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By J. T. Eash, E. M. Wise

Platinum and palladium are the most generally useful, most ductile and least rare members of the platinum family. They have many important applications in the pure state but for other applications it is frequently desirable to harden them and otherwise modify their properties by alloying small amounts of the other platinum group metals with them. These alloys are frequently required to withstand very drastic forming operations and to possess certain mechanical properties to fulfill specific requirements. For these reasons a knowledge of the tensile properties and annealing characteristics of pure platinum and palladium as well as their more useful commercial alloys is important to the user and the fabricator. The present work was undertaken to fill this need. Rather brief (5 min.) annealing treatments were employed to render the data of maximum practical value and all tests were conducted upon 0.050-in. dia. wire, initially reduced 50 per cent in area by cold drawing, for the same reason. Conclusions 1. Pure (thermocouple grade) platinum reduced 50 per. cent by cold drawing exhibits the following tensile properties: ultimate tensile strength, 36,000 lb. per sq. in.; proportional limit, 27,000 lb. per sq. in.; elongation, 2.5 per cent in 2 in.; reduction in area, 95 per cent. When fully annealed by treatment at 1100°C. its properties are: ultimate tensile strength, 20,700 lb. per sq. in.; elongation, 30 per cent in 2 in.; reduction in area, 93 per cent. 2. The addition of alloying elements in moderate amounts markedly increases the strength and annealing temperature without much detriment to the ductility. The behavior and properties of variously hardened platinum alloys are considered in some detail. The behavior of a 20 per cent iridium

Jan 1, 1935

By J. T. Eash, E. M. Wise

Platinum and palladium are the most generally useful, most ductile and least rare members of the platinum family. They have many important applications in the pure state but for other applications it is frequently desirable to harden them and otherwise modify their properties by alloying small amounts of the other platinum group metals with them. These alloys are frequently required to withstand very drastic forming operations and to possess certain mechanical properties to fulfill specific requirements. For these reasons a knowledge of the tensile properties and annealing characteristics of pure platinum and palladium as well as their more useful commercial alloys is important to the user and the fabricator. The present work was undertaken to fill this need. Rather brief (5 min.) annealing treatments were employed to render the data of maximum practical value and all tests were conducted upon 0.050-in. dia. wire, initially reduced 50 per cent in area by cold drawing, for the same reason. Conclusions 1. Pure (thermocouple grade) platinum reduced 50 per. cent by cold drawing exhibits the following tensile properties: ultimate tensile strength, 36,000 lb. per sq. in.; proportional limit, 27,000 lb. per sq. in.; elongation, 2.5 per cent in 2 in.; reduction in area, 95 per cent. When fully annealed by treatment at 1100°C. its properties are: ultimate tensile strength, 20,700 lb. per sq. in.; elongation, 30 per cent in 2 in.; reduction in area, 93 per cent. 2. The addition of alloying elements in moderate amounts markedly increases the strength and annealing temperature without much detriment to the ductility. The behavior and properties of variously hardened platinum alloys are considered in some detail. The behavior of a 20 per cent iridium

Jan 1, 1935

By Thomas M. Drown

THE means relied on to attain uniformity in Bessemer steel may be enumerated as follows I. The appearance of the flame. II. The appearance of the slag. III. The spectrum of the flame. IV. Examination of the steel itself. At present, I wish briefly to bring forward a few considerations with reference to the last two mentioned, namely, the conditions favoring the employment of the spectroscope and examination of the steel. From the amount of careful investigation which has been devoted to the examination of the Bessemer flame by the spectroscope, both on the part of scientists and practical metallurgists, one might reasonably expect some results definite and satisfactory in their nature, first, as regards the nature of the flame, and second, as to the practical value of the spectroscope as a guide in conducting the process. We find, in fact, however, that uncertainty and confusion still exist. In Germany, where this subject has received the greatest attention, it is now very generally conceded that manganese is the cause of the well-known groups of dark bands that characterize the Bessemer spectrum. Nor is it easy to see how we can avoid accepting this conclusion, when Wedding and Von Lichtenfels have produced the manganese spectrum and found it to correspond closely with that shown by the Bessemer flame. But it is evident, on a moment's reflection, as Roscoe has recently brought forward, that manganese cannot be the only cause of the Bessemer spectrum, for we notice the characteristic bands quite as

Jan 1, 1873

By P. L. Menaul, P. P. Spafford

This paper discusses the most dangerous form of corrosion encountered in condensate-well oil production, the discovery of the agent causing this corrosion and the remedial chemical treatment proved effective by field use. The injection of ammonium hydroxide, even as little as one quart per day, has proved effective in preventing gas-condensate well corrosion. The injection of "Bone oil" is applied to wells producing brines containing calcium and magnesium salts. Introduction The severe corrosion of equipment in high pressure gas condensate wells has been a problem for several years and numerous papers have been presented on the subject. The term "gas condensate" or "distillate well" is applied to a distinct variety of hydrocarbon producing well, the characteristics of these wells being high bottom-hole (formation) pressures and temperatures and high gas production. These wells usually produce about 40 gal of water per million cubic feet of gas and the gas contains from 0.1 pct to 2 pct carbon dioxide. In the operation of this type of well, the operators soon noted severe internal corrosion of the pipe carrying the production. In some instances the dl tubing has been found to be corroded to perforation in eight months. The high well head pressures of 2500 to 8000 psi makes any weakening of the well equipment by corrosion extremely hazardous. Bursting of the well equipment results in very expensive repair operations and may result in the loss of valuable production, loss of the costly well, or even loss of life. In November 1944, a gas-condensate well in a Gulf Coast field producing from 9500 ft showed a tubing leak. The well was "killed" by filling it with mud through the tubing, and then the tubing was pulled. Corrosion was found to have caused several perforations in the tubing, Fig I. While the mud was being circulated to kill the well, a high pressure jet from the corroded hole in the tubing perforated the casing and damaged the well to the extent that the cost of repairs amounted to $75,000. In November 1944, another gas-con-densate well in a Gulf Coast field producing from 11,400 ft showed tubing failure. This well had been producing an average of 2,500,000 cu ft of gas daily for two years. In the workover of this well, it was found that a hole one inch in diameter had corroded through the tubing and that corrosion had reduced the wall of the tubing to less than half the standard thickness over large areas of the interior of the tubing. It was found that corrosion had also caused two leaks in the casing. After four months spent in an attempted workover failed to make the well safe for further production, the well was plugged and abandoned at a total loss of $300,000,00.

Jan 1, 1948

By P. L. Menaul, P. P. Spafford

This paper discusses the most dangerous form of corrosion encountered in condensate-well oil production, the discovery of the agent causing this corrosion and the remedial chemical treatment proved effective by field use. The injection of ammonium hydroxide, even as little as one quart per day, has proved effective in preventing gas-condensate well corrosion. The injection of "Bone oil" is applied to wells producing brines containing calcium and magnesium salts. Introduction The severe corrosion of equipment in high pressure gas condensate wells has been a problem for several years and numerous papers have been presented on the subject. The term "gas condensate" or "distillate well" is applied to a distinct variety of hydrocarbon producing well, the characteristics of these wells being high bottom-hole (formation) pressures and temperatures and high gas production. These wells usually produce about 40 gal of water per million cubic feet of gas and the gas contains from 0.1 pct to 2 pct carbon dioxide. In the operation of this type of well, the operators soon noted severe internal corrosion of the pipe carrying the production. In some instances the dl tubing has been found to be corroded to perforation in eight months. The high well head pressures of 2500 to 8000 psi makes any weakening of the well equipment by corrosion extremely hazardous. Bursting of the well equipment results in very expensive repair operations and may result in the loss of valuable production, loss of the costly well, or even loss of life. In November 1944, a gas-condensate well in a Gulf Coast field producing from 9500 ft showed a tubing leak. The well was "killed" by filling it with mud through the tubing, and then the tubing was pulled. Corrosion was found to have caused several perforations in the tubing, Fig I. While the mud was being circulated to kill the well, a high pressure jet from the corroded hole in the tubing perforated the casing and damaged the well to the extent that the cost of repairs amounted to $75,000. In November 1944, another gas-con-densate well in a Gulf Coast field producing from 11,400 ft showed tubing failure. This well had been producing an average of 2,500,000 cu ft of gas daily for two years. In the workover of this well, it was found that a hole one inch in diameter had corroded through the tubing and that corrosion had reduced the wall of the tubing to less than half the standard thickness over large areas of the interior of the tubing. It was found that corrosion had also caused two leaks in the casing. After four months spent in an attempted workover failed to make the well safe for further production, the well was plugged and abandoned at a total loss of $300,000,00.

Jan 1, 1948

By Carl R. Christiansen, James J. Scott

Advance mine planning, coupled with good mining practice, can be employed to develop underground space in stone mines for future industrial usage. To assure the developer the maximum return on his investment, initial planning should consider all aspects of the commercial operation, including surface layout, mining, and underground industrialization. The modular concept of mining to compartmentalize the space offers several advantages over conventional methods. Some expenditures can be considered as mining costs with a reduction of profit from stone production while lowering the capital requirements for conversion for usable space.

Jan 1, 1977

By Louis D. Huntoon

After the completion, in 1905, of the Hammond Mining and Metallurgical Laboratory of the Sheffield Scientific School, Yale University, it became necessary to secure and assay a large assortment of ore-samples, and to arrange the results in such a manner as to admit of use with the least amount of work on the part of the instructor. At first, pulp-samples, together with their respective assays, were secured from the mines, smelters, and public aesayers, but this practice did not prove satisfactory. It was not only difficult to secure a suffciently large supply of material, but it was also impossible to secure the proper assortment required for instructing students. It involved considerable work for the donors to select the samples and furnish a record of the assays, and also for the instructors to examine each pulp and determine its character. Some of the samples did not contain a sufficient quantity of pulp for the student to check his work in case his first assay did not correspond to the record. In order to increase the number of samples and to vary the character of the material, pulp-samples were later mixed with barren rock and with sulphides, but this method also was unsatisfactory and has been discontinued. At present, small lots of ore are secured by gift or purchase from engineers, public assayers, and the managers of mines, mills, and smelters. These lots weigh from 10 to 100 lb. each, and are rarely finer than 0.25 in. in size. The larger samples permit of a careful study by the instructor in order to determine the best method of assaying to be followed. In universities in which assaying is taught the record of the samples should fulfill the following requirements:

Jan 1, 1910

By J. M. McDowell

A study has been made to deter~r~irre how the behavior of a water drivee reservoir changes as a function of the permeability of the formation and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rote of nat11rn1 water influx is also studied, (IS well as the influence on the influx of the position of water injection we1ls with reference to the oil-water contact. The results are determined by the use of an electrical reservoir analyzer and are plotted as families of curves of pressure, natural water influx, and water injection vs time or cumulalive production. Two size aquifers are studided. One is limited with a 36-inile radius, and the, other approximates an infinite reservoir. The field remains the same in all respects for the completed. study except that the permeability is changed to agree with that assumed for the aquifer. 1 N TR ODUCTI ON this study was undertaken in -dcr to determine how the pres- sure decline and water influx of a water drive field would change as a function of the rate of fluid withdrawals, as a function of the permeability of the formation, and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rate of natural water influx was also studied as was the position of water injection wells with reference to the oil-water contact. The information has been determined by the use of an electrical reservoir analyzer1, sometimes referred to as a Carter type analyzer. This instrument is an analog type computer which can be set up to represent a water-drive oil field. It can reproduce the past performance of the field in terms of analogous electrical quantities when the proper circuit analog of resistors and condensers has been determined, also, it can determine the future behavior for any method of production which may be selected, or permit the comparison among several different methods. Although most applications of the reservoir analyzer"" have been to thc study of specific field performance, it is intended to use the analyzer here to help understand how various reservoir characteristics effect the final performance of the field and to sec under what conditions water injection will be of benefit and to what extent. Within the oil industry the performance of water-drive reservoirs was first described analytically by LV. Hurst' and M. Muskat2 for certain types of boundary conditions. The solutions of the equations developed involved products of exponential functions and Bessel functions. Later publications by Hurst4 and van Ever-clingen" and the hooks of Muskat6 gave further information on reservoirs with other boundary conditions. They also presented rather extensive curves and tables to help evaluate the analytical expressions involved. A rccent series of publications by Chatas. bascd on the work of Hurst and van Everdingen, gives quite complete charts and tables of data to evaluate the pressure decline or water influx in infinite or limited radial reservoirs. and in linear reservoirs. The curves in all of these publications are given in dimensionless form

Jan 1, 1956

By Klaus Schoenert

In the analysis of comminution processes, it is necessary to have a detailed knowledge of such subprocesses as: transportation of the particles to the zone where they are stressed; the stressing of particles to a level high enough for breakage; removal of the fragments that are smaller than the limit size from the grinding zone; and prevention of agglomeration of the fine fragments. Breakage phenomena of particles is the most difficult subprocess to understand. It can be understood only by applying the principles of fracture physics to obtain information about the stress-strain field in particles which are loaded either by compression or by impact, and by using this theoretical knowledge to interpret experimental results obtained from single particle crushing studies. Two important features of the "Science of Communition" are discussed: the fracture physics and crushing under controlled conditions with special reference to single particle crushing, packed bed crushing, measurement of energy needed for fracture, fragment size distribution, and new surface area produced. The important features of these aspects are detailed, namely, energy balance of a crack, influence of environment, specimen size problems, and energy utilization in single particle crushing.

Jan 1, 1973

OFFICERS AND DIRECTORS For the year ending February, 1932 PRESIDENT ROBERT E. TALLY JEROME, ARIZ. FREDERICK W. BRADLEY SAN FRANCISCO, CAL. WILLIAM H. BASSETT,P WATERBURY, CONN KARL EILERS NEW YORK N. Y.

Jan 1, 1929

By John C. Smock

The question of the proper valuation of mines of iron ore was suggested to me by the difficulties experienced in getting answers for the United States Census Office, while I was engaged in the work of collecting the statistics of mines in New Jersey and New York. The answers to the questions relating to values of real estate of mine properties varied so greatly that it was necessary to revise them according to some general principles of valuation. Generally the returns of mine proprietors seemed to be too low. There were, however, examples of what would be termed excessive valuation. The subject appeared to be of practical importance, and led to the paper here presented. The following table of selected mine statistics is given, prefacing the discussion of the principles of valuation. It is in part made up of census returns and partly of data obtained directly from mine owners and managers. The mines which were selected for the several groups and mining districts include nearly all of those from which the more full and carefully filled returns were received, and are also representative of their respective districts. Hence the averages obtained from them become good types of these groups or districts. The mines of New Jersey appear in six groups, each containing from three to eleven mines, or, in all, thirty-four mines. The magnetic iron ores of New York are in four well-marked groups, and there are twenty-six mines in them. Then follow the red hematite mines of St. Lawrence and Jefferson counties; and, lastly, the brown hematite groups of Dutchess and Columbia counties, and those of the adjacent parts of Connecticut and Massachusetts. The whole number of mines represented by the table is eighty-eight, of which twenty-eight are hematite mines. The first column gives the value of the real estate; the second that of the plant; the third is the sum of these two, or the capital invested. Then follow the number of men employed, the amount of wages paid during the census year, and the value of materials used in mining and preparing the ores for market." The seventh column gives the total expendi-

Jan 1, 1882

By Wittenau, E.

OPERATION of a pilot mill of 100 tons' daily capacity during 1930 and 1931 proved that the copper minerals of the Colorado and Clay sections of the Morenci ore body could be successfully concentrated by the flotation process. Economic conditions caused postponement of further testing work until late in 1938 when the former No. 6 Concentrator at Morenci was converted into an experimental mill of 1500 tons' daily capacity which was known as the Test Concentrator. The Test Concentrator began continuous operation on April 3. 1939, using such crushing and grinding equipment of the No. 6 Concentrator as was appropriate. Modern classifiers and certain flotation machines were installed and later other types of flotation machines, a large grate-type grinding mill. mechanical screens, a short-head cone crusher, and a disk filter were added to the test equipment. Operation was uninterrupted until Dec. 31, 1941.

Jan 1, 1942

By Rebecca Mae Summer

Increasing urbanization and industrial activity require increased supplies of sand and gravel. This means expanded surface mining and despoiled land near population centers. Highly competitive land use demands justify serious consideration of premining planning for multiple land use and reclamation concurrent with mining. 1-5 Formulating solutions to environmentally and economically sound uses requires a comprehensive approach based on properties of the natural resource base--geology, soils, and water. A study of sand and gravel mining within Pleistocene-Holocene fluvial deposits in Colorado County. Texas [(Fig. 1)] illustrates how physical limitations imposed by the resource base are determined.6,7 Data from drillers, logs of water wells, test boreholes, field observations, and laboratory analyses are used to evaluate these physical controls. Knowledge of the thickness and composition of overburden aids in developing optimum reclamation and revegetation plans. Most of the overburden in the study area [(Fig. 2, 3)] is a clayey mud with variable amounts of silt and fine sand. A comparative textural analysis of overburden and native soil is used to assess changes incurred by mining and for evaluating other physical characteristics, e.g., ability to support crops, permeability. and shrink-swell potential. Textures are correlated with soil types found in the area [(Table 1)] to get an approximation of probable surface properties expected from these mined materials. Results of textural analyses [(Table 2)] indicate that separating topsoils from overburden during mining is not necessary because the range of overburden textures is about that of native soils. However, more data is needed on nutrient deficiencies to evaluate fertilizer requirements for successful revegetation.*6

Jan 1, 1979

By J. L. Lamon, W. Crafts

P. Coheur and L. Habraken—We read this paper with great interest and are glad to congratulate the authors for their valuable work, supplying an important contribution to the mechanism of tempering on the carbides in vanadium steels. We are in a good position to appreciate this work since we have been studying, for more than a year, Cr-Mo steels of a composition similar, but less highly alloyed (namely 0.1 pct C, 3 pct Cr, 1 pct Mo). Our results are quite in concordance with the authors', however, we wish to point out that it is very interesting to use equally the electron microscope in order to observe the variations of microstructure in steels. We have studied simultaneouslv the evolution of the carbides in situ with the electron microscope, and, after extraction, again with the electron microscope, and then with X-rays. The first results which we have obtained have been communicated at the Congress of Delft (July 1949) and at the "Journbes de la Metallurgie" in Paris (October 1949). These may be summarized as follows: After tempering with varying either the tempering temperatures or the tempering times, the carbides show two evolutions. The first one is connected to the carbides existing in the steels, principally in the boundaries of the grains. For some groups of steels these carbides may coalesce and for other groups they may

Jan 1, 1951

By B. W. Levinger

THE system Ti-CI- has been studied by several investigators." ' Though titanium and chromium are completely miscible at high temperatures, an intermediate phase of the approximate atomic proportions TiCr, has been identified at various compositions between 60 and 68 wt pct Cr. The structure of this phase was established as the cubic C15 (MgCu2) type with 24 atoms per unit cell and a lattice parameter 6.929 kX.2 During a study of the ternary system, Ti-Mo-Cr,5 the existence of a high temperature modification of the TiCr, phase was discovered. In a series of alloys annealed at 1300°C and containing from 60 to 70 wt pct Cr and 5 pct Mo, a new phase was present which did not correspond to either ß solid solution or TiCr,. By trial, the new phase was identified to be of the hexagonal C14 (MgZn2) structure with 12 atoms per unit cell. Further work showed that the hexagonal structure was. in fact, also present in binary Ti-Cr alloys quenched from high temperatures. To make the identification more certain, the intensities of the various reflections were calculated assuming a composition TiCr2 and C14 structure. Table I lists reflection planes, interplanar distances, calculated intensities, and a comparison of these values with the lines of a binary Ti-Cr alloy (66 pct Cr) annealed for 20 min at 1385°C and water quenched. Since high angle lines were more diffuse, the correspondence between visually observed and calculated intensities was not as good at these angles. Lattice parameters were computed to be a = 4.922 kX, c = 7.945, c/a :- 1.614. The corresponding interatomic distances are: titanium to titanium distance, 3.00:, kx, chromium to chromium distance, 2.43, kX, titanium to chromium distance, 2.88,, kX. These compare to 3.00, 2.45, and 2.87 kX in the cubic phase, respectively.' The atomic positions in the C14 structure are as follows: Titanium 1/3, 2/3, Z; 1/3, 2/3, 1/2: 2/3, 1/3, i; 2/3, 1/3, (1/2-z); Chromium 0, 0, 0: 0, 0, 1/2; 2x, 2, 1/4; 232, x, %; X, 22, 1/4; X, 2x, 3/4; x. x, 1/4; x, x, 3/4; The values of x and z were calculated for the alloy mentioned and found as follows: z — 0.061, x = 0.165. The values assumed in the intensity calculations were those for an ideal close-packed lattice or z = 1/16, x = 1/6. Work in the Ti-Mo-Cr system indicates that y2 the hexagonal modification of TiCr2, is the stable phase above 1300°C, while y1 with the cubic structure is stable below 1000°C. X-ray examination of a number of alloys annealed at intermediate temperatures showed that the hexagonal and cubic phases can coexist. Alloys quenched from 1000°C and annealed at 1100" and 1200°C showed small amounts of y2 at the higher temperature. A considerable amount of y, seemed present, however, in cast alloys annealed at 1100°C. It further appears that there is a small but definite solubility range for both phases in the ternary system. Acknowledgment The results of this paper represent work carried out in conjunction with a project sponsored by Watertown Arsenal, Contract No. DA-11-022-ORD-272. References 'M. K. McQuillan: Journal Inst. Metals (1951) 79, p. 379. 2 P. Duwez and J. L. Taylor: Trans. ASM (1952) 44, p. 495. W. J. Van Thyne,. H.. D. Kessler, and M. Hansen: Trans. ASM (1952) 44, p. 974. 1 F. B. Cuff, N. J. Grant, and C. F. Floe: Trans. AIME (1952) 194, p. 848; Journal of Metals (August 1952). Unpublished Research, Armour Research Foundation. "H. J. Wallbaum: Ztsch. Krist. 103, p. 391.

Jan 1, 1954

Jan 1, 1935

By Carl L. Renzoni

INTRODUCTION This paper defines equity as the issuance of a permanent interest in the business on a broadly distributed basis. As such, it excludes the issuance of equity to either a merchant bank or to another corporation. Nearly twenty years ago the equity markets were very simple: The instruments used were primarily common shares, convertible debentures or convertible preferred shares. Another equity-type option often used, especially by junior companies, was the sale of joint venture interests. Issue sizes were generally in the order of $25 - $100 million and issues were syndicated primarily in North America and Europe by one or two investment dealers. Mining corporations today benefit from a market with much more depth. Issues are syndicated by dealers on a truly international basis, and issue sizes now often range up to $300 million. Moreover, dealers are now willing to take significant risk in buying the issues for redistribution. This discussion of trends in equity markets will encompass: 1) common shares 2) warrants to buy common shares 3) convertible debentures 4) commodity backed instruments A review follows of events that affect the mining industry and investment dealers as they have a bearing on the equity markets for the metal producers. FACTORS AFFECTING THE MINING INDUSTRY The current business cycle, up to October 1987, had been characterised by a buoyant stock market and depressed base metal prices. Mining companies entered this period with weak balance sheets and little prospect of cash flows meeting capital needs. The issuance of equity and the sale of assets were used extensively to reduce debt to manageable levels. During this period, the relative high price for gold, and more important, the very high earnings and cash flow multiples afforded to gold producers, caused companies to target gold as the only game in town. The need for capital to acquire and develop gold properties prompted an unprecedented volume of equity issues. (Burns Fry led or co-managed over $1 billion of mining equity issues per year during this period). This high demand for equity capital by the industry prompted an increase in the use of equity instruments, such as commodity backed instruments. In addition, government tax incentive programs in Canada, such as flow-through shares, allowed smaller companies to raise significantly more equity than would otherwise have been possible. Over $1 billion in flow-through equity was raised in 1987 alone. The abundance of flow-through capital in Canada made it easy to form a new company. One flow-through share fund developed a system of providing the working capital required for a company to be eligible to receive flow-through share capital so that an entrepreneur required only a mining property to get started. Many new companies were formed and several flourished in a buoyant stock market environment to the point that market capitalizations grew to $100 million or more. The current period is in stark contrast to that before October 1987. The equity markets are generally available to the resource industry only on a window basis and only for senior companies and for special situations. The industry is benefitting from buoyant metal prices, and bankers are anxious to provide debt capital. Investment dealers previously processing several equity issues

Jan 1, 1990

By K. H. Coats

This paper presents the development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertical direction due to router flow are taken into account. A vertical permeability equal to a fraction of the horizontal permeability is also included in the model. The solution is given in the form of a dimensionless pressure-drop quantity tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservoir pressure from a known water-influx rate, to predict water-influx rate (or cumulative amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. The model is applied in example problems to gas-storage reservoirs, and the difference between reservoir performances predicted by the thick sand model of this paper and the horizontal, radial-flow model is shown to be appreciable. INTRODUCTION The calculation of aquifer water movement into or out of oil and gas reservoirs situated on aquifers is important in pressure maintenance studies, material-balance and well-flooding calculations. In gas storage operations, a knowledge of the water movemenr is especially important in predicting pressure and pore-volume behavior. Throughout this paper the term "pore volume" denotes volume occupied by the reservoir fluid, while the term "flow model" refers to the idealized or mathematical representation of water flow in the reservoir-aquifer system. The prediction of water movement requires selection of a flow model for the reservoir-aquifer system. A physically reasonable flow model treated in detail to date is the radial-flow model considered by van Everdingen and Hurst.1 In many cases the reservoir is situated on top of the aquifer with a continuous horizontal interface between reservoir fluid and aquifer water and with a significant depth of aquifer underlying the reservoir. In these cases, bottom-water drive will occur, and a three-dimensional model accounting for the pressure gradient and water flow in the vertical direction should be employed. This paper treats such a model in detail — from the description of the model through formulation of the governing partial differential equation to solution of the equation and preparation of tables giving dimensionless pressure drop as a function of dimensionless time. The model rigorously accounts for the practical case of a vertical permeability equal to some fraction of the horizontal permeability. The pressure-drop values can be used in given equations to predict reservoir pressure from a known water-influx rate or to predict water-influx rate (or cumulative amount) when the reservoir pressure is known. The inclusion of gravity in this analysis is actually trivial since gravity has virtually no efFect on the flow of a homogeneous, slightly compressible fluid in a fixed-boundary system subject to the boundary conditions imposed in this study. Thus, if the acceleration of gravity is set equal to zero in the following equations, the final result is unchanged. The pressure distribution is altered by inclusion of gravity in the analysis, but only by the time-constant hydrostatic head. The equations developed are applied in an example case study to predict the pressure and pore-volume behavior of a gas storage reservoir. The prediction of reservoir performance based on the bottom-water-drive model is shown to differ significantly from that based on van Everdingen and Hurst's horizontal-flow model. DESCRIPTION OF FLOW MODEL The edge-water-drive flow model treated by van Everdingen and Hurst1 is shown in Fig. la. The aquifer thickness b is small in relation to reservoir radius rb. water invades or recedes from the field at the latter's edges, and only horizontal radial flow is considered as shown in Fig. 1b. The bottom-water-drive reservoir-aquifer system treated herein is sketched in Fig. 2a and 2b. Here the aquifer

By William Fink

MANY investigators have attempted to determine the true nature of the internal changes taking place during aging. Merica, Waltenberg and Scott1 were the first to propose a theory of age-hardening. They attributed the age-hardening of duralumin to the precipitation of minute particles of the compound CuA12. Later Zay Jeffries and R. S. Archer2 augmented the above theory by suggesting that the small CuA12 particles acted as "keys" causing "slip interference." Many other investi-gators3 have devoted much time to the mechanism of age-hardening, some corroborating the "precipitation" and "slip interference" theory, others coming to different conclusions because of effects that to them seemed unexplainable by the early theories; e.g., the increase of electrical resistance upon aging, the fact that no change in lattice parameter could be detected during the early stages of aging even at elevated tempera-tures, and the fact that the density did not change as would be predicted. In 1932, Merica revised4 his earlier precipitation theory to take care of these presumably anomalous effects. This revised theory, the "knot" theory, assumes that substantial age-hardening occurs before actual precipitation of solute as discrete particles. The assumed mechanism is one of diffusion of solute atones into groups forming distorted regions which act as "hard" spots and cause slip interference. These "knots" are assumed to have approximately the same lattice arrangement as the solvent.

Jan 1, 1936

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,' based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry' has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962