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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 Howard N. Eavenson

WHEN the A.I.M.E. was formed 75 years ago the bituminous coal industry was in its swaddling clothes, although it had been operating for more than a century and coal was being mined in every state now producing it, and its output had long passed that of anthracite. In 18/1, the value of bituminous coal was about seventy per cent of the value of all metals produced and more than one fifth of the value of all products of mines, both metallic and nonmetallic.[1a] While many of the operating mines then shipped by rail, most of the development was along waterways, although the canal era of transportation was nearly at its end. Coal mining is a heavy industry and one of the best measures of its progress is its output throughout the period. Fig. 1 shows this graphically from 1800 to 1945. From 1870 to 1910, the production-which is very nearly the consumption-almost doubled every decade, a most amazing growth. In 1918, in World War I, a peak was reached and a decline began, which ended in 1932. A gradual recovery then started, interrupted in 1938 but culminating in the record output of 1944, when, owing to World War II, a tonnage of 619,576,000 was produced. It is evident that the forces leading to the continuous increase ending in 1918 have spent themselves and that only unusual conditions will require so large a production again. The postwar conditions of World War II will probably

Jan 1, 1947

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

BLAMEY STEVENS, Nogales, Ariz. (written discussion *).-This subject should be approached boldly from the purely physical standpoint. There are usually many known ways of making chemical deposits of any particular mineral and probably many more ways that are still unknown. With-physical-effects; .however, there-are, in-general, only one or two, or possibly three, ways that will pass muster before the physicist, when he realizes the geological conditions to be harmonized with the physical ones. Let us consider the second way that Mr. Taber describes: "It (the mineral matter transported in solution) may enter along a fracture, bedding plane, or similar passage, and, as it is deposited, force the wall rock apart, thus making room, for the growing vein," because it is the one Mr. Taber chooses for the great bulk of metalliferous veins. By "forcing the wall rock apart" Mr. Taber indicates that he means that the process of crystallization or-solidification of the mineral in the vein forces the walls apart. To prove this, he offers a great variety of geological evidence, which, from the physical standpoint, is entirely superficial. From the geological standpoint the evidence is the best to be had, but it is entirely negative and one single grain of really positive evidence will entirely offset it. Suppose it be granted that there is a considerable force of crystallization. It is well known among physicists that, other circumstances being equal, the crystal would rather form where it does not have to exert that pressure; or, to be more exact, where it is not necessary for the crystal to

Jan 12, 1918

By Raymond D. Daniels, Frank E. Rizzo, James D. Gerber

ThIS discussion describes a method for the addition of small amounts of oxygen to columbium (niobium) in an accurate and reproducible manner. The method is based on the complete reduction by columbium of a carefully weighed amount of another metal oxide. The equilibrium Pq associated with Cb-CbO mixtures is extremely low, e.g., 10"25 atm at 100O°C, and the pressures over Cb-0 solutions are even lower. The equilibrium Pq associated with a given metal-metal oxide mixture can be easily obtained, with the aid of a Richardson-Jeffes chart.' Although columbium should effectively reduce almost any metal-metal oxide combination, the proper choice of a metal-metal oxide system is complicated by the low rate of oxygen transport in the gas phase at low oxygen pressures and the difficulty in reducing any columbium suboxide formed during the reduction of the oxygen source material. Thermodynamically, oxide formation on columbium will be avoided so long as the oxygen partial pressure over the columbium is below the equilibrium pressure associated with the mixture Cb-CbO. The logical choice of a source for oxygen would appear to be a mixture of Cb-CbO, since oxide formation would be precluded by nucleation difficulty. But calculations using the kinetic theory of gasses indicate that, for a temperature of 900°C, the reaction would proceed too JAMES D. GERBER, formerly Research Assistant, University of Oklahoma, Norman, Okla., is Research Metallurgist, Air Force Weapons Test Laboratory, Kirtland Air Force Base, N. Mex. FRANK E. RIZZO, Junior Member AIME, formerly Assistant Professor of Metallurgy, University of Oklahoma, is Associate Professor of Metallurgy, University of Texas at El Paso, El Paso, Tex. RAYMOND D. DANIELS, Member AIME, Professor of Metallurgical Engineering, University of Oklahoma, is an NSF Fellow, Institute de MBtallurgie Structurale, Universite de euch:tel, Neuchitel, Switzerland. Manuscript submitted October 28, 1968. IMD

Jan 1, 1970

By Walter Dake

THE mining engineer is being more generally called on to examine and report on properties where the introduction of mechanical loaders is proposed, and as the use of these labor-saving devices presents an entirely different problem from that of hand-loading, an outline of procedure is herewith pre¬sented based on five years of intensive field experience in making such studies. It is impossible to outline an examination which will cover every condition but the most important variables are noted and the re¬port may be amplified or abridged to suit individual mine requirements. There are, of course, exceptional cases in which a single minor variable will determine the final conclusion; the result of mechanical loader application can be, estimated within close limits by considering all variables listed and taking into account the sum of all those found to be applicable to the property under examination. It is necessary that a high degree of accuracy be exercised in the analysis of conditions, and that a relatively narrow margin be figured on all estimates of tonnage outputs and costs. In making an examination for this purpose the data as to company name, business address, name of mine, geographical location, rail or water connections, type of mine (whether shaft, slope, or drift), and the name of seam should, of course, be included, to be followed by the minimum, maximum, and average thickness of seam, a brief description of the charac¬teristics of the coal, the impurities contained, location of regular impurities or partings, together with nota¬tion as to quality, uses, and-markets for the coal. It is also necessary to make cross-sections of the seam so that face preparation may be studied in an effort to eliminate all regularly-occurring impurities at the working place. The possibilities for further cost re¬ductions by the removal and gobbling of partings under¬ground before mechanically ? loading out a face are sufficiently great to warrant careful study and analysis. The classification of the mine from the standpoint of gaseous or non-gaseous operation will determine the general type of electrical equipment needed. A notation regarding the power whether generated at the mine or purchased, together with the amount, voltage, and type of current available is necessary since these matters determine the exact type of elec¬trical equipment to be used. A brief description of the ventilating system, giving type of fan, amount. of air delivered, water gage, and whether force or ex¬haust type, will enable the engineer' to figure venti¬lating requirements per man under mechanical loading practices. The pitch of seam in degrees, the pitch of working faces, and a brief description of rolls or horsebacks should be included, as these affect the efficiency of mechanical loading and, therefore, the economic re¬sults obtainable. -Notations should be made as to the amount of water found in working faces, and whether pumping, sprinkling or rock-dusting methods should be considered. As the character of the floor affects the operation of the machine at the face if a cater¬pillar-tread type, its hardness should be determined, and also whether impurities consisting of floor ma¬terial are likely to be loaded with the coal. The char¬acter of the roof and overlying stratification determine the mining system and width of roof span at work¬ing faces. It therefore directly regulates the amount of tonnage to be loaded by machines without a move from one place to another.

Jan 12, 1927

By W. N. Poundstone, P. C. Thakur

Introduction Horizontal drilling in coal mines is a relatively new technology. The earliest recorded drilling in the United States was done in 1958 at the Humphrey mine of Consolidation Coal Co. for degasification of coal seams. Spindler and Poundstone experimented with vertical and horizontal holes for several years. They concluded in 1960 that horizontal drilling in advance of underground mining appeared to offer the most promising prospect (for degasification) but effective and extensive application would be dependent upon the ability to drill long holes, possibly 300 to 600 m, with reasonably precise directional control and within practical cost limits (Spindler and Poundstone, 1960). Mining Research Division of Conoco Inc., the parent company of Consolidation Coal Co., began a research program in the early 1970s to achieve the above objective. The technology needed to drill nearly 300 m in advance of working faces was developed by 1975 and experiments on advance degasification with such deep holes began in 1976. Preliminary results of this research have already been published (Thakur and Davis, 1977). To date nearly 4.5 km of horizontal holes have been drilled for advance degasification and earlier results were reconfirmed. In summary, these are: • The greatest impact of these boreholes was felt in the face area where methane concentrations were reduced to nearly 0.3% in course of two to three months from original values of nearly 0.95%. • The methane concentration in the section return reduced to 50% of its original value immediately after the boreholes were completed, indicating a capture ratio of 50%. • The total methane emission in the section (rib and face emission plus the borehole production) did not increase but rather gradually declined with time. • Initial production from 300 m deep boreholes in the Pittsburgh seam varied from 3 m3/min to 6 m3/min but then slowly declined as workings advanced inby of the drill site (well head) exposing a larger surface area parallel to the borehole. Encouraged by these results, it was decided to design a horizontal drilling system that would be mobile and compatible with other face equipment. A mobile horizontal drill can be divided into three subsystems: the drill rig, the drill bit guidance system, and borehole surveying instruments. The drill rig provides the thrust and torque necessary to drill 75- to 100-mm diam holes up to 600 m deep and contains the mud circulation and gas cuttings separation systems. The drill bit guidance system guides the bit up, down, left, or right as desired. Borehole surveying instruments measure the pitch, roll, and azimuth of the borehole assembly. Additionally, it also indicates the thickness of coal between the borehole and the roof or floor of the coal seam. Thus, it becomes a powerful tool for locating the presence of faults, clay veins, sand channels, and the thickness of coal seam in advance of mining. In recent years, many other potential uses of horizontal boreholes have come to light, such as in situ gasification, longwall blasting, improved auger mining, and oil and gas production from shallow deposits. The purpose of this paper is to describe the hardware and procedure for drilling deep horizontal holes. The Drilling Rig [Figures 1 and 2] show the two components of the mobile drilling rig: the drill unit and the auxiliary unit. The equipment (except for the chassis) was designed by Conoco Inc. and fabricated by J. H. Fletcher and Co. of Huntington, WV. The drill unit. It is mounted on a four-wheel drive chassis driven by two Staffa hydraulic motors with chains. The tires are 369 X 457 mm in size and provide a ground clearance of 305 mm. The prime mover is a 30-kw explosion-proof electric motor which is used only for tramming. Once the unit is Crammed to the drill site, electric power is disconnected and hydraulic power from the auxiliary unit is turned on. Four floor jacks are used to level the machine and raise the drill head to the desired level. Two 5-t telescopic hydraulic props, one on each side, anchor the drill unit to the roof. The drill unit houses the feed carriage, the drilling console, 300 m of 3-m-long NQ, drill rods, and the electric cable reel for instruments. The feed carriage is mounted more or less centrally, has a feed of 3.3 m, and can swing laterally by ± 17°. It can also sump forward by 1.2 m. The drill head has a "through" chuck such that drill pipes can be fed from the side or back end. General specifications of the feed carriage are: [ ] The auxiliary unit. The chassis for the auxiliary unit is identical to the drill unit but the prime movers are two 30-kW explosion proof electric motors. It is equipped with a methane detector- activated switch so that power will be cut off at a preset methane concentration in the air. No anchoring props are needed for this unit. The auxiliary unit houses the hydraulic power pack, the water (mud) circulating pump, control boxes for electric motors, a trailing cable spool, and a steel tank which serves for water storage and closed-loop separation of drill cuttings and gas.

Jan 1, 1981

By C. A. Stetefeldt

In my paper on "The Consumption of Fuel in the Taylor Gas-Producer Plants at the Aspen and Marsac Mills" (Trans., xxiii., 134), I mentioned that in the plant which I had designed for the Ontario mill, the gas-tubes were to be covered with thin, corrugated sheet-iron, over which a coating of asbestos-magnesia would be spread in order to effect a good insulation and keep the gas as hot as possible. At the Ontario mill, two Stetefeldt furnaces and two revolving driers are fired with gas. One furnace is connected with a Taylor producer of 5 feet diameter, and the other furnace and the two driers are heated by the gas from a Taylor producer of 7 feet diameter. In the latter case the gas-tubes are necessarily somewhat long, and the cleaning of them takes time. In order to prevent overheating of the tubes during that operation, it has been found advantageous not to provide them with an insulating covering. If a tube becomes red-hot at any place by the burning of soot, this is at once observed, and the tube is closed until it cools down. The tubes con-

Jan 1, 1895

By Ulick Evans

I SHOULD like to commence by saying how much I appreciate the honor which the American Institute of Mining and Metallurgical Engineers has done me in inviting me to visit your country, and to deliver this lecture before you. In choosing a subject, and in deciding what to include and what to omit, I have endeavored to discuss as far as possible work carried out recently in Europe with which you may not be unduly familiar. It would be poor return for your hospitality, and a mistaken sort of compliment indeed, if I were to load the lecture with accounts of researches 'carried out in your own country-researches with which you are probably better acquainted than I. Not that I have in any way excluded work done on, this side of the Atlantic from my survey; one would indeed find it difficult to write on this, or on any other branch of science, without mentioning American work. But I have endeavored as far as possible to concentrate on aspects of the case which will, I hope, be comparatively fresh to you, and I feel fairly certain that this will be in accordance with your own wishes. If a strip of iron is heated strongly at one end, the other end remaining cold, there is produced over the heated portion a layer of oxide scale, the thickness of which diminishes steadily with the distance from the hot end. Somewhere in the middle of the strip, the thickness of the oxidized layer will become comparable .to the wave length of light, and over this region the thin films give rise to a series of beautiful interference tints, commonly known as "temper colors." The colors are caused by the fact that two trains of light waves are reflected respectively from the outer and inner surfaces of the oxide film, .and the possibility arises that the "crests" of one series of waves may coincide with the "troughs" of the other, thus diminishing the intensity of the light of some particular wave length. The state of affairs in this part of the strip is shown diagrammatically in Fig. 1, in which the film thickness is enormously exaggerated, of course, in comparison with the length of the strip; the

Jan 1, 1929

By James P. Dr. Kimball

SULPHUR is always present in mineral coal of every variety. In the oxidized state it may exist as sulphuric acid in combination with a base. In the unoxidized state it exists in combination with iron as bisulphide of iron. It is also supposed by some chemists to exist in unknown combinations with the organic elements of the coal. This supposition requires the demonstration as a fact that certain coals yield more sulphur than what may exist in a free state, or what belongs to recognized combinations, not only with the accompanying iron but with other inorganic bases abundantly occurring in coals, but which unfortunately are very rarely estimated. This practically as well as theoretically important question it is at present impossible to decide, simply for want of available thorough ultimate coal analyses including the ash. Such analyses, at the best imperfect, are laborious and intricate, and therefore seldom made, the much simpler proximate analyses, so-called, being resorted to by most chemists for technical purposes, and commonly substituted for more scientific work even in the laboratories of government surveys. And it is unfortunate enough that few ultimate analyses are extended to the composition of the ash, much less to its relation to the original constitution of the coal. Sulphur chiefly occurs in most coals in the form of yellow pyrites (pyrite) and white pyrites (marcasite), both minerals, characterized by differences in crystalline form and in physical properties as well as in color, but having the same chemical composition (FeS2). No coal is entirely free from one or both of these dimorphous forms of bisulphide of iron. It may be disseminated through the mass so as to be invisible, in plates or scales between the laminæ of the coal, or in conspicuous segregations or nodules, sometimes of considerable dimensions. Coals greatly differ as to the proportion of sulphur which they contain. They also differ as to the relative proportion in which its several forms of combination occur. Such qualitative and quantitative disparities are scarcely, if at all, more marked in separate coal seams of a uniform type than in different parts of one and the same coal seam, whether it be considered locally as constituted of several

Jan 1, 1880

By George Holderer

THE relation between man-hours of labor and production may be correlated for any industry, and already it has been widely used in piece-work studies. It is not in general use as yet for recording labor efficiency of an enterprise or an industry. An exception to this is the Cement Institute, which tabulates the man-hours used in each operation and FIG. 1.-LABOR PRODUCTIVITY IN COPPER MINING. thus gets the total man-hours per barrel of cement. The writer knows of one steel company that keeps a complete record of man-hours for every operation from mining the ore to finishing the product. No doubt many others find the information useful, and such a study could be of value to the mineral industries.

Jan 1, 1935

By S. Beatty

RECENT experimental results' on the superconductive properties of vanadium indicate that the magnetic behavior of the metal is greatly affected by internal strains caused by mechanical work, and particularly by oxygen and nitrogen impurities. These result in an increase in the hardness of the metal such that metallurgists' have used hardness as a measure of the impurities. An increase in the impurities should also be reflected in a change of lattice parameter with increasing impurity content. The lattice parameter of vanadium prepared by the thermal decomposition of the iodide has been determined by two workers. Neuburger3 obtained a value of a, =3.0338 ± 0.0003A for the body-centered cubic lattice by means of the powder method. The work of Katelaar is referred to by van Arkel4 in which a value of a0 = 3.025 is given. Four samples were used for this investigation. Sample A, the vanadium of the highest purity in the group, was obtained by means of the thermal decomposition of vanadium diiodide and deposited on a 3 mil diam tungsten filament in the form of crystals. The second sample, labeled B, was obtained by the calcium reduction of the pentaoxide at a sufficiently high temperature to give a melt. A third sample, C, was obtained in the same manner as B but remelted in a pure argon atmosphere. The last sample, D, was prepared by the calcium reduction method and the fine powdered vanadium was then sintered by means of applied heat and pressure. Samples A, B, and C were thus essentially free of mechanical strain in their preparation. Sample D was annealed in a high vacuum at 800°C. The samples were prepared for X-ray diffraction analysis such that all additional strain by cold work or by contamination with oxygen and nitrogen was kept at a minimum. Powder obtained from filings was deemed unsuitable since this would require annealing to get rid of the cold work. A heat treatment up to 1000°C at 10-6 m pressure might still increase the impurity content by means of adsorbed oxygen from residual gas in the vacuum chamber. The most satisfactory samples were prepared for back-reflection film techniques. Samples were cut to size, etched with hydrobromic acid, and mounted in Bakelite. They were then lightly polished on 3-0 paper and lightly etched. Chemical and Hardness Analysis of Samples Spectrographic analyses were made of the four samples and indicated similar metallic impurities for the group. The major metallic impurity in each sample was iron, which was less than 0.01 pct. The sum of the other metallic impurities was approximately 0.1 pct. The carbon content was assumed low by virtue of the methods of sample preparation. The principal impurity difference between the samples was in the oxygen and nitrogen content.

Jan 1, 1953

By T. J. Koppenaal, M. E. Fine

A yield point effect attributed to short-range ordevi?g (SRO) occurs in Cu base Al. At at 296°K varies with heat treatment, decreasing as the annealing ternperature is raised .from 433Oto 598°K. Davies aid Cahn' observed a corresponding decrease in SRO. (523 °K anneal, measured at 77°K) is approximateZy proportional to the variations of A7 with strain rate and testing temperature are also Consistent with the idea that is associated with SRO. A preliminary investigation of the tensile properties of a Cu-Al single crystals showed the presence of a rather strong yield-point effect (drop in flow stress after initial yielding). The object of this research was to investigate its origin and behavior. a Cu-Al alloys are particularly interesting because diffuse X-ray scattering measurements by Davies and Cahn,' Houska and Averbach,' and Borie established the presence of short-range order. The degree of local order may be changed with heat treatment.' cottrel14 suggested that the presence of local order might result in a yield-point effect, and thus the possibility exists here for experimentally ascertaining the importance of short-range order with respect to yield points in these alloys. Since a 12 pct difference exists between the atomic sizes, elastic or Cottrell locking5 must also be considered. Further, Howie and swanne have shown that the stacking fault energy of copper is reduced by aluminum additions. The width of extended dislocations should thereby increase. hus the conditions appear attractive for Suzuki locking.' Finally, the possibility of stress-induced order at dislocations, schoeck locking,' must also be examined, EXPERIMENTAL PROCEDURE Alloys up to 14 at. pct Al were prepared by induction melting high-purity (99.999 pct) Cu and (99.996 pct) Al in a graphite boat under a dynamic vacuum of 5 X 10o mm of Hg. After homogenizing the ingots at 900°C for at least 24 hr under vacuum, they were rolled with intermediate anneals to strips 1.55 mm thick. Single crystals 10 in. long were grown by lowering strips, contained in a split graphite mold sealed in fused quartz at 5 X lo-' mm of Hg, through a single coil induction heater at a constant rate of 1/2 in. per hr. Tensile specimens 1.25 in. long were cut from the single crystal strips and reduced cross sections about 0.7 in. long and 3.0 to 3.5 mm2 in area were introduced by filing and abrading.8 To remove the worked portion about 10 pct of the cross-sectional area was removed by etching. Back-reflection Laue photographs of a filed and etched specimen were taken before and after annealing at 900°c for 24 hr. Small, well defined Laue spots were obtained with no visual difference in the two photographs. Further, specimens with and without the reduced sections began yielding at about the same stress. Hence, for our purposes, filing and abrading did not affect the structure of the specimens. Each single crystal specimen was annealed at 900° c in vacuum for at least 24 hr and furnace cooled; while cooling through the range of 250o to 200°c, the rate was about 55°C per hr. Orientations were determined by the usual back-reflection Laue

Jan 1, 1962

By A. M. Gaudin

Jan 1, 1962

By A. J. Weinig

THE Liberty Bell cyanide precipitate is unique in that it is apt to vary widely in composition in the course of very short, periods of time, and a method of refining and melting that would prove highly satisfactory at one cleanup would yield almost an hopeless "mess" it a second. Table I gives a general conception of the wide range in grade and composition of those raw precipitates. It is evident that no one standard flux could be expected to produce a high-grade bullion with such a widely variable precipitate, and that any method of treatment with acid requires most careful consideration. Refining by Acids Naturally, our first efforts to improve our precipitates were directed along the lines of acid treatment. Table II embodies the results of careful sampling and analysis of one cleanup at the time when wet refining reached its maximum development at this mill. We have now discarded all methods of wet refining, successfully replacing them by amore scientific method of flux calculation described herein, but it is believed that a general description of this wet refining is warranted as it throws some interesting side lights on acid refining in general.

Jan 3, 1916

By William Kent

I DESIRE to place on record in our Transactions a recent innovation in blast-furnace practice, namely, the introduction at the Lucy Furnaces, in Pittsburgh, of four water-tube steam-boilers, of the Babcock and Wilcox pattern, aggregating 832 horse-power, builder's rating, or 9,568 square feet of heating-surface, utilizing the waste gases of the furnaces as fuel. The boilers are set in two batteries, each of 416 horse-power, and each battery occupying a ground-space of 22 feet 7 inches by 20 feet 4 inches. The accompanying dram-

Jan 1, 1885

IT IS impossible to speak in exact terms of the effect that selective flotation has had, is having, and may have on the State of Utah. Its results enter into the economic structure of the state in so many ways and its ramifications are so widespread, that every line of industry is affected. Some effects can be definitely determined; others can be reasonably approximated; but the effect as a whole can not be set out in exact figures. Utah is essentially a mining state; mining is its basic industry and always will be. Agriculture, equally a basic industry, and of course, equally vital, can be practiced on only 6 per cent. of the 85,000 square miles of its area. It follows, therefore, that the economic future of this state depends upon a development of its natural resources. About 6 or 7 years ago, the mining industry in Utah was at a low ebb. This condition was caused partly by postwar conditions and other temporary causes, but prevailed also, which was most important, because the direct-smelting ores of the state were being rapidly exhausted and the cost of treatment of complex ores was almost prohibitive. Furthermore, the wet concentration of low-grade ores was unsatisfactory and did not result in producing a good smelting product. On visualizing this situation, one of the large smelting companies in the valley had the courage, ability and faith to develop and expand the principles involved in selective flotation of complex ores. This example has been followed by other smelting and reduction companies and the result has changed the entire aspect of the mining industry in Utah. The utilization of the zinc in the low-grade, lead-zinc-silver ores was the principal problem to be solved. The average yearly production from the State of Utah for the 10 years beginning 1914 and ending 1923, was something less than 10,000 tons of zinc concentrates. This period includes the world war, when abnormal prices stimulated production. In 1924, selective flotation began to be practiced on a considerable scale, replacing concentration by gravity and bulk flotation which had been used generally until this time. PRODUCTION AND VALUE OF ZINC CONCENTRATES The production of zinc concentrates during 1924 was approximately , 24,000 tons, or twice the average yearly production of the previous 10

Jan 1, 1928

By W. H. Blauvelt

The only way in which the difficult problems of classification of coal for the manufacture of by-product coke can be solved is to analyze them by the use of scientific data. It is very easy to adopt classifications for coal for the manufacture of by-product coke along certain lines; we can easily say that for a certain class of metallurgical operation coke made from bituminous coal must not contain more than so much sulfur or more than so much ash and should yield certain returns in the by-products, tar, ammonia, benzol, gas, etc. Those points we are fairly clear on and I think it is hardly worth while to discuss them because I presume that they are familiar to most of us who have any occasion either to make coke or to use it. But there is a field in the manufacture of coke which we know very little about. For example, we are operating a plant on a certain mixture of coal. Suddenly our blast-furnace man or the user of the coke tells us the coke is not as good as it was before. The coke is analyzed and the coal is analyzed. Everything seems to be about the same as it was— the ash is the same, there is no more sulfur, and so on—but the coke, for the use to which it is put, particularly in the blast furnace, is wrong. What happens? The management decide to try a slightly different coal mixture. They do not necessarily raise the total hydrocarbons, the volatile matter in the mixture, nor change the sulfur or the ash, but they do make a change which improves the value of the coke for metallurgical use. The reason for this difficulty, as I see it, is the " combustibility " of the coke—I hesitate to use the word, but it is the best one I have available. Combustibility of Coke We know now that the combustibility of coke is a very vital point in many metallurgical processes and I think one of the most notable instances of the proof of this is the experience of the Carnegie Steel Co. in the production of coke at its Clairton plant. The history of that

Jan 1, 1930

By M. C. Udy, P. C. Rosenthal

THE use of minute boron additions to steel has been given considerable attention in recent years. Comparisons made between boron-free and boron-containing heats of otherwise identical analysis have indicated, beyond a doubt, the potent effect of boron for increasing hardenability. The actual hardenability increase has been expressed as a multiplying factor, or in terms of the percentage of other alloying elements boron might replace, The present study presents the results of a systematic survey of. the use of boron as an addition to two types of alloyed steels and as a replacement for various percentages of molybdenum in these steels, Both cast and wrought steels of the two basic compositions were prepared. Molybdenum, because of its scarcity at the time the investigation was started, was selected as the element to be replaced by boron. Attention was also given to the effects of boron on other properties of the steels, particularly their notched-bar toughness, to investigate other advantages or limitations of this element as an alloy addition. EXPERIMENTAL WORK Steels Investigated The two basic compositions used in this survey of boron as a replacement for molybdenum are given in Table I. The cast steels were higher than the wrought steels in silicon content to improve the casting quality. [ ] Each of these base steels, both cast and wrought, was made with molybdenum contents of o, 0.10, 0.20, 0.30, or 0.40 per cent, the total comprising 20 steels. In addition, each of these 20 compositions . was prepared with boron additions in amounts of 0.0015, 0.003, and o,006 per cent as ferroboron; and in amounts of 0.002 and 0.005 per cent as two com¬mercial intensifier alloys, designated alloys A and B. The boron-treated steels totaled 100, and the entire series 120, Test Procedure Each steel was melted as an individual heat in a 50-lb., magnesia-lined induction furnace. Ingot iron scrap or mixtures of ingot iron and steel scrap were used for melting stock. Deoxidation was carried out in the furnace with o.10 per cent aluminum. The aluminum addition was

Jan 1, 1946

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1'2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:' Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal'3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.' Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968