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By Wayne L. Dowdey

With proud humility and keen anticipation, I accepted the office of President of the Institute one year ago, and it is with a great deal of pride in you-our membership that I make this report. You are the reason for a productive and prosperous year for AIME. Superior, good or satisfactory results were experienced in 1978 from almost everything we did as a leading engineering technical society. I recognize and pay tribute to the WAAIME organization. Their work is vital to our efforts, and their programs have proven effective. WAAIME can depend upon our continuing support.

Jan 6, 1979

By B. K. Asdell

Crude kaolin exhibits a wide particle size range in which kaolinite is the predominant mineral. Bene-ficiation by wet processing produces high-brightness white pigments. The wet processing techniques peculiar to kaolin beneficiation are emphasized in this article in some detail. Included are discussions of long-distance pipeline transportation, centrifuga-tion, flotation, spray drying and shipment as 70% solids slurry. Georgia, a state seldom considered to be an important mineral producer, has one surprising feature — it is the nation's largest producer of kaolin. Kaolin is a highly important raw material in the paper, rubber, ceramic whiteware, paint and chemical industries. In 1965, more than 2.7 million tons of kaolin were produced in this state, a 150,000-ton increase over the preceding year, and production continues to climb. Strictly defined, the term "kaolin" applies to a group of hydrous aluminum silicates in which kaolinite is the predominant mineral. Kaolinite is inherently white, non-abrasive, chemically inert, and of a very fine particle size, ranging from sub-micron to 40-microns equivalent spherical diameter. An electron-micrograph of kaolinite is shown in Fig. 1. The particles finer than about 2 microns are thin, elongated plates, hexagonal in outline. The larger particles, coarser than 2 microns, are predominantly vermicular in outline with a foliated structure. Table I shows a typical chemical analysis of commercial, wet-processed kaolin compared to pure kaolinite. The sedimentary Cretaceous deposits of the Coastal Plain are the source of most of the kaolin produced in the Southeast. These deposits are of relatively high purity, and it is not uncommon to find the clays running greater than 90% kaolinite. Beneficiating plants using wet processing techniques are most numerous in an area within about 50 miles east of Macon, Ga., in a band approximately 15 miles wide. Kaolin may vary widely in quality from one deposit to another, or within the same deposit. The qualities critically examined are brightness index as measured by reflectance, viscosity of water suspensions, bleachability and particle size distribution. Crude kaolin always contains sand and mica in varying amounts, along with small amounts of many other minerals. These are classed collectively as "grit" because; they are generally coarser than 325

Jan 1, 1968

By H. l. Burghoff, D. E. Lawson

The presence of tellurium in copper and, by inference, in copper alloys, has been considered seriously detrimental and has been avoided. In particular, very small amounts of tellurium have been found to produce red-shortness, although the effects on cold-working and ordinary physical and mechanical properties have not been known so definitely. References in the literature are few, but as long ago as 1881, Eglestonl reported that 0.083 per cent tellurium in fire-refined copper rendered the copper red-short and therefore worthless for hot-rolling. In hot-rolling copper cakes containing this amount of tellurium, he found that fine cracks appeared in the cakes on the first pass through the rolls, the cracks opening further in successive passes. When cold, the metal was said to be tough and malleable. A few years ago, during the course of an investigation in our laboratory on copper-base alloys, it was found that tellurium-bearing alloys could be machined much more freely than similar alloys not containing tellurium. The study was pursued further in this direction, and considerable data were obtained, which indicated that certain tellurium-bearing alloys might have properties of commercial interest. The work eventually led to patent protection,2 a wide range of tellurium-bearing copper-base alloys being covered. This article presents results obtained on the effect of tellurium on the mechanical properties of three copper-base alloys: commercial bronze (90 Cu, 10 Zn), 1.5 per cent tin bronze (98.5 Cu, 1.5 Sn), and silicon bronze (96 Cu, 3Si, 1 Zn). Several alloys were cast in each series, with tellurium content ranging from 0 up to about 1 per cent. The alloys were melted under charcoal in a clay-graphite crucible, using a high-frequency induction furnace, and were cast without undue difficulty in rod form, 15/8 in. in diameter. Charges for the zinc and tin series were made up from the following materials: cathode copper, electrolytic zinc, tin, and tellurium in slab

Jan 1, 1938

By H. l. Burghoff, D. E. Lawson

The presence of tellurium in copper and, by inference, in copper alloys, has been considered seriously detrimental and has been avoided. In particular, very small amounts of tellurium have been found to produce red-shortness, although the effects on cold-working and ordinary physical and mechanical properties have not been known so definitely. References in the literature are few, but as long ago as 1881, Eglestonl reported that 0.083 per cent tellurium in fire-refined copper rendered the copper red-short and therefore worthless for hot-rolling. In hot-rolling copper cakes containing this amount of tellurium, he found that fine cracks appeared in the cakes on the first pass through the rolls, the cracks opening further in successive passes. When cold, the metal was said to be tough and malleable. A few years ago, during the course of an investigation in our laboratory on copper-base alloys, it was found that tellurium-bearing alloys could be machined much more freely than similar alloys not containing tellurium. The study was pursued further in this direction, and considerable data were obtained, which indicated that certain tellurium-bearing alloys might have properties of commercial interest. The work eventually led to patent protection,2 a wide range of tellurium-bearing copper-base alloys being covered. This article presents results obtained on the effect of tellurium on the mechanical properties of three copper-base alloys: commercial bronze (90 Cu, 10 Zn), 1.5 per cent tin bronze (98.5 Cu, 1.5 Sn), and silicon bronze (96 Cu, 3Si, 1 Zn). Several alloys were cast in each series, with tellurium content ranging from 0 up to about 1 per cent. The alloys were melted under charcoal in a clay-graphite crucible, using a high-frequency induction furnace, and were cast without undue difficulty in rod form, 15/8 in. in diameter. Charges for the zinc and tin series were made up from the following materials: cathode copper, electrolytic zinc, tin, and tellurium in slab

Jan 1, 1938

By S. R. Gilbert, B. W. Burdett, L. B. Hales

INTRODUCTION Grinding control is currently the most publicized control subject in the minerals industry. Flotation control and crushing control have not as yet received the widespread attention that grinding control has. The primary reasons for this center around the high capital costs of grinding equipment and the fact that grinding mills are extremely energy inefficient. In a typical copper concentrator the energy requirements to produce refined copper are: (1) [Total Energy Distribution (Kw-hr/yr)% Mining4.93 x 10817.3 Mineral Processing9.63 x 10833.8 Smelting and Refining13.9 x 10848.9] One-third of the total energy used for copper production is for mineral processing. A breakdown of this energy into process steps yields the following: [Total Energy Distribution (Kw-hr/yr)% Crushing and Grinding 7.16 x 108 73.8 Flotation 0.76 x 108 7.8 Materials Handling1.78 x 10818.4] It is apparent that comminution operations consume the largest proportion of the energy for processing and as such become major targets for improvements in efficiency. Unfortunately, size reduction operations are extremely inefficient. Efficiency calculations for grinding range from less than 0.1% to about 5% depending on the evaluation criteria. Because of these facts, grinding control has been and will continue to be the focus of major process control efforts. OBJECTIVES AND BENEFITS All benefits achieved as the result of grinding control are derived from modifying physical parameters which improve the efficiency of the grinding mill. These parameters include:

Jan 1, 1982

By J. L. Huitt, B. B. McGlothlin, J. J. Day

Laboratory tests were made with pure minerals and actual reservoir rock samples to study the effects of hydrothermal (steam m hot water) treatments on reservoir rock properties. These tests showed that hydro-thermal treatment of many reservoir rocks can result in significant rock softening. The softening was attributed primarily to the partial destruction of dolomite and kaolinite and the synthesis of montmorillonite in the presence of excess silica. In many cases, the softening was great enough to cause considerable healing of propped fractures; therefore, a serious reduction in welt productivity could result. In other tests it was found that the addition of ammonia to a hydrothermal treating fluid in a concentration as low as 0.013 Ib/lb of water not only could prevent rock softening but could cause rock hardening. The results of X-ray diflraction analyses of rock samples showed that when ammonia was added to the treating fluid, ammonium-mica and analcite were formed instead of montmorillonite. No significant permeability damage was observed in the sandstones that were subjected to the ammonia-hydro-thermal environment; in some sandstones, permeabifity improvements resulted. INTRODUCTION As the use of steam or hot water becomes more prevalent in well stimulation methods. the need for information on the effects of such treatments on reservoir rock properties becomes increasingly apparent. Several works have been published on high-temperature changes in rock properties,',' but these are more applicable to in situ combustion operations than to steam or hot water injection processes. The mineralogical literature contains many publications which report on the changes occurring with various pure minerals in hydrothermal systems. A review of this literature denotes the ease with which entirely new, crystalline mineral phases can be synthesized from other minerals in hydrothermal environments at temperatures, pressures and residence times typical of those encountered in oilfield thermal recovery or stimulation processes. Discussions of many of these experiments are given by Deer et al. Grim,' Roy et al., Zen\ and Hawkins.' One of the most significant of these pure mineral studies is the hydrothermal synthesis work of Levinson and Vian" in which montmorillonite was synthesized from naturally occurring minerals; i.e., kaolinite, quartz and carbonate minerals (particularly dolomite). These reactions occurred at 575F in only 2 days and at 300F in 5 days. These results may be applicable to petroleum reservoir rocks since the minerals studied were those which are commonly found in sandstones. Furthermore, the environmental conditions imposed in the studies were very similar to those involved in thermal stimulation of petroleum reservoirs, e.g., steam or hot water injection. Other studies have suggested that weak rocks could be hardened by "electrochemical induration", a process in which an electric current is applied to a clay-containing rock body. These tests can be regarded as hydrothermal treatments since they were conducted in some instances with aqueous solutions and since clay temperatures during the electrical treatment reached a maximum of about 100C. Although a number of studies of the reaction of pure minerals have been reported, very little has been published on the reactions of petroleum rock-hydrothermal systems. No work has been reported on preventing the more detrimental rock changes in rock softening which might occur during the injection of steam or hot water into reservoirs. The studies described in this paper were conducted to provide such information. EXPERIMENTAL APPROACH The laboratory tests included studies of the effect of hydrothermal treatment on core samples from several different reservoirs. The hydrothermal treatments (simulated steam treatments) were conducted with distilled water at 575F, for the most part, for periods of 2 to 6 days. This temperature level was selected because it represented that temperature which would probably prevail in several cases under consideration for steam injection projects. The core samples, as well as the pure mineral samples, were contained in high-pressure stainless steel, autoclave-type pressure vessels. The effects of the hydrothermal treatments were evaluated by measuring the penetrometer hardness, formation rock embedment strength and permeabilities of the core samples before and after the treatments (Fig. 1)'" In addition, the mineralogical changes in the specimens were studied by X-ray diffraction. Concomitant with the core sample studies, the mineralogical changes were studied in greater detail by conducting hydrothermal synthesis experiments with pure minerals at similar temperature levels and residence times. For the most part, samples of finely-crushed pure dolomite.

By R. H. Card

THE geophysicist is interested greatly in the resistivities of different formations or parts of the earth's crust; sometimes he is interested in a single figure in the nature of an average, or what may be called the effec-tive resistivity, of all the formations or parts of the crust at a given location to a certain depth. Conversely, the engineer whose work is concerned with the coordination of power and communication lines in such a manner as to avoid electrical interference between these two types of facilities is concerned very much with this effective resistivity; to a lesser extent he is interested in the resistivities of individual forma-tions. In connection with his work the coordination engineer often estimates the effective resistivity; of the earth from measurements of the mutual impedances of lines; in other instances he derives front measure-ments of a different type the resistivities of different layers of the crust and synthesizes these to obtain an estimate of the effective resistivity. In connection with problems concerning the coordination of power and telephone lines, measurements from which earth resistivities can be estimated have been made at many points in the United States by the American Telephone and Telegraph Co. and its associated companies, in cooperation with various power companies and with railroad companies having electrified sections of line. Other such measurements have been made by the Joint Subcommittee on Development and Research of the Edison Electric Institute and the Bell Telephone System. A study has been made of the correlation of these data with the ages and types of materials of the strata of the earth's crust at each of the test locations. The purpose of this study has been primarily to provide information to assist in predicting the order of magnitude of effective resistivities to be used in the preliminary consideration of problems con-cerned with the coordination of power and communication lines. To make the results of such a study, most useful, it is essential that the geo-logical data to be secured when such a prediction is wanted be readily obtainable. Data on the ages of strata and the types of materials com-posing geological structures can usually be obtained, therefore particu-

Jan 1, 1937

By William G. Pariseau, H. Douglas Dahl

Recent subsidence legislation indicates that mining engineers would be welt advised to be able to predict and control surface damage caused by mine subsidence. To date, such an ability is practically nonexistent. Model analysis is suggested as one of the alternative paths available which might yield fruitful results. Similitude requirements developed for a self-loaded body in static or quasi-static equilibrium indicate that complete similitude without centrifuging is an impracticability. However, a pilot experimental study which used a simplifying assumption to correctly model mine subsidence has produced results in qualitative agreement with field observations. The purpose of this paper is to present a discussion of the various approaches that can be taken in the study of mine subsidence phenomena. Particular attention is focused upon the rational selection and use of laboratory models. Broadly interpreted, mine subsidence is the deformation of the rock mass enclosing a mine. Depending upon a number of factors, the movement of the subsiding rock mass may disrupt gas and water lines or other buried utilities, damage surface structures such as buildings and bridges, dislocate streams, roads, and rail lines, aggravate acid mine drainage and fire problems, and generally mar the landscape. It is clearly a problem that no mine manager can safely ignore. It is also a problem that will grow with the general population increase. In the following discussion, a summary review of past and present approaches to subsidence studies is given. The possibilities of duplicating subsidence phenomena in laboratory models are examined, and an analysis of a particular type of model is presented. Some preliminary results obtained from a model of the particular type analyzed are then discussed. REVIEW OF PREVIOUS WORK Historically, subsidence investigations have been empirical studies in the field and laboratory or theoretical analyses of mathematically idealized media. Empirical and theoretical work in the United States has generally lagged behind investigations abroad. In the United States, field studies are mostly pre-World War 11. These are summarized in the Mining Engineer's Handbook. ' Field studies in Europe are more recent and more extensive. Those made in Great Britain are summarized in the Subsidence Engineers Handbook2 and represent observations made at 157 different collieries. Such studies by themselves are of limited usefulness as are all empirical studies. One can never be certain that conditions at one mine will be similar enough to those at another to warrant the drawing of like conclusions. European subsidence formulas rely heavily upon the "angle of draw" and "critical area" concepts. The angle of draw is defined as the angle between a vertical line through the face, and another line extending from the face to the surface at the point where movement is zero. The critical area is defined in relation to the least extraction necessary to produce maximum subsidence. Fig. 1 illustrates the angle of draw and critical area concepts. First and second "limits of influence" are also shown. The angle of draw and associated critical area concept are obviously not well defined, being dependent upon the accuracy of the surface survey. In Great Britain, the angle of draw has increased through the years from about 26 to 35°. In the United States, zero and negative angles of draw have been reported. In the authors' opinion, these purely geometrical concepts represent an oversimplification of subsidence phenomena and their use, in the United States at least, should be discouraged. Empirical observations of laboratory models containing layers of earth, sand, clay, and plaster were made by Fayol (cited by Peele) as early as 1885. An outgrowth of his work was the "dome theory," a verbal description of what is assumed to occur in subsiding rock masses. The dome theory has since fallen into disrepute. Theoretical analyses worthy of the name treat a subsiding rock mass as a deformable body. In these analyses, the actual rock mass is replaced by an idealized material that deforms according to a simple stress-strain relationship. The stress equations of equilibrium expressing the Newtonian laws of mechanical action and the geometry of strain furnish additional equations that must be satisfied. A loading criterion-generally understood, and in some cases stated explicitly-completes the theory.

Jan 1, 1969

By F. W. Warnaars

The Los Bronces copper deposit is located on the west side of the Andes Mountains in central Chile about 54 km (34 miles) northeast of Santiago. The deposit consists of a hydrothermal breccia complex that was emplaced in the western part of an earlier porphyry copper mineral system. This system exhibits propylitic, sericitic, silicic to potassic hydrothermal alteration with disseminated and stockwork copper-molybdenum sulfide mineralization over an area of about 12 km2 (5 sq. miles). The Rio Blanco Mine, about 800 m (0.5 miles) east of Los Bronces, is an underground block caving mine located in the central part of this system. The mineralization at Rio Blanco is characterized by one of the highest primary copper grades known for porphyry copper systems. Present mining at Los Bronces is from an open pit located in the northern part of a hydrothermal complex that is composed of at least seven different copper-bearing tourmaline breccia pipes. Together these pipe form one large contiguous body about 2 km (1.2 miles) long and 0.7 km (0.4 miles) wide at the surface. This body crops out at elevations of between 3.5 and 4.1 km (2 and 2.5 miles) above sea level. Each breccia pipe has a characteristic shape, matrix, type and degree of mineralization and alteration. Quartz, tourmaline, specularite, anhydrite, pyrite, chalcopyrite, sericite, chlorite, and rock flour are present in significant quantities in most breccia matrices. The clasts consist mainly of quartz monzonite, andesite, and minor amounts of quartz latite porphyry. The seven different breccia pipes are identified, from oldest to youngest, as Ghost, Central, Western, Infiernillo, Fine Gray, Anhydrite, and Donoso. The breccias coalesce, interfinger, or display gradational contacts. In places they form sharp contacts with each other and with the surrounding intrusive or volcanic host rocks. Early breccias are disrupted or cut by subsequent breccia events. Explosive emplacement was followed by collapse after the release of hydrothermal pressures. The Los Bronces breccia complex has sharp contacts with the surrounding intrusive stock and andesites. These contacts dip inward on the north, west, and south margins. The eastern contact is nearly vertical and/or dips slightly outward and suggests a westward tilting of the body of about 15° after emplacement. The breccia complex is not fully explored at depth, but is known to extend at least below the 3 km (2 mile) elevation in its central eastern part, about 1 km (0.6 miles) below the highest breccia outcrop. Primary copper sulfide minerals are most abundant in the Donoso and Infiernillo breccias where the matrix consists mostly of tourmaline, quartz, sulfides, specularite, and/or chlorite with minor amounts of rock flour, sericite, and clay. The volume of the matrix material is mostly smaller than in the other breccias. Secondary enrichment enhanced the primary copper grade in the southern two-thirds of the Los Bronces breccia complex and in much of the surrounding porphyry system. Primary grades of 0.3% to 0.5% copper have been enriched to approximately 0.9%. This enrichment may extend from surface outcrops to a depth of more than 500 m (1, 640 ft) in more permeable parts of the breccia complex. A leached and oxidized capping of variable thickness covers a large part of the enriched layer and exceeds 300 m (984 ft) at one location. The shape and depth of the enrichment blanket and the capping suggest that the enrichment process is still active.

Jan 1, 1983

By Manfred Schmellenkamp

During the lust half-dozen years, longwall mining has taken on a new look, much of which is due to the introduction of self-advancing roof supports from Europe. Here is a report on two longwall operations, one which started up in 1956, the other in 1962. It is a story of manually set, friction- type props us, the new European type; the story of an 18-ton per man-shift operation us one of 50 tons per man-shift.

Jan 6, 1963

By W. F. de Lange, M. I. Brittan

A mathematical model of the Western Holdings gold concentrator in South Africa was generated by multiple regression analysis of routine plant operating data. Interpretation of the computer results and application of the model indicated that significant economic improvement in gold recovery could be realized by relatively minor modifications to the circuit. The modifications made are described and the economic benefits resulting from the increased gold production are assessed. Comparison, of the projections of the mathematical model with actual plant performance is illustrated.

Jan 1, 1976

By W. A. Straw

IN the manufacture of telephone apparatus a number of nonferrous sheet metals are blanked and formed to produce a wide variety of parts, which are generally small in size because of space and weight requirements. Many are given sharp bends in forming, so that they may be assembled into compact units. This study covered sheet metal of the alloys of brass, phosphor bronze and nickel silver that are most extensively used by our company. In general, the sheets range from 0.005 to 0.100 in. in thickness and from 1/4 hard to extra spring temper in hardness. As many parts function as flat springs, and others require the maximum stiffness for structural reasons, a large percentage of the metal is used in the hard and spring tempers. So, because of the necessity for the minimum radius of bend consistent with the maximum in hardness, there has been a need for information as to the forming characteristics of these sheet metals in the various alloys, tempers and thicknesses. The literature yields relatively little regarding such forming characteristics, so that designers of apparatus and tools have been largely dependent upon past experience or tool tryouts for guidance. In presenting tabular data intended as a basis for selecting the temper of the metal and radius of the bend, we recognize the influence of many other factors which are not covered in this study. For example, the angle of the bend and conditions of the metal, such as grain size and presence of impurities, as well as conditions of the fabricating process, such as rate of forming and adjustment of the tools, may all affect the result. In addition, a bumping operation subsequent to forming, which is frequently used to set the bend, increases the strain on the metal. We wish to emphasize the fact that this is not considered a scientific investigation of the formability of materials or an attempt to correlate forming, characteristics with various other properties of the metals, except in so far as such properties are controlled by commercial limits on composition and temper.

Jan 1, 1931

By J. Rourke, F. S. Minshall, E. G. Zukas, C. M. Fowler, O&apos

The Hugoniot curves were determined for Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si. The pressure of the transition increased as the silicon content of the alloy increased. Single crystals of 2.9 wt pct Si-Fe were also studied. The pressure of the transition was not dependent on crystallo-graphic orientation. All of the Neumann bands (mechanical twins) were attributable to (112) planes but not all of the {112} planes showed twin markings. A thorough study of the iron Hugoniot (the relationship between specific volume and pressure) under plane wave shock loading revealed a pressure transition at about 130 kbar shock pressure. The results of this investigation were reported by Bancroft, Peterson, and inshall1 in 1956. At the time of this discovery, it was felt that this was probably the a, to y transition normally found in iron and many of its alloys. Subsequently a number of iron alloy systems were surveyed in which the alloying element has a considerable effect on the normal a, to y transformation. The influence of carbon and nickel and/or chromium have already been reported.2,3 At the present time, there appears to be some doubt that this pressure transition is the usual a, to y transition In this study, Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si were chosen for several reasons. To the present, the transition has been found only in iron-base alloys which were originally in the a, phase (bcc). Secondly, the y loop at atmospheric pressure extends to only about 2.5 wt pct Si. If the transition were a, to y, then one might expect a rather drastic pressure effect for alloys containing more than 2.5 wt pct Si. Finally, single crystals of Fe-Si alloys large enough for shock loading studies are readily available thereby making it quite easy to determine the effect of crystal orientation on the transition pressure and on the twinning behavior of the alloy. EXPERIMENTAL PROCEDURE Fe-Si alloys containing up to 7 wt pct Si were produced by normal vacuum casting procedures. Single crystals of Fe-2.9 wt pct Si were purchased from Monocrystals Co., Cleveland, Ohio. The orientations of these crystals were determined and samples cut so that the shock wave would be parallel (to within 1.5 deg) to either the (loo), (Ill), or (112) principal orientations. Three distinct experimental testing techniques were used. First, the pin technique, described elsewhere,4 was used to determine the transition pressure for the polycrystalline alloys as well as for the (111) and (112) orientations of the 2.9 wt pct Si single crystals. Secondly, the recovery studies, described in detail in an earlier paper,2 were used for determining the effect of alloy composition and crystal orientation on the plastic II compression-plastic I rarefaction interaction zone for several specific shock pressures. Finally, measurements of pressures above the two-wave threshold were made on the polycrystalline alloys so that more complete Hugoniot curves could be constructed for this alloy system. The optical techniques described by Rice et al.5 were used to measure the shock and free surface velocities of the samples from which the Hugoniot data were obtained. This method is applicable only in the single wave region, since velocities are obtained from the measured total transit times of the disturbances through measured sample thicknesses.

Jan 1, 1963

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By E. A. Khopunov, V. I. Revnivtsev

The process of triboelectric separation from the point of view of its potential for selective separation of various mineral particles can be described as "dry flotation." Large scale practical applications of this technique are limited because suitable models which can describe contact charging of mineral particles have not been developed. Among the various concepts a promising one is an attempt to change development in dielectric minerals within the limits of contact phenomenon in semiconductors. Experimental investigations reported in this paper indicate that the charge development is mainly a result of contact electrification of dielectric minerals characterized by "donor" and "acceptor" type energy spectra due to lattice defects.

Jan 1, 1980

By M. D. Cooper

Production of both anthracite and bituminous coal in 1954 was about 16 pct below 1953. Estimates on Dec. 1, 1954, indicated 27 million tons of anthracite and 385 million tons of bituminous. Decline in production was due principally to lower demand by the steel industry and the railroads, although competition from other fuels also affected coal. The year was notable for vigorous effort by the coal industry to promote the use of its product. A Cabinet Committee on Energy Supplies and Resources Policy and an Interdepartmental Committee on the Soft Coal Industry were set up by the Administration in Washington. A Governors' Fuel Conference was also organized.

Jan 3, 1955

By Arthur Taggart

A GENERAL awakening of interest among mill men concerning the mechanical efficiencies of their crushing machines is evident from a perusal of the recent files of mining publications. Considering the large part of the power bill which must be debited to the crushing department, such. interest is natural. When, however, the articles on the subject are read, the only statement upon which the writers agree is that fine grinding consumes a large amount of power, and that the machine which, from a concentration standpoint, offends as a slime producer is, for that reason, a serious offender in wasting power. When the mill man attempts to find a method for measuring the power wasted, or to compare the efficiency of one machine with that of another for the same work, he is confronted with a choice of methods which lead to conflicting results. There are two reasons why the work of crushing is not more generally understood. In the first place, experimental data are difficult to obtain; and in the second place, before these data can be put in general form certain assumptions must be made. A difference in these assumptions by different investigators has led to conflicting conclusions. This conflict has resulted in the proposal of two laws. The first of these is the so-called Rittinger's law, which is variously stated as follows: . "The work of crushing is proportional to the reduction in diameter."-R. H. Richards: Ore Dressing, p. 304 (1903). "The Work required to crush rock is very nearly proportional to the reciprocals of .the diameters crushed to."-A. Del Mar: Engineering and Mining Journal, vol. xciv, No. 24, p. 1129 (Dec. 14, 1912). "The Work done in crushing is proportional to the surface exposed by the operation, or better expressed for this purpose, the Work done on a given mass of rock is proportional to the reciprocal of the diameter of the final product, assuming that all the mass has been reduced to one exact size, which is only theoretically possible."- A. 0. Gates: Engineering and Mining Journal, vol. xcv, No. 21, p. 1039 (May 24, 1913).

Jan 1, 1914

By L. C. Morganroth

Magnesite both Massive and Crystalline MAGNESITES are. of two general classes-massive and crystalline. Massive magnesite occurs in serpentine, being formed by the breaking down or decay of serpentine-making minerals or rocks as olivine, etc. (All the magnesia contained by the olivine is not liberated, as a portion goes to make up the serpentine; the breaking up of this serpentine later forms more magnesite.) Serpentine in various stages of transformation is found in the vicinity of magnesite deposits. Massive magnesite is very widely distributed. It is found in Greece, . California, Africa, India, Australia, Mexico, South America, and deposits of varying sizes occur in several of the European countries. Those on the Island of Euboea, Greece, are probable the most important deposits of this character of magnesite. They have been worked for a number of years, the principal quarries or mines being 3 miles in the interior from the village of St. George. (St. George is on the west coast of the island, between the towns of Limni and Khalkis.) (Figs. 1 and 2). -The magnesite occurs in veins or lenses in serpentine. Some of these lenses are very large; one worked several years ago was approximately, 50 ft. in thickness, 75 to 100 ft. high and 300 ft. or more in length. The magnesite is pure white and makes a very prominent feature of the landscape. While massive magnesite is widely scattered over the world, many of the deposits are in veins too thin to work. The usual mode of occurrence is in the form of stock work, the deposits in Venezuela, Mexico, and many of those in California, being of this form. The veins vary in thickness from the thinness of paper up to several inches, running in all directions, occasionally leading to a mass or nucleus of some,size. The spaces between the veins are filled with a disintegrated serpentine in the form of sand. Several of the deposits in California would probably be workable, if they were more favorably situated with reference to transportation, but by far the majority of the deposits are too poor to work. At one deposit,

Jan 9, 1914

By L. H Levenson, Charles S. Barrett

The orientation of metal crystals and grains, both large and small, can be detcrmined conveniently and accurately without the use of X-ray apparatus. This seems to be appreciated by so few metallurgists that it may be useful to explain in detail the method we have found most satisfactory in the laboratory—the reflection of light from crystallographie etch pits. This note includes a description of a suitable inexpensive instrument and instructions for etching various metals and for plotting the data. As the stereographie projection is used to facilitate handling the data, this note may he considered as an appendix to an earlier review of the metallurgical uses of the stercographie projection.' Various methods involving etch pits have been used by other investigators. Bridgman's method2 consists of attaching the specimen to a sphere (a transparent sphere is convenient4 , holding it at arm's length, and marking a spot on it when it has been turned so that the eteh pits reflect light into the eye of the observer from a lamp standing behind him. It has an accuracy of about 2" and is extrernely rapid. A greater accuracy can be obtained by having the reflected light fall on a screen, as has been done by Czochralski,5 Chalmers,6 and Schubnikov.7 All of these methods have been intended for undeformed single crystals. Tammann and his coworkers3,8 developed a method for estimating the number of grains in a polyerystalline aggregate having orientations in a given region of the stereographic triangle and thus obtained statistical information about deformation and reerystallization textures. While the method has had some use in recent years,9 it is not applicable to the majority of problems in physical metallurgy. Smith and Mehl10 determined orientations by plotting the directions of the sides of individual etch pits on a stereographic projection. The accuracy is limited to about 3" and the method requires careful polishing and high magnification.

Jan 1, 1940

By Charles S. Barrett, L. H. Levenson

The orientation of metal crystals and grains, both large and small, can be detcrmined conveniently and accurately without the use of X-ray apparatus. This seems to be appreciated by so few metallurgists that it may be useful to explain in detail the method we have found most satisfactory in the laboratory—the reflection of light from crystallographie etch pits. This note includes a description of a suitable inexpensive instrument and instructions for etching various metals and for plotting the data. As the stereographie projection is used to facilitate handling the data, this note may he considered as an appendix to an earlier review of the metallurgical uses of the stercographie projection.' Various methods involving etch pits have been used by other investigators. Bridgman's method2 consists of attaching the specimen to a sphere (a transparent sphere is convenient4 , holding it at arm's length, and marking a spot on it when it has been turned so that the eteh pits reflect light into the eye of the observer from a lamp standing behind him. It has an accuracy of about 2" and is extrernely rapid. A greater accuracy can be obtained by having the reflected light fall on a screen, as has been done by Czochralski,5 Chalmers,6 and Schubnikov.7 All of these methods have been intended for undeformed single crystals. Tammann and his coworkers3,8 developed a method for estimating the number of grains in a polyerystalline aggregate having orientations in a given region of the stereographic triangle and thus obtained statistical information about deformation and reerystallization textures. While the method has had some use in recent years,9 it is not applicable to the majority of problems in physical metallurgy. Smith and Mehl10 determined orientations by plotting the directions of the sides of individual etch pits on a stereographic projection. The accuracy is limited to about 3" and the method requires careful polishing and high magnification.

Jan 1, 1940