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By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

By W. C. Merrill, P. G. Nahin, A. Grenall, R. S. Crog

A progress report of an experimental investigation into the role of clay in reservoir performance is presented. The Paper gives some of the reasons for considering clay as a significant component and outlines the objectives of a broad field of stud) which it is intended to pursue. Descriptions of the analytical methods used are given; these include X-ray diffraction. elec tron miscroscopy, thin section petrography, infrared spec-troscopy, and cation exchange analysis. A suite of the more important clay minerals has been assembled and characterized l~y these methods for use as standards in core analysis. From the data obtained it appears that although no one method of analysis is diagnostic for all of the clay minerals the infrared technique shows considerable promise in this direction. For the present, one or more supplementary methods should be used to confirm the clay mineral identifications. The methods of analysis are applied to field cores taken from repesentative and widely differing strata especially as regards their susceptibility to damage by fresh water. well.; completed in the stevens and Gatchell zones in San Joaquin valley are I,articularly clear-cut examples of this behavior with stevens zone wells being more adversely affected by fresh water. cores from these zones have been studied and are discussed. It appears that differences in this behavior can be ascribed to differences in the nature of the contained clays. The value of the infrarecl spectra of the clay fractions in establishing the identity of the predominant clay minerals is given particular emphasis. INTRODUCTION It is a challenge to the technical resources of the petroleum industry that when the economic limit of production is reached, from 40 to 70 per cent of the oil in California reservoirs remains unproduced even by use of the best presently known methods of recovery. The magnitude of this abandoned volume of oil can be appreciated when it is considered that to 1950 in excess of 8 billion bbll has been produced from California reservoirs with estimated economically recoverable reserves in known fields and pools totaling nearly 4 billion bbl.24 If for every barrel of oil produced there is at least another barrel still in place, it is evident that the revenue obtained from the recovery of only a .few per cent of this volume would repay the cost of the required research manyfold. From well completion experience. production behavior, and a growing body of laboratory data it now appears certain that the mineral composition of a producing stratum has an important bearing on the productivity and ultimate yield. In addition to the organic component and water, the cores con,ist of gravel, sand. silt, and clay" in diverse variety of (a, composition and (b) texture. It is the composite effect of these two factors which is probably responsible in large measure for the way in which the oil flows to the well. The role of the clay and fine-size accessory minerals is not clear but there is a growing opinion, based on their physical and chemical properties, that it is a significant one. of particular importance are the prime facts: 1. The silt and clay fractions of the reservoir matrix possess the highest surface area per gram, and 2. The silt and especially the clay fractions are the most chemically reactive of the inorganic constituents present. Only within the last few years has the knowledge of clay mineralogy and the techniques of identifying the clay minerals reached such a stage as to enable reliable inquiry into the composition of argillaceous sediments.2,8,10,11,12,16,26 It is the purpox of this and succeeding papers to add to the fund of information on the role which these materials play in the production of petroleum from California formations by correlating their presence and associated properties with observed reservoir behavior. In the present paper attention is directed to their possible influence on damage by fresh water. OBJECTIVES The attack on this problem divides naturally into two broad phases: 1. Determination of the nature of the clays and their relationships to the other mineral components, and 2. Determination of the physico-chemical relationships between the clays and the interstitial fluids. In the work described in this paper the emphasis has been on phase 1, which stems logically from the necessity of identifying and understanding the materials to be dealt with in Phase 2. Based on the authors' present opinion that not all of the minerals which occur in oil-bearing formation are of equal importance in their effects on the flow and recovery of oil, it was decided to focus attention first upon the clay minerals content and then. later perhaps. work into the field of the normally larger size non-clay minerals and fractions. The

Jan 1, 1951

By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By K. E. Brown, F. W. Jessen

By utilizing an 8,000-ft experimental field well equipped with 10 gas-lift valves and 10 Maihak pressure recorders, gas-lift tests were conducted with port sizes ranging from 5/16 through I in. The well was equipped to provide accurate means of measuring surface pressures, temperatures, quantity of injection gas and fluid production. The tests were conducted in 2%-in. OD tubing, and the well was making 95 per cent water. A complete evaluation of gas-lift-valve port sizes shows the relationship of per cent recovery, gas-liquid ratios, minimum pressure created at the operating valve and horsepower requirements for each port. The length of time necessary for the fluid in the tubing to reach equilib.rium conditions after each cycle was recorded. Fallback of fluid at depths of 477, 969, 1,685, 2,493 and 4,290 ft was noted. For each port size, pressure loads of 2.50, 300, 350, 400 and 450 psi were lifted with a valve operating at approximately 550 psi at 6,000 ft. Gas-liquid ratios for each load were varied from excess gas to a gas volume per cycle whereby the load failed to reach the surface. Numerous curves are presented in evaluating the accumulated dara. The results show a 1-in. port to be the most efficient under all conditions. The production of intermittent liquid slugs against different-sized surface chokes was evaluated. These tests were conducted from a 7/16-in. ported valve at 4,072 ft. Tests indicate that, when possible, a %-in. in diameter choke or larger should be used at the surface. In the past few years most of the advancement in gas-lift operations has been made in continuous-flow operations. Yet, it is estimated that at least 70 per cent of the wells on gas lift in the United States are of the intermittent type. Since the term "slug flow" is sometimes used in both intermittent- and continuous-flow operations, it would be well to distinguish between the two types of flow. Continuous-flow gas lift is defined as a method whereby the fluids are produced at a continuous rate at the surface. This generally requires a continuous injection of gas through a surface choke; however, various other control devices sometimes are installed to eliminate freezing, to shut-off gas during natural flow periods, etc. The actual flow of fluids in the tubing may be of the slug type (one of many flow patterns known to exist in continuous flow). Intermittent flow is defined as a method of gas lift whereby the liquid is produced in separate piston-type slugs. Perhaps this type of flow could best be thought of as a ballistic-type flow where the liquid leaves bottom as a piston, propelled by a slug of expanding gas. Gas generally is injected through some type of control at the surface at predetermined intervals. However, the valve may have characteristics whereby gas can be injected through a small choke and still result in a ballistic-type flow. The purpose of the experimental work was to evaluate the most efficient port size to be used on the operating valve for the ballistic type of lift and, in addition, to establish the importance of utilizing a surface choke large enough to allow slugs to be produced without detrimental effects. This work is part of a compre- hensive study of both intermittent-and continuous-flow gas lift, representing a joint project conducted by the Ohio Oil Co., the Sun Oil Co., Otis Engineering Corp, and The U. of Texas. The problem of evaluating port sizes has been given little previous attention. Some work undoubtedly has been done which has not been published to date. Some tests were conducted when the wireline, mechanically-opened valve (Nixon) first came on the market. This valve was capable of utilizing full tubing area as its port size. It is known that this was a very efficient valve, but to the authors' knowledge the results of tests have never been published. EXPERIMENTAL EQUIPMENT These tests were conducted on an actual field well, the Ohio-Sun Unit Well No. 2-E, in the North Markham-North Bay City field, Matagorda County, Tex. The well incorporated 23/8-in. OD tubing and produced 95 per cent water. Since the running of equipment was to be quite elaborate and expensive, a well was selected in which both intermittent- and continuous-flow tests could be conducted. This particular well was capable of producing in excess of 1,000 B/D of liquid (95 per cent salt water), yet with a 3/64-in. in diameter bottom-hole choke, production was controlled to 82 B/D. Most of the intermittent tests were conducted at this low rate. Figs. 1 and 2 show all the surface and down-hole equipment. As can be seen, every attempt was made to insure that ample equipment was available for reliable testing procedures. Fig. 1 shows the surface testing equipment. The input gas was controlled first by a regulator, then

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By J. Chipman

There is no better way of paying tribute to the memory of a scientist than by developing and carrying forward those ideas which he has contributed to science and which are for us the very essence of his immortality. For a lecturer who has not had the great privilege of stdying under Professor Howe or 'ven of knowing him in person, these ideas must be transmitted through the printed word. It is our great good fortune that Professor Howe left to us a rich heritage of publication, not only in his classic monograph on the "Metallography of Steel and Cast Iron" but in a wealth of earlier hooks and papers in the transactions of this Institute arid of other scientific and engineering bodies. An outstanding characteristic of this published record is the great breadth of interest and of vision which it portrays. His was riot a narrow specialization in only the scientific aspects of ferrous metallographg. On the contra1y many of his important contributions had to do with a far broader field of metallurgicial endeavor. He insisted that his students be well grounded in 1 he fundamentals underlying the whole field and not led into the narrow groove of specific applications. Among his first major publications we find papers on copper smelting, extraction of nickel, the efficiency of fans and blowers, thermic curves of blast furnaces, the cost, of coke, and the manufacture of steel. These are the papers of a metalhurgical engineer and it was among engineers that Henry Marion Howe made his early and well-merited reputation. These early engineering contributions display very clearly the strongly sctientific inclination of their author. The classic work on "The Metallurgy of Steel" published in 1890 contains a thorough and critical discussion of all that was known at the time concerning the alloys of iron and of what we would now call the physical metallurgy of steel. In addition it describes steel-making processes in use and some that had become obsolete, and points out in critical fashion the reasons for success and failure. Steel mill design and layout were included as well as some pertinent discussion of refractories. The book is indeed an embodiment of one of Howe's outstanding characteristics—breadth. It is both the science and the engineering of steel production as known in that day. One of Howe's earliest technical papers was entitled "What is Steel?" That was nearly seventy-five years ago when many new processes and new kinds of steel were being developed. The time was ripe for such a question and the answers which Howe was able to give were helpful in understanding the phenomena of heat treatment. Twenty-five years ago Professor Sauveur repeated the question as the title of the first Henry Marion Howe Memorial Lecture. It seemed to him that this question, "What is Steel?," had served as Howe's motto throughout the remainder of his life. Today I shall present for your consideration a question of another sort: "What is Sletallurgy?" Perhaps it is not too much to hope that in the answer we may obtain a clearer and possibly broader view of the nature of our science and our profession. The time is ripe for giving careful consideration to what we mean by metallurgy. If our Metals Branch is to become in fact an American institute of Metallurgical Engineers, it is essential that we understand what is meant by metallurgical engineering. I am convinced that the best interests of the profession have not been served by a narrow interpretation of these terms. We must now place emphasis on the breadth of metallurgy as a science and as an engineering profession. With its usual brevity and wit. Webster's dictionary definesmetallurgy as "the science and art of extracting metals from their ores, refining them and preparing them for use." I shall riot assume that the words "science" and "art" and "metal" are so well understood as to require no defining but others among our contemporaries are better qualified than either your lecturer or the dictionary to present the broad meanings of these terms. When we say that metallurgy is among the oldest of the arts we are not classing it with painting or sculpture or music but rather with the making of tools or weapons or the building of bridges or chariots or cathedrals. In short we are saying that metallurgy is among the oldest of the engineering professions. The question " What is metallurg ? " has been one of rather more than ordinary concern to those of us who have the task of developing a curriculum for the education of students in this field. This development has been going on in a number of universities over a period of some years. but there seems to be as yet no unanimity as to what such a curriculum should contain. I believe there is fairly complete agreement that it must be founded upon sound

Jan 1, 1950

By J. W. Snavely

WITH all the advantages of handling bulk materials by means of belt conveyor also go some problems, one of the most persistent being that of cleaning. When sticky materials are being carried; the build-up of material on the return idler rolls results in difficulty of belt training. Much attention has been given to the problem of cleaning conveyor belts, and a great variety of cleaning devices have been developed. Even the best involve troublesome maintenance, and none can completely remove the fine particles imbedded in the belt cover, which cause rapid wear of the return idler rolls, and at the same time, of the belt cover as well. One of the major rubber companies has been promoting a two-way belt system, in which the conveyor belt is given two successive 90" twists at each end to enable it to carry material in both directions simultaneously. For many years the flat belt transmission industry has installed quarter-turn and half-turn twists in countless numbers of instances. While quarter-turn and half-turn twists in transmission belts is a familiar application, the 180" twist apparently has never been previously attempted with a conveyor belt. About a year ago, two officials of the National Iron Co. of Duluth, Lester and Lewis Erickson, proposed twisting the return run of a conveyor belt on an installation that they were designing for one of the major iron ore producers. Since then the soundness of the idea has been demonstrated, both in theory and by practical test, with the result that the installation of two conveyor belts involving the twisting of the return run is now under way. These two installations are designed to have the return run of the conveyor belt twisted 180" as it leaves the snub pulley at the head drive. The clean underside of the belt is thus placed against the idlers on the return run as well as on the carrying run. Just before it enters the tail pulley, the belt will be twisted an additional 180°, restoring it to its normal position. Because this twisting of the return run of a conveyor belt is a radical departure from accepted practice, an elaborate and extensive test was conducted early in 1950 to demonstrate that this twisting of the return run could be done successfully, also to establish application data for accomplishing this twisting, and to determine if any special equipment would be required. In studying this concept of twisting the return run of a conveyor belt, a number of problems need to be solved, primarily the ones brought about by deliberately introducing an unequal distribution of stress across the conveyor belt and controlling that maldistribution of stress, while confining it to the return run portion. The tension conditions existing in the return run of a conveyor belt are clear to all designers. First, the return run carries the initial or slack side tension of the conveyor belt, the tension that must be supplied to the return run to provide proper frictional contact between the belt and the driving pulley so that the necessary power can be transmitted from the driving pulley to the belt without slippage. This slack side tension is supplied to the belt by means of takeups, either of the gravity type, which can be vertical or horizontal, or by means of the screw type. With inclined or declined belt conveyors the slope tension also must be considered, which is the tension imposed by the weight of the belt hanging from the top pulley. This slope tension frequently can furnish part or even all of the initial tension required. The maximum value of the slope tension will be at the top pulley, and it decreases in direct proportion to the length. In addition to the foregoing, it frequently is desirable to impose arbitrarily additional slack side tension to provide sufficient tension at the loading point at the tail, so that the belt will adequately support its load between the carrying idlers. Design Conditions for Twisting A number of design conditions exist, which must be satisfied successfully to accomplish the twisting of the return run without exceeding normal working limits in any portion of the conveyor belt. It is obvious that the belt edge, in its relation to the center of the belt, must stretch in making a twist, because as the twist is accomplished, the belt edge travels through a longer path than does the center of the belt. It is further obvious that if the edge of the belt is stretched, a redistribution of stress in the belt is required to allow this edge stretching. Moreover, this stress will be unequal across the width of the belt, having a maximum value at the edges, with a minimum value at the- center of the belt. With correct initial tension in the return run of a conveyor belt, the existing slack side tension will be unequally distributed when a twist is introduced. A condition then exists in which the edge stresses,

Jan 1, 1952

Jan 1, 1924

By J. Chipman, G. G. Hatch

T. ROSENQVIST*—It is a pleasure to see the excellent way in which the experimental part of this work has been handled. There seems to be little doubt that the distribution data obtained corresponds most closely to thermodynamic equilibrium under the prevailing reducing conditions, namely equilibrium with graphite and one atmosphere CO pressure. The desulphurization curves in Fig 10 show the same general feature as the curves given by Holbrook and Joseph, but the distribution ratios are from 20 to 40 times greater—undoubtedly due to a closer approach to true equilibrium. In the theoretical discussion, the authors calculate a theoretical distribution (S) ration -jg-. which they find to be about 50 times greater than the experimental. The deviation is so great that the basis for their calculation needs a more thorough examination. The authors base their thermodynamic calculation on free energy expressions where diluted solutions of FeS and CaS are used as standard states. (The activity coefficient in diluted solutions is taken to equal unity.) Such a standard state will change when the nature of the solvent is changed. Taking the free energy of the reaction [FeS] ? (FeS), Eq 2, which is derived from the distribution of sulphur between an iron and a FeO-melt, it is very unlikely that the free energy of this reaction will be the same for a distribution between pig iron and a calcium silicate slag. Therefore a more fundamental basis for the thermodyuamic calculations seems needed, where all thermodynamic equations are referred to unambiguously defined standard states. The most natural standard states for CaO and CaS are the pure solid substances at the same temperature. As standard state for sulphur in iron, pure liquid FeS can be used. This rules out Eq 2 [FeS] ;=s (FeS) because ?F° = 0. The standard equation will then be: FeS, + CaO6 + Cgraph ?Fei + CaS8 + CO. vFo1773 = 25,000 cal It would be more universal and also simpler to refer the escaping tendency of sulphur in liquid iron to the corresponding H2S/H2 ratio which can readily be determined experimentally. As standard state a gas mixture H2S/H2 = 1/1 can be used. (This corresponds at the temperature of liquid iron closely to one atmosphere S2 vapor.) Thus the standard equation for the sulphur reaction can be formulated as follows: H2S0 + CaO3 + Cgraph ?H2o + CaS8 + COg The standard free energy of this reaction has been calculated from the best available data to AF°m3 = —35,000 cal. This gives for the equilibrium constant at 1500°C Now, the solubility of CaS in blast furnace slags has been determined by McCafferey and Oesterle* and corresponds at 1500°C to about 10 pet S (varying somewhat with the composition of the slag.) If the activity of CaS is assumed linear between 0-10 pet as curve 1, (see Fig 11), then acaO = 0.1 (S); (S) being wt. pet sulphur in the slag. For a diluted solution of sulphur in an iron melt saturated with carbon, the ratio H2S/H2 is, according to Kitchener, Bockris and Liberman,f about 0.01 [S], [S] being wt. pet sulphur in iron. Substituting these values in the expression for Kp we find The value 2.103 is only 4 times greater than the experimental coefficient found by Hatch and Chipman, but the value is very sensitive to a small error in AF°. A better agreement with the experimental distribution coefficient can be obtained if one assumes the activity of CaS to run like curve 2 (Fig 11). This (S) will give a lower theoretical W, value, a value which varies with (S) exactly as Hatch and Chipman learned. Such a shape of the activity curve, which corresponds to a positive deviation from Raoult's law, is actually to be expected from the fact that liquid silicate and sulphide phases usually show incomplete miscibility. A closer agreement between experimental and theoretical data can not be expected before we have more complete data for the individual activities of CaS and CaO in the slag. The activities acaS and Ocao referred to the solid phases as standard states, are exact defined quantities contrary to the somewhat undefined expression "free lime," and they are independent of any theory for the constitution of liquid slag. J. CHIPMAN (authors' reply)—The authors wish to thank Mr. Rosenqvist for his very interesting and useful thermodynamic addition. Curve 2 of his figure offers the needed basis for explaining the increase in the ratio (S)/[S] with increasing sulphur content. Attention is called to an error in the printed paper: Fig 2 and 3 are reversed. M. TENENBAUM*—In the figures showing the relationship between excess base and sulphur distribution (Fig 6, 7 and 9) the slope of the curve tapers off in the negative basicity range. Somewhat the same thing is observed with open hearth slags. In that case, the fact that some sulphur distribution between slag and metal is obtained with negative basicity is interpreted as indicating some dissociation of the lime silicate compounds whose existence in oxidizing basic slags has been used to explain various observed phenomena with regard to other slag-metal reactions. In the case of the blast furnace slags, the reduced slope of the sulphur distribution curve with decreasing excess base is attributed to the amphoteric effect of alumina. Has the possibility of other explanations been investigated ?

Jan 1, 1950

By F. J. Plecity, J. T. Michalak, W. C. Leslie

Isothermal recrystallization and grain growth in zone- and vacuum-melted irons and Fe-Mn alloys, up to 0.60 pct Mn, were studied in the range 480° to 650° C, after 60 pct cold reduction. In initial stages, rate of grain growth and rate of recrystallization of iron decrease with time. The recrystallization is typical of a growth-controlled process, and rate of growth is determined by the extent of recovery. Mn decreases rates of growth and of recrystallizatzon. The recrystallization process changes at about 0.30 pct Mn and nucleation may become time-depetzdet~t. In recent years, considerable effort has been expended in determining the effects of solute elements on recrystallization and boundary migration in fcc metals. The results have indicated that the effects produced by single solute additions are dependent upon both the element added and its concentration.'-' In contrast, there have been very few attempts to determine the characteristics of recrystallization and boundary migration in high-purity bcc metals, especially after heavy deformation, and the effects thereon of single solute elements.9-11 This study was undertaken to determine the recrystallization characteristics of various "high-purity" irons and the effects of manganese additions at two levels of base purity. It was hoped that the information obtained would improve our understanding of the recrystallization of pure metals and aid in formulating a theory for the effect of solute elements. The interest was not entirely academic, for the annealing of low-carbon steels, which is of very great commercial importance, is but poorly understood. MATERIALS The compositions of the irons and iron-manganese alloys used are listed in Table I. The zone-melted iron and Fe-Mn alloys were made by Battelle Memorial Institute. Iron S-1 was arc-melted in a water-cooled steel mold in an argon atmosphere. The ingot was forged into a bar, then given two horizontal zone-refining passes in an alumina boat. Iron V-4 was treated in a similar manner, but was not zone-refined. The iron for the zone-melted Fe-Mn alloys was induction melted in vacuum in MgO crucibles and cast into alumina molds. The ingots were forged into bars, machined to shape, and a groove milled down one side of each. The best available electrolytic Mn was placed in the grooves, and the bars were zone melted. The vacuum-melted Fe-Mn alloys were induction melted in this Laboratory in MgO crucibles and poured into cast-iron molds. Iron V-5 was purchased from National Research Corp. in the form of a small vacuum-cast ingot. The low-carbon steel was made by induction melting in air at the U.S. Steel Corp. Applied Research Laboratory. The history of the materials prior to the final cold reduction differed; these details are given in the Appendix. The penultimate grain size of the principal materials was kept in the range ASTM 2 to 4, except for the low-carbon steel. PROCEDURES The cold work prior to the final recrystallization anneal was kept constant at 60 pct. It is known that rolling procedure can influence the kinetics of recrystallization of ironI2; therefore, all specimens were rolled in one direction only, between clean,

Jan 1, 1962

By Stephen B. Castor

The rare earth elements (REE) which include the 15 lanthanide elements (Z = 57 through 71) and yttrium (Z = 39) are so called because the elements were originally isolated in the late 18th and early 19th centuries as oxides from rare minerals. Most REE are not as uncommon in nature as the name implies. Cerium, the most abundant REE (Table 1), comprises more of the earth's crust than copper or lead. Many REE are more common than tin and molyb¬denum, and all but promethium are more common than silver or mercury (Taylor, 1964). Promethium (Z = 61) is best known as an artificial element, but has been reported in very minute quantities in natural materials. Lanthanide elements with low atomic numbers are generally more abundant in the earth's crust than those with high atomic numbers. In addition, lanthanide elements with even atomic numbers are two to seven times more abundant than adjacent lan¬thanides (Table 1) with odd atomic numbers. The lanthanide elements traditionally have been divided into two groups: the light rare earths (LREE), lanthanum through eu¬ropium (Z = 57 through 63); and the heavy rare earths (HREE), gadolinium through lutetium (Z = 64 through 71). Although yttrium is the lightest REE, it is usually grouped with the HREE to which it is chemically and physically similar. The REE are lithophile elements (elements enriched in the earth's crust) that invariably occur together naturally because all are trivalent (except for Ce+4 and Eu+2 in some environments) and have similar ionic radii. Increase in atomic number in the lanthanide group is accompanied by addition of electrons to an inner level rather than the outer shell. Consequently, there is no change in valence with change in atomic number, and the lanthanide elements all fall into the same cell of the periodic table. The chemical and physical differences that do exist within the REE group are caused by small differences in ionic radius, and generally result in segre¬gation of REE into deposits enriched in either light lanthanides or heavy lanthanides plus yttrium. The relative abundance of individual lanthanide elements has been found useful in the modelling of rock-forming processes. Comparisons are generally made using a logarithmic plot of lanthanide abundances normalized to abundances in chondritic (stony) meteorites. The use of this method eliminates the abundance vari¬ation between lanthanides of odd and even atomic number, and allows determination of the extent of fractionation between the lanthanides because such fractionation is not considered to have taken place during chondrite formation. The method is also useful because chondrites are thought to be compositionally similar to the original earth's mantle. Europium anomalies (positive or negative departures of europium from chondrite-normalized plots) have been found to be particularly effective for petrogenetic modelling. REE were originally produced in minor amounts from small deposits in granite pegmatite, the geologic environment in which they were discovered. During the second half of the 19th century and the first half of the 20th century, REE came mainly from placer deposits. With the exception of the most abundant lanthanide el¬ements (cerium, lanthanum, and neodymium), individual REE were not commercially available until the 1940s. Since 1965, most of the world's REE have come from two hard rock deposits: Mountain Pass, United States, and Bayan Obo, China. GEOGRAPHIC DISTRIBUTION OF REE DEPOSITS More than 70% of the world's REE raw materials come from three countries: China, the United States, and Australia. China emerged as a major producer of REE raw materials during the 1980s, while Australian and United States market share decreased dramatically (Fig. 1). Table 2 gives recent annual production figures along with estimated reserves by country, and Fig. 2 shows loca¬tions of significant REE mining. MINERALS THAT CONTAIN REE Although REE comprise significant amounts of many minerals, almost all production has come from less than ten minerals. Table 3 lists minerals that have yielded REE commercially or have po¬tential for production in the future. Extraction from a potentially economic REE resource is strongly dependant on its REE miner¬alogy. Minerals that are easily broken down, such as bastnasite, are more desirable than those that are difficult to dissociate, such as allanite. In general, producing deposits contain REE-bearing min¬erals that are relatively easy to concentrate because of coarse grain size or other attributes. For more thorough discussions of REE¬bearing minerals see Mariano (1989a) and Cesbron (1989).

Jan 1, 1994

By H. D. Hodges, J. K. Godbey

In order to better understand the fracturing process, bottom-hole pressures were measured during a number of typical fracturing operations. A recently developed system was used that allows simultaneous surface recording of both the bottom-hole and wellhead pressures on the same chart. The results from six fracruring treatments are summarized on the basis of the pressure data obtained. Al-though no complete analysis is attempted, the value of accurate pressure measurements is emphasized. Important characteristics of the bottom-hole pressure record do not appear at the wellhead because of the damping effect of the fluid-filled column. In four of the six treatments described, the formations apparently fractured during the initial surge of pressure with only crude oil in the well. The properties of the fluids used during the treatments are given and the fluid friction losses are obtained directly from the pressure records. This technique is also shown to be adequate for determining when various fluids, used during the process, enter the formation. INTRODUCTION Hydraulic fracturing for the purpose of increasing well productivity is now accepted in many areas as a regular completion and workover practice. Numerous articles have appeared in the literature discussing the various techniques and theories of hydraulic fracturing'. In general, three basic types of formation fractures are recognized today. These are the horizontal fracture, the vertical fracture, and fractures along natural planes of weakness in the formation'. Any one or all three of these fracture types may be present in a fracturing operation. However, with only the wellhead pressure record as a guide, it is difficult at best to determine if the formation actually fractured, and is almost impossible to determine the type of fracture induced. These difficulties arise in part because the wellhead pressure record, especially when fracturing through tubing, does not accurately reflect the pressure variations occurring at the formation. Several factors contribute to this effect and preclude the possibility of using the wellhead pressure as a basis for accurately calculating the bottom-hole pressure. These factors are: 1. The compressibilities of the fluids which damp the pressure variations. 2. The changes in the densities of the fluids or apparent densities of the sand-laden fluids. 3. The flowing friction of the various fluids and mixtures, which is dependent on the flow rates and the condition of the tubing, casing, or wellbore. 4. The non-Newtonian characteristics of a sand-oil mixture and its dependence upon the fluid properties, the concentration of sand, and the mesh size used. 5. The unknown and variable temperatures throughout the fluid column. Because of these reasons it was determined that in order to obtain a more accurate knowledge of the nature of fracturing, the bottom-hole pressure must be measured along with the pressure at the surface during a fracturing treatment. Even with accurate pressure data, a reliable estimate of the nature of fracturing is still dependent upon knowledge of the tectonic conditions. However, the hydraulic pressure on the formation is basic to any approach to a complete analysis. In order to accomplish this objective a system was developed to record the wellhead and bottom-hole pressures simultaneously at the surface. By recording both pressures on a dual pen strip-chart recorder, it was possible to greatly expand the time scale so that rapid pressure variations would be faithfully recorded. By such simultaneous recording, time discrepancies inherent in separate records are eliminated, thus overcoming one of the most difficult problems associated with bottom-hole recording systems. This paper illustrates the results obtained by using this system during six typical fracturing operations. All of these tests were taken in wells that were treated through tubing. By a direct comparison of the wellhead and bottom-hole pressures, the importance of obtaining complete pressure information during a fracturing treatment is emphasized. THE INSTRUMENTATION AND PROCEDURES The bottom-hole pressure measuring instrument consisted of a pressure-sensing element, a telemetering section, and a lead-filled weight or sinker bar. The pressure-sensing element used was an isoelastic Amerada pressure-gauge element. By using an isoelastic element, no temperature compensation was necessary in the tests described, since the temperature was believed to be well below the maximum temperature limit of 270°F. The rotary output shaft of this helical Bourdon tube element was coupled to a precision miniature potentiometer. The rotation of the pressure-gauge shaft thus changed the resistance presented by the potentiometer

By F. C. Bond

SIZE of grinding media is one of the principal factors affecting efficiency and capacity of tumbling-type grinding mills. It is best determined for any particular installation by lengthy plant tests with carefully kept records. However, a method of calculating the proper sizes, based on correct theoretical principles and tested by experience, can be very helpful, both for new installations and for guiding existing operations. As a general principle, the proper size of the make-up grinding balls added to an operating mill is the size that will just break the largest feed particles. If the balls are too large the number of breaking contacts will be reduced and grinding capacity will suffer. Moreover, the amount of extreme fines produced by each contact will be increased, and size distribution of the ground product may be adversely affected. If the balls added are too small, grinding efficiency is decreased by wasted contacts that are too weak to break the particles nipped; these largest particles are gradually worn down in the mill by the progressive breakage of corners and edges. Ball rationing is the regular addition of make-up balls of more than one size. The largest balls added are aimed at the largest and hardest particles. However, the contacts are governed entirely by chance, and the probability of inefficient contacts of large balls with small particles, and of small balls with large particles, is as great as the desired contact of large balls with large particles. Ball rationing should be considered an adjunct or secondary modification of the principle of selecting the make-up ball size to break the largest particle present. Empirical Equation In 19521,2 the author presented the following emerical equation for the make-up ball size: B - ball, rod, or pebble diameter in inches. F = size in microns 80 pct of new feed passes. Wi - work index at the feed size F. Cs - percentage of mill critical speed. S — specific gravity of material being ground. D == mill diameter in feet inside liners. K - 200 for balls, 300 for rods, 100 for silica pebbles. Eq. 1 was derived by selecting the factors that apparently should influence make-up ball size selection and by considering plant experience with each factor. Even though Eq. 1 is completely empirical, it has been generally successful in selecting the proper size of make-up balls for specific operations. But an equation based on theoretical considerations should be used with more confidence and have wider application. The theoretical influence of each of the governing factors listed under Eq. 1 was accordingly considered in detail, as described below, and a theoretical equation for make-up ball sizes was derived. Derivation of Theoretical Equation Ball Size and Feed Size: The basis of this analysis is that the largest ball in a mill should be just sufficient to break the largest feed particle into several pieces, excluding occasional pieces of tramp oversize. In this article the size F which 80 pct passes is considered the criterion of the effective maximum particle feed size. The smallest dimension of the largest particles present controls their breaking strength. This dimension is approximately equal to F. As a starting point for the analysis it is assumed that a 1-in. steel ball will effectively grind material with 80 pct passing 1 mm, or with F- 1000µ or about 16 mesh. The breaking force exerted by a ball varies with its weight, or as the cube of its diameter R. The force in pounds per square inch required to break a particle varies as its cross-sectional area, or as its diameter squared. It follows that when a 1-in. ball breaks a 1-mm particle, a 2-in. ball will break a 4-mm particle, and a 3-in. ball a 9-mm particle. This is in accordance with practical experience, as well as being theoretically correct. Confirmation of this reasoning is supplied by the Third Theory of Comminution," which states that the work necessary to break a particle of diameter F varies as F. Since work equals force times distance, and the distance of deformation before breaka4e varies as F it follolvs that the breaking force should vary as F½ These relationships are expressed in Table I, with a 1-in. ball representing one unit of force and breaking a 1-mm particle. This establishes theoretically the general rule used in Eq. 1 that the ball size should vary as the square root of the particle size to be broken. Ball Size and Work Index: The work input W required per ton" varies as the work index Wi, and the

Jan 1, 1959

By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.' These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar's cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967

By E. J. Rapperport, E. D. Levine

The boundaries of the (a +ß) field in the Al-Li system were determined between 150°and 550°C utilizing quantitative metallography and lattice-parameter measurements. The solubility of lithium in aluminum decreases from 12.0at. pct Li at 550°C to 5.5 at. pct Li at 150°C. P Al-Li is saturated with aluminum at 45.8 at. pct Li and has this boundary value constant over the temperature range 150°to 550°C. THE solid solubility of lithium in aluminum has been determined by several investigators, 1-6 but, as shown in Fig. 1, there is little agreement among the various determinations. The earliest investiga-tions'-' are suspect because of the use of impure materials. Although high-purity materials were employed in more recent work,4'5 the experimental techniques may have led to contamination of the specimens. Probably the best work has been that of Costas and Marshall,6 who obtained close agreement between results obtained by two independent phase-boundary techniques: electrical resistivity and mi-crohardness. No detailed studies of the solubility of aluminum in the bcc ß phase, Al-Li, have been reported. Cursory investigations1,2,6 have indicated only that the (a+ß) -p boundary lies between 40 and 50 at. pct Li and is relatively independent of temperature. The present work was undertaken in order to provide an independent check on Costas and Marshall's determination of the solubility of lithium in aluminum, to extend knowledge of this solubility limit to temperatures below 225°C, and to make an accurate determination of the solubility of aluminum in Al-Li. EXPEFUMENTAL Alloy Preparation. In view of the difficulties encountered in previous investigations of the A1-Li system, close attention was paid to the use of methods of alloy preparation and treatment that would minimize contamination. Aluminum sheet (99.99 + pct Al) was vacuum-induction melted in a beryllia crucible to remove hydrogen. Lithium (99.9 pct Li) was charged with pre-melted aluminum into a beryllia crucible, in a helium-filled drybox. The crucible was sealed in a Vycor tube and transferred from the drybox to an induction furnace. Melting of alloys was performed by induction heating in a helium atmosphere. Solidification was accomplished by means of a suction apparatus, shown in Fig. 2, in which the alloy was forced by changes of pressure into a 3/16-in. inside diam closed-end beryllia tube. This technique produced rapid solidification of a small portion of the melt, resulting in alloys with a high degree of homogeneity. Typical lithium distributions are presented in Table I. Transverse sections 1/8 in. long were cut from the alloy rods, and each section was split in half longitudinally. One half of each section was analyzed for lithium, and the opposing halves were employed for phase-boundary determinations. Lithium contents were determined by flame photometry with an accuracy of 1 pct of the amount of lithium present. Thermal Treatments. Homogenization and equilibration heat treatments were performed in electrical-resistance furnaces with temperatures controlled to ± 2OC. Calibrated chromel-alumel thermocouples were employed to measure temperature. Homogenization was performed in helium-filled l?yrex tubes for 1 hr at 565°C. The encapsulated specimens were then transferred directly to furnaces maintained at lower temperatures for equilibration. Equilibration times were 2 hr at 550°C, 8 hr at 450°C, 27 hr at 350°c, 90 hr at 250°c, and 285 hr at 150"~. These times were chosen on the basis of conditions employed by previous investigators. Alloys were quenched from the equilibration temperatures by breaking the capsules into a silicone oil bath. By performing all possible operations either in sealed capsules or in a helium-filled drybox, the specimens were given minimum exposure to the atmosphere. Quantitative Metallography. Metallography of Al-Li alloys is difficult because of the atmospheric reactivity of the ß phase. It was found possible, however, to prepare surfaces of good metallographic quality by preventing contact with moisture during preparation. Grinding through 4/0 paper was performed in the drybox. The specimens were then transferred under kerosene to the polishing wheel. Three polishing stages were employed: 25-p alundum with kerosene lubricant on billiard cloth, 1-µ diamond paste on Microcloth, and 1/4-p diamond paste on Microcloth. Between stages the samples were cleaned by rinsing in trichloroethylene and buffing

Jan 1, 1963

By A. Szirmae, Hsun Hu

The early stages of recrystallization in a 70 pct cold-rolled Si-Fe crystal of the (110) (0011) orientation were studied with a Siemens electron microscope. Orientation studies based on electron-diffractzotz. patterns confirm the results of previous texture analysis. The driving energy for recrystallizatior and the critical radius for growth were calculated from the dislocation energy and the energy of the subgrain bourzdaries, and it was found consistent with the observed size of the recrystallized grains. The recrystallization characteristics of crystals with different initial orientations are discussed. The recrystallization of cold-rolled (110)[001] crystals of Si-Fe has been widely studied by various investigators.1-4 Their results on both deformation and annealing textures are in good agreement. The rolling texture after 70 pct reduction consists mainly of two crystallographically equivalent (111) [112] type textures and a minor component of the (100) [011] type. The latter is derived from the deformation twins, or Neumann bands, which are formed during the early stages of deformation and later rotate to the (100) [011] orientation upon further rolling reduction. Between the two main (111) [112] type textures, there is some orientation spread, because of which very low intensity areas appear in the pole figure. If these very low intensity areas are considered to be a very weak component in the texture, then a (110) [ 001 ] orientation may be assigned to them. When this rolled crystal is annealed at a sufficiently high temperature for recrystallization, the texture returns to a simple (110) [001]. The purpose of the present investigation was primarily to seek a better understanding of the recrystallization process by using the electron transmission technique. The (110) [0011 type of crystal was selected because orientation data for it are well known from previous studies with conventional techniques. Direct observations on the recrystallization of such a crystal have also been made by using a hot-stage inside the electron microscope, and the results will be reported in another paper. MATERIAL AND METHOD A single-crystal strip of the (110) [001] orientation was prepared from a commercial grade 3 pct Si-Fe alloy by the strain-anneal technique.= The strip was approximately 0.014 in. thick, and was rolled 70 pct at room temperature to a thickness of 0.004 in. Specimens were cut from the rolled strip and were annealed in a purified hydrogen or argon atmosphere. They were then electrolytically polished in a chromic-acetic acid solution to very thin foils. Best results were found by polishing first between two narrowly spaced flat cathodes with the specimen edges coated with acid-resisting paint, followed by polishing between two pointed electrodes until a hole appeared in the center as described by Bollmann.6 It was found that a thin transparent film always formed along the thin edges of the polished specimen. This film was then removed by rinsing the specimen very briefly in a solution of alcohol with a few drops of HF or HCl. RESULTS AND DISCUSSION 1) The Deformed Crystal. From the electron-diffraction patterns taken at various areas of an as-rolled specimen, the texture components as deduced - from ordinary pole-figure analysis were confirmed. Over most of the areas where orientation was examined, a (111) pattern with a [112] direction parallel to the rolling direction was obtained. This corresponds to the main deformation texture of the (111) [112] type. In a few areas the diffraction pattern was (100) [Oil], corresponding to the minor-texture component derived from the Neumann bands. The (110) [001] orientation, which corresponds to the very weak intensity area in the pole figure, was found infrequently. A typical example of the deformed matrix having the (111) type main texture is shown in Fig. 1, where (a) is the microstructure and (b) is the diffraction pattern taken from that area. It was also frequently observed that in other areas more or less continuous rings of weaker intensity were superimposed on the simple (111) diffraction pattern, suggesting the presence of a wide range of additional orientations. Other evidence indicated that the recrystallization characteristics are different in these two different types of areas. The hot-stage observations which provide this evidence will be discussed in another paper. AS shown in Fig. l(a), numerous dislocation-free areas of very small size are embedded in the "clouds" of high-dislocation density. This indicates that the deformation of a single crystal, even after a rolling reduction of 70 pct, is far from uniform on a micro-

Jan 1, 1962

By R. W. Regehr, R. A. Burmeister

Epitaxial growth of GaAs 1-xPx on germanium substrates was achieved using an open tube vapor transport system. The compositional range of 0.3 < x < 0.4 was examined. The best results were obtained with (311) orientation of the germanium substrate. The physical and chemical properties of the resulting layers were investigated using several techniques. Spectrographic analyses of the layers indicate substantial incorporation of germanium into the GaAs t-X Px layer. Evidence is presented which indicates that this incorporation occurs via a vapor phase transport process rather than by solid phase dijfu-sion. Electrical measurements suggest that the germanium thus incorporated behaves predominantly as a deep donor in the compositional range of 0.33 < x * 0.40 and has a deleterious effect upon the luminescent properties of GaAs1-x Px. The increasing technological importance of GaAs1-xPx for use in light-emitting devices has led to an evaluation of several aspects of existing growth processes. The method most commonly used to prepare GaAs1-xPx for electroluminescent device applications is vapor phase epitaxial growth on GaAs substrates.&apos;-4 In a typical electroluminescent diode structure the active region of the diode is entirely within the epitaxial layer and thus the electrical properties of the substrate are relatively unimportant since it is effectively a simple series resistance (assuming hetero-junction effects to be negligible). The use of germanium rather than GaAs as the substrate material is of interest for several reasons. First, GaAs of reasonable structural quality has been epitaxially grown on germanium4-2 and it is reasonable to expect that GaAs1-xPx could subsequently be deposited on the GaAs layer. Second, germanium substrates are readily available with both lower dislocation densities and larger areas than GaAs. Finally, single crystals of germanium are more economical than GaAs single crystals. The principal objective of the present investigation was to test the feasibility of growing GaAs1-xPx epi-taxially on germanium substrates, and to evaluate the properties of such layers with regard to electroluminescent device requirements. The approach used was to a) demonstrate epitaxial growth of GaAs1-xPx on germanium, and b) characterize the relevant structural, electrical, and optical properties of the GaAs1-xPx layers. The possibility of germanium incorporation into the grown layers was of special interest since there was some indication of this in previous studies of GaAs growth on germanium.5&apos;11,12 Although a study of the electrical properties of germanium in GaAs1-xPx was not an intent of this investigation, several features of the electrical properties of the layers grown in the present study which appear to be due to germanium are described. EXPERIMENTAL PROCEDURE The open-tube vapor transport system used for the epitaxial growth of GaAs1-xPx is illustrated in Fig. 1. This system utilizes the GaC1-GaC13 transport reaction and is similar in most respects to the larger system described elsewhere.&apos; The germanium substrates were n-type, with a resistivity of 40 ohm-cm (Eagle-Picher Co.). These were cut to the orientations of {100), {111), and (3111, and were mechanically polished and chemically etched in CP-4 (5 min at 0°C) prior to growth. In some cases, a GaAs substrate was employed in addition to the germanium. The orientation of the latter was {loo}, and they were also mechanically polished and chemically etched prior to growth. The initial composition of the deposited layer was pure GaAs. After approximately 10 microns of GaAs was deposited on the germanium substrate, the phosphorus content of the layer was gradually increased over a distance of approximately 15 microns to the desired concentration and maintained at this value throughout the remainder of the growth. Typical operating parameters used during growth are given in Table I. Selenium was used as a n-type dopant in several runs to facilitate comparison of the electrical properties of the layers grown on germanium with those of layers grown on GaAs substrates, which are usually doped with selenium. The concentration of H2Se in the gas phase was adjusted to a value which would normally yield a carrier density of 1 to 5 x 101 7 at room temperature in layers grown on GaAs substrates. The terminal surfaces of the epitaxial layers were examined by optical microscopy for structural characteristics. Laue back-reflection photographs (Cu radi-ation) were also made on the terminal surface to verify the epitaxial nature of the deposit. After these steps

Jan 1, 1970

By F. W. Jessen, James N. Howell

The accumulation of paraffin deposits in tubular goods has been recognized as a major production problem since the inception of the petroleum industry. This problem is not limited to any particular geographical area nor is it limited to a specific type of crude oil.&apos; Generally speaking, "paraffin" deposition pertains to the deposition of any predominately organic material in flow lines, and possibly even at the sand face, which would hamper the production of oil. In some fields, a continuous effort is required to remove deposits of paraffin and in order to accomplish this, many unique methods have been devised. The best solution to this problem, however, is to prevent the formation of such deposits. One method which has been tried in a number of fields is the use of plastic pipe. The purpose of this investigation is to compare the relative effectiveness of several plastic materials to aid in the reduction or prevention of paraffin accumulations in surface flow lines. COMPOSITlON OF PARAFFIN DEPOSITS By definition, paraffin deposits are those materials which are insoluble in crude oil at the prevailing producing conditions of temperature and pressure. Such deposits1 s usually consist of small particles of petroleum wax intermixed with resins, asphaltic material, and crude oil. They may also contain a variety of foreign materials such as sand, silt, water, various metal oxides, sulfates and carbonates of iron. barium, and calcium. The petroleum waxes deposited in flow strings usually consist of both a "hard" and a "soft" wax fraction. These waxes are largely aliphatic hydrocarbons with smaller amounts of aromatic and naphthenic compounds. Nathan&apos; has classified the hard and soft wax fractions. The aliphatic hydrocarbons present are those of high molecular weight with high melting points. Reistle3 pointed out that these high molecular weight compounds first separate from the oil due to a sharp decrease in solubility as the melting point increases. The identification of the resins and asphaltic materials rests, at present, on an arbitrary solubility procedure. Under certain conditions, materials which are insoluble in pentane (ASTM D-893) are defined as resins and asphalts. Subgrouping of these materials is made on decreasing solubility in benzene and carbon disul-fide. Shock&apos; found some correlation be-tween the solvent response and the pentane insoluble content of paraftins: higher pentane insoluble fractions are less soluble in any of the commonly used commercial solvents. PARAFFIN CONTROL METHODS The methods used in oil fields to prevent and remove paraffin accumulations can be grouped into four general classes: (1) operative methods, (2) physical methods, (3) chemical methods, and (4) combination of any of these. Operative methods attempt to prevent the formation of paraffin deposits while the other methods are concerned primarily with the removal of these deposits. Plastic coated pipe has been used for a number of years to prevent cor- rosion in wells, and in manv instances paraffin deposits have -been greatly reduced. Field observations have indicated that plastic coated pipe not only reduced paraffin accumulation but in some cases eliminated deposition completely; however, data are needed to demonstrate the relative effectiveness of plastic materials. Deposition Apparatus The pipe used to determine the effect of velocity on rates of deposition was %- and 2-in. nominal diameter, and 5 ft in length. Steel, butyrate, rigid PVC, kralastic resin-type plastic pipes, epoxy coated pipe, PVC lined glass fiber pipe, and aluminum pipe were tested. Steel pipe was used as a control. Fig. 1 is a schematic diagram of the apparatus showing the relative position of the separate units making up the equipment. In order to facilitate the installation and removal of the test pipes in the apparatus, O-ring seals capable of sustaining pressures of 50 psi were provided at each end. Test pipes were submerged in a cold water bath maintained at or below room temperature by circulating water through copper cooling coils packed in ice. A hot water bath equipped with immersion-type heaters, stirrers, and a thermoregulator was used to maintain the temperature of the oil prior to introduction into the piping manifold. The capacity of the oil reservoir was 30 gal. A 33-gal/min centrifugal pump, capable of producing turbulent flow velocities in the test pipes, was used to circulate the oil through the system when using %-in. pipe; and a 70-galjmin centrifugal pump was used in later tests using 2-in. pipe. A by-pass arrangement made it pos-

By E. P. Pfleider, Rolland L. Blake

IT is generally believed that the amount of diamond drilling will increase appreciably in the next decade, as the seaarch for minerals throughout the world becomes more difficult and intense. An attendant problem may be one of short diamond supply, resulting in higher bit and drilling cost. With this background, the U. S. Bureau of Mines&apos; and the School of Mines at the University of Minnesota&apos; have established comprehensive research programs in diamond drilling. One of the several aims is the design of a more efficient bit, which would lower diamond consumption and increase rate of advance, both essential in reducing drilling costs. The objective of the specific research problem" discussed in this paper was an investigation of the cutting action of the cliamonds set in a diamond drill bit, cutting action meaning the manner in which the diamonds cut or. loosen the minerals in the rocks being drilled. In the literature on cutting action such descriptive terms are used .as: grinding, wearing, cutting, breaking, shearing, scraping, melting, and chipping. These actions were seldom described or defined. Grodzinski describes the cutting action of a single diamond in the shaping of certain types of material as "breaking out chips of the material." Brittle mate-. rials break as small separate chips, and tough materials, because of heat generated, give a continuous chip. Deeby said about diamond drills: "When diamonds are forced into the formation and rotated, they either break the bond holding the rock particles together, or they cause conchoidal fracture of the rock itself. The former action occurs when drilling in sandstones, siltstones, shales, etc. and the latter action when drilling in chert, flint, or quartz." He said that diamonds cut on the "grinding principle" but he does not define or elaborate on this action. The cutting action of diamonds on glass was first investigated about 1816 by Dr. W. H. Wol-laston, an English physicist. The best glass-cutting diamonds have a natural or artificially rounded cutting edge. This edge first indents the glass and then slightly separates the particles, forming a shallow and nearly invisible fissure. Since none of the material is removed, this action is one of splitting rather than cutting. No other reports of research work on the cutting action of the diamond were found, and further work was considered justified and advisable. It is impractical, even if possible, to observe directly the cutting action of a diamond drill bit in rock; therefore it was necessary to devise an indirect method. It was believed that a study of the following three observations would lead to a better understanding of the cutting action: 1—the appearance of the minerals or rock surface in the bottom of the hole, 2—the size, shape, and other characteristics of the drill cuttings, and 3—the condition of the diamonds in the bit. The cutting action in a particular rock probably varies with bit pressure and speed. If the bit were slowly lifted off the rock, the effect of decreasing pressure might obliterate those bottom hole characteristics that are specific at the test pressure. Likewise, if the drill were stopped with the bit still in contact with the bottom of the hole, then decreasing speed effects would tend to obliterate the characteristics at the set test conditions. Therefore, in order to preserve those cutting effects impressed on the rock at test conditions, it seemed necessary to lift the bit off the bottom of the hole almost instantaneously once drilling conditions, i.e., revolutions per minute, pressure, and water flow became constant. In addition to observing the cuttings, the bit, and the bottom of hole, it seemed desirable to collect some quantitative data for purposes of correlation with the observations and for a record of bit performance. Consequently such data as revolutions per minute, force applied, and rate of advance of the bit were recorded. Six rock types, listed in Table I, were chosen for the tests. It was felt that these rocks had most of the variable characteristics of texture, bonding, and mineral hardness met in the common rocks generally being drilled. The sandstone was so poorly cemented as to be friable, even though most of the cement was silica. The limestone, though well cemented, was quite porous. Originally it was planned to conduct the tesk work with a full-scale drill unit, using EX bits, 7/8-in. core, 11/4-in. OD. The drill worked well, but was too cumbersome for rapid, accurate drilling of many short holes (1 ½-in.) in varied rock types. A new

Jan 1, 1954

By S. Gstalder, J. Raynal

Consideration was given to simple tests which could be performed on rocks to give a measure of rock drillability. Various methods of breaking rocks were considered and the hardness test developed by Schreiner was selected for this study. The test involves application of an increasing load on the rock face through a flat-faced cylindrical punch until rupture occurs. Test results show that hardness is a good measure of the breaking strength of rocks. Useful relationships are shown to exist between hardness and other physical quantities such as specific disintegration, Young&apos;s modulus and sonic velocity. Specific disintegration (volume of rock broken per unit of work input) provides a possible means of comparing the effectiveness of other methods of rock breakage. The relationship between hardness and sonic velocity may be very significant for it may be possible to deduce rock drillability from sonic log data. provided that a mineralogical factor is taken into account. TO test further the results of the work, laboratory drilling tests were performed which closely simulated down-hole pressure conditions. Correlations of drilling results with rock hardness measurements were quite good. It was concluded that rock hardness, as measured in the laboratory or as deduced from sonic logs, could be used in relations for predicting rock drilling performance. INTRODUCTION Drillability of rocks cannot be defined in an absolute manner by a single quantity or measured by a single test. Resistance of rock to drilling depends to a large extent upon the means used for rock destruction. This complicates drillability classification of rocks for there may be as many classifications as there are methods of rock breakage without known functional relations between them. The objective of this work was to develop. in terms of rock destruction behavior, means of selecting the best drilling method for a given rock or the conditions for optimum output from a given drilling method. ANALYSIS OF ROCK DESTRUCTION TESTS Gauthier and Baron&apos; have reviewed the many test methods which have been developed for determining the resistance of rocks to breakage. These include drilling tests, punch tests, scratch tests, resistance to shock, wear tests, etc. A standard drilling test might be to determine the time required to drill a standard depth (1/16 in.) in a rock using a bi-cone microbit (1 1/4-in. diameter) when a standard load (417 Ib) is applied at a standard speed of bit rotation (110 rpm). From the standpoint of similarity, the results of microbit drilling tests would seem to be most representative of the several methods suggested above. However, evaluation of drilling performance by this method is only qualitative and cannot be applied directly to actual drilling conditions. Punch tests basically measure rock hardness. Punches of various shapes and sizes, including small cones for Vickers&apos; and Knoop&apos;s tests, the wedge for Epstein&apos;s test and the right circular cylinder for Schreiner&apos;s test, have been used. Results of these tests lead to a quantitative hardness classification which would seem to be related to the resistance of rock to bit-tooth penetration. Scratch tests are related to the resistance of rocks to abrasion such as would be encountered in drilling with diamonds. Either the width of the scratch obtained at a fixed load or the load required to give a scratch of a fixed width may be used to evaluate surface hardness of the rock. This should be related to the resistance of the rock to wear. The above tests, and probably many others. give relative measurements of the breakage or destruction characteristics of rocks. There is no direct relation between results of these tests and the drillability of rocks. Also, the tests each measure different quantities which have different dimensions and they do not permit direct comparison of numerical values. As one step in rectifying the above difficulties. it is proposed that the results of all test methods be expressed in terms of volume of rock destroyed per unit of work required; this is referred to as "specific disintegration". Test results may then be reported in a form which shows both a classification of rocks in regard to each method and a comparison of methods with regard to each rock. The disadvantage in using specific disintegration is the difficulty of measuring this quantity with accuracy. The volume of rock damage is difficult to measure. as is the true value of work input. Rock heterogeneity adds to the

Jan 1, 1967