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By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By O. U. Bradley

THE extent of losses, due to evaporation, sediment, and water, in crude oil stored in steel tanks, is a very interesting question, and particularly so at this time, when every reasonable measure should be employed to eliminate all possible losses of this important natural product. Available information on this subject is incomplete; e.g., during the development of the Cushing Field, considerable surplus oil was stored in steel tanks, but from time to time, owing to changes in weather, somelosses by evaporation and short storage room on the leases, these tanks were topped out, thus rendering inaccurate any system designed to determine the average rate of evaporation or other losses of the oil over a given period. , Furthermore, the losses, as shown by the records at the time, as a result of hasty gages, failed to take into account the temperature and gravity of the oil. Losses may be classified roughly as occurring from evaporation, presence of sediment and water, and leakage. The coefficient of expansion and contraction of crude oil, in relation to temperature conditions, is of material importance; also, the rate of evaporation is dependent upon the gravity of the oil, as the escape of the lighter hydrocarbons in fresh Cushing oil, of from 40 to 42 gravity, on a warm day is considerable, and from available records of temporary storage, it is safe to assume that a loss of 1 to 13 per cent. in volume will easily occur in light crude oil of Cushing grade over a period of. 6 months, including the summer season. The presence of sediment, water, and other impurities, in the oil will also cause, more or less deterioration in quality, particularly when the fresh production is run direct from the. gage tanks, or from the wells on the lease to steel storage, as is often the case when an oil field is being rapidly developed. The bad oil will settle to the bottom of the tanks and may be determined by thiefing and running a centrifuge test on the sample. The amount of water in the oil depends entirely on the conditions under which it is produced. Sometimes in large producing wells, with heavy gas pressure, some water may come in with the oil, particularly if the well has been drilled to the top of a water sand. Under these conditions, cut oil is often produced, which, if not settled out, is carried over into the steel tanks.

Jan 7, 1918

By H. P. Allen

THE Achotla mill of the Cia. Minera de Pe[n]oles is of special interest in that it is one of the few still employing the chloridization process. The ore milled comes from the Suriana mine and consists of both oxide and sulphide, from neither of which can the gold or silver be extracted by a simple cyanide treatment. The mill was built in 1927, after several years of study in the development of the process1, and operated from December of that year until October 1930. Operations were resumed in February 1935, and have been continuous since, treating approximately 5000 tons per month, while the mine is getting up to full tonnage of 6500 tons per month. Transportation Of Supplies The property is in Guerrero, Mexico, some 175 km. by airline southwest of Mexico City. The mill site is at Temisco (Fig. I), 8 km. from the Balsas River and 4.8 km. by aerial tram from the mine. At Temisco are the general office, shops, warehouses and laboratory serving both mine and mill. Here sufficient water is available either from a small creek running through the property or from the Balsas River, also convenient and ample storage space for the tailings. With the exception of the mine timber and a few native building materials which may be obtained locally, all supplies for both mine and mill are brought down the Balsas River from Balsas, the terminal of a Mexican National Railway line out of Mexico City. The method of transportation on the river is interesting. Rapids with very fast water are numerous, prohibiting the use of mechanically propelled boats. Those used resemble large, flat-bottomed rowboats some 22 ft. long by 8 ft. wide (Fig. 2). They are manned by two oarsmen sitting in the bow, each handling one large oar, and usually another man in the stern who, with his oar, assists in steering the boat, especially when the rapids are run. From 3 to 7 tons of freight are carried on each boat, depending upon the stage of the water, which governs also the time

Jan 1, 1937

By W. D. Robertson, H. H. Uhlig

INTRODUCTION THE intermetallic compounds Mg2Sn and Mg2Pb are two of the important series of stoichiometric compounds pounds which magnesium forms with elements of the fourth group of the periodic system, Since there is a complete series, of compounds, all possessing the same comparatively simple structure, a unique opportunity is presented to study their properties with respect to increasing atomic number of the anion as it varies from silicon and germanium, through tin and lead. The present work deals with the two lower members of this group, and it is hoped eventually that additional data regarding the silicide and germanide will be obtained. The results of such a complete study provide part of the essential basis for the empirical correlation and theoretical treatment which, in other systems, has contributed to an understanding of intermetallic compounds and the metallic state in general. Some experimental data are already available in the literature, However, they re fragmentary and limited in significance owing to the methods of preparation employed and the impure materials available at the time, It was our objective, therefore, using pure metals and improved metallurgical methods of preparation, to produce stoichiometric compounds of high purity for the study of their electrical and chemical properties. We felt that a detailed investigation of chemical properties, about which relatively little is known, combined with electrical properties, would be a significant contribution to the understanding of these compounds and in particular to the mechanism of corrosion associated with types of bonding in alloy systems. The chemical studies are reported elsewhere. PREVIOUS INVESTIGATIONS Previous work concerning the electrical properties of these compounds was undertaken in connection with the establishment of the two phase diagrams which are available in Hansen1 and Beck,2 The first comprehensive investigation of the electrical conductivity of magnesium-tin and magnesium-lead alloys was made by Kurnakov and Stepanov.3 This was followed by Grube and Vosskühler4 who studied electrical conductivity and thermal expansion over a wide range of temperature and who, unlike Stepanov, appreciated the significance of the large solid solubility of tin in magnesium and took some precautions to obtain an equilibrium state. However, at the time these investigations were made, neither pure magnesium nor

Jan 1, 1948

By F. Lynwood Garrison

It is not intended to make in the present paper any deduction or to formulate any theories from the results obtained by experiments. The further expenditure of considerable time and labor would be required to obtain a sufficient basis for positive assertions as to the microscopic structure of the different varieties of iron and steel, and the structural changes which take place in them. It is therefore my purpose at this time to offer simply a synopsis of the general results arrived at in a few months' work, a brief description of apparatus used, and a few hints as to the preparation and preservation of the material which it is intended to investigate. The study of the microscopic structure of iron and steel is not altogether new. Some attention has been given it in both England and Germany. But the foreign publications on the subject have thus far been confined, so far as I am aware, to two papers, one by Herr Martens, of Berlin, contributed to the Verein zur Befoerderuny des Gewerbfleisses and the other a lecture by Dr. H. C. Sorby of Sheffield. Dr. Sorby, it seems, was induced to investigate the subject as bearing on the structure of meteoric iron ; and the results he obtained are certainly very interesting. At the Boston meeting of this Institute, in February, 1883, Mr. J. C, Bayles called attention to the subject in a neat and exceedingly interesting paper, in which the work of Messrs. Martens and Sorby was summarized,* and original suggestions were added. It is at present difficult to say what will he eventually the practical value of the microscope, thus employed, in the sciences of engineering. The role which it seems most likely to play is that of' an adjunct to the testing-machine, and not (as some have supposed) a rival to the chemical laboratory. That it will be a most valuable accessory seems, to say the least, highly probable. I need hardly go at length into the details of preparing the material for examination. Mr. Bayles has described the process in such a plain and comprehensive manner that if his instructions are

Jan 1, 1886

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By C. R. Boyd

The region to which I have the pleasure of calling your attention, though limited in area, is remarkable for the quantity and purity of its mineral deposits, and in these respects it would be difficult to find its equal anywhere. IRON ORES. The red and brown hematites, pipe ore, and semi-magnetites, from which is made in charcoal furnaces the highest quality of iron for car-wheels, extend through the counties of Giles, Montgomery, Pulaski, Wythe, Smyth, Washington, Bland, Tazewell, Russell, Scott, Lee, Floyd, Carroll, and Grayson, Virginia, and run over into Ashe County, North Carolina. One locality of semi-magnetite, in the centre of the great Giles County basin, has in sight, by actual measurement, 50,000 tons of ore, which, according to Prof. Fesquet, contains 69.74 per cent. of iron and no phosphorus. In the great brown-ore belt, which passes through the counties of Montgomery, Pulaski, Wythe, Smyth, and Washington, there is an extraordinary deposit of more than a million tons. A small section of this very long vein, on Cripple Creek, in the County of Wythe, yields an ore which, analyzed by Mr. James Aumann, gave the following results: Metallic iron,........58.15 Water,.........12 96 Alumina,........2.32 Silica,.........1.09 Phosphorus,.. none. At one point towards the western end of Red Land Mountain, in Pulaski County, New River section, I measured a body of ore in this belt which will yield, to a depth of 150 feet, over 8,000,000 tons, and the deposit extends far below the 150 feet measured at the upper part. Again, at Rich Hill, near the mouth of Reed Island Creek, these veins show extraordinary surface development, giving an ore of very great purity. At numerous places, also, in the counties of Giles, Bland, Tazewell, Russell, Scott, Wise, and Lee, these brown and red iron ores are exposed in such vast quantities as to baffle both description and measurement. That of Chestnut Flat, in Giles County, back or west of the Angel's Rest Mountain, is an easily reducible ore, blood-red when crushed, of which there are fully 300,000 tons in sight. Its analysis is as follows :

Jan 1, 1880

By Robert I. Jaffee, Bruce W. Gonser

RECENT work by the authors1 established the constitutional diagram of the gold-germanium system. Of particular interest in the simple euctectiferous system was the eutectic alloy at 12 per cent Ge, which melted at the very low temperature of 356°C. and had an unusually fine eutectic structure. It was of interest to investigate the effect of third components on the melting point, microstructure, and strength of this alloy, and in this work the effect of copper is discussed rather completely, with less complete data on the effects of silver, platinum, nickel, and zinc. No reference in the literature has been found on ternary systems with gold-germanium. MATERIALS AND ALLOYING As in the work on the binary system, gold-germanium, the germanium used in this investigation was the cyanide-reduced, 99.9 per cent product, produced by the Eagle-Picher Co. Fine gold sheet from Handy and Harmon, pure platinum sheet from the American Platinum Works, copper magnet wire from Anaconda, nickel wire assaying 99.6 per cent Ni, and electrolytic zinc were used for alloying. To make the alloys, charges of the pure metals were put in a graphite crucible and melted in an atmosphere of pure hydrogen. The temperature was brought up to about 1050°C., and the metal allowed to freeze in the crucible. Except with alloys containing zinc, melting losses were consistently less than a few milligrams. When zinc was a component, weight losses up to half the weight of the zinc present were incurred, and the alloy compositions were calculated by assuming the entire weight loss to be that of zinc. In all other cases the composition of the alloys could safely be taken as that of the charge. The ingots, as solidified, were segregated, the heavier primary phases being at the bottom and sides of the ingots and the lighter primary phases at the top, but by sectioning the entire ingot vertically for microscopic examination, this factor could be evaluated. Ingots for microscopic examination weighed one gram, and those for thermal analysis weighed three grams. THERMAL ANALYSIS In this work, the eutectic line composition and thermal arrests were desired, and, after microscopic exploration had established the position of the eutectic line at a given percentage of the third component, a thermal analysis was run at that composition. The method of thermal analysis used in the work on the binary Au-Ge system,1 a method particularly well suited for a small quantity of material, was used in this work. Clearly defined arrests were obtained, although with some alloys containing platinum

Jan 1, 1946

By Harry L. Brown, James M. Dickinson, Philip E. Armstrong

The elastic stiffness coefficients of niobium have been rneaslrred from -150°C to over 650 C and ave in accord with the anomalous temperature dependence previously observed for Young's modulus. This unusual behavior has been shown to be the result of changes in the relative values of the shear elastic coefficients. The bulk modulus remained essentially constant over the temperature range studied, while changes in the shear coefficients produced a more nearly isotropic behavior as the temperature increased. A number of investigators have reported data on the temperature dependence of Young's modulus of polycrystalline niobium. The values cited for the room-temperature modulus ranged from 0.71 to 1.17 x 10" dynes-cm-' (10.3 to 17.0 x lo6 psi) and in each case the modulus was observed to decrease with increasing temperature. In our recent study,8 both polycrystalline and single-crystal samples of essentially strain-free high-purity niobium showed a Young's modulus whose temperature dependence as well as magnitude was strongly dependent on specimen orientation. This was shown to be the result of changes in the relative magnitude of the two shear moduli, C and C'. Young's modulus of polycrystalline samples with strong [110] textures and Young's modulus of single crystals whose orientations were away from the [loo] actually increased as much as 12 pct between room temperature and 1000°C. While studies on the residual effects of previous fabrication, thermal treatments, and impurity contents will probably resolve the problem of the widely differing Young's modulus values observed in polycrystalline niobium, a more complete description of the elastic properties requires an evaluation of the single-crystal elastic constants. A knowledge of these constants can provide a clearer picture of the nature of the temperature dependence, as well as establish a basis for predicting the modulus behavior of polycrystalline niobium, both in the randomly oriented condition and with various fabrication textures. The effects of residual strains on the elastic behavior then can be separated from orientation effects. EXPERIMENTAL METHOD Thin rod-resonance techniques were used to obtain both the Young's modulus and shear modulus of single-crystal specimens. The determination of these moduli as functions of the crystallographic orientation of the specimen axis provided sufficient information to permit calculation of the single-crystal elastic constants. The necessity for torsional as well as longitudinal measurements led to the design and assembly of a vertical-tube vacuum furnace incorporating probes for the simultaneous determination of both longitudinal

Jan 1, 1967

By Philip B. Dettmer

Up to now we have spoken optimistically of the many potential savings in capital and operating costs to be obtained from the selection of larger diameter and horsepower grinding mills. Such mills may well be the correct choice for one grinding plant but could be absolutely wrong for another plant. It is emphasized here that many significant factors other than the capital cost, labor, grinding media and power savings are involved in the sizing and selection of the optimum grinding circuit. The following discussion covers some of these factors and their relationship to larger mill design. The first consideration is: What is the grinding circuit supposed to do? In most instances it is one or both of the following: 1. Grind the feed material fine enough to liberate the desired minerals but with a minimum of over- grinding. Examples are preparation of ore for flotation, gravity separation, etc. 2. Grind to some pre-specified particle size or particle surface area. Examples of this are cement manufacture or the preparation of feed material for pelletizing; other examples are preparation for chemical reactions or ceramic manufacture.

Jan 5, 1965

By F. V. Lenel

INTRODUCTION Two years ago in Chicago a seminar was held on the theory of sintering of pure metal powders As an introduction to this seminar Dr Rhines1 gave an excellent survey of the literature on this subject His method of presentation was to summarize the experimental observations on sintering and from them to develop a composite theory of sintering in which he combined all the important contributions to the theory into one organic whole In contrast to the mechanism of sintering of pure metal powders, which, of course, always takes place in the solid phase, sintering in the presence of a liquid phase, cannot be treated as one unified mechanism, such as the sintering mechanism of pure metals The reason is that there are really several mechanisms depending upon the type of alloy system which is sintered and the field of its constitutional diagram in which the sintering takes place Two mechanisms have been investigated and will be reviewed in this paper In the first mechanism the liquid is present during the entire time while the compacts are at the sintering temperature In other words they are sintered between the liquidus and the solidus of the alloy System and are heterogeneous during the entire sintering cycle The second mechanism applies to alloys in which the liquid phase is formed during the sintering process, but disappears before the sintering process is completed through diffusion and formation of a solid solution These alloys are therefore homogeneous at the end of the sintering cycle This second mechanism is more complicated because of the two stages of sintering, the liquid and the solid, as they may be called It is therefore not surprising that the few detailed investigations of sintering in the presence of a liquid phase have been concerned with heterogeneous sintered alloys, namely the tungsten-nickel-copper alloys, which is the so-called "heavy alloy," and the cemented carbides The mechanism of sintering of these systems is characterized by the fact that theoretical or near theoretical density is attained during sintering, while simultaneously a distinct grain growth takes place through solution of the smallest grains of the solid phase in the liquid phase and reprecipitation on the larger grains In the first part of the survey this sintering mechanism which is called for short the heavy alloy mechanism is treated in detail In the second part of the survey experimental observations for the sintering of homogeneous sintered alloys where the liquid phase disappears before the completion of sintering are discussed Much less systematic work has been done on these alloys to which the commercially important porous bronzes and the iron-nickel-aluminum permanent magnet alloys belong Emphasis will be laid throughout this survey upon the microstructural and density changes during sintering because the sintering mechanism can usually be described directly by these changes Other

Jan 1, 1948

By M. Cohen, R. J. Teitel

There is considerable interest in beryllium because of its low density (1.84 g per cu cm), high modulus of elasticity (40 X 106 psi), high melting point (1280°C), and special nuclear characteristics. Moreover, it has fair resistance to corrosion and oxidation. However, the purest beryllium known to the authors is relatively brittle at room temperature, and cannot be fabricated readily. The search for improved properties leads naturally to investigations of beryllium alloys and the phase relationships upon which they are based. The present paper is concerned with the alloys of beryllium and iron, primarily from the standpoint of the equilibrium diagram. Iron was selected (1) because of its all-round importance in metallurgy, and (2) because the beryllium-iron system is known to be quite complex. The most recent diagram in the literature is that of Gaev and Sokolov,' and covers only the iron-rich end up to 16 wt pct beryllium. Beryllium markedly restricts the austenitic field, closing the gamma loop at about 0.4 wt pct (3 at. pct). On the other hand, beryllium is soluble in a-ferrite up to a maximum of 7.5 wt pct (34 at. pct) at the eutectic temperature of 1160"C. The eutectic composition lies at 10 wt pct beryllium (42 at. pct) and corresponds to a mixture of or and FeBez (called j3 in the present paper). The solid solubility of beryllium in the a phase decreases with decreasing temperature, and makes precipitation-hardening possible. These findings substantiate the earlier work of Oester-held,2 Wever and Mueller3 and Laissus.4 In addition to the FeBe2 (ß) mentioned above, Misch6 has reported on FeBes, and indicated evidence for another compound containing still more beryllium. A preliminary diagram by Gordon,5 not hitherto published, is given in Fig 1. Besides the phases previously named, there are shown a solid solution of extended range (e), a compound of limited solubility (t), and a high temperature phase (7). Beryllium is designated as 8. The t field contains the compound composition FeBea, and the f phase undoubtedly corresponds to the beryllium-rich compound found by Misch.6 The region around the { phase was proposed by R. J. Teitel based on Gordon's data. The details of the diagram are self-explanatory. It was the unusual complexity of this system that prompted the authors to undertake the present studies. By the same token, more emphasis was placed on the beryllium-rich than the iron-rich end of the diagram. Exprimental Details RAW MATERIALS The beryllium employed in this investigation was one of the purest grades available. Its chemical analysis after vacuum melting is given in Table 1. The metal assayed 99.4 wt pct beryllium. Vacuum melted electrolytic iron of purity shown in Table 1 was the source of iron.

Jan 1, 1950

By A. Eilers

A MARKED peculiarity of most of the smelting-works of the Far West is the looseness with which accounts of the operations are kept. Indeed, probably over half of the works do not keep any detailed accounts at all, the yearly gross statement of profit or loss being considered sufficient for all purposes. The reasons for this must apparently be sought in the as yet unsettled state of all business relations, and in the deplorable fact that only in isolated cases educated metallurgists are in charge of the smelting-works. Continual and regular assays of the ores, by-products, and slags, are almost unknown, so that it is impracticable to ascertain, even approximately, the losses in the smelting processes. Of cases where regular accounts are kept of the quantities of ore smelted, of the composition of charges, and of the fuel consumed, I know only two or three. Under these circumstances it is extremely difficult to collect figures which cover the operations for a considerable length of time, and which are so valuable for the metallurgist, who wishes to get an insight into the economy of smelting operations, as shown by practice. Figures obtained by personal observation, which can of course cover only the brief space of the visit of the travelling metallurgist, must, therefore, be made to replace the more valuable data. The writer has had occasion, during the last and the preceding summer, to visit the larger number of the Western lead-smelting works, and offers, in the following pages, such data relating to the economy of lead-smelting in the blast furnace at various works, as he has been able to obtain. The only object in doing so is to place these figures on record, so that they may be from time to time supplemented with other data, which are now wanting. I. EUREKA CONSOLIDATED COMPANY'S SMELTING-WORKS. These works smelt the ores from the mines of the same company on Ruby Hill, Eureka, Nevada. The supply is almost unlimited,

By W. J. Rooney, James Fisher, W. O. Hotchkiss

During the summer of 1927, the Department of Terrestrial Magnetism of the Carnegie Institution of Washington joined with the Michigan College of Mining and Technology in conducting a series of earth-resistivity measurements in the Michigan copper country. The geological structure in this section is quite varied and fairly well known. The purpose of the investigation was to discover the correlation between the variations in electrical resistivity of large masses of soil and rock in place and the geological structure below the surface. The work done may be roughly divided into two parts: (1) Measurement and study of the variations in resistivity with depth, or with volume, to establish such general relations as exist between the two; and (2) the determination of the specific resistivity of various formations in order to make available more fundamental data which may aid in the interpretation of the results of the former type of measurement. A report by Mr. Rooney, which gives in detail the measurements made and the results obtained, forms the basis for this article. Measurement and Study of Variations in Resistivity The possibility of applying data from measurements of the physical properties of earth material to the study of the geological structure has long been recognized, and a number of methods for determining the position and character of concealed rock strata by means of seismic, gravitation, magnetic and electrical measurements made on the surface are being used with varying degrees of success. One physical property which varies widely for different materials, and hence affords an opportunity for distinguishing between them, is their electrical resistance. Locations • were selected where the geological structures were well known and where the depths to the water level and bed rock had been determined by drilling. The problem was to determine the value of measurements of resistivity and its variations as indications of the geological structure below the surface.

Jan 1, 1929

By Rex B. McLellan

Studies of the eyuilibrzum between ferrite and austenite with gas mixtures (CO + CO2 and H2 + CHe) have been used as a means of deducing the energy and vibrational entropy of carbon atoms in dilute interstitial Fe-C solutions. A simple model for dilute interstitial solutions is given which enables a solubility equation for the equilibrium between the gas mixtures and the solid to be deduced. This solubility equation is used to estimate the partial In this work measurements of the equilibrium between dilute solid solutions of carbon in iron and gaseous mixtures of CO2 + CO and CH4 + Hp have been analyzed using theoretical solubility equations deduced from a knowledge of the thermodynamic parameters of the gas mixtures and an appropriate model for the solid solution. The solubility equations are deduced by equating the chemical potential of carbon atoms in the gas thermodynamic functions of dilute Fe-C solutions from the measured equilibrium between the solid and the gas mixtures. It is shown that the vibra-tional entropy of a carbon atom in a and y iron is smaller than the corresponding entropy 01. a nitrogen atom in solid solution inferrite or austenite and that there is little difference between the vibrational entropies of both nitrogen and carbon atoms in ferrite and austenite. and solid phases. The chemical potential of carbon in the gas is found from a simple statistical mechanical analysis of the gas mixtures utilizing spec-troscopic data while that for carbon in the interstitial solution is found from a model in which the carbon atoms act as bound oscillators distributed in a random fashion in the solution. The solid solution is dilute enough to enable solute-solute interactions to be ignored. Thus the configurational entropy of the solution is ideal but the mixing entropy contains additional excess terms due mainly to the vibrational changes occurring on solution formation. The partial excess entropies (and the partial energies) do

Jan 1, 1965

By Robert Maes, Robert de Strycker

The solidifzcation reactions in the Cu-Sn-As system were determined by microscopic examination, thermal analysis, and X-ray diffraction. The system presents no ternary compound. There is a quasi-binary section, of a simple eutectic type, between the compounds Cu5As2 and SnAs; the system presents, in addition, one ternary eutectic reaction, one ternary peritectic reaction, and seven transitional reactions. The temp-peratures corresponding to each of these reactions were determined, most of them with an accuracy of *lLC. The isothermal lines of the liquidus surface were also established for almost the entire diagram. NO reference was found in the literature relative to the Cu-Sn-As phase diagram and this is believed to be the first study on this subject. The Cu-Sn diagram was taken from Hansen and Anderko;' it is represented by Fig. 1, with the phase designation which will be used in the remainder of this work. For the Cu-As diagram, the solution proposed by Hansen and ~nderko' must be modified to take account of recent data, principally from Heyding and Despault~ and from Hume-Rothery and Burns; this yields the diagram represented by Fig. 2. As for the Sn-As diagram, it is not established with certainty, particularly so far as concerns the solid solubility of tin in arsenic and the solidification reactions near the compound SnsAsz. For this last point, Hansen and Anderko propose two solutions: congruent melting of Sn3Asz with a eutectic SnsAsZ + SnAs or incongruent melting implying a peri-tectic reaction L + SnAs = Sn3As2. Microscopic examination of the few binary alloys prepared in this composition range made us prefer the second of these solutions, which gives the diagram shown by Fig. 3. EXPERIMENTAL METHODS The experimental techniques used in this work were microscopic observation and thermal analysis; a few X-ray diffraction patterns were taken to verify the

Jan 1, 1967

By William B. Phillips

The concentration of natural magnetites has been carried on in this country for several years, and more or less information has been collected on the subject. Various inventors, availing themselves of the magnetism which is inherent in such ores, have devised machines for separating the impurities from the ore by means of the electric current; and a greater or less degree of success has rewarded their painstaking and persevering efforts. We are now fairly in position to judge of the value of the process as applied to such material. It is not my purpose to speak of this matter further than may be required by the emergencies of the case. I shall assume that most engineers and metallurgical chemists are already acquainted with what has been done at the Chateaugay mines, at Mineville, at the Benson mines, at the Weldon and Ogdensburgh mines, and at Cranberry; although, at this latter place, there has not been so much done as we could wish. I shall not now speak of the various types of separators. From the time of William Fullarton, to whom was granted an English patent, in 1792, for separating iron-ore by the application of magnetic attraction, down to the present time, a great. many devices have been suggested, and a great many patents taken out for this purpose; but it is not necessary now to enter upon a discussion of their merits. Perhaps, at some future meeting of the Institute, after we shall have experimented further with some of the machines on the market, there may be an opportunity to contribute something to the current knowledge of the efficiency and economy of separating-machines. In this paper I propose to give, as briefly as possible, the results already reached in converting a non-magnetic ore into magnetic ore, and then concentrating it over a magnetic separator of the alternate-polarity type. I am aware of the work

Jan 1, 1896

By Rodney P. Smith

THE solubility of columbium nitride in ? iron has been determined for the temperature range 1191o to 1336°C from the nitrogen content and metallogra-phic examination of a series of Fe-Nb alloys.* (0.0 to 0.92 pct Nb) equilibrated with a purified gas mixture of 1 pct hydrogen in nitrogen. The method is the same as that used by Darken, Smith, and Filer' to determine the solubility of aluminum nitride in y iron. The variation in the furnace temperature during an equilibration period was about ± 2.0°C. Each sample was approximately 1/2 in. wide, 2 in. long, and 1/16 in. thick. A time series at 1200°C using samples of highest columbium content indicated that one day was sufficient for equilibrium; however, to be on the safe side all samples were left in the furnace for either two or three days. Afterequilibration, the samples were brought to room temperature by quenching in water. The experimental results are shown in Fig. 1. To be in accord with the values reported by Wriedt and Gonzalez2 and the temperature coefficient of our results at higher temperatures, the nitrogen content of iron at 1191oC is assumed to be slightly lower than our experimental value. Our data for the single-phase regions are not sufficiently accurate to establish an interaction coefficient for nitrogen in these alloys. However, the change in nitrogen content with change in alloy content for a number of systems (Fe-N-A1;3,1 Fe-N-Ni;372 Fe-N-Si.3949 Fe-N-V;3,5 Fe-N-Cr;3,6 Fe-N-Mo3,7) has practically the same value for the liquid alloy at a temperature near 1600°C as for the solid alloy at temperatures near 1200oC when the alloy content is below a few percent. On this basis the lines through the single-phase regions have been drawn with a slope corresponding to an increase in nitrogen of 0.0013 pct per 0.1 pct Nb.3 The straight lines through the two-phase regions were drawn with a slope corresponding to a one-to-one atom ratio of nitrogen to columbium in the nitride. The X-ray

Jan 1, 1962

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By John S. Brown

IN 1925 the writer undertook a detailed statistical study of all producing areas in the Joplin district as a basis for evaluating programs and measuring objectives. For this purpose, the published figures in the yearly volumes of Mineral Resources were used, supplemented for earlier years by publications of the Missouri Geological Survey and other local and less official sources. When all else failed, the available data were projected backward to hazard a reasonable guess as to the unrecorded early output of important areas. Fortunately, the proportion of such prehistory production is not a large factor in any of the totals. These results were used during the next few years to measure the relative importance of various producing areas and to predict the peak period of development of the all-important Picher field. For the purpose of this review, the charts have been completed to the end of 1950. During World War 11, the U. S. Bureau of Mines became interested in a similar study and issued comprehensive statistical tabulations of data up to 1945 ( Info. Circular 7383), which have been checked against the figures used herein. This tabulation, however, does not include all the earlier data used by the writer nor does it offer any estimates of the wholly unrecorded era in the beginnings of the earlier camps.

Jan 9, 1951