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By Ancel St. John

DURING a session on coal and coke at the February, 1926, meeting of the American Institute of Mining and Metallurgical Engineers, the writer called attention to the important work on the X-ray analysis of coal1,2 being carried on in England by C. Norman Kemp and his associates. This aroused so much interest that a paper on the subject was requested for the October meeting. It has seemed advisable to make this paper a preliminary survey of the present status in the application of X-ray methods to coal problems and to follow it from time to time with further articles as the art develops. A survey of this sort naturally divides itself into two parts, radioscopic analysis of the distribution of constituents through the body of the coal, and diffraction analysis of the state of association of the elementary components. In this article the subject matter concerning radioscopic analysis has been drawn almost entirely from the writings of Kemp and his associates and the illustrations have been specially furnished by him. It is a pleasure to record here a great indebtedness for this courtesy and cooperation. The subject matter and illustrations concerning diffraction analysis are taken from the author's unpublished researches.

Jan 10, 1926

By S. B. Twiss, P. R. Basford

The relationship between areas of iron powders, briquettes, and sintered compacts and tensile strength has been determined. It has been found necessary to distinguish between two types of areas which exist in such powders—a macroscopic area due to the shape and size of particles and a microscopic area due to pores and cracks in the surface. Only the macroscopic area, specifically the area due to particle irregularity, contributes to tensile strength; the microscopic area cannot be forced into contact with adjacent particles ond does not participate in bond formation. Of the two methods of area measurement employed in this study—permeability to liquids and gas-phase adsorption—only the former is useful for determining the roughness factor. A measure of this roughness, (area measured by permeability to liquid) -f- (orea of powder with the same size distribution, but made up of spherical particles), is shown to be uniquely related to tensile strength at constant density. The other important factors in determining the strength of sintered-metal compacts are the density and presence or absence of surface oxide. THE manufacture of metal parts by the process of powder metallurgy is an important and rapidly growing industry. Progress has been rapid and continuous, largely because of the excellent research in the field. Nevertheless, the process remains inherently complex and empirical. Several investigators have shown that the properties of the final compact must depend on many variables; namely, shape,' size distribution,"-" nd compositiona of the original particles, the pressure necessary to compress to the desired density, the density of the compact, the time and temperature of sintering, and so on. Through the application of some new techniques to the study of powders and compacts, and the correlation of a number of observations of known variables, the present paper attempts to clarify and simplify the underlying theory of the powder-metallurgy process. Any theory must start with the obvious fact that the strength of a compact, its most useful property, is due to the formation of welded areas between adjacent particles, and attempt to deduce what effect other variables will have on (a) the area and (b) the intrinsic strength of these welds. Such welded areas can be demonstrated by electron micrographs, as in Fig. 1. It was believed that (a) could be most directly studied by means of surface-area measurements on the original powders and on the compacts made from them; the area decrease should be related closely to the welded area. A representative group of eleven iron powders from commercial sources, and made by a variety of processes, was chosen for this study. In addition to the surface-area measurements, correlations were established between the tensile strength and all the known variables which might possibly affect it. The results are quite unexpected. They indicate that the situation is much simpler than the authors had anticipated. The strength of the sintered compact is determined, indeed, by no more than three variables; viz., the irregularity of the original particles, the density of the compact and, in exceptional cases, the amount of surface oxide. All three had been recognized previously as having some effect on the tensile strength, but in the absence of the special techniques and interpretations to be developed here, there could be no suspicion that they were the only relevant variables. Materials and Methods Material—All the iron powders were commercial products obtained from the Amplex Division of Chrysler Corporation. Powders A, B, C, and J were very pure electrolytic iron. Powder D was made from oxidized scrap reduced by heating with an excess of cast iron. Powder E was a high-grade iron ore reduced by hydrogen. Powder I was prepared by atomizing molten cast iron in an air blast, quenching the droplets in cold water, and crushing the coarse powder. Mill scale (oxide) is added and the mixture heated to reduce the high carbon content. The other powders were all prepared by reduction of iron oxides, such as mill scale. They

Jan 1, 1959

By H. A. Wriedt

Zinc-vapor pressures in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C were measured by an isopiestic method. Thermody-na?nic properties of zinc in these solutions were derived directly and those of iron with a Gibbs-Duhem integration. Zirzc and iron exhibit large, positive, and moderately temperature-sensitive deviations from ideality. Excess enthalpies and Gibbs energies are positive in the ranges studied. It has been establzshed in relating published phase equilibria to the Gibbs energies of forming solid solutions that positive departures from ideality also exist in the fcc solutions. Tlze stability, as defined by Darken, of the bcc solutions is small but positive at 703.5"C. Its decrease with decreasing temperature indicates that a miscibility gap may exist in the stable or metastable bcc solutions at lower temperatures. The changes of thertnodynanlic properties relatable to changes in magnetic state are minor compared to other changes due to alloying. The accuracy with which the relation between lattice parameter and composition of the bcc solutions is known has been improved. Zinc increases the lattice parameter of a iron by O.ZOZA per unit atom action zinc to at least NZn = 0.25. TO our knowledge, only Ciganl has previously investigated thermodynamic properties of the bcc solutions of the Fe-Zn system. He measured zinc-vapor pressures in the temperature range from about 320" to 360°C by an effusion technique. We have measured the vapor pressures of zinc in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C by an isopiestic technique. This investigation and the pursuant thermodynamic computations are part of a program for studying several properties of these solid solutions. In the appendix we report a remeasurement of the relation at room temperature between the lattice parameter and zinc content. Related work not reported herein embraces measuring the diffusivity2 of zinc in ferrite at 700" to 900°C and the Curie point temperature3 as functions of composition. EXPERIMENTAL METHOD AND APPARATUS Purified iron at a series of constant temperatures was saturated with zinc at a series of constant zinc-vapor pressures, the range of conditions being so limited that the equilibrated solid solutions were ferri-tic. The equilibration was conducted in long capsules, Fig. 1, that had been evacuated, gettered with titanium, and sealed. The purified iron, part of a vacuum-melted ingot of electrolytic-iron stock (Glidden Co. 1044-grade), had the impurity contents listed in Table I. It was used in the form of millings about 0.001 in. thick. A zinc of 99.999 pct purity (United Mineral and Chemical Corp.) and later one of 99.9999 pct purity (Cominco Products, Inc.) were used, with no observed difference in results. Sufficient zinc was placed in the capsule (separate from the iron and kept at a different temperature) to supply the vapor phase and the iron alloy, while leaving a pool of pure liquid zinc throughout the run. The imposed temperature of the residual zinc pool fixed the vapor pressure of zinc throughout the capsule; condensation was avoided at other locations by making this the lowest temperature in the capsule. Two common complications of nonisothermal systems were, we believe, effectively absent from ours: first, molecular species other than monatomic have no appreciable concentration in zinc vapor at 700" to 900~~: second, the development of zinc-pressure differentials in the capsules was suppressed by use of relatively large-diameter tubing and the absence of diluents in the zinc vapor other than desorbed impurities. The specimens and zinc pool were located at two isothermal zones (each ranging within 1°C over several inches) of a wire-wound, 37-in.-long vertical-tube furnace. The required temperature distribution was achieved by external adjustment of the currents in three electrically isolated windings. The temperatures of the isothermal zones were controlled independently by ther-

Jan 1, 1968

Jan 1, 1955

By A. S. Odeh

This paper analyzes the effect of limited entry to flow at the wellbore on the steady-state productivity of a well. Wells that have been opened to flow along a fraction of their productive interval are termed wells with limited entry. Previous work treated the cases of a partially penetrating well, a well producing from the central portion of the productive interval and a well in which several intervals equally spaced were open to flow. In this paper the open interval can be located anywhere within the productive interval. Thus, in a sense, it generalizes previous work. The finite cosine transform was used to arrive at a solution for steady-state flow of a slightly compressible fluid. The solution was programmed for a CDC 1604 computer. Numerical vaIues for rd = 660 ft, r, = 1/4 ft, and range of sand thickness of 20 to 200 ft are presented in graphical form. The effect of rd and r, values on the result is shown in a table. The correct calculation of skin and damage ratio in the presence of limited entry to flow is explained and illustrated by examples. Moreover, the paper shows how to calculate the net decrease in productivity due to the combined effect of limited entry and perforations. INTRODUCTION In some wells only a fraction of the productive interval is open to flow. Location of this fraction is usually dictated by formation characteristics and reservoir behavior. For instance, if a gas cap exists, the open interval is located away from the gas-oil contact to prevent any possible gas coning. Wells that intentionally have been opened to flow along a fraction of their productive formation are tened wells with limited entry. Obviously, unintentional completions of this type also exist. Limited entry to flow decreases well productivity. Magnitude of the loss depends on the fraction of the formation open to flow, on the thickness of the sand, on the location of the open interval and on the ratio of rd /r, where r , is well radius and rd is the drainage radius of the well. The use of pressure buildup data on producing wells to calculate the condition of the formation around the wellbore is an accepted practice. van Everdingenl and Hurst2 introduced the concept of she skin factor s considered to be due to a thin layer of different permeability immediately around the wellbore. These authors dealt with the case of a well of complete radial geometry, i.e., a well with open-hole completion that completely penetrates the formation. The presence of a low-permeability skin results in a loss of productivity, as does limited entry. Therefore, if pressure buildup data obtained on a well with limited entry are used to establish the presence or absence of skin (i.e., formation damage), and a correction is not made for this loss of productivity, the calculations would result in an erroneous skin value. They might indicate the presence of formation damage when in reality there is none, or they might indicate a value larger than the true value. This could lead to an incorrect basis for planning remedial measures. Muskat3 studied the problem of partially penetrating wells for the case of incompressible flow. He presented equations and figures which allow estimation of loss in productivity. Brons and Marting,4 using equations based on Nisle's work,5 studied the loss of productivity for three cases. The first was for a partially penetrating well; the second was for a well producing from only the central portion of a productive interval; and the third was for a well in which several intervals equally spaced were open to flow. Their work was for steady-state depletion-type reservoirs wherein the well radius of drainage is established and the fluid is considered to be slightly compressible. Considered in this paper is the problem of wells with limited entry in which the open intervals are located anywhere within the productive sand. The finite cosine transform is used to arrive at a

Jan 1, 1969

By Verne E. Hooker, Robert M. Becker

The evaluation of in-situ rock stresses from measurements of the change in diameter of a borehole that is stress-relieved by overcoring has become a common practice. Generally the stress evaluation has been based on isotropic relations whereas rock in varying degrees is aniso tropic. A plane elasticity solution fora circular hole along one axis of an orthotropic medium has been adapted to evaluation of in situ stress. The necessary elastic parameters for this evaluation may conveniently be obtained from static tests on the overcore in conjunction with a consistent orthotropic thick-wall cylinder solution. The method and equations for the laboratory and field evaluations are summarized and illustrated. The determination of in-situ rock stresses from boreholc deformation measurements has gained widespread acceptance. Hastl measured the change in diameter of a borehole that was stress-relieved by drilling a larger concentric core; this overcoring method has produced a major portion of the field data for recent stress evaluations in rock. These evaluations are based on the elastic properties of the rock, which are conveniently determined by testing the overcore.6-8 The stress evaluation and the overcore testing procedures generally assume isotropic relations whereas rock is anisotropic in varying degrees. Recently, an anisotropic plane stress solution was adapted for evaluation of in-situ stress9 and a related plane strain solution was developed for the testing of stress-relief core. 10 The present paper unifies the stress evaluation and overcore testing procedures for a general class of anisotropic rock. Equations are presented for calculating the state of stress in a plane normal to the borehole, and a consistent thick-wall cylinder solution is given for determining the necessary elastic properties. In addition, a complete example of stress evaluation from laboratory and field data is presented, and the order of error in computing the state of stress from isotropic relations is illustrated. Several limitations of the results should be emphasized. All results assume small linearly elastic deformations of a homogeneous medium. Rock characterized by orthotropic, transversely isotropic, and isotropic elasticity is considered; however, the anisotropic results assume a special relation among certain elastic constants in addition to geometric orientation with respect to a plane of elastic symmetry. For some stress determinations in rock, these may be severe limitations. On the other hand, the anisotropic evaluation procedure involves little additional effort and is much more flexible than the corresponding isotropic evaluation procedure. The collection of field data is identical. The laboratory determination of elastic parameters is no more difficult and time-consuming for the anisotropic than for the isotropic model. Only the calculations require some additional effort for the anisotropic evaluation, and this additional effort is eliminated by use of a small computer. The flexibility of the anisotropic procedure is greater because more than two independent elastic constants are available in fitting rock data. For the special relationship assumed among orthotropic constants, five independent elastic constants are available for the determination of in-situ secondary principal stresses as compared with two independent elastic constants for the isotropic model. Much of the material presented is either directly from the literature or adapted from the literature through superposition or the usual transformations. Consequently, only enough detail for clarity of presentation is included. RELATIONS FROM ANISOTROPIC ELASTICITY Materials that have three mutually orthogonal planes of elastic symmetry are called orthotropic. By directing the axes of the coordinates perpendicular to these planes, Hooke's law for an orthotropic solid 11 is

Jan 1, 1970

By Leon Eliel

TEN years ago a broad knowledge of aerial mapping, coupled with a smattering of geology, qualified one to speak on the subject of the appli-cation of aerial mapping to geology. Today, with aerial maps a common tool in the hands of expert geologists on every continent throughout the world, it would be nothing short of presumptuous for the author of this paper, who is not a geologist, to give any geological statements on his own authority. Relatively, today we are only purveyors of general geological gossip, with a definite case here and there by way of illustration. But we can present a story of the really marvellous strides that have been made in the evolution of aerial mapping, built around a skeleton of geological tidbits, from which some useful conclusions may be drawn. The average geologist goes about reading his aerial maps much as one would approach the problem of deciphering a cryptogram. To begin with, typical key expressions appear in recurring sequences and under certain conditions. If once the meaning of these isolated bits of infor-mation can be ascertained, the message begins to take meaning. In a similar fashion, the geologist works out his key from aerial maps of territory with which he has some familiarity. He learns that a certain type of thin, white line may mean a vein of quartz. He sees that a certain change in the photographic tone of vegetation on the ground reflects two kinds of soils on opposite sides of, a contact. He sees that a certain type of alignment of topographical features often means a fault. He learns that by the erosion pattern .he can frequently distinguish soft formations from harder ones. And so, bit by bit, he ties together the information of the picture with his experience on the ground until he develops a reasonably creditable capacity of interpretation. Through the complete gamut of surface conditions, ranging all the way from flat, arid, exposed desert terrain to dense jungle, or rugged mountains, the evidence from which the geologist must make his inter-pretation varies with bewildering profusion. The quality of photographs which are obtainable may range from perfect pictures in the desert to almost useless smudges in the steaming jungles. One thing he has learned with certainty-the airplane carrying its mapping camera is a superb reconnaissance tool, only awaiting his ingenuity in correlating the pictures with the ground to simplify most exploratory problems.

Jan 1, 1936

By Charles P. Berkey, Joseph H. Sinclair

This paper describes the results of a visit to the Santa Elena Peninsula, Ecuador, in January and February, 1921. On account of the complicated folding and faulting of the rocks and the peculiar occurrence of petroleum, field work was possible on only a few of the many geological problems and the results here published are only a contribution to the solution of the general problem. We know of nothing published on the geology of the district, except one account, in Spanish and German, by Theodor Wolf. The Santa Elena peninsula, the most important headland of the coast of Ecuador, lies two degrees south of the equator. The chief town, Santa Elena, is about 75 miles west of Guayaquil, the main seaport of Ecuador. The nearest developed oil field is the Zorritos of northern Peru, 120 miles south across the Gulf of Guayaquil. If newspaper reports are true, viz. that the Anglo-Ecuadorian Oilfields, Ltd., has recently brought in a 700-bbl. well on the coast of the peninsula near Ancon, the district may become important in the production of petroleum. At the time of our visit, the best way to reach the peninsula was by a steamer of the Pacific Steam Navigation Go., southward from Panama and northward from Guayaquil. About once a week, one of these steamers anchored 1/2 mile off shore near the village of Salinas, an important cable station. An alternative route, in the dry season, is by automobile from Guayaquil. In February, 1921, a railway bed had been graded part way between Guayaquil and Salinas, but this was detcriorating rapidly because of lack of funds to continue construction or to keep in repair that portion already completed.

Jan 1, 1923

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By J. G. Early, F. V. Lenel, G. S. Ansell

The isothermal shrinkage rates of copper-powder compacts were determined in the temperature range from 760o to 1060oC. The rates for compacts fabricated from a pure spherical copper powder were compared, on the one hand, with those fabricated from a spherical powder containing a dispersion of aluminum oxide in the copper matrix and, on the other hand, with those fabricated from a pure copper powder having irregularly shaped particles. The irregular copper-powder compacts shrank much faster than the spherical copper-powder compacts and these, in turn, shrank faster than dispersion -strengthened copper -powder compacts. The experiments were run under a small external load. By varying this load, the stress dependence of the isothermal shrinkage rate could be measured for compacts from spherical-copper powders. This stress dependence was found to be approximately proportional to the 4th (dispersion-strengthened alloys) or 4.5th (pure metals) power of the stress. It is concluded that the material-trans port mechanism is due to dislocation climb rather than to Herring-Naharro creep. In this investigation the isothermal shrinkage rates of compacts made of copper powder with an average particle size of 70 g in the temperature range from 780o to 1060°C were studied. The aim of the investigation was to determine the mechanism of material transport responsible for the shrinkage of these compacts. Since the phenomenon observed in this investigation was shrinkage of compacts at high temperatures, it will be necessary to consider all the material-transport mechanisms possible in sintering. It is unlikely that evaporation and condensation, surface diffusion, or even volume diffusion of vacancies, in which surfaces of small radius of curvature are vacancy sources and those of larger radius of curvature vacancy sinks, will materially contribute to a sintering process involving shrinkage, i.e., one in which the centers of adjacent particles move towards each other. The two principal mechanisms which were considered were the so-called Nabarro-Herring mechanism and a plastic deformation mechanism by dislocation movement. Both of these mechanisms were originally conceived to explain creep, i.e., the plastic deformation of metals at elevated temperatures under a constant applied stress. The shrinking of metal-powder compacts which was studied in this investigation can be readily treated as a creep process. This means that the shrinkage rates observed are considered as creep rates under the influence of an applied stress. It is true that the stresses in sintering experiments are generally not constant but decrease continually with time, but, by considering creep rates or shrinkage rates over a relatively short time interval, the small changes in stress during this time interval can generally be neglected. Nabarro-Herring microcreep is a high-temperature deformation mechanism which is caused by a diffusional flow of vacancies from boundaries under a tensile stress towards those under a compres-sive stress. Herring1 has shown that in this type of microcreep the strain rate e is proportional to the applied stress and follows an equation of the form ma, aexp(-Q/RT) [l| where <j is applied stress, Q is the activation energy for self-diffusion, R is the gas constant, and T is the absolute temperature This type of creep can explain the shrinkage of a porous compact. The surface of the pores are subjected to the tensile stress of surface tension, while the grain boundaries are under a compressive stress also due to surface tension. Vacancies diffuse from the pore surface through the lattice to the grain boundaries, where they are eliminated. In order to maintain vacancy equilibrium at the pore surface the vacancies leaving the region of the pore surface are replenished from the volume of the pore, which means that the pores shrink.

Jan 1, 1964

By E. W. Engle

Fox several years the Fansteel Products Co. has been engaged in the production and development of various of the rarer metals. It is at present engaged in the commercial production of tantalum, tungsten, and molybdenum in a very high state of purity. The information contained in this paper is partly a general compilation from various sources and partly information obtained as a result of recent years of work in the laboratory of this company. Tantalum, tungsten, and molybdenum form a group peculiar to themselves among the commercially available metals. Their very high melting points (tantalum 2770° C., tungsten 3350° C., and molybdenum 2550° C.) set them apart so far as the metallurgical processes for their production are concerned. Further, when properly prepared and treated they will stand a somewhat unusual degree of cold work, that is work below the temperature at which marked crystal growth takes place. Such cold-worked metal may show a high tensile strength; tantalum to 130,000 lb. per sq. in., tungsten to 490,000 lb., and molybdenum to 260,000 lb., in the form of fine wire. In physical appearance, these metals are not unlike some steels; they may be better described by saying that polished tantalum some¬what resembles lead; polished tungsten, iron; and polished molybdenum, nickel. The polished surfaces of all three remain untarnished in ordinary air. Air containing corrosion-producing impurities will, in general, show molybdenum the least resistant to corrosion and tantalum the most resistant. Molybdenum has, however, a high degree of resistance to corrosion by hydrochloric acid, a property that should render it of commercial interest. On the other hand, it is markedly attacked by some of the weaker organic acids.

Jan 3, 1925

By D. A. Koss, R. O. Gordon

Changes in the ultrasonic attenuation in steel specimens have been observed during tensile tests. Samples of AISI 1020, 1045, and 1095 steel quenched and tempered to a spheroidized condition have been used. Both attenuation and microstrain measurements fail to reveal preyield dislocation motion in the as-tempered specimens. Upon reapplication of the load to samples in the strain-aged condition there is a large preyield attenuation increase but no observable micvostrain up to 90 pct of the flow stress. These and other observed changes can be related to changes in the free disloca-tion density and the average dislocation segment length. The results show that the increase inflow stress in the strain-aged condition is caused by increased fric-tional stresses rather than by dislocation pinning. Strain aging is found to proceed through three distinct stages. The second of these follows the t2,3 law and is characterized by an activation energy of 20 kcal per mole. RECENT years have seen substantial progress in the understanding of the sharp yield-point phenomenon in metals; the influence of solute atom pinning of dislocations, of dislocation multiplication, and of the stress dependence of dislocation velocity on the stress-strain curve has been investigated. Evaluation of the relative importance of these factors in the various metals and alloys is not complete, however, because observation of the stress-strain curve alone is not sufficient to determine the yield mechanism. In the experimental study of the sharp yield point it would be desirable to be able to directly observe the dislocations in a bulk specimen. Ideally, the observations should be made during deformation because of the rapidity of recovery processes in lightly strained metals. While direct observation of dislocations under these conditions is not possible, certain physical properties sensitive to the dislocation structure can be observed while a test specimen is undergoing deformation. Of these properties, one of the most useful is the ultrasonic attenuation. The total observed attenuation, a, is due to a number of causes: acoustic diffraction, scattering by inhomogeneities in the structure, heat flow, magnetostriction, and dislocation damping. Satisfactory measurements of the absolute a are difficult to make because all of these factors cannot be evaluated in any given specimen, but changes in a due to changes in the dislocation contribution alone can be reliably observed by appropriate technique. Because dislocation damping is sensitive to small concentrations of long, free dislocation segments, observation of acoustic attenuation due to dislocations is particularly useful in the study of the early stages of plastic deformation. In the experiments to be described, acoustic-attenuation measurements have been made on steel samples as these were pulled through their yield in tension. While many details of dislocation-damping phenomena in the bee metals remain obscure, the main characteristics of this type of internal friction are established. At low strain amplitudes and at frequencies well below that of dislocation resonance (the conditions of these experiments) the dislocation contribution to a is given by1 where A is the density of freely oscillating dislocation segments, L is the average segment length, B is the damping constant for a moving dislocation, w is the frequency, O is an orientation factor, C is the dislocation line tension, and t is a numerical factor relating average segment length to the distribution of lengths. Because of its fourth-power dependence on L, a is highly sensitive to changes in dislocation free segment length such as might arise from unpinning, recovery, jog formation, or dislocation intersection. The above equation is not valid near the resonant frequency of dislocations, but the segment length in steel is believed to be much too short to cause over-damped resonance near 10 Mc; this will be discussed later. In the present experiments plastic-strain measurements with a sensitivity of 2 x 10-5 were also made during the early stages of loading in order to detect preyield strain. The general plan of the experiments is to observe

Jan 1, 1967

By Cyril Stanley Smith

Although alloys of copper and silicon were examined several years ago,&apos; and their excellent mechanical properties were shown, it was not until C. B. Jacobs 2 introduced manganese in small quantities to the alloys that they became of commercial importance. A few years ago The American Brass Company took over the patents and commenced to manufacture the alloy under the name "Everdur." The present study of the constitution of the ternary system was undertaken in order to reach a fuller understanding of the behavior of the alloy. Review of Previous WORK on the BinaRy Systems There have been no papers published dealing with the constitution of the ternary system, although some tests of the mechanical properties have been described," which indicate that there is a change in solubility with temperature. Copper-silicon System The copper-silicon system has been studied in detail by the author and is described in two papers published in 1928.V he portion of the diagram up to 8 per cent. silicon, as determined by this research, is reproduced in Fig. 1. The author&apos;s previous papers include a complete review of the work of other investigators and it is not necessary to deal further with this system here. Copper-manganese System The copper-manganese system has been investigated by several workers, notably Lewis,5 Wologdine,6 Sahmen7 and Schemtschuschny,

Jan 1, 1930

By A. R. Hendrickson, C. F. Smith

Hydrofluoric-hydrochloric acid mixtures have been successfully used to stimulate sandstone reservoirs for a number of years. Hydrofluoric acid (HF) has a specific reactivity with silica which makes it more effective than HCl for use in sandstone. Kinetics of the reactions of HF have been studied to determine the related effects of reservoir composition, temperature, acid concentration and pressure on the spending rate of HF. Secondary effects from by-product formation are noted and described. Predictions are made concerning the improvement in productivity resulting from HF treatment of skin damage. The kinetic order of HF reaction in sandstone was experimentally determined to be first order, i.e., the reaction rate is proportional to concentration. HF reacts faster on calcite than on clay, which, in turn, is faster than the reaction rate of HF on sand. Static conditions retard the HF reaction rate. As HF is forced into cores, there is a temporary reduction as a function of flow rate and acid concentration. Extensive deposition of calcium fluoride in acidized cores was not observed. Although some CaF, was defected, it was not considered a major source of damage in cores containing moderate amounts of carbonate. Other fluosilicates could be potentially more dangerous than CaF, in reducing permeabiliry. INTRODUCTION Hydrofluoric acid has been widely used in stimulation treatments since 1935, when mud acid was introduced to the petroleum industry. Originally, this hydrochloric-hydrofluoric acid mixture was intended to remove mud filter cake, but it has since been successfully applied to many other oilfield problems. Mud acid treatments have been unusually successful in sandstone reservoirs where hydrochloric acid is unreactive due to a lack of enough calcite in the formation. The relatively small amount of hydrofluoric acid present (2.1 per cent) reacts with sand grains, clays and traces of calcite which are generally present in sandstone reservoirs. Since hydrofluoric acid (HF) is the key to mud acid success, this research effort has been dedicated to gaining a more thorough understanding of the basic chemical and physical principles involved as HF reacts. Hydrofluoric acid&apos;s reactivity with silica makes it unique in application. Other mineral acids such as hydrochloric, sulfuric or nitric are unreactive with most silicious materials which comprise sandstone formations. A typical sandstone reservoir may contain 50 to 85 per cent silicon dioxide, more commonly called sand or quartz. Hydrofluoric acid reacts as follows: 4HF + SiO2 + SiFO + 2H2O The silicon tetrafluoride (SiF,) is a soluble gas, in some ways similar to CO2, and is capable of undergoing further reaction when held in solution by pressure. These reactions will be considered in detail later. Kinetics of the reactions of HF have been studied to determine the effect of reservoir composition, temperature and pressure on the spending of the acid. Secondary effects from by-product formation have been noted and described. The individual reactions of HF on quartz, glass and clay are reported. Mathematical correlations have been drawn, then applied to studies of HF spending in cores obtained from actual producing sandstone formations. The research reported herein is only the beginning of a continuing approach to better understanding and use of HF in petroleum reservoirs. THEORY AND DEFINITIONS Through the years, a concentrated effort has been made to understand the effects of many variables on hydrochloric acid (HCI) spending in limestone. Hendrickson el al., have given mathematical relationships for HC1 reactions which made possible the engineered approach to acidizing. The same variables—temperature, acid concentration, formation composition, pressure and permeability-porosity relationships—which affect HC1 behavior in limestone also govern HF behavior in sandstone. Insoluble by-products of HF reaction have been isolated and identified. Their effect on fluid flow has been measured under varying conditions in an attempt to evaluate the extent of possible damage and means of eliminating it. In general, HF follows the same reaction paths as HCI. It will react with limestone and dolomite with speed and ease. Thin sections of acidized cores show the reaction of HF with limestone or calcite faster than its reaction with either clay or sand. When HF reacts with calcite (CaCO,), theoretically, calcium fluoride (CaF2) is precipitated, and has been blamed as a major cause of reduced permeability. On the other hand, pH and pressure such as that encountered in an underground formation under acid treatment definitely retard CaF2 formation,&apos; so the whole question of CaF, deposition in wells is a subject for study.

Jan 1, 1966

By Charles Wraith

THE property of the Roan Antelope Copper Mines, Ltd., is situated at Luanshya, north-central part of Northern Rhodesia, and is connected with the main line of the Rhodesia Railways, Ltd., by a 24-mile branch line from N&apos;dola. Most of the material and supplies that are not available in Africa are shipped into the country via Beira, on the East Coast of Africa, a distance of 1473 miles from Luanshya and the nearest ocean port. The output of copper is shipped by rail to Beira and thence by boat to the market. Passenger travel is mostly via Cape Town, a distance of 2162 miles from Luanshya. Excellent passenger trains operate on regular schedules between Cape Town and Northern Rhodesia. Luanshya is 13° south of the equator at an elevation of 4000 ft. above sea level, and has a mild healthful climate. During the rainy season, from October to March, the rainfall averages 53 in. The area is pro-fusely covered with vegetation. An ample supply of water for industrial and domestic purposes is available throughout the year. The more important supplies for smelting purposes, such as wood, coal, limestone, silica, quartzite, and clay for "dolly" mud, are con-veniently available. Excellent grades of coal, coke and firebrick are obtained from the Wankie Colliery Co., Ltd., Southern Rhodesia. The Wankie colliery has just completed the erection of equipment for the manufacture of silica brick. An ample supply of quartzite of good grade is available for this purpose. Silica brick is also obtained from the Belgian Congo and from India. Limestone is quarried from a large deposit a few miles from Bwana Mkubwa, which is 30 miles by rail from the smelter. An abundant supply of clay for "dolly" mud and for lining launders is available within a short distance of the smelter.

Jan 1, 1933

By Dr. O’Neil Thomas J., Donald W. Gentry

There are mines that make us happy, There are mines that make us blue, There are mines that steal away the tear-drops As the sunbeams steal away the dew. There are mines that have lost the ore chute faulted, When the ore&apos;s forever lost to view, But the mines that fill my heart with sunshine, Are the mines that I sold to you. -Anonymous INTRODUCTION The preceding chapters have discussed, in various degrees of detail, the primary considerations necessary to perform a cash flow analysis of a mining-related investment opportunity. Although the previous discussions regarding the manipulations, calculations, and interrelationships of the various components of the pro forma income statement were illustrated in the text, many individuals are un- familiar with the format and appearance of a final spread sheet for the evaluation of a mining property. As a result, it seems appropriate to conclude this book with an abbreviated case study of an actual mine property (currently in production) showing the cash flow analysis and some back-up data. Obviously all of the supporting data and calculations for the case study presented cannot be provided; however, reference is made to the major assumptions utilized and to the appropriate procedures employed in the calculations, as described elsewhere in the text. The problem associated with using any case study for illustrative purposes is that one tends to be overwhelmed by detail. For instance, specific costs, prices, expenditure timings, and other variable values may be challenged because they either do not conform to one&apos;s expectations or are not consistent with specific operating experiences. When this occurs the instructional value of the problem becomes obscured. The purpose of most case studies, and particularly the one presented in this chapter, is to expose the student to the methodology, procedure, and format associated with performing a cash flow analysis of a mining property. It is not to laboriously wade through the specific details associated with operating and capital cost development, mine plans, or equipment schedules. It should be noted, how- ever, that the values represented in this case study result from specific mine plans, operating procedures, equipment spreads, manpower requirements, and other en-

Jan 1, 1984

By M. C. Flemings, F. R. Mollard

Two-phase Pb-Sn alloys, ranging in compositiotz from 12 to 26 at. pct Pb, were unidirectionally solidified in a convection-fvee system, with thermal gradients in the liquid of up to 480°C per cm. Plane front solidification Loas achieved in all alloys at sufficiently steep gradient and slow growth rate. Conditions causing breakdown of the interface to a cellular or dendritic structure were roughly as predicted by a sinlple constitutional supercooling criterion. Structures of alloys of near-eutectic composition, solidified with plane front, exhibited a lamellar structure; the alloys furthest from the eutectic exhibited a rod-like morphology. Assumptions used in a previous paper for calculations of solute redistribution in two-phase plane front growth are shown to be reasonable for Pb-Sn alloys. Results of calculations are in good agveement with experiment. These show that variations in growth rate during solidification of the composite produce marked changes in average composition of the solid. IN a previous paper, Part I,&apos; conditions necessary for plane front solidification of two-phase alloys were discussed and calculations given on solute redistribution in this type of solidification. This paper, Part 11, describes experiments on Pb-Sn alloys, designed to check the assumptions of the analyses presented, and to demonstrate their applicability to a given alloy system (Pb-Sn). APPARATUS AND PROCEDURE General. A vertical crystal growing unit was built for the study as described below, and "normal solidification" employed throughout (i.e., the ingot was completely melted except for a portion near the bottom end and then solidification initiated). The furnace was designed to permit achieving very low interface velocities, and steep gradients, in essential absence of convection; it is sketched in Figs. 1 and 2. Simple heat flow considerations indicated choice of a small-diameter specimen (ingot) to achieve high thermal gradients; ingot size chosen was 0.3 cm in diam. The ingots were held inside silica tubes 0.06 cm wall thickness. The requirement for an essentially convection-free system was met by use of the vertical furnace with the heat source over the heat sink, as well as by use of the small diameter ingots. In addition, by selection of tin-rich Pb-Sn alloys, the diffusion boundary layer (lead-rich) was denser than the bulk liquid and would not cause convection. The only apparent driving force for convection in this system was the small transverse temperature gradient resulting from heat flow into the samples from the furnace. Such convection must have been small, however, since 1) no temperature fluctuations in the melt were noted in the recordings, which would have indicated turbulent convection, and 2) experimental results obtained and described below could not have been achieved in presence of significant convection. Ingot Preparation. Pb-Sn alloys ranging from 12 to 26 at. pct Pb were prepared from high-purity lead and tin (99.9999 pct pure metal). Each alloy was prepared by first melting the pure metals in the proper ratio in air, in a Pyrex container. The melt was then stirred thoroughly with a graphite rod and cast into a preheated graphite mold. Ingots were then prepared from these castings for use in the actual experiments; each ingot consisted of a rod of alloy, 15 cm long in a 25-cm-long transparent fused-silica tube, 0.3 cm ID and 0.06 cm wall thickness. One chromel-alumel thermocouple, made with 0.004-in.-diam wire and protected by a two-hole alumina tube, was inserted into each ingot. The 1.5 cm of the thermocouple nearest the bead were protruding from the alumina tube and were coated with a very thin layer of boron nitride paste which provided electrical insulation while allowing good heat conduction. The electrically welded junction size was about that of each wire and the cross section of the two wires represented about 0.3 pct of the sample cross section. Including the coating, the thermocouple cross section still represented less than 0.5 pct of the ingot cross

Jan 1, 1968

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.&apos;a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.&apos; However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.&apos; They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan&apos;gin&apos; using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By C. O. Rison

HIGH explosives, particularly nitroglycerin, have been used in torpedoes for the purpose of shooting oil and gas wells for more than 60 years. The early history of the oil industry in Pennsylvania is not clear as to who actually torpedoed the first well, although in 1865 the Roberts Torpedo Co. procured a patent covering the process. Gunpowder was first used, although nitroglycerin was substituted shortly afterwards. Wells are shot for the purpose of increasing the flow of oil and gas A shot-hole in the producing horizon, with its contributory fissures and fractures, increases the area of and stimulates drainage into the hole. The shot-hole also acts as a collecting basin from which the oil is pumped. As a rule, hard or close-grained sands or limes are shot, other more or less porous and soft formations usually do not require shooting. and might be injured by blasting. Shooting is also resorted to in mechanical trouble such as straightening crooked holes, sidetracking pipe or tools, and for severing frozen strings of casing or drill pipe. Explosives arc also used sometimes to extinguish oil or gas-well fires although that work, which involves unusual conditions and methods, does not properly come within the classification of oil-well shooting. Some Factors to Be Considered in Shooting Wells Although nitroglycerin has been used extensively for more than half a century in shooting oil and gas wells, there is still a great deal of uncertainty as to the proper method of shooting or the amount of explosive required to produce best results in a particular formation. The possibility of shooting unproductive or cavey formations above or below the productive horizons, shooting into lower water, destroying casing seats, and the splitting or collapsing of casing strings, are factors that require consideration. The engineering departments of a number of the larger oil companies are making a study of methods of shooting, and the amounts of liquid nitroglycerin or other explosives required in shooting various productive

Jan 1, 1929