for the determination of the effective radii of the component atoms. In these AB2 phases the B atoms are arranged in close packed straight lines, and their distances are related in a simple manner to the lattice parameters.8 The present work was undertaken in order to find out whether or not the B transition element in such AB2 Laves phases can be replaced to an appreciable extent by silicon. In cases where extensive substitution proves to be possible, the "average atomic radius for the B site" at various silicon contents was to be determined, and the effective atomic radius of silicon calculated by extrapolation to complete replacement of the B component by silicon. The following ternary systems were studied: Ti-Mn-Si, Ti-Fe-Si, V-Co-Si, V-Ni-Si, Nb-Fe-Si, Nb-Co-Si, Ta-Fe-Si, Ta-Co-Si, and Mo-Fe-Si. In all of these alloy systems, the Laves phase solid solutions were found to extend over a considerable range of silicon content. As previously reported,4"8 in the V-Co-Si, V-Ni-Si, and Mo-Fe-Si ternary systems Laves phases do occur, even though there are no corresponding binary Laves phases. In stabilizing the Laves phase, silicon acts as if it were decreasing the effective electron concentration of the alloy.8 A more detailed study of the boundaries of the Laves phases in the V-Co-Si and V-Ni-Si systems has been made and will be published elsewhere. In both cases, the elongated Laves phase fields extend parallel to the B-Si side of the composition triangle, clearly showing that silicon is substituting for cobalt, respectively, nickel over a wide range of compositions. The binary Laves phases NbCo2 and TaCo2 have the cubic MgCu2-type structure. It was found that, in both ternary systems with silicon, again the MgZn2-type hexagonal Laves phase is stabilized and that this phase extends to high-silicon contents. In each ternary system at least three Laves phase alloys of the composition A(B1_xSix)2 were used, x here denoting the fractional substitution of the B-transition element atoms by silicon. The alloys, listed in Table I, were prepared by arc melting in argon. Each specimen was water quenched after a homogenizing anneal of 3 days at 110(FC, except for the Mo-Fe-Si alloys, which were annealed at 1200°C. Metallographic examination showed that most of the homogenized alloys consisted of a single phase, although some had minor amounts of a second phase, as shown in Table I. X-ray diffraction patterns were prepared using an asymmetrical focusing camera of large resolution and Fe Ka radiation. The patterns were indexed, and the lattice parameters of the hexagonal Laves phases were determined from the available diffraction lines of highest indices: (213), (205), and (313). The lat-

Jan 1, 1963

Accessions AMERICAN ELECTROCHEMICAL SOCIETY, TRANSACTIONS, vol. 33. Bethlehem, Pa. 1918. AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS, BULLETIN, vol. 2. 1918. (Gift of the Association.) AMERICAN YEAR BOOK: 1915. Edit by Francis G. Wickware, New York. 1919. (Gift of D. Appleton & Co.) ANNUAIRE DE LA HOUILLE BLANCHE FRANCAISE. ` By M. Auguste Pawlowski. 2d year. 1918-1919. Paris. (Gift.) BLACK DIAMOND, Vol. 60, Jan.-June, 1918; vol. 61, July-Dec., .1918. (Gift.) Chicago. CANADIAN MINING INSTITUTE, TRANSACTIONS, vol. 21. 1918. Montreal, Quebec. COMPTES-RENDUS DE L'ATHÉNÉE LOUISIANAIS, vol. 4, No. 3. (Gift of Wm. Beer.) EFFICIENCY OF NATURAL GAS AT Low PRESSURES. Abst. of testimony of Samuel S. Wyer before the Corporation Commission of Oklahoma, February 4, 1919. Printed by Empire Gas & Fuel Co., Kansas City, Mo. GEOLOGICAL. INSTITUTION OF THE UNIVERSITY OF UPSALA, BULLETIN. Edit. By Hj. Sjögren. vol. 14, 1917; vol. 15, 1916; vol. 13, pt. 2, 1916. (Gift.) HYDROGENATION OF OILS. Catalyzers and catalysis and the generation of hydrogen and oxygen. By Carleton Ellis. 2d edition. New York. 1919. (Purchase.) INSTITUTE OF METALS, JOURNAL, vol. 26. No. 2. Edited by G. Shaw Scott. London. 1918.

Jan 6, 1919

By E. L. BROKENSHIRE

FLUORSPAR, a little known non-metallic mineral, referred to technically as fluorite, chemically as calcium fluoride, is a compound of calcium and fluorine in the ratio of one molecule of calcium to two of fluorine. By weight it is composed of 51.3 per cent of calcium and 48.7 per cent of fluorine. Its specific gravity is 3.2. It is brittle, has a hardness of four and can be easily scratched with a knife. It weighs about 200 Ib. per cubic foot and has a melting point of 1650" F. The color of fluorspar ranges from pure white and opaque white, according to its purity, to various hues of yellow, green, pink, lavender, blue and brown, to bluish black. Although the lumps have color, when ground the fluorspar becomes pure white. The reason for this is because the mineral usually carries no fixed pigment, the color being produced by the re- fraction of light rays within the crystal structure and small quantities of organic matter which readily oxidizes. It crystallizes in the isometric system with perfect octahedral cleavages.

Jan 1, 1929

Jan 1, 1885

By Gill Montgomery

At this moment in the history of the world, the all- pervading and universally most important fact is that the world population is beginning to outgrow its food supply, and the United States has suddenly lost its ability to give away huge food surplus to any nation in the world with a food shortage problem. This, of course, means that, all of a sudden, our government must completely reverse its former bureaucratic stance regarding crop controls and agricultural price supports, to out-right incentives to increase farm production and bring more idle land into food-growing use.

Jan 2, 1967

By Kennedy, Joseph E.

MANY things must be considered in coming to a decision as to what type of crushing and grinding equipment is to be used for preparing run-of-mine ore for concentration, amalgamation, flotation, or cyanidation. This paper is intended in no sense as a thorough discussion of these various factors, but rather contains a few observations based on a wide experience in the manufacture and application of milling machinery. One important governing factor is the tonnage to be dealt with. In large plants treating several thousands of tons in eight hours, a large jaw or gyratory crusher of substantial construction is standard equipment for reducing ore to 8 or 10 in. or finer. In open-pit work, using power shovels with 4- or 5-yd. dippers, a jaw crusher should have a receiving opening of 48 by 60 in., or 60 by 84 in., so that dynamite or hand sledging will not be required for breaking to a finer size before primary crushing. The coarsely broken ore is then conveyed by a belt to vibrating screens, the oversize from which is again conveyed by belts to secondary crushers having openings of 12 or 14 in., the product from which is conveyed to storage. From storage, the material goes to a finishing gyratory for reduction to 1/4 in. or finer.

Jan 1, 1936

By E. H. Crabtree

IN an ideal mill, with perfect milling operations, the mineral extraction would be 100 per cent, the, concentrate would be 100 per cent mineral, the tailing would assay zer.0 mineral and the milling cost would be zero dollars. Such an operation can, of course, never be attained. We can only strive to approach it as nearly as possible and in doing so most recognize .the fact that the three primary factors in milling: assay of concentrate, assay of tailing, and cost of operation bear a definite economic relationship to each other. This relation will change from time to time and will be different for different mills, depending on milling equipment, character and quality of feed, market conditions, and other factors. It is granted that for a given operation there is an economic point, but the location of this point is difficult. It is for the purpose of making some of these economic points a little more tangible that this paper has been prepared.

Jan 1, 1930

By C. E. Tsoutrelis

A new method for determining rock drillability in diamond drilling is discussed; the method takes into consideration both penetration rate and bit wear. The method is based on drilling a rock specimen under controlled laboratory conditions using a model bit. The technique used for determining the experimental variables is extremely simple, quick, and reliable. Drillability is then determined by the mathematics of drilling. In considering the different factors that affect diamond drilling performance, the nature of the rock to be drilled is of outmost importance since it affects significantly the drilling costs and such other variables as bit type and design, drilling thrust, and bit rotary speed. Many attempts have been made to study this effect by correlating actual drilling performances either to certain physical properties of the rock being drilled1-? or to test drilling data obtained under laboratory conditions.7-13 These attempts were aimed at providing a reliable method of predicting by simple means the expected rock behavior in actual drilling, thus giving the engineer a tool to use in estimating drilling performances and costs in different types of rock. The purpose of this paper is to describe such a method by which rock drillability (a term used in the technical literature to describe rock behavior in drilling) could be determined in diamond drilling. It is believed that the proposed simple and reliable method will cover the need of the mining industry for a workable method of measuring the drillability of rocks. It should be emphasized, however, that since drill-ability depends on the physical properties of rock and each drilling process (diamond, percussive, rotary) is affected by different or partly different rock properties,14-l6 the proposed method of determining rock drillability cannot be extended to the other drilling processes. The results presented in this paper form part of an extensive three-year research program carried out by the author in the laboratories of the Greek Institute of Geology and Subsurface Research. During this period the effects of the physical properties of rocks and of such operational variables as drilling thrust and bit rotary speed in diamond drilling were investigated in detail. DRILLABILITY CONCEPT The literature is not devoid of drillability studies. While there are a number of investigators1,3,5-7,9-0,12-13,17 who have attempted to establish by direct methods (i.e., drilling tests under laboratory conditions) or indirect (i.e., through a physical property of rock) an index from which the drilling performance in a given rock may be estimated, very few6-7,9,12, of the proposed methods seem to be of much practical value to the diamond drilling engineer and none to date has been universally accepted. Commenting on the proposed methods for assessing rock drillability, Fish14 remarks that "for a measure of drillability to be accepted it is essential that penetration rate at a given thrust and bit life are elucidated as otherwise the method is of little value." This statement should be examined in more detail by making use of the penetration rate-drilling time diagram obtained in drilling a rock under constant operational conditions. Furthermore, the merits of using this diagram to describe rock drillability will be pointed out. At the same time reference will be made to this diagram when discussing some previously proposed methods. Fig. 1 illustrates such a diagram for three rocks,A, B, and C, which have been diamond drilled under identical conditions. It is assumed here that rocks A and B have the same initial penetration rate, i.e., VOA = Vog, but since rock B is more abrasive than A, rapid bit wear occurs and as a result the fall of its penetration rate with respect to time is more vigorous than in rock A. This is shown graphically by a steeper V = f(t) (0 curve in this rock than in rock A. Rock C has a lower initial penetration rate, due to higher strength properties16 but since it is not very abrasive, only a slight fall of its penetration rate occurs during drilling (in this category are some limestone and marbles with compressive strength above 1000 kg per sq cm). It follows from the foregoing considerations that the characteristic for each rock curve (I) is a function of (i), the penetration rate of the rock Vo recorded at the instant of commencing drilling, which determines the starting point of the curve (1) on the y-axis and (ii), the abrasive rock properties which determine the rate of fall of Vo with respect to time. Thus, curve (I) provides an actual picture of the rock behavior in drilling for given operational conditions, and it can be used with complete satisfaction to assess rock drillability. It can be seen clearly from Fig. I that proposed methods for assessing rock drillability by measuring the

Jan 1, 1970

By Gordon B. Brox, Joseph F. Mcaleer, Charles C. Goddard, Edward P. Shea, Robert G. Ingersoll, Lester G. Zeihen, George J. Burns, John M. Guilbert, Richard N. Miller, Charles Meyer

The Boulder batholith is a composite intrusive in which the Butte quartz monzonite is the dominant rock type. Quartz porphyry dikes intruded the quartz monzonite in directions which were subsequently followed by the eastwest- striking Anaconda system of veins, the earliest major veins in the district. Anaconda veins are faulted by northwest-striking veins of the Blue system, which are most prominent in the central third of the district. Anaconda veins are the major producers in the western third of the district and also in the eastern third, where the "horsetail" zones break off from them. Individual oreshoots are thousands of feet long as well as deep on both systems of veins, but they are generally more persistent and thicker on the Anaconda veins. Viewed broadly, the mineralization in the big veins is arranged in crudely concentric zones of zinc and manganese around a central zone of copper. Only slightly offset from these zones, but earlier structurally, is a zone in which quartz-molybdenite veinlets are prominent. This zone tops at about the 2800 level and widens downward. The pattern of distribution of Cu-Fe-S series minerals in the large veins of the copper zone is not symmetrical with respect to the metal zones. There is a fringe of chalcopyrite-bornite all around the copper front. However, within the copper zone, pyrite-chalcocite-enargitecovellite- digenite assemblages are prevalent near its eastern edge from the 3800 level to the surface, whereas deep on the large Anaconda veins in the western part of the copper zone, chalcopyrite is dominant. Here the chalcopyrite grades upward into bornite-chalcocite ores and eastward into the high-sulfur assemblages of the Leonard mine. Sericite-biotite-K-feldspar alteration envelopes, containing up to about 2 per cent copper as chalcopyrite, are present on some of the quartz-molybdenite veinlets at deep mine levels in the molybdenite zone. These envelopes contrast sharply mineralogically and chemically with the later sericitic and argillic alteration envelopes around Main Stage veins. K'0-Ar'0 ratios indicate that they may be older by about 4 m.y. Secondarily enriched copper ores are mined in the Berkeley pit in the southeastern part of the district. At the present time they account for about half of Butte's production of copper.

Jan 1, 1968

By Thomas Harris

This paper. was written in conjunction with the work being undertaken by the Technical Committees on Classification of Coal, and an effort has been made to compile information relative to the use of coal for stationary steam generation in order to use this information to assist the Committee on Classification of Coal for the ultimate purpose of elimination of losses both by the' reduction of indivi-dual effort and waste in the consumption of material. Under the auspices of the National Association of Purchasing Agents, a questionnaire was drawn up to develop this information from stationary steam plants throughout the United States. in order to consolidate the information de-veloped from the many hundreds of boiler tests on coals consumed by various coal¬burning equipment. These questionnaires covered: 1. The company reporting, location and method of delivery to the plant. 2. Complete coal date, including description of coals used (with. sufficient space to- include first, second and third, preference) on--source of coal used,- complete-analysis and factors affecting choice of, coal used. 3. Plant data, divided into - A. Hand fired, B. Overfeed stokers,. . C. Underfeed stokers, D. Traveling grate stokers, E. Pulverized coal, and included complete description of furnace data, draft data, coal-burning rate, type of stoker, type of pulverizer, efficiency date and remarks.

Jan 1, 1933

By J. T. Lapsley, I. I. Cornet, A. E. Flanigan, R. Hultgren, J. E. Dorn

With the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that procedures of heat treating common magnesium casting alloys be investigated systematically. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. Research on the solution heat treatment and aging of magnesium alloy AZg2, (formerly ASTM No. 17; also known as Dowmetal C or AM26o) which was done under "Restricted" Project NRC-2I, in 1942-1943, and reported in detail in a final report to the OSRD on September 3, 1943, is the basis of this paper, which has been released for publication by the OSRD. American experience with magnesium alloys prior to World War II was limited, although some of these alloys had been in commercial use since 1909. Requirements of the aircraft industry for light alloys made it imperative to understand and utilize the advantageous strength-weight properties of magnesium castings. Magnesium casting alloys are commonly solution heat- treated to increase their ultimate tensile strength and ductility; this treatment may be followed by an age hardening at elevated temperatures, which raises the tensile yield strength but diminishes the ductility. In the present investigation, AZp was studied to determine the effects on properties of various solution heat treatment and aging schedules. The principles of heat treatment of magnesium alloys are the same as for other non-ferrous alloys. The alloy studied, AZp, has a nominal composition of 9 pct aluminum, 2 pct zinc, and minor constituents. Fig I shows, by the projection of isothermal sections on the concentration plane, the solubility surface1 of the ternary magnesium-rich solid solutions as determined by X ray 'analysis. From this figure it may be seen that above approximately 375°C (707OF), AZp alloy is a single phase alloy at equilibrium; below this temperature the equilibrium condition is a two phase alloy. The beta constituent which precipitates from the solid solution exerts a hardening effect. Because the zinc concentration is only 2 pct, ancl because of its solubility relations, AZqz resembles a binary alloy of magnesium with aluminum. The solubility curve1 of Fig 2 shows how rapidly the solubility of the beta phase decreases with decreasing temperatures. Unlike many aluminum alloys, magnesium alloys do not age harden at room temperatures; precipitation hardening of AZ² alloy is performed at about 177°C (350°F). At this temperature about 3 pct aluminum

Jan 1, 1949

By AIME AIME

WHETHER by the Mohawk Trail, Sound steamer, air plane, railroad or any other route or mode of locomotion, all roads will lead to Boston the week of National Metal Congress, Sept. 21-25. The Institute of Metals and Iron and Steel divisions of the Institute are then to meet jointly at the Hotel Statler, and the American Society for Steel Treating, the American Welding Society, the Society of Automotive Engineers and the Iron and Steel Division of the American Society of Mechanical Engineers present carefully planned programs at their respective sessions. The National Metal Exposition will be held on Commonwealth Pier.

Jan 1, 1931

By Victor A. Phillips

A series of specimens of a Cu- 3.23 pct Co alloy were prepared with particle diameters from zero to 590A. The samples were then cold-rolled 95 pct and the effects of the particle size on the behavior on annealing for hr at temperatures between 100" and 900°C were studied (by hardness, light, and electron metallography). Particles, particularly for d r 105 to 590A, greatly impeded softening and vecvystallizn-tion, and tended to give elongated grains. Particles deformed fairly homogeneously with the ,matrix, be- IN a previous study by the author,' the growth of cobalt-rich precipitates was followed electron microscopically in Cu-3.12 Co alloy as a function of aging, typically at 650°C. The coherent spherical precipitates grew to 520 + lOOA average diam before spontaneously losing coherency and developing (111) facets. Stretching a few percent after precipitation 2aused loss of coherency to occur sooner at about 220A average particle diam. The particles apparently retained their fcc structure after loss of coherency. coming lau2ellae. For d = 55 to 180A, these lamellae gave streak-contrast effects apparently due to coherency strains , and spheroidized on annealing at 600" to 650°C, forming coherent particles. Particles of d = 250 ov 320A lost coherency during t-olling, giving incoherent lamellae. Recrystallization apparently occured by growth of new grains into unrecrystallized (recovered) material at temperatures below that at which cobalt atoms had much mobility. The present study was undertaken to explore the effect of cobalt-rjch particles of various average sizes from 50 to 600A diam on the isochronal annealing behavior of copper after heavy cold rolling. The previous work' was used as a guide in preparing the two-phase series of prerolling structures. The solution-treated alloy was also rolled for comparison. A further question of interest in the present study was whether dislocation and particle hardening were additive, since the prerolling structures covered the full range unaged - peak aged — overaged, and further precipitation might occur on annealing after cold rolling. Although there have been exhaustive studies of the isothermal2"6 and is~chronal annealing behavior of

Jan 1, 1967

By A. J. Stosick, J. R. Hoffman, E. Rudy, St. Windisch

The binary alloy system Mo-C zoas investigated by means of X-ray, metallog/aphic, thermoanalytical, and melting-point techniques on chemically analyzed specimens. The system, Fig. 39, is characterized by three congruently melting, intermediate phases, Mo2C, n MoCi-x, and aMoC1-,, of which only Mo,C is stable at temperatures below 1650°C. Substoichio-metrzc (~32.5 at. pct C) dimolybdenum carbide undergoes a homogeneous sublattice order-disorder transformation at temperatures of approximately 1400°C, whereas hyperstoichiorrletric compositions undergo a discontinuous Phase change. The order-disorder transitions in the Me, C phases are discussed in terms of the structural changes involved in the transformation processes and the absence of long-range sublattice coherency in stoichiometric or hyperstoiclziomet-ric compositions attributed to the impossibility of obtaining long-range order in a linear chain of alternating carbon atoms and vacancies. From the experimental phase relutionships and the known thermody-namic data for Mo2 C, limits for the free energies of formation for the high-temperature phases r) MoC1-, and aMoC1-, are deriued and found to be in good agreement with data previously obtained from phase equilibria in ternary metal-carbon systems. IN the course of studies of the high-temperature phase relationships in ternary systems of refractory transition metals with carbon,' a number of inconsistencies found in previous work necessitated a reex-amination of some of the related metal-carbon binaries. A reassessment of the binary system data also seemed

Jan 1, 1968

By Paul T. Benson

MOST important of the various departments of a custom smelter, so far as the financial welfare of the plant and the confidence of shippers are concerned, is that responsible for correct weights, accurate moisture sampling, and the obtaining of control samples that are strictly representative of the lot of ore from which they come. Treatment rate schedules are based on the metal content of ores received, reduced to dry weight. These rates must be low enough to keep the ship- per from taking his business else- where and still must allow the smelter a profit. Assay results, likewise, must satisfy the shipper, but if they show too high a metal content for the ore they represent, the smelter will actually lose money. It is always considered, and constant checks through umpire assays prove, that laboratory results are closely correct, so the bur- den of the plant profit and loss and the satisfaction of the shipper rest squarely upon the sampling department.

Jan 1, 1936

By Yasushi Ishikawa

The fact that the degree of granulation and the state of granulated particles of sinter raw mixtures are the influential factors in ensuring coke combustibility and permeability during sintering has been clarified. Based on this knowledge, Nippon Steel developed the divided coke-addition process and the technology to utilize binder, and applied them on a commercial scale. Productivity and sinter quality are thereby greatly improved with a significant reduction in fuel consumption.

Jan 1, 1977

By George Burrell

J. S. HALDANE, M. D., F. R. S., Oxford, England (communication to the Secretary?).-The valuable paper of Messrs. Burrell and Gauger is of special interest to me as, through the courtesy of the management, I had an opportunity of visiting the Portland mine, Cripple Creek, in 1911, in connection with the investigations on acclimatization to high altitudes, carried out on Pike's Peak, near Cripple Creek, by Professors Yandell, Henderson and Schneider, Dr. Douglas and myself.1 The analyses of one or two samples of the vitiated air were entirely confirmatory of those of the authors. A fatal accident owing to two men being lowered down a shaft filled with the gas had occurred in a neighboring mine just before our visit.

Jan 12, 1916

By T. F. Witherbee

THE Fletcherville Furnace was built in 1864 and 1865, making its first blast from August until October of the latter year, when it was blown out to prevent its "bunging-up." Repairs were made in time to enable it to be blown in again December 12th, 1865, the blast ending October 7th, 1866. Total product 1921.15 tons iron, an average of 6.8.2.5 tons per day, from ores yielding 44.8 per cent. Consumption of charcoal 223.2 bushels per ton of iron. The furnace journal up to this time shows no record of furnace dimen¬sions, or temperature of the blast, but as near as can be ascertained, they were as follows, viz. Height of stack, 42 feet. Diameter of bosh, 11 feet. Angle of bosh, 7 1/2 inches to 12 inches rise, about 58°. Diameter of open tunnel head, 42 inches. Number of tuyeres 3; each 3 inches in diameter. Dam 15 inches high. Tuyeres 24 inches high. Tymp 22 1/2 inches high. Diameter of steam cylinder, 20 1/4 inches. Stroke 5 feet. Diameter of blast cylinder, 64 inches. The engine is direct-acting horizontal non-condensing. December 26th, 1.866, the furnace was again put in blast, having been considerably altered in the crucible; the height of stack, bosh, and tunnel head remaining as before. Six tuyeres were put in, three in each of the side arches. The hearth or crucible was rectangular in form, 3 feet wide x 32 feet long x 62 feet high. Inclination of bosh 58°. Height of tuyeres 26 inches ; nozzles 2 1/4 inches diameter. Temperature of blast estimated to be about 500°.

Jan 1, 1874

By KENNETH CROPPER

USUALLY we forget about the things which move along smoothly. There are no causes for worry when there are no troubles. But when troubles arise we must put forth some thought and effort to alleviate them. No one "worries about his automobile until it begins to knock, develop flat tires, or refuses to start. However, when these ailments become apparent we get wide awake on the spot, and do our best to repair the car. So we find ourselves now. The old bus seems to hit all the ditches. There is rough ground on all sides and none of us is able to do anything toward improvement. A state of pessimism stares us in the face, and there is sufficient cause for it. With lead at 3.75 cents, copper about 8 cents, zinc under 4 cents, -and silver about 26 cents, one has a reason for grief. When we think of the 5000 or less men employed in Utah mines and smelters in 1931, as compared with about 12,000 in 1929, the calamity seems even worse. In view of the present economic crisis we cannot even think of new men getting a job.

Jan 1, 1931

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.