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By Dale A. Vaughan, Oliver M. Stewart, Charles M. Schwartz

Solid-solubility limits at 1500°, l000q and 500°C for carbon, nitrogen, and oxygen in high-purity tantalum were determined by X-ray lattice-parameter methods. For carbon, the solubility was found to be 0.17 at. pct at 1500°C, and less than 0.07 at. pct at 1000°C. A nitrogen solubility of 3.70 at. pct at 1500° C decreases linearly with temperature to 2.75 at. pct at 1000°C, and 1.8 at. pct at 500°C. In the case of oxygen, the solubility was found to be 3.65 at. pct at 1500°C, 2.95 at. pct at 1000°C, and 2.5 at. pct at 500°C. The phases Ta2C, the low-temperature modification of Ta205, and Ta,N of unknown composition but which has a superlattice structure based upon the original bcc tantalum lattice have been identified as the initial precipitates in the respective systems. Metallographic methods were employed to verify the X-ray analyses. The etching behavior of Ta is discussed in terms of lattice i?rzperfections and precipitate phases. The excellent fabricability, high melting point, and nuclear properties of tantalum are responsible for interest in this refractory metal. Data on the solid solubility of the interstitial elements (oxygen, nitrogen, and carbon) in tantalum and on the precipitate phases are somewhat limited. The significant contributions are discussed below. Because the purity of electron-beam melted tantalum (only recently available) is considerably higher than that used in previous studies, the present investigation was initiated. Gebhardt et all-3 have investigated the tantalum-oxygen and tantalum-nitrogen systems with particular reference to the changes in physical properties and to the rates of reaction between these gases and the metal. The solubility of oxygen in tantalum was reported2 to be 3.7 at. pet at 1500°, 2.3 at. pet at 100O°C, and 1.4 at. pct at 750°C. Schonberg4 reported that several oxide phases (Ta40, Ta,O, TaO and Ta,05) exist while X-ray studies by Gebhardtl showed only two oxides, Ta,05 and an unidentified phase which was associated with a platelet-type precipitate. La-gergren and Magneli,' however, questioned the existence of compounds other than the two allotropic modifications of Ta,05 for the tantalum-oxygen system. In the case of nitrogen, the solubility was estab- lished by Gebhardt3 to be of the order of 7 at. pct at 1800°c. The solubility was reported to decrease rapidly with temperature, and, although no limits were established, a precipitate phase was observed by Gebhardt except when the high-nitrogen specimens were cooled very rapidly from the reaction temperature of 1800c. He reported the initial precipitate phase to be a tetragonal distortion of the bcc tantalum lattice while Schonberg6 reported the phase lowest in nitrogen Jo be a cubic super-lattice with a cell size of 10.11 A. Two other nitride phases, Ta,N and TaN, were reported; these appear to be isomor-phous with the carbides of tantalum. The tantalum-carbon system was investigated by Ellinger7 and by Lesser and Braurer. Two compounds, Ta,C and TaC, were reported to exist, each with a range of composition. The solubility of carbon in tantalum was found to be practically nil at all temperatures. Thus, of the interstitial elements which are present in small amounts in high-purity tantalum, carbon might be expected to form precipitates. The present investigation was initiated to obtain additional data on the solid-solubility limits of these interstitials at 1500°, 1000°, and 500' with particular emphasis on the distribution and the identification of the precipitate phases. EXPERIMENTAL WORK AND RESULTS In the present investigations of the solid solubility and of the precipitate phases in the systems tantalum-nitrogen, -oxygen, and -carbon, high-purity tantalum was reacted with high-purity gases, homogenized at 1800°c, and annealed at and quenched from 1500°, 1000,

Jan 1, 1962

By F. Keller, A. H. Geisler

ALTHOUGH the subject of precipitation from solid solution appears to be one of the more profitable fields in metallurgy for study with the electron microscope, few comprehensive studies have yet been made. Occasionally electron micrographs have been published that illustrated alleged precipitation in various alloys, but frequently the apparent size, shape and distribution of the particles do not fully agree with those expected from theory or from observations of the precipitate when the particles have grown to a size resolvable with the light microscope. The presence of a Widmanstätten pattern for submicroscopic precipitate particles has been demonstrated for only a few aged alloys.1 The initial problem has been the development of suitable techniques for applying the transmission-type instrument to a field that has been inherently associated with reflection-type microscopes. The various techniques have been the subjects of numerous publications, and instead of describing them individually here it will suffice to say that the oxide film method has proved to be the most satisfactory method yet found for studying the microstructure of aluminum alloys with the electron microscope. This method has the definite characteristic advantage that the actual surface layer of the specimen is examined and not a plastic or silica replica. Doubtless suitable methods for forming and removing the oxide film could be developed for alloys of other metals. The purpose of this report is to point out the characteristics of the oxide film method that have been observed during the studies of numerous aged aluminum alloys and to present the results of these studies. PREPARATION OF SPECIMENS The oxide film method for preparing specimens of aluminum alloys for examination in the electron microscope has been described in detail previously.1,2 Briefly, the procedure consists of preparing the metallographic specimen, forming the film by anodic oxidation and removing the film from the prepared surface of the oxidized specimen. The specimen is polished according to the usual procedure for microscopic examination.3 The specimen may then be etched to remove flowed metal but etching to attack the alloy constituents or to leave them in relief as in the replica processes is not necessary. Electrolytic polishing is not generally recommended. Deep-etched specimens are used frequently, however, since they provide information that is not revealed by polished specimens and frequently present the same information more clearly than do the polished specimens. The surface preparation of specimens to be deep-etched is not important, since specimens that have been subjected to the first wet polishing operation are generally used, but frequently the as-rolled surface is suitable. These specimens are then etched using a suitable macroetching reagent.

Jan 1, 1946

By W. N. Lacey, B. H. Sage

THE results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of gravel screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. INTRODUCTION Gravel screens have been placed in water and oil wells for a number of years1,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. INFLUENCE OF GRAVEL SCREENS UPON PRODUCTIVITY The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the. average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized- spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1941

The elite group of companies below represent the mining sector of Fortune magazine's June Directory listing the 500 U.S. industries that chalked up the largest dollar sales volume in 1966. The companies are listed according to their 1966 sales rank, which is given along with their 1965 rank for comparative purposes. All of the firms except two-Freeport Sulphur and Texas Gulf Sulphur-were in the Fortune Directory last year, and both these exceptions have been counted among the top 500 in former years. The one mining name that is missing from last year's list-Consolidation Coal-has actually jumped from number 217 to 4 by virtue of its merger with Continental Oil. As can be seen from the Industry Medians, the mining industry as a whole boosted its sales 17.8%, in 1966, making it the seventh largest gainer among the 22 industrial classifications covered in the Directory. By comparison, 1965 mining sales increased 10.2%, a gain which was surpassed by 13 other industries. In two other comparative tables, mining leads the field, topping the entire list in return on sales and in assets per employee.

Jan 8, 1967

By F. M. Lewis, J. F. Meyers

This second progress report of grinding presents comments regarding ball consumption and data pertaining to the hydroscillator, which is closed circuited with the tricone mill. A study and postulate of how balls function is presented. The paper summarizes cost reduction obtained by the method of "grinding for the tail race" rather than for "mesh tons." AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of —200-mesh produced a very creditable figure. Hydroscillator Operation The machine as now developed has proved dependable and easy to operate. It starts easily under full load and responds quickly to operating adjustments. The hydraulic holes in the oscillating plate do not plug when shut down under full load. Absolutely clean hydraulic water is essential. An Elliott water screen or similar device should be an essential part of the machine to keep all scale and trash of all kinds from the hydraulic compartment. The shift operators have expressed approval of the machine. In table I we show a typical screen analysis of the hydroscillator rake sand as compared to conventional classifier rake sand on our ore. We have previously reported that of the 28.7 pct reduction in power, the hydroscillator contributed 6 pct, on a —200-mesh basis. This is a conservative figure. Some of our test runs indicated that the saving was as high as 10 pct. Laboratory studies by the Dorr Co. engineers indicate that still greater efficiency is possible. Nevertheless, the 10-ft plate is overflowing 2100 tons per day at 3 to 4 pct + 65-mesh, which is a very creditable performance by

Jan 1, 1951

By F. M. Lewis, J. F. Meyers

This second progress report of grinding presents comments regarding ball consumption and data pertaining to the hydroscillator, which is closed circuited with the tricone mill. A study and postulate of how balls function is presented. The paper summarizes cost reduction obtained by the method of "grinding for the tail race" rather than for "mesh tons." AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of —200-mesh produced a very creditable figure. Hydroscillator Operation The machine as now developed has proved dependable and easy to operate. It starts easily under full load and responds quickly to operating adjustments. The hydraulic holes in the oscillating plate do not plug when shut down under full load. Absolutely clean hydraulic water is essential. An Elliott water screen or similar device should be an essential part of the machine to keep all scale and trash of all kinds from the hydraulic compartment. The shift operators have expressed approval of the machine. In table I we show a typical screen analysis of the hydroscillator rake sand as compared to conventional classifier rake sand on our ore. We have previously reported that of the 28.7 pct reduction in power, the hydroscillator contributed 6 pct, on a —200-mesh basis. This is a conservative figure. Some of our test runs indicated that the saving was as high as 10 pct. Laboratory studies by the Dorr Co. engineers indicate that still greater efficiency is possible. Nevertheless, the 10-ft plate is overflowing 2100 tons per day at 3 to 4 pct + 65-mesh, which is a very creditable performance by

Jan 1, 1951

By R. E. Lindstrom, D. G. Peterson, H. J. Heinen

Alkaline alcohol solutions were investigated by the Federal Bureau of Mines for improving the desorption rate of gold and silver from metal-laden activated carbon generated in gold processing circuits. Factors affecting the desorption, such as temperature, alcohol content, type of alcohol, and alkalinity, were studied. Nearly complete metal desorption was obtained in 5 to 6 hr at 80º C using a solution containing about 20 vol-pct alcohol and 1 pct sodium hydroxide. Sodium sulfide was shown to be effective for selectively precipitating silver from the carbon strip solutions, thereby providing a means for producing high- purity gold by subsequent electrolysis.

Jan 1, 1976

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By Joseph Hays

MORE years ago than I care to admit I conferred the title of "combustion engineer? upon my-self since nobody else would confer it. I thought at the time, and for some, years thereafter, that my field was limited to the precincts where the fuel was being burned, but I found that I could stand in the door of the furnace room and hear distressed heat units calling for help all over the plant. Some of them were over-worked, others were compelled to do useless work, and still others, anxious to render a proper account of themselves, were not permitted to do any sort of work at all and were utterly wasted. The combustion engineer has something to do at that interesting occasion when the heat unit is being born in the furnace, but his responsibility does not end there. He must follow the little fellow throughout the entire period of its hectic existence in the plant and see that it gets a fair chance and a square deal everywhere. I fear that the general impression of the combustion engineer's duties is much as mine was in the beginning; that his job is limited to the implements and processes incident to the specific operation of converting fuel into active, heat energy and of applying it to the boiler, the still, or what-not, with the least possible waste. But is it not true that a heat unit saved in a remote corner of the plant means just as much to the fuel account as another saved at the furnace? And if nobody else is looking after the heat units out on the range why should the combustion engineer spend all of his time hanging around the corral? If combustion engineer is not a broad enough title to cover the man in charge of a general heat unit rescue campaign call him any-thing else you please. The job is all that counts. The name means nothing. A skunk by any other name would smell as bad. The greatest field I have ever found for general "heat rescue" work is the oil refinery. In refining we first put heat into the oil and then take it away from the vapor. The greatest heat losses occur during the cooling operation, but there are losses, many of them preventable, either wholly or partly, at every step of the several processes in oil refining.

Jan 3, 1928

Correlation between Metallography and Mechanical Testing By H F MOORE (Henry Marion Howe Memorial Lecture Trans, vol 120 11,000 words ) The lack of effective correlation between metallography and mechanical testing from the days of Reaumur to the present is noted, and two general problems of such cor¬relation are stated (1) the correlation of qualitative test results with quantitative, and (2) the correlation of average results with maximum or minimum results Some correlation has been achieved, notably in the field of heat-treatment and in the study of elastic strength of metals Correlation is in the process of being developed in several other fields, including the quantitative study of the effect of grain size of metal on mechanical properties, of grain size and type of crystalline structure on the sensitivity of metals to weakening at holes, notches and other "stress raisers," and in the study of the starting phases of spreading, "fatigue" cracks Correlation of mechanical test results and metallographic study is needed in the study of such problems as the various theories of failure of metals, the meaning of and tests for service ductility of metals, and the relative damaging effect of defects inherent in metals, such as minute cracks and segregation, as compared with the damaging effect of "imposed" stress raisers, such as screw threads, sharp shoulders, etc The neces¬sity for more correlation of metallography and mechanical testing during student days is emphasized, and also the need of a better understanding on the part of engi¬neers of the significance and limitations of metallographic apparatus and results and of X-ray diffraction This should be matched by a better understanding on the part of metallurgists of the significance and limitations of mechanical tests of metals, of testing machines and strain-measuring apparatus

Jan 1, 1937

By S. Kobayashi, A. E. Armenákas, C. Mylonas

Earlier work1-4 has shown that commercial mild steels under static loading at the lowest natural operating temperatures fracture in a brittle manner only when damaged by a suitable history of straining. Notched and then compressed plates have fractured in subsequent tension at loads as low as 10 pct of the limit load and precompressed smooth bars at a subsequent extensional strain as low as 0.01. The comparison of the average net fracture stress with the flow limit stress was shown to be an excellent criterion of brittle or ductile behavior of mild steel structures when only loads and general stress levels are known. The present investigation shows that the deformation at fracture is a far more sensitive measure of brittleness than the fracture stress. Both criteria, deformation and stress, are used to determine the amount of uniform precompression of two mild steels, ABS-B and Project E-steel, resulting in brittle fracture under the strong constraint of a subsequently machined severe circumferential groove. The fracture stress equaled or exceeded the theoretical flow limit Ól = 2.680., ('based on the elevated yield stress at each prestrain) up to prestrains of about 0.20 and then fell off to about 1 at prestrains of 0.60. Yet a prestrain of only 0.05 reduced the elongation at the shoulders by a factor of about 4. The total plastic elongation of a region surrounding a sharp notch in prestrained steel deternines whether or not fracture will be initiated in large structures, hence is a direct and realistic measure of the remaining ductility and provides an excellent test of the material's resistance to embrittlement. ALMOST all engineering structures of mild steel which failed in service in a so-called "brittle" manner exhibited appreciable local plastic deformation (more than 1 pct) and a mixture of "cleavage" and "shear" fracture surfaces. Furthermore, the peak local stress in an advancing crack is always high. Such simple criteria as pure cleavage, absence of plasticity, or fracture stress, so useful in other fields, are insufficient to characterize brittleness in engineering structures at ordnary temperatures. The "brittle)' behavior of engineering structures is caused by the limited ductility at cracks or notch regions, as shown by recent work at Brown University summarized and extended in Refs. 1 to 4. It was also shown that the local ductility of mild steel may be catastrophically reduced by a suitable strain and temperature history similar to those which may occur in real structures. Localized yielding begins at the notch roots at low loads but is contained by surrounding elastic regions. The plastic strains are hence small. They increase slowly with the load up to the flow limit or limit load for an ideally plastic material. Unrestricted plastic flow then occurs. At such strains the real material locally st rain-hardens and fractures. With work-hardening materials no flow limit exists, and the transition from low to high plastic strains is gradual but increases more rapidly at loads close to the flow limit of an equivalent perfectly plastic material. When the available ductility is sufficient for reaching the limit load, the behavior is normal or "ductile". With insufficient ductility, fracture will occur at a low load and will be defined as "brittle". Accordingly the sufficiency or not of the ductility at a notch is reflected in the magnitude of the fracture load or average net stress as compared with the limit load or flow limit. The application of this criterion gave surprising results. Service failures under semistatic loading occurred mostly below the limit load, hence were "brittle". On the contrary all static tests with undamaged commercial mild steels reached the limit load in spite of the deepest notches and temperatures below Charpy impact transition (say about -30°F or higher). Notched bars showed no brittleness even under fully dynamic axial loading up to 1.5 x107 psi per sec at -23°F and about 2.5 x l06 psi per sec at -ll0°F, but broke in a brittle manner at -200°F and l03 psi per sec.' To propagate a fracture at low load, experimenters had to trigger it by superimposing a strong dynamic impact at a notch cooled by liquid nitrogen as in the Robertson5 or Esso tests.' Once started the cracks would run through warmer regions of smaller stress. Obviously the ductility of the apparently undamaged commercial steels was "sufficient" in the laboratory tests but not in the service fracture, where it must have been reduced by some embrittling procedure of fabrication or service. These conclusions were confirmed by the achievement of low static stress (brittle) fracture initiation in unwelded steel after a local reduction of ductility by simple prestraining. Symmetrically notched plates of undamaged mild steel cooled below the Charpy V-notch transition range were tested in central static tension: Undamaged plates withstood loads of limit intensity, but when subjected to prior in-plane com-pressive prestraining perpendicular to the notch axis and to accelerated aging, the plates fractured completely or partially at very low static loads, as low as one-tenth of the flow limit.2-4 However, damage could not be easily related to the strongly variable prestrain around a sharp notch. To obtain easier strain measurements, it was decided to use axially precom-pressed bars and bent bars. Final testing was done by

Jan 1, 1970

By C. B. Manula, H. Gezik

In planning modem-day mining operations, management needs to pass from the area of subjective decision-making to an area of objective decision-makirlg. Planning procedures currently being practiced by many mine managers depend primarily on common sense and trial-and-error methods which oftentimes never reach optimum solutions. For this reason, an attempt is made to provide an understanding of linear programming to solve production planning problems. More specifically, a linear programming model is proposed to solve the production scheduling problem as it was found to exist in the crushed stone industry. Optimal production scheduling is of prime concern here, since the industry has to cope with seasonal demands for its products. The solution, as determined through the application of the model, provides management not only with an optimal production schedule but also with the following information regarding the improvement of existing facilities: (I) the location of bottlenecks which limit production and profit; (2) the directions in which the company i fixed equipment should be expanded or modified; and (3) the evaluation of unused resources. Future trends in stone production will quite likely parallel those in the construction industry. Continued record expenditures for structures such as dams, highways, and buildings are the reasons for this accelerated growth. Production forecasts for the next decade are predicted to be around one billion tons with an approximate 7% annual increase. The problem of increasing production from 570 million tons in 1966 to 1 billion tons by 1976 offers no small challenge. This situation is further compounded by other problems and economic factors. Population expansion, government regulation, labor agreement, and changes in technology wd cause managers and operators to be confronted by many more complexities than characterize present-day operations. Some of these. problems and economic factors are: (1) In some metropolitan and other urban areas, easily accessible sources of stone are almost depleted. Transportation costs will be a prime concern of the industry. (2) Population growth has forced residential expansion to a point where many quarry operators must conform to urban and suburban regulations. (3) Government regulation in regard to air and water pollution, noise, and reclamation as well as zoning developments necessitate that crushed stone producers keep abreast of changing conditions and requirements. (4) The crushed stone industry operates under pressure of a highly competitive situation. Every company's objective is to retain a favorable marketing position by exercising great attention to production and marketing costs. This is rather difficult, since the crushed stone industry is one segment of modern mining which has to cope with a seasonal demand for its products. Among the problems posed here, the one of exercising great attention to production and marketing costs is of current interest to management. Under seasonal demand conditions, this problem creates further difficulties for managers who need to plan and forecast. STATEMENT OF THE PROBLEM Various methods of Operations Research have been developed to handle a problem whose genesis is explained above. It is very seldom, however, that these quantitative means are used in practice by the mining industry. This paper describes the use of Operations Research methods to solve a production planning problem when demand is seasonal. The seasonal production planning problem is an important one because of the substantial costs associated with changing production, employment, and inventory levels to adjust to seasonal sales patterns. Most companies try to operate within reasonable levels of employment changes and hold inventories within storage capacities. In general, little or no attempts were made to develop minimum cosl schedules or to provide objective means to compare various production policies. When demand varies within a fixed time period, 11:-oduction requirements may be met by following one

Jan 1, 1970

By Nelson P. Hulst

To those who have had the happy privilege of friendship with George W. Goetz, the announcement of his death has brought great sadness. He was born in Milwaukee, Wisconsin, February 17, 1855, and died January 15, 1897. In his boyhood days, when I first came to know him, his frank, trustful manner; his eyes brimming with truthfulness; his eagerness, never obtrusive, to gain knowledge from all whom he met; and his equal readiness to give without ostentation of his store, constituted a personality which at once commanded confidence and won friendship. I am told that as a scholar of five years he was conspicuous for brightness, a show-pupil, who was called on to recite when visitors were present at school. Yet this in no way spoiled him. His modesty was too strong a trait in his character to be overcome by any attention which might, be expected to arouse vanity. In his simple-heartedness he was pleased then, as he always was in his maturer years, to give of his knowledge for the gratification of his listeners, with never a thought of himself. So strong was this characteristic that in a brief autobiography, in the form of a letter to his wife and children, found among his papers, he excuses himself to them for recounting what he had accomplished in his life-work. As a preface to this autobiography (which, it seems, was prepared on the eve of a sudden journey to California, taken February, 1895, for his health) he says: " I am writing this rather hastily, and I

Jan 1, 1898

By J. W. Cuthbertson, R. A. Cresswell

THE constitution of Cu-rich alloys with 1.5 to 13.5 pct Sn and 0.25 to 3.0 pct Be and the precipitation-hardening characteristics of alloys with 1.5 to 13.5 pct Sn and 0.25 to 1.0 pct Be have been examined. The hardness and tensile strength of the alloys examined increase markedly after solution treatment at 700°C followed by heat treatment at temperatures between 200" and 450°C. By a combination of cold work and heat treatment, hardness values similar to those exhibited by commercial Be-Cu alloys containing 2.25 pct Be can be obtained with ternary alloys containing 9 pct Sn and 0.75 pct Be and containing 10 pct Sn and 0.5 pct Be. Marked hardening effects occur with alloys containing even less beryllium. By heat treatment alone, a hardness value of 310 diamond pyramid hardness can be obtained from an alloy containing 10 pct Sn and 0.75 pct Be. Preliminary tensile tests have shown that an ultimate tensile strength of 110,000 psi with an elongation of 23 pct is obtainable by precipitation hardening an alloy with 8 pct Sn and 0.75 pct Be. The precipitation-hardening process has been followed microscopically for certain alloys and the inference is that, while the initial hardening effect is probably explained by the precipitation of the ß phase of the Cu-Be system, further hardening, proceeding at a much slower rate, also occurs, apparently as a result of precipitation of phases of the Cu-Sn system, particularly precipitation of the 6 phase at temperatures below 350". The presence of the e phase of the Cu-Sn system in certain alloys at temperatures below 350°C has been confirmed. Tin-bronzes are widely used in engineering applications where a combination of high strength and good resistance to corrosion is wanted. The maximum strength is induced in these alloys by cold working, and it would be an advantage for many purposes if high strength could be achieved alternatively by an age-hardening process. While Cu-Sn alloys have a good fatigue resistance they can be surpassed in this respect by Cu-Be, but the use of the latter alloy is limited by its high cost. If, by adding beryllium to tin-bronze, the properties of the respective binary alloys could to some extent be combined, a most attractive alloy should result. As pointed out by Raynor,¹ beryllium is on the borderline of the zone of favorable size factors for copper, and the solid solubility of beryllium in copper is consequently much more restricted than if the size factor were strongly favorable. The size factor is sufficiently favorable, however, to permit an increase in solid solubility with rise in temperature, and there is thus a composition range in which CU- Be alloys are susceptible to hardening by precipitation heat treatment. Although the a phase of the Cu-Sn system is similarly susceptible to precipitation treatment, the time necessary to establish equilibrium in commercial alloys of this type is usually so great that age hardening becomes impracticable. The addition of beryllium to Cu-Sn alloys would appear to offer a means of conferring on the latter useful age-hardening properties. Masing and Dahl² and others have, in fact, shown that the addition of beryllium to Cu-Sn a solid solutions renders these alloys susceptible to precipitation hardening and after such hardening confers on them an encouraging improvement in physical properties. If this improvement could be achieved by the addition of substantially smaller amounts of beryllium than are customarily found in binary Cu-Be alloys, the ternary alloys should possess economic advantages which might make them more attractive than the binary alloy for some applications. Binary Systems Copper-Tin: The constitution of these alloys is now reasonably well known and is summarized in the equilibrium diagram published by Raynor.³ The following observations, due to Raynor,¹ on the structure of those phases of the Cu-Sn system that are likely to be found in the ternary alloy system will facilitate the subsequent discussion on the examination of that system. The ß phase is an electron compound at the electron-atom ratio 3:2 and has a body-centered cubic crystal structure. This phase is stable only down to 586°C, at which temperature it decomposes eutectoidally into the a and y phases. The y phase has a structure that is also based on the cubic system. This phase is stable down to 520°C, at which temperature it decomposes eutectoidally into the a and d phases. The d phase is an electron compound (Cu³¹Sn8) which has a crystal structure analogous to that of 7 brass. This phase is stable from 590" to 350°C; on prolonged annealing at the latter temperature it breaks down into a mixture of the a and E phases. The e phase is an electron compound (Cu³Sn) having the electron-atom ratio 7:4. Its structure may be regarded as a superlattice based on the close-packed hexagonal system. This phase is stable from 676°C to room temperature. The primary solid solubility of tin in copper increases to a maximum of 15.8 pct as the temperature falls from that of the peritectic reaction to 586°C. The solid solubility remains constant from 586" to 520°C. At lower temperatures the solubility decreases progressively. Below 350°C the fall in solubility is pronounced and is associated with the precipitation of the e phase. This precipitation is very sluggish and does not normally occur under service conditions. Copper-Beryllium: The Cu-Be system has been investigated by Borchers' and others. Raynor5 summarized the present state of information on it.

Jan 1, 1952

By ALEXANDER L Hay, Alexander L.

THE Sydney coal field, the largest and most valuable in Nova Scotia, is on the northeastern coast of the Island of Cape Breton, extending from Mira Bay on the south to Cape Dauphin on the north, a distance of 30 miles, and has a general dip northeast under the sea. The field embraces the mining villages of Morien, Birch- grove and Reserve and the towns of Dominion, Glace Bay, Waterford and Sydney Mines. The city of Sydney is about midway between the northern and southern extremities of the field and on the western fringe of the productive coal measures. Sydney harbor crosses the coal field, cutting off direct rail connection between Sydney Mines and the greater part of the field to the southeast.

Jan 1, 1928

By S. G. Cupschalk, F. A. Dahlman, J. J. Wert

Studies have been undertaken to determine the indicidual effects of particle size, degree of long-range ovder, antiphase domain size, and root mean square stran on the microhardness and yield strength of ordered alloys. Dnta have been analyzed for Cu3Pt initzally ordered to a value of 0.82 and after deformations of 1 and 6 pct. It was observed that deformation fleatly reduced the degree of long-range order. Furtherrnore, wztkin this range of relatively small deforntntlons, the average particle size changed very little while the antiphase domain size was greatly reduced. Smultaneosly, the mcrohardness changed by a factor of two durzng the deforrtation process. PREVIOUS studies have reported some of the effects of cold work on the broadening of X-ray diffraction peaks. These investigations were performed on powder and wire samples representing both ordered and disordered states; i.e., the specimens were initially studied in a severly cold-worked condition. By comparing the difference in line shape between the annealed and cold-worked peaks, fundamental information was obtained concerning particle size, strain distribution in different crystallographic directions, degree of long-range order, and change in antiphase domain size. Considerable theoretical work has been done concerning the analysis of diffraction data obtained from cold-worked metals. Stokes' expressed the change in diffraction profiles in terms of Fourier coefficients. Much of the work in this area has been summarized by warren2 in an extensive review article concerning the analysis of plastic deformation by X-ray diffraction. Cohen and Bever3 applied these techniques in studying the effects of cold work on alloy systems exhibiting long-range order. They utilized the Fourier coefficients of fundamental peaks in conjunction with those of the superlattice peaks to determine the change in antiphase domain size. Little work of this nature has been reported for ordered systems that have undergone small degrees of plastic deformation. The purpose of this investiga-tion was to determine the effects of small deformations in such a material with respect to particle size, strain distribution in various crystallographic directions, antiphase domain size, degree of long-range order, and hardness. EXPERIMENTAL PROCEDURE CusPt was used for the initial investigation since the order-disorder transformation takes place with- out a change in crystal structure. The transformation is readily detectable via X-ray diffraction techniques due to the large difference in the scattering factors of copper and platinum. Additionally, the alloy is relatively low melting (approximately 1300°C) and is easily deformable in both the ordered and disordered states. 1) Specimen Preparation and Cold Working. A 100-g, 12-in. diam., cylindrical specimen of Cu3Pt was prepared by melting and casting 99.99 pct pure Cu and Pt i.n vacuo. Prior to any mechanical working, the material was homogenized in a vacuum for 60 hr at 100O0C, and surface defects were removed by machining to a depth of approximately 116 of an in. The material was then cold-rolled, with an intermediate anneal, into a strip approximately 12 in. wide by 14 in. thick. Straightening and flattening removed another 0.025 in. from the thickness. After a recrystallization treatment at 750°C for 30 min, the specimen was slow-cooled from 55OoC, at the rate of 6°C per hr, down to 150°C to induce superlattice formation. This treatment yielded an ASTM grain size of 7 and a degree of long-range order equal to 0.83 0.06. After obtaining X-ray and Knoop hardness data, the sample was cold-rolled approximately 0.75 pct in one pass through a hand-operated jewelers' mill. X-ray and hardness data were again obtained and the specimen was reduced an additional 5.41 pct in a single pass through the mill. 2) X-Ray Measurements. The specimen was examined in the ordered condition and after the two degrees of cold working previously mentioned using a General Electric XRD-5 unit equipped with a spectrometer and scintillation counter. Using Mo-Ka radiation with a zirconium filter, six orders of the 100 reflection were obtained. It was anticipated that point counting would be necessary for an accurate determination of the low-intensity peaks and tails: however, it was demonstrated that, by using a scanning speed of 0.2 deg per min and the appropriate time constant, the recorded data were sufficiently accurate. Thus, for ease of experimental procedure, all peaks were recorded on chart paper. Specimen position in the holder was considered to be insignificant after making a series of measurements of the same peak area in different positions with respect to the beam. Since peak overlapping did occur at high values of 20, it was necessary to separate the peaks graphically prior to analyzing the data in order to minimize this source of error. The peak tails were also carefully drawn to obtain the best possible data. Fourier coefficients of the line profiles were calculated on an IBM 7072 computer, and graphical meth-ods2j3 were employed in analyzing the results. For this type of calculation, in which the line profile is represented by intensities taken at set intervals, the intervals selected must be sufficiently small to give an accurate representation of the line profile. It was decided that for 20 = 0.02 deg the line profiles were

Jan 1, 1967

By Oliver Bradley

THE utilization of casing-head gas in the manufacture of casing-head gasoline by both the absorption and the compression method is a most important factor in the conservation of our natural resources.. Any industry connected with the oil business, in general, possesses particular attraction for a large number of people not conversant with its basic principles, for the reason that the large fortunes made in the production and utilization of petroleum and its products have been given undue prominence. The general impression of the public that enormous profits are to be realized in the casing-head gas industry with minimum expenditures of both capital and effort has, in a large measure, accounted for the phenomenal expansion of the industry in recent years and, likewise, has resulted in many mistakes and loss of investment funds. It is true that many installations have been very profitable, but such instances are always the result of careful planning, experienced judgment and conservative estimates. The inception and subsequent activity in the manufacture of casing-head gasoline, enabling the business to assume an important position in the petroleum industry, are of, comparatively recent origin, as its greatest growth, particularly in Oklahoma, occurred during the years 1917 and 1918. Much information must yet be secured and systematized concerning the methods of manufacture of gascline from high-yield casing-head gas, and a large field is still open for the application of accumulated experience and good engineering practice in devising better methods of extracting gasoline from casing-head gas of the poorer grades. The absorption process is coming into general use as a most efficient system of treating casing-head gas, and even so-called dry gas. In fact, there is a decided tendency toward the universal adoption of the absorption process as against compression methods. However, a general discussion of the relative merits of these two systems is not within the scope of this article.

Jan 9, 1920

By M. A. El-Aouar

Drilling muds are complex colloidal systems. In an effort to analyze the physical properties that affect their performance at high temperature, an investigation was made of the hydrothermal stability of the monoionic hydrogen, calcium and magnesium forms of montmorillonite and attapulgite. Samples were heated to 400°1F in a simple autoclave and analyzed for cation exchange capacity, c-axis X-ray diffraction spacing and pH factor us sodium hydroxide titration dependence. Out of the six monoionic clay minerals tested, calcium montmorillonite and magnesium attapulgite showed the least base exchange capacities and were relatively unaffected to heat. It is concluded that, of the six clays studied, these two clays were the most suitable forms for use in drilling fluids. INTRODUCTION The drilling of deep wells is dependent upon the drilling mud, and problems frequently arise concerning the effect of mud temperature and prolonged heating. Drilling muds are complex colloidal systems. In an effort to analyze their behavior in deep, hot boreholes, it was thought desirable in this investigation to study suspension of pure, monoionic montmorillonite and attapulgite clays before and after hydrothermal heating. Chemically, clays are hydrated aluminum silicates, such as montmorillonites and attapulgites. The structure of montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. Attapulgite consists of double silica chains running parallel to the c-axis with the chains linked together at their longitudinal edges. The apexes of the tetrahedrons in successive chains point in opposite direc-tions.4,7,10 One of the most important characteristics of clay minerals is their property of sorbing certain anions and cations and retaining them in exchangeable state. The property of exchange capacity is measured in terms of milliequivalents (meq) per 100 gm of clay. The cation-exchange capacities are taken at pH 7 from titration curves which show the relation between pH and milliequivalents of added NaoH.9,11 The following are causes of cation exchange: (1) broken bonds around the edges of the silica alumina units would give rise to unsatisfied charges, which would be balanced by adsorbed cations; (2) substitution within the lattice structure of trivalent aluminum for quadrivalent silicon in the tetrahedral sheet and of ions of lower valence; and (3) the hydrogen of exposed hydroxyls may be replaced by a cation which would be exchangeable. The primary techniques employed to study the effects of hydrothermal treatment were titration curves and X-ray diffraction analyses. Titration curves were useful in characterizing the nature of the clay mineral surface and the stability of the various samples to attack by acid or alkali before and after hydrothermal treatment. X-ray diffraction analyses were used to determine changes in the nature and crystal structure of the minerals present and to determine the cations in exchange positions on the montmorillonite samples. EXPERMENTAL PROCEDURE PREPARATION OF SAMPLES Selected samples of Wyoming bentonite and attapulgite clay from mines along the Georgia and Florida border were purified by centrifugation to remove all particles larger than 2 microns. In preparing magnesium attapulgite, first a 1.00-normal solution of magnesium acetate was prepared. The pH of the solution was adjusted to 7.0 by adding magnesium oxide. One hundred grams of attapulgite clay were mixed in a blender for 30 minutes with the magnesium acetate solution. The attapulgite solution was left overnight, and then filtered in a Buchner funnel. The suspension was leached with further quantity of magnesium acetate solution and then washed with distilled water for 20 days, after which the filtrate was free from magnesium ions. The concentration of magnesium attapulgite in the clay slurry was adjusted and determined quantita-

By AIME

D R. GILLSON, who was born in Evanston, Ill., in 1895, is another one of those geologists who received his early inspiration and foundation in his science from that great teacher at Northwestern University, the late Professor U. S. Grant, and then went on to give his time and interest to Institute affairs-like those other Northwestern men, Arthur Blair, Gilbert Cady, Charlie Behre, Evan Just, Ian Campbell, Clayton Ball, and many others. After serving in the Navy in the first World War as, of all things for a geologist, a commissary officer on a transport, he went on to MIT and took his doctor's degree under Waldemar Lindgren in 1923. He even assisted in mineralogy at Harvard and thus had training under another great teacher, Charles Palache. He taught mineralogy and petrography at MIT from 1923 to 1928. After several summers of field work as an assistant in the U. S. Geological Survey, Dr. Gillson joined the staff of the du Pont company.

Jan 1, 1947

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.