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By Walter S. Tower

IN making comparisons of steel industries, one country with another, the convenient common denominator is annual capacity to make raw steel in the form of ingots. It is always necessary, however, to remember that there are different methods of figuring such capacity. For most countries no official figures on capacity are available, and the only authentic data on production are now six or eight years old. But in spite of those limitations on the accuracy of statistical comparisons, any flaws in the figures are probably not serious enough to alter materially the larger conclusions which may be drawn from them.

Jan 1, 1944

By W. H. Herrnstein, J. B. Clark, E. C. Utley, A. J. McEvily

The ratio of the endurance limit (10' cycles) to tensile strength of age-hardened aluminum alloys is approximately 0.3, whereas the ratio for annealed alloys is about 0.5. The lower value for the age-hardened alloys has been associated with the instability of coherent precipitate during cyclic loading, but it has not been definitely established whether this instability is due to overaging or reversion during cyclic loading. The results of the present investigatzon support the reversion viewpoint. In this work specimem of 2024-T4 aluminum alloy were aged for 16 hr at 150°C after cycling for 10 pct of the life at 25.000 psi. These specimens were then tested to failure and exhibzted a marked increase in fatigue life. It is proposed that during the early stages of fatigue in this alloy dislocations cut through the coherent precipitate and bring about the reversion of the precipitate. Subsequent aging at 150ºC induces reprecipitation in the precipitate-free zones so that the weakened regions are strengthened and the fatigue life is extended. It Is recognized that the fatigue strengths of precipitation hardened aluminum alloys are unusually low relative to their tensile strength.'-= This feature is illustrated in Fig. 1 where it can be seen that age-hardened alloys have lower fatigue ratios (the ratio of the fatigue strength to the tensile strength) than those in the annealed or cold worked state. Further, as shown in Fig. 2, the more an alloy is dependent upon precipitation hardening for its total strength, the lower is the ratio of the fatigue strength to the tensile strength. This state of affairs has been associated with an instability of the metastable metallurgical structure of precipitation hardened aluminum alloys during cyclic loading. Evidence2 in support of this view is that the fatigue ratio increases in these alloys as the test temperature is lowered, thereby indicating that thermo-mechanical instability, rather than some other factor such as a non-uniform distribution of precipitate, is the factor responsible for the low fatigue ratio at room temperature. Two mutually exclusive proposals have been ad- vanced to account for this instability. Hanstock has proposed that overaging takes place during cyclic loading, and in support of this view, Broom et a1.2 have indicated that an overaging process might be promoted by the large numbers of vacancies which are created during cyclic loading. The creation of vacancies by radiation4 has been shown to lead to rapid overaging. Hanstockl obtained visual evidence of overaging in an aluminum alloy after cyclic loading, but in this instance it has been pointed ou? that because of the high frequency used (60,000 cpm) the observed effect may have been due to normal high temperature precipitation around energy dissipating cracks. Efforts to discern visual evidence of overaging in this alloy at lower test frequencies were not successful.3 The alternative postulate3 is that reversion takes place during cyclic loading and leads to localized soft spots at which fatigue cracks are readily initiated. Evidence for this process has recently been provided by Polmear and Bainbridge5 who demonstrated metallographically that regions depleted of precipitate were created during cyclic loading of an aluminum alloy. Inasmuch as precipitate particles bordering the depleted region had not grown in size, it was concluded that the solute atoms which had constituted the missing particles had gone back into solution. No mechanism for the reversion process was presented. The present study was undertaken to investigate further the conditions leading to instability during cyclic loading, and to determine whether reversion or overaging had taken place as a result of cyclic loading. BACKGROUND AND TEST PROCEDURE In order to differentiate between the processes of reversion and overaging, rest periods at an elevated temperature, which ordinarily would insure additional precipitation, were used in this investigation. It was expected that after a period of cyclic loading an elevated temperature rest period would result in a decrease in the remaining life of the specimen if overaging were occurring during cyclic loading, whereas in the case of reversion, reprecipitation would occur and the fatigue life would be extended. Such an expectation is based on the assumption that the crack-nucleation phase is a significant portion of the total fatigue life, and that such a treatment is of influence in the crack-nucleation stage and is relatively unimportant thereafter.

Jan 1, 1963

By H. Tabachnick, N. Hedley

The extraction of gold and silver from ores with alkaline cyanide solutions is well known. Cyanide solutions are also good solvents for many base metal minerals, particularly most of the copper minerals. Leaver and Woolf,1 who determined the solubilities of copper minerals in 0.10 pct sodium cyanide solution, showed that malachite, cuprite, chalcocite, and bornite are readily soluble in cyanide; least soluble are chalcopyrite and chrysocolla. The Mining Chemicals Laboratory of American Cyanamid Co. has studied the possibilities of using cyanide solutions for leaching base metals. In this article the authors present the results of their experiments with cyanide leaching to reduce the copper content of a zinc concentrate from 0.050 pct to the desired specification of less than 0.02 pct. Zinc Ore Sample: The sample of commercial zinc ore used in this investigation to produce zinc concentrates was ball mill feed ranging from 1/2 in. to fines. The ore was crushed to —10 mesh and riffled into 600-g charges for zinc flotation. Analysis revealed 4.54 pct Zn and 0.005 pct Cu. Examined microscopically, the ore consisted essentially of cream-colored sphalerite and carbonate gangue. It contained a small amount of pyrite, partly tarnished. The only copper mineral identified was chalcopyrite, mostly smaller than 20µ, some of which occurred as attachments on sphalerite. Flotation Procedure: Batches of zinc concentrates were made as required according to the following general procedure. A 600-g charge of —10 mesh ore was ground for 4 min at 60 pct solids in a laboratory steel rod mill. Screen sizing showed it to be all —35 mesh with 42 pct —200 mesh. The pulp was transferred to a Fagergren laboratory flotation machine, diluted to 25 pct solids and conditioned for 5 min with 0.6 lb per ton CuSO4, . -5H2O. It was then conditioned with 0.10 lb per ton Sodium Aerofloat promoter and floated for 5 min with pine oil as frother and creosote as froth stiff-ener. The pH during flotation was 8.5. A typical analysis of zinc concentrate subjected to leaching is 44.41 pct Zn and 0.051 pct Cu. The ratio of concentration was close to 10 to 1. Leaching Procedure: Aero Brand cyanide, technical calcium cyanide analyzing 49.5 pet NaCN equivalent, was used for all cyanide leaching tests. For each test three rougher concentrates floated as described were combined (total weight close to 180 g) and the water content adjusted to 150 ml. The percent solids in the pulp was thus 55. After a weighed amount of cyanide flakes had been added, the pulp was agitated on rolls for a given period, then filtered and washed. Filtrate and washed concentrate were assayed for copper content. The procedure for ammonia leaching was similar to the cyanide process. A series of tests was run in which the effects of ammonia as a solvent for copper in the zinc rougher concentrate were investigated. In each test 180 g of zinc rougher concentrate was leached with 150 ml of ammonia solution. Various strengths of ammonia and times of leaching were investigated. The results are shown in Table I. It is apparent that ammonia was a poor solvent for copper in the zinc concentrate; 60 min of agitation with a relatively strong NH:, solution extracted only 2 pct of the copper. CYANIDE LEACHING TESTS Effect of Solution Strength: The solvent effects of 0.125, 0.187, and 0.250 pct NaCN equivalent solutions were compared for leaching periods of 15 min. Residue and filtrate were assayed for copper content. The copper content of the filtrate plus wash was calculated back to the original volume of cyanide solution (150 ml). The effects of cyanide strength are given in Table II, It will be noted that 15 min leaching with 0.25 pct NaCN equivalent solution extracted 74.6 pct of the copper in the zinc concentrate. The leached product assayed 0.013 pct Cu, appreciably below the required specification of 0.020 pct. Effect of Leaching Time: Portions of zinc concentrate were leached with 0.25 pct NaCN equivalent

Jan 1, 1961

By J. Brett, L. Seigle, L. Castleman, T. Montelbano

Impurity-induced low-temperature recrystallization of cold-worked tungsten was inuestigated with emphasis on the influence of nickel on the reaction. Palladium, nickel, aluminum, manganese, platinum, and iron greatly lower the recrystallization temperature of doped tungsten, which zs normally very high, but the recrystallization temperature of electron-be am zone-refined tungsten wzre is slightly raised by conlacl with nickel. Recrystallization can be induced at low temperature by the presence of solid nickel on the surface of doped tungsten wire, but apparently not by exposure to nickel vapors alone. Approximately 200 ppm of Ni dijjused into 10-mil wires at 1200 from a deposit of nickel on the surface produced total recrystallization, whereas more than 600 ppm of Ni could be absorbed frotn a vapor source without altering the fibrous structure of cold-worked tungsten. Once initiated, nickel-induced recrystallization required a continued source of' nickel for propagation of the recrystallization front. The solubility of nickel in fibrous 10-mil W wire was approximalely 500 ppm at 1150' C, and the activation energy for penetration of the recrystallization front was 52 kcal per mole. In many applications the usefulness of tungsten depends on critical control of its structure. Cold-worked tungsten with the fibrous structure developed by suitable thermo-mechanical treatment has a low, but technologically significant, ductility. It has long been known1 that traces of nickel, and perhaps other metals, are profoundly deleterious in doped tungsten, because they induce recrystallization at low temperature, which produces a brittle, equiaxed grain structure. This effect appears to be an exception to the general observation that recrystallization is impeded and the recrystallization temperature raised by the presence of impurities.2"9 Previous studies7-'' of the annealing and recrystallization of tungsten wire have divided the phenomenon into prior recovery stages, primary recrystallization and secondary recrystallization. The present investigation is concerned principally with primary recrystallization which is defined here as the replacement of the fibrous structure of deformed tungsten by equiaxed grains. The objective of this study was to explore the nickel-induced recrystallization reaction in tungsten and attempt to elucidate its mechanism. As well, an effort to define which other elements give rise to low-temperature-induced recrystallization was carried out. EXPERIMENTAL PROCEDURE The procedure adopted for these experiments was essentially to bring nickel and other elements into diffusive contact with cold-worked tungsten wires. The process of recrystallization was followed as a function of time and temperature by light and electron microscopic observations. First the influence of nickel on the recrystallization temperature of arc-melted, zone-refined, and variously doped tungsten wire was determined by electroplating a deposit of nickel on the surface of the wire and annealing at a variety of temperatures for 3 hr. The chemical analyses of the tungsten wires used in this investigation are given in Table I. The surface of the tungsten wire was etched with Murakami's slution' and approximately 0.005 in, of Ni was deposited from a Watts-type low pH bath14 for the conditions of these experiments. Variations in plating thickness from about 0.001 to 0.005 in. had no discernible influence on the resulting structures. The wires were then annealed in an atmosphere of dry hydrogen to establish the recrystallization temperature. Concurrently, un-plated specimens were annealed to establish the recrystallization characteristics of nickel-free wire. The criterion of recrystallization was that the fibrous structure be completely replaced by equiaxed grains after a 3-hr treatment of temperature. This provided more reproducible results than use of the first recrystallized grain or a fixed proportion of re-crystallized structure as the critical observation. The structures encountered in longitudinal and transverse sections were examined by both light and electron microscopy at magnifications up to X32,000 using parlo-dion-carbon replicas shadowed with platinum for the latter method. Second, the influence of a variety of metals on the recrystallization temperature of 0.010 in. D alumina-silica doped tungsten wire, AW136-64, was determined. The elements were applied by electroplating whenever possible. Alternatively, they were vapor-plated on the tungsten wire and a greater thickness built up by coating with a dispersion of metal powder in nitrocellulose lacquer. Elements not amenable to either of these procedures were merely slurry coated on the tungsten. The recrystallization temperature was determined as above. Third, the nickel-induced recrystallization process in doped wire was studied more closely by electroplating 8 mils of Ni on 65-mil alumina-silica doped tungsten wire, AW153-NS10, and exposing the wire to temperatures of llOO°, 1200°, or 1300°C for various times in a hydrogen atmosphere. A circular recrystallization front, 'Onsisting of equiaxed grains, developed at the periphery Of the coated tungsten wire, and the advance of this front into the fibrous interior was studied. These experiments employed relatively coarse 0.065 in. D wire because the 0.010 in. D wire recrystallized too quickly to permit observation of the pene-

Jan 1, 1969

By Thomas C. Wilder

The activities of both components and the partial and integral molar thermodynamic properties of mixing for the liquid Al-Ge system at 1200°K and for the gertnanium-rich Al-Ge liquidus have been determined from data for eighteen alloys of compositions in the range 0.0593 < 0.880 using the reuersible gal-vanic. cell in the temperature interval 9320 to 1258°K. The liqui-dus compositions above 93 2 °K loere also ve determined by observing the discontinuities in the C us T plots for the high-melting alloys. This system shows moderate negative deviation from ideality throughout, the values for y° being 0.212 and 0.189 for aluminum and germanium, respectively, at 1200°K. Pavtial molar Properties of aluminum on the germanium-rich solidus and at infinite dilution in Ge(s) oboue 932°K were estimated from the foregozng measurements and the equlibrium data of previous investzgators. RECENT compilations of data1" have shown an increasing demand for knowledge of the thermodynamic properties of mixing of metallic alloy systems. In the case of binary-liquid systems where one of the components is a semiconductor this information is useful because, primarily, properties of the second (dopant) component on the liquidus, solidus, and at infinite dilution may be determined more accurately than from calculations based on the phase diagram. In this investigation a reversible galvanic cell was used to determine the chemical potential of aluminum in the two-phase region, liquid + [Ge], on the germanium-rich side of the A1-Ge system in the temperature range 932" to 1193°K. In addition, similar measurements for homogeneous liquid A1-Ge alloys for the entire composition range were obtained for the temperature interval 932" to 1258°K. The cell used was: The experimental technique and the treatment of the data were essentially the same as described earlier394 and are elaborated upon only briefly here. Each cell consisted of a liquid aluminum anode and three A1-Ge alloy cathodes of different composition which were held in Morganite alumina crucibles. The alloys were made up from aluminum and germanium weighed to the nearest 0.1 mg to a total weight of 5 to 10 g. Aluminum was a gift of Aluminum Co. of America and had a purity of 99.995+ pct. Germanium of transistor grade was a gift of Bell Telephone Laboratories. The four electrodes were contained in a larger alumina crucible which also held the prepurified fused chloride electrolyte. Contact to the electrodes was made by tantalum wire leads sheathed in alumina. The tantalum leads were centered in the electrodes by suitable positioning of an alumina radiation shield which fitted on the top of the - alulnina crucible. Two chrome l-alumel thermocouples, sheathed in quartz wells, completed the internal cell arrangement. The entire assembly was enclosed in an alumina tube, fitted with a water-cooled copper head so the system could be evacuated and then flushed with purified argon. *

Jan 1, 1967

By R. C. Gifkins, A. Gittins

A. Gittins and R. C. Gifkins (University of Mel-houvne)— Evidence from somewhat similar experiments to those described in this paper has led us to the conclusion that possibility 2) of the four listed on p. 319 is a description of what happens in grain boundary sliding. That is, sliding is limited by accommodation deformation, it being necessary to the Continuance of sliding that this accommodation should take place. An example of such accommodation, though probably not the most important, is fold formation at triple points. The evidence and arguments for this point of view are set out in Refs. 14 to 16. In particular, an experiment with a lead bicrys-tall5 seems to support point 2) rather than 3). In creep of this specimen it was found that at least 90 pct of the extension of a zone 0.3 mm wide at the boundary was supplied by sliding at the boundary. The sliding was localized in a region at the boundary very much smaller than 0.3 mm, in fact, in a region too narrow to resolve optically. In poly crystalline Specimens&apos; there appears to be a surface effect, as found by Rachinger," but it appears that this may not manifest itself at low strains. "Low strains" means <10 pct for a Pb-TI alloy, <2.5 pct for magnesium or "Magnox" A12 alloy, or <40 pct for a 0 brass. Up to this extension the sliding, measured by the mean vertical step at boundaries, is proportional to extension. We are able to say this with some confidence, since the error bars on our points are statistically derived. Our results would lead us to think that the error bars on other work, including that of Mullendore and Grant, are much too large at low strains to show this

Jan 1, 1963

GENTLEMEN Herewith are transmitted reports from the Treasurer and of the principal standing committees of the Institute. To these special reports members are referred for details as to the year&apos;s work. Despite the unfavorable business conditions obtaining throughout the year, the Institute was able to carry on its various activities without curtailment and without drawing on the surplus accumulated through previous years. In fact, small additions were made to the Life, Member¬ship and various other funds. It is highly desirable that such additions should continue to be made, especially to the Life Membership fund, for reasons reported last year. At present, money must be used from current receipts in order to enable the Institute to fulfill its obligations to those who on joining the organization commuted their dues by a single payment. In addition, with the passage of years the number increases of those who have paid dues forty years or more and who, by reason of age or dis¬ability, are unable longer to practise their profession. These men have supported the Institute through their active professional life and it would be a pity to lose them as members through resignation or for failure to keep up their dues. In accordance with the By-laws the Board has authority to advance such members, on application, to the Honor Roll of Senior Members and to relieve them from further payment of dues. It has been the policy of the Board to do this liberally, but to keep up this, as well as to meet other obligations, it is necessary for money to be provided. It has been estimated by the Treasurer that nearly $50,000 additional should be placed in the Life Membership fund as soon as possi¬ble to meet these obligations without using current income and to that end it is necessary, not only to avoid running behind currently but to earn, if possible, some surplus each year. The small amount transferred to the Life Membership fund from surplus this year was, as a matter of fact, made possible by certain members paying personally bills that were properly chargeable to the Treasury. Such generosity is common among those active in Institute work and probably no year would have closed with a surplus except for it.

Jan 1, 1923

By Herbert Haas

GEORGE W. HAWKINS, Tucson, Ariz. (communication to the Secretary*).-The paper by Mr. Haas will no doubt be followed with considerable interest, as it covers the power-plant problem in quite a comprehensive way, including not only the usual operating costs but also the fixed charges on the investment, and for load factors ranging all the way from 25 to 100 per cent. and fuel oil ranging from $1.25 to $2 per barrel. The very fact, however, that his paper does cover such a wide range of conditions, makes it the more imperative that any conclusion drawn from his analysis be very carefully considered for any specific case, for in making such analysis the type of prime mover and size must be selected for some one condition which might not be the proper selection had some other condition been assumed as the basic one, resulting in an unfavorable comparison under all conditions except that condition assumed. From the reasons given by the author for his selection of the large turbine units, it is evident he had in mind very high load factors, ranging

Jan 12, 1916

By P. D. Bush, E. H. Gates, M. D. Vijayaraghavan, L. F. Engle

The process developed over the last few years by Republic Steel Corporation in conjunction with Colorado School of Mines Research Institute has been used as a basis for the conceptual engineering of full size plants. The paper will cover the equipment design criteria, equipment design itself, and the integration of the complex unit operations. There are unique features of agitation and use of gas media through- out. The paper will provide an illustrative example of the process requirements for a variety of raw material feeds. It will discuss the materials of construction approach required.

Jan 1, 1973

University of Alabama-University, Alabama, Mining and Metallurgical Society, William L Mason University of Alaska-College, Alaska, Mining Society of the University of Alaska, E H Beistline University of Arizona-Tucson, Arizona, Miners Society, S L Smith Birmingham-Southern College-Birmingham, Alabama, Pick and Hammer Club, Daniel D Arden University of California-Berkeley, California, Mineral Technology Association, Jack Washburn Carnegie Institute of Technology-Pittsburgh, Pennsylvania, The Metals Club, Gerhard Derge Case Institute of Technology-Cleveland, Ohio, Case Metallurgical Engineering Society, Robert F Hehemann City College of New York-New York, New York, CCNY Student Chapter AIME, Daniel T O&apos;Connell

Jan 1, 1957

By C. L. Siebenthal

C. E. SIEBENTHAL, ? Washington, D. C.-From being one of the most maligned of metals-a veritable bugaboo-cadmium has almost overnight become respectable, though its slender claim to respectability rests almost wholly on the possibility of its substitution for tin. Preliminary to any campaign for such substitution, particularly for enforced substitution, the possible supply of cadmium should he determined as closely as possible; for that reason the statistical inquiry of which this paper embodies the results was undertaken. Production Cadmium is marketed in two forms, as metallic cadmium, in sticks or bars, and as cadmium sulfide, the pigment. The metal has found its greatest field of use in this country as a component of an easily fusible alloy that is used in automatic fire extinguishers. The sulfide is .used to some extent in paints but chiefly to give color and luster to glass and porcelain. The metal was first made in this country by the Grasselli Chemical

Jan 12, 1918

By Frederick N. Rhines, Robert F. Mehl

IT has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick&apos;s law (equation 1 below), ‡ in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick&apos;s law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Zedele and of Zedele.§ These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a singles olid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By G. W. P. Rengstorff, L. E. Olds

High purity molybdenum ingots containing controlled amounts of a single impurity element (oxygen, nitrogen, or carbon) were prepared. These ingots were tested for ductility by bending test specimens at various temperatures. The relationship between the plastic behavior of the ingots and their chemical composition has been determined. MANY proposed applications for molybdenum require ductility at or near room temperature. At the present time, it is possible to obtain wrought molybdenum with considerable ductility only if special fabrication techniques are used to control the grain structure. Starting with are-cast or powder metallurgy ingots, the usual methods for obtaining ductility rely on fabrication procedures that result in fibered microstructures in the finished product. Recently, it has been found that the ductility of either powder metallurgy or are-cast molybdenum can be improved by uniform recrystallization of the metal to a very fine equiaxed grain structure.&apos; The need for a fibered or a fine grained structure may limit the practical usefulness of molybdenum. For example, welding. which may be used in fabricating the metal, generally produces coarse grained structures that lead to brittleness. This applies, certainly, to currently available commercial molybdenum. Although commercial molybdenum is brittle when the grains are coarse, it has been shown experimentally that fine grained structures are not always essential for ductility. For instance, as-cast molybdenum with a coarse columnar grain structure is ductile if it is sufficiently pure.&apos; Because high purity cast molybdenum has good ductility even when coarse grained, it is probable that the brittleness in coarse grained commercial molybdenum is caused by the impurity content of the metal. Although the general effects of impurities on the cold ductility of molybdenum have been known in a qualitative manner for some time, no quantitative evaluation of these effects has been available. The present investigation was made in order to determine more accurately the effects of oxygen, nitrogen, and carbon on the cold ductility of cast molybdenum. Oxygen has long been known to be detrimental to ductility, although the minimum amount which will embrittle molybdenum has been open to speculation. Parke and Ham" showed that ingots with oxygen contents above 0.003 pct could not be forged. Maringer and Schwope have described the embrittle-ment of molybdenum wire by oxygen. A discussion on the effects of heat treatment on the distribution of oxygen in molybdenum has been given by Perry, Spacil, and Wulff." Although nitrogen would also be expected to have harmful effects on ductility, no extensive work has been done previously to determine whether this is so. However, Tury and Krausz" found that wires presumably with less than 0.007 pct N were brittle. Carbon is added to commercial cast molybdenum for deoxidation. Parke and Ham" have shown that molybdenum containing as much as 0.06 pct C could be forged if the oxygen was kept below 0.003 pct. Also, Bruckart and others&apos; found that the room temperature ductility of sintered molybdenum improved with carbon contents up to 0.84 pct. However, Rengstorff and Fischer&apos; found that residual carbide particles in cast molybdenum apparently had an unfavorable effect on room temperature ductility.

Jan 1, 1957

By R. W. Snyder, W. H. Guilinger, B. S. Gottfried

Two numerical methods are presented JOT solving the equations Jor one-dimensional, multiphase /low in porous media. The case oF variable physical properties is included in the Formulation, although gravity and capillarity are ignored. Both methods are analyzed mathematically, resulting in upper and lower bounds for the ratio of time step to mesh spacing. The methods are applied to two- and three-phase waterflooding problems in laboratory-size cores, and resulting saturation and pressure distributions and production histories are presented graphically. Results oJ the tuo-phase flow problem are in agreement with the predictions of the Buckley-Leuerett theory. Several three-phase flow problems are presented which consider variations in the water injection rate and changes in the initial oil-and ujater-saturation distributions. The results are different physically from the two- phase case; however, it is shown that the Buckley-Lez~erett theory can accurately predict fluid interlace velocities and displacing-fluid frontal snturations for three-phase flow, providing the correct assumptions are made. The above solutions are used as a basis JOT et~aluuting the numerical methods with respect to machine time requirements and allowable time step for a fixed mesh spacing. INTRODUCTION Considerable progress has been made in recent years in obtaining numerical solutions of the equations for two-phase flow in porous media. Douglas, Blair and Wagner2and McEwenll present different methods for solving the one-dimensional case for incompressible fluids with capillarity (the former using finite differences, the latter with an approach based upon characteristics). Fayers and Sheldon4 and Hovanesian and Fayers8 have extended these studies to include the effects of gravity. West, Garvin and Sheldon, l4 in a pioneer paper, treat linear and radial systems with both capillarity and gravity and they also include the effects of compressibility. Douglas, Peaceman and Rachford3 consider two-dimensional, two-phase, in compressible flow with gravity and capillarity and Blair and Peaceman1 have extended this method to allow for compressible fluids. No one, however, has examined the case of three-phase flow, even for the relatively simple case of one-dimensional flow of incompressible fluids in the absence of gravity and capillarity. In obtaining a numerical technique for simulating forward in situ combustion laboratory experiments, Gottfried5 has developed a method for solving the one-dimensional, compressible flow equations with any number of flowing phases. Gravity and capillarity are not included in the formulation. The method has been used successfully, however, for two- and three-phase problems in a variable-temperature field with sources and sinks. This paper examines the algorithm of Gottfried more critically. Two numerical methods are presented for solving the one-dimensional, multi-phase flow equations with variable physical properties. Both methods are analyzed mathematically, and are used to simulate two- and three-phase waterflooding problems. The numerical solutions are then taken as a basis for comparing the utility of the methods.

Jan 1, 1967

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman&apos; developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,&apos; and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,&apos; as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman&apos;s work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

R. G. BROWN, Bodie, Cal.: Mr. Rickard&apos;s paper, with its valuable illustrations, brings into fresh clearness the game of hide-and-seek which the miner must play with his ore-deposit; but, more than this, it goes far towards classifying those perplexing idiosyncrasies which, while unclassified, constitute a labyrinth almost without clue. Probably every engineer can add to the list by the mention of at least one fresh detail from his own experience, and I for one would like to comment on two of Mr. Rickard&apos;s divisions. To what he has written about " walls within walls" and " walls without walls," the accompanying Figs. 1 and 2 may be appropriate, the more so as they represent conditions obtaining in a part of the Butte copper-belt more typical of the copper-veins as a whole than the Gagnon, which, in some respects the most interesting mine in the camp, stands almost alone in many particulars. (See nuns., xvi., 62.) Fig. 1 was sketched in January, 1895, in the stopes above the 700-foot level of the Colusa-Parrot mine, east of the Parrot and southwest. of the Anaconda. The stope, the commercial foot-wall of which is shown at A, was 30 feet wide at this section, the pay-ore being massive chalcocite, jumbled with bornite, pyrite, quartz and thoroughly broken-down granite. A and At are inch-thick seams of black talc; B, B&apos; and B" are also talc, possibly 1/8-inch thick. In the plane of the section the "banded quartz " and " quartz and pyrite " were both of too low grade for extraction, but 5 feet back along the stope had been of fair value. The granite with quartz and bornite between Bt and A&apos; was pay-ore, but that to the right of B" was not. In both cases the ferro-magnesian minerals had been removed, leaving, where not obscured by ore, faint, dark patches. Between A&apos;

Jan 1, 1897

By W. J. Reagan

THE problem of increasing output and decreasing percentage of rejections is a vital one in the manufacture of steel of any kind. The making of basic open-hearth steel for use in rolled steel wheels, tires for locomotive and car wheels, and forgings of various kinds, is a highly specialized industry. The increase in weight of railway rolling stock of all kinds, and the high speed that the public demands of transportation facilities, make it imperative that steel for use in this class of material shall be of the highest quality obtainable. During the past few years it has been the writer&apos;s good fortune to have opportunity-to study the defects in basic open-hearth steel, and also the results obtained by various changes in open-hearth practice, on such defects. The opportunity for study and the details available are rarely found in the manufacture of steel of any kind. It seems reasonable to assume that many of the results determined here can be applied to the production of steel of other types with a decided improvement in quality, a decrease in the percentage of rejections and an increase in output. All of the material described is basic open-hearth steel with the following range of analysis: carbon, 0.50 to 0.85 per cent.; phosphorus and sulfur, 0.04 coax.; silicon, 0.15 to 0.35; manganese, 0.50 to 0.75. All of this material is bottom-cast, therefore tapping and pouring temperatures are higher than in top-cast production. Ingots used in this type of work are of standard length with varying diameters. The ingot is known as duodecagonal, or twelve-sided. The standard body length is 88 in. and the hot top length, 14 in. Fig. 1 shows a typical ingot of this type. The diameter varies from 13 to 30 in. Ingots for special forgings, which cannot be made in molds of standard size, are made in molds of various sizes and designs. These ingots are sliced cold, into blocks of various lengths, depending upon the weight of the forging to be made. Fig. 2 shows the ingot-after coming from the slicing lathe. Just sufficient metal remains between blocks to hold the ingot in one piece while it is being removed from the lathe; then steel wedges are inserted between the blocks and the blocks are broken apart. This affords abundant opportunity for inspection, as the interior of the

Jan 1, 1930

By B. M. Loring, I. R. Krame, F. M. Walters

NO observations on the mechanical properties of man-manganese alloys have been published since pure manganese became readily available, either distilled manganese or electrolytic manganese. The purpose of this investigation was to determine whether iron-manganese alloys are essentially brittle, as reported by Hadfield,&apos; or whether the lack of ductility observed was due to impurities in the alloys that he studied. Experimental Methods The alloys were melted in a roo-lb. high-frequency induction furnace with a magnesia crucible, using ingot iron and electrolytic manganese. The heats were split, the first giving six 18-lb, ingots and the second three. Each successive heat was higher in manganese and about 0.3 per cent silicon was added as ferrosilicon. The alloys forged without difficulty and were given a 9&apos; per Published by permission of the Navy Department. Manuscript received at the office of the Institute June 28. 1941. Issued as T.P. 1369 in Metals Technology. September 1941. * Division of Physical Metallfirgy Naval Roscarch Laboratory. Anacostia Station Washington. D. C. 1 References are at the end of the paper. 4 cent reduction to ¾-in. rounds. The chemical analysis of the alloys is given in Table I. The forged rods were homogenized for 224 hr. at r150°C. (2100°F.) and air-cooled. The alloys were tested in two conditions of heat-treatment: (I) as normalized from 870°C. (1600°F.) and (2) normalized from 870°C. and tempered for I hr. at 540°C. (Iooo°F.) and air-cooled. The tensils specimens were 0.505 in. in diameter with a 2-in. gauge length, and the impact specimens were v-notch Charpy. The proportional limit and yield strength were taken from the stress-strain diagrams drawn by a Peters recorder. The data obtained from the tensile test and the hardness measurements are given in Table 2. Specimens that were normalized are designated by N; those that were normalized and tempered by T. Alloy G was tempered after forging (D).

Jan 1, 1942

By B. M. Loring, I. R. Krame, F. M. Walters

NO observations on the mechanical properties of man-manganese alloys have been published since pure manganese became readily available, either distilled manganese or electrolytic manganese. The purpose of this investigation was to determine whether iron-manganese alloys are essentially brittle, as reported by Hadfield,&apos; or whether the lack of ductility observed was due to impurities in the alloys that he studied. Experimental Methods The alloys were melted in a roo-lb. high-frequency induction furnace with a magnesia crucible, using ingot iron and electrolytic manganese. The heats were split, the first giving six 18-lb, ingots and the second three. Each successive heat was higher in manganese and about 0.3 per cent silicon was added as ferrosilicon. The alloys forged without difficulty and were given a 9&apos; per Published by permission of the Navy Department. Manuscript received at the office of the Institute June 28. 1941. Issued as T.P. 1369 in Metals Technology. September 1941. * Division of Physical Metallfirgy Naval Roscarch Laboratory. Anacostia Station Washington. D. C. 1 References are at the end of the paper. 4 cent reduction to ¾-in. rounds. The chemical analysis of the alloys is given in Table I. The forged rods were homogenized for 224 hr. at r150°C. (2100°F.) and air-cooled. The alloys were tested in two conditions of heat-treatment: (I) as normalized from 870°C. (1600°F.) and (2) normalized from 870°C. and tempered for I hr. at 540°C. (Iooo°F.) and air-cooled. The tensils specimens were 0.505 in. in diameter with a 2-in. gauge length, and the impact specimens were v-notch Charpy. The proportional limit and yield strength were taken from the stress-strain diagrams drawn by a Peters recorder. The data obtained from the tensile test and the hardness measurements are given in Table 2. Specimens that were normalized are designated by N; those that were normalized and tempered by T. Alloy G was tempered after forging (D).

Jan 1, 1942

1944 WALTER HULL ALDRIDGE New York, N Y 1946 PETER M ANDERSON Johannesburg, South Africa 1946 CHARLES CAMSELL Ottawa, Ont, Canada 1946 CHARLES AUGUSTUS CARLOW Fife, Scotland 1949 ERLE V DAVELER New York, N. Y 1951 EVERETTE LEE DEGOLYER Dallas, Texas 1946 CECIL H DESCH London, England 1946 WILLIAM FRASER London, England 1917 HERBERT HOOVER New York, N. Y 1941 DANIEL COWAN JACKLING San Francisco, Calif. 1950 ZAY JEFFRIES Pittsfield, Mass 1939 HENRY KRUMB New York, N Y 1942 ESSINGTON LEWIS Melbourne, Vic, Australia 1944 WALTER C. MENDENHALL Washington, D. C 1942 PAUL DYER MERICA New York, N Y 1938 A M PORTEVIN Paris, France 1934 T A RICKARD Victoria, B C, Canada 1946 JOHN R SUMAN Houston, Texas 1946 WONG WEN-HAO Chungking, China

Jan 1, 1952