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By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By Albert Ledoux

SEVERAL years ago my firm was representing the Mt. Lyell Co. of Australia, which was shipping its blister copper to a refining works in the United States. After the contract had been running for many months, the superintendent of these works discovered that if water was poured upon the surface of the bars much of it would disappear into the interior through blow holes. -Some experiments made by him showed that this could be a considerable amount, so that copper which had been rained on before it was weighed, although the surface appeared dry, nevertheless would contain water. It had frequently occurred in our experience-as samp-lers that the drillings from a lot taken by boring would come out quite wet, and in some cases, indeed, water would drip into the sample pan placed below the bars, due to the fact that the drill had penetrated a cavity or cavities containing water, which presumably got into the cavities at the time the copper was water-cooled after casting, there being, perhaps, no outlet to the surface. So far as I know, until this discovery at the refining works, no. one had thought that rain could penetrate into the interior of blister copper; at least in any quantity sufficient to be considered.

Jan 10, 1922

By Hans Lundberg

IN ORDER to comprehend the help and information that may be expected from electrical prospecting, it is necessary to have at least a general knowledge of the methods and principles involved in preparing and interpreting results obtained in the field. Electrical prospecting is rather complicated, both in theory and practice, and in order to make a brief description clear to the practical mining man it has been necessary to idealize and generalize the problems, at the risk of having such simplification criticized by the theoretical man. This simplification must not be misinterpreted as showing a lack of theoretical knowledge. FIG. 1.-FLOW OF CURRENT IN AND AROUND A CONDUCTING BODY. For its operation, electrical prospecting mainly, depends on the fact that most metallic ores conduct an electric current much more readily than barren rocks. If an electric current flows through a block of ground within which a body of chalcopyrite is enclosed in country rock of. schist, the current will find less resistance to its passage through the chalcopyrite than through the schist, even though the passage through the latter be much shorter. This is because the longer path through the chalcopyrite offers less resistance, owing to the superior electrical conductivity of the chalcopyrite (Fig. 1).

Jan 1, 1928

By J. L. Jernegan

In a former paper laid before the Institute, entitled Lead and Silver Smelting in Chicago, I endeavored to give a description of the manner in which argentiferous lead ores from the far West were treated in that city, and also described the method employed in the desilverization of the silver-lead produced from the ores. It will perhaps be remembered, that very siliceous ores, principally from the Emma mine, Utah, containing over 40 per cent. of silicic acid, were then being treated at the works of the Chicago Silver Smelting and Refining Company in the reverberatory furnace, with the use of metallic iron, in the form of borings, as a precipitating medium for the lead ; and that the extraction of the silver from the resulting bullion was effected by the Balbach process. The Swansea Works, also the works at Brighton, just outside of this city, and those of S. P. Lunt, were at that time treating ore of a similar character by the same method. The inadequacy of the process for the ores then under treatment was, in a manner, pointed out by me in the paper above referred to. Since the time of its writing, many and important improvements have been made in the metallurgical treatment of western ores in Chicago. Most ores are now roasted previous to reduction, and the latter operation is conducted in the shaftfurnace instead of the reverberatory. Such is the fact at least at the Swansea Works, the largest in the city, and here it was where the first steps were taken in this direction. In selecting these works as the subject of this paper, I am in hopes that the description given of the varions metallurgical operations, as they are there now conducted, will serve to give an idea of the improvements introduced

INTRODUCTION TO MINERAL INVENTORY The first explanations to be made must answer the questions: What is a mineral inventory, and how is a mineral inventory different from an ore reserve? The term mineral inventory is a relatively new designation-born of the computer age and grown to common usage with the development of computer techniques for extending drill-hole sample values to regularly gridded data blocks representing in situ mineral values. The term has been generally accepted by geologists and engineers because it has a precise meaning which avoids many of the ambiguities of ore reserve. A mineral inventory is an estimated inventory of mineral in place and is usually achieved by dividing the deposit into regularly spaced gridded blocks to which are assigned estimated values using various extension techniques. A mineral inventory makes no presumptions about the mineability of the blocks or their cutoff grade. Such parameters are implied with the use of the term ore reserve. Ore has a specific definition (see Chapter 1) and ore reserve must reflect that definition and thus has economic and mining constraints. An ore reserve will be different under different economic and mining conditions and is subject to reclassification by many factors. The term mineral inventory avoids all such ambiguities. A mineral inventory estimate may be good or poor according to how much is known about the deposit, how extensively it has been sampled, and what techniques have been employed to assign estimated grade to the blocks. Such an inventory, however, does not change with time, economic conditions, or mining technology, but only with new and better data and methods. Thus, the mineral inventory is an excellent designation for describing mineral value distribution within a deposit's geological setting. The techniques for assigning values and tonnage to mineral blocks or panels are the subjects of this chapter. Whether a summation of the blocks be called a mineral inventory or mineral reserve is not important. Many conventional methods for computing reserves of minerals refer to the methods in terms of ore reserve calculations. OBJECTIVES OF MINERAL INVENTORY OR RESERVES Mineral inventories are computed for the purpose of determining the quantity, the quality or value, and the spatial distribution of potentially economic minerals within the earth. Such computations are made at all stages in the life of a mineral extraction process, from the early exploration phase to the final year in the life of a mine. To quote Popoff (1966, p. 2), "They are the most responsible and irreplaceable tasks in the valuation of a mineral deposit. Efficiency in extraction and productiveness is impossible without accurate reserve computations." The accuracy of estimate required for each of the three parameters of quantity, value, and location is dependent upon the objective for which the reserve estimate is being made. Again quoting Popoff (1966, p. 2): Reserves are computed to determine the extent of exploration and development; distribution of values; annual output; probable and possible productive life of the mine; method of extraction and plan design; improvements in extraction, treatment, and processing; and requirements for capital, equipment, labor, power, and materials. Such computations are used to assist development

Jan 1, 1980

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 V. M. Lovell

The recovery of apatite from the phoscorite ores occurring in the Transvaal, Republic of South Africa, involves a flotation process that is particularly difficult to characterize from a fundamental point of view. However, the reagents used, (tall oil fatty acid, nonylphenyltetraglycol ether, sodium silicate, and sodium hydroxide) can successfully bring about a separation of apatite from dolomitic calcite, which is the most troublesome gangue component. Recently, it has been demonstrated with some flotation feeds that the addition of certain polysaccharides can improve the flotation significantly. It has been shown that the metallurgy obtained is closely linked to the nature of the froth, and this, in turn, is influenced, often dramatically, by the presence or absence of certain of the reagents. The character of the froth depends less on the inherent frothing ability of these reagents than on the presence or absence of fine mineral particles in the froth, and on their surface characteristics and state of aggregation. The polyglycol ether and the polysaccharides have been shown to affect these properties, and it is suggested that a major function of these reagents is to modulate the properties of the fine particles in the pulp, thereby changing the character of the froth and giving rise to improved results.

Jan 1, 1976

By K. C. Sclater, B. R. Stephenson

Recent progress in oil-recovery methods has brought into prominence gas-energy relations in oil sands. The greater the effort made to utilize this gas-energy relationship to the best advantage in oil recovery, the greater becomes the need for more precise information concerning physical conditions as they actually exist in an oil well. The intelligent use of gas-oil ratios when considering production efficiency has been the subject of much recent discussion. It has been stressed that the pressure as well as the volume of gas must be known when considering the efficiency of a producing well on an energy basis. When methods of production are compared on an energy basis it implies a knowledge of pressure, temperature and physical properties of the fluids at the bottom of the well. In questions concerning gas-lift and the pressure control of wells usually there is a wide variance of opinion among engineers when energy relations come up for discussion. Perhaps this difference f opinion can be traced to erroneous assumptions made with regard to the physical conditions existing within the well. If erroneous assumptions are made it follows that computations based on these assumptions will give results which also will be in error. That erroneous assumptions are made is not to be wondered at because when handling a fluid composed of gas and oil, we are dealing with a complexity of hydrocarbon components each varying to some degree in physical and chemical properties. This means that the physical state of the gas and oil will depend not only on temperature and pressure but that it will be influenced also by the relative amounts of the various hydrocarbon components present. If water is present the problem becomes still more complicated. From these considerations alone it would appear that we can well afford to give some thought to devising more positive methods or means for obtaining data on physical conditions within the well rather than depend entirely on computations from casinghead data. If these data

Jan 1, 1929

By H. Shaw

It is now generally recognized that the gravitational method of geophysical surveying is a valuable aid in elucidating the geological structure of the subsoil and enables the practical geologist to deduce the presence of useful deposits. The particular suitability of the torsion balance to the location of large and important subterranean structures has given rise to a wide application of this method by many of the important oil companies in their search for future supplies, and so intense have been these efforts that little has been heard of the method in other connections, with the exception of occasional references to its application in the location of hidden deposits of metallic ores, salt and lignite, and a number of accounts of its use in the elucidation of geological structures. Its success in the location of salt domes is well known, and establishes it as one of the most important of the geophysical methods, especially for the indirect location of oil. In the British Isles, however, no large occurrence of oil is likely to be revealed, and here the practical application of the gravitational method has been restricted almost entirely to the search for ores. This type of survey possesses well marked characteristics, and presents a gravitational problem that has necessitated the development of a special and probably unusual plan of campaign, full details of which it is hoped will shortly be published. The problems and difficulties encountered in this work are of necessity fundamentally related to those met with in the search for oil by means of the torsion balance, but they also possess several special and distinctive features which undoubtedly differentiate them from the obstacles confronting the oil prospector, and which call for special consideration and treatment. In certain of the various oil-producing areas of the world, and particularly in the Gulf Coast region, the geology may be regarded as comparatively simple, while the oil is usually associated with a large and well defined structure such as a salt dome or anticline, which is capable of giving gravitational indications sufficiently extensive to be detected by the torsion balance over a fairly wide area of the ground surface. It is customary, therefore, during the preliminary survey of an area for oil, to

Jan 1, 1929

By Richard A. Mullins, James J. Merle

Systematic sampling and analysis in coal-washing plants results in product control and economical operation. A well-organized laboratory system reduces operating costs and increases sales if the operating and sales companies make full use of information it supplies. The operating cost of a control laboratory is less than 1 pct per ton of coal produced.

Jan 5, 1950

By Elliott J. Roberts

In spite of the fact that the percentage of true colloids in an ore grind is very small,' these pulps exhibit many of the properties of true colloidal suspensions. A quartz particle, appreciably finer than 10 microns in diameter, has a settling rate so low that at a dilution of 5:l or over, the capacity of a settling tank to settle such particles would be uneconomical if the individual particle rate prevailed. However, by grouping the finer particles into aggregates or flocs, the settling rate can be increased to an economical value. The colloidal chemistry of pulp thickening is thus chiefly concerned with particles having diameters of between 1 and 10 microns, although particles as coarse as 40 microns in diameter are more or less involved. These particles must be associated in such a manner that they settle at an economical rate and give a clear, supernatant liquid or overflow. The treatment of the subject may be divided into three phases, cach phase having a more or less different colloidal aspect. The first phase is the problem of getting the pulp or suspension into the proper condition of flocculence; the second is the behavior of the flocculent pulp in its initial and intermediate stages of settling; the third is the behavior of the flocs in the find period of settling or thickening stage. Let us look first into the methods and mechanism of obtaining the flocs and then consider their behavior and properties. Flocculation Colloids are merely ordinary substances reduced to a very small particle size, the upper limit being placed by definition at 1 micron (0.001 mm.) diameter by the soil chemists and at from 0.2 to 0.1 micron by various other colloid chemists. The lower limit is reached only when the particles approach molecular dimensions. The term L'colloid" should not necessarily imply lack of crystallinity. Particles as small as 0.01 to 0.02 micron give perfect X-ray patterns, while with 0.005 micron particles the bands on the powder photograph are merely broaderled and diffused.2

Jan 1, 1935

By E. S. Burnett, R. V. Higgins, H. C. Miller

Information obtained from subsurface pressure and ,temperature measurements in oil wells now is recognized as invaluable to geologists, engineers, and operators of oil properties. Available only during the past few years, data resulting from subsurface-pressure surveys in oil wells already have found widespread application in the estimation of reserves and in the planning of comprehensive oil-field development programs. Subsurface pressure and temperature data, together with measurements of fluid volumes produced by individual wells and specific gravities of the fluids, also are included in the fundamental information essential in studying the movement of oil, gas and water through reservoir sands to wells. Heretofore, laboratory findings were relied upon almost entirely for information pertaining to the mechanics of flow of fluids through porous media, because there was no way to check laboratory results with actual performance in underground formations until subsurface pressure and temperature instruments were developed. Laboratory and field experiments now lend themselves to closer correlation—a fact that will accelerate the interpretation of many phenomena that occur when oil and gas flow through reservoir rocks, thousands of feet below the surface of the earth. This paper summarizes the results obtained thus far in a Bureau of Mines study of certain data pertaining to subsurface pressures and production of wells producing oil and gas (and water). For wells that have been studied, flowing naturally under volumetric or hydraulic control, a simple relation has been found between the mass rate of fluid (oil, gas and water) production and the corresponding drop in pressure in the reservoir sand. The equated relation embodies a productivity factor or "index" expressed in terms of mass rate of fluid production per pound drop in pressure through the sands. The equation as developed is an expression of the ability of a well to produce, which permits comparison on a uniform basis of the productivities of different wells. The study shows also that over the range of observed data a productivity factor

Jan 1, 1937

By B. S. Butler, H. D. McCaskey

The New London copper mine, about 8 1/2 miles east of Frederick, Md., was visited by the writers for a few hours in the spring of 1909 and the following brief notes on ore specimens collected are presented as a contribution to studies in chalcocite ores. For certain data on the structural and areal geology of this portion of Maryland the writers are under obligation to the unpublished notes and maps of Arthur Keith. The detailed study of the ores is the work of B. S. Butler. The deposit here discussed has many similarities to those of the Virginia district of Virginia and North Carolina, which have been described by Gratonl and Laney,2 except that in the deposits of the New London mine chalcocite is by far the most important ore mineral, while in the Virginia deposits bornite is commonly the most important sulphide. In the New London occurrence calcite is the most important gangue mineral. Field relations The -town of Frederick lies in the center of a narrow belt of limestone ranging in age from Ordovician on the east to Cambrian on the west. This belt is about + mile wide at Noland's Ferry, on the Potomac, and broadens to a width of 3 miles at Frederick. The general direction is east of north. The eastern boundary is, in places, a fault plane along which a series of metamorphic rocks of presumptive pre-Cambrian age have been thrust up. These ancient rocks, for several miles east and west of New London, are phyllites in the main, but closely inter-folded near the New London mine are long, narrow lenses of epidote

Jan 1, 1915

By V. G. Cawagdan, E. M. Sacris

The performance of the grinding circuit, from the initial stages of operation to the present, is discussed. The mill efficiency as measured by the Bond (Bond and Maxson, 1943) grindability data and the operating work index is presented. The objective was to produce a sand cyclone overflow containing not more than 6% 210 µm (+ 65 mesh). This has never been attained, even at low milling rates. Significant improvements in throughput were achieved by instituting equipment changes and process modifications within the grinding circuit. Grind improvements were achieved with enlargement of cyclone spigots, grinding at reduced densities, and decreasing the opening of the ball mill discharge. Additional grinding capacity was realized by converting the concentrate regrinding mill into a secondary ball mill. The previous 20% 210 µm (+ 65 mesh) grind improved to under 15% 210 µm (+ 65 mesh). The latest approach to solving the coarse grind problem is also discussed.

Jan 1, 1985

By R. J. Marcotte, C. T. Eddy, R. J. Smith

The objectives of the investigation herein reported were to determine: (I) the S-curves for certain selected cast steels, (2) whether or not the published S-curves for wrought steels are satisfactory for use on cast steels of similar composition, and (3) to prepare hardenability curves of the selected cast steels. In order to make the final comparisons between cast and wrought steel more completely tangible, it was deemed advisable not only to determine S-curves for the steels submitted in the cast condition but also to roll some of the cast-steel test bars and determine comparison S-curves on such wrought material. This procedure eliminates the composition variable and makes it possible to reveal the differences resulting from plastic deformation of the cast structure in addition to providing the comparison with published data on wrought steels. Cast Steels The cast steels selected for the preparation of S-curves, or time-temperature transformation curves, were similar to S.A.E. series 1030, 2330, 4130 and 4330. Of these the 1030 was supplied by The Crucible Steel Casting Co., Cleveland, Ohio, and the other three by The Sawbrook Steel Castings Co., Lockland, Ohio. The steels were furnished in the as-cast condition. The manufacturers supplied the chemical analyses and the properties that could be obtained in the heat-treated condition—all of which is summarized in Table I. The metallographic and dilatometric procedures and equipment were in general standard. The specific technique employed was described in a report of the Steel

Jan 1, 1945

CHUQUICAMATA, as the Chile Copper Company's mine is known, has the largest developed deposit of copper ore in the world. Indeed, it is improbable that its equal will ever be found. The Union Miniére du Haut Katanga, operating in the Belgian Congo, may some day surpass Chuquicamata in the total amount of copper produced; or one of the companies developing the rich copper region of Northern Rhodesia may ultimately outdo it. But in each instance, the ore will come from a group of mines separated by 80 miles or more; whereas the deposit at Chuquicamata is one vast integral mass containing as a minimum probably 1,000,000,000 tons of ore, averaging better than 8.5 per cent copper, and as a maximum-well, most any reasonable figure might err on the low side. Utah Copper approaches Chuquicamata more nearly than any other in tonnage of exploitable ore; but Utah's ore is less than half as rich. The figure for the aggregate copper content of the reasonably assured ore at Chuquicamata is breath-taking at 50,000,000,000 pounds. Other distinctions has Chuquicamata: It was the first of the Porphyry Coppers to use leaching as the method of treating the ore; its plant cost for producing is lower than that of any of the others, only Braden and Utah being close rivals; and it was worked for its copper long before any of the others. According to an authentic article published in Ingeniería Internacional (May, v 1982) the Incas smelted copper ores from Chuquicamata prior to 1536. Diego de ALnagro, to whom Charles V, King of Spain, generously allotted a one-fourth portion of South America lying south of Cuzco, the Inca metropolis, made an expedition into Chile in 1534. Better known to history, perhaps, is Pizarro, who was awarded the area immediately north, and who proceeded

Jan 1, 1933

By Courtenay de Kalb

So far as the writer is aware, no detailed investigation into the behavior of ores or rocks when subjected to crushing under digerent conditions has yet been made. He cannot himself claim to have carried such investigations very far; but the results of some studies which he has been pursuing for a couple of years, as opportunity permitted, seem sufficiently interesting and suggestive to warrant a brief statement of them, preliminary to nildertaking a more exhaustive course of experiments. Criticisms and suggestions are earnestly invited, with a view to making these studies as instructive as possible. As a part of the examination of ores, preparatory to concentration, my students have been required to take lots of 100 pounds each, and crush them. These are then screened through a series of hand-sieves, 15 inches in diameter. The products remaining on each screen are weighed, and from the results is plotted a curve, called the sizing-curve. It was assumed at first that different ores would yield, under like conditions of crushing, curves showing unlike characteristics as to the quantities remaining on the various sieves. After a number of such curves had been obtained it became evident, as often happens, that this a priori reasoning was faulty. The curves presented practically identical characteristics, and only by varying the crushing-conditions were variations in the curves obtainable. Another peculiarity, which was as little anticipated, appeared by inspection of these results, namely, that successive crushing to smaller sizes did not greatly augment the quantities of the filler products, so long as the machines employed applied the crushing-force to the ore-particles in the same manner. In these experiments the fines were not eliminated between successive crushings. I believe it will be readily admitted that rock can be crushed

Jan 1, 1899

By N. J. Grant, K. M. Zwilsky

A series of copper-alumina dispersion strengthened alloys were prepared using three different copper and two different alumina powder sizes. Improvements in strength of up to ten times that of pure copper were found in room-temperature as well as elevated-temperature stress-rupture tests. Conductivity values remained from 70 to 90 pct that of pure copper. The best alloys were based on the finest metal powder (1 p) and contained from 7.5 to 10-0 vol pet of 0.018 or 0,033 p alumina. DISPERSION strengthening of metals consists of strengthening a metal matrix by the addition of oxides or other refractory constituents, followed by strain hardening, in order to reinforce the base material and extend its temperature range of application. Since the discovery of SAP by lrmannl and Von zeerleder2 in 1949, many investigators have reported data obtained on a variety of metal-inert oxide alloys.3-7 The present work deals with the mechanical mixing of copper and alumina powders. While several techniques of introducing the second phase have been investigated to date, mechanical mixing so far has been recognized as the simplest, least expensive, and most universally applicable technique that can be used to obtain an ultrafine dispersion of inert particles. In the present case, the effects of changing the metal particle size, the oxide particle size and the volume percent of oxide were investigated. This work is an extension of a previous study.6 EXPERIMENTAL PROCEDURE The starting materials were three different grades of copper powder and two different alumina powders. The three metallic powders were -74 µ(- 200 mesh) electrolytic copper powder consisting of irregular equiaxed particles having a normal screen distribution and analyzing 99.5 pct Cu, and two powders having a 5-µ and 1-µ particle size, average, respectively. The latter powders were produced by the hydrogen reduction of purified sulfate solutions at elevated temperature and pressure and were furnished by the Sherritt Gordon Mines, Ltd. The alumina used was obtained from Godfrey L. Cabot Co., under the trade name of Alon C, one batch of powder having a particle size of 0.018 µ, the other a particle size of 0.033 µ. The crystal structure of these alumina powders was found to be cubic gamma. Each batch of powder was mixed in a Waring Blendor for a total of 15 min, followed by a low-temperature reduction in hydrogen and vacuum compacting in cylinders which were hydrostatically pressed at 35,000 psi to give a compact that could be handled conveniently. Six of the compacts were hydrogen sintered at 900°C while the remaining four were sintered at 1000°C. Subsequently, all compacts were hot extruded at 760°C with a reduction of area ratio of approximately 20 to 1. Evaluation of alloys included density and resistivity measurements, room-temperature tensile tests, stress-rupture tests at 450°C plus one other temperature per alloy, hardness tests, microstruc-tural examination, X-ray analysis of the dispersed phase after dissolving the metal phase, and oxidation studies on two of the alloys. A vacuum-melted, wrought copper rod was tested together with these alloys for comparison purposes. RESULTS Table I is a summary of the compositions, sintering temperatures, densities and conductivity values of the ten alloys prepared. All alumina additions are given in volume percent, and will be referred to as

Jan 1, 1962

By C. E. Birchenall, M. H. Davis

The rate of oxidation of titanium in the temperature range 650° to 950°C has been measured. 'The linear rate law obtained is explained by interface reaction control of the process. Tracer experiments indicate the oxygen diffuses in at least one phase of the scale. THE kinetics of oxidation of titanium, principally at low temperatures and under varying oxygen pressures, have been reported.¹,² In the present investigation the rates of oxidation of titanium have been determined by the gravimetric method in the temperature range 650" to 1000°C under 1 atm of oxygen. Some of the scales formed were powdered and an endeavor was made to identify the phases present by X-ray diffraction. Alexander and Pigeon1 ascribe a logarithmic rate law to the growth of thick films formed at temperatures up to 565"C, and Gulbransen and Andrew' suggest that the parabolic rate law holds up to 600°C. In both cases large initial deviations from those relationships are apparent and no explanation is offered. In the present experiments it is shown that a linear rate law holds in the temperature range 650" to 1000°C, and it is suggested that the initial deviations observed are due in part to a spurious surface area effect and also to the high solubility of oxygen in titanium metal. Positive information on the mechanism of oxidation is not available, but oxygen ion diffusion through the lattice is inferred from the re- sults of trace experiments. X-ray analysis of the scale confirms Gulbransen and Hickman's' observation on the presence of rutile TiO². Experimental Details The titanium used in these experiments was prepared by the reduction of titanium tetrachloride with magnesium and was used in the form of rolled sheet. Samples approximately 0.040x0.5x0.75 in. were cut and polished to a fineness of 4/0 on metal-lographic polishing papers. Individual samples, suspended on a platinum wire, were lowered into the hot zone of a furnace, in vacuo, by means of a winch, and oxygen was admitted after the desired temperature was attained. The increase of weight of single samples oxidized for fixed times at certain temperatures was determined by weighing the sample before and after oxidation on a chemical balance. In these instances the sample was used for only one time at one temperature. In some cases the course of oxidation was followed by attaching the sample to a sensitive spring balance and noting periodically the extension of the spring with time of oxidation. Kirkendall type experiments were carried out by marking the surface of the titanium prior to oxidation with a solution containing radioactive silver. After drying, the specimen was heated in vacuo to decompose the silver nitrate used, leaving a small amount of metallic radioactive silver on the surface. Following oxidation, these samples were mounted, ground, and then placed in intimate contact with

Jan 1, 1952