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By John K. Gustafson

The title of my talk is "The Gold Miner and the Future of Gold." This title might just as accurately have been stated as "Gold and the Future of the Gold Miner." Since prehistoric times gold has been sought by mankind for its beauty and its unusual physical and chemical properties. Early in the dawn of civilization it became the ultimate unit of value and lubricated trade between peoples. For at least 6000 years, gold has been used to barter for other commodities. It has been prospected for, treasured, made into works of art and personal adornment, and from time to time has been the object of conquest. Because of its predominant role in recent centuries as a basis for money, economists began to think of it solely in these terms. Annoyed by the disciplinary pressure of gold on the money manager's desire to manipulate money, the famous economist, John Maynard Keynes, characterized it as a "barbaric relic of the past", a characterization repeated by William McChesney Martin, Jr., when he was head of the Federal Reserve Bank. Gold, however, has physical and chemical properties that make it one of the most useful metals in the modern world.' It is the most ductile metal known. An ounce of gold, for example, can be drawn into a continuous wire over 35 miles long. It also is so malleable that an ounce of gold can be beaten into films ten one-millionths of an inch thick sufficient to cover 68 sq ft of surface. It has a density of 19.3 and is so heavy that 1 cu ft of gold weighs more than half a ton. Gold is nonmagnetic and has a high electric conductivity, only slightly less than silver and copper. Gold is so inert to all the chemicals found in nature that gold coins and jewelry buried beneath the soil or at the bottom of the sea for thousands of years appear to be as bright and perfect as when they were first immersed. Finally, gold has an extremely high reflectivity both to light and infrared rays. Because of these qualities, in addition to its rare beauty, industrial and artistic uses of gold have been growing rapidly. On a world basis, a recent study estimated that in 1960 about 750 tons of gold were used for fabrication, and that the amount had grown to about 1296 tons in 1968. My objective in this talk is to discuss with you the present and future supply of and demand for gold on a worldwide basis and the effect these forces are likely to have on the price the miner can expect to receive for the gold he produces. This is a highly controversial and risky subject to discuss before any audience. Nevertheless, it is a subject that I live with constantly as Chairman of the

Jan 1, 1972

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970

By Walter Fuchs

IT is now generally conceded that coal is the product of deposition and transformation of debris of forests and swamps.29 Ample data are available to illustrate the metamorphosis of biochemical substances through biological action; other data show the progressive regional metamorphism existing in coal beds;25 and numerous examples of change effected by intrusion of igneous dikes into coal deposits have been established.23 However, often the relative importance of the biological and the geological factor in determining the character of the various natural coals is a debatable question. Since both biological and geological factors are ever present in nature, the problem, at first glance, would appear to resemble certain probability problems: specifically the simultaneous toss of two coins, with the biological factor as heads and the geological as tails. The probability is 2:I for the combined effect of both factors, as compared to the exclusive effect of either one. if the a priori probability is the same for each factor. This condition can be analyzed by a thermodynamic treatment of data, which may be obtained from a consideration of pertinent biological, chemical, geophysical and geological facts. SYNOPSIS OF BIOLOGICAL AND CHEMICAL FACTS The biosphere is not sterile; i.e., microorganisms are always present. Microorganisms have been established in the ocean deep, under the ice of the polar regions, in the sand of the deserts, and in swamps far below the surface. The various biological media may be acid, neutral, or alkaline, and they may or may not be readily accessible to air. Microorganisms are encountered almost everywhere, except where the temperature is not within the range tolerable by microbial life. Of course, with changing conditions, the type of microorganisms will change. All chemical products of life-proteins, fats, carbohydrates, lignins, waxes, resins may serve as a habitat of microorganisms. In the decomposition of a medium, some microorganisms macerate organic matter mechanically and remove certain constituents for their own nutrition; others decompose a large part of the organic matter but may leave certain constituents undecomposed. Some attack only certain specific ingredients of the organic matter. All of them build up cell substance. The nitrogen content of the medium largely determines the degree of decomposition. Below 1.7 per cent nitrogen, growth of microorganisms and hence decomposition of organic material is retarded; consequently organic material will accumulate. l7,32 Such accumulations of organic material may give coal eventually. Coals differ in type and rank. The nature of the original vegetation and the conditions attending the transformation of the accumulated debris determine the type of coal such as bright, splint, cannel, and algal or boghead coals. Chemical analysis of representative samples of a given type of

Jan 1, 1941

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By C. A. Stiles, J. W. Nyhus

Erie Mining Co. is a 10.3-million-tpy pellet producer on the east end of the Mesabi Range 60 miles north of Duluth. Its complex includes facilities for mining, crushing, grinding and beneficiation in addition to a pellet plant and power plant. A 74-mile railroad links the mine and plant to Taconite Harbor on the shore of Lake Superior. The concentrate recovery ratio at Erie is about 1: 3, and this, along with stripping activity, makes it necessary for the company to mine nearly a million tons of material a week. At the outset, all crude ore mined at Erie was hauled entirely by rail, but with expansion into additional mining areas, the company made a gradual transition towards truck-to-rail haulage. Today, in Erie's 11th year of operation, over 50% of all crude taconite mined is transported by truck to loading pockets where it is transferred to rail cars. Future years will see more taconite moved in this manner. Thus, the company has an increasing interest in tire performance.

Jan 6, 1969

By S. C. Sun, A. M. Gaudin

This paper presents the results of a. study of the relationship of the electrokinetic or zeta potential to flotation phenomena. The relationship is established on the experimental evidence that mineral behavior in flotation and in cataphoresis is generally governed by the chemical properties and amount of the reagents adsorbed at mineral surfaces. Cataphoresisl-5 or electrophoresis is the name given to the movement of a charged particle in a liquid medium under the influence of an applied electric field. Mineral behavior in cataphoresis, as indicated by the magnitude and sign of its ionic charge, can be represented by the term zeta potential. In this paper, the zeta potential represents the difference in potential between the immovable liquid layer attached to the surface of a solid particle and the movable liquid layer in the body of the liquid, and is the result of the tendency of ions on the surface of the particle and within the liquid boundary layer to establish a condition of equilibrium. A high positive zeta potential means that the mineral surface is dominated by cations, a high negative zeta potential indicates domination by anions, and a low zeta potential indicates that the surface is influenced almost equally by cations and anions. In terms of observed quantities the zeta potential is given by the relation _ 4µ(300)² Z= kx in which z is the zeta potential expressed in in volts, µ the viscosity of the solution in poises, u the velocity of particles in centimeters per second, x the impressed potential gradient in volts per centimeter, and k the dielectric constant of the solution in c.g.s. units. A convenient source for the derivation of the equation is the book by Thomas. The term zeta coefficient is an expression coined to denote the difference between the magnitude of the zeta potential of a mineral suspended in solution A, and that of the same mineral suspended in solution B, which consists of solution A and an additional chemical agent, but is at the same pH. For example, the difference between the zeta potential of galena particles in distilled water and that in any chemical solution at the same pH is a zeta coefficient. Or, when the zeta potential of a mineral particle is measured first in distilled water, then in a mixture of water and copper sulphate, and finally in a mixture of water, copper sulphate and xan-thate, we can calculate the zeta coefficient

Jan 1, 1947

By A. M. Gaudin, S. C. Sun

This paper presents the results of a. study of the relationship of the electrokinetic or zeta potential to flotation phenomena. The relationship is established on the experimental evidence that mineral behavior in flotation and in cataphoresis is generally governed by the chemical properties and amount of the reagents adsorbed at mineral surfaces. Cataphoresisl-5 or electrophoresis is the name given to the movement of a charged particle in a liquid medium under the influence of an applied electric field. Mineral behavior in cataphoresis, as indicated by the magnitude and sign of its ionic charge, can be represented by the term zeta potential. In this paper, the zeta potential represents the difference in potential between the immovable liquid layer attached to the surface of a solid particle and the movable liquid layer in the body of the liquid, and is the result of the tendency of ions on the surface of the particle and within the liquid boundary layer to establish a condition of equilibrium. A high positive zeta potential means that the mineral surface is dominated by cations, a high negative zeta potential indicates domination by anions, and a low zeta potential indicates that the surface is influenced almost equally by cations and anions. In terms of observed quantities the zeta potential is given by the relation _ 4µ(300)² Z= kx in which z is the zeta potential expressed in in volts, µ the viscosity of the solution in poises, u the velocity of particles in centimeters per second, x the impressed potential gradient in volts per centimeter, and k the dielectric constant of the solution in c.g.s. units. A convenient source for the derivation of the equation is the book by Thomas. The term zeta coefficient is an expression coined to denote the difference between the magnitude of the zeta potential of a mineral suspended in solution A, and that of the same mineral suspended in solution B, which consists of solution A and an additional chemical agent, but is at the same pH. For example, the difference between the zeta potential of galena particles in distilled water and that in any chemical solution at the same pH is a zeta coefficient. Or, when the zeta potential of a mineral particle is measured first in distilled water, then in a mixture of water and copper sulphate, and finally in a mixture of water, copper sulphate and xan-thate, we can calculate the zeta coefficient

Jan 1, 1947

Jan 1, 1943

Jan 1, 1943

By M. N. Brodie, John Chapman

INTRODUCTION - DEFINITION & HISTORICAL PERSPECTIVE While this symposium is concerned with comminution which, by definition, relates to all stages of size reduction of an ore body to a form suitable for mineral separation, the electrical drive aspect of the grinding section will receive most attention in contrast to the crushing, screening and materials handling elements of the process. The reason for this is that today's large mills, thirty feet diameter and upwards, present mechanical and electrical problems which require a degree of sophistication in their solution not previously required. The ability to satisfy these demands, so far as electrical technology is concerned, largely results from the development of semi-conductor devices. These can now handle typical electrical distribution power levels within remarkably s m all volumes and with high efficiency when compared with the motor-generator sets, mercury arc rectifiers, rotating amplifiers, magnetic amplifiers and vacuum tubes which were commonly used to provide speed and torque controls as recently as the early nineteen-sixties. The hardware available to the electrical engineer has changed dramatically whereby even the simplest control system formerly using hard-wired relays is now superseded by the program m able logic controller with its computer-like memory containing the sequence of operation, in other words, the software. Reverting now to the mineral process itself, it is assumed that the ore body has been mined using explosives and is delivered to the concentrating plant in its 'run of mine' form. The problem becomes one of reducing the material to a size which will permit an acceptable recovery of the mineral with the most economical use of energy. The size of 'run of mine' material will range from about minus five feet for high tonnage open pit operations to minus two feet for the smaller underground mine. The final reduction in size may range from minus ten mesh to minus two hundred mesh (exceptionally as fine as minus six hundred mesh) depending upon the concentration method and dissemination of the mineral values within the ore. There is no single circuit that satisfies all applications, but the pattern of metallurgical equipment use shown in Table 1 appears discernable from current practice, in general terms.

Jan 1, 1982

By J. A. Burkhardt

Field measurements and theoretical studies have been made of pressure surges—momentary variations in fluid pressure—produced by movement of pipe in mud-filled boreholes. Pressure measurements were recorded by five pressure gauges located at various positions in the borehole. An important positive pressure peak was found to occur as the casing moved with maximum velocity. Important negative peaks were found as the casing was lifted from the slips and as brakes were applied to stop pipe movement. A rigorously formulated theory has successfully predicted the sequence and magnitudes of these positive and negative surges and has established a basis for understanding how they occur. Both the measurements and theory indicate that the most important pressure surge is usually due to viscous drag of the flowing mud. The theory of viscous-drag pressure surges has been approximated by simplified graphs and calculation procedures to facilitate ready use in field operations. Comparison of measured results with those predicted by the simplified theory shows that the magnitude of this surge can be predicted accurately. INTRODUCTION It is widely recognized that raising or lowering pipe in a fluid-filled borehole produces momentary variations in fluid pressure, commonly called pressure surges. Both negative (or "swabbing") surges and positive (or "fracturing") surges may occur. In 1934, Cannon1 measured the negative surges and showed that they could be large enough to cause flow of formation fluids into the well-bore and, in extreme cases, lead to blowout conditions. Later, Coins2 measured the positive surges associated with lowering pipe. His results and subsequent field operations strikingly demonstrated that pressure surges could be an important factor in some cases of lost returns. In addition, although the evidence is less clear than in the case of blowouts and lost returns, other investigators 3, 4 feel that pressure surges probably play a part in many instances of minor gas cutting, salt-water flow and other hole trouble. The importance of pressure surges in drilling operations led naturally to attempts to explain the physical causes, nature and magnitude of the surges. Cardwell5 was the first to publish a theory which allowed the quantitative prediction of momentary pressure variations. He assumed that the drilling fluid was a 300-cp Newtonian fluid in turbulent flow. Most field muds have a considerably lower viscosity and are generally believed to be Bingham plastic in nature.6 However, card-well's results were useful because they were presented in a form convenient for field use and, in some cases, gave a reasonably accurate predicted value for the maximum pressure surge. Subsequently, Ormsby7 published a more comprehensive theory of pressure surges. He discussed both laminar and turbulent flow and considered the theory of mud-bypass devices for reducing pressure surges. As a consequence of his more rigorous approach, his results were more accurate but more complex and difficult to use. Further, both Ormsby and Cardwell considered only the pressure surge arising from viscous drag of the moving mud. Clark later published idealized graphs of surges and presented equations for predicting their magnitudes. In addition to pressure variations arising from viscous drag, he considered those caused by inertial effects. His theory was in this respect more complete than those of Cardwell and Ormsby, although he did not discuss pressures due to breaking of the gel. Furthermore, his equations, while not exceptionally complicated, were too complex for ready use at a drilling location. One difficulty common to all three theories is that none was tested rigorously by direct comparison with measured pressure surges. Their accuracy, therefore, could, not be demonstrated. Further, the two theories based on most realistic assumptions (Ormsby and Clark) required the solution of one or more rather complex algebraic equations. The research described in this paper was undertaken to supplement that described and to overcome some of the difficulties noted. It seemed obvious that a fully satisfactory study of pressure surges should encompass three main phases. 1. A valid theory useful in all field situations must be developed. This theory must be based upon realistic assumptions, must be formulated rigorously and should lead to clear concepts whereby the nature of pressure surges can be easily understood. 2. The theory, however complex and involved, ultimately must be presented in simplified form for convenient field use. This may involve extensive machine computations and the use of figures and empirical equations. 3. The accuracy of the simplified equations must be established by comparing measured pressure surges with those predicted by the theory. These must agree both in their characteristic nature and in magnitude. 'This means that careful measurements of surges occurring in actual field operations must be made.

By Peter F. Weiss, H. Riedler, I. M. Moschitz, A. Olsacher, G. B. Fettweis

CONTENTS : 1. NATURAL FACTORS Geology Petrography and Rock Mechanics Mining System Orientation Rock Bolting System Movability of the Ore Grain Size Distribution Permeability Contamination Value of the Ore Hydrology 2. TECHNICAL FACTORS Height Length and Width Drawing Areas Time Factor Water Predrainage Surf ace Draining Underground Draining Advancing Slitting Sequence of Development Initiation of the Caving Process Drawing Rate 3. SPECIFIC MINING RULES Advancing Development Drawing Rate Interruption of Drawing (Water Distribution, Concentration of Mud, Dilution) Blasting 4. CONTROLS Safety Controls for Operation Computerised Drawing Control Structure of the Computer Program Hard Ware Print Outs 5. SUMMARY 6. ACKNOWLEDGEMENTS 7. REFERENCES Under the heading "Development System for Block Caving under Severe Conditions" a report was presented to this congress regarding a magnesite mine using block caving for several years. On account of the experience gathered in this mine and the results of far reaching exchange of experience, as well as under due consideration of the international literature it is tried to systematically list and briefly discuss the following factors that have to be considered for development and draw control of block caving. 1. NATURAL FACTORS It is self evident that this implies all those circumstances given by nature and which cannot be altered by man. Any mining activity is subjected to those and the success is depending on how far technology can be adjusted to those conditions. Geology Deposits of considerable thickness with rather steeply inclined flat-faced contacts are optimal for block caving. While vertically there is practically no limitation- for the deposit, theoretically, the smallest horizontal basis apt for operating block caving is the minimum area necessary to get the rock to completely cave in by undercutting and drawing. Practically, only consider- ably bigger main dimensions are found, mainly because of technical factors (machinery and equipment) and economic factors (cost ratio of exploration vs. development, danger of contamination).

Jan 1, 1981

By H. Morgolin, M. A. Greenfield, P. A. Farrar

In attempts to correlate mechanical properties with microstructure, it is desirable to determine the effect of ß grain size. Determination of 6 grain size is not a problem where a has precipitated at ß grain boundaries. However, in alloys which have been processed to produce an equiaxed a +ß structure the ß grain size is difficult to determine because ß grain boundaries do not etch. The ß grain size can sometimes be laboriously determined by searching for grains which have some a! outlining the 6 grains. This difficulty of ß grain size determination in equiaxed a + ß alloys can be overcome by heating below the ß transus temperature for a short time and water quenching. Fig. 1 shows the starting equiaxed a + ß structure of the Ti-5.25A1-5.5V-0.9Fe-0.5Cu alloy used in this investigation, and Fig. 2 shows the microstructure of the same sample water-quenched after heating 1 min at 1675"F, which is 25°F below the 0 transus. The heavily etched microstructure consists of some equiaxed a! in a structure showing considerable amounts of transformed ß. The ß grain

Jan 1, 1969

By P. O. Metz, E. L. Wiehe, J. S. Foster

BASED on their analyses of growth kinetics, ibbs' and Harris et al.' have recently proposed that the rate of subcritical graphitization of steel is controlled by the rate of diffusion of carbon in ferrite. illert has concluded that this is the rate controlling growth mechanism when the growing graphite particles are relatively large. Harris et al.' also propose that the matrix surrounding a growing graphite particle is plastically deformed to make room for the growing particle. If this plastic deformation does occur, then preferred recrystallization may be observed around the larger particles. If diffusion of carbon in ferrite is rate controlling, then a graphite particle growing in a matrix of, say, tempered martensite or pearlite, should be surrounded by a carbide depleted zone. Thus, the simple metallographic experiments reported here are sufficient to determine whether or not diffusion of carbon in ferrite is the dominant mechanism for the growth of graphite in steel. The present investigation considers graphitization in five alloys. The compositions are given in Table I. Graphitization was carried out at three temperatures: 900°K (627"C), 950°K (677"C), and 990°K ('717°C). Samples were reacted in both the martensitic and the pearlitic initial conditions. In the hypoeutectoid steels, Sets 7 and 8, .and in the hypereutectoid Fe-C binary, Set 6, graphitization was very limited after 1000 hr at temperature. In these samples graphite particles observed were less than 10 p in diam. In the hypereutectoid commercial steels, Sets 1 and 3, large graphite particles (100 p) did not appear until after 250 hr at temperature. The limited number of graphite particles observed and the range of sizes obtained prohibited measurement of growth rates in this investigation. However, in all samples showing graphitization, neithe a carbide depleted zone nor recrystallization was observed. illert's model predicts that diffusion of carbon in ferrite should become dominant for graphite particles larger than about 300 p in diam. The largest graphite particle observed in this investigation was approximately 450 p in diam. No evidence of carbide depletion was noted. Fig. 1 shows a typical graphite particle. This nodule is from an initially pearlitic sample from Set 3 after

Jan 1, 1970

By Kenneth F. Whinery, John M. Campbell

Basically, the Buckley-Leverett theory involves two systems which are similar in nature but are differentiated by time. These systems may be described by the fractional flow and frontal advance equations which essentially characterize the mechanics of oil movement while being expelled from the reservoir. The fractional flow equation originally developed by Leverettl may be expressed in the more usable form The development of this equation is based on Darcy's law describing fluid flow through porous media and applies to the flow at only one point (it is a point function). For simplification, the fractional flow equation is written in the above form because the capillary forces always increase the fractional flow of the displacing phase regardless of the direction of flow or the displacing phase. If, for simplicity, the effects due to gravity and capillary pressure differences are neglected, the fraction of the displacing fluid, f, at any point in the flowing stream is related to the properties of the system by 1 Thus, it is seen that in the absence of capillary and gravitational effects, fd for a given sand and fluids varies only with saturation and pressure. The magnitude of the viscosity ratio, —a has an effective range (range of about 30) in the system where gas is displacing oil and a much smaller range for water displacing oil. In order to make the fractional flow equation more versatile, it is necessary to connect the fractional flow at a given point and saturation with time. This problem was approached by Buckley and Leverett" who developed the frontal advance equation, Eq. 3 states that the rate of advance of a plane that has a fixed saturation, Sd, is proportional to the change in composition of the flow stream caused by a small change in the saturation of the displacing fluid. It is, essentially, a transformation of a material balance equation representing the net rate of accumulation of the displacing phase within a homogeneous sand block. This accumulation is proportional to the difference between the rate at which the displacing fluid enters the sand and that at which it leaves. Eq. 3 describes the velocity with which a plane of constant displacing phase saturation advances through a porous system. Buckley and Leverett," Babson,' Kern," Welge, and others have adequately discussed the basic mechanism and application of the fractional flow and frontal advance equations. APPLICATIONS OF THE FRONTAL ADVANCE THEORY TO PETROLEUM RECOVERY Two general applications of the Buckley-Leverett frontal advance theory involve the system in which the oil is being displaced by an expanding gas cap overlying the oil zone and that in which the oil is being displaced by water. Displacement by Gas in the Presence of an Immobile Water Saturation A system in which gas is the displacing phase may be thought of as having two forces effecting the displacement process. These forces are the gravitational force and that force exerted by the displacing gas. The gravitational effects control the displacing efficiency of the gas. The gravitational effect will be less at higher rates of flow, thereby reducing the effectiveness of the displacement of the oil by the gas. The more efficient displacements occur at flow rates which are less than the gravity free fall rate. Capillary forces can be neglected without materially changing the magnitude of the gas saturation. The Mile Six pool is used herein to illustrate the calculating procedures in evaluating gas drive-gravity drainage field perfomlance. These calculations represent the determination of the gas-oil contact when the distribution of the hydrocarbon pore volume is considered. Two methods

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By Ling Yang, John Henderson

Self-diffusion coefficients of copper in molten copper have been measured by the capillary reservoir method in the temperature range 1140o to 1260°C. The results can be represented by the equation D = [(1.46 * 0.01) x 10-3) exp [(-9710 * 710)/RT] cm2/sec. The energy of activation agrees within the limit of experimental uncertainty with that for viscous flow. The relationship between the diffusivity and coefficient of viscosity is best described by the equation D = kT/4pnr cm2/sec. MEASUREMENT was made of the self-diffusion coefficient of copper in molten copper in the temperature range 1413º to 1533ºK, using the capillary reservoir technique and CU64 as the radioactive tracer.The procedures for filling the capillaries, making the diffusion run and evaluating Dcu from the counting results were the same as described previously.1,2 All experimental operations involving the melt were carried out in a purified argon atmosphere. A graphite crucible, enclosed in a McDanel tube, was used as a container for the melt because of its satisfactory nature as a refractory material and the low solubility of carbon in copper. Graphite was also used for the capillary material. A McDanel thermocouple sheath, to which graphite radiation shields were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube, the capillaries could be lowered into or raised out of the melt. A Globar furnace with a constant temperature zone (± 2°C) of 2 in. was used to heat the assembly. The temperature of the furnace was the equilibrium value corresponding to a given setting of the transformer. Temperature was measured with a Pt-10 pct Rh/Pt thermocouple and varied during a run

Jan 1, 1962

By Frank W. Dickson, George Tunell

Five hot spring areas of the western United States show evidences of present day deposition of HgS; two also show evidences of accompanying Sb2S3 deposition. Sulfide minerals are depositing at or near the surface from hot waters that differ for each spring ai:ea in amount and kinds of dissolved matter. All the springs contain dissolved substances that act as buffering agents and that cause increased alkalinity with increasing temperature. Transport of Sb2S3 is possible in H2O and in boron and sulfide solutions. Increasing alkalinity and temperature enhance stibnite solubility. Quantitatively important transport of HgS appears restricted to alkaline sulfide solutions that contain HgS2=. Elemental mercury probably forms in deep hot waters because HgS breaks down into mercury and sulfur above 200°C, and free S is removed by reaction with water. Elemental mercury should accompany HgS2= in solutions that were at 200°C or higher. Cinnabar deposits from saturated alkaline sulfide solutions because of combinations of temperature decrease, dilution, oxidation, and reactions with wall rock: Amedee Hot Springs, Boiling Springs, and Coso Hot Springs are areas in which HgS is the only sulfide deposited. Hot waters at Amedee and Boiling Springs are supersaturated with HgS or transport colloidal HgS. Steamboat Springs waters deposit mainly silica and stibnite, but they have deposited HgS recently. Sulphur Bank waters deposit mostly stibnite and some HgS. The hot-spring waters of all springs represent highly modified deep water. Field and laboratory studies support the concept of transport of HgS in moderately alkaline sulfide solutions as HgS2=. Fluctuating deposition of stibnite and cinnabar reflects availability of sulfide or variations in deep-source HgS and Sb,S,. Silica and HgS dissolve mutually in alkaline sulfide solutions, and cinnabar and quartz would be expected to deposit simultaneously. Free mercury given off by hot-spring waters would impregnate country rocks.

Jan 1, 1968

By John W. Cahn, David A. Karlyn, Morris Cohen

The massive B(bcc) — am (fcc) transformation in Cu-Zn alloys has been studied isothermally by pulse-heating the retained ß phase from room temperature to the reaction temperatures. The transformation is found to occur only in the single-phase a region of the equilibrium diagram. The massive growth rate is of the order of 1 cm per sec and is constant at each temperature, usually after a delay time of some milliseconds. The delay time depends on the reaction temperature in C-curve fashion, while the growth rate increases monotonically with temperature over the single-phase range. The absence of isothermal massive transformation in the two-phase region does not arise from slow growth rates at such temperatures, but because the reaction cannot get started there. It is proposed that the massive transjormation initiates at small preexisting a particles which have rejected zinc into the surrounding 0 matrix. Only within the single-phase region can these particles consume the excess zinc during diffusion-controlled growth and thereby accelerate to the steady-state massive growth rate. The onset of massive growth marks the end of the delay time, and the growth rate then becomes interface-controlled. These isothermal transformation characteristics explain why the usual composition range for massive-kinetic studies by quenching is so limited. The same principles can be extended to more complex alloy systems by recognizing that the single-phase region in which the massive transformation can occur may not be stable with respect to phases not participating in the reaction. MASSWE transformations are now recognized as a regular class of solid-state reactions involving no compositional change (like martensitic transformations) and no shear displacements (unlike martensitic transformations). The name was first coined by Greninger1 in 1939 to describe the coarse grains of fcc a solid solution generated via a fast reaction from the parent bcc 0 solid solution in Cu-A1 alloys. However, some 9 years earlier, phillips2 had already described a similar transformation in the Cu-Zn system. The fact that the massive a formed as a single phase during drastic quenching from the 0 region of the equilibrium diagram signified that compositional changes were precluded. and the reaction was presumed to take place as in a one-component polymorphic transition by nucleation and growth. Phillips also observed that the occurrence of the massive transformation in the Cu-Zn system was extremely sensitive to alloy composition. For example. in a Cu-37.3 at. pct Zn alloy. the ß — am (am = massive transformation product) reaction was found to predominate and was not suppressed by iced-brine quenching from the 0 region. whereas at compositions greater than 38.3 at. pct Zn the massive reaction did not appear at all. Knowledge concerning massive transformations has bee11 substantially enhanced over the years by Massalski and his coworkers; an excellent summary of his papers and the current understanding of this type of reaction has been published recently by Barrett and ~assalski." he massive transformation product grows in roughly nodular form. often with irregular boundaries but sometimes with almost planar interfaces. The latter may have simple crys-tallographic indices relative to the 0 matrix. or the indices may be complex just as in the case of mar-tensites.'1 Little is known about the existence of orientation relationships between the massive and parent phases. A striking feature of massive transformations is that the massive units start almost exclusively at grain boundaries of the parent phase and frequently propagate on a broad front across matrix grains and grain boundaries of various orientations. Because of the rapid growth rate, it is thought that the interface motion is controlled. not by long-range diffusion. but by thermally activated atom jumps across the transformation boundary.

Jan 1, 1970