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By G. A. Crowe, W. T. Bishop

WHILE the literature in the United States on general polarographic technique is extensive, very little appears to be directly applicable to the analysis of flotation tailings. For this reason, it seemed worth while to present a few polarographic methods of ore analysis that have been in constant use in the laboratories of the Hercules Experiment Station for the past few years. At the time of our initial investigation of the polarographic method, there was little or no mention of its specific application to flotation tailings. It was therefore necessary for us to establish suitable conditions for the analysis of our flotation tailings and to consider possible interfering constituents. The polarograph, or dropping mercury electrode, method was discovered in 1925 by J. Heyrovsky and M. Shikata,1 of the Charles University, Prague. This method has since received extensive development and the literature contains many articles on the use of the polarograph for the quantitative determination of metals as well as anions, oxygen in solution, and reducible organic compounds. Kolthoff and Lingane,2 by the publication of their book, "Polarography," in 1941 did much to advance the knowledge and use of the polarograph. In chapter 25 of that book, methods for the polarographic analysis of brass, steel and iron products, alloys, and zinc ore are given. Aluminum,3 cadmium,3.4 cobalt,4 copper,3-9 gold,10 iron,3,11 lead, 3,12,13 molybdenum," nickel,4.8,9 tin,15 and zinc3,4,5,7 in ores have been analyzed by the polarograph. However, most of the work on tailing samples has been published in Russian journals and translations are not yet readily available. In this paper we will describe the method that was developed and used in our laboratory for the determination of copper, zinc, and lead in flotation tailings. PRINCIPLE OF THE METHOD The polarograph is an instrument for applying a potential to a mercury pool and a dropping mercury electrode separated by a solution, and for measuring the resultant electrical current. The procedure is essentially a small-scale electrolysis, in which the voltage required to reduce or oxidize the material identifies it qualitatively and the current measures the concentration quantitatively. Different constituents in a sample may often be determined simultaneously provided they reduce at sufficiently different voltages. An example is the determination of copper and zinc in the same solution. The reduction potentials are quite far apart, as shown in Fig. I. The polarographic method is particularly useful in the range of concentration between those normally determined by spectographic and chemical methods. In

Jan 1, 1946

By J. W. Byrkit

Design features and operating methods at the new Ajo smelter are described in detail. Successful operation of a novel method of handling and charging wet concentrates to a deep bath type reverberatory furnace contribute to the daily production of 200 tons of anodes with good results from the standpoint of both metallurgy and economy. THE New Cornelia Branch of the Phelps Dodge Corp. is located at Ajo, Ariz. Large scale mining operations were started at Ajo in 1917, when a 5000 ton leaching plant was put in service to treat the copper carbonate ore that overlaid the sulphide ore-body. In 1924 a 5000 ton flotation plant was built to treat the sulphide ore and the leaching operation was abandoned a few years later. Changes in practice and additions to plant facilities have resulted in a gradual increase in the milling rate which now approaches 30,000 tons daily. Prior to the erection of the Ajo smelter, flotation concentrate was shipped by rail to Douglas, Ariz, where it was treated in the Phelps Dodge smelter. Construction of a one reverberatory furnace smelter to produce an average of about 200 tons per day of copper anodes at Ajo was started early in 1949. Initial heating of the reverberatory furnace was begun on June 21, 1950. Charging the furnace was started on july 8, and the first anodes were cast on July 14. Neither the anode furnace nor the reverberatory furnace has cooled since the initial firing. Fig. 1 is a photograph of the new smelter. Built primarily to eliminate the '300 mile haul of concentrate to the Douglas plant, the new smelter was designed to treat the Ajo concentrate, with a minimum of capital investment. A novel, and relatively simple, method of concentrate handling and furnace charging made unnecessary the installation and operation of expensive storage facilities and reclaiming equipment, and obviated the necessity of holding in storage large quantities of copper-bearing materials. (Patents are pending in the United States and abroad on the Ajo process.) In the selection and arrangement of equipment, consideration was given to the full utilization of all smelting facilities, reducing the amount of idle equipment to a minimum. The layout of the smelter is shown in Fig. 2. The important problem of internal transportation was minimized by arranging the reverberatory furnace, converters, and anode furnace in a compact group and providing storage bins inside the smelter building, within reach of overhead cranes, for fluxing materials and other supplies needed in the daily operation. This can be seen in the sectional view of the smelter given in Fig. 3. Incorporated in the design were many innovations in smelting equipment intended to facilitate operations and effect economies in maintenance expense and manpower requirements. Table I gives operating data of the entire plant. Metallurgy The metallurgical practice at Ajo is based essentially upon the use of a single, deep bath reverberatory furnace for smelting wet concentrate, without concentrate storage facilities. The large reservoir of slag and matte maintained in the furnace serves to equalize, to some extent, the day to day variations in the nature and grade of concentrate and permits

Jan 1, 1954

By Louis E. Toth, Alan W. Searcy

A modification of Le Claire's microscopic model for self-diffusion is developed in a form suitable for prediction of activation energies for diffusion in disordered substitutional solutions as well as in pure metals Bonding is considered as a localized interaction, and the energy of bonding between atoms of different types is taken as the arithmetic mean of the energies in the pure elements. The activation energies for vacancy formation and migration in substitutional alloys are shown to depend on the empirical constants developed for self-diffusion when the equations are adjusted for the mole fractions of the two elements. The differences in activation energies between alloys and pure metals are calculated and compared with the experimental differences. MaNY different correlations have been proposed for use in predicting activation energies for self-diffusion or diffusion in dilute alloys. Usually theories for self-diffusion cannot be applied to alloys nor can theories for dilute alloys be satisfactorily adapted to self-diffusion. We present here a correlation scheme which can approximate activation energies for diffusion, vacancy formation, and atom migration in substitutional-alloy systems of any concentration. The activation energy for self-diffusion QD has been correlated to the melting temperature Tm,1, 2 the sublimation energy L,,l the heat of fusion Lf,3 crystal structure, and valence.4 Working with mechanical parameters Le claire5 proposed that the activation energy for vacancy migration Qm could be related to appropriate shear moduli. He also proposed that the activation energy for vacancy formation 62, is proportional to Ls. THEORY We consider that Le Claire's expression for 4, is satisfactory. But an alternate expression for Qm in terms of the bulk modulus is just as satisfactory from a theoretical point of view for the prediction of the energy of vacancy migration in pure metals and can more easily be used for alloys. In order for Qm to be a minimum, not only the moving atom but also adjacent and nearby atoms must undergo distortions. These distortions are neither isotropic as is implied by a correlation with the bulk modulus nor unidirectional as implied by a correlation with a shear modulus, but are complex and multidirectional. A complete analysis in terms of the bulk modulus and all the shear moduli is not yet available. In a first approximation in which only one parameter is used, there is no obvious theoretical reason to prefer the shear modulus over the bulk modulus. The bulk modulus is a much more convenient parameter for use in predicting Qm. Shear moduli are known for less than half of the metallic elements while bulk moduli are usually available. Furthermore, because of the directional dependence of shear moduli, their estimation for alloys appears inherently more difficult than is the estimation of bulk moduli. We assume that the bulk modulus Bs reflects an average value of the shear moduli such that the strain energy at the point of maximum distortion of the lattice during vacancy migration can be expressed as

Jan 1, 1964

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

The October issues* of the Journals of the three AIME Societies carried a brief resume of the historical development of various technical and professional organizations which in some immediate or remote way affect the individual member of AIME. This resume was presented by the Institute Committee on Inter-Engineering Society Cooperation. Recently, several plans have evolved designed as a first step to provide a so-called "unity organization" for the entire engineering profession. Almost all of the plans involve Engineers&apos; Joint Council, Engineers&apos; Council for Professional Development, and National Society for Professional Engineers in some way or other. Hence our committee is presenting to our membership a resume of the recent activities of the two umbrella organizations and of NSPE. More detailed information on any of these organizations may be obtained from annual reports published by the organizations.

Jan 2, 1961

By B. Alexander, G. Derge W. Peifer

This is part of a research project in the Metals Research Laboratory of Carnegie Institute of Technology, sponsored by the Carnegie-Illinois Steel Corporation. In organizing our program it became apparent that the problem of analyzing molten steel for hydrogen must be divided into two parts: (I) the correct analysis of a given sample, and (2) the correct sampling of the bath. Emphasis has been placed upon these divisions in the order named because methods of sampling cannot be evaluated until a satisfactory method of analysis is available. Vacuum fusion was selected from the list of possible analytical methods because it seemed to us to offer the best possibilities for giving rapid, accurate results on solid steel samples. A number of objections have been raised against this method as usually practiced. We have sought to meet some of these by proper design of the apparatus. Experiments will be described which show that others are not valid. In the conventional apparatus the sample is held under high vacuum for a period of several hours before it is actually analyzed and one might expect considerable hydrogen to escape during this period. We have provided a means of introducing the sample to the vacuum just before analysis. Another difficulty has been that the entire apparatus has been designed primarily for the purpose of analyzing for oxygen, which constitutes upward of go per cent of the total gases evolved from the sample The volume and pressure measurements have therefore been insensitive to the relatively small amounts of hydrogen present. This difficulty obviously can be taken into account in any apparatus designed especially for the amounts of hydrogen expected. Analysis in Vacuum-fusion Apparatus A number of experiments were carried out to determine the importance of several factors that have been stated as possible sources of error or uncertainty in vacuum-fusion analysis for hydrogen; namely, that hot graphite will absorb some of the gases, that metal vapor will cause discrepancies, and that low results may be obtained as a result of the water vapor (produced by the oxidation of the hydrogen) dissolving in the butyl phthalate of the manometer, or that the blanks obtained from the apparatus are so great as to make the method inaccurate. The experiments also checked on the accuracy and feasibility of using differential freezing as a method of gas analysis in a vacuum-fusion apparatus.

Jan 1, 1945

By Luis N. Henriquez

One form of encouragement for the small copper mining sector in Chile has been the construction and management of custom mill facilities to process the ore. The paper describes an economic analysis framework for the evaluation of government custom milling opportunities. Feasible mill locations and capacities within a region are selected and the infrastructure and milling costs associated with each combination of location and capacity are assessed. For each combination, the economics of developing and operating known copper deposits in the region is evaluated, and an optimum cut-off grade and mine capacity is selected for the deposits which justify development. Since the total ore supply from mines in the region may exceed a particular custom mill capacity, mine development is scheduled to optimize the economics of the mill facility. Finally, the best custom mill location and capacity is selected on the basis of overall costs and benefits. A copper mining region in northern Chile is used to illustrate the application of the model. A mobile mill approach is examined and compared with the fixed location mill alternatives. Results are analyzed as a function of copper price.

Jan 1, 1977

The Naval Consulting Board is asking the aid of all the members of the Institute in its effort to help solve the submarine problem. Probably every member of the Institute has some suggestion, and while each one of these may be of only slight value in furnishing the remedy, the aggregate may be of great service. Every member of the Institute will soon receive a pamphlet known as Bulletin No. 1 of the Naval Consulting. Board of the United States in which full information and instructions will be given to all of those who are willing to assist. It is hoped when this information is received the members of the Institute will give it their prompt attention and write as soon as possible to the Secretary of the Naval Consulting Board, 13 Park Row, New York, N. Y.

Jan 9, 1917

By Colman Goldberg

IT is customary to plot crystallographic planes or axes on a Wulff stereographic net which is ruled with parallels of latitude and meridians of longitude. If a single crystal is placed at the center of a sphere, the coordinates of a crystallographic plane or axis are the coordinates of the point where the axis intersects the sphere. The standard (HKL) projection is the projection for which the sphere is rotated so that the (HKL) pole is at the center of the projection. Schiebold and Sachs&apos; and many others have published standard projections for the more important planes of a cubic crystal. With Tables I and 11, it is possible to plot any plane (HKL) of a cubic crystal on a standard (001) projection if the absolute values of the individual H, K, and L are nine or less, which is almost always the case. Using the methods outlined by Barrett,&apos; the standard (001) projection can be rotated so that any arbitrary plane is at the center of the projection. The tables are believed to be important for two reasons: 1—The heretofore published standard projections usually are not of the proper size to fit the stereographic nets available. With these tables a standard projection can be made which will be of exactly the proper size for the available stereographic net. 2—With the tables, planes that do not appear on the previously published standard projections can be easily plotted. For these reasons, the tables are especially useful in the study of optical reflections from etched surfaces and can also be used to make a standard projection for the axis which is normal to the macroscopic surface. (This axis can be found by X-ray or optical methods.) Then if the crystal is etched, the effect of the etchant can readily be determined by comparing the latitude and longitude of the reflecting planes (as determined with an optical goniometer) with the standard projection that has been prepared. Use of the Tables Fig. 1 shows the meridians and parallel which have been designated as zero longitude and latitude. The tables themselves are self-explanatory. The

Jan 1, 1953

By Walter C. Holmes

IN the recently published book entitled "Man in a Chemical World," by A. Cressy Morrison, the several pages discussing explosives were included in the chapter on "Serving Industry." Such a classification is entirely correct, as blasting explosives function only as a tool for accomplishing certain useful work, a tool which is completely destroyed in one use. Explosives are so important to industry and to modern society, in fact, that it seems impossible to imagine the existence of civilized nations without access to commercial explosives as ready servants. Two main types of explosives are now in use, the low-velocity or deflagrating type, such as black powder, which is adapted for use in coal mining and other applications where a slow, heaving effect is desired, and high explosives of the dynamite type,

Jan 1, 1938

By R. B. Gilmore

It has been the custom of the Railroad Commission of Texas to hold hearings each month with respect to existence and imminence of waste of oil and gas in Texas and its prevention, and to issue orders restricting the production of oil to the reasonable market demands and allocating production to the various fields in Texas. The practice of designating the actual days during the month on which wells are to be shut down was discontinued in the order for November 1942, and orders issued thereafter contain only the number of shut-in and producing days for the month. Orders issued by the Railroad Commission are divided into two main subdivisions, the first a general shutdown order of all oil wells in the various fields in Texas, and second, the exception of certain fields to this general order. Table I shows the producing days for all of the fields in Texas for 1944 under the first of these classifications : The fields that have producing schedules varying from the general order may be divided roughly into three subdivisions, as follows: Table 2 shows the producing days for certain fields that were prorated as a group throughout 1944. Other fields which were occasionally included with this group were also prorated under the general order and by special orders. The producing days for these irregular fields are shown in Table 4. In Table 3 are listed fields that were exempted from any shutdown days during December 1944, the majority retaining this exception throughout 1944. Certain fields included in the general order were added to this group on the first day of the month shown.

Jan 1, 1945

By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

By Wei-Kao Lu

A general rate equation is derived for gas -solid reactions in metallurgical processes by considering the contributions of chemical reaction at inter-phase boundaries and diffusion through the solid product layer simultaneously. This equation takes care of the whole range continuously from purely diffusion control to purely chemical reaction control. The parabolic law,&apos; McKewan&apos;s equationa derived with the assumption of interface area control and the equation derived by Kawasaki et al. with the assumption of purely diffusion control are found as the limiting cases of the corresponding forms of the general rate equation. Many metallurgical processes involving gas-solid reactions have been extensively studied. The common examples of these processes include the reduction of oxides to metallic products, the roasting of sulfides to oxides or chlorides and the oxidation of metals. Gas-solid reactions consist of at least two kinds of steps; one involves the transport of reactant and product to and from the reaction zone and the other is the chemical reaction taking place at the interphase boundaries. In the limiting cases one or the other of the above mentioned steps will be much slower than the other and is then rate controlling. For example, the oxidation of metals is diffusion controlled and obeys the parabolic law.&apos; On the other hand, if the diffusion rate is much larger than the chemical reaction rate then it will be controlled by the chemical reaction rate. This latter case occurs for the reduction of iron oxides studied by McKewan. If the rate of diffusion and of the chemical reaction have the same order of magnitude, a more detailed analysis is necessary. Thus at the beginning of the reaction when the solid and gaseous reactants are in direct contact, the reaction should be chemical reaction rate controlled as no diffusion process is involved. At the other extreme as the reaction zone moves further into the solid, the diffusion distance becomes greater and the diffusion rate continuously decreases. Eventually, therefore, for a sufficiently large sample the rate must become diffusion controlled. As the transition from one controlling step to the other must be continuous, we cannot describe this transition period by either of the two limiting cases. In this paper the author attempts to derive a general rate equation for gas-solid reaction systems. This is effected by considering the rates of diffusion and chemical reaction simultaneously from the state of pure diffusion control to pure chemical reaction control. I) DERIVATION The system under consideration is made of at least three phases, namely the gaseous one, the solid reactant, and the solid product as shown in Fig. 1. The notations are listed at the end of the paper. The mass transfer process involves the diffusion of reactants and products across the solid product layer. It is reasonable to consider that no chemical reaction will take place in the solid product layer with respect to both gaseous reactant and product. For the characteristics of local equilibrium of the system, the diffusion process is really in a quasi-steady-state. It will be proved in the following paragraphs. Then we can invoke the law of conservation of mass valid for all chemical species passing through the layer. The solid reactant sphere has an initial radius, ro, after a fraction of completeness of the reaction, the unreacted core has a radius ri, where r, is in the solid product region. Let Cg be the activity of gaseous reactant in the

Jan 1, 1963

By Fred Witt, Milton Schwartz

ESTABLISHED methods for obtaining quantitative pole figures for flat sheets1"5 can be extended to apply to thin films on a substrate. The mode of scanning the sample is exactly the same as described in the references? but consideration is given to the fact that the scattered X-ray intensities are due to both the thin film and its substrate with appropriate attenuation factors. The purpose of this paper is to describe a method to obtain the scattered intensities from the film alone for subsequent pole-figure determinations. Fig. 1 shows the four possible general positions of the film (f) and its substrate (s) with respect to the incident X-ray beam (I,). In this paper it will be assumed that the plane of the sample is normal to the plane of the diffractometer. In the diagrams the line jV is the normal to the flat sample and the line P is the trace of the diffracting crystallographic planes in the plane of the diffractometer. The angle of tilt, a, is the positive acute angle measured from the line N to the line P; if this angle is measured clockwise then a is said to be in the positive a region; if this angle is measured counterclockwise then a is said to be in the negative a region. For the reflection cases, the total scattered intensity, at the proper Bragg angle for a particular set of planes, is due to that scattered by the film Vf) and that scattered by the substrate. The beam incident on

Jan 1, 1967

By T. D. Mueller, H. Dykstra

This paper describes a method for obtaining compositions of gas and oil phases in equilibrium with each other at a given reservoir temperature and pressure as lean or enriched gas is injected into a reservoir oil not in equilibrium with the gas. The method is based on calculation of equilibrium constants, K, from the equation log Kp = A + B F, where p is pressure and F is component characterization factor. A and B are constants that vary with a composition parameter. The paper explains how A and B could be determined with a minimum amount of data. The method consists of calculating equilibrium constants as a function of liquid composition and using the K&apos;s to calculate changes in compositiort of injection gas as it successively contacts original resetvoir oil at the gas-oil front and the change in composition of reservoir oil as it is successively contacted by the injection gas in the vicinity of an injection well. An iterative process is required. Two examples of the method are given which show how oil and gas compositions and properties are calculated with the aid of a computer. INTRODUCTION The calculation of recovery from lean-gas or enriched-gas injection into a saturated or under-saturated reservoir oil requires a knowledge of how phase properties change in a reservoir between injection well and producing well. To determine the phase compositions or properties experimentally would be difficult and time consuming, especially if one wanted to look at the effect of various injection gas compositions. For some fields an engineer would want to make preliminary calculations on the economics of gas injection before he makes the decision to spend a corrsiderable sum of money for laboratory work to obtain the necessary fluid properties. A method for calculatine compositions and properties based on a minimum of laboratory data is described. The minimum amount of data required is injection gas and reservoir oil composition and injection gas solubility as a function of pressure for an undersaturated oil, or the compositions of mixtures of reservoir fluid with two or more enriched gases, which mixtures have a bubble-point pressure that is the same as the expected average displacement pressure. On the other hand, if the economics appear to be attractive, more laboratory data can be obtained in the form of equilibrium constants for three or more mixtures of the reservoir fluid and injection gases. The method is based on the calculation of K&apos;s from the equation, log Kp = A + B F, where K is equilibrium constant, p is pressure and F is component characterization factor. This method of plotting K data by means of the above equation is described by Hoffman, Crump and Hocott.1 A and B are constants that vary with a composition parameter. It is shown how experimental data are used to determine how A and B vary with composition. BASIS OF METHOD EQUILIBRIUM CONSTANTS Equilibrium constant (K) data are required for this method. The K of each component is obtained from an equation that gives the product of K and pressure as a function of component characterization factor. The characterization factor F = b(l/Tb — l/T), where b is a constant characteristic of a given component, Tb is the boiling point in OR at atmospheric pressure of the given component, and T is the temperature of the system in OR. This method of plotting K data is described by Hoffman, Crump and Hocott.l The straight-line equation of the log Kp - F plot is log hp = log Kop +BFi, where Kop is at F =0, i designates the component, and B is the slope of the line. The factor F can be

Jan 1, 1966

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport&apos;s scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By A. Yoshikawa, T. Sugeno

To detenmine the origin of the sharp fatigue limit in many ferrous metals, S-N curvces were determined in push-pull fatigue at 18.6 kc per sec at room temperature and - 67°C for various kinds of iron. These differed in carbon and nitrogen content and grain size (25 and 2500 grains per sq mm). Sharp knees appeared in the S-N curves of fine-grained specimens with high interstitial content at both temperatures. In coarse-gruined specimens, knees were not sharp .regardless of the interstitial content and the testing temperature. It is concluded from these results that the controlling factov for the appeavance of the sharp fatigue limit is not strain aging but grain size. It has already been mentioned that iron and some iron alloys show fatigue curves characterized by a more or less sharp knee and a fatigue limit.&apos; Explanations of the origin of this characteristic behavior of fatigue in iron appear to fall into two broad classes. One is concerned with interstitial impurities through the aging or locking effect and the other is based on intrinsic plastic properties of iron. Levy and sinclair2 and Lipsit and Horne3 have suggested that the fatigue limit observed generally in iron and steel is due to interstitial solute aging during the course of fatigue. On the other hand, Thompson and wadsworthl have suggested that the fatigue limit may be analogous to the sharp yield point, in the sense that alternating stresses above the fatigue limit are necessary to break down the dislocation locking. However, there are some experimental results which cast doubt on the general validity of these suppositions.4-8 Ferro and Montalenti&apos; have recently suggested that the typical form of the fatigue curve of iron seems to come from an intrinsic plastic characteristic of the iron structure. This suggestion is based on the experimental result that pure iron containing an insufficient amount of interstitial solute to alldw appreciable strain-aging effects still showed a fatigue limit at room temperature. Although systematic investigations on the effect of grain size are scarce, it is thought that this effect is important in relation to the sharp fatigue limit. In fact, sensible differences were observed by Oates and Wilson4 in fatigue behaviors of a low-carbon steel depending on grain size. Ideally, the fatigue limit will be defined as the upper limit of stress amplitudes at which the life is infinite. This ideal fatigue limit can never be determined because of the limited time available for experiments, and moreover scattered data points often leave the construction of S-N curves somewhat arbitrary. And, it is usually stated that a material has a fatigue limit when its statistical S-N curve becomes apparently parallel to the N axis with a more or less sharp knee. The meaning of the fatigue limit and the sharp knee will be discussed in detail in relation to the construction of S-N curves. The origin of this sharp knee was investigated by determining S-N curves of iron for various interstitial contents, testing temperatures, and grain sizes. EXPERTMENTAL PROCEDURE The material as received was a commercial-grade low-carbon steel in the form of 4-mm-diameter rods with the following composition in weight percent: C, 0.09; Si, 0.017; Mn, 0.43; P, 0.006; S, 0.012; Cu, 0.11. Five different groups of specimens were tested. The grain sizes and interstitial contents in each group are given in Table I. The specimens of group C-02 were decarburized by annealing for 100 hr at 700°C, followed by an additional 100 hr at 850°C in wet hydrogen. Specimens of groups N-2 and N-9 nitrided in a mixed atmosphere of ammonia and hydrogen after an initial treatment identical to group C-02. The specimens of group C-9 were prepared in a manner similar to those of group C-02, except heat treatment was carried out in a vacuum. After polishing their surface with emery paper, the specimens of all groups were given a final anneal for 30 min at 930°C and air-cooled in an evacuated quartz tube. For group C*-9 this

Jan 1, 1965

By A. C. Emery

The physical and chemical properties for the metalliferrous feed materials to the Imperial Smelting Process blast furnace are defined and the means of achieving these properties by the sintering or briquetting routes discussed. Modern sinter plant performance data is included with a plant flow sheet showing draughting patterns. The necessity for ensuring an adequate SO2 content in sinter machine gases when roasting sulphide materials to enable conversion to sulphuric acid in a contact acid plant is described. The ability of the process to consume limited quantities of oxide materials, residues from other processes and other secondary sources is discussed. The argument for a briquetting route is developed out of this limitation and the merits of cold and hot briquetting examined. Development work on the hot briquetting route for this purpose is briefly described and several flow sheets outlining possible applications for hot briquetting to different raw material situations including the preparation of low lead charges for the furnace are presented.

Jan 1, 1977

By R. Maddi, I. R. Kramer

The delay time for the initiation of slip was studied in single crystals of a brass, aluminum, and ß brass. A delay time for slip was found in ß brass when the specimens were tested below room temperature; however, one was not found for a brass or aluminum. A general theory for the existence of the brittle transition temperature is proposed. A LTHOUGH a considerable amount of effort has A been devoted to the study of the deformation and fracture of single crystals, the vast majority of the work was concerned with static tests or with tests carried out at relatively slow strain rates. The necessity for the study of a possible incubation time for slip becomes apparent when the various theories which have been postulated for the elucidation of the mechanism of slip are considered. The existence of an incubation period would strongly indicate that slip occurs by a process of nucleation and growth; whereas the absence of an incubation would present rather convincing evidence that slip occurs by a cataclysmic process. In addition to shedding light on the process of plastic deformation, an understanding of the early stages of plastic deformation may be helpful in finding an explanation for the brittle behavior of the body-centered metals under certain conditions. It is well known that these metals, such as iron, molybdenum, tungsten, ß brass, etc., will become brittle as the test temperature is lowered or the strain rate is increased. In spite of the fact that this subject has received considerable attention since the turn of the century, no adequate theory exists today which explains the phenomenon. In the ductile temperature range the metal breaks with a "fibrous" fracture after considerable slip has taken place. In the brittle temperature range the metal fails essentially by cleavage on the {loo) planes: however, some plastic flow is always present even in the most brittle fractures. It is possible, as will be explained later, to ascribe this brittle behavior to the length of the incubation time for slip. Clark and Wood,&apos; using polycrystalline metals, showed that a delay time existed for the yield point in mild steels and that the delay time depended upon the applied stress. These authors stated that the delay time was observed only with those materials for which the stress-strain curve showed a definite yield point. In their work only the mild steel specimens exhibited a delay time at the yield point, while the other materials studied-type 302 stainless steel, SAE 4130 normalized steel, SAE 4130 quenched and tempered steel, 24s-T aluminum—did not show a delay time. These authors&apos; in an extension of their work, found that as the temperature was lowered the delay time was increased. It is, then, the purpose of this investigation to measure or to set an upper limit on the delay time for plastic flow in single crystals of a brass, aluminum, and ß brass. The delay time will also be studied as a function of temperature. The incubation time may be measured by determining the length of time the specimen will support a stress without slip occurring when the stress is greater than the static critical resolved shear stress. In order to accomplish these measurements use was made of a pendulum which was so designed that a single crystal specimen could be placed at various positions along its length. When a pendulum is struck by another pendulum of the same length, an elastic wave is transmitted down the bar with the velocity of sound in the material and is reflected from the far end of the bar. The reflected wave then travels back and unloads the stress until it reaches the impacted end of the bar and the two pendulums separate. The length of time that the specimen is subjected to the stress is equal to the time it takes for the stress wave to travel twice the distance from the specimen to the end of the bar. The stress applied to the specimen is governed by the velocity of impact of the two pendulums. The stress at which the specimen first suffers plastic: deformation was determined in these experiments by examining the specimen under the microscope for the first appearance of slip lines and by measuring the residual strain after each impact. In these experiments the critical resolved shear stress was approached from the low stress side and no attempt was made to determine it exactly. To determine it exactly, it would have been necessary to find that stress at which slip would have just started. However, since the stresses were increased in rather small increments the critical stress is believed to be approached rather closely, as will be seen from the experimental results. The critical stress will be taken as the highest stress obtained before the onset of plastic deformation. The stresses

Jan 1, 1953

By Arthur Baker III

The orebodies are long bedding-plane lenses of chalcopyrite and sphalerite, associated with garnetite masses. Most of the orebodies are within a 50-ft thickness of Cambrian limestone; other Paleozoic limestones and dolomites are locally metamorphosed but only slightly mineralized. Pre-mineral faults are numerous, but shallow folds were the main ore-localizing structures. JOHNSON camp is in the northwestern part of Cochise County, Ariz., about 50 miles east of Tucson. The nearest major mining districts are Tombstone and Bisbee, respectively 27 and 50 miles to the south, and the Superior-Miami-Globe-Ray porphyry copper group, about 90 miles northwest. Like many mining camps of the Southwest, Johnson camp is said to have been worked by the Spaniards. The first production on record was in the early 1880&apos;s, when an unknown amount of oxidized copper-silver ore in the Peabody mine was mined from replacement orebodies in the Pennsyl-vanian Naco formation. From 1904 to 1911 outcropping oxidized ores in the Cambrian Abrigo formation were worked, and an estimated 100,000 tons of copper ore were shipped. In 1912 the first large sulphide orebody of the district, the Republic Manto orebody, was discovered, and in the following few years some 250,000 tons of predominantly sulphide ore were shipped. The average grade of this ore was approximately 4.5 pct Cu, 6 pct Zn, 0.8 oz. Ag, and 0.001 oz Au. The Republic, Copper Chief, and Mammoth mines were the principal producers during this period. Mining ceased in the district after 1920, and until 1943 only small-scale leasing operations were carried on. In 1943 all the mines that had been productive were acquired by the Coronado Copper and Zinc Co., the present operators, and in the 10 years since that time the district production has amounted to approximately 350,000 tons of milling ore averaging 2 pct Cu and 6 pct Zn. Most of this ore was produced from the Republic and Mammoth mines, but since 1950 a large part of the production has been from the new Moore mine. The total known production from the district, then, is about 3/4 million tons of copper and copper-zinc ore of low grade. All of this ore was produced from orebodies associated with garnetite in the middle member of the Cambrian Abrigo formation. In addition to this known production, an unknown tonnage of ore was extracted from the Peabody mine orebodies that lie in the Pennsylvanian Naco formation. Published information on the geology of the district is limited. Aside from brief references in various mining journals, only three papers on the district have been published.1-3 One of these is a U. S. Bureau of Mines report on a diamond drilling program, one is a brief paper on the general geology of the district, and the third is a report on geochemical experiments, with a section on the occurrence of the orebodies. The last two are by John Cooper, of the United States Geological Survey, who has done much detailed work in the area. Stratigraphy The rocks of the mineralized area are Paleozoic sediments ranging in age from Cambrian to Penn-sylvanian. Several disconformities are present in the stratigraphic column, the most important one being between the Cambrian Abrigo formation and the Devonian Martin formation. There are no angular unconformities. Within the district, the Paleozoic sediments lie in a fairly uniform monocline, striking northwest and dipping 30" to 50" northeast. This local monocline is part of a domal struc-ture centered in the Little Dragoon mountains to the southwest. The Texas Canyon stock, a quartz monzonite body intruded probably during the Laramide revolution, lies south of the mineralized area (Ref. 2, p. 33). The Paleozoic rocks dip away from the stock, and on the surface are separated from it by at least 1500 ft of Pre-Cambrian rocks. The outcrop pattern of the northeastern edge of the stock suggests that it may dip gently northeastward, passing below the mineralized area at moderate depth. No quartz monzonite has been found in mine workings or diamond drill holes, which reach to depths of 1000 ft. The only igneous rock found in the mineralized area is a lamprophyre dike cutting the Naco limestone in and near workings of the Peabody mine. With the exception of the lowermost beds—the Bolsa quartzite and the shaly lower member of the Abrigo formation—the Paleozoic sediments are predominantly carbonate rocks, Fig. 1. The middle member of the Abrigo formation, which contains the principal ore-bearing beds, is limestone, with thin shale partings throughout most of its 250-ft thick-ness. Near the top of this member is a sandy bed some 25 ft thick. The upper member of the Abrigo formation and the lower half of the overlying Devonian Martin formation are dolomitic, with num-

Jan 1, 1954