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By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By W. J. Helfrich, C. L. Sollenberger

Many present direct reduction processes utilize iron ore concentrates for the production of sponge iron and the sponge iron is usually preferred as an agglomerate. Pelletizing a high grade iron oxide concentrate prior to reduction is a simple approach to the high capacity production of a uniform and agglomerated sponge iron product. The present paper describes the effect of different atmospheres and physical characteristics on the reduction of pelletized iron oxide concentrates. The kinetics of iron oxide reduction have been I studied by numerous investigators1-4 and a rate equation for the hydrogen reduction of hematite and magnetite has been proposed. Mc Kewan' obtained kinetic data for the reduction of hematite spheres sintered at 13'70°C (2498'F'). The kinetics of magnetite reduction was studied by Quets. He compacted the oxide at a pressure of 1 ton per sq cm and sintered the specimens to densities of 95 to 96 pct of theoretical. These studies demonstrated that the reduction of iron oxide is a topochemical process and that the rate of reduction is proportional to the receding surface area of remaining iron oxide. Thus, the measurement of the kinetics of iron oxide reduction depends upon the development of a measurable and well defined interface between metal and reacting oxide. It is evident that the reduction rate will be constant only when the rate of formation of the reaction product layer is constant. It was recognized by Joseph' and Edstrom' that the physical character of the oxide will determine the configuration of the interface between oxide and metal. The reduction of oxides which exhibit few pores or no interconnected pores should proceed by topochemical processes. However, if a massive or dense crystalline ore cracks during the reduction of the oxide, thus allowing the reduction to Proceed away from a well defined oxide/metal interface, then the observed reduction rate will vary or change during reduction. From a process standpoint, it would be difficult to apply absolute reduction rates determined for crystalline or nonporous iron oxide to the direct reduction of a porous pellet of iron ore concentrate. Most present direct reduction processes are attempts to utilize iron ore concentraates in the production of sponge iron. The sponge iron is usually preferred in an agglomerated form for subsequent melting practices. Pelletizing a high grade iron oxide concentrate prior to reduction is a simple approach to the high capacity production of a uniform and agglomerated sponge iron product. One process for preparing such a product has already been de-scribed. This paper describes the effect of different atmospheres and physical characteristics on the reduction of pelletized iron oxide concentrates. ORE CONCENTRATES STUDIED A magnetite concentrate from Reserve Mining Co. and a hematite concentrate from U.S. Steel Corp. were used in preparing pellets for these experiments. A head analysis of these concentrates is given in Table I. To compare the reduction rates of pelletized concentrates, it was necessary that each pellet contain equal amounts of oxygen which could be removed by reduction, regardless of the oxidation state, i.e., Fez% or Fe304. Also, because of the difficulty in preparing spherical pellets of uniform size, weight, density, and porosity for experimental purposes, pellets of a cylindrical shape were formed in a press.

Jan 1, 1961

By H. H. Rachford, D. W. Peaceman

A system of partial differential equations describing miscible displacement of fluids in porous media is derived The system takes into account the influence of gravity, the spatial distribution of permeability, diffusion, and fluid viscosities and densities. A numerical procedure for approximating solutions to the differential systems has been tested for a horizontal two-dimensional geometry. In end-to-end displacements of oil with less-viscous solvents, the numerical solutions exhibited fingering qualitatively similar to that observed in laboratory models. Small random spatial variations in permeability about the mean value are sufficient to initiate fingering. Quantitative comparisons of computed results with laboratory data show good agreement. INTRODUCTION Miscible flooding of oil by solvent is receiving increasing consideration for field use.1-4 Unfortunately, such floods potentially present severe problems in loss of recovery through the by-passing of oil by expensive solvent. Consequently, their economic evaluation requires sound techniques for predicting recovery. The purposes of this work are to present a finite-difference method for calculating the multidimensional displacement of oil by solvent and to investigate the validity of the method by comparing results of calculations with data from displacements in laboratory models.5 The formulation of the method to simulate the model experiments treats a case of limited scope in the description of solvent flooding in the reservoir. The model experiments were carried out with fluids that were assumed to form an incompressible, ideal, two-component system with constant diffusivity. Establishing the validity of the method even in its present form provides a major step toward the goal of quantitatively evaluating individual solvent flooding projects. First, it demonstrates the fea- sibility of calculating the course of displacements which are dominated by an inherent macroscopic instability, i.e., viscous fingering. In addition, the method provides almost the only practical means of examining the effect of the size and extent of reservoir inhomogeneities on the development and propagation of the fingers, taking into account the important influences of diffusion and gravitational segregation. It might be inferred that such studies cannot yield results of practical value because in displacements dominated by macroscopic instability the pattern of finger development and the resulting performance should depend critically on small variations in the geometric distribution of reservoir inhomogeneities. The present method offers the capability inherent in computational techniques of predicting performance reproducibly with any arbitrary distribution of reservoir properties and, as such, provides a means of evaluating the sensitivity of behavior to uncertainties in reservoir definition and, thus, assessing the reliability of prediction of performance. THE PHYSICAL PROBLEM DATA USED FOR QUANTITATIVE TESTS OF CALCULATIONS In this work, a calculation for treating the miscible-displacement process is tested by comparing calculated results with experimental data. The experiments chosen for comparison have been described in detail,5 and the quantitative features are summarized in a later section. Briefly, oil was flooded by solvent of equal density from a thin rectangular channel in Lucite packed with uniform Ottawa sand. Under these conditions, two-dimensional geometry is considered adequate to represent the process. Inasmuch as the present work is concerned with testing of the method by comparison with specific two-dimensional data, the system of equations presented in the succeeding section will be oriented to defining the physical system specifically. THE DIFFERENTIAL EQUATIONS Suppose x, y to be a Cartesian co-ordinate system and define h(x, y) to be the height of a point above a horizontal reference plane. It will be assumed

By George Cole

WHILE many parts of Canada's pre-Cambrian shield are well served by railway, it is frequently necessary for prospecting purposes to proceed farther into areas in-accessible by rail. To such areas in summer the canoe was at one time the accepted means of travel for the prospector while the dog team was much used in winter. Al-though summer travel was much improved by the development of the outboard motor, the lack of facilities for cheap transporta-tion has been a serious hindrance to the employment of capital in opening up the distant fields. The pre-Cambrian surface of Manitoba, like that of Ontario, is hummocky, with rounded hills and ridges of rock alternating with basinlike depressions and valleys oc-cupied by lakes and rivers or by many low-lying portions covered with muskeg. Routes to the mines have not usually been direct or easy and seasonal vagaries have presented problems in themselves. In summer, water transportation may be the cheapest method for the longer dis-tances but it is not every water route that will satisfy the conditions of loading freight onto a boat or scow and of conveying it without interruption to its destination. By its location, a mine may require a large program of boat transportation in summer over part of its route, to be followed by winter freighting for the remainder. In order to carry on development and produc-

Jan 1, 1940

By Stanley F. French

ELECTRICAL power and distribution for the sulphide ore plant is an addition and extension of the existing power system which has served the oxide reduction plant since its inception in 1914. The power plant is located at Tocopilla on the west coast of Chile, some 90 miles from Chuquicamata. A brief description of this plant and the existing transmission system is necessary to an understanding of the problems involved in the provision for the sulphide plant load. Originally the Tocopilla power plant consisted of four Escher Wyss turbines driving Siemens Schuckert generators, each rated 10,000 kw. At various times, units of 10,000 and 20,000 kw were added, all of which operated at 215 psi and 600°F at throttle. In order to improve the economy of the station, a Topping unit was installed in 1938 together with a high-pressure steam generator of 360,000 lb per hr capacity. This unit is rated at 11,000 kw and was designed for 750 psi, 880°F. The exhaust from this turbine passes to the low pressure station header for operation of part of the low pressure turbines. Total kw generated by the high pressure boiler, topping turbine and associated low pressure turbines totals 33,000 kw and the total station capacity is 113,000 kw. This installation proved one of the most successful of its kind, operating almost continuously. The original plant was of German design and consequently European characteristics were incorporated into the system, the frequency being 50 cycles and voltages of 500, 5000 and 100,000 were used for low, generator, and transmission voltages,

Jan 1, 1952

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.'-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.' Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By C. L. Rabe

The Muddy and Dakota sands, more commonly known as the "D" and "J" sands, respectively, of the Denver-Julesburg Basin are correlative over a large area. It is reasonable to believe, therefore, that depositional environment throughout the Basin was comparable. Local variations in sand development do occur, however, and productivity is often governed by permeability as well as structural position. Experience indicates permeability is commonly a function of cementing material. While cases of siliceous or calcareous cementing have been observed, the bonding material is, for the most part, clay. Under the latter circumstance, clay should bear some relation to permeability. Similarly, gamma radiation should bear some relation to the amount of clay. This study was undertaken to determine if a cross relation exists between gamma radiation and permeability. RESULTS OF INVESTIGATION A qualitative relation does exist between gamma radiation and permeability for clay-bonded Muddy and Dakota sands of the Denver-Julesburg Basin. This is illustrated graphically by Fig. 1, which shows corrected gamma ray deflection vs permeability for five wells over an area approximately 50 miles long and 8 miles wide. The "corrected" gamma ray deflection cannot be read directly from the gamma ray survey in all cases. It became apparent early in the investigation that methods would have to be developed for converting all gamma ray surveys to a common deflection scale and to correct for thin bed effects. COMMON SCALE DEFLECTION Because all logs are not recorded in the same calibration units or at the same sensitivity, it was felt they could be most readily converted to a common scale by measurement of deflection in inches from zero. Initially, four wells in the Jacinto field of Nebraska were carefully correlated, and selected intervals were planimetered to obtain average deflections. Average deflections of planimetered intervals from three of the wells were plotted vs those of the fourth well which was to be used as a common reference. The plots are shown in Fig. 2. While results obtained by this method in the Jacinto field were relatively good, the planimetered intervals were not easily correlated with logs from other fields. Furthermore, the planimetric method is laborious and not readily adapted to routine operations. Deflection of the "Bentonite marker" was found to

Jan 1, 1958

By J. R. Lewis

During the past few years there has been considerable interest in the sizing and the preparation of the iron ore fed into blast furnaces. Furnacemen know that proper sizing of ore tends to increase the efficiency of the furnace. It has been shown by Joseph1 and his associates that there is a direct relationship between the porosity of an ore particle and the time required for its reduction in the blast furnace. This relationship may be stated as follows: All other factors remainig constant, the time for reduction of a given sample of ore is inversely propor-tiofid to its porosity. As a consequence, large pieces of very porous ore, say 3 or 4 in. in cross section, will be completely reduced by the time they reach the hot zone just above the tuyeres, while large pieces of dense, nonporous ore may reach the hot zone with their centers unreduced. This means that for the latter complete reduction will be accomplished by the so-called "direct method;" i,e., where carbon reacts directly with the ore. Some recent work by philbrook2 seems to contradict this rule. He found that of two unlike ores he studied, the one with the lower porosity reduced more readily. He explained his results as "possibly due to an apparently greater tendency of the rA, ore (lower porosity) to crack during preliminary dehydration and during reduction." This brings his results in line with the rule stated above. It is not the author's intention to enter into a discussion of the merits of "direct" versus "indirect" reduction. It is enough to Say that, in general, indirect reduction is desirable. For the greatest efficiency, Gruner's theorem3 requires that all reduction in the blast furnace be indirect. Joseph seems to believe this also, because in his recent article on Some Comparisons between Iron Ore, Sinter and Nodules as Blast Furnace Feed4 he concludes that: "In genera', the carbon in blastfurnace coke is used most efficiently when the largest amount of the carbon charged reaches the tuyeres." However, P. V. hlartin,3 in an excellent paper, has shown that some direct reduction may actually increase the efficiency of the furnace; that is, increase its rate of production while maintaining maximum fuel economy. For nonporous ores there is more opportunity to have an excess of direct reduction unless the factors that make for indirect reduction are favored; for instance; the Proper sizing of the Ore particles' Another factor that has an important bearing on the reduction rate, as it is affected by particle size, is the flow of heat into the particle. The ore particle

Jan 1, 1948

By J. R. Lewis

During the past few years there has been considerable interest in the sizing and the preparation of the iron ore fed into blast furnaces. Furnacemen know that proper sizing of ore tends to increase the efficiency of the furnace. It has been shown by Joseph1 and his associates that there is a direct relationship between the porosity of an ore particle and the time required for its reduction in the blast furnace. This relationship may be stated as follows: All other factors remainig constant, the time for reduction of a given sample of ore is inversely propor-tiofid to its porosity. As a consequence, large pieces of very porous ore, say 3 or 4 in. in cross section, will be completely reduced by the time they reach the hot zone just above the tuyeres, while large pieces of dense, nonporous ore may reach the hot zone with their centers unreduced. This means that for the latter complete reduction will be accomplished by the so-called "direct method;" i,e., where carbon reacts directly with the ore. Some recent work by philbrook2 seems to contradict this rule. He found that of two unlike ores he studied, the one with the lower porosity reduced more readily. He explained his results as "possibly due to an apparently greater tendency of the rA, ore (lower porosity) to crack during preliminary dehydration and during reduction." This brings his results in line with the rule stated above. It is not the author's intention to enter into a discussion of the merits of "direct" versus "indirect" reduction. It is enough to Say that, in general, indirect reduction is desirable. For the greatest efficiency, Gruner's theorem3 requires that all reduction in the blast furnace be indirect. Joseph seems to believe this also, because in his recent article on Some Comparisons between Iron Ore, Sinter and Nodules as Blast Furnace Feed4 he concludes that: "In genera', the carbon in blastfurnace coke is used most efficiently when the largest amount of the carbon charged reaches the tuyeres." However, P. V. hlartin,3 in an excellent paper, has shown that some direct reduction may actually increase the efficiency of the furnace; that is, increase its rate of production while maintaining maximum fuel economy. For nonporous ores there is more opportunity to have an excess of direct reduction unless the factors that make for indirect reduction are favored; for instance; the Proper sizing of the Ore particles' Another factor that has an important bearing on the reduction rate, as it is affected by particle size, is the flow of heat into the particle. The ore particle

Jan 1, 1948

By Eric J. Jette, Frank Foote

The unusual physical, electrical and magnetic properties of the iron-nickel alloys has given rise to a voluminous literature. This work will be reviewed critically in "The Alloys of Iron and Nickel," a monograph of the Alloys of Iron Research Series, soon to be published. In what follows we shall therefore confine ourselves to those of the earlier investigations that involved the use of X-ray crystal-structure methods. The earliest X-ray work on the iron-nickel system was by Miss Andrewsl. Using the powder method of X-ray analysis purely as a means of identifying the phases present, she located a region between 20 and 30 weight per cent nickel in which body-centered and face-centered phases coexisted. No lattice constants nor details of heat-treatment were reported. Bain2 also reported some qualitative observations. McKeehan3 made a systematic investigation over the whole of the system, giving many of his alloys four and some five different heat-treatments. In alloys furnace-cooled from 900' to 950' C. he found two coexisting phases between 0.15 and 30 per cent nickel. The precision of the lattice-constant measurements was low in comparison with what can be obtained today. Even for alloys of the same heat-treatment, differences in the constants were often between two and ten parts per thousand. In regions where no change of lattice constant with heat-treatment should occur, differences of the same order of magnitude were found. Since the maximum change in the lattice constant of nickel with change of composition is only about 2 per cent of the constant for pure nickel, these variations in the constants for a given alloy cause the points to "scatter" badly about any curve that may be drawn to represent them and it is difficult to interpret such results. In spite of this, McKeehan shows that the lattice constant of nickel increased as the iron content increased. His results for the alpha-iron phase are less conclusive. Osawa4 also investigated the entire system. For alloys slowly cooled from 1150' C. and then filed into samples for X-ray analysis, he found

Jan 1, 1936

By Frank Foote, Eric J. Jette

The unusual physical, electrical and magnetic properties of the iron-nickel alloys has given rise to a voluminous literature. This work will be reviewed critically in "The Alloys of Iron and Nickel," a monograph of the Alloys of Iron Research Series, soon to be published. In what follows we shall therefore confine ourselves to those of the earlier investigations that involved the use of X-ray crystal-structure methods. The earliest X-ray work on the iron-nickel system was by Miss Andrewsl. Using the powder method of X-ray analysis purely as a means of identifying the phases present, she located a region between 20 and 30 weight per cent nickel in which body-centered and face-centered phases coexisted. No lattice constants nor details of heat-treatment were reported. Bain2 also reported some qualitative observations. McKeehan3 made a systematic investigation over the whole of the system, giving many of his alloys four and some five different heat-treatments. In alloys furnace-cooled from 900' to 950' C. he found two coexisting phases between 0.15 and 30 per cent nickel. The precision of the lattice-constant measurements was low in comparison with what can be obtained today. Even for alloys of the same heat-treatment, differences in the constants were often between two and ten parts per thousand. In regions where no change of lattice constant with heat-treatment should occur, differences of the same order of magnitude were found. Since the maximum change in the lattice constant of nickel with change of composition is only about 2 per cent of the constant for pure nickel, these variations in the constants for a given alloy cause the points to "scatter" badly about any curve that may be drawn to represent them and it is difficult to interpret such results. In spite of this, McKeehan shows that the lattice constant of nickel increased as the iron content increased. His results for the alpha-iron phase are less conclusive. Osawa4 also investigated the entire system. For alloys slowly cooled from 1150' C. and then filed into samples for X-ray analysis, he found

Jan 1, 1936

By John Chipman, Raymond L. Orr

Recently reported high -temperatlnre thermal data have been incorporated in a reuieu' of the therinody-r~ar,zic propesties of iron. The recent data permit mot corlsisterlt and reliuble choices to be made for many of the pvoperties, resnlling in bettev eslablished tabrtlations of the thermodynamic functions. Values of Cp, h°t- - H°298. s°t - S2sa, and (G°T -H298/T are tabulated for -the solid and liquid phases of iron in both stable and melastable regions. Consistency of the tabulations has been maintained to the precision necessr~vg to yield the Gibbs energy change belween the bcc (a, 8) and fcc (y) phases of iron at temperatures pertinenl to alloy studies. THE importance of the metal iron has stimulated many investigations of its thermodynamic properties at elevated temperatures. Reviews and summaries of the data have appeared from time to time. Among these the 1951 paper of Darken and smith' deserves highest recognition for the quality of its criticism and for the precision and thermodynamic consistency of its tabulations. These and the more recent table of Kaufman, Clougherty, and weiss2 reproduce the Gibbs energy of the (a, 6)--Y transformation with sufficient sensitivity for alloy studies. Other recent compilations of equal validity3-' make no attempt to do this. Since this Gibbs energy change is not greater than 22 cal per g-atom over the temperature range 1100° to 1800°K, it is obviously desirable to tabulate values of (G°t - H298)/T to four places of decimals even though the absolute accuracy would not warrant such precision. The necessity for reconsideration of the problem is emphasized by the recent publication of several important researches on the enthalpy and heat capacity of iron. The older work is well-covered in the reviews cited and will be mentioned here only when actually employed in the tabulations. GAMMA IRON Transition temperatures are taken from the selec -tions of Elliott and Gleiser,5 based on the work of Boulanger7 and earlier workers. For the a-y (A3) transition at 1184°K we retain the value 215 cal per g-atom adopted by Darken and smith.' It has received confirmation in the recent work of Dench and Kubaschewski,' and of Braun8 using adiabatic calori-metry, and of Wallace, Sidles, and Danielson10 using a pulse heating technique. The enthalpy data of Olette and ferrier" and of Anderson and Hultgren12 at higher and lower temperatures may be extended to 1184°K to give the following values which are adjusted to the required value of ? 1184 Ha,1184 Ha 298 = 8030 cal per g-atom [11 hr,1184-ha298 = 8245 cal per g-atom [2]

Jan 1, 1968

The U. S. Navy Department has perfected plans for the enrollment and training of considerable numbers of engineering officers. A school for this purpose, the U. S. Navy Steam Engineering School, has been established by the Department at Hoboken, N. J. The school is open to men between the ages of 21 and 40 who meet the physical requirements of the Navy, who are of thorough ability and officer-like character and who have completed the mechanical or electrical engineering course at certain recognized technical schools, or who possess an education and experience adjudged to be an equivalent thereof. Enrollment in the U. Naval Reserve Force of men properly qualified may be made at any Naval enrolling office, notation being made of the applicant's qualifications and desire to be detailed to this school. Applicants will be enrolled as Chief Machinist Mates, and during the course of instruction will draw the pay of this rating, $83 per month, plus $60 per month paid as subsistence. Upon graduation, men will be commissioned as Ensigns in the U. S. Naval Reserve, with a salary of $1700 per year. The duty to which a graduate of this school will be assigned will be that of an engineer officer in the auxiliary service of the Navy. Special provision has been made for the continuance of the school with proper material by a Navy regulation which permits undergraduates of the Freshman, Sophomore, and Junior Classes in recognized engineering schools to enroll in the Naval Reserve Force with the rating of Seaman 2d Class, and continue their courses at the institutions where they have matriculated. Such men will be called into active service after their graduation, and can at that time, if they are qualified to pass an officers' physical examination, apply for admission to the U. S. Navy Steam Engineering School. Men who are registered in the draft, either graduates or undergraduates, may enroll with the proper enrolling officer by securing from their draft board a letter of release, which in all probability can be obtained for this purpose. The aim of this school is not simply to produce engineers, but to produce naval engineering officers in the true sense of the word. The course of instruction covers a period of five months, arranged in four periods.

Jan 10, 1918

By A. R. Elsea, C. C. McBride

HIGH-TEMPERATURE alloys, that is, alloys that are strong at high temperatures, have become increasingly important with the development of modern aircraft engines. Many alloys of this type are available. However, metallurgists do not have a clear understanding of the phases or structures which are responsible for these high-temperature properties. If these basic factors were understood, it might be possible to make better or cheaper alloys for service at high temperatures. For this reason, an investigation of the fundamental factors promoting high-temperature strength in alloys was started at Battelle Memorial Institute. This was to have included a study of the relationship between the structure and properties of cobalt-chromium base alloys of the vitallium type. It soon became clear that the structure of vitallium is quite complex and that the equilibrium diagrams which should explain these structures were unreliable. As a result, the cobalt-chromium binary diagram was determined as the first phase of this investigation1. This diagram is shown in fig. 1. During the study of the cobalt-chromium binary system, it was learned that these alloys may pick up considerable nitrogen when melted and heat treated in air. The extent to which nitrogen affects the various reactions in cobalt-chromium base alloys was not known, but there were indications that this impurity might be responsible for some of the erratic test results obtained for vitallium. Consequently, nitrogen was the first ternary addition studied. Thereafter the work was extended to ternary additions of iron and of nickel. This paper describes the investigation of the effects of nitrogen, iron, and nickel upon the reactions in cobalt-chromium alloys with 80:20 and 68:32 cobalt-chromium ratios. Experimental Work Alloy Preparation: A series of cobalt-chromium base alloys containing various amounts of the third element being studied were made for both the 80:20 and the 68:32 cobalt-chromium ratios. Electrolytic chromium, cobalt, and iron, and reagent-grade nickel powder were used as melting stock. Table I contains the chemical analyses of these materials. The charges were melted in alun-dum thimble crucibles which absorbed chromium oxide and effectively deoxidized the melts. These crucibles were supported by close-fitting graphite sleeves so that if they cracked during melting the metal would not be lost. Carbon increases, during

Jan 1, 1951

By Henry A. Wriedt, John Chipman

Equilibrium in the reaction of hydrogen gas with oxygen in liquid nickel, iron, and their alloys has been studied at temperatures of 1500° to 1700°C. The equilibrium con^stant, 0/p, [% O], is greater in nickel then in iron by a factor of 45 at 1594 C. In the alloy steel range, the activity coefficient of oxygen is slightly increased by the presence of nickel. NICKEL is more resistant to oxidation than is iron, in both the solid and the liquid state. The solubility of oxygen,' however, is greater in nickel than in iron. The two metals and their liquid alloys constitute an interesting series of solvents in which the chemical behavior of oxygen can be studied by methods similar to those used for liquid iron.' Experimental Method The furnace assembly, including the tube for preheating the entrant gas, was the same as that described by Gokcen and Chipman. " controlled mixture of water vapor, hydrogen, and argon preheated to approximately the melt temperature impinged upon the surface of the liquid metal. The charge, weighing about 35 g, was held in an alumina crucible at constant temperature in the gas stream for a prolonged period, then quenched in a stream of cold helium, sampled, and analyzed for oxygen by the vacuum fusion method. The temperature of the liquid metal was measured by a Leeds and Northrup optical pyrometer which had been checked against a similar instrument certified by the National Bureau of Standards. The freezing point of electrolytic iron in hydrogen, taken as 153j°C, was used for frequent checks. This point and the emissivity determined by Dastur and Gokcen" established the transmissivity of the optical system. The emissivities of Fe-Ni alloys at 1535" are known from the experiments of Smith and Chipman,h nd it was assumed that the variation with temperature is parallel with that of iron. Recorded temperatures are probably accurate within k5"C. Preparation of Gas Mixtures—Since the ratio H,O:H, had to be much higher for nickel than for iron, it was found convenient to construct two separate systems for gas preparation. In both cases, the ratio of argon to the sum of the other two gases was at least 4, the proportion of hydrogen and water vapor being varied to produce H,O:H, ratios from 0.2 to 70. The primary purpose of the argon was to diminish the errors caused by thermal separation' in the gas phase. In addition, its presence lowered the saturation temperature required for a given H,O:H, ratio and minimized the difficulty of preventing condensation. Both systems were modifications of the one used by Dastur and Chipman.' For H,O:HI ratios greater than 2, welding-grade argon purified by passage over magnesium chips at 620°C was mixed with hydrogen produced in the electrolytic cell shown in Fig. 1. The design was based on a cell used by Bodenstein and Pohl," the important features of which area nickel wire cathode and sodium hydroxide solution as the electrolyte. The rate of hydrogen evolution was controlled by a calibrated ammeter and a rheostat in the circuit, the current efficiency being taken as 100 pct. Precise control of the argon flow rate at about 300 ml per min was achieved by means of a capillary flowmeter having a controlled pressure drop. The molar flow rate was measured volumetrically before each run, and a constant flowmeter setting was maintained thereafter. The A-H, mixture passed through a water saturator of the type previously described," the saturation temperature being maintained automatically with a fluctuation of k0.04"C. The tube between saturator and furnace was heated by a resistance winding. The system was of all Pyrex construction with the exception of the stainless steel tube containing magnesium chips. This was connected with the glass tubing at the upstream end by

Jan 1, 1957

By C. S. Barrett, P. Coheur

AXnealing twins are common in the microstructure of copper that has been rolled and recrystallized. In such samples it follows that a twin relationship should exist between components of the re-crystallization texture,' and several examples of this have been reported. For example, twin relationships have been found in recrystallized electrolytic copper sheet, as indicated in Fig. I, from a paper by Coheur and Lejeune.2 In this pole figure the cube texture (100) [001] is indicated by the hollow squares in the lower half of the figure (the pole figure for 200 reflections) and in the upper, (III), part of the figure. The texture contains, in addition to this orientation, the first-order twins of it, shown in the figure by the filled triangles. This orientation relation has been suggested by others also, under certain annealing conditions,3'4 although pole figures have not been published to confirm it. Some orientations in recrystallized sheets are identical with their twins, because of the symmetry elements of the texture— this is true, for example, with the (113) [ZII] texture so commonly reported for brass—hence it appears impossible in such samples to decide whether the twin relationships result from twinning or merely from the symmetry of the deformation process. The present investigation of a commercial copper strip seems to yield an example in which annealing twins account unambiguously for the principal orientations present. It proves to be a case, also, for which the recrystallization texture cannot be viewed as derived from the deformation texture by a first or second-order twinning mechanism. Materials and Methods The samples investigated were of secondary copper (melted in belgium) to which 0.19 per cent iron had been added to raise the recrystallization temperature. How much the orientation characteristics of this metal can be ascribed to the iron content and how much to other impurities or to melting and pouring practice have not been investigated.* The rolling was done in one direction only, on a mill with rolls of about 20-cm diameter. A strip I. cm wide was reduced from 5 mm thickness to 0.05 mm by several cold passes at commercial speeds. The samples cut from this 99 per cent reduced strip were X-rayed throughout their entire thickness. A pole figure made soon after rolling and annealing was identical, within experimental error, with one that was made when a two-year interval occurred between rolling and annealing. X-ray patterns were made on a camera2 that traversed

Jan 1, 1947

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore- guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. THE following question has been suggested for discussion: [t] "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein.[t] Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line? In some multivein districts the line for any given vein may be approximated by simple interpolation or extrapolation. Where this is possible the bottoms of the lowest ore shoots in the various veins are points on an imaginary, gently rolling surface. The trace of this surface upon the vein is our critical line for that vein. The imaginary surface rolls so gently that it may be projected from two or more known veins to an unexplored vein near by. Here is a criterion for the bottoming of ore that has nothing to do with changes in the appearance of the vein in question; it rests solely on the depth at which the ore bottomed in adjacent veins. The method is not applicable in districts only slightly explored in depth, nor where the lower limit of the ore-bearing horizons

Jan 1, 1939

By C. S. Barrett, P. Coheur

AXnealing twins are common in the microstructure of copper that has been rolled and recrystallized. In such samples it follows that a twin relationship should exist between components of the re-crystallization texture,' and several examples of this have been reported. For example, twin relationships have been found in recrystallized electrolytic copper sheet, as indicated in Fig. I, from a paper by Coheur and Lejeune.2 In this pole figure the cube texture (100) [001] is indicated by the hollow squares in the lower half of the figure (the pole figure for 200 reflections) and in the upper, (III), part of the figure. The texture contains, in addition to this orientation, the first-order twins of it, shown in the figure by the filled triangles. This orientation relation has been suggested by others also, under certain annealing conditions,3'4 although pole figures have not been published to confirm it. Some orientations in recrystallized sheets are identical with their twins, because of the symmetry elements of the texture— this is true, for example, with the (113) [ZII] texture so commonly reported for brass—hence it appears impossible in such samples to decide whether the twin relationships result from twinning or merely from the symmetry of the deformation process. The present investigation of a commercial copper strip seems to yield an example in which annealing twins account unambiguously for the principal orientations present. It proves to be a case, also, for which the recrystallization texture cannot be viewed as derived from the deformation texture by a first or second-order twinning mechanism. Materials and Methods The samples investigated were of secondary copper (melted in belgium) to which 0.19 per cent iron had been added to raise the recrystallization temperature. How much the orientation characteristics of this metal can be ascribed to the iron content and how much to other impurities or to melting and pouring practice have not been investigated.* The rolling was done in one direction only, on a mill with rolls of about 20-cm diameter. A strip I. cm wide was reduced from 5 mm thickness to 0.05 mm by several cold passes at commercial speeds. The samples cut from this 99 per cent reduced strip were X-rayed throughout their entire thickness. A pole figure made soon after rolling and annealing was identical, within experimental error, with one that was made when a two-year interval occurred between rolling and annealing. X-ray patterns were made on a camera2 that traversed

Jan 1, 1947

By N. Jaffee, J. E. Dorn

An activation energy of 27,400 5 1000 cal per mole was obtained for the creep of poly crystaLline aluminum over the temperature range of 273° to 350°K, at strains varying from 0.003 to 0.230. Stresses varied fronz 2250 to 6000 psi, strain rates from 0.1145 x 10-5 to 29.5 x 10~s min.-1. A strain temperature-compensated time correlatzon was oblained indicating that the structure was depedent solely upon the strain at a given stress; X-ray diffraction analyses and tensile tests on precrept specimens verified this. PREVIOUS investigations1 have revealed that the apparent activation energies for creep of high-purity polycrystalline aluminum are insensitive to the applied stress, strain, and strain rate. On the other hand, the apparent activation energy is dependent on the temperature1,2 as shown by the data reproduced in Fig. 1. Each plateau of this curve is associated with a unique rate-controlling dislocation mechanism for thermally activated creep. It is now very well-established that over the high-temperature range, where the activation energy is about 35,500 cal per mole, the creep rate is controlled by the dislocation climb mechanism. 3 Over the intermediate range of temperatures, from about 260° to 370°K, another unique activation energy, namely 28,000 cal per mole, is obtained. Current evidence strongly supports the contention that cross slip is the rate controlling mechanism for creep in this case: 1) Crystal recovery can occur by a number of mechanisms prominent among which are climb and cross slip. Astrom,4 using the Borelius micro-calorimeter, reported rapid crystal recovery of cold-worked polycrystalline A1 at 340° to 370°K giving an activation energy of 28,000 cal per mole and additional recovery at 455° to 478°K giving an activation energy of 3 6,000 cal per mole. Whereas the latter recovery process was clearly associated with the dislocation climb mechanism, the former, 28,000 cal per mole process could have arisen as a result of the cross-slip mechanism. 2) Single crystals of high-purity A1 favorably oriented for octahedral glide exhibit an activation energy for creep of about 3400 cal per mole over the range from 0° to 400°K and that of about 28,O:O cal per mole over the range from 600° to 775°K . Whereas the lower activation energy process is accompanied by the development of sharp slip-band traces, the 28,000 cal per mole process was uniquely characterized by extensive cross slip. 3) Theoretical calculations by Seeger and schoeck6 suggest an apparent activation energy for cross slip in A1 of about 24,000 cal per mole and another theoretical estimate by Friedel 7 gives the observed 28,000 cal per mole as the theoretical activation energy. It is therefore consistent with this evidence to, at least tentatively, ascribe the 28,000 cal per mole creep process in A1 to the operation of cross slip as the rate controlling mechanism. Although creep has been rather well-explored in the dislocation climb range, very little, excepting perhaps the activation energy, is known about creep in the cross slip range. This investigation was undertaken, therefore, to reconfirm the activation energy for creep in polycrystalline A1 in the intermediate temperature range and to study the strain-time relationship for creep at a constant stress in the cross slip region. EXPERIMENTAL PROCEDURE AND TECHNIQUE The three types of high-purity A1 alloy specimens described in Table I were used in this investigation. Specimens were milled from 0.100 in. thick cold-rolled sheets with their tensile axes in the rolling direction following which they were given a recrys-tallization and grain growth heat treatment at temperatures well above those which were subsequently employed in the creep tests.

Jan 1, 1962

By P. S. Rudman

The allotropic volume changes of the ,metallic elements are reviezoed with the conclusion that in general atomic volume is conserved to better than 1 pct in such transformations. A table of the atomic volumes of the metallic elements is given and its use in considering the size factor in alloys is discussed. The importance of the concept of atomic-size factor, due to Hume-Rothery and coworkers,' is firmly established. Most attempts at quantitative formulations of this concept have employed the atomic radius (half some interatomic distance) as the measure of size and innumerable tables of such radii exist. This is probably, however, an unfortunate choice of parameter. Firstly, discussion in terms of interatomic distances requires a knowledge of the crystal structure. While this is known, except for a few cases, for the elemental structures, there are still many undetermined alloy structures. Secondly, except for the simpler structures, face-centered cubic (Al),* body-centered cubic (A2),* and hexagonal-close-packed (A3).* with ideal axial ratio, there is no unique in- teratomic distance, an m y decision must be made as to which distance, or which average of the distances, should be used. However, the most important point is that for metals the dominant bonding parameter can generally be expected to be atomic volume and not interatomic distance. This is perhaps most explicitly stated in the Wigner-Seitz cellular method.' In this approximation, cellular polyhedra of atomic volume v are replaced by spheres of radius Y,: 4/3 ?rs3 = v. That is, there is no reference to the interatomic distances. If atomic volume is in fact the dominant parameter, then in allotropic transformations we might expect to find atomic volume approximately conserved. For example, in the A1 ? A2 transformation we would thus have

Jan 1, 1965