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By D. P. Morton

SINCE 1023, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (I) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.' This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as loo, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods. Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. 2 (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should he the same. It is neces-

Jan 1, 1941

By D. P. Morton

Since 1923, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (1) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.l This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as 100, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods, Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. a (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should be the same. It is neces-

Jan 1, 1942

By D. P. Morton

Since 1923, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (1) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.l This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as 100, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods, Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. a (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should be the same. It is neces-

Jan 1, 1942

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By W. A. Johnson, F. N. Rhines, W. A. Anderson

The rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish- able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1942

By W. A. Anderson, F. N. Rhines, W. A. Johnson

THE rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1941

By W. A. Anderson, F. N. Rhines, W. A. Johnson

The rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish- able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1942

By E. S. Machlin

The kinetics of vacuum distillation, vacuum-melt surface reactions, crucible-melt surface reactions and boiling are analytically investigated. No disagreement with experiment is obtained upon applying a rigid flow model to describe the behavior of the melt in the vicinity of reaction surfaces. The theory focuses attention upon measureable parameters rather than upon the adjustable parameter, stagnant layer thickness, associated with other theories. The rigid flow theory is thus capable of quantitative evaluation and experiments to achieve this evaluation are suggested. KINETICS, rather than thermodynamics, often determine the degree of refinement achieved in vacuum melting. There is little understanding, however, of the kinetic principles involved in vacuum refining. This paper represents an attempt to achieve this understanding. There are two reactions which need to be con- sidered. The first is the refining reaction. The second shall be called the polluting reaction. It is the reaction associated with the introduction of components of the crucible into the melt. The mechanisms of both reactions are unknown. Many models can be constructed to describe either the refining or polluting reactions. For example, consider the refining reaction C + Q = CO(g). One model that can be imagined is that the carbon and oxygen combine in the melt to form CO which then diffuses to a melt-

Jan 1, 1961

By A. B. Stevens, C. J. Coberly

The absolute porosity of a rock or sand may be defined as the volume of the interparticle space expressed as a percentage of the total rock volume. The effective porosity as contrasted with the absolute porosity is the volume of the interparticle spaces which intercommunicate with passages of sufficient size to permit the entrance or recovery of gas or oil, also expressed as a percentage of the total rock volume. A knowledge of effective porosity is of prime importance in estimating the ultimate recovery to be expected from oil and gas-bearing formations. The determination of the effective porosity of a rock includes the measurement of two values: (I) the volume of the rock as a whole, and (2) the volume of the grains and sealed pore space. This paper deals with a new apparatus which has been called a "hydrogen porosimeter" for determining the volume of the grains and the sealed pore space. This volume is determined by means of the pressure relations established in the instrument by the introduction of a known quantity of hydrogen. The Hydrogen Porosimeter The apparatus used in this work consists of an upper chamber for measuring the gas, a lower chamber for holding the sample to be tested, a gage for measuring the pressures, a tank of hydrogen, and the necessary connections. (Figs. 1 and 2.) Of the several gases that might be used for this work, hydrogen has been chosen for three reasons: (1) it deviates less from the gas laws than most gases; (2) it readily penetrates the sample; (3) it is absorbed less than most gases by the solids and liquids with which it may come in contact. Method of Operation After placing the sample to be tested in the lower chamber, the apparatus is thoroughly flushed with hydrogen to remove all air from the system, which is then brought to atmospheric pressure Po. The valve connecting the two chambers is next closed and the pressure in the upper chamber is brought up to a pressure PI by admitting gas from the tank.

Jan 1, 1933

By John Dilworth

THIS paper treats primarily of the valuation of developed coal properties by the method of capitalizing their estimated average future earnings. However, in it reference is also made to valuations of undeveloped coal lands and to various methods of appraisal other than by future earnings. FUNDAMENTAL VALUATION PRINCIPLES Before discussing in detail coal property valuations, a few statements bearing on the general subject will be made to present certain of the writer's views on the question as a whole. 1. A certain property at a given time has but, one true value. This is not universally admitted. The appraiser rather frequently finds that a coal owner has in mind three valuations for his holdings; one, the figure at which he feels they should be appraised for taxation purposes; another, the much higher one that should be used if a loan is to he negotiated on the property; and a third, intermediate between the other two, the price for which he would be willing to dispose of his holdings were they for sale. The last is usually nearest to the true value, and because this is so the statement is generally accepted that the fair value of such a property is the price arrived at by negotiation between a willing seller and a willing buyer who are otherwise disinterested. 2. Notwithstanding the foregoing, it is only very generally and approximately true that the proper measure of the value of a given developed1 coal acreage is the unit or per-acre price for which one or more bodies of similar coal in the salve district have been sold recently. To give a few reasons why such a measure of value can not be strictly applied, it may be noted:

Jan 1, 1927

By John Sherbourne

Much valuable scientific research has been performed in recent years on the subject of phase behavior of hydrocarbons. ? 1-11 Engineers employed in petroleum production are interesting themselves in this work as well as in methods of applying the fundamental data available to the solution of their various problems. Recently a number of papers have been published in which applica-tions of phase behavior have been made to specific cases pertaining to critical phenomena.)12-16 Little effort, however, has been made in the literature to show the relation between changes occurring in the critical region and the more common phase behavior, therefore it is believed that a presentation of the fundamentals of phase behavior with reference to hydrocarbons is timely. Study of phase behavior is not new. In the metallurgical field, knowledge of heterogeneous equilibria has advanced tremendously, particularly with reference to solid-solid and solid-liquid behavior. Much is known about vapor-liquid equilibria too, but few engineers are familiar with this subject. ?

Jan 1, 1940

By Robert E. Campbell

Mining geophysics in 1969 marked a year of growth and consolidation in the application of ground and airborne geophysical methods and techniques with a 20% rise in expenditures for world-wide exploration. Growth was determined by questionnaire survey of industry, geophysical contractors, universities and government agencies conducted by the Society of Exploration Geophysicists. Relative position of metlhods is shown in the accompanying table on page 87. Methods and Techniques Electromagnetic airborne and ground methods showed the largest gains in the utilization of VLF-EM instrumentation. The VLF-EM instrument is a directional radio receiver which is tuned to distant radio transmitters in the 15 to 25 kilohertz band range. It measures vertical real and imaginary components of the magnetic field vector, and is used in geological mapping and surveying for various types of conductors in the ground. Ground VLF-EM instruments, Ronka EM-16 and Radem, are manufactured by Geonics, Ltd., Toronto, Ont., and Crone Geophysics. Ltd., Port Credit. Ont.

Jan 1, 1970

By Nelson Severinghaus

THE Rock Chapel plant of Consolidated Quarries Corporation (Fig, 1) is three miles northeast of Lithonia, DeKalb County, Georgia, It was opened about eight years ago for crushed stone aggregate. This paper reviews a number of experiments that have been tried in drilling and blasting, and gives the practice in use today. It also presents several theories on the action of explosives in this type of blasting. FIG, 1.-PLANT OF CONSOLIDATED QUARRIES CORPORATION, WITH QUARRY AT UPPER LEFT. The rock worked is a bare dome of granite gneiss about 3000 ft. in diameter, rising 150 ft. above the surrounding ground (Fig. 2). It is uniform in composition and quality, without seams, and extends down-ward to unknown depth below the quarry floor. A water well drilled 600 ft. remained in the same rock. The principal difficulty encountered in blasting is an easy split, which tends to break down the rock in large blocks.

Jan 1, 1938

By A. S. Nowick, E. S. Machlin

One of the main criteria used to rate the heat-resisting properties of alloys is stress rupture.' During a stress-rupture test a tensile specimen is held under a constant load at a constant temperature until it fractures. The chief measurement made during this test is the time requird for rupture at the specific test stress and temperature. It was found empirically from a series of stress-rupture tests at a constant temperature that when the logarithm of the time for rupture is plotted against the logarithm of stress a straight line is obtained within experimental error This method of showing stress-rupture data has been adopted by many investigators and the NACA.' By interpolation and extrapolation from these plots, values of the stresses required to rupture the specimens (the rupture strengths) in 10, roo, and 1000 hr are obtained for specific temperatures. Alloys are then rated for a particular application on the basis of their rupture strengths at the rupture life that most nearly represents the application. Inasmuch as stress rupture is an important criterion in rating heat-resisting alloys, it would be advantageous to know the quantitative dependence of the time lor rupture on stress, temperature, composition, and structure. In order to obtain this information, an investigation was made at the NACA Cleveland laboratory during the spring of 1945. The theory of rate processes was used because it has been found to apply to certain processes such as chemical reactions, viscous flow, and creep that occur at a definite rate for given conditions. It was thought that stress rupture was such a process. An equation was derived that gives, for a given composition and structure, the dependence of the time for rupture on stress and temperature. The investigation is part of a general program to provide information that will lead ultimately to the development of better alloys in order that the efliciency and power output of gas turbines used in aircraft propulsion can be increased. Theory The theory of rate processes will first be discussed as a general theory. It will then be shown that if stress rupture of heat-resisting alloys can be treated as a rate process, certain equations must be satisfied. Later sections will then show that these equations are satisfied. General Theory of Rate Processes The theory of rate processes5 developed by Eyring and others has been applied to chemical reactions as well as to other processes such as viscosity of liquids and diffusion. In every case in which rate-process theory can be applied, there is a small subdivision, so that the macroscopic process is the net effect of all the small processes. This smallest subdivision is called the "unit process." For example, in a chemical reaction the unit process is

Jan 1, 1948

By A. S. Nowick, E. S. Machlin

One of the main criteria used to rate the heat-resisting properties of alloys is stress rupture.' During a stress-rupture test a tensile specimen is held under a constant load at a constant temperature until it fractures. The chief measurement made during this test is the time requird for rupture at the specific test stress and temperature. It was found empirically from a series of stress-rupture tests at a constant temperature that when the logarithm of the time for rupture is plotted against the logarithm of stress a straight line is obtained within experimental error This method of showing stress-rupture data has been adopted by many investigators and the NACA.' By interpolation and extrapolation from these plots, values of the stresses required to rupture the specimens (the rupture strengths) in 10, roo, and 1000 hr are obtained for specific temperatures. Alloys are then rated for a particular application on the basis of their rupture strengths at the rupture life that most nearly represents the application. Inasmuch as stress rupture is an important criterion in rating heat-resisting alloys, it would be advantageous to know the quantitative dependence of the time lor rupture on stress, temperature, composition, and structure. In order to obtain this information, an investigation was made at the NACA Cleveland laboratory during the spring of 1945. The theory of rate processes was used because it has been found to apply to certain processes such as chemical reactions, viscous flow, and creep that occur at a definite rate for given conditions. It was thought that stress rupture was such a process. An equation was derived that gives, for a given composition and structure, the dependence of the time for rupture on stress and temperature. The investigation is part of a general program to provide information that will lead ultimately to the development of better alloys in order that the efliciency and power output of gas turbines used in aircraft propulsion can be increased. Theory The theory of rate processes will first be discussed as a general theory. It will then be shown that if stress rupture of heat-resisting alloys can be treated as a rate process, certain equations must be satisfied. Later sections will then show that these equations are satisfied. General Theory of Rate Processes The theory of rate processes5 developed by Eyring and others has been applied to chemical reactions as well as to other processes such as viscosity of liquids and diffusion. In every case in which rate-process theory can be applied, there is a small subdivision, so that the macroscopic process is the net effect of all the small processes. This smallest subdivision is called the "unit process." For example, in a chemical reaction the unit process is

Jan 1, 1948

By A. S. Nowick, E. S. Machlin

ONE of the main criteria used to rate the heat-resisting properties of alloys is stress rupture.1 During a stress-rupture test a tensile specimen is held under a constant load at a constant temperature until it fractures. The chief measurement made during this test is the time required for rupture at the specific test stress and temperature. It was found empirically from a series of stress-rupture tests at a constant temperature that when the logarithm of the time for rupture is plotted against the logarithm of stress a straight line is obtained within experimental error.2~3 This method of showing stress-rupture data has been adopted by many investigators and the KACA.4 By interpolation and extrapolation from these plots, values of the stresses required to rupture the specimens (the rupture strengths) in 10, 100, and 1000 hr are obtained for specific temperatures. Alloys are then rated for a particular application on the basis of their rupture strengths at the rupture life that most nearly represents the application. Inasmuch as stress rupture is an important criterion in rating heat-resisting alloys, it would be advantageous to know the quantitative dependence of the time for rupture on stress, temperature, com- position, and structure. In order to obtain this information, an investigation was made at the KACA Cleveland laboratory during the spring of 1945. The theory of rate processes was used because it has been found to apply to certain processes such as chemical reactions, viscous flow, and creep that occur at a definite rate for given conditions. It was thought that stress rupture was such a process. An equation was derived that gives, for a given com- position and structure, the dependence of the time for rupture on stress and temperature. The investigation is part of a general program to provide information that will lead ultimately to the development of better alloys in order that the efficiency and power output of gas turbines used in aircraft propulsion can be increased. THEORY The theory of rate processes will first be discussed as a general theory. It will then be shown that if stress rupture of heat-resisting alloys can be treated as a rate process, certain equations must be satisfied. Later sections will then show that these equations are satisfied. General Theory of Rate Processes The theory of rate processes5 eveloped by Eyring and others has been applied to chemical reactions as well as to other processes such as viscosity of liquids and diffusion. In every case in which rate- process theory can be applied, there is a small subdivision, so that the macroscopic process is the net effect of all the small processes. This smallest subdivision is called the "unit process.'' For example, in a chemical reaction the unit process is

Jan 1, 1947

By V. S. Rood

Typical System of Workings THE general system of workings at the Utah-Apex is similar to that found in many of the western metalliferous mines. There is a vertical three-compartment shaft extending to the surface, from which the various levels have been driven to the orebodies. The 1000-ft. (305-m.) level, about ¾ mile long, was driven as a haulage and drain adit. Geology The formation is a flat north-dipping series of alternating limestone and quartzite beds. Extensive north-south faulting and-fissuring have taken place, resulting in the formation of large replacement orebodies in the crushed zones in the limestone. The orebodies are irregular in shape and size, but follow closely the trend of the mineralizing fissures. The ore consists of galena, pyrite, sphalerite and small values in silver and gold. Large masses of non-commercial pyrite are frequently found in or adjacent' to the orebodies, and more or less pyrite is found for some distance in the walls of the orebodies. Lenticular bodies of a black pyritic shale also occur in the zones where extensive faulting has taken place.

Jan 6, 1918

By Walter S. Weeks

THE subject of the flow of air through a mine under the influence of natural ventilation has proved an elusive one. To my knowledge only cut and try algebraic solutions have been used where multiple paths are involved. The object of this paper is to present a method for the graphical determination of the flow induced by the natural ventilation pressure (N.V.P.) alone or in combination with a fan. The N.V.P., measured in pounds per square foot, induced by two columns of air between two horizontal planes at different elevations, is equal to the difference in weight of the two columns, assuming each to have a cross-sectional area of 1 sq. ft. Pressure in pounds per square foot is converted into inches of water by dividing by 5.19. Methods of calculating the N.V.P. have been discussed in the literature. In this paper, for simplification of exposition, the change in pressure due to the weight of superimposed air will be assumed directly proportional to the length of the column. The actual methods of calculating the N.V.P. do not affect the solutions to be presented. It must be realized that the precision to be obtained from the small- scale, inked diagrams presented is not as great as would be obtained from large-scale, penciled curves that would be used in practice. The accuracy of the curves does not warrant reading "volumes" closer than the nearest thousand cubic feet per minute. CASE I. DUCTS IN SERIES The simplest type of problem is to determine the flow when two shafts are connected by a crosscut, as shown in Fig. 1. In this example, the resistance of the shafts is to be taken as 0.0001 in. of water for a flow of 1000 cu. ft. per minute for a length of 1000 ft. The resistance of a crosscut is to be taken as 0.0005 in. of water for a flow of 1000 cu. ft. per minute. The small pressures necessary to cause changes in velocity will not be considered, because the accuracy of other obtainable data does not warrant their consideration.

Jan 1, 1938

By A. S. Odeh

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

Jan 1, 1969