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By B. Russell, J. R. Tuffley

The stability regions of the normal sulfate and the various basic sulfates of lead in 02-SO2 and PhS-SO2 gas atmospheres were calculated from available thermodynamic data over the temperature range 600o to 1200oC. Roasting experiments were carried out on samples of synthetic lead sulfide at various temperatures and for various roasting times. Compounds in the oxidized surface layers were identified by X-my techniques. The order in which the various reactions occurred was determined by considering the experimental results in conjunction with the thermodynamic calculations. The results of these investigations were applied to the sintering of lead sulfide concentrates, and the extent to which each of the various reactions occurred in a sinter bed was determined. PRODUCTS which may be formed during the roasting of PbS are PbS04, PbSO4. PbO, PbSO4 . 2PbO, PbSO4 . 4PbO, PbO, and Pb.1, 2 The formation of some sulfates has been studied by a number of investigators3-' whose experiments have mostly been confined to the temperature range between 500" and 850°C. Culver, Gray, and spooner3 were able to isolate the reactions which formed PbSO4 and PbSO4. PbO by carefully controlling the compositions of the roasting gases. The kinetics of these reactions were studied within the temperature range 673" to 807°C. Gardner4 and Merrick5 also studied the kinetics of oxidation of PbS. Gardner disregarded the existence of basic sulfates and, as a result, misinterpreted some of his experimental data. Merrick recognized that most of the products of oxidation were mixtures of basic sulfates, but was unable to identify the individual components. Hoschek6 oxidized PbS in air at temperatures up to 800°C. The products were analyzed after roasting had proceeded for some minutes, but no attempt was made to follow the reactions in the initial stages. Consequently, no roasting mechanism was derived. He also showed that PbSO4 and PbSO4 - 4PbO decomposed slowly in air at temperatures in the region of 800°C. The stability regions of sulfates in the temperature range 500" to 850°C have been only partially determined, while practically no information is available for higher temperatures. In the lead sintering process, PbS concentrates are roasted at temperatures within the range 1000o to 1200°C. In order to investigate sulfate formation, it is necessary to determine the effects of temperature and gas composition upon the various oxidation reactions and upon the regions of stability of the various lead sulfates. Kellogg and Basu2 introduced an equilibrium diagram similar to those in Figs. 1 to 3 which provides a convenient medium for represent-

Jan 1, 1964

By W. T. Roberts, N. G. Turner

A study of the fatigue properties of several grades of commercially pure titanium has established that the strain-aging process is of minor importance in the development of a fatigue limit and a relatively high fatigue strength ratio. Metallographic observations and damping measurements at room temperature indicate that striations are able to spread from grain to grain only at stress levels above the fatigue limit. This suggests that the fatigue limit represents the stress above which large-scale dislocation unlocking takes place. Fatigue tests on annealed material at - 60" and - 196" c showed that under conditions when a thermally activated diffusion process would be suppressed the fatigue limit is not eliminated. Prestraining at room temperature did not have a detrimental effect on fatigue strength at room temperature but a decrease was recorded at — 60°C. This is further evidence that initial dislocation locking is a important strengthening mechanism. TITANIUM and titanium alloys have S-N curves with a definite fatigue limit, and a high ratio of fatigue limit to UTS can be attained. Other materials which show similar fatigue characteristics are mild steel and some Al-Mg alloys. The fatigue limit of these materials has been associated with their strain-aging capacity. It is well-known that commercial-purity titanium contains interstitial impurities which can give rise to a sharp yield point, and a small strain-aging effect following static strain has been demonstrated.7 This type of aging reaction is differentiated from the dynamic aging process when aging occurs during plastic deformation, and which is generally observed at elevated temperatures. In a titanium at room temperature, dislocation locking is associated with the interaction of interstitial oxygen, nitrogen, and carbon atoms with dislocations. Ehr-lich has shown that the distortion produced by introduction of these atoms into the hcp lattice has no shear stress component and hence there is no interaction between the stress field and the screw component of a dislocation. Thus the dislocations as a whole are only weakly locked. It is clear that strain-aging effects in hcp a titanium will be much less pronounced than those observed in bcc iron and steel. In recent years, the attribution of the fatigue limit solely to strain aging has been questioned. It has been pointed out that a definite fatigue limit is observed at temperatures as low as -196°C in some titanium alloys,' and strain aging is not expected to be effective at this temperature. The role of initial locking of dislocations in determining fatigue behavior has been examined in low-carbon steel by Oates and Wilson. They showed that under conditions in which the aging potential is low the factors which control the buildup of local stresses and hence affect dislocation unlocking, e.g., grain size, are important. There are indications that other metals can have a definite fatigue limit with no established strain-aging capacity, an example being magnesium12 which has the same crystal structure as a titanium. The spread of plasticity from grain to grain in hexagonal metals may be more difficult than in cubic metals because of the limited number of slip systems in the former, and this may account in part for their fatigue behavior. The present work was undertaken to elucidate the relative importance of crystal structure, strain aging, and initial dislocation locking in determining the properties of commercially pure titanium when subjected to cyclic stressing. 1) EXPERIMENTAL METHODS Three grades of commercial-purity titanium were used and a material of lower interstitial content was prepared by melting high-purity Japanese sponge titanium (referred to as H.P. Ti). The compositions and typical mechanical properties of the materials are shown in Table I. Fatigue tests were made in push-pull (zero mean stress) using an Amsler Vibraphore machine at a frequency of about 160 cps. Two types of fatigue specimen were used—one with a waisted gage length for determination of S-N curves and the other with a parallel gage length for metallographic studies and damping measurements. After careful machining and mechanical polishing, all specimens were electropolished prior to fatigue testing. The electrolyte consisted of 10 parts methyl alcohol, 6 parts 2-butoxyethanol, and 1 part perchloric acid (SG 1.54) and it was maintained at a temperature of -10" to -20°C during polishing. Tests at room temperature were normally carried out with the specimen immersed in a silicone oil bath which could be heated for elevated-temperature tests.

Jan 1, 1969

By Persifor Frazer

The mines which I am about to describe are all situated in the northern part of the States of Nuevo Leon and Coahuila, Mexico, between the twenty-sixth and twenty-seventh degrees of latitude. They might be grouped, orographically, into four classes: 1. Those in the Sierra de la Ygnana chain; 2. Those in the Sierra de Gomez chain; 3. Those in the Cerro Mercado; 4. Those in the Sierra de San Marcos chain. (See large map.) The first two of these may be further arranged in one geographical district, to which the name, "the Villaldatna. district," may be applied, and the last may be ascribed to the geographical district of " Monclova." Geologically described, the country rock, in which four of the six mines occnr, is a limestone, concerning which a few words will be said further on, to wit.: The Arroyo (gulch), the Montanos and the Pinitos (pines), in the Villaldama district, and La Paloma (the dove), or Iron Mine, in the Monclova district. The San Rafael appears to lie in granite, or a heavy-bedded gneiss, presenting most of the characteristics of the latter, though the contact plane of the limestone is not far off. It is certainly worthy of attention that the ore occurs in that portion of the crystalline rock, which is nearest to the limestone, and it has been thought by some observers to be a true contact vein. It is well known that veins of this character are very often distinguished for constancy and richness. Although the undersigned cannot entirely free himself from the impression that this proximity of different formations has had an important influence in the origin of the part of the vein on which this mine is situated; still he was unable to establish it actually at the contact of the limestone and granite, but rather a short distance within the latter. Two openings of the Riojas vein were respectively in limestone and in rotten whitish granite, but this fact, if established (as by the correspondence of the strike line of the vein in direction with that of a line joining the

Jan 1, 1884

By John G. Tate, George W. Nicolson, James L. Bruce

For more than 25 years modern mining has been carried on in the Island of Cyprus, Mediterranean Sea, by the Cyprus Mines Corp. of Los Angeles, Calif. The general features of these operations have been described.' From 1935 to June 30, 1940, top slicing in the Mavrovouni mine produced in excess of 2,000,000 long tons. The rate for the last part of this period was approximately 50,000 tons per month. Description of Ore Bodies The shape Of the Ore body now being top sliced in the Mavrovouni mine is an inclined irregular pyritic pipe or chimney of large dimensions) extending from unknown depths below the bottom level at elevation 250 ft below sea level) to the highest level at elevation 400 ft above sea level. The present surface above the ore body lies between 550 and 650 ft elevation. Undoubtedly the Ore body extended to surface and was Mined by the ancients by opencast and underground methods. The old pits were gradually filled up by erosion until now they show as slight depressions in the topography. The largest area of the Ore body is at elevation 170 ft below sea level, where the horizontal section is almost elliptical, with a width of 600 ft and a length of 1000 ft. Below this elevation the shape of the ore body continues to be elliptical but with reduced dimensions. Above this elevation it rises flatly towards the south with a substantial depression in the upper-side of the chimney and irregular ridges or wings rising on each side. It gradually grows smaller as it rises. The ore body is a pyritic replacement of andesitic extrusives which occur as flows and pillow lavas. With the exception of the upper portions of one or two small offshoots rising from the main ore body, all ore is completely surrounded by andesite. Most of the andesite lying above the ore body is covered by marl and Clay sedimentaries of Miocene and later age, The Miocene is presumed to be older than the ore mineralization. That portion of the andesites which lies between the sedimentaries and the ore body has been broken by slumpage, and weathered, and iron-Stained by the descending meteoric waters, It is a mass of crushed material that caves and follows downward readily as the top-slice stopes retreat. The main ore body is a heavy cupreous pyrites mass assaying on the average about 4.0 pet Cu; 48.0, S; and 42.0, Fe. In places the copper drops below 1.0 pet. on the borders of this heavy sulphide ore body lie disseminated cupreous pyrites ore deposits of large dimensions. some portions of these appear to be closely related to the heavy sulphide ore, as the ratio of copper to pyrite is about the same. The greater part of the disseminated ore, most of which lies immediately to the east of the main Ore body, contains less than 0.10 pct Cu and about 25.0 to 30.0 pct S. 'This probably can

Jan 1, 1949

By Paul Foote

MOST of the treatises on metallurgy intimate that simultaneously with the development by the atomic physicist of a really satisfactory theory of the atom will be inaugurated a new epoch in the science of metals. Metallurgically and metaphorically, we shall dwell in the Utopia of Sir Thomas More. It is my privilege this afternoon to demonstrate that this state has not arrived. An atom is a miniature planetary system consisting of a positively charged nuclear sun about which revolve electrons each carrying the negative charge e. The charge on the nucleus is + Ze where Z is the atomic number and the number of planetary electrons in a neutral atom is equal to Z. These electrons are arranged in several groups having different binding energies. Ordinary x-ray phenomena relate to processes occurring deep within the atom, usually with electrons in the so-called K or L shells. Such electrons in the heavier atoms are so closely bound to the nucleus that the forces exerted by neighboring atoms in a solid are relatively inappreciable. For most practical x-ray investigation, the atom may, be considered as in the gaseous phase completely isolated from its neighbors. The K radiation from an element in the gaseous state, in the solid or liquid phase, or even in combination with other elements in all its possible valences, is almost identical. ? Visual and ultraviolet spectroscopy is concerned with disturbances of the most loosely, bound outer or valence electrons of the atom, always in the vapor state. The remarkable progress of the last year in both theo-

Jan 2, 1926

By C. R. Kuzell

INTRODUCTION KNOWLEDGE of the thermal capacity of gases is of great importance in making metallurgical calculations. The metallurgist is, frequently called upon to investigate and determine furnace efficiencies in which the heat carried into or out of the furnace by gases is a large item in the heat balance. Not only do such problems present themselves in the determination of furnace efficiency, but also in the study of the application of heat is accessory apparatus, such as stoves, regenerators, waste-heat boilers, driers,.etc. The thermal effect of the use of excess air in the combustion of fuel, the theoretical temperatures of combustion, the quantity of heat in hot blast at various temperatures, the effect of hot blast on furnace temperatures, are a few more examples of frequently occurring calorific problems involving gases. So many are the applications of the data on the heat capacity of gases that the subject merits careful study. The heat in a gas maybe due to its heat of combustion, if it is a combustible gas, and to its temperature. The latter is called its sensible heat and is the heat absorbed or evolved by a gas as its temperature is raised or lowered. The heat of combustion of gases is well established and is commonly known. The values can be found in almost any mcdern treatise on metallurgy. The sensible heat of gases has not been so well established because it is in most cases a function of the temperature, and the values of specific heats of gases over a wide range of temperatures have only recently been determined. It is the purpose of this paper to deal with the sensible heat of gases.

Jan 8, 1914

By W. B. Boggs, J. N. Anderson

An account of the operation of the Noranda smelter covering the period from December, 1927, when the smelter started, until December, 1929, was given in a paper published by the Canadian Institute of Mining and Metallurgy early in 1930.' The object of the present paper is to review matters of interest in the original paper and to describe the present construction and operation of the smelter, with particular reference to the reverberatory-furnace practice. The Noranda smelter was built by Noranda Mines, Ltd., from the designs of A. E. Wheeler, consulting metallurgist of New York, for the reduction of ores and concentrates from the Horne mine and to treat, on a custom basis, ores and concentrates from other mines in the Rouyn district. The smelter is at Noranda, about 330 miles directly north of Toronto. Construction work was started in June, 1926, and copper was first produced in December, 1927. The smelter was built throughout as two duplicate units, each with a rated capacity of 500 tons of ore per day. Operations were started with one unit and after several months it was found that one unit alone could smelt 1000 tons of ore a day. At that time there was only one hoisting shaft, No. 3, and its hoisting capacity and the capacity of the original crushing plant were insufficient to supply ore for the two units at the increased tonnage. Accordingly No. 4 shaft was sunk and a new crushing plant provided to handle the ore hoisted there. Operating two units at capacity also required the installation of two more converters to treat the additional quantity of matte produced. This work was completed in the latter part of November, 1929, and since then both smelter units have been operating continuously. In 1928, a mill to treat 500 tons a day of concentrating ore was completed. Since then the concentrator capacity has been increased twice, and at present 2000 tons a day of ore are being concentrated. The layout of the surface plant of the mine, concentrator and smelter is shown in Fig. 1 and the general plan in Fig. 2. The smelter is shown in more detail in Fig. 3. The original hoisting shaft, No. 3, is now used only for handling men, supplies and waste rock, and the original crushing

Jan 1, 1934

By W. Bradley, R. G. Hall

This paper will attempt to show how a metallurgical problem at one California quicksilver mine was solved, and how the solution was applied successfully at another mine. The pronouns "we" and "our," as used below, refer '0 the Bradley 'lining Co. of San Francisco. The term "concurrent firing" for the purpose of this paper can be defined as feeding and firing a a kiln at the same end—that is, of course, the upper end' This is as opposed to "countercurrent firing," the orthodox method, in which a kiln is fed at the upper and fired at the lower end. The terms "quicksilver" and "mercury" are used interchangeably. Early References The earliest work on nonferrous metallurgy, we believe, was The Pirotechnia of Vannocio Biringuccio,l its first edition having been printed in Italy in 1540. Quoting from its chapter entitled "Concerning Quicksilver and Its Ore": Quicksilver ... is one of the gods and has divine strength in itself, and also, to the annoyance of the alchemists, it is winged. Hence, when it sees that it is in gravest danger, it loosens itself from . . . every bond . . . and fies away into the heavens, escaping from the hands of those who crucify it. Almost laughing, it leaves all its adversaries mocked and scorned, with their phials and filters empty . . . How thorough a job, under certain conditions, it can do of mocking its adversaries and leaving their phials and filters empty, was found out four centuries later at the Sulphur Bank mine, on the east shore of Clear Lake, in Lake county, California, The other mine mentioned in the title is the Reed, in Yolo County, California, 35 miles by road southeast of Sulphur Bank, Reed and Sulphur Bank ranked respectively Nth and seventh in U. S. production in 1943. The earliest direct reference we can find to furnacing troubles at these mines was by Thomas Egleston in 1890.2 Speaking of Sulphur Bank, Egleston says: of there is more sulphur than cinnabar in the ore, which is a detriment to both . . . making the sulphur impure, and rendering the cinnabar difficult to work on account of the soot. In some of the early . . . furnaces the accumulation of soot from the excess of sulphur has been known to penetrate as far as the fan blower at the end of the . . . condensers, and completely prevent its revolution. In order to get rid of the inconvenience of this accumulation . . . , as well as to get a commercial value from the sulphur, it (the sulphur) is now separated by steam and sold. It is claimed that the sulphur alone pays all the expenses of ... the mine. The mine was first worked for sulphur, and the cinnabar it contained was considered to be an inconvenience, and was carefully picked out and thrown away, as its richness and value were not

Jan 1, 1949

By W. C. Ellis, E. S. Greiner, M. E. Fine

Discontinuous changes of Young's modulus, internal friction, coefficient of expansion, electrical resistivity, and thermoelectric power are evidence for a transition in chromium near 37OC. Although the X-ray diffraction pattern gives no clue, a difference between the thermal expansivity and the temperature dependence of the lattice parameter suggests a crystal-lographic change. Young's modulus data disclosed another transition near THE thermal dependence of a number of proper- ties of chromium indicates a transition occurring over a temperature range near room temperature. Bridgman' noted this first from a minimum in the electrical resistivity near 12°C. In a sample of greater purity, Sochtig' observed the minimum at 41 °C. Erfling3 reported an inflection in the thermal expansivity curve at 36°C. These temperature-dependence curves are reversible with no hysteresis being detected. No discontinuity or inflection has been observed in the heat capacity' or the paramagnetic susceptibility.' Likewise, no one has noted a change in crystal symmetry. In the present investigation Young's modulus, internal friction, coefficient of expansion, electrical resistivity, illustrated in Fig. 1, lattice constant, Fig. 2, thermal electromotive force, Fig. 3, and paramagnetic susceptibility, Fig. 4, were measured over an extended temperature range. The samples were prepared in two ways: (1) By cold pressing a sintered electrolytic powder compact,' and (2) by electroforming from an aqueous solution. The electroformed samples were prepared by R. A. Ehrhardt and G. Bittrich by plating on copper or nickel tubes from an aqueous solution according to the method of Brenner, Burkhead, and Jennings.' The pressed powder samples (method 1) were finally annealed at 1400°C in purified helium: the electroformed samples, packed in powdered chromium, were vacuum-annealed at 1000°C. From the composition of the original powder' the purity of the pressed powder samples is estimated to be 99.8 pct Cr. Spectrochemical analysis furnished by E. K. Jaycox, revealed only slight traces of impurities in the electroformed sample (less than 0.001 pct), neither iron nor nickel being detected. Chromium deposited by this method is reported to contain approximately 0.05 pct 0.- Methods and Data Young's Modulus: For measurement of Young's modulus, an annealed, pressed powder sample, 0.114 x0.237x1.845 in., and an electroformed sample, 0.10 in. od, 0.01 in. id, and 1.86 in. long, were prepared. The resonant frequencies of the rod samples in forced longitudinal vibration were measured at a series of temperatures from —192" to 200°C by a method previously de~cribed.6,7 Because the samples were nonferromagnetic, iron- silicon or molybdenum permalloy tips (0.013 in. thick) were soldered to the ends. The softening temperature of the solder limited the temperature of measurement. Young's modulus, E,, of chromium at temperature, T, may be calculated from the resonant frequency of the composite rod, f,; the thickness of the tips, t; the length of the chromium sample at 25°C, l,.; the density of chromium at 25°C, pc (7.20 g per cc);5 and the thermal expansivity, Al/l25. Modulus differences for two temperatures, ET and E, are accurate to +0.002x10" dynes per cm2. ET = 4PAlc+2tyf Young's modulus at 25°C, Fig. la, is 28.2~10" dynes per cm' (40.8xlO" si) in wrought chromium (upper curve). The modulus of the electroformed sample is apparently lower due to cracks. From the modulus measurements two transitions were observed: one with a critical temperature at 37°C, the other at —152°C. Internal Friction: The internal friction, 1/Q, was determined from the width, Af, of the strain amplitude-frequency curve at 0.707 times the strain amplitude at resonance;' the internal friction, 1/Q, then equals Af/f. Fig. lb shows a sharp peak in internal friction at 38°C. The internal friction of the electroformed sample had a similar maximum. Thermal Expansion: The expansivity measurements, shown in Fig. 2, covering the temperature range —195" to +400°C were made by D. MacNair in an interferometric dilatometer8 sing a sample consisting of three pyramids 0.25 in. high prepared from wrought electrolytic chromium. Below —120°C the experimental points deviated up to ±2x10 from the drawn expansivity curve in Fig. 2 because of decreased precision of the quartz wedge thermometer at low temperatures. Near 38°C the thermal expansivity curve, Fig. 2, goes through an inflection corresponding to a minimum in the coefficient of expansion, Fig. ld, and a relative volume decrease on heating. Electrical Resistivity: The variation of electrical resistivity with temperature measured by the po-tentiometric method is also shown in Fig. l. The resistivity of the wrought chromium (upper curve) at 20°C is 13.6 microhm-cm; of electroformed chromium (lower curve) 12.8 microhm-cm. The lower value reflects higher purity and agrees closely with a published value." A minimum at 40°C occurs in the resistivity curves of both samples. No conclusive evidence for a transition near — 150°C was observed, but the points, Fig. 1, appear to deviate from a smooth curve between —120" and —160°C.

Jan 1, 1952

By M. R. Geer, H. F. Yancey

With the exception of pneumatic processes and a few special beneficiation methods of comparatively limited application, all mechanical coal-cleaning and mineral-dressing processes involve the admixture of solid particles with a liquid, generally water. Upon completion of the beneficia-tion process the solids must be reclaimed from the water. With coarse particles separation of solids from water is accomplished readily by the simple expedient of screening, but recovery of fine solids presents a much more difficult problem. Thickening and dewatering are practiced so generally, both within the mineral industry and elsewhere, that they have been the subject of study through the years and a number of processes for making the solid-liquid separation have been developed. Dorr-type thickeners have been standard equipment lor many years, and more recently driers employing centrifugal force have gained in popularity.' A cyclone device employed to thicken the loess suspension is a novel feature of the loess heavy-medium coal-cleaning process developed by the Netherlands State Mines in the thirties. The cyclone thickener was first mentioned by Driessen2 in 1939 in a paper describing the loess process and has been the subject of two more recent reports by the same author.3 The cyclone does not differ greatly from cyclone dust collectors used in this country for years, except that it is operated wet rather than dry. Advantages of the cyclone over other thickening devices are its simplicity of construction, high capacity, and the fact that, having no moving parts, it is simple and inexpensive to operate. The Bureau of Mines became interested in the cyclone after one of the present authors observed it in operation in the Netherlands in 1945. The first experimental work with the cyclone conducted by the Bureau of Mines was an investigation of the unit functioning as a heavy-medium cleaner for fine coal—a use for the cyclone that was conceived long after it had been perfected as a thickener. The results of this investigation were published last year.4 The present investigation deals exclusively with operation of the cyclone as a thickener. Object and Scope of Investigation Although the cyclone thickener has been dealt with in three reports by Driessen, its use as a thickener was not the principal subject of any of these reports and therefore neither the cyclone itself nor its operation was described completely. The design of the cyclone was described only in a very general way, only limited operating results were given, and virtually nothing was disclosed about the influence of the various possible operating variables. Moreover, the Netherlanders apparently had employed the cyclone exclusively for thickening loess and had not employed it On coal 'lurries. One English colliery has used a cyclone to thicken coal slurry,5 and as it appeared that

Jan 1, 1949

By Reginald E. Hore

Since the discovery of silver at Cobalt, Ontario, in August, 1903, more than 100,000,000 oz. of silver have been produced by the mines in the Nipissing district, and there is reason to believe that at least as much more will be produced in the nex five years. The estimated value of the aggregate output o ore to the end of 1910 is $48,327,280. The ore yielded 93,977,833, oz. of silver and was mined at a net profit of abou $16,000,000. For 1910 the production was 30,558,825 oz., valued at $15,436,894, and yielding a profit of about $9,000.000. The details of the production of the Cobalt district for the years 1904 to 1909, inclusive, as reported by the Ontario Bureau of Mines, are given in Table I. The shipments from Cobalt are in the form of smelting-ore, concentrates from milling-ore, and bullion. The smelting-ore is largely high grade, averaging about 3,000 oz. per ton A smaller return is from what is called low-grade ore and which

Jan 1, 1912

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By R. V. Higgins

This paper presents a computer method to obtain the shape factors and equal cell volumes of the channels for any well spacing pattern from a potentiometric model. By using this program the authors have processed the data for the seven-spot, direct line-drive and the staggered line-drive patterns. The data for the five-spot pattern had been previously processed by a noncomputer method and are included for completeness. The shape factors and volumes for the channels are presented in tables for those who want to use them to process data using their own permeability relationships and viscosities of their reservoir oils. The authors have used the data and sets of representative permeability curves to process sample calculationr of waterflood performances. The comparison of the calculated results shows that the influence of well spacing is small. The permeabilities of the reservoir rock to oil and water had a greater influence on oil recovery for a given pore-volume throughput of water than the well spacing pattern. The more water-wet the reservoir rock, the better the possibility of permeabilities which are conducive to good recovery. The viscosity of the reservoir oil also influences the recovery more than the well spacing pattern. The reduction in the percentage recovery of oil with increase in viscosity of the reservoir oils is small when oil viscosities are in the range of 0.1 to 3. Above this range the reductions in recoveries are extensive. Sample comparisons of the time required for different patterns to recover the oil are presented. Results of an example calculation are given to show the effect of the permeability profile on recovery. INTRODUCTION The effect of well spacing pattern on the recovery of oil when flooding with either gas or water has been studied by many investigators. Muskat et al.1 presented an analysis using conductivity, sweep efficiency and unit mobility to the time of breakthrough. Dyes et al.2 used experimental techniques (X-ray shadowgraphs) and different mobility ratios. They presented quantitatively the relationship between mobility and sweep efficiency at and after breakthrough. Hauber3 presented a method to predict waterflood performance for arbitrary well spacing patterns and mobility ratios. Craig et al.,4 using techniques similar to Dyes et al. to determine sweep efficiency for a five-spot pattern, added the use of relative permeability curves at breakthrough and thereafter. Douglas et al.5 sed rela- tive permeabilities and continuously changing saturations throughout the entire five-spot flood pattern. In obtaining their solutions they used finite-difierence equations. Hig-gins and Leighton6,7 also used relative permeabilities and continuously changing saturations throughout the pattern before and after breakthrough. They employed techniques that process a flood-pattern calculation on the computer in about one minute. The methods of Douglas et al. and Higgins and Leighton both checked closely the laboratory results for a wide range of mobility ratios. This paper presents some sample performances calculated by the Higgins and Leighton method that show the effect on recovery of different permeabilities and viscosities using the seven-spot, the line-drive and the staggered line-drive, as well as the fivespot flood pattern. No previous paper has presented these data using different permeability curves and continuously changing saturations throughout the flood patterns. The paper also presents (1) the results and analyses of the flood-pattern prediction, (2) the computer techniques for determining the shape factors and volumes from the potentiometric models for the foregoing flood patterns, and (3) the shape factors and volumes of the channels of the flood pattern in the event reservoir engineers may like to process waterflood calculations using their own permeability curves and reservoir oils. DESCRIPTION OF METHOD VOLUMES AND SHAPE FACTORS The use of channels taken from a potentiometric model (see Fig. 1) to aid in calculating the performances of water floods of nonlinear patterns has been thoroughly explained in the literature.0,7 Therefore, very little theory, discussion, or proof regarding this phase will be repeated in this paper. The computer method presented in this paper to calculate the volumes and the shape factors of the channels of potentiometric models employs the trapezoidal rule for the volumes and the Pythagorean theorem (the hypotenuse equals the square root of the sum of the squares of the two sides of a right triangle) for the shape factors. In calculating the volume of a channel, the area of each cell in the channel is determined and then multiplied by the thickness to obtain the volume. In determining the areas of the cells, trapezoids are constructed whose vertical sides are spaced Ax apart, as shown in Fig. 2. The length of the sides is the difference between an ordinate cut off by the top and bottom of the cell — usually equipo-tentials. The coordinates of the points along an equipo-tential or streamline are obtained by Lagrange's8 equation of interpolation for which the constants are coordinate points at the intersections. Three intersections for con-

Jan 1, 1965

By H. H. Klepfer, K. J. Gill, P. Chiotti

SOME observations relative to the U-Zn system have been made by other investigators. Chipman1 and Carter2 have reported the preparation of several U-Zn alloys and point out that these alloys are generally difficult to prepare. Chipman1 reported evidence for a high melting compound at about 90 atomic pct Zn and the possible existence of a eutec-tic between the compound and uranium. Raynor," in a theoretical discussion of the alloying properties of uranium, included zinc among the elements predicted to have little or no solubility in a, p, or y uranium. In the present investigation, thermal analyses, X-ray, metallographic, and vapor-pressure data were obtained to determine the phase boundaries. The relatively high zinc pressure over most of the alloys at temperatures of 900 °C and above proved troublesome and special techniques had to be employed in preparing suitable alloys. Materials and Preparation of Alloys The metals employed in this investigation were Ames Laboratory biscuit uranium containing less than 500 ppm total impurities and Bunker Hill slab zinc or Baker Analyzed reagent granulated zinc, both with a purity of 99.99+ pct. Due to the high vapor pressure of zinc and the high reactivity of both uranium and zinc with oxygen at only moderately high temperatures, alloys were prepared in closed containers which had either been evacuated or evacuated and filled with helium. High purity magnesia, magnesia containing 10 pct calcium fluoride, and tantalum proved to be suitable crucible materials. Tw-o different procedures, described below, were used to prepare alloys, the latter being the most satisfactory. The metals, uranium turnings and granulated zinc, were cleaned with dilute nitric acid, rinsed, dried, and placed immediately in a helium-fill'ed dry box. The two metals were placed' in a 10 mil Ta crucible. The charge was enclosed in the tantalum crucible by welding on a preformed tantalum cap. This assembly was enclosed inside a stainless steel (AISI 309) bomb. The bomb was made by welding a piece of stainless steel plate on each end of a stainless steel pipe. All these operations were carried out in a helium atmosphere. These assemblies were heated in a muffle furnace at temperatures between 1100" and 1200°C for 10 to 15 min or held as long as 15 to 20 hr in the 950" to 1000°C temperature range before quenching. Spectrographic and chemical analyses showed no tantalum pickup by the alloys, indicating no reaction between the alloys and the crucibles. However, some of these crucibles failed, probably due to imperfections in the welds of the stainless steel or tantalum crucibles. The second and most satisfactory method was to prepare the alloys by powder metallurgy techniques. The procedure was to press degreased and acid-etched uranium turnings with granulated zinc into 20 g compacts under 20,000-psi pressure. The compacts were placed in MgO crucibles, and sealed in evacuated Vycor or fused silica tubes. The alloys were then heated as long as two weeks at about 550°C in a muffle furnace. The pressed compacts were observed to expand by several volume percent during heating and it was necessary to make allowances for this expansion in order to avoid breaking the crucible and Vycor tube. This method was found very satisfactory for preparing alloys which were suitable for thermal analysis or vapor pressure studies. Experimental Methods and Results The phase diagram for the U-Zn system at 1 atrn pressure, shown in Fig. 1, is based primarily on vapor pressure measurements and on thermal analysis taken at temperatures below 950°C. Fig. 2 shows the U-Zn diagram at 5 atrn pressure, constructed on the basis of thermal analysis of alloys in sealed containers up to 1150°C and on the basis of metallographic, X-ray, and analytical data. The alloys sealed under vacuum were actually under their own vapor pressure and those sealed in an atmosphere of helium were under an additional pressure due to the helium. At temperatures up to 1100°C the zinc pressure is 5 atrn or less for these alloys; consequently the maximum pressure over the alloys sealed under a helium atmosphere was 10 atrn or less at temperatures up to 1100°C. Changes in pressure of this order of magnitude do not appreciably alter the position of most solid-solid or liquid-solid phase boundaries. In constructing the phase diagram for a pressure of 5 atm, the effect of pressure on all phase boundaries except those for liquid-vapor or solid-vapor regions was considered negligible.

Jan 1, 1958

By Clarence Zener

Contents Page General Principles................................................................. 551 Equilibrium Diagrams......................................................... 551 Nucleation................................................................... 553 Kinetics of Phase-boundary Propagation......................................... 553 Kinetics of Growth of New Phase............................................... 556 Spheroidization............................................................... 560 Pure Iron-carbon System........................................................... 561 Formation of Pearlite.......................................................... 561 Interlamellar Spacing........................................................ 562 Pearlite C-curve............................................................. 563 Bainite Formation............................................................. 565 Formation of Martensite....................................................... 570 Loss of Tetragonality of Martensite.............................................. 570 Effect of Alloys upon Decomposition of Austenite..................................... 572 Pearlite...................................................................... 572 Bainite and Martensite......................................................... 574 Time-temperature-transformation Curves............................................. 576 Appendix A............................................................. ......... 579 Appendix B....................................................................... 580 Appendix C....................................................................... 580 The present investigation started in an attempt to understand certain details of the decomposition of austenite, and of the effect of alloying elements thereon. As the investigation proceeded it became apparent that not only these details, but all the general features of austenite decomposition, could be understood in terms of fundamental physical principles. Since the direct applicability of these physical principles has not been previously recognized, it was decided to incorporate the original results of the investigation into a review of the general subject of the kinetics of austenite decomposition. This review constitutes the present article. An extended summary of the results is given on pages 576 to 579. This article, which deals with the kinetics of phase transformations, may appropriately be considered as a sequel to two recent articles1,2 from this laboratory on the equilibrium relations in medium alloy steels.

Jan 1, 1947

Jan 1, 1923

By AIME AIME

THE autumn is the time that nearly all the special groups within the broad field of the Institute's activitives chose for their own special meetings. The big annual meeting in New York in February has its own special advantages, but to realize them involves sacrificing others. A meeting of a smaller group with the subjects brought up for discussion much more closely limited to a single field of interest has some advantages that a big general meeting cannot possibly have. And so the custom has gradually developed of having these smaller meetings in the autumn, at con¬venient places, so the men will not have to travel too far from the job to be present. Sometimes the meetings have for their field of interest a single phase of mineral technology, and are called divisional, and at other times they cover a diversity of topics that are locally important in that geographical area, and are then called regional meetings. Of the five meetings to be held this fall, four are divisional and one regional. Two of the divisional meetings are to be held in the same place at the same time, but with programs so arranged that they do not conflict.

Jan 1, 1930

By R. K. Buhr, H. Thresh, M. Bergeron, F. Weinberg

The microsegregation of nickel and chromium in directionally solidified AISI 4340 steel castings has been measured using electron probe microanalysis. Minimum concentrations were observed to occur at the center of the dendrite stalks, as reported previously. However, the position of the maximum concentrations could not be determined from the dendrite configuration. An etching technique has been developed which shows the position of maximum concentration. Measurements were made of the distribution of nickel and chromium in the dendritic structure. The ratio of maximum to minimum concentration was determined as a function of primary dendrite arm spacing for both as-cast and partially homogenized materials. The results are compared with observations reported in the literatuve. A S part of an investigation of solute segregation in directionally solidified AISI 4340 steel casting, electron probe microanalysis was used to measure the distribution of nickel and chromium in the dendritically segregated material. This complemented the observations on the segregation of radioactive phosphorus obtained by autoradiographic techniques in the same castings.' Kattamis and I?lemings2 have reported similar measurements, using electron probe microanalysis, on dendritically segregated AISI 4340 steels. They found minimum solute concentrations occurred at the center of dendrites, maximum concentrations occurred in the center of interdendritic regions, for symmetrically oriented dendrites, and a regular variation of concentration within dendrite arms. The ratio of maximum to minimum concentration was found to be essentially independent of position in the castings, except near the chill surface where it was somewhat higher. Assuming complete diffusion in the liquid and no diffusion in the solid during freezing, they considered that isoconcentration curves in the steel were homothetic. As a result, isoconcentration curves of the various elements, contour surfaces of dendrites produced by isothermal-transformation studies, and the contour of the solid-liquid interface would all be similar, and could be superimposed by a uniform expansion or contraction of the contours. Preliminary results of the present investigation suggested that isoconcentration curves were not homothetic. It was also evident that points of maximum concentration could not be predicted from the dendrite configuration. Since the ratio of maximum to minimum concentration appeared to be an important parameter in defining the overall segregation in a casting, other techniques for determining the point of maximum concentration were investigated. In addition the overall solute distribution associated with the dendritic structure was examined for both nickel and chromium, and the consistency of the distribution for neighboring dendrites was determined. METHOD Fifty-pound heats of AISI 4340 steel were cast in a manner similar to that used by Flemings et al3 with a water-cooled copper base plate and exothermic sides and top. The nominal composition of the material was C, 0.41 pct; Mn, 0.66; Si, 0.35; S, 0.012; P, 0.010; Ni, 1.88; Cr, 0.95; Mo, 0.28. The steel solidified directionally from the chill surface, with a dendritic structure which increased in dendrite arm spacing with increased distance from the chill. Results of the general investigation of the cast structure and segregation of radioactive phosphorus in these castings have been reported elsewhere.' For the present measurements, sections were cut from the casting at several distances from the chill surface. The sections were subsequently heat-treated, mounted, and then polished on a plane perpendicular to the general freezing direction of the casting. Electron probe microanalysis was carried out with the JEOL-JXA3 microprobe using a voltage of 25 kev and beam current of 0.15 µa. The take-off angle is 22 deg. Quartz crystals were used in the spectrometers and measurements made for Ka radiation from both nickel and chromium simultaneously. A thin layer of carbon was deposited on all specimen surfaces prior to examination in the microprobe. Early measurements were made on polished surfaces, with indentation marks produced by a hardness tester to indicate the area of interest. It was found desirable to use etched surfaces, as opposed to polished surfaces, to reduce sample preparation time and more readily relate the microprobe scan to the structure. To determine if this could be done, without introducing significant errors, a series of measurements were made on polished and etched surfaces of the same specimen. Both polished and etched surfaces produced similar results within normal scatter as shown in the observations. Subsequent measurements were then made on etched surfaces. Measurements with the microprobe analyzer were made by point counting, for periods of 100 sec, at 10-µ intervals. Ten-second counts were made on pure nickel and chromium standards, incorporated in the specimen mount before and after each set of measurements. The results were adjusted for background, then corrected for dead time using the expression:

Jan 1, 1969

By R. D. Pehlke, J. V. Gluck

A study was made of the effect of small additions of metallic solutes on the thermodynamic activity of zinc in dilute solution with molten bismuth in the range 450o to 650°C. The experimental measurements were made in a multielectrode galvanic cell using. a fused LiCl-KCl electrolyte. The activity of zinc in binary solution exhibited a strong positive deviation from Raoult's law and obeyed Henry 's law to at least 0.050 mole fraction. The ternary addition of lead, gallium, or indium increased the activity of zinc. Cadmium or tin additions slightly decreased the zinc activity. Copper, mercury, silver, or antimony caused moderate decreases, while gold strongly decreased the zinc activity. The results are expressed in terms of Wagner's interaction parameter ejZn and a second-order cross-interaction parameter. The interactions for copper, gold, silver, and antimony showed a linear dependence with reciprocal absolute temperature, while the other interactions were essentially independent of temperature over the experimental range. Since tin and antimony decreased the zinc activity, the hypothesis of a purely periodic variation with atomic number was rejected. A semiquantitative explanation was possible with a free-electron model when relative electronegativities were used to express changes in the electron/atom ratio caused by the solute addition. Random solution and quasi-chemical models correctly predicted the majority of the interactions for which binary data were available to apply them. A knowledge of the thermodynamic interactions in liquid (and solid) metallic solutions is of considerable theoretical and experimental interest in the formulation of quantitative thermodynamic relations for metallurgical processes. The approaches to defining the interactions may be either phenomenological (i.e., "What mathematical function adequately describes observed behavior and permits extrapolation to new situations?") or theoretical, such as a specific model

Jan 1, 1968

By E. H. Jr. Dix

THE consideration of alloying elements for aluminum has led to a series of investigations of the equilibrium relations between aluminum and those alloying elements. Therefore, the aluminum end of the aluminum-antimony diagram has been studied. The general form of the aluminum-antimony equilibrium diagram has been worked out by Campbell and Mathews1 and by Tammann.2 Campbell and Mathews described principally the beginning of solidification. They found the curve of beginning of solidification to rise gradually from the melting point of pure aluminum to a maximum at about 67 per cent. aluminum. After a slight lowering of the curve at a little greater antimony concentration the curve again rises to a maximum at 18.4 per cent. aluminum, which corresponds to the compound AlSb. The curve then drops to the melting point of pure antimony. Tammann explained the maximum occurring at about 67 per cent. aluminum as the result of the slow formation of the single compound AlSb. The space lattice of the compound AlSb, according to Owen and Preston,3 is face-centered cubic, the antimony atoms being intermeshed with an identical aluminum lattice. Very little, if any, work has been done on aluminum alloys containing small amounts of antimony.

Jan 1, 1930