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By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By R. Maddi, I. R. Kramer

The delay time for the initiation of slip was studied in single crystals of a brass, aluminum, and ß brass. A delay time for slip was found in ß brass when the specimens were tested below room temperature; however, one was not found for a brass or aluminum. A general theory for the existence of the brittle transition temperature is proposed. A LTHOUGH a considerable amount of effort has A been devoted to the study of the deformation and fracture of single crystals, the vast majority of the work was concerned with static tests or with tests carried out at relatively slow strain rates. The necessity for the study of a possible incubation time for slip becomes apparent when the various theories which have been postulated for the elucidation of the mechanism of slip are considered. The existence of an incubation period would strongly indicate that slip occurs by a process of nucleation and growth; whereas the absence of an incubation would present rather convincing evidence that slip occurs by a cataclysmic process. In addition to shedding light on the process of plastic deformation, an understanding of the early stages of plastic deformation may be helpful in finding an explanation for the brittle behavior of the body-centered metals under certain conditions. It is well known that these metals, such as iron, molybdenum, tungsten, ß brass, etc., will become brittle as the test temperature is lowered or the strain rate is increased. In spite of the fact that this subject has received considerable attention since the turn of the century, no adequate theory exists today which explains the phenomenon. In the ductile temperature range the metal breaks with a "fibrous" fracture after considerable slip has taken place. In the brittle temperature range the metal fails essentially by cleavage on the {loo) planes: however, some plastic flow is always present even in the most brittle fractures. It is possible, as will be explained later, to ascribe this brittle behavior to the length of the incubation time for slip. Clark and Wood,' using polycrystalline metals, showed that a delay time existed for the yield point in mild steels and that the delay time depended upon the applied stress. These authors stated that the delay time was observed only with those materials for which the stress-strain curve showed a definite yield point. In their work only the mild steel specimens exhibited a delay time at the yield point, while the other materials studied-type 302 stainless steel, SAE 4130 normalized steel, SAE 4130 quenched and tempered steel, 24s-T aluminum—did not show a delay time. These authors' in an extension of their work, found that as the temperature was lowered the delay time was increased. It is, then, the purpose of this investigation to measure or to set an upper limit on the delay time for plastic flow in single crystals of a brass, aluminum, and ß brass. The delay time will also be studied as a function of temperature. The incubation time may be measured by determining the length of time the specimen will support a stress without slip occurring when the stress is greater than the static critical resolved shear stress. In order to accomplish these measurements use was made of a pendulum which was so designed that a single crystal specimen could be placed at various positions along its length. When a pendulum is struck by another pendulum of the same length, an elastic wave is transmitted down the bar with the velocity of sound in the material and is reflected from the far end of the bar. The reflected wave then travels back and unloads the stress until it reaches the impacted end of the bar and the two pendulums separate. The length of time that the specimen is subjected to the stress is equal to the time it takes for the stress wave to travel twice the distance from the specimen to the end of the bar. The stress applied to the specimen is governed by the velocity of impact of the two pendulums. The stress at which the specimen first suffers plastic: deformation was determined in these experiments by examining the specimen under the microscope for the first appearance of slip lines and by measuring the residual strain after each impact. In these experiments the critical resolved shear stress was approached from the low stress side and no attempt was made to determine it exactly. To determine it exactly, it would have been necessary to find that stress at which slip would have just started. However, since the stresses were increased in rather small increments the critical stress is believed to be approached rather closely, as will be seen from the experimental results. The critical stress will be taken as the highest stress obtained before the onset of plastic deformation. The stresses

Jan 1, 1953

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By R. G. Garlick, H. B. Probst

Tungsten single-crystal specimens of various orientations were deformed in tension at room temperature. Slip traces indicated both (112)(111) and (110) (111) slip; however, about 10 pct plastic dejormation was required bejore these traces could he seen. Resolzled shear-stress considerations indicated that at least some of the particular systems observed were not those on which slip initiated hut were secondary systems. This is highly probable, considering the high plastic strains involved. Analysis of the stress data with respect to possible slip systems indicated that slip must have been initiated at stresses below the proportional-limit stresses measured. ALTHOUGH there is general agreement that slip deformation in fcc and hep metals takes place on the plane of close packing and in the direction of close packing, there is no such agreement for slip in bcc metals. It is generally agreed that the close-packed direction (111) is the slip direction, but investigations have led to conflicting descriptions of the slip plane. As Hoke and Maddin1 point out, there are essentially four points of view. 1) Deformation in bcc metals is composite shear on (112) and (110) planes or on nonparallel (110) planes, and any apparent slip on other planes can be accounted for completely by slip on these planes. Chen and Maddin have reported this to be the possible case for molybdenum." 2) Slip occurs in the (111) direction and is limited to {110), {112), and (123) planes (the three closest packed planes of the lattice). 3) Slip occurs in a (111) direction, but not necessarily on planes of close packing (banal slip). 4) Slip occurs in those directions and on those planes for which ß, the ratio of Burgers vector to interplanar spacing, is a minimum. The slip systems of the bcc metal tungsten have never been fully determined, although several investigators have reported pertinent results.3"7 The present work was initiated to determine the active slip systems in tungsten at room temperature, the critical resolved shear stresses associ- ated with these systems, and the orientation dependency of operative systems. These features of tungsten deformation at room temperature have never been reported in the literature. The authors find this somewhat surprising, particularly in view of the availability of tungsten single crystals since the advent of electron-beam zone-melting techniques and the widespread interest in refractory metals. It would seem apparent that such work has been attempted but the results have not been reported, possibly due to the conflict with deformation theory. The results of the present work conflict with any straightforward description of deformation based on the proposed explanations of slip in bcc metals. Although these conflicts have not been resolved, a presentation of the problem seems in order and should be of value to others working in this field. MATERIALS AND PROCEDURE Single-crystal tungsten rods of 1/8-in. diameter were grown from undoped commercial rod by one-pass electron-beam zone melting in apparatus previously described by witzke.8 Representative analyses of the rod before and after melting are given in Table I. There was no detectable zoning of impurities during melting. Buttonhead tensile specimens, as shown in Fig. 1, were machined from single crystals. Two flats 90 deg apart were ground in the gage length of each specimen. These flat surfaces facilitated the analysis of slip traces. No attempt was made to position these flats with respect to the crystal orientation. The worked surface layer of the machined specimens was removed by electrolytic polishing in a NaOH solution. Tensile-axis orientations were determined by standard Laue back-reflection techniques. The sharpness of the Laue spots indicated that the crystals were free of strain.

Jan 1, 1964

By J. C. Williams, M. J. Blackburn

MANY aspects of the formation of the metastable w phase in titanium-transition metal alloys have been described in several recent papers.1-4 These papers have reviewed earlier work on the w phase and have further defined most of the important features related to the formation of this phase, e.g-., its crystal structure, composition, and morphology. There are, however, several important points regarding formation of the w phase in titanium alloys which have been described in less detail. Two of these are the relationship between lattice misfit and w phase morphology and the influence of lattice misfit on the mode of formation of the equilibrium a phase. In this communi- cation we will present transmission electron microscopy results relevant to these two points. The alloys used in this study were prepared by non-consumable electrode arc melting, each 30-g button being remelted a minimum of twelve times. The alloy compositions we have studied are listed in Table I. Thin foils were prepared using standard techniques described elsewhere. Two distinct c' phase morphologies have been reported in earlier papers. The phase is ellipsoidal in the Ti-Mo3 and Ti-Nbl system and cubical in the Ti-V3 system. Results of the present study show that the w phase is also cubical in Ti-Mn, Ti-Fe, and Ti-Cr alloys as illustrated in Fig. l(b) to (d). Fig. l(a) shows the ellipsoidal morphology in Ti-MO3 for comparison purposes. It was suggested in an earlier paper3 that the w phase morphology may be controlled by the lat-

Jan 1, 1970

By H. Buttner, F. H. Udin, J. Wulff

GRAIN boundaries, the interface between adjacent crystals differing only in respective orientation, have been the object of much experimental and moderate theoretical attention for many years. The earlier experimental work was primarily concerned with the effect that grain boundaries have on the physical behavior of metals, while the basic nature of the boundaries themselves drew only secondary attention. A complete turnabout has been witnessed in more recent years, however, as researchers are now undertaking investigations bearing as directly as possible on the character and physical properties of the grain boundary. Quite comprehensive reviews of the past literature on the subject of grain boundaries have been reported on numerous occasions by various authors, and together these references represent a thorough coverage.'-? It becomes evident in these reviews and other papers"" that the properties of grain boundaries can be explained by regarding a grain boundary as a crystalline region of transition between two unmatched grains. Studies show that grain boundaries have a definite interfacial energy. By measuring the geometry about a point where three interfaces meet in equilibrium, the energy of any two boundaries can be measured with respect to the third. If the absolute interfacial energy of one boundary is known, the absolute energy of the other two boundaries can be calculated. This apparently holds true for any system of phases and interfaces.""25 Most studies have been carried out on solid-solid or liquid-solid systems, or systems of both. However, if about the point of intersection one phase is vapor and the other two are disoriented grains, then two interfaces are surfaces, and one is a grain boundary. Investigations leading to relative grain boundary energy for this particular system have been made by Fullman,23 Greenough and King," and Bailey and Watkins." Herring" treats the system mathematically and arrives at an equation, which appears as Eq. 1, in a form consistent with the reference angles indicated in Fig. 1, ( d?1 ?n = x sina + cosa ( ------- 2 ?2 Sinß da + C0Sß (d?2/d As the system of interfaces comes to equilibrium, a groove of angle appears at the intersection of the grain boundary with the surface, an effect first observed by Rosenhain and Humfrey." Eq. 1 is essentially a summation of the vertical components in Fig. 1 set equal to zero, where ?1 and ?2 are surface tension vectors lying along the side of the groove at point 0 in the groove root. The differential vectors represent the forces tending to rotate the surface into a position that will expose a crystal cleavage surface of lowest energy. Chalmers, King, and Shuttleworth- simplify Eq. 1 by assuming the differential vectors equal to zero, ?1 = ?2= ?Surface and arrive at the following equation: ?B = 2?s cos [2] Greenough and King24 use Eq. 2 for determining the grain boundary energy of silver using prepared bi-crystals of known orientation. Bailey and Watkins25 have done the same for copper, as did Chalmers and others on lead. These authors report the grain boundary values as ratios relative to the surface energy. In the above work, the orientation of grains forming the grain boundary in all cases was controlled so

Jan 1, 1954

By David White

IN these days, when detailed investigations of stratigraphy, structure, and sand conditions so frequently result in the discovery of new oil fields, and applause from oil companies and the public, geologists do well to walk humbly, and punctiliously to admit that the geologic principles controlling the distribution of oil and gas have as yet been discovered only in part, and that what remains yet to be learned is probably vastly more than what is already known. The few experiments already at-tempted have been fragmentary, and somewhat desultory, and however positive each of us may be with respect to certain theoretical conclusions, many of the fundamental questions as to the origin and mode of occurrence of petroleum are subject to radical disagreement. Of the chemical changes attending the generation of petroleum from organic matter, little is actually known. Most of the postulated formulas are liable to be misleading, through ignorance of essential factors. Open-mindedness is therefore a prime essential at the present stage of our science. Nevertheless, adopting the hypothesis that oil originates in some manner fundamentally connected with the organic theory, and in possible departure from such open-mindedness, the writer will pay no attention to the so-called inorganic theory, since every attempt to apply this theory to the study of old oil fields, or to the discovery of new ones, affords cumulative evidence of its inadequacy. In this paper, some of the factors affecting the occurrence of petroleum that the writer believes worthy of consideration by the prospector for oil in any new region will be discussed. Some of these, which are less generally understood, will be considered somewhat in detail. Other points, the significance of which cannot now be determined, require more field study, and for that reason are here brought to the attention of the field geologist. On the other hand, certain theoretical points which do not bear especially on the oil possibilities of a new region will be given little

Jan 2, 1920

By J. H. Hollomon, L. D. Jaffe, M. R. Norton

In the practical heat-treatment of steel the decomposition of austenite usually occurs during cooling rather than at constant temperature. Nevertheless, the course of this decomposition has generally been studied only isothermally. Isothermal studies are not only simpler experimentally, but have the great theoretical advantage that one of the variables, temperature, is constant. It is the purpose of this paper to outline the principles that govern the relations between isothermal and anisothermalt‡ decomposition of austenite, to present and systematize the available experimental information, and to indicate the gaps in the existing knowledge. Some of the experimental information is the result of new work.§ Most of it is derived from scattered data in the literature. Many of these data were obtained incidentally in the course of research on other subjects and their significance has not been pointed out and perhaps not understood. It is hoped that this paper will aid future planning of more extensive research on anisothermal decomposition. Method In order to study the relations between isothermal and anisothermal decomposition, it appears fruitful to view anisothermal decomposition as taking place at a series of constant temperatures1 (except for the martensite reaction, which does not occur isothermally to an appreciable extent). When the time the steel is at each temperature is finite, the over-all amount of the reaction is considered to be the sum of the amounts occurring at each of the successive temperatures. During continuous cooling or heating, the time the steel is at each temperature and the difference between successive temperatures can be considered to approach zero. The over-all amount of transformation will then be given by integration over the range of temperatures involved. This point of view is advantageous in that it considers anisothermal transformation to be a series of isothermal transformations. The problem thus becomes one of determining the effect of partial decomposition at any given temperature upon subsequent decomposition at another temperature. Single Anisothermal Reaction Consider a phase brought to a temperature at which it is unstable, held there until it has partially transformed, and then brought to another temperature at

Jan 1, 1947

By L. D. Jaffe, M. R. Norton, J. H. Hollomon

In the practical heat-treatment of steel the decomposition of austenite usually occurs during cooling rather than at constant temperature. Nevertheless, the course of this decomposition has generally been studied only isothermally. Isothermal studies are not only simpler experimentally, but have the great theoretical advantage that one of the variables, temperature, is constant. It is the purpose of this paper to outline the principles that govern the relations between isothermal and anisothermalt‡ decomposition of austenite, to present and systematize the available experimental information, and to indicate the gaps in the existing knowledge. Some of the experimental information is the result of new work.§ Most of it is derived from scattered data in the literature. Many of these data were obtained incidentally in the course of research on other subjects and their significance has not been pointed out and perhaps not understood. It is hoped that this paper will aid future planning of more extensive research on anisothermal decomposition. Method In order to study the relations between isothermal and anisothermal decomposition, it appears fruitful to view anisothermal decomposition as taking place at a series of constant temperatures1 (except for the martensite reaction, which does not occur isothermally to an appreciable extent). When the time the steel is at each temperature is finite, the over-all amount of the reaction is considered to be the sum of the amounts occurring at each of the successive temperatures. During continuous cooling or heating, the time the steel is at each temperature and the difference between successive temperatures can be considered to approach zero. The over-all amount of transformation will then be given by integration over the range of temperatures involved. This point of view is advantageous in that it considers anisothermal transformation to be a series of isothermal transformations. The problem thus becomes one of determining the effect of partial decomposition at any given temperature upon subsequent decomposition at another temperature. Single Anisothermal Reaction Consider a phase brought to a temperature at which it is unstable, held there until it has partially transformed, and then brought to another temperature at

Jan 1, 1947

By E. R. Borcherdt

RECENT years have seen great progress in drilling practices. The partial change from heavy drills and stopers to lightweight airleg machines has had great impact on stoping and drifting methods. The change was sparked, of course, when the Germans applied tungsten carbide to drill bits during World War II. This invention made it possible to drill nearly cylindrical blastholes, with a very mini- mum of drill steel changes, so that small fast-cutting bits* could be used without sacrifice of powder-loading density at the bottom of the hole. This is one of the few instances of increased efficiency through reduction in size. Usually the opposite is true. Application of these lightweight drills and small bits has lessened the vibratory stresses set up in the drill steel rod, and rod breakage has been greatly reduced. During the past several years phenomenal reduction in drill steel breakage has resulted from the use of carburized rods. These rods are now supplied by several manufacturers, with carburization of both the exterior and interior surfaces of the hollow drill steel. The rods are heat-treated over their entire length after the completion of bit connections, collars, or lugs (in the case of 7/8 Hex and round steel). This eliminates breakage from the usual metallurgical notch existing in conventional rods-there are instances of more than 2000 ft of drilling in hard ground before breakage. Steel rod failure results from fatigue checks, at right angles to the rod axis, progressing to a point where parting or breaking of the rod occurs. There are many of these checks in a used rod. Only the most advanced check causes the break, but with a small additional amount of drilling another check advances to the breakage point, and most of the value of reconditioning is lost. Since the development of carburized rods, the practice of discarding drill rods after the first break may be economically justified.

Jan 4, 1957

By Walter Miller

AFter a year's continued impact of war, the task of the petroleum-refining industry stands out clearly and looms up in larger aspect. This time it is not, as it was so largely in the first World War, simply a matter of increased quantity—more and more of the same petroleum products that had substantially been standard for years. In this era the emphasis is largely on newer and improved materials which had been produced, if at all, in comparatively insignificant quantities, and for which manufacturing equipment was not available on a large scale. At the beginning of 1942 four great product needs (besides a number of lesser ones) confronted the industry: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for aviation and Army equipment service, and petroleum chemicals for synthetic rubber manufacture. The difficulty in presenting a review of engineering progress in petroleum refining during 1942 is that there is so little one is free to say about so much which has been and is being accomplished. At the opening of 1942 the program was to increase the then existing capacity of 50,000 bbl. a day of aviation gasoline to over 150,000 bbl. daily by building new plants at an estimated installation cost of $150,000,000. Later in the year. after the announcement by President Roosevelt of a large increase in the program for war-plane building, additional contracts were made between the Reconstruction Finance Corporation and rehers to raise the capacity to 250,000 bbl. per day. The greatly increased scope of the war activities in all parts of the world, the obligation of the United States as the arsenal of the United Nations, and the greater importance and use of bomber, transport, and cargo planes will undoubtedly bring about plans and installations for a further increase in production of aviation gasoline over the present announced plan. In this connection, Jesse Jones, Reconstruction Finance Corporation Chairman, announced that as of Oct. 31 the R.F.C. had through its subsidiary Defense Plant Corporation entered into contracts for the construction, expansion, or equipping of 28 plants to increase 100-octane aviation gasoline production, but gave no data on 'capacity involved or completion dates. His list did not, of course, include a number of existing plants, and some installations being made by companies who are themselves financing the construction. Production from existing operating installations was materially increased in a number of instances as a result of pooling knowledge of improvements in operation and also by the exchange of Components going into 100-octane blend to enable greater quantities of aviation gasoline to be produced from the over-

Jan 1, 1943

By Walter Miller

AFter a year's continued impact of war, the task of the petroleum-refining industry stands out clearly and looms up in larger aspect. This time it is not, as it was so largely in the first World War, simply a matter of increased quantity—more and more of the same petroleum products that had substantially been standard for years. In this era the emphasis is largely on newer and improved materials which had been produced, if at all, in comparatively insignificant quantities, and for which manufacturing equipment was not available on a large scale. At the beginning of 1942 four great product needs (besides a number of lesser ones) confronted the industry: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for aviation and Army equipment service, and petroleum chemicals for synthetic rubber manufacture. The difficulty in presenting a review of engineering progress in petroleum refining during 1942 is that there is so little one is free to say about so much which has been and is being accomplished. At the opening of 1942 the program was to increase the then existing capacity of 50,000 bbl. a day of aviation gasoline to over 150,000 bbl. daily by building new plants at an estimated installation cost of $150,000,000. Later in the year. after the announcement by President Roosevelt of a large increase in the program for war-plane building, additional contracts were made between the Reconstruction Finance Corporation and rehers to raise the capacity to 250,000 bbl. per day. The greatly increased scope of the war activities in all parts of the world, the obligation of the United States as the arsenal of the United Nations, and the greater importance and use of bomber, transport, and cargo planes will undoubtedly bring about plans and installations for a further increase in production of aviation gasoline over the present announced plan. In this connection, Jesse Jones, Reconstruction Finance Corporation Chairman, announced that as of Oct. 31 the R.F.C. had through its subsidiary Defense Plant Corporation entered into contracts for the construction, expansion, or equipping of 28 plants to increase 100-octane aviation gasoline production, but gave no data on 'capacity involved or completion dates. His list did not, of course, include a number of existing plants, and some installations being made by companies who are themselves financing the construction. Production from existing operating installations was materially increased in a number of instances as a result of pooling knowledge of improvements in operation and also by the exchange of Components going into 100-octane blend to enable greater quantities of aviation gasoline to be produced from the over-

Jan 1, 1943

By John S. Bell, J. M. Shepherd

pressure difference of 280 psi measured initially on opposite sides of the major fault in the Hawkins Field led to pressure determinations in the Woodbine sand throughout the East Texas basin. Considering the large area, there is unusually good correlation between pressure losses and points of major withdrawals, these losses indicating that the basin pressure has been materially reduced by withdrawals, primarily from the East Texas Field and secondarily from the old fault-line fields of Limestone and Navarro counties, with the pressure loss varying inversely with the log of the distance from these two main areas of basin withdrawals to the measurement points. Apparently faults located throughout the basin serve as local blocks to continuous pressure gradients. INTRODUCTION The pressure anomalies found in the Hawkins Field, Wood County, Texas,' shortly after discovery have led to an area-wide investigation of the pressure distribution within the Woodbine sand of the East Texas basin. These pressures were obtained by drill-stem tests made for that sole purpose while drilling wildcat wells to deeper horizons. The Woodbine sand of Gulf Cretaceous Age is or has been productive of oil and gas in 42 different fields, with the 28 oil fields currently active having produced 118,000,000 bbl of oil during 1949. With one exception, producing energy for all Woodbine reservoirs has been from water drive provided predominantly by expansion of the tremendous volume of water contained in the Woodbine sand. This producing mechanism was recognized at an early date and was described mathematically by

Jan 1, 1951

By John S. Bell, J. M. Shepherd

pressure difference of 280 psi measured initially on opposite sides of the major fault in the Hawkins Field led to pressure determinations in the Woodbine sand throughout the East Texas basin. Considering the large area, there is unusually good correlation between pressure losses and points of major withdrawals, these losses indicating that the basin pressure has been materially reduced by withdrawals, primarily from the East Texas Field and secondarily from the old fault-line fields of Limestone and Navarro counties, with the pressure loss varying inversely with the log of the distance from these two main areas of basin withdrawals to the measurement points. Apparently faults located throughout the basin serve as local blocks to continuous pressure gradients. INTRODUCTION The pressure anomalies found in the Hawkins Field, Wood County, Texas,' shortly after discovery have led to an area-wide investigation of the pressure distribution within the Woodbine sand of the East Texas basin. These pressures were obtained by drill-stem tests made for that sole purpose while drilling wildcat wells to deeper horizons. The Woodbine sand of Gulf Cretaceous Age is or has been productive of oil and gas in 42 different fields, with the 28 oil fields currently active having produced 118,000,000 bbl of oil during 1949. With one exception, producing energy for all Woodbine reservoirs has been from water drive provided predominantly by expansion of the tremendous volume of water contained in the Woodbine sand. This producing mechanism was recognized at an early date and was described mathematically by

Jan 1, 1951

By A. Kaufmann, B. Cullity, G. Bitsianes

T0 determine the bulk of the phase diagram, techniques for melting, thermal analysis, heat treatment, metallography, and X-ray diffraction that have already been described were used.' It proved difficult to get definitive results for most of the alloy system because of the large number of compounds, their high melting points, and their extreme brittle-ness which made metallography difficult. The final phase diagram, essentially as shown in Fig. 1, was issued with considerable trepidation.' The phase relationships at the two ends of the system were defined with satisfactory accuracy. In the central region between U,Si, and USi, there was great uncertainty concerning the melting points and even the composition of the compounds. At the uranium end of the system, it is quite clear that a eutectic exists at about 985 °C and approximately 8 or 9 atomic pct Si. The a-to-8 transformation is not appreciably altered by silicon, but the 8-to-y transformation is raised to about 795°C. There is appreciable solid solubility in y-uranium, as demonstrated by the micrographs of Fig. 2. The occurrence of the E phase was not suspected at first, since the alloys as melted and furnace cooled gave no X-ray diffraction or thermal arrest indication of it. However, suitable metallography revealed a rim around each of the compound particles as shown in Fig. 3. Heat treatment above 600°C revealed that the rim was another phase which formed by peritectoid reaction between uranium and U,Si,. This reaction proceeds slowly and it is difficult to get it to go to completion. Consequently, there is some uncertainty concerning the exact composition of P and the exact peritectoid temperature. On the basis of various metallurgical studies, it was decided that the most probable composition for t was about 23 atomic pct Si. Metallographic examination shows the closest approach to a single phase at this composition. Likewise, density and hardness measurements of heat-treated alloys shown in Figs. 9 and 10 show a change in slope at 23 pct Si. This is revealed most clearly by plotting the difference in hardness or density between chill-cast and heat- treated alloys as shown in Fig. 4. Zachariasen2 was able to index the diffraction lines of P and to determine the arrangement of the atoms in the unit cell. He concluded that the composition must be US. However, it is felt that the metallurgical studies are reliable and that Zachariasen's X-ray work does not furnish positive proof that the P phase exists exactly at the stoichiometric composition U3Si. There are many instances in alloy systems where a phase does not occur at the composition dictated by the molecular structure. It is possible that the chemical analyses used in the present work were subject to some systematic error. This seems unlikely, however, since recent work in several laboratories seems to show excess compound at 25 atomic pct Si.

Jan 1, 1958

By F. N. Rhines

STUDIES upon the sintering of metal powders, in the solid state, have led to the proposal that the surface energy of the powder particles provides the driving force that causes points of contact between pairs of particles to grow into broad welds which isolate the residual vacant space into pores that tend to spheroidize and gradually to diminish in total volume.' Investigators differ with regard to the mechanism of the movement of the metal, under the influence of surface energy, to accomplish these changes. One school asserts that there is a mass movement of the metal, referred to as a "viscous flow," while the other school prefers to view the movement as a self diffusion process, wherein individual atoms are, transferred without disturbance of the basic pattern of the crystal lattice. Extensive experimental studies upon the sintering of copper, conducted recently by A. J. Shaler,2 have been in- terpreted by their author as support for the viscous flow mechanism of transport, the theory of which was developed originally by J. Frenkel.3 Duplicating a portion of this work with minor changes, G. C. Kuczynski4 is led to the alternate view, namely, that the initial stages of sintering, at least, proceed as a self-diffusion process. Both of these investigations were designed to deal with an isolated unit of sintering, i.e., with the shrinkage of a single pore, or with the growth of a single point weld. It remains to ascertain the behavior of a typical metal powder compact composed of a large number of particles of varying size and sintering to a body with a multiplicity of pores. The observation of density changes alone during sintering is not sufficient in such a case; it is essential to know how the internal geometry of the compact changes. This has been the object of the present investigation, the results of which are used to support the self-diffusion mechanism of sintering. The present studies consist in the measurement of the number of pores as a function of size and time at temperature during the sintering of a copper compact made from a commercial copper powder lightly pressed and sintered in several different atmospheres. A brief survey was made also of the change in shape of the pores, under the influence of the same variables. All of this was done by direct observation with the microscope. Densities were measured on the same sample. It is found that, while the compact is exhibiting an overall shrink-

Jan 1, 1951

Several of the current concepts of brittle fracture involve consideration of, the existence of defects or flaws. Griffith 1 observed that the tensile strength of brittle materials was several orders of magnitude less than might be expected from the calculated strength of the molecular bonds. He was able to show that the stress concentration at the tip of an elliptical crack is sufficient to raise the local stress level many fold. He therefore proposed that real materials do contain such stress risers in the form of minute cracks and that this accounts for the rather large difference between theoretical and actual strengths of brittle materials. The degree of stress magnification depends to a great extent upon the orientation of the crack with respect to the general stress system, and to the general geometry of the crack. It is but a small step to extend the theory to include flaws and defects of other sorts which, though they may be less tractable mathematically than cracks, may still function as stress risers in a real sense in real materials. Brace 2 proposed that the application of the Griffith theory to rock material could be tested in two ways: "(a) by finding the orientation of cracks from which macroscopic fractures have developed and (b) comparing failure strengths from tests at different conditions of loading." In 1963 the author and coworkers at the Bureau of Mines, Twin Cities Mining Research Center, working on a problem involving relationships between strength, sonic velocity, and microstructure "eveloped an experimental technique to examine several somewhat similar questions; namely. does the frequency of occurrence of actual or potential stress risers dictate the relative strength of the material as proposed by Weibull;4 can actual flaws or defects in the rock structure be identified and related to strength and perhaps other properties in accordance with Griffith's theory; and is the anisotropic strength and elastic behavior of certain rocks related to the preferred orientation of these actual or potential stress risers? The experimental approach developed to answer these questions appears equally applicable to the testing of Griffith's theory as proposed by Brace. Basically the approach consists of a series of point-load tensile tests followed by petrofabric examination of thin sections prepared from the specimens in order to identify and apply a quantitative measure to microstructural defects which may have contributed to the failure process. In the point-load test, tensile stresses are induced by a compressive load applied to the center of a disc-shaped specimen by means of two opposing hemispherical indentors. Failure generally occurs as a single fracture parallel to the axis of loading and bisecting the disc. Because of the geometrical symmetrical the induced tensile stresses are symmetrical about the loading axis

Jan 1, 1967

By J. L. Swedlow, M. L. Williams

Two standard techniques for assessing fracture initiatlon in sheet specimens involve measurements of 1) the applied load of fracture which, via linear fuacture mechanics, is used to find the fracture tough/less SC (or SIC), and 2) the velative displacement of fracture of the opposite free faces of the crack (COD). In the past, the quantitative association between these two parameters has not been determined in detail, owing to the mathematical difficulties of computing. the stress and strain fields in the combined elasto-plastic flow near the crack. Using a numerical technique Irecently developed and applied to a 7075- TO' aluminum plane stress specimern, the two parameters noted have been determined and associated quantitatirely. CONSIDERABLE effort has been expended in selecting a rigorous yet practical manner for predicting fracture. The usual point of departure is the modified Griffith criterion in which the mechanism of energy dissipation is reflected in Sc (or SIC), the parameter of "fracture toughness". Sc. differs from the surface energy used by Griffith in perfectly brittle fracture in that it includes the effect of plastic flow in the vicinity of the crack tip. Because plastic flow alters the stresses and displacements predicted from the usual linear theory of fracture mechanics, and because analysis of the nonlinear stress-strain field has presented great obstacles: only estimates of several pertinent quantities have heretofore been available. Nevertheless, two parameters have often been measured experimentally althougll usually just at the point of fracture. These are the energy release rate, or fracture toughness 9, (or I,), and the crack-opening displacement (COD). Such observations have been used in connection with frarture criteria and have been most helpful in design, although their application requires care with respect to changes in geometrical configuration from that upon which the criteria were based 1,2 Recently, however, a reasonably accurate and comprehensive method for analyzing the elasto-plastic flow has been devised and applied to plane stress specimens having arbitrary octahedral stress-strain curves.3 It thus becomes feasible to compute, albeit numerically, both the fracture toughness and crack opening as functions of the applied tensile loading on a typical specimen geometry. As a result, it is now possible to associate these two parameters quantitatively, and thereby to associate data obtained by one method with data pertaining to the other. ELASTIC ANALYSIS For the case of linear elasticity, it is relatively easy to deduce the connection between various measures of crack deformation. Using, for example, the singularity analysis, it is found that the leading term of the Airy stress function x f°r symmetrically applied loadings on an isotropic medium is

Jan 1, 1968