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By AIME AIME

THIS journal is fully indexed-every issue, as soon as published-in a set of card?, which thus brings ready to your hand any article on any subject in this journal or in any one of 1700 other journals in all languages. This Engineering Index Service, instituted in January, 1928, is to be found in the Public Libraries of Newark, Cleveland, Bridgeport, Baltimore and the John Crerar Library, Chicago. Engineers in any field who live or work in New Jersey will find this mammoth index to the latest engineering literature in the Public Library of Newark, N. J.

Jan 1, 1929

By N. J. Themelis, R. V. Flint

In a four-year period between 1973-76, the Metal Mining Division of Kennecott Copper Corp. conducted a company-wide program of operations improvement which involved line and staff personnel from all company functions. Specialist teams performed detailed studies of all operational aspects at Kennecott's four copper mines and concentrators, four smelters, and two electrore-fineries. The specific recommendations that resulted may transform the Metal Mining Division into the country's lowest cost producer of copper by the mid-1980s. In this article, N. J. Themelis and R. V. Flint describe the mechanics of MMD's integrated approach to operations improvement.

Jan 6, 1979

By Fred C. Bond

THEM is acute need for a method that will measure the size distribution of finely divided materials, particularly when the particle sizes are smaller than the openings of the finest screen cloth regularly available for testing. Several methods and types of apparatus are in common use, but none are entirely satisfactory for all purposes. The commonest methods are microscopic grain counts, elutriation by liquids or air, and sedimentation. Valuable results have been secured by air elutriating devices, typified by the Haultain Infra-Sizer and the Pearson Air Analyzer. These are especially useful in obtaining sized fractions that can be examined and analyzed separately. They are particularly advantageous because the sizes of the samples produced are adequate for a considerable amount of subsequent manipulation and testing. The sedimentation methods, such as the Wagner and Klein turbidimeters, and the sedimentation balance, do not deliver sized fractions, but they do provide a means for reasonably rapid comparative determinations of fineness and surface area, which are important in many industries. The sedimentation balance consists essentially of a balance pan suspended in a liquid that contains falling particles. These are weighed as they settle onto the pan, and the time rate of settling is determined. The size distribution is computed from the settling rate. The balance appears to be inherently more accurate than any of the other methods, and it has served a useful purpose in the study of numerous problems, but there have been limitations which have restricted its scope of application. Because of the essential simplicity of the method, it was felt that intensive investigation might lead to modifications that would make it a valuable tool for the operators in industries that require precise information regarding the results secured from grinding equipment. A large number of size-distribution determinations below 200 mesh were required in connection with a particular research problem in fine grinding. The sedimentation balance was used in this investigation, and a technique was gradually developed that ultimately gave good results. A serious difficulty appeared early in the work. It was discovered that less material always settled on the sedimentation pan and more on the bottom of the containing jar than could be accounted for by calculation, and also that the material that settled to the bottom of the jar outside the edges of the pan was considerably finer than that on the pan. This segregation was so great that the distribution obtained for the finer sizes was obviously very much in error; material ground to about the degree of comminution of cement might have only 60 per cent of the calculated weight actually settling on the pan, and the error increased with the fine-

Jan 1, 1939

By C. R. Van Hise

[Concluding Contribution of Prof. Van Hise to the Discussion of his Paper, and Others on the Same General Subject, presented at the Washington Meeting, February, 1900 (see Trans., xxx., 27, 177, 323, 424, 5 S); also of the contributions of Vogt, De Launay, Beck, Lindgren, hemp, Rickard, Bain, Keyes, Collins and Adams, presented at the Richmond Meeting, February, 1901, and printed in the present volume.] IN June, 1900, shortly after my paper was published in the Transactions, I made a briefer statement* before the Western Society of Engineers covering the same `round, which, in certain respects, is somewhat of an improvement. For instance, instead of using the terms descending and ascending with reference to the waters resulting in the two concentrations, my modified statement is as follows " The first concentration of many ore-deposits is the work of a relatively deep water-circulation, while the reconcentration is the result of reactions upon an earlier concentration through the agency of a relatively shallow water-circulation. Commonly the deep water circulation is lacking in free oxygen, and contains reducing agents, and the shallow water contains free oxygen. The deep water is therefore a reducing, and the shallow water an oxidizing agent."† Of the papers upon ore-deposits which, in vol. xxx. of the Transactions, follow my own, or which were presented at the Richmond meeting, a considerable number are wholly confirmatory of the conclusions which I have presented. Among these are the Washington paper of Emmons upon the Secondary Enrichment of Ore-Deposits‡ and his discussion at Richmond of other papers,§ that of Weed upon the Enrichment of Gold and Silver Veins,[ ]the discussion of Emmons', and at Richmond of Weed's paper by Collinst and Prof. De Launay,† the paper of Lindgren on Metasomatic Processes in Fissure Veins,¶ that of-Rickard upon the Formation of Bonanzas in the Upper Portions of Gold Veins,** and the remarks of Bain upon the Mississippi Valley lead- and zinc-deposits.†† It is therefore un-

Jan 1, 1902

By R. C. Temps, G. E. Aiken

Compania de Acero del Pacifico, S.A., the sole Chilean steel producer, is adding to the expanding Chilean economy with development of the El Algarrobo mine. Expected to go on stream early in 1962, Algarrobo is a conventional open pit mine that will include facilities for ore extraction, crushing and screening, rail transport to the harbor at Huasco, modern ship-loading equipment and maintenance shops. CAP anticipates producing 1.38 mil- lion tons annually of high-grade ore for national and world market consumption. Chilean and North American management and engineering teams combined more than a decade ago in the financing and building of CAP'S Huachipato integrated steel plant. A similar performance is being achieved in northern Chile near the town of Vallenar with the opening of a 50-year supply of iron ore from the Algarrobo deposit. This successful intra-American undertaking deserves special mention in these times when some U.S. foreign assistance programs must be defended, particularly with respect to Latin America. North American financial participation in Algarrobo, through the Export-Import Bank of Washington, represents the greatest portion of the $24 million being invested.

Jan 3, 1962

By E. W. Pehrson, J. W. Furness

THE five charts presented here- with are part of an original group prepared by the U. S. Bureau of Mines showing the international trade in the principal metals and metallic ores. Charts 011 anti- mony, chromite, copper, lead, manganese, mercury, nickel, tin, tungsten, and zinc were published in the February, 1936, issue of the Engineering and Mining Journal. Those shown here include bauxite, aluminum, iron ore, pig iron, and the platinum-group metals.

Jan 1, 1936

AARONS, J. BOYD, Major. AGNEW, FRANK VANS. ALLEN, HERMAN H., Private, D Co., 8th -Reserve Engineers. BAINS, THOMAS M., Major, Engineer Officers' Reserve Corps. BANKS, H. R., Lieutenant, Canadian Engineers, B. E. F. BARBOUR, PERCY E., Deputy Supt. (Captain), New York State Troopers; Captain, 22d Regiment, N. Y. N. G. BARLING, H. B., Ist Lieutenant', Engineer Officers' Reserve Corps. BIGELOW, BRAXTON. BLOOMFIELD, E. C., Lieutenant. , BORROW, F. K. BROCK, R. W., Major, 19th Reserve Battalion of Canadians. BROOKS, ALFRED H., Captain, Engineer Officers' Reserve Corps. BROWNE, DE COURCY, 1st Lieutenant, Ordnance Dept., Fortress Monroe, Va.

Jan 9, 1917

By Carl Wagner

J. Pearson (British Iron and Steel Research Association, London, England)—Dr. Wagner has referred to the work of Richardson and Dancy and Gellner and Richardson on the reduction at 900 °C of wiistite films on iron. He has assumed that iron ions and electrons migrate backwards to the iron-wustite interface and that the reduced iron grows on the metal substrate. This would be a possible explanation of the results of these workers were it not for the fact that, as stated by Gellner and Richardson but not stressed, this growth in the center of the specimen can occur even

Jan 1, 1953

By AIME AIME

AT A meeting of the Iron and Steel Institute held in London on May 6, Dr. J. E. Stead was formally inducted into the chair by Dr. Eugene Schneider, the retiring president. After presenting the Bessemer gold medal to Harry Brearley, of Sheffield, England, for his distinguished services to the British steel industry, Doctor Stead delivered his presidential address, a masterly review of iron and steel making progress during the past 50 years, emphasizing economy in production, and pointing out suggestions for future improvement. A considerable portion of the address was devoted to blast-furnace operation.

Jan 1, 1920

By O. U. Bradley

The methods of handling the oil output of the Mid-Continent fields are not unlike those practised in other oil fields of the United States, and it is not expected that this paper will present any entirely novel ideas. Some features of the practice of handling this oil may be of interest, however. Wooden Gaging Tanks Practically all of the oil sold to pipe line? and other purchasing agencies throughout the Mid-Continent field is gaged from wooden tanks. Steel gaging tanks are slowly coming into use, and are preferable in many ways—leakage and evaporation are reduced, and the strapping and recalculation of capacities are unnecessary. The wooden tanks are slightly coned to facilitate tightening the hoops. The sizes in common use are 250, 500, 800 and 1600 bbl. The number and the capacity of the gaging tanks upon any producing oil property depend upon its production, and the facilities for disposing of the output. The 1600-bbl. size was the most common in the Cushing field, particularly during the period of flush production. The tanks are distributed over the leased premises in groups of two, three, and four tanks each, and these are filled from flow tanks, or through direct pipe connections with the heads of the wells. Flow tanks are merely temporary reservoirs to facilitate the transfer of oil from the wells to the gaging tanks. They diminish fire risk, and are considered indispensable on small producing properties where water is pumped with the oil, as they permit the refuse and water to 'settle out before the production is run to the gaging tanks. strapping and Calculations After a gaging tank has been strapped (measured) and its contents computed, a deduction of 3 per cent. is made from its computed volume. The strapping of a tank requires four steps: (1) The outer circumferences

Jan 1, 1920

By W. J. Taylor

The discussion on my paper entitled "Experiments with a Straight or No-bosh Furnace," read at the Philadelphia Meeting, September, 1884 (Transactions, vol. xiii., p. 489), suggests the propriety of slipplementing it with another, giving my views as to the cause of the failure, which was so decided as to create surprise among furnace men. As then stated, the Chester (8. J.) furnace, which had been 60 feet high, and 13 feet in diameter at the bosh, was altered to an 8-foot bosh, with a 7-foot hearth, 7-foot stock-line, and 4-foot bell,

Jan 1, 1886

By T. A. Read, H. K. Birnbaum

STRESS-induced twin boundary motion in the AuCd ß'phase (52.5 at. pct Au 47.5 at. pct Cd having an orthorhombic structure (space group D h)' was discussed for the case of transformation twins.' Mechanical twinning, i.e., introduction of new twin orientations by the applied stress was sometimes observed in the ß' phase which contained two transformation twin orientations. (See Ref. 2 for experimental details.) The transformation twins terminated at the mechanical twin boundary; the two initial orientations having been twinned to the new orientation as shown in Fig. l. In a "hard" tensile instrument, formation of each mechanical twin was accompanied by a sharp drop in load (and an audible click) resulting in a typical serrated load-extension curve. The mechanical twins increased in width and additional twins were nucleated as the load increased until the entire specimen was occupied by the mechanical twin orientation. A restoring force2 caused the mechanical twin and transformation twin boundaries to return towards their initial configuration on releasing the load. In a stabilized specimen* the total strain introduced by mechanical twinning was recovered on releasing the applied stress. Initial and final microstructures were identical. After decreasing gradually to a critical width, mechanical twins suddenly disappeared accompanied by audible clicks and sharp increases in load (measured at a constant rate of crosshead motion in a "hard" machine). Mechanical twins could be stabilized in any position by maintaining the applied load for a sufficient time, indicating a decrease in restoring force with time similar to that observed for transformation twins.' Orientation relationships for mechanical and transformation twins were determined and are shown in Fig. 2. The mechanical twin, T3, was twin related to transformation twin, T,, by reflection in (1ll), and twin related to transformation twin, T2, by reflection in (111)T, . T, was related to T, by reflection in(ll1)T1 . The "average" mechanical twin composition plane lay several degrees from (1ll), . In every specimen which mechanically twinned, orientation T3 was most highly favored by the applied stress, i.e., it was the twin orientation which provided the greatest change in length compatible with the direction of applied stress

Jan 1, 1961

By Walter J. Johnson

The coals in northern Wyoming and Montana are free-burning and non-caking and range from lignite to bituminous C in rank. Strip and underground mining are employed to supply railroad, utility, industrial, and domestic fuel. The market area includes Iowa, Nebraska, Minnesota, North and South Dakotas, Wyoming, Montana, the Pacific Northwest, and western Canada. THE larger producing coal mines in northern Wyoming are located in the Powder River Basin lying between the Black Hills region of South Dakota, eastern Wyoming, and the Big Horn Mountains in north central Wyoming, see Fig. 1. The mines are located particularly in the area along the route of the Chicago, Burlington & Quincy Railroad from Gillette, Wyo., to a point approximately 15 miles northeast of Sheridan, Wyo. Fig. 2 is a graph of coal production in the state of Wyoming from 1918 to 1951. Across the Big Horn Mountains lies the Big Horn Basin, situated between the Big Horn Mountains and the Rocky Mountains proper. Mining in the Big Horn Basin is almost entirely confined to a small area known as the Gebo Field, near the town of Kirby, which is located on the Chicago, Burlington & Quincy Railroad. This paper will describe present operating areas, making only brief reference to the history of mining and marketing primarily because of the large area to be discussed. The coal beds presently mined in the Powder River Basin are all of Tertiary age and are of Fort Union and Wasatch formations of Paleocene and Eocene ages, see Fig. 3. The Fort Union formation, consisting of 2000 to 3200 ft of alternate sandstone, shale, and coal, is divided from oldest to youngest into the Tullock, Lebo Shale, and Tongue River members. Most of the mineable coal is in the Tongue River member, which is 500 to 800 ft thick. The Carney coal bed, varying from 7 to 20 ft in thickness, is considered the base of the Tongue River member. About 85 ft above the Carney is the Monarch bed, ranging from 18 to 42 ft in thickness. At approximately 210 ft above the Monarch is what is locally known in the Sheridan district as Dietz No. 3 bed, which varies from 12 to 30 ft in thickness. One hundred feet above the Dietz No. 3 is Dietz No. 2 bed, which is 7 to 12 ft thick. At about 100 ft above the Dietz No. 2 is Dietz No. 1 bed, 7 to 15 feet in thickness. Two hundred and fifteen feet above Dietz No. 1 is the Smith bed, approximately 5 ft thick. One hundred twenty-five feet above the Smith is the Roland bed, which is estimated to be approximately 13 ft thick. The Roland bed is considered the base of the Wasatch formation, which in the Powder River Basin is 1000 to 3500 ft thick and is composed largely of shale, sandstone, and coal. The foregoing measures are the only ones above the Tongue River member that have been mined in the Sheridan field. To the east of the Sheridan field, particularly in the area of Gillette, the Roland bed is considerably thicker and is considered the thickest and most extensive coal bed in Wyoming, reaching a maximum thickness of 106 ft. From 125 to 225 ft above the Roland lies the Arvada bed, average thickness 9 ft. Three hundred seventy-five to four hundred feet above the Arvada is the Felix bed, which reaches its maximum thickness of 30 ft near Echeta on the Chicago, Burlington & Quincy Railroad. East of the Powder River the bed averages more than 10 ft in thickness, but it thins in a northwesterly direction. The highest mineable coal in the Powder River field is the Healy bed, about 400 ft above the Felix bed and exposed only in the highest parts of the area where much of it has been burned along the outcrop. Where it has not been burned, the thickness at most of the outcrops is 10 to 15 ft.

Jan 1, 1954

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By J. L. Wyatt

THE smelting of ilmenite to produce a slag rich in titanium, with pig-iron as a byproduct, introduces new concepts in electric smelting metallurgy. Titanium slags are characterized by low electrical resistance, thereby requiring a different type of electric furnace operation, and power supply sources substantially different from those encountered in normal steel melting and siliceous ore smelting furnaces. This paper describes special apparatus for determining specific electrical resistivity of titanium slags, and reports the values obtained on slags encountered in the process of smelting ilmenite ores. In an induction furnace under conditions approximating normal furnacing operation, 25 general heats and 6 special standardization and comparison heats were run. Results indicate relatively low resistivity. Resistivity depends primarily on slag composition, and, to a lesser degree, on temperature. During the summer of 1947 a cooperative project between the National Lead Co. and the Bureau of Mines was conducted at Boulder City, Nevada, in the Electrometallurgical Laboratories of the Bureau. The project involved smelting of ilmenite ores in electric furnaces, and has been reported in detail.' The author participated as a member of the staff of the National Lead Co. during the entire campaign. One outstanding characteristic of the titaniferous slags, their apparently excellent and variable electrical conductivity, was considered sufficiently important to warrant further study. Although little electric smelting of iron ores has been done in the United States, a certain amount of information is available for comparative purposes. Personal experience in smelting siliceous iron ores in electric furnaces furnished further information for comparison. In general, silicate slags are relatively poor conductors of electricity. Current flow during smelting operations may be maintained through a floating layer of coke on top of the slag bath, or through a bath of molten iron, beneath the slag. Silicate slags are not sufficiently conductive to furnish a path for current passage when normal furnace voltages are used. Experimental smelting of a silicate iron ore was undertaken for comparative purposes. A fluid melt was not obtained until the FeO content was reduced to 15 pct. The resistivity increased as the FeO content decreased, FeO compounds being the most conductive of the various oxides in such a normal slag system. The converse appears to be true in slags containing large percentages of TiO2. It has been found that titanium slags become molten with FeO percentages in excess of 30 pct, and that the conductivity becomes generally better as the FeO con-tent of the slag diminishes. This phenomenon was demonstrated in the furnacing operations at Boulder City. During the initial smelting period furnace electrodes could be held immersed several inches in the slag, with tap selectors set for a no-load voltage of 70 v. As the FeO content decreased, the furnace electrodes would "walk up," until at one point in the process the tips would break the surface and arc on top of the slag. This was undesirable since direct arcing caused losses of important flux additions. The slag compositions under study at that time were such that losses due to surface arcing sometimes caused viscous slags to be formed. Forcing the electrodes into the slag bath by manual control to prevent surface arcing resulted in excessive power input and lack of control. Suitable low voltages were not available. Measurement of the electrical resistivity of titanium slags at various operating temperatures and slag compositions was undertaken. It was believed that this information would be of use in the design of electric furnaces suitable for smelting ilmenite, with voltages, electrode sizes, and electrode spacing adapted specifically to titanium slags.

Jan 1, 1951

By Jonathan Ludlow, Paul J. Guay

Based on two studies that were funded by the U.S. Department of Energy, the authors provide an overview of the benefits expected from mining deeper webs on United States longwalls. The first study, completed in November 1979, identified the limits and potential gains from taking deeper webs with presently available equipment. The second on-going study discusses the conceptual design and benefits of a future system for taking very deep webs.

Jan 1, 1981

By C. D. Wiseman

THE concept of alloying to increase the strength of metals originated during the bronze age. However, at the present time there is no single theory capable of explaining all of the observed strengthening effects of alloying elements on the mechanical properties. In general, it may be said that solid solutions are stronger than the pure metal and that the strengthening effect increases with increasing alloy content. Various theories for solution hardening have been proposed, the first of which was presented by Rosenhain who suggested that the alloying elements roughened the slip planes, thereby requiring a higher stress to initiate slip. Recent work by French and Hibbard2 confirmed Norbury's3 conclusion that those alloying elements which cause a greater change in lattice parameter have larger effects on hardness. However, a given change in lattice parameter produced by different alloying elements does not cause the same change in hardness. A further refinement was suggested by Dorn, Pietrokowski, and Tietz4 who considered differences in valence between the solute and solvent with the change in lattice parameter to explain the plastic properties of aluminum alloys. Allen, Schofield, and Tate5 further investigated the valency contribution to solution strengthening by testing some copper-base solid-solution alloys having constant electron densities. Tensile tests performed on these alloys gave identical stress-strain curves even though the atomic size effect, which varied by a factor of two, was neglected. The advent of dislocation theory6-8 provided a new and powerful tool capable of explaining many phenomena of plastic deformation and indicated new approaches to solution hardening. The basic con- cept of recent theories is that solution hardening is not due to stresses associated with randomly dispersed solute atoms, but rather to a nonuniform distribution of the solute. This conclusion was reached by consideration of the effective tension present on each dislocation line and the ability of a dislocation to pass an obstacle. cottrell suggested the possibility that the internal stresses due to randomly distributed solute atoms would offer essentially no resistance to the passage of dislocations. He reasoned that an edge dislocation may be considered as a rigid line discontinuity. As the dislocation moved through a crystal, the random stress fields would be equally distributed along its length. Since half of the stress fields would be acting to move the dislocation forward and the other half trying to move it back, the net effect on the dislocation would be zero. Thus the randomly distributed solute atoms would not contribute appreciably to solution strengthening. Mott and Nabarro10 considered the dislocation as a flexible, rather than a rigid, discontinuity. They obtained a simple model for a dislocation moving in a lattice having precipated particles, where the dislocation would actually bend around the obstacle until it would loop back onto itself to rejoin and then continue onward. Their work indicated that the minimum radius of curvature of the dislocation line, under the action of an external stress and in the region of an internal stress, would be such that the dislocation would be unable to pass through a matrix containing small closely spaced precipates by the looping process. The dislocations would tend to remain rather straight, approaching the condition of Cottrell's rigid dislocation. Hence, the strengthening must not be due to random solute atoms; however, it might be due to the concentration of atoms, either as clusters of like atoms or as short-range ordered regions, or to the concentration of solute atoms around dislocations. To date, four mechanisms of solution strength-

Jan 1, 1959

By C. S. Smith, L. W. Kempf, C. S. Taylor

The thermal conductivity of aluminum alloys is of considerable industrial importance. This is particularly true in such applications as internal-combustion engines where one of the principal reasons for the use of these alloys is their relatively higher thermal conductivity. In spite of this, relatively few data are available on this property of aluminum alloys. The reason is quite apparent to anyone concerned with the experimental determination of coefficients of thermal conductivity. This determination, in theory so simple, is extraordinarily difficult if any high degree of precision is desired. Fortunately, some .knowledge of the relationship between thermal and electrical conductivity has permitted the use of the latter physical property in deducing the relative approximate values of the thermal conductivities of metals. This fundamental relationship, first enunciated by Wiedemann and Franz' as applying to metallic elements and later shown by Lorenz2 to be applicable to alloys within a single metallic system, has been of service in the industrial application of metals. The electrical conductivity of metals is easily determined with a high degree of precision. It is, therefore, quite desirable that the relationship between electrical and thermal characteristics be determined with the greatest possible precision. This paper presents data on the electrical and thermal conductivities of a number of aluminum alloys of industrial importance. Literature on Thermal Conductivity of Aluminum Alloys Masumoto3 determined the electrical and thermal conductivities of 18 aluminum alloys. His results indicated a relatively constant relationship between thermal and electrical conductivity.

Jan 1, 1937

By Robert A. Rapp, Jan E. Verfurth

From the measurement of internal-oxidation band widths in Ag-In and Cu-A1 alloys, products for the solubility No and the diffusivity Do of oxygen in silver and apparent NODo products in copper have been obtained over a range of temperature. The NODO products for silver are in agreement with the product of the individually determined No and Do values of Eichenauer and Müller. Although interstitial diffusion of oxygen in silver is expected, the temperature-independent factor Do of the diffusion coefficient does not agree well with the theory of Wert and Zener. For Cu-A1 alloys internal oxidation does not follow the expression derived for ideal kinetics, since the apparent NODo product calculated from internal-oxidation measurements is a function of the alloy content in the specimen. Thus, unequivocal values for No or DO or even the product NODO in copper are not available from the literature. RELIABLE values for the saturation solubility NO and diffusivity DO of oxygen in fcc metals are lacking and difficult to determine, partially because internal-friction measurements are not applicable. Permeability experiments and Sieverts7-type adsorption -desorption methods3 have met with difficulty; however, Eichenauer and Müller4 have recently reported on the solubility and diffusivity of oxygen in silver as determined by the latter technique . Rhines, Johnson, and Anderson,5 and independently Meijering and Druyvesteyn,' introduced the possibility of deriving values for the product NODO in a metal from measurements of the widths of internal-oxidation zones (subscales) formed during the internal oxidation of alloys. In addition to these authors, several other investigators7-9 have made such measurements in various silver and copper alloys at various temperatures, mostly using me- chanically polished specimen surfaces. The purpose of this investigation was to determine over a range of temperature the calculated products NODO in silver and copper from systematic measurements of the widths of internally oxidized zones in Ag-In and Cu-A1 alloys, using specimens with electro-etched surfaces. Consider the internal oxidation of a dilute solid-solution alloy in which the base metal is not oxidized. If diffusion of oxygen is the rate-controlling step, then the depth 5 of the internal-oxidation zone is given by where y is a dimensionless parameter and t the oxidation time. Based on the solution of the diffusion equation, wagnerl0 has shown that under certain conditions several mathematical simplifications may be used in the evaluation of y, so that Eq. [I] may be expressed for the case that y « 1, and y(Do/DB) 1, where N(so)the is the equilibrium solubility (mole fraction) of oxygen in the solvent metal for the given oxidizing atmosphere, is the mole fraction of the solute metal in the bulk alloy, 4 is the diffusivity of the solute in the base metal, and v is the ratio of oxygen atoms to solute atoms in the precipitated oxide BO,. Rearranging Eq. [2] Maak' has derived an expression analogous to Eq. [3] for the case that an external-oxide scale, in addition to an internal-oxidation zone, is formed. For this combined external and internal oxidation for the case that 5/2 where 5 is the distance of the internal-oxidation front from the original external s.urface, and X is the distance of the external oxide/metal interface from the original external interface. The function F is defined by the expression

Jan 1, 1964

By W. Hurst

What is entailed here is the extension of the sinzplified material balance formulas to encompass interference between oil fields. As previously reported, the ex-plicitness as so revealed for the cunzulative pressure drop as a function of all factors contributing to its change in the material balance equation, is now transcribed through the inter-conzmunicating aquifer to effect an increased pressure drop on an adjoining field by interference. Such is performed by mathematical analyses and the application of the Laplace transformations. What is accomplished is that the reiteration problems previously associated with interference studies are nullified, since volumetric changes for the fluids in situ are automatically adjusted by the explicitness so expressed, and what pertains to the superposition principle applies only to the impeded water drive upon a su.bject field, which is likewise incorporated in the over-all pressure drop that results. The mathematics treats with the rigorous solution of the problem, as well as with methods easily amenable to numerical interpretation by the practicing engineer. In all cases, however, what is deduced for areal extents, reveal interference between wells when time becomes large that further substantiate the analyses. Probably of equal significance, all variables and for/nation characteristics are accounted for. This applies to the differences in PVT analyses that occur from field to field and the physical parameters associated with the lithology of the reservoirs. The latter is deduced from a rigorous interpretation of the unsteady-state flow problem for sands of different permeabilities in series. Thus, what purports to be a trial-and-error calculation to include variations in sand conditions within the intercommunicating aquifer to define water drive has little importance compared to the designation of such paranzeters at the reservoir to constitute the essential criteria. INTRODUCTION In a recent publication, the reader has been introduced to the simplified material balance formulas,' It has been shown that the complexities formerly associated for identifying and determining reservoir pressure in the material balance relationship can be resolved by treating with the Laplace transformations, the inversion of which reveals pressure as an explicit function of all factors contributing to its change. For an under saturated oil reservoir, this constitutes an integrated effect from the inception of production; and for a saturated oil reservoir, such represents a survey traverse. However, what is most important, for the first time we are able to express the pressure change in a reservoir directly to the oil, gas and water produced, and to the physical parameters of the formation, in the same manner that reservoir pressure has served in the past to define well interference — which opens up this avenue of endeavor for investigating interference between oil fields. The occurrence of interference is by virtue of the juxtaposition of two or more oil reservoirs producing in the same aquifer. Thus, in any one field, the extended production so incurred creates a pressure lowering in the field, as well as in the aquifer, which can now be transcribed by these simplified material balance formulas to the adjoining reservoir to observe the increased pressure change so induced. These effects are retroactive from field to field, to reveal a pressure drop far in excess of normal depletion to evidence the interference pattern that can result. Such is the purpose for the present undertaking — to develop the mathematical physics treating with this phenomenon of interference between oil fields, employing the simplified material balance formulas. Since Ref. 1 often will be referred to in the text, it is identified as "The Simplification", in the same connotation that another paper has been referred to as the "Laplace Trans-formation. However, the amount of material to be covered in these passages is substantial; therefore, the total emphasis will be placed upon developing these fundamental ideas treating with interference rather than attempting to offer work curves, which always can be prepared. For the practical application of these simplified material balance formulas that form the framework of the present development, the reader will find a comprehensive treatment in the Appendix of Ref. 1, illustrating a factual field example. In essence, what is proposed by this presentation is to make available to the practicing engineer a simplified means to treat with interference between oil fields, independent of the complex machine computations that have attended such undertakings in the past. As the problem unfolds, a common pattern will be discernible, whereby the many reiteration processes that previously required computing devices are eliminated.