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By M. E. Gershon

A mixed-integer formulation of the mine scheduling problem is discussed and applied for the purpose of optimizing both the mine production sequencing and the mill blending and processing problem simultaneously. Previous attempts at solving these problem separately, although successful, fail to take into account the interrelationships between these problems. Project structure selves as the outline of this paper Generalized in its organization, this concept is useful for long, intermediate, and short range scheduling. Actual applications that show the concept also is applicable to mining a variety of ore are mentioned.

Jan 1, 1984

By Frank W. Osterwald

Violent, spontaneous destruction of coal faces and ribs during, what are commonly called, bumps endangers and at times destroys life and property in mines of the Book Cliffs coalfield, Carbon County, Utah. Because these mines supply much of the coking coal for the West Coast steel industries, mining is necessary, although costs are high and operating conditions are very difficult at times. As operations continue, mining will go to greater depths, and the difficulties will increase. Whether or not mining can be continued successfully depends in part on whether or not incidence of bumps can be controlled successfully. For this reason, the U.S. Geological Survey, at the request of and in cooperation with the U.S. Bureau of Mines, undertook a study of the Sunnyside No. 1 mine to determine what geologic factors were related to the incidence of bumps. This report presents the preliminary results of that study and indicates that some observable geologic features in the mine may be related directly or indirectly to bumps, and that other features may be used to infer stress distribution around workings that will aid in design of roof support measures. Coal is mined in the Sunnyside No. 1 mine from depths as great as 2500 ft by room-and-pillar methods. The surface topography is rugged with many steep cliffs and deep canyons, hence the load on the coal varies greatly within short distances. Much of the Sunnyside coal is under high stress, and while being mined, it shatters continuously' and falls from the face. Continuous shattering (bumping) makes mining easy, but if the shattering is interrupted, greater stress is built up and violent bumps may result when the coal is mined.

Jan 4, 1962

By A. A. Scheil, S. I. Hoyt

In technological studies on steel considerable emphasis has been placed on the identification of the foreign inclusions, testimony of which is adequately given in the metallographic literature covering methods for their identification. The outstanding accomplishment in this field is the scheme devised by Campbell, Comstock and Wohrman for identifying various oxides, sulfides, silicates and other constituents by systematic etching tests and microscopic examination.' The time involved in carrying out this procedure has led to attempts to secure quicker methods, or at least to shorten the time required to secure essential information. An example of this is the use of dark field illuminatin,2 but when this was tried out by the authors it was found that cavities and pits on the polished surface appeared bright on a dark field and could not be distinguished from small glassy inclusions. Still another means is the Leitz Ultropak, an instrument equipped with optical units for the illumination of the specimen by reflected light to secure an effect similar to dark field illumination. The structures are made visible in exceedingly sharp details by utilizing the inherent properties of the samples, such as refractive index, absorption coefficients and reflection powers. We have had no experience with the Ultropak, but a recent paper by Benedicks and Löfquist3 describes methods for determining the refractive index of (Fe, Mn) O and MnS by the use of this equipment. Presumably this method would be subject to about the same limitations as dark field illumination, though the, feature added by Benedicks and Löfquist appears to offer great promise in inclusion identification.

Jan 1, 1935

By A. A. Scheil, S. I. Hoyt

In technological studies on steel considerable emphasis has been placed on the identification of the foreign inclusions, testimony of which is adequately given in the metallographic literature covering methods for their identification. The outstanding accomplishment in this field is the scheme devised by Campbell, Comstock and Wohrman for identifying various oxides, sulfides, silicates and other constituents by systematic etching tests and microscopic examination.' The time involved in carrying out this procedure has led to attempts to secure quicker methods, or at least to shorten the time required to secure essential information. An example of this is the use of dark field illuminatin,2 but when this was tried out by the authors it was found that cavities and pits on the polished surface appeared bright on a dark field and could not be distinguished from small glassy inclusions. Still another means is the Leitz Ultropak, an instrument equipped with optical units for the illumination of the specimen by reflected light to secure an effect similar to dark field illumination. The structures are made visible in exceedingly sharp details by utilizing the inherent properties of the samples, such as refractive index, absorption coefficients and reflection powers. We have had no experience with the Ultropak, but a recent paper by Benedicks and Löfquist3 describes methods for determining the refractive index of (Fe, Mn) O and MnS by the use of this equipment. Presumably this method would be subject to about the same limitations as dark field illumination, though the, feature added by Benedicks and Löfquist appears to offer great promise in inclusion identification.

Jan 1, 1935

By Charles W. Tandy, Wm. I. Weisman

Sodium sulfate is an important industrial chemical, being one of perhaps a dozen or so chemical commodities that are produced and consumed in the United States in quantities exceeding one million short tons per year. In recent years over half of the country's production of sodium sulfate has come from natural sources, whereas 20 years ago only 25% was derived from these sources. Production of natural sodium sulfate from various types of deposits is the main source of this chemical in Canada and Mexico, and probably in Argentina, Chile, and the USSR. [Table 1] illustrates the growth in production of natural sodium sulfate in the United States. Mineralogy and Physical Properties Sodium sulfate is widespread in occurrence and is a common constituent of many mineral waters, as well as seawater. Many of the saline or alkali lakes throughout the world contain varying amounts of sodium sulfate. In its natural form it is found as the hydrous salt, mirabilite, commonly called Glauber's salt, and as thenardite, the anhydrous variety. The largest quantities occur in the form of mirabilite. Sodium sulfate is found in varying degrees of purity, from theoretically pure efflorescent crystals of mirabilite to combinations and admixtures of other salts and impurities. It is a common constituent of some brines, and it is from this source that much is extracted commercially. Sodium sulfate is also found combined with other compounds, such as the mineral glauberite, the double salt of anhydrous sodium and calcium sulfate, and blödite, the double salt of sodium sulfate and magnesium sulfate. While these and other minerals containing sodium sulfate are not economically important, they are of interest because of their frequent occurrence. The reader is referred to other publications (Cole, 1926; Dana, 1932; Grabau, 1920) for descriptions of these minerals. Only the two economically important minerals, mirabilite and thenardite, will be described herein. Mirabilite, Na2SO4 • 10H2O, contains 55.9% water of crystallization. It is noted for its efflorescence or spontaneous loss of water. On

Jan 1, 1975

By Bernhard Blumenthal

A melting process was developed by which high purity electrolytic uranium crystals can be converted into sound ingots without serious contamination. Careful preparation of the crystals, melting in a high vacuum, and directional solidification led to a metal of better than 99.993 wt pct purity. The metallographic examination showed a substantially clean metal with only residual amounts of a second phase which responded to heat treatment. The density of high purity uranium is 19.05 g per cu cm. FOR the study of the fundamental properties of uranium and its alloys, a base metal of high purity is needed, and an investigation was started at Argonne several years ago to examine various methods of preparing high purity uranium. Early success was achieved by the fused salt electrolysis process in preparing high purity metal in crystal form,' and the problem became that of melting the crystals into ingots without contamination. The electrolytic crystals contained a few ppm of heavy metals, less than 15 ppm C, and large quantities of potassium and lithium in the form of trapped fused salt electrolyte. On melting in vacuo in magnesia or urania crucibles, the metal picked up considerable quantities of carbon and some iron, copper, and silicon but lost most of the potassium and lithium. It was not metallographically clean, and much research work was necessary to determine the optimum melting conditions for minimum contamination. This work has resulted in the development of a melting procedure by which sound ingots can be prepared with only a limited contamination by carbon. In the section entitled "Melting of the Electrolytic Metal," the equipment and processes that have been developed for melting the electrolytic crystals are described in detail. The "Metallography" section is devoted to the metallography of high purity uranium, and the section "Density of High Purity Uranium" contains the first property measurement on high purity uranium—a density determination. Melting of the Electrolytic Metal Apparatus—Melting and Vacuum Equipment: Uranium may be melted in either resistance or induction-type electric furnaces. Resistance heating was found to be preferable to induction heating for melting down the electrolytic crystals, for several reasons: Although induction heating permits fast heating, this advantage cannot be utilized when crucibles with limited thermal shock resistance are used. Temperature control of induction-heated melts is poor, and the stirring effect increases the rate of contamination of the melt from the crucible, slag, or the furnace atmosphere; liquation and controlled solidification are difficult to carry out. Because of these objections, resistance heating was chosen. A 10 kw Globar resistance furnace of low heat capacity permitted uniform heating of a uranium charge to its melting point in 45 min. The furnace was insulated with a removable aluminum shield so that, after melting and removal of the shield, the furnace could be quickly cooled to room temperature. The furnace was equipped with an apparatus for directional solidification; see Fig. la. The crucible was suspended in the center of the furnace; and when the melting was complete, the crucible was slowly lowered into the cold end of the furnace tube. Solidification took place upward from the bottom; and when the rate of lowering was small, a sound ingot free from sink holes and shrinkage cavities was produced. To remove the large quantities of gas contained in the electrolytic crystals, melting in a high vacuum is mandatory. While, from the standpoint of contamination, melting in a highly purified argon atmosphere appeared feasible, lithium and potassium removal proved less efficient under such conditions. Also, a vacuum-melted ingot has a cleaner surface than one melted in an inert atmosphere. The vacuum system must be of very high pumping speed and leak tight so that a vacuum of less than 2x10-7 mm Hg is attainable when the system is pumped down cold. The system must have a high pumping speed, so that the pressure maximum which may rise to 1x10-4 mm during heating can be quickly reduced

Jan 1, 1956

By G. W. P. Rengstorff, L. E. Olds

High purity molybdenum ingots containing controlled amounts of a single impurity element (oxygen, nitrogen, or carbon) were prepared. These ingots were tested for ductility by bending test specimens at various temperatures. The relationship between the plastic behavior of the ingots and their chemical composition has been determined. MANY proposed applications for molybdenum require ductility at or near room temperature. At the present time, it is possible to obtain wrought molybdenum with considerable ductility only if special fabrication techniques are used to control the grain structure. Starting with are-cast or powder metallurgy ingots, the usual methods for obtaining ductility rely on fabrication procedures that result in fibered microstructures in the finished product. Recently, it has been found that the ductility of either powder metallurgy or are-cast molybdenum can be improved by uniform recrystallization of the metal to a very fine equiaxed grain structure.' The need for a fibered or a fine grained structure may limit the practical usefulness of molybdenum. For example, welding. which may be used in fabricating the metal, generally produces coarse grained structures that lead to brittleness. This applies, certainly, to currently available commercial molybdenum. Although commercial molybdenum is brittle when the grains are coarse, it has been shown experimentally that fine grained structures are not always essential for ductility. For instance, as-cast molybdenum with a coarse columnar grain structure is ductile if it is sufficiently pure.' Because high purity cast molybdenum has good ductility even when coarse grained, it is probable that the brittleness in coarse grained commercial molybdenum is caused by the impurity content of the metal. Although the general effects of impurities on the cold ductility of molybdenum have been known in a qualitative manner for some time, no quantitative evaluation of these effects has been available. The present investigation was made in order to determine more accurately the effects of oxygen, nitrogen, and carbon on the cold ductility of cast molybdenum. Oxygen has long been known to be detrimental to ductility, although the minimum amount which will embrittle molybdenum has been open to speculation. Parke and Ham" showed that ingots with oxygen contents above 0.003 pct could not be forged. Maringer and Schwope have described the embrittle-ment of molybdenum wire by oxygen. A discussion on the effects of heat treatment on the distribution of oxygen in molybdenum has been given by Perry, Spacil, and Wulff." Although nitrogen would also be expected to have harmful effects on ductility, no extensive work has been done previously to determine whether this is so. However, Tury and Krausz" found that wires presumably with less than 0.007 pct N were brittle. Carbon is added to commercial cast molybdenum for deoxidation. Parke and Ham" have shown that molybdenum containing as much as 0.06 pct C could be forged if the oxygen was kept below 0.003 pct. Also, Bruckart and others' found that the room temperature ductility of sintered molybdenum improved with carbon contents up to 0.84 pct. However, Rengstorff and Fischer' found that residual carbide particles in cast molybdenum apparently had an unfavorable effect on room temperature ductility.

Jan 1, 1957

By G. Krauss, W. Pitsch

The fine structure of the bcc martensite formed in an Fe-33 wt pct ATi single crystal of arrstenite is sho~on by transmission electron microscoPy to consist of combinations of transformation twins, stacking faults, deformation twins, and regular arrays of parallel screw dislocations. These structures constitute evidence for the multiple lattice-invariant deformations which operating during the formation of martensite could produce the real habit-plane scatter measured by a two-surface analysis of the plates formed in the single crystal of this investigation and reported in the literature for other Fe-Ni rnartensites. CRYSTALLOGRAPHIC theories1,2 of martensitic transformation show that the habit plane of martensite in a parent lattice is dependent in part upon an inhomogeneous distortion or lattice-invariant deformation which takes place on a fine scale within a martensite plate during its formation. Several recent theoretical papers3,4 have addressed themselves to an analysis of a wide variety of conceivable lat-tice-invarient deformations and the habit planes which they produce, while experimental investigation have been concerned with either the measurement of habit planes or the description and identification of the martensitic fine structure which reflects the nature of the lattice-invariant deformation operating during transformation. In Fe-Ni alloys with subzero Ms temperatures, the group of alloys with which this paper concerns itself, habit planes have often been found to scatter an amount greater than might be expected from possible experimental errors,5-7 and fine twinning has been identified as a major constituent of the fine structure of martensite.8-11 It has been suggested3,4 that more than one type of invariant shear occurs during martensitic transformation. This possibility has been experimentally supported12,13 by the observation of both dislocation configurations and twinning in a single martensite plate. The purpose of this paper is to report additional evidence for multiple lattice-invariant deformations in martensite and so to account for the real scatter in the habit planes of the martensite plates formed in Fe-Ni alloys. EXPERIMENTAL PROCEDURE The Fe-Ni single crystal was produced by pulling a high-purity iron and nickel charge through a single-crystal vacuum furnace in an alumina crucible. The crystal was double-melted to promote homogeneity and to increase its size by further additions on the second pass. In its final form the crystal was 4 cm in diam and 5 cm long. The nickel and carbon contents were analyzed at 32.9 and 0.006 wt pct, respectively. The austenite of this alloy first transformed to martensite by bursts at about -120°C, and, to preserve as much of the austenite as possible, all transformation was performed just below -120°C. Some observations were made on transformed samples which had been heated for 2 min at 340°C. It is assumed that the features of the martensite of these samples, Figs. 1 and 4, are the same as those of the as-quenched martensite. Orientation of the crystal by X-ray diffraction established 10.735 0.609 0.3161? as the axis of the crystal, an orientation that was checked within 2 deg by neutron diffraction. Further checks by electron diffraction of samples cut normal to the axis confirmed this orientation within the larger limits of error inherent in electron diffraction of thin foils. The X-ray orientation was the one used for the two-surface analysis of the martensite habit planes. A two-surface analysis was performed on the quadrant of the single crystal which had been oriented by both X-ray and neutron-diffraction techniques. Photomicrographs at X50 were made on two surfaces along an edge 2 cm long. Fiducial marks and the fact that many of the plates were almost completely surrounded by retained austenite made good matching of individual plates on two surfaces possible. The habit-plane trace on a surface was taken as the best line parallel to the long axis of a plate. A measure of the accuracy afforded by this criterion was provided by a family of very large plates which appeared at intervals along the entire 2 cm length of the edge. The plates all had habit-plane traces within 2 deg of one another. Many of the plates did not show midribs and, therefore, the use of midribs7 to represent habit-plane traces was not feasible in this investigation. The over-all experimental accuracy is estimated to be better than ±2 deg. Samples for transmission examination in a Siemens Elmiskop I at 100 kv were prepared by cutting 2-mm-thick discs from the single crystal, removing about 0.5 mm by chemical polishing,14 trans-

Jan 1, 1965

Continued Discussion of the papers of Van Hise, Emmons, Weed and Lindgren, Bans., xxx., 27, 177, 424, 578. See also the papers of Vogt, Kemp, Rickard, Blake and Lindgren, at pp. 125, 169, 198, 220, 226, and also the final contribution of Prof. Van Hise, p. 284 of the present volume. All the foregoing, together with the discussion here following, are included in the special volume, "The Genesis of Ore-Deposits," issued this year by the Institute. H. Foster Bain, Des Moines, Iowa (communication to the Secretary):* The zinc- and lead-deposits of the Mississippi valley, which it has been my fortune to study, give particularly good examples of many of the principles of ore-deposition formulated by Prof. Van Hise. Perhaps there is nowhere clearer evidence supporting his fundamental tenet., that ore-bodies are to be regarded as a result, and as merely one of the phases, of the work of underground waters. The facts regarding the mines of the upper Mississippi valley have been given in some detail for Wisconsin by Prof. Chamberlint and, more recently, for the mines west. of the Mississippi by the Iowa Geological Survey.‡ Fortunately, also, the processes of underground water-circulation have been studied in some detail in connection with the investigation of artesian waters throughout the region.$ In Missouri and Arkansas the mines and ore-bodies have been much studied ; but the general problems of the circulation of underground waters have been neglected. During the season just closed the writer has been engaged in a re-study for the United States Geological Survey of the zinc- and lead-deposits of the Ozark region, with special reference to those of the . Joplin area; and his full report is now in preparation. It has been interesting to note how fully the statement that the orebodies result from the general action of underground waters is

Jan 1, 1902

By H. K. Work, G. H. Enzian

In the manufacture of steel for commercial purposes, the deoxidation practice used, i.e., the method and degree of deoxidation, is an important factor affecting the structure and mechanical properties of the finished steel. Deoxidation practice exerts a pronounced influence not only on the soundness of the ingots but also on the reaction of the steel to a number of mechanical and thermal treatments. The first mentioned effect of deoxidation is more or less obvious and was first demonstrated, though perhaps not fully appreciated, by Robert Mushet when, in 1856, he added speigeleisen to low-carbon bessemer blown metal. In 1861. Bessemer patented the addition of one pound per ton of silicon to his blown metal to "cause the metal to lie quietly in the mold." The second effect of deoxidation-—that is, the effect on the properties and behavior of the steel—is, one might say, more subtle, and certainly not as well understood as the first, although in many cases it is the more important consideration. This paper is limited to a discussion of only the second effect of deoxidation and: in particular, to the effect on the strain-sensitivity of low-carbon steels. General Discussion Originally it was thought that the function of a deoxidizer was to combine with the oxygen present in the steel as iron oxide and prevent its subsequent evolution as a gas. -More recently it has been realized that a deoxidizer does more than this. Frequent reference has been made to the effect of deoxidizers on the nitrogen in the steel, and some attention has also been paid to hydrogen. As a consequence of the above situation any study of deoxidation must be concerned with the gas content of the steel and the effect of the deoxidizer on the gases involved. The term "gas content" as used here refers to gases extracted from steel during melting in vacuum rather than to elements present in steel in the gaseous state. The extracted gases, at least in the case of oxygen and nitrogen, are generally accepted to be products of decomposition of oxides, nitrides, or other more complex compounds. The manner in which deoxidation affects the gas content of steel and the significance of gases in steel have been and still are subjects of considerable speculation. No attempt will be made here to give a complete discussion of the literature on this subject but a few references will be cited for purposes of illustration. N. Hamilton1 found a correlation between the oxygen content of alloy steel and the behavior of the steel during tube piercing. Davenport, Bain, and others associated oxygen with aging properties of steel while Köster5 and a number of others6-lo made similar claims for nitrogen. Daniloff, Mehl, and Hertyll stated that "deoxidation decreases the susceptibility of steels to aging directly

Jan 1, 1945

By Gilbert Santoro

In this study tantalum carbide filaments of various compositions in the fcc region were prepared by heating a tantalum wire in a measured amount of hydrocarbon vapor. Such properties as tensile strength, transverse-rupture strength, microhard-ness, lattice parameter, electrical resistivity, and magnetic susceptibility were measured as a function of carbon content. Some of these properties showed a maximum or a minimum between a carbon-to-tantalum molar ratio of 0.80 and 0.85, the composition range at which the color changes from metallic gray to gold. The recent literature has shown that in the large homogeneity range for the fcc phase of the Ta-C system there is a marked variation for such properties as microhardness,' electrical resistivity, ' thermodynamic properties,z'3 lattice parameter and superconductivity. In addition to the technological interest of these variations within a single phase, important theoretical benefits may ensue from a continuous investigation of properties vs stoichiometry in tantalum carbide and other refractory defect compounds, for example the effect of the metal-metal distance and crystal structure upon bond formation and electronic structure. Whether there is a similar variation of the tensile strength is of practical importance. Of theoretical interest would be the knowledge of how the magnetic susceptibility varies with carbon composition. Both of these properties, as well as the transverse-rupture strength, were determined for tantalum carbide filaments in the fcc phase region. The lattice parameter, the electrical resistivity, and the microhardness were also investigated and compared with values appearing in the literature. EXPERIMENTAL PROCEDURE Material Preparation. Tantalum carbide specimens of various carbon content were prepared by statically carburizing high-purity tantalum filaments in measured quantities of pure hydrocarbon gas. The filaments, which were 10 mil in diameter and 20 or 40 cm long, were heated by their own resistance at temperatures from 1800" to 2200°C using alternating current in some cases and direct current in others. Tantalum wire from two sources was used. One had a reported purity of 99.96 wt pct Ta. The ingot from which this wire was drawn had been electron beam-melted as the final step in its purification. The reported purity of the other wire, which was prepared by a powder metallurgical process, was 99.88 wt pct Ta. The impurities of both tantalum sources are listed in Table I. Spec-trographic-grade toluene or research-grade propane was used as the source of carbon. The apparatus for the carburization of the filaments is shown schematically in Fig. 1. The system was evacuated to 1 x l0-' mm of Hg when using the electron beam-melted tantalum and to less than 1 p when using the less-pure tantalum. Neither the difference in the base vacuum, nor in the hydrocarbon gas, nor in the tantalum filaments resulted in any detectable difference in the properties studied in this work. However, only the carbides prepared from the higher-purity tantalum were used in the magnetic-susceptibility determinations. Once the base vacuum had been reached, the system was flushed with the hydrocarbon and re-evacuated. For any desired composition of the carbide, hydrocarbon gas was allowed to leak into a constant-volume flask to a predetermined pressure. These pressures were measured by a Cartesian diver-type mercury gage with a range from 0 to 20 mm and with a scale expanded to nine times. The hydrocarbon gas was allowed into the reaction tube and the filament was quickly raised to the reaction temperature. The slack in the filament due to thermal expansion was taken up by drawing out the movable electrode with a screw mechanism. The filaments were kept at temperature from a few minutes to 200 hr. In the majority of cases the heating time was 6 hr. The reaction tube was cooled by cascading water on its outer surface. By means of an ammeter and a voltmeter the electrical resistance at the reaction

Jan 1, 1963

By Claudia Gasparrini

Silver occurs in nature in major, minor and variable amounts in a very large variety of minerals and in several mineral species in the same ore. Because these minerals may respond differently to the same flotation or leaching agents, detailed studies to establish the correct silver mineralogy become essential for optimum recoveries in those situations where the silver is treated as a primary product. On the other hand, fine grain sizes, which often affect gold recoveries, are not generally as critical in silver metallurgy, due to the lower market price which allows for more of the element to remain In the tailings before incurring in economical losses.

Jan 1, 1984

By Bruce E. Grant, Thomas Jancic, Lawrence G. Dykers, Frank Buchella

Principal factors influencing equipment selection can be grouped into five basic categories: tonnage requirements, ore and waste; topography and property line considerations; ore control requirements; physical characteristics of ore and waste; and climatic considerations. Loading, transporting and ground preparation equipment are largely determined by tonnage requirements. Large size equipment is appropriate for a production of about six million tpm, medium size for three million tons and small size for one million tons or less.

Jan 12, 1973

By R. W. Snyder, W. H. Guilinger, B. S. Gottfried

Two numerical methods are presented JOT solving the equations Jor one-dimensional, multiphase /low in porous media. The case oF variable physical properties is included in the Formulation, although gravity and capillarity are ignored. Both methods are analyzed mathematically, resulting in upper and lower bounds for the ratio of time step to mesh spacing. The methods are applied to two- and three-phase waterflooding problems in laboratory-size cores, and resulting saturation and pressure distributions and production histories are presented graphically. Results oJ the tuo-phase flow problem are in agreement with the predictions of the Buckley-Leuerett theory. Several three-phase flow problems are presented which consider variations in the water injection rate and changes in the initial oil-and ujater-saturation distributions. The results are different physically from the two- phase case; however, it is shown that the Buckley-Lez~erett theory can accurately predict fluid interlace velocities and displacing-fluid frontal snturations for three-phase flow, providing the correct assumptions are made. The above solutions are used as a basis JOT et~aluuting the numerical methods with respect to machine time requirements and allowable time step for a fixed mesh spacing. INTRODUCTION Considerable progress has been made in recent years in obtaining numerical solutions of the equations for two-phase flow in porous media. Douglas, Blair and Wagner2and McEwenll present different methods for solving the one-dimensional case for incompressible fluids with capillarity (the former using finite differences, the latter with an approach based upon characteristics). Fayers and Sheldon4 and Hovanesian and Fayers8 have extended these studies to include the effects of gravity. West, Garvin and Sheldon, l4 in a pioneer paper, treat linear and radial systems with both capillarity and gravity and they also include the effects of compressibility. Douglas, Peaceman and Rachford3 consider two-dimensional, two-phase, in compressible flow with gravity and capillarity and Blair and Peaceman1 have extended this method to allow for compressible fluids. No one, however, has examined the case of three-phase flow, even for the relatively simple case of one-dimensional flow of incompressible fluids in the absence of gravity and capillarity. In obtaining a numerical technique for simulating forward in situ combustion laboratory experiments, Gottfried5 has developed a method for solving the one-dimensional, compressible flow equations with any number of flowing phases. Gravity and capillarity are not included in the formulation. The method has been used successfully, however, for two- and three-phase problems in a variable-temperature field with sources and sinks. This paper examines the algorithm of Gottfried more critically. Two numerical methods are presented for solving the one-dimensional, multi-phase flow equations with variable physical properties. Both methods are analyzed mathematically, and are used to simulate two- and three-phase waterflooding problems. The numerical solutions are then taken as a basis for comparing the utility of the methods.

Jan 1, 1967

By Warren B. Davis

Introduction If a subject this broad were to be covered in even moderate detail, it would require a set of books about the size of an encyclopedia. Since an acceptable length for this paper is a small fraction of one book, it will have to consist of a few samples of the subjects that I think are the most pertinent to World Fossil Fuel Economics. I plan to discuss the trends in world energy demand, particularly in the U. S. and Europe; the consumption patterns and cost patterns of oil, gas and coal; the prospects of synthetics; and some of the effects of government regulation of fuel economics. World Energy Demands Fig. 1 shows Free World energy consumption by principal areas for the period from 1950 to 1970 and a forecast for the period from 1970 to 1985. These figures include only the measurable forms of energy. An example of energy consumption that is not measured is the wood a peasant might cut in the forest and bum in a fireplace to heat his home. This omission probably is a very small part of the total. This forecast is not identical with that of Wayne E. Glenn (see Page 22), but the differences in total energy consumption are not significant. The U. S. consumption, which was 55 percent of the world total in 1950, had declined to 45 percent by 1970, and is expected to decline further to 38 percent by 1985. Western Europe has consumed 28 percent of the total from 1950 to 1970 and is expected to lose share slightly between 1970 and 1985. The most spectacular gainer is Japan, which increased consumption from 2.5 percent in 1950 to 7.5 percent in 1970, and is expected to reach nearly 17 percent by 1985. The over-all Free World total has grown from 62 quadrillion Btu (equivalent to 29 million B/D of crude oil) in 1950 to 151 quadrillion by 1970, an average growth rate of 4.5 percent/year. This total is expected to grow at a rate of 5 percent/year between now and 1985, reaching 315 quadrillion Btu (equivalent to nearly 150 million B/D). Fig. 2 shows which fuels supplied this energy between 1950 and 1970, and gives an estimate of how it will be supplied between 1970 and 1985.

Jan 1, 1971

By H. L. Stone, A. O. Garder

A numerical method of solving the partial differential equations which describe the one-dimensional displacement of oil by gas has been presented. Possible extension of the method to treat multidimensional flow is discussed, and the limitations of this extension are indicated. Using this method, it is possible to allow for the existence of a gas cap, the presence of any number of gas-injection or oil-production wells and the evolution of dissolved gas from the oil. It is also possible to allow for variation in the cross-sectional area, elevation, porosity and permeability of the reservoir. The influence of relative permeability and the force of gravity in the direction of flow upon the displacement is considered. The influence of capillary pressure upon the flow and the effect of gravity in the direction perpendicular to flow are neglected. The physical properties 01 the fluids are considered to be Junctions of pressure only, and equilibrium between contiguous phases is assumed. The numerical calculations can be readily carried out by the use of a digital computer. Several example analyses have been performed using the IBM 704 computer, and about one-third of an hour of computing time was required per case. Reservoir behavior predicted by use of this numerical method was compared to data obtained by other methods for three cases — complete pressure maintenance, dissolved-gas drive and gas-cap drive. The independent solutions to these problems were obtained by analytical solution, laboratory experiment and field data, respectively. Agreement of the numerical solution with data from these sources was good; this agreement establishes the convergence and accuracy of the numerical method. INTRODUCTION Most petroleum reservoirs can be produced by any one of several alternative programs. When a reservoir is produced by primary methods, production economics can be influenced by controlling the number and location of wells and the flow rate of each well. An even greater influence may be achieved by augmenting the recovery of oil obtainable by primary methods. This can be accomplished by injection of fluids such as water, natural or enriched gas or a bank of light liquid hydrocarbons. Selection of the most desirable operation requires a means of predicting the reservoir behavior which will result from each of the several alternative programs. The purpose of this paper is to present a mathematical method for predicting the behavior of reservoirs produced by gas-cap drive, dissolved-gas drive or pressure maintenance by gas injection. The method described herein takes cognizance of phase changes caused by a decline or an increase (due to gas injection) in reservoir pressure, of the presence of a gas cap and of the effect of gravity on the flow of gas and oil. Relative permeability relationships are used to define the flow properties of the rock. Allowance is made for variation in cross-sectional area, elevation, permeability and porosity of the reservoir. Both the influence of capillary pressure upon the flow and pressure gradients in the gas cap are neglected. Whenever a liquid phase and a gas phase are in contact, they are assumed to be in equilibrium. The physical properties of the fluids are considered to be functions of pressure only. Therefore, if the method is to be used to predict the effects of a gas-injection program, mixtures of the injected gas and formation crude should-have the same physical properties as mixtures of formation gas and crude. The equations to be presented in this paper apply only to a one-dimensional case; therefore, they neglect the influence of gravity in the direction transverse to the flow. As is well known, this gravitational influence may lead to overriding of oil by gas. Consequently, this procedure as presented is most applicable to long, thin reservoirs for which gravity overriding is not important. On the other hand, the equations presented can be generalized to treat multidimensional flow and, hence, to consider gravity overriding, if desired. A word of caution on two points is advisable here, however. First, the authors have not demonstrated the accuracy of the numerical technique for multidimensional flow. Second, and more important, capillary pressure will often be of importance in multidimensional problems. Obviously, in such cases a generalization of the

By R. J. Wygal

A method is presented by which homogeneous, isotropic, and reproducible aggregates of particles such as glass beads, sand, ground glass, etc., may be prepared simply and quickly by using a "particle distributor". Several applications of the packing method to the construction of model reservoirs are described. The flow characteristics of these packings me given. Some factors which limit the usefulness of unconsolidated packs for simulating reservoir rock are overcome through artificial cementation of the aggregates. INTRODUCTION Many laboratory studies of porous media are based on experiments using test packs of sand, glass beads and other granular materials. More confidence can be had in the results of such studies if the test packs are known to have uniform properties throughout, to be mechanically stable and to be accurately reproducible. This paper presents a method by which such packs of a variety of shapes and sizes may be constructed using a particle distributor. Some factors which limit the usefulness of unconsolidated packs as a means for simulating reservoir rock are described. A method of overcoming these limitations, which involves artificial cementation of the packs, is presented. DEVELOPMENT Particles packed by the tamping or vibrating techniques are usually either non-uniform or mechanically unstable. An invention by Currie and Gregoryl overcomes these difficulties to some extent. The invention is based on the use of a stream of falling particles impinging on and passing through a distributor matrix of several layers of closely spaced spheres. The particles are well dispersed by numerous collisions with the spheres. They become homogeneously distributed at some distance below the distributor matrix and at that position are collected in the sample container. This apparatus, however, was found to be ineffective when small particles were used since small particles accumulate on the top surfaces of the spheres. An improved distributor matrix was made, first in the form of a stack of five sieves, and then in the more adaptable form of spaced layers of wire screen. Fig. 1 shows a longitudinal view through a five-layered distributor of eight-mesh wire screen. This device gives excellent results.* Fine particles pass through the distributor with very little hold up. The fine structure of the wire matrix with its many deflecting surfaces ensures good particle distribution. There are no dead areas immediately below the screen as were sometimes observed to occur below a matrix of spheres. Using such a device, 20-30 mesh sands were packed to a porosity of 32.1 per cent at rates varying from 0.17 to 6 lb/rnin. The lowest porosity achieved by tamping small increments of similar sands into a container was 33 per cent. Motion pictures at 3,000 frarnes/sec of the surface of a growing pack of 2-3/4 mm glass beads have helped to show the mechanism by which packs of low porosity are obtained. The beads, although packed at the rate of 5 lb/min, were observed to hit the pack surface singly, for the most part, and at well spaced points of impact. Part of their energy is transferred to surface beads which are thereby

By Frederick N. Rhines, Robert F. Mehl

IT has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), ‡ in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Zedele and of Zedele.§ These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a singles olid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By J. A. Norden

MUCH has been written concerning the hoisting equipment of various mines -throughout the country, but most of the literature on the subject, if not all, describes equipment of extraordinary capacity and the small and medium-sized outfits have been neglected. The hoisting equipment here described is capable 'of handling about 1200 tons per day. It has not been worked, to capacity, but 600 to 700 tons, together with men and materials, have been handled in two shifts without any great effort. Only one shaft extends from the surface to the lowest levels of the mine; see Fig. 1. It is composed of three compartments, two of which are used for hoisting and the third for water, air, and electrical lines, and for sinking purposes. In 1909, this shaft was raised from the 1000-ft. (304-m.) level to the 700-ft. There a station was cut and an air hoist installed. At this time all mining operations were confined to the upper levels of the mine; that is; above the 700-ft. The. ore was-dropped to this level through chutes from the 300-, 400-, 500-, and 600-ft. levels and then lowered in cars on cages to the 1000-ft., which is the main haulage adit, the mill and railroad bins being about 3000 ft. from the shaft. Orebodies were, in due time, developed on the 1000-ft. level and below. Therefore, in 1913, the shaft was sunk to the 1150-ft. level and thereafter sinking was continued at regular intervals until the 1500-ft. level was reached. But, hoisting from the 1300-ft. level was a difficult, and slow process with the antiquated air hoist, so, in 1916, it was derided to raise the shaft to the surface and install a modern, electrically operated hoist. This was completed early in 1917 and the hoist was in operation in March of that year.

Jan 8, 1920

By G. S. Ansell, J. Weertman

The creep behavior of an aluminum alloy hardened with a finely dispersed phase of aluminum oxide was investigated. The as-extruded alloy shows an approximate steady-state creep in which the creed rate depends exponentially on the applied stress. The activation energy of creeb is abbroximately 150,000 cal per mole. The recrystallized alloy shows no steady-state creep. ONE method of improving the creep resistance of a metal is to introduce a finely dispersed second phase into the metal matrix. The improvement of the creep resistance has been qualitatively explained by assuming that the dispersed second-phase particles act as obstacles to dislocation motion. If the main effect of second-phase particles is simply to hinder dislocation motion then it is possible to derive a high-temperature creep equation for a dispersion-hardened alloy in a straightforward manner. In the Appendix of this paper such an equation is derived from a creep model which works very well for pure metals. Recently, F. V. Lenel has fabricated, for the first time, powder extrusions of aluminum-aluminum oxide in a large-grained recrystallized form. This alloy, designated as MD 2100, consists of a fine dispersion of aluminum oxide plates in a matrix of commercial purity aluminum. A considerable amount of investigation has been carried out concerning the microstructure and physical properties of this alloy.&apos; ) The aluminum oxide is present in the form of flakes 130A units thick and 0.3 u on edge. They are dispersed in the aluminum matrix with an average spacing of approximately 0.5 jx. The spacing varies in the range of 0.05 to 1.5 µ. The alloy structure is extremely stable at high temperatures. For this reason the alloy offers a unique opportunity for a fundamental study of creep of a very finely dispersed two-phase alloy. Lenel supplied specimens in both the unrecrystallized and recrystallized condition. This paper reports high-temperature creep experiments carried out on these specimens. The results obtained were rather unexpected. No steady-state creep was observed in the recrys-tallized material. In fact, after some transient creep which takes place upon loading, the creep rate is essentially zero ( < 10-8per min). If the second-phase particles acted solely as obstacles to the motion of dislocations, measurable steady-state creep would be expected. Since none is observed it appears that the main effect of the fine dispersion in the recrystallized material is to inactivate the dislocation sources themselves, rather than hinder the motion of dislocation loops created at these sources. EXPERIMENTAL DETAILS Specimens were tested in wire form, 0.087 in. in diam for the as-extruded alloy, and 0.035 in. in diam for the recrystallized alloy. These samples were held in friction-type wire grips; a gage length of 2.5 cm was used for all the creep tests. The specimens were held at 600°C in the test apparatus for at least 15 hr prior to each test. The tests were run under the condition of constant loading and, since the creep strains were small, can be considered as constant stress tests. The temperature of testing was held constant within 3°C. Elongations were measured with an optical cathetometer which was capable of measuring strains as smaIl as 0.00012. This allowed the measurement of strain rates as low as l0-8&apos;per rnin. In addition to the creep tests optical micrographs were made in order to determine both the grain size and microstructure of these materials. RESULTS Fig. 1 shows a few typical creep curves obtained from the as-extruded material. The elongations were somewhat erratic, but each curve shows a region of quasi-steady-state creep from which an approximate steady-state creep rate can be obtained. In general the higher the stress at a given temperature, the greater the total elongation before fracture. The lower the applied stress, the longer is the region where the creep rate is almost constant. Summary data from the creep tests of the as-extruded material are listed in Table I. The steady-state creep data of the as-extruded material for a range of stresses at a constant temperature follow a creep equation of the type creep rate = K&apos; = A exp (&) [11 where A and B are constants, k is Boltzmann&apos;s constant, T is the absolute temperature, and a the stress. The standard error of estimate of the data received is less than one order of magnitude. As shown in Fig. 2, if one compensates the creep-rate data for the effect of temperature over the range of test temperature, the steady-state creep data roughly follow a creep equation of the type Temperature compensated creep rate = K* = A exp

Jan 1, 1960