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By John M. Logan, John Handin

Quasi-dynamic triaxial compression tests have been done for the first time at confining pressures to 7 kb. The intermediate strain-rate apparatus employs a gas loading cylinder which allows axial strain rates up to 102/sec on a sample 2 cm in diameter and 4 cm long. Samples can be deformed at confining pressures to 7 kb. Strain gages bonded to the loading piston and to the jacketed specimen allow internal measurements of load and sample strains respectively. Westerly granite has been deformed at confining pressures to 7 kb, room temperature, and axial strain rates of 10-2 to 1/sec. An increase of ultimate strength with confining pressure was found as expected. The ultimate strength was also found to vary directly with increasing strain rate; the rate of rise increases with confining pressure. Brittle deformation has dominated the sample behavior. Solenhofen limestone has been deformed at confining pressures to 3 kb, room temperature, and axial strain rates of 10- to 10/sec. The brittle-ductile transition was found to take place at about 1.5 kb confining pressure at a strain rate of 10/sec.

Jan 1, 1971

By C. M. Wayman, R. Bullough

The rediffraction of Bragg diffracted beams by differently oriented regions (such as twins) of a crystal may give rise to "extra" reflections or reciprocal lattice points. These two papers are concerned with predicting these additional reflections which result from twin related regions of a lattice. Analysis is made for {111}fcc twins, (112)bcc twins, and {hkil}hcp twins. It is first required, knowing the specific variant of the twinning plane in each case, to predict the positions of the twin reflections relative to the matrix reciprocal lattice. Once this is done, the positions of the "extra" multiply diffracted reflections may be deduced. Part I is devoted to establishing "selection ru1es" for twinning, i.e., the necessary and sufficient conditions for the existence of twinned reciprocal lattice points. 1. INTRODUCTION. Transmission electron diffraction patterns are frequently complicated by multiply diffracted beams. Pashley and stowell1 have recently demonstrated that certain extra reflections in evapo- rated films of gold result from the rediffraction of matrix Bragg diffracted beams by (111) microtwins in the gold. It was previously (and erroneously) suggested 2,3 that observed "irrational" reflections in fine-grained gold were due to the presence of some hcp gold. A similar situation exists, apparently, for some bcc materials; fine (112) twins in bcc martensite in Fe-Ni alloys4 give rise to extra reflections. There are many other examples. The number of transmission electron microscopic investigations is continually increasing, and because of the importance of double (and multiple) diffraction in the interpretation of diffraction patterns, it was judged that a detailed elaboration of the principles involved is desirable, as well as the extension of these principles in reasonably closed form to other crystal structures, particularly bcc and hcp. The present analysis considers double diffraction caused by (111) twins in fcc metals, (112) twins in bcc metals, and {hkil} = {hkl) twins in hcp metals. For each case of twinning, the various possible (variants of) twins give rise to a set of interpenetrating reciprocal lattices. The relative spatial arrangements of these reciprocal lattices can be deduced (Part I) and are expressed in terms of simple "selection rules". The resulting sets of interpenetrating reciprocal lattices are then analyzed for possible doubly diffracted reflections (Part II). The notation used, and some important formulas are given in Appendices I and 11.

Jan 1, 1967

By Gerald Edmunds

The liquidus line on the phase diagram for temperature versus composition of a binary alloy system, representing the boundary between the homogeneous melt and the heterogeneous melt plus solid, besides showing the minimum casting temperature, is useful in determining eutectic compositions and the presence of phase changes such as peritectic transformations and intermetallic compound formation. The liquidus often is determined by the cooling curves of thermal analysis, but supercooling frequently occurs, so that the temperature values are low. An alternative method, the one employed here, consists of determining the composition of samples of the melts from heterogeneous alloys that are at equilibrium. With meticulous attention to fundamentals, this method is capable of yielding values limited in precision only by the temperature control and measurement and analyses. Apparatus By starting, on the one hand, with a supersaturated solution and allowing the excess solute to precipitate, and on the other hand with an undersaturated solution and allowing more of the solute to be dissolved, both processes being carried out at the same temperature, equilibrium may be said to have been approached from both directions; that is, from above and from below. If the analyses show the solutions to contain the same fraction of solute when equilibrium has been approached from above and from below, one is assured that equilibrium has been reached in both determinations. In order to carry out such determinations, it is necessary to have equipment for obtaining and maintaining the proper temperatures; for holding the melt, measuring its temperature, and stirring, sampling and analyzing it. The present work required temperatures from 420° to 900°C. The equipment consisted of: A furnace, which was a vertical alundum tube, 13/4-in. diameter inside and 18 in. long, wound with Nichrome resistance wire, surrounded by a 3-in. i.d. alundum tube wound for 5 in. of length near each end, for compensation of end losses. This muffle was contained in an iron shell with Transite end plates, the intervening space being packed with Sil-O-Cel. The outside dimensions of the furnace were 12 in. in diameter by 181/2 in. in height. Heating current was supplied by three independent variable-voltage transformers (Variac), one connected to each end compensator winding and manually controlled, and one connected to the main winding through a series resistance of 5 ohms. This resistance was short-circuited for

Jan 1, 1944

By Gerald Edmunds

The liquidus line on the phase diagram for temperature versus composition of a binary alloy system, representing the boundary between the homogeneous melt and the heterogeneous melt plus solid, besides showing the minimum casting temperature, is useful in determining eutectic compositions and the presence of phase changes such as peritectic transformations and intermetallic compound formation. The liquidus often is determined by the cooling curves of thermal analysis, but supercooling frequently occurs, so that the temperature values are low. An alternative method, the one employed here, consists of determining the composition of samples of the melts from heterogeneous alloys that are at equilibrium. With meticulous attention to fundamentals, this method is capable of yielding values limited in precision only by the temperature control and measurement and analyses. Apparatus By starting, on the one hand, with a supersaturated solution and allowing the excess solute to precipitate, and on the other hand with an undersaturated solution and allowing more of the solute to be dissolved, both processes being carried out at the same temperature, equilibrium may be said to have been approached from both directions; that is, from above and from below. If the analyses show the solutions to contain the same fraction of solute when equilibrium has been approached from above and from below, one is assured that equilibrium has been reached in both determinations. In order to carry out such determinations, it is necessary to have equipment for obtaining and maintaining the proper temperatures; for holding the melt, measuring its temperature, and stirring, sampling and analyzing it. The present work required temperatures from 420° to 900°C. The equipment consisted of: A furnace, which was a vertical alundum tube, 13/4-in. diameter inside and 18 in. long, wound with Nichrome resistance wire, surrounded by a 3-in. i.d. alundum tube wound for 5 in. of length near each end, for compensation of end losses. This muffle was contained in an iron shell with Transite end plates, the intervening space being packed with Sil-O-Cel. The outside dimensions of the furnace were 12 in. in diameter by 181/2 in. in height. Heating current was supplied by three independent variable-voltage transformers (Variac), one connected to each end compensator winding and manually controlled, and one connected to the main winding through a series resistance of 5 ohms. This resistance was short-circuited for

Jan 1, 1944

By H. F. Yancey, M. R. Geer, Franklin T. Davis

Coke with low phosphorus content is required by some of the electrometallurgical and chemical plants recently attracted to the Pacific Northwest by the hydroelectric power available from Bonneville and Grand Coulee dams. Shipping such coke into the area from eastern points involves a high freight charge, and during wartime consumes precious rail and ship-bottom space, so it is highly desirable to produce coke from the coking coals of Washington to meet the requirements of these industries. Although coke has been made from Washington coals since 1884, little has been known about their phosphorus contents or about the extent to which phosphorus could be reduced by cleaning, An investigation was undertaken, therefore, to determine the manner in which phosphorus occurs in the coking coals of Washington and its amenability to removal by ordinary coal-washing methods. Previous Work Phosphorus is a deleterious element in coke used for numerous metallurgical processes, including the production of pig iron, yet comparatively little published information is available on the occurrence and elimination of phosphorus in any of the coals of this country. A variation from 0.009 to 0.062 per cent phosphorus in various horizons of the Pittsburgh bed in the Connellsville region of Pennsylania has been reported,' and a reduction in phosphorus content from 0.020 per cent in the raw coal to 0.018 per cent in the washed coal was obtained in washing coal from the same bed in the Pittsburgh area;2 the latter figures represent average analyses for a year's operation of the washery on about 800,000 tons of coal. A reduction in phosphorus content from 0.018 to 0.011 per cent in washing coal from the Pittsburgh bed at another washery was observed, and the same report provides data on the phosphorus reduction obtained by separating 10 other coals on a bath of 1.35 specific gravity.3 European investigators have been especially active in correlating phosphorus content with petrographic analysis; fusain and durain generally contain the highest percentage of phosphorus, but this relationship is not universal.4 Some of these investigators have found that phosphorus is removed in the coal-washing process,5 but others have observed that the clean coal contained as much or even more phosphorus than the raw coal.'

Jan 1, 1944

By M. R. Geer, Franklin T. Davis, H. F. Yancey

Coke with low phosphorus content is required by some of the electrometallurgical and chemical plants recently attracted to the Pacific Northwest by the hydroelectric power available from Bonneville and Grand Coulee dams. Shipping such coke into the area from eastern points involves a high freight charge, and during wartime consumes precious rail and ship-bottom space, so it is highly desirable to produce coke from the coking coals of Washington to meet the requirements of these industries. Although coke has been made from Washington coals since 1884, little has been known about their phosphorus contents or about the extent to which phosphorus could be reduced by cleaning, An investigation was undertaken, therefore, to determine the manner in which phosphorus occurs in the coking coals of Washington and its amenability to removal by ordinary coal-washing methods. Previous Work Phosphorus is a deleterious element in coke used for numerous metallurgical processes, including the production of pig iron, yet comparatively little published information is available on the occurrence and elimination of phosphorus in any of the coals of this country. A variation from 0.009 to 0.062 per cent phosphorus in various horizons of the Pittsburgh bed in the Connellsville region of Pennsylania has been reported,' and a reduction in phosphorus content from 0.020 per cent in the raw coal to 0.018 per cent in the washed coal was obtained in washing coal from the same bed in the Pittsburgh area;2 the latter figures represent average analyses for a year's operation of the washery on about 800,000 tons of coal. A reduction in phosphorus content from 0.018 to 0.011 per cent in washing coal from the Pittsburgh bed at another washery was observed, and the same report provides data on the phosphorus reduction obtained by separating 10 other coals on a bath of 1.35 specific gravity.3 European investigators have been especially active in correlating phosphorus content with petrographic analysis; fusain and durain generally contain the highest percentage of phosphorus, but this relationship is not universal.4 Some of these investigators have found that phosphorus is removed in the coal-washing process,5 but others have observed that the clean coal contained as much or even more phosphorus than the raw coal.'

Jan 1, 1944

By C. M. Nickerson

In times of overproduction such as the operators have been struggling against for the past several years it is the practice of the oil industry to shut in certain wells in order to reduce the flood of oil. The purpose of this paper is to present certain variations in production of oil wells when the offset wells are shut in. The scope of the study has been confined to California fields, and more especially to those of the San Joaquin Valley. The accepted definition of a shut-in well is a well where production has been suspended by closing in the casinghead arid tubing or by cessation of pumping. The immediate effect of such a procedure, of course, is to reduce the oil production from the lease, which is the result desired. However, it appears that certain types of wells vary widely in production of oil, gas and gasoline after adjacent wells have been shut in, which variation has a very material effect on the ultimate recovery of oil from the property. The increase or decrease in the oil production itself may not be of sufficient volume to occasion comment, but wide fluctuations in the gas and gasoline recovery under the changed conditions arc of the utmost importance in the future recovery of oil. The scope of this paper includes: (I) the effect on producing oil wells of shutting in offset wells, the wells being studied in three groups arranged according to their relative stages of depletion; (2) probable source of excess gas and the effect on the ultimate recovery of oil; (3) suggested procedure when wells are shut in; (4) methods that could be employed to prevent undue migration of gas from the shut-in area; and (5) the need for future studies of the situation. Three Classes of Producing Oil Wells For the purposes of this paper producing wells in California have been arranged in three groups according to the age of the well, or to the relative stage of depletion of the producing zones. The first group consists of those wells with a high fluid level, or in other words those wells whose fluid levels are a considerable distance above the top of the perforations. This type of well is in the flush period of its life and ordinarily produces

Jan 1, 1929

By O. N. Carlson, A. L. Eustice

The tensile properties of iodide vanadium were determined as a function of hydrogen concentration. It was shown that the presence of 10 ppm H is sufficient to cause embrittlement of vanadzum over a limited temperature range. The temperature of the observed ductility mininlum is approximately -l00°C, this being a function of strain rate and hydrogen concentration. The yield stress of hydrogenated vanadium is raised sharply in the brittle temperature range. THE present investigation was initiated to determine the effect of hydrogen on the tensile properties of high-purity vanadium as a function of temperature and the role of hydrogen in the brittle-ductile transition. Loomis and Carlson&apos; reported a change from ductile to brittle behavior in iodide vanadium at -110°C with a return of ductility at temperatures below -140°C. Vanadium wire containing 270 pprn of hydrogen was brittle at room temperature while wire containing 100 ppm was ductile under the same conditions. Roberts and Rogers&apos; reported a ductile-brittle-ductile fracture sequence in vanadium containing 400 to 600 ppm of hydrogen. Their data show that hydrogenated vanadium is ductile at 150"C, brittle at room temperature and ductile again at -196°C. Magnusson and Baldwin found a minimum in ductility in vanadium containing 80 ppm hydrogen from tensile tests performed at several strain rates. Information available on the vanadium-hydrogen equilibrium system4 is somewhat incomplete. The absorption of hydrogen is exothermic in accordance with the decline in solubility with rising temperature. The limit of solid solubility at temperatures below 400°C has not been determined due to the difficulties in obtaining equilibrium at these temperatures. Data on the hydrides of vanadium are rather limited. Roberts6 studied the structure of VD,., by neutron diffraction, and observed the ordering of the deuterium atoms below -65°C into a primitive cubic cell with a lattice constant about twice that of the disordered bcc vanadium solid solution. EXPERIMENTAL PROCEDURE Vanadium of 99.9 pct purity was prepared by the iodide refining process6 for use in this investigation. This vanadium contained the following analyzed impurities; <20 pprn calcium, 150 ppm carbon, 200 ppm chromium, 30 ppm copper, 10 ppm hydrogen, 200 ppm iron, <20 ppm magnesium, <20 ppm nickel, <5 ppm nitrogen, 150 ppm oxygen, <50 ppm silicon, and <20 ppm titanium. specimen Preparation—Tensile specimens were machined from swaged rods of iodide vanadium. The

Jan 1, 1962

By J. T. Ryan

SiR Humphry Davy&apos;s epoch-making treatise delivered on Nov. 9, 1815, before the Philosophical Society of London, first announced and demonstrated a flame safety lamp for detecting methane in mine air. Coal mining was known in England as early as 1180, more than 600 years before the advent of a safe lighting and gas-detecting appliance. Mining, no doubt, took place first in outcrop coal, and danger from gas did not become apparent until the workings became deeper and more extensive. Davy&apos;s lamp did much to increase the safety of miners, and a modified Davy lamp is still widely used for detecting the presence and approximate amount of combustible gas in mine air. No factor in coal mining has improved more rapidly during the past 15 years than safety measures. This progress came about not only as a result of the workmen&apos;s compensation laws now in force in most of the states of the Union, but because the research work of the U. S. Bureau of Mines had demonstrated some dangers incident to coal mining which were not considered to be serious matters prior to that time. Electric power and explosives are necessary but potential hazards in American coal mines. A general mechanization program is now under way, while the mines are growing deeper and more extensive. Consequently ventilation problems are more complex and a demand has been created for positive detecting devices for carbon monoxide as well as methane. Scientists and manufacturers, working hand in hand during the past 10 years, have invented and developed appliances which make systematic and effective examination of mine air possible. The object of this paper is to describe briefly the approved testing devices in use today, with the hope that they may lead to the saving of life. Two Groups of Dangerous Coal Mine Gases Dangerous coal mine gases may be placed in two groups: (I) those that are dangerous because of their explosive properties, and (2) those that are dangerous because of their toxic properties. Methane (CH4) is the important gas of the first group, and in so-called gaseous mines constantly exudes from the coal and rock; it may accumulate and form an explosive mixture. The explosive range of methane-air mixtures is well defined. The low limit is 5 per cent., the high limit 15 per cent., and the most explosive

Jan 1, 1927

By W. A. Backofen

THE preferred orientations, or textures, resulting from many of the various methods for testing and forming metals have been the subject of numerous investigations.1,2* Despite this large amount of work, however, only a few limited studies have been made of the texture that is developed by torsional deformation. Ono3 found that in severely twisted wires of copper and aluminum a [Ill] direction lies parallel and a [1101 direction perpendicular to the longitudinal axis of the wire. Sachs and Schiebold4 have reported that a double-fiber texture exists in a twisted aluminum wire with both the [Ill] and [loo] directions parallel to the axis of the wire. Twisted iron wires have also been examined by Ono.8 Both the [1101 and [1121 directions were reported as parallel to the axis of the wire. Goss5 concluded from a study of twisted rods of a low-carbon steel that the preferred orientation existing at fracture is quite complex, but that many grains have a [1101 direction parallel to the axis of the wire. In addition to the earlier experimental work, some suggestions have been made about the possible nature of the torsion texture. These suggestions are based on the results of many experiments which indicate that the cold-working texture of a particular metal is largely determined by the geometrical change in shape that the metal undergoes during plastic deformation.1,6 Hibbard and Yen7 have considered the problem of deformation textures and have presented an analysis which is able to explain why equivalent changes in shape should yield similar textures. Therefore, a knowledge of the principal strains associated with torsional deformation would seem helpful in the interpretation of the torsion texture. The necessary analysis has been made of the state of strain in an element of metal lying in the surface of a cylindrical rod or tube that has been subjected to pure torsion.8,9 This analysis shows that the directions of the principal normal strains rotate continuously within a torsion specimen while it is being twisted. After the first infinitesimal amount of twisting, these directions make angles of 45" with the longitudinal axis of the bar. They rotate from this position as twisting proceeds, and after an infinite amount of twisting, the direction of the principal tensile strain is perpendicular, and the direction

Jan 1, 1951

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.‡ Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation; 2.3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By M. R. Geer, Franklin T. Davis, H. F. Yancey

COKE with low phosphorus content is required by some of the electrometallurgical and chemical plants recently attracted to the Pacific Northwest by the hydroelectric power available from Bonneville and Grand Coulee dams. Shipping such coke into the area from eastern points involves a high freight charge, and during wartime consumes precious rail and ship-bottom space, so it is highly desirable to produce coke from the coking coals of Washington to meet the requirements of these industries. Although coke has been made from Washington coals since 1884, little has been known about their phosphorus contents or about the extent to which phosphorus could be reduced by cleaning. An investigation was undertaken, therefore, to determine the manner in which phosphorus occurs in the coking coals of Washington and its amenability to removal by ordinary coal-washing methods. PREVIOUS WORK Phosphorus is a deleterious element in coke used for numerous metallurgical processes, including the production of pig iron, yet comparatively little published information is available on the occurrence and elimination of phosphorus in any of the coals of this country. A variation from 0.009 to 0.062 per cent phosphorus in various horizons of the Pittsburgh bed in the Connellsville region of Pennsylania has been reported,1 and a reduction in phosphorus content from 0.020 per cent in the raw coal to 0.018 per cent in the washed coal was obtained in washing coal from the same bed in the Pittsburgh area;2 the latter figures represent average analyses for a year&apos;s operation of the washery on about 800,000 tons of coal. A reduction in phosphorus content from 0.018 to 0.011 per cent in washing coal from the Pittsburgh bed at another washery was observed, and the same report provides data on the phosphorus reduction obtained by separating 10 other coals on a bath of 1.35 specific gravity.3 European investigators have been especially active in correlating phosphorus content with petrographic analysis; fusain and durain generally contain the highest percentage of phosphorus, but this relationship is not universal.4 Some of these investigators have found that phosphorus is removed in the coal-washing process,5 but others have observed that the clean coal contained as much or even more phosphorus than the raw coal.6

Jan 1, 1944

By A. Bar-Or, G. Hirsch, P. Wynblatt

The rates of nucleation and growth at various temperatures in U-0.45, 1.1, and 1.35 at. pet Cr alloys were determined, providing a qliantitative proo-f that the transformation under study is controlled by nucleation and diffusional growth. The linear relationship, log NV US 1/T2, suggests that the nucleation of the alloys is probably controlled by the classical law of nuclei formation. The established linear relationship, log G us 1/T, in the three alloys suggests that growth in each alloy is controlled by bidimensional nuclei formation. It was established that both the rate of growth and the rale of nucleation are retarded by chromium. Using classical formulae, sApN and sApG (the ß/a apparent interphase energies) were calculated from the nucleation and growth results, respectively. It was found that their values are of the same order of magnitude. However, why sApN is unaffected by the addition of chromium, while sApG increases with it, needs further clarification. In the last few years, an appreciable amount of research has been conducted into the mechanism of the ß —a transformation in uranium and uranium alloys. Recently, Burke1 reviewed the published work concerned with this transformation. He concluded that in dilute uranium alloys it is firmly established that, at high temperatures in the a range, ß decomposes by a diffusional process. However, he based his conclusion either on experiments dealing with the over-all transformation,2 or on qualitative results.3 It was felt that a better insight into the mechanism of transformation could be gained from the quantitative measurements of growth and nucleation rates, which we aimed to carry out in the present work. In a previous work,4 we have shown that a rim of a grains is formed during isothermal transformation at the high a range. The thickening of this rim with time was used for measuring the rate of growth in U-0.45 at. pet Cr.5 This method was also used in the present work for two more alloys. For meas- uring the rate of nucleation, a method of quenching and macroetching was developed to allow differentiation between a grains formed during isothermal transformation at the upper a range and those formed after quenching, Fig. 1. EXPERIMENTAL WORK AND RESULTS The Rate of Nucleation. The measurement of the rate of nucleation was effected by counting the num-

Jan 1, 1965

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy&apos;s Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy&apos;s Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By B. E. Lindsly

The withdrawal of gas and/or oil in appreciable quantity from a natural oil reservoir causes the pressure within the reservoir to diminish, and if the oil is completely saturated with gas, this dissolved gas begins to evolve from solution. The liberation of gas from solution in oil causes the oil to change in several ways, the principal changes being: (1) reduction in volume or "shrinkage"; (2) increase in specific gravity (decrease in degrees A.P.I.); (3) decrease of energy in the oil; (4) increased viscosity; (5) increased surface tension. As the writer&apos;s investigations have been concerned more with the first three items than with changes in viscosity and surface tension the following discussion relates particularly to the volumetric shrinkage of the oil, to the increased specific gravity, and to the decreased energy in the oil, each caused by the liberalion of dissolved gas. One of the most surprising facts that have developed in the study of high-pressure well-head and "bottom-hole" samples is the great reduction in volume that occurs in some oils when the naturally dissolved gas is liberated. High-pressure samples taken from well heads in the Oklahoma City, Kettleman Hills and Ventura, Calif., fields decreased in volume from 11.2 to 40.5 per cent when the dissolved gas was liberated in reducing the pressure on the sample to atmospheric. The amount of shrinkage an oil undergoes when gas is liberated depends upon the quantity of gas liberated and also upon its composition. A given volume of the heavier gases, propane and butane for example, will occupy more space in the oil than an equal volume of methane. The reason for this probably is that the molecules of the heavier gases are larger than those of the lighter gases. When gases are not in solution, and particularly when they are at low pressures, the distance between the gas molecules is so much greater than the dimensions of the molecules themselves that the mere size of the molecules has little effect upon the space occupied by the gas, Avogadro&apos;s hypothesis, which in effect states that all gases under the same conditions have the same number of molecules per unit volume, relates to this phenomenon. The fact that the heavier gases occupy more space than the lighter gases in the oil, and

Jan 1, 1934

By H. J. Struth

Conditions in the gasoline market undoubtedly influence the oil industry&apos;s general economic situation to a greater degree than perhaps any other single factor. No matter how efficiently the oil industry manages to conduct its producing operations, a drop in the price of gasoline exerts definite pressure upon the posted price of crude oil in the field. Efforts of the recent past have shown that profits from the producing division of the industry are closely tied in with the course of the gasoline market. When refinery gasoline prices are depressed, as they have been during recent months, it is utterly impossible for purchasers to maintain a crude market that is commensurate with the cost of production, regardless of how well balanced the producing situation may be. In fact, the producer can no longer regard his operations in the light of an independent unit of the oil industry, since his financial well-being is directly dependent upon the well-being of the refiner. Because gasoline is the principal constituent of crude oil, it is obvious that profitable refining operations can only be maintained through profitable gasoline markets. Likewise, when the price of gasoline influences a profit for the refinery it also influences the prosperity of the producer, through the advent of higher and more profitable posted prices for crude oil in the field. Financial results for 1932 showed material improvement over the preceding year, primarily because the price of gasoline was maintained at levels somewhat above those of 1931. Consequently, the producer was able to record improvement in the crude market, through a somewhat higher level of posted prices. While effective methods of prora-t,ion of crude production are given credit for the advance recorded in the crude market last year, it is also a fact that the advent of higher prices for gasoline had a direct influence upon the posted prices of crude oil. For example, when gasoline was sold in Group 3 at 2 3/4 a gallon in June and July, 1931, the price of 36-gravity Mid-Continent crude was down to its lowest point of only 18c a barrel. As refinery prices advanced, however, there was a corresponding advance in posted prices of crude oil. Thus, when Group 3 gasoline commanded a price of 5c a gallon

Jan 1, 1933

By David A. Keys

The actual procedure in estimating depth of overburden from magnetic observations made on the surface will vary with the form of the deposit and any theoretical discussion will apply only so far as the form of the deposit conforms to the mathematical premises on which the theory is based. Since the shapes of natural deposits in the field cannot be expressed rigorously in mathematical form, the best that can be done is to assume some simple form and deduce results. Fortunately many small variations in form produce only slight changes in the estimated depth of overburden, therefore the methods have a definite practical value. For the theoretical treatment, magnetic ore deposits may be divided roughly into three classes, depending upon whether the magnetic anomalies may be considered to arise from (1) a single magnetic pole, (2) a dike or (3) a magnetic doublet. Particular cases, falling under one or other of these classes, have been discussed by different authors.1"4 In general, it may be stated that when the magnetic effects as measured on the surface are due only to one pole of the body, the other pole being so remote that its effect may be neglected, the resultant anomaly F at any point will vary as the inverse square of the distance r of the point from the pole, which may be expressed mathematically by F = k/r2, where k is a constant. When the deposit occurs in the form of a long, thin dike, the resultant anomaly will be of the form F = k&apos;/r and when the deposit is in the shape of a lens, so that both poles have an appreciable effect on the surface, the result will be similar to that caused by a magnetic doublet, and the form will be F = k&apos;/r3. The particular class under which a deposit falls may be deduced from the results of the magnetic survey. The second class is readily found, but there may be difficulty in deciding between the first and third. Isody-namic contours of both the vertical and horizontal anomalies will often be a good guide in making a correct decision. The correctness of the theoretical calculations may be checked in two ways. The first is to make laboratory models of various known shapes and pole distributions, to calculate the anomalies to be expected

Jan 1, 1940

By David A. Keys

The actual procedure in estimating depth of overburden from magnetic observations made on the surface will vary with the form of the deposit and any theoretical discussion will apply only so far as the form of the deposit conforms to the mathematical premises on which the theory is based. Since the shapes of natural deposits in the field cannot be expressed rigorously in mathematical form, the best that can be done is to assume some simple form and deduce results. Fortunately many small variations in form produce only slight changes in the estimated depth of overburden, therefore the methods have a definite practical value. For the theoretical treatment, magnetic ore deposits may be divided roughly into three classes, depending upon whether the magnetic anomalies may be considered to arise from (1) a single magnetic pole, (2) a dike or (3) a magnetic doublet. Particular cases, falling under one or other of these classes, have been discussed by different authors.1"4 In general, it may be stated that when the magnetic effects as measured on the surface are due only to one pole of the body, the other pole being so remote that its effect may be neglected, the resultant anomaly F at any point will vary as the inverse square of the distance r of the point from the pole, which may be expressed mathematically by F = k/r2, where k is a constant. When the deposit occurs in the form of a long, thin dike, the resultant anomaly will be of the form F = k&apos;/r and when the deposit is in the shape of a lens, so that both poles have an appreciable effect on the surface, the result will be similar to that caused by a magnetic doublet, and the form will be F = k&apos;/r3. The particular class under which a deposit falls may be deduced from the results of the magnetic survey. The second class is readily found, but there may be difficulty in deciding between the first and third. Isody-namic contours of both the vertical and horizontal anomalies will often be a good guide in making a correct decision. The correctness of the theoretical calculations may be checked in two ways. The first is to make laboratory models of various known shapes and pole distributions, to calculate the anomalies to be expected

Jan 1, 1940

By Robert Bedford

THE objects of this paper are: 1. To give cost data on drilling obtained at the North Star mine in California; 2. To describe the methods of testing drills employed there, giving the results of shop tests, and the correlated data obtained underground; 3. To demonstrate that these tests form a satisfactory basis upon which to judge rock drills. The rock at this mine is either close-grained diabase in the upper levels, or tough grano-diorite in the lower levels. The vein, which has an average dip of 23°, consists of about 5 ft. of "formation" lying between walls of unaltered country rock. Of the 5 ft., solid quartz and stringers make up 18 in. of pay ore. The formation, which consists of but slightly altered country rock, is almost as hard as the unaltered walls. From 4 to 42 ft. is sent to the mill. One-third of the holes are drilled in the quartz; two-thirds in the formation. The holes are about 42 ft. deep and break on the average of 1.15 tons per hole. The average number of holes per stope drill shift is at present 5.65. The number of drill shifts throughout the mine in 1913, was 18,679, and the cost of labor for drilling, power, supplies, upkeep of machines and air lines, tool sharpening, and distribution, amounted to 33 per cent. of total mining expense. To do this work there are in commission 43 No. 12A, three No. 17V and eight No. 16V Waugh stopers, three Jackhamers, two Waugh pluggers, and 17 No. 8 ,and two No. 7 water Leyners. For the past three years a record has been kept of the repairs on each machine and number of shifts operated by it. The figures given in Tables I and II for the cost of repairs per drill shift have been taken from this record. The underground air pressure is about 90 lb. The air consumption per drill shift was measured by, aerometers. The leakage of pipe lines between compressor and meter is not included. From the number of pieces of steel sharpened for each type of drill during the year the average used per drill shift has been ascertained. For other supplies the figures given represent a year&apos;s average.

Jan 8, 1914

By Gifford E. White

Explanations of the basic procedure for making earth-conductivity studies by the Eltran method have already appeared in several placeS. 1,2,3 In its essentials, this method consists of applying step functions of voltage to one pair of earth grounds and measuring the transient potential resulting at a separate pair of ground points. As previously pointed out,&apos; the transient potential resulting from a suddenly applied steady voltage is the indicia1 transfer function of Carson1 6 which has been extensively studied in network theory. The discussion here, with one special exception, will ignore the problem of how the physical configuration of the earth affects the transient response voltage; it appears that this phase of the problem has been solved in only a few special cases having any direct bearing on the prospecting problem. Entirely distinct from the potential-theory aspect of the conductivity problem is the interesting material that can be had from studying the well-known network relations between cause and effect in linear circuits, and thus deducing criteria for the application of the several experimental methods available. To do this, only one assumption need be made about the nature of the earth. The earth is to be considered a linear conductor within the tolerance of ordinary measurements. The discussion will be restricted to collinear electrode configuration like that of Fig. I, since this is the only type of spread practical for use with driving currents that vary with time. Here one pair of grounds carries the driving current, and in line with these and external to them is a RECORDING Fair of potential probes. The problem will be to consider the relation between the different voltages appearing between the potential circuit terminals when various types of driving voltage sources are inserted in the current circuit. Suppose that the grounding points G, and G2 make good contact with the earth, and that a battery of sufficient voltage to produce one ampere of direct current is introduced into the current circuit by the closing of a switch. The potential transient response to such a voltage can be measured by taking an oscillogram at the potential Directors terminals, giving the time function that has been called A(l).4 This time function has been solved for analytically in the case of a homogeneous earth,"&apos; and the

Jan 1, 1946