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By Roderick K. Davey

Introduction in any business, it is essential that we select those alternatives which are not only technically feasible, but will be the most profitable to the business m terms of corporate objectives Some of the studies and activities requiring support of financial analysis to select the alternatives which most closely satisfy the management objectives and technical considerations are as follows 1 ) Cutoff grade determination. 2) Ore reserve estimation. 3) Production forecasts (long- and short-term) for an operating mine, development of a new mine, or expansion of an existing mine. 4) Evaluation of haulage alternatives. 5) Evaluation of equipment.

Jan 1, 1979

By John Hall

THE Fremont test for measuring the energy consumed in breaking a notched bar of steel is not so well known in this country as it deserves to be. The test specimen used in this test is about 3/8 by 1/4 by about 1 1/4 in., notched with a hack saw on the lower side to cause the piece to break at a fixed point. A weight of 10 kg. falling 4 m., and provided with a knife or chisel which strikes the specimen, breaks the test piece by impact. The residual force in the falling weight after it has broken the specimen is recorded by a suitable device, and the difference between the total energy and the residual energy of the weight (in kilogrammeters) is the force consumed in breaking the specimen. An experience of several years with the Fremont testing machine has shown its great value in readily detecting brittleness not revealed by tensile testing or slow bending testing. I this paper it is proposed to discuss (1) the supersensitiveness of the test as applied to cast steel and (2) its value in revealing the effect of heat treatment under certain conditions. .

Jan 7, 1913

By Cyril Wells, Robert F. Mehl

The purpose of this investigation was to prepare high-purity iron-carbon alloys, to determine as precisely as possible the A3(GOS), the Acm(SE), and the A1(PSK) transformation temperatures in the meta-stable iron-iron carbide system (up to 1.4 per cent C), and to study the influence of carefully controlled and constant rates of heating and cooling (1/8 to 2o C. per minute) upon the transformation temperature and upon the resulting microstructure. Apart from the general metallurgical importance attending the completion of such a task, it will be noted that highly precise transformation temperatures are of interest and importance in the thermodynamic study of this system1. Several determinations of the iron-iron carbide diagram have been made2. These suffer generally from the low purity of the alloys used, and from the application of methods of investigation of low sensitivity. Attempts to compare and weight the many data available in an effort to construct as accurate a diagram as possible have, in the main, been unsuccessful. In general, the wide differences in the results of different workers, the lack of complete analytical data, the omission of important details relating to the heat-treatment of the alloys, and the meager description of the methods of investigation applied, render such a process of averaging nearly meaningless. It may be seen from the summaries by Epstein2 and Körber and Oelsenl that variations as great as 30' C. exist in the reported data on the A3 temperatures in iron-carbon alloys. Fortunately, the Aa temperature in pure iron is now known to be 910" C. ± 1° C.3 The best recent work on iron-carbon alloys is that of Esser4 on hypoeutectoid steels and that of Sato5 on both hypoeutectoid and hyper-eutectoid steels. Esser made a dilatometric and magnetic study of iron and iron-carbon alloys containing 0.06 to 0.86 per cent C, for which a high purity is claimed. Presumably the electrolytic iron was reasonably pure, but the alloys contained considerable impurities, on the average totaling 0.35 per

Jan 1, 1937

By I. Lowthian Bell

THERE has been probably no improvement introduced into the manufacture of iron which created more surprise in the minds of practical smelters and of scientific men than Neilson's discovery of the hot blast. In 1829, Messrs. Dunlop & Co. consumed at the Clyde Works, near Glasgow, nearly 7 3/4 tons of coal to make a ton of pig iron, of which about 20 cwts. was employed under the boilers of the blowing engines, leaving nearly 7 tons for the consumption of the furnace itself. In the year 1833, by heating the air to 612° F. (322° C.), they reduced the 7 3/4 tons to 3 tons by the mere burning of 8 cwts. of coal in the apparatus for raising the blast to this temperature. The statement just given is strictly true in a commercial sense, but when we come to consider the question as one of physical science, it is necessary to eliminate some of the conditions which conduced to so extraordinary a result. Anterior to Neilson's time the fuel employed in smelting iron was coke, and it was supposed at that period, erroneously, however, that coal in its raw state, when burned with cold air, was totally unfit for the purpose in question. This mineral, as it was obtained from the Lanarkshire coal-field, contained about 35 per cent. of volatile matter, but the process of charring it was performed in so unskilful a manner that instead of receiving 88 cwts. of coke from 135 cwts. of coal, 60 cwts. only was the product of the operation. Again, the reduced consumption of carbon in the furnace itself was accompanied by a corresponding diminution of blast, and this was followed by an economy of half a ton in engine coal. After making a proper allowance, however, for all these collateral circumstances, we are within the mark when we admit that in actual coke, which is really the form the fuel has to assume before it is burnt in the blast-furnace, not less than 30 cwts. was saved by heating the blast to 615° F. (322° C.). This unexpected economy, be it remembered, was obtained by the combustion of the 8 cwts. of coal, somewhat wastefully applied in the hot-air apparatus. Numerous have been the opinions advanced by different authorities in the scientific world to account for the apparent anomaly, but none,

Jan 1, 1877

By Robert J. De Angelis, James H. Barker

An improved method for solving dynawzical dislocation problems using a digital computer is described in this paper. Interactions between two distinct types of dislocations were studied: attractive screw dislocations; and Lomer lock forming dislocations. One dislocation is positioned in the lattice and is initially at rest, while the other dislocation is moved through the lattice on an intersecting slip plane at a constant velocity in the range 0.5 to 0.999C. (C is the transverse velocity of sound.) The results obtained from these computations indicate that screw dislocations account for a small fraction of the total strain over a wide portion of the range of velocities studied. They further indicate that mixed dislocations mainly repel other dislocations in the neighborhood of the active glide plane. From this a possible explanation for cell formation is put forth. The density of Lomer locks expected to exist after a strain of 0.2 was found to be 1.4 x 106 cm-2 which is in good agreement with indirect experimental estimates. IN the past, predictions of favorable or nonfavorable dislocation reactions were based on the associated changes in elastic strain energy. Such considerations take no account of the probability of the two dislocations coming into contact to react. Venables1 was the first to approach these probabilities by considering the interactions between two moving screw dislocations on perpendicular glide planes. Because of the restrictive types of dislocations and glide plane geometry employed, his results have limited application to metallic crystals. The work to be presented here develops a general approach to solving dynamical dislocation problems; either dislocation-dislocation interactions, presented here in detail, or dislocation interactions with any other suitably defined stress field. Two types of dislocation-dislocation interactions common to face centered cubic (fee) materials are considered: those between pure screw dislocations of opposite sign on intersecting slip planes and those between mixed dislocations on intersecting slip planes, that can react to form a perfect dislocation. This latter reaction, referred to as the Lomer reaction, produces a locked product dislocation that finds it energitical favorable to disassociate into two Shockley partials and a stair-rod dislocation. This partial configuration known as a Lomer-Cottrell (L-C) lock plays a major role in work hardening of fee crystals. seeger2 names the L-C lock as the prime contributor to Stage II hardening while Kuhlmann-wilsdorf3 and Meakin and Wils- dorf4 also state that it is a significant contributor to work hardening. However, with a few notable exceptions,5-7 direct observations of the Lomer lock and the L-C lock by electron transmission microscopy are scanty, and even these are subject to other interpretations.5,6 In a study of partial dislocations present in austenitic stainless steel, whelan8 did not observe any L-C locks at the head of pile-up groups. This result contradicted existing work hardening theories and led him to postulate an alternate theory based on the stress required to break away dislocations intersecting a pile-up group, from their stacking fault nodes. Due to the importance of the Lomer reaction in producing L-C locks which are an essential feature in current work hardening theories and because there exist no data giving direct quantitative values for the density of locks, and because there has even been some doubt expressed as to whether this important reaction occurs at all, a study of the dynamic behavior of the mixed dislocations which form the Lomer lock was undertaken. Due to their ability to cross-slip with relative ease, screw dislocations play an important role in the deformation of fee crystals. For this reason, the second type of reaction considered here is between screw dislocations of opposite sign. In addition, computations in volving screw dislocation interactions are relatively simple, thus providing a convenient check on the cornputational scheme employed. DEFINITION OF PROBLEM The force exerted on a dislocation due to a generalized stress field is given by the Peach and Koehler9 equation: Here t2 and b2 are respectively the tangent and Burgers vectors of the dislocation, and T1 is the stress dyadic defining the local stress field. The stress field may be externally applied or generated internally by the presence of a lattice defect, such as a second dislocation, as is the case in this work. Frank10 has shown that an equivalent momentum, P, of a screw dislocation can be defined by: Here, EST is the total energy of a screw dislocation and ESo is its rest energy. The left side of Eq. [2] is the time derivative of momentum and the right side is the position derivative of the energy due to the dynamical nature of the dislocation. The total energy of a dislocation is the sum of the potential and kinetic energies. Weertman11 has developed the expressions which were used here; these give the potential and kinetic energies of uniformly moving edge and screw dislocations in an isotropic medium.

Jan 1, 1969

By G. Howell Clevenger

FORMERLY great divergence of opinion existed in regard to the influence of copper in steel, as affecting its various physical properties. More recently the investigations of Stead,1 Breuil,2 Wigham,3 Burgess and Aston,4 Ball and Wingham,5 Miiller,6 Dillner,7 and others have shown fairly good agreement in the major points. Copper steel has been shown by these investigators to possess special properties which make it valuable for certain uses. The general range of composition of the useful alloys of copper and iron, and of copper, iron, and carbon, has been quite definitely established, for the former by Burgess and Aston,8 and for the latter by Breuil 9 and Stead.10 Stead 11 has removed one difficulty in reconciling certain of the earlier data by calling particular attention to the influence of carbon in copper steels. Another point which caused confusion in the earlier investigations, particularly in regard to " red-shortness," was the presence of sulphur. Failure to note the presence of sulphur often led to attributing " red-shortness " to the presence of small amounts of copper. Turner 12 has called attention to the fact that where copper exists in an iron ore it often occurs as the sulphide, so that the presence of copper in steel made from such ores might also, necessarily, mean the presence of sulphur. It is evident that the effect in this case might be quite different than where pure copper was added.

Jan 10, 1913

By Will B. Jamison

Man's material advance from one level of civilization to the next has involved the development of new, more useful tools and the utilization of energy greater than he alone could produce. These two essentials for material progress have developed at an ever increasing rate in the last century. While the first really successful use of mechanical energy derived from burning fuel was in James Watt's steam engine which pumped water from coal mines in Cornwall about 1770, there was still very little use of mechanical energy in mining by 1900 except for pumping and hoisting. Compressed air, having some of the characteristics of steam and which operated engines not unlike steam engines or steam hammers, powered the first attempts to mine coal with energy greater than human muscle could provide. When direct current-powered traction cars replaced horse-drawn transportation cars on city streets, it was natural that direct current locomotives should begin to replace animal and human power in mine haulage. Slowly, trolley and battery locomotives were developed and introduced. With d-c systems being established for haulage, it was natural that improved cutting machines should be developed and powered by d-c motors. Thus began the years of

Jan 5, 1960

By Guy Bjorge

IN recent years the Homestake mine has been served by three shafts, the B. &. M., the B. & M. No; 2 and the Ellison, supplemented by an inside shaft, the Milliken, extending from the 2000-ft. level to the 3200-ft. level. In 1932, when a new operating shaft was under consideration, the bottom of the mine was at the 3200-ft. level. The B: & M. and the B. & M. No. 2 shafts were down to the 1550-ft. level and the Ellison was being deepened from the 2600 to the 3200-ft. level. All ore was hoisted at the B. & M. and-Ellison shafts. Levels below the 2600 level, which were under development only, were served by the Milliken shaft. Below the 1550-ft. level, the mine was served only by the Ellison shaft from the surface. Within a few years, when ore reserves above the 1550-ft. level would be depleted, operation would be limited to the Ellison shaft and the auxiliary underground shaft. The Ellison shaft alone was not adequate for hoisting the entire output from the deeper levels and also handling all men and supplies. Further-more, assurance of safety and uninterrupted operation required- two fully equipped shafts to the deeper levels. Therefore a new operating shaft was authorized in November, 1932, and was named for A. J. M. Ross, the mine superintendent.

Jan 1, 1935

By H. W. Hitzrot

THE new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addition of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis- charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure-the new fine-ore bin designed arid built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work. The many ideas and opinions behind this achievement were all ably organized and executed by the Hollinger milling and engineering staffs, anti not a few were directly initiated by them. Excellent cooperation was afforded by the Hollinger staff to the engineers helping to conduct the grinding and classification test program. It was the author's privilege

Jan 1, 1939

By Robert M. Keeney

Important recent developments in the melting and annealing of non-ferrous metals include: 1. Melting of nickel silver in the vertical ring induction furnace. 2. Electric melting of stereotype metal. 3. The rotary-drum gas-fired brass melting furnace. 4. The low-frequency coreless induction furnace. 5. Finishing annealing of brass sheets with city gas1 replacing wood in the large brass-rolling mill. 6. Electric annealing of brass and copper tubing and sheets. 7. Replacement of oil by gas and electricity in the annealing of nickel-silver shells and stampings. Melting Nickel Silver in Vertical Ring Induction Furnace Although over 90 per cent. of the output of the brass rolling mills in the United States is now melted in electric furnaces,2 until recently a considerable part of the output of nickel silver has been the product of the pit fire. The application of the electric furnace to the melting of nickel silver has been slow for several reasons: (I) Until recently no lining has been available that gave a satisfactory life in the vertical ring induction furnace when melting nickel silver; (2) the rocking arc furnace so widely used in the foundry does not appear to have been favored by the rolling mill for melting nickel silver, possibly because the gases present may affect the quality of the alloy; and (3) the exclusive rights to the use of the high-frequency coreless induction furnace (which has proved very satisfactory for melting nickel silver) for the wrought brass industry are controlled by one concern. A little over one year ago the first vertical ring induction furnace to be used for melting nickel silver in the Naugatuck Valley was placed in operation. This was followed by two more in the same mill, and by

Jan 1, 1930

By F. Weinberg

It has been suggested, for some time, that the behavior of metals under high-temperature creep conditions is strongly influenced by the behavior of the grain boundaries present in the material. This has led to a number of investigations1-6 in which attempts were made to measure the properties of the grain boundaries themselves, both to determine their contribution to the creep process and to obtain further knowledge of their intrinsic structure and properties. The present investigation was undertaken to extend the observed data under more closely controlled experimental conditions and to attempt to clarify sonie of the discrepancies in the literature. A brief report of the preliminary results has been published.7 EXPERIMENTAL PROCEDURE For the present investigation, controlled orientation specimens were used having plane boundaries which terminated at the specimen surface. Trierys-tal specimens were used instead of the bicrystal type of Puttick and King,' in order to simplify the gripping technique required to apply a shear stress along the boundary. The aluminum used was obtained from the Aluminum Francaise and was of 99.994 pct purity, containing 0.002 pct each of Cu, Fe, and Si. The aluminum tricrystals were grown horizontally from the melt, in graphite boats, and in an argon atmosphere, following the technique developed by Chalmers.' The orientation of the tricrystals was controlled by using seed crystals separated by mica inserts. Thermal conditions were adjusted to produce tricrystals having boundaries which were macroscopically straight, parallel to the growth direction, and perpendicular to the top surface. Following growth, the tricrystals were carefully cut with a jeweller's saw to the test specimen shapes shown in Fig. l(a) and l(b). In Fig. 1(a), the boundaries subjected to shear stresses are indicated AB and CD: Points A and C are the ends of the mica inserts separating the seed crystals; points B and D are at lateral cuts made in the specimen. It was found that the slots left by the mica inserts at A and C had to be enlarged slightly, by cutting, to ensure that the boundary terminated freely at these points. A shear stress was applied to the boundarks by gripping the upper two legs in file-faced Inconel grips and suspending a weight from the lower part of the specimen held in similar grips, as shown schematically in the diagram. The test specimens shown in Fig. 1(b) were cut from long

Jan 1, 1959

By Cyril Smith

ALTHOUGH not of the same importance as electrical conductivity, the capacity for conducting heat is nevertheless a very important property of metals and alloys. A knowledge of thermal conductivity is of value in selecting alloys for many purposes and in the calculation of the efficiency of apparatus which is being designed. Unfortunately, the determination of thermal conductivity is extremely slow and tedious, consequently few data have been obtained. A further reason for the lack of information is that there has long been an impression that the thermal conductivity of an alloy is directly proportional to the electrical conductivity and that it can therefore be calculated from the latter. The Wiedemann-Franz-Lorenz law of constant ratio of the two conductivities holds with a considerable degree of precision for all the pure metals, but appreciable deviations occur in certain alloys-particularly those containing nickel-and it seems difficult to predict exactly what the ratio will be. Therefore direct determinations of thermal conductivity should be made whenever the results are, needed with any accuracy. This research is intended eventually to cover all the alloys of copper that are of commercial importance, including the binary alloys of copper with zinc, tin, aluminum, nickel, silicon, manganese, cadmium and phosphorus, and the ternary alloys copper-nickel-zinc, copper-nickel-silicon, copper-manganese-silicon, copper-zinc-tin, etc. Most of these alloys are customarily used in the wrought condition and therefore were tested in the form of annealed rods. A limited number of sand castings were also obtained and examined. This paper contains a complete review of all the previous work that has been done on copper alloys, and includes a detailed description of the apparatus and method of procedure used in the present research, together with the new results obtained on the copper-zinc series, which is the only one completed at the present time. Subsequent papers describing the other alloys will contain the experimental results and discussion only.

Jan 1, 1930

By A. Aly Selim, Bruce D. Hanson

A computer model capable of simulating the basic production system in a variety of underground mining methods has been developed at the U.S. Bureau of Mines Twin Cities Mining Research Center. The simulation of the basic production system at the working face, which includes drilling, blasting, mucking, and roof bolting, is described in this paper. The model is event-oriented; that is, the status of the system is updated at the occurrence of an event. All event or activity times, including failure and repair of equipment, are treated as stochastic variables. A location dimension, in addition to the time dimension, is used, allowing the simulation of systems with a number of stopes or faces. To aid the user in determining the efficiency of his system, the model provides several reports. An event or activity report gives the frequency of occurrence, total active time, and cumulative delay statistics for each event. An equipment report delineates the availability and utilization of all equipment. A production report provides information on various performance measures such as tons produced and holes drilled. The cost report gives the cost of various elements in the system. Operating data from an actual mining situation were used in validating the model. In addition to the description of the model, examples of simulation experiments which were performed on a room-and-pillar mine system are given. Use of the model to determine methods for improving the efficiency of the system is discussed.

Jan 1, 1976

By J. L. Ratliff, R. I. Jaffee, H. R. Ogden, D. J. Maykuth

An experimental program was carried out to improve the low-temperature ductjlity of tungsten through the combined use of dispersed oxides for grain-size control and Groups VII and VIII metal additions for matrix softening. Separate binary -alloy studies showed that increasing amounts of finely dispersed thoria or zirconia and critical amounts of rhenium, osmium, and iridium were effective in significantly reducing the ductile-to -brittle bend transition temperature of tungsten as well as in increasing its re crystallization temper - LIKE most of the high-melting point bcc metals, tungsten undergoes a marked transition from ductile to brittle behavior with decreasing temperatures. The material factors which influence the transition temperature include grain size, metal purity, and the presence of dispersed phases. ature and decreasing its recrystallized grain size. The beneficial effects shown by each of these additions on transition temperature and grain size in binary combinations appeared to be additive in tevnary combinations. Thus, combined additions of 2 to 8 vol pct thoria with 5 pct Re, 0.87 pct Os, or 0.30 pct Ir were effective in lowering the transition temperature of tungsten pom 2000 to 75"C, increasing its re crystallization temperature from 1600 to 1800°C, and decreasing its recrystallized gain size from 1175 to 6800 grains per sq mm. The mechanism by which these factors are operable in tungsten is not yet clearly understood. Nevertheless, it has become increasingly apparent that the interrelationship of grain size and matrix composition governs to a large extent the degree of low-temperature ductility which can be achieved. Though it is not possible to accurately assess the relative importance of these variables, the available evidence suggests that, at low temperatures, grain-size effects predominate over purity effects. This was indicated in recent studies by Allen, Maykuth, and Jaffee,' involving single crystals containing 20 to 40 ppm 0 and 1 to 30 ppm C. Thus, while each

Jan 1, 1964

By Morris M. Fine, Norwood B. Melcher

As a raw material, prereduced pellets can be considered symptomatic of the quiet revolution taking place in the quality and grade of blast furnace burdens for the past decade. In 1954, the average analysis of ores from U.S. ranges in the Great Lakes area was 50.86% Fe (natural), 10.22% SiO2, and 10.90% moisture; ten years later, the average was 56.67% Fe (natural), 8.13% SiO2, and 6.17% moisture. The advance in Canada was even more pronounced in a lesser number of years. In 1957 the average product of Canadian ore-producing areas was 51.62% Fe (natural), 8.59% Si02, and 8.02% moisture; in 1964, the average grade was 59.59% Fe (natural), 6.27% SiO2, and 3.94% moisture.2 These dramatic data are testimony to the giant strides made in iron ore improvement, and the next logical step is prereduction. Prereduction can well be considered as a beneficiation step in which oxygen is the gangue. Since the ultimate objective of milling and smelting is iron metal, non-metallic constitutents in general, whether oxygen or silica, are contaminants. The past and continuing attack aimed at lowering the silica content of concentrates is succeeding. One need only thumb through the Grade Name listings of the American Iron Ore AssociationVo note that virtually all commercial pellets contain less than 8% silica, many are lower than 6%, and a few below 45%. With natural technical evolution, it is expected "many" rather than "few" will ultimately be in the last category and further mechanical concentration will have reached the point of diminishing returns. At this level, oxygen would constitute the only major diluent worthy of attack.

Jan 7, 1966

By R. F. Mehl, B. Lustman

The formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.' It is necessary here only to cnumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type—i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained—the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [i] where X is the thickness of the alloy layer, k thc reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.$ In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varics with temperature according to the Arrhenius equation: k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. Ali phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By R. F. Mehl, B. Lustman

The formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.' It is necessary here only to cnumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type—i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained—the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [i] where X is the thickness of the alloy layer, k thc reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.$ In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varics with temperature according to the Arrhenius equation: k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. Ali phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By J. G. Richardson, K. H. Coats

During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and high rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leuerett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas. INTRODUCTION In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of the gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating — for given aquifer characteristics and fluid properties — the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formula1 and Buckley-Leverett2 method have some applicability to the problem; Woods and comer3 reported one-dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer.4 Douglas, Peaceman and Rachford5 presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek,6 Blair and peaceman7 and Goddin.8 Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here. One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques might reasonably be applied. However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability, porosity, reservoir thickness and dip angle.

By Leo P. Tarasov

Magnetic torque studies of ferromagnetic single crystals have been carried out in a number of laboratories during the last decade&apos;s2 and some work has been reported on polycrystalline material showing preferred orientation. Goss3 used the method extensively in developing electrical sheet with desirable magnetic properties, but he used it as a control rather than as a means of studying the texture. Bozorth4 made a quantitative correlation of a torque curve he obtained from some cold-rolled iron with the texture as determined from X-rays, but did not extend his studies beyond the one specimen. Other studies, which have been reported from time to time2,5 have also been incomplete in the sense that no effort was made to study a whole series of samples, differing only in degree of cold reduction or in the annealing temperature, in order to ascertain the effect of such treatments on the texture as revealed by torque measurements. It is the purpose of this investigation to make such a study, mainly in order to see how useful the method can be made when used under favorable circumstances and to find what kind of a correlation can be expected between magnetic and X-ray studies of texture. Before proceeding further, it is desirable to say a little about single crystals, so as to make clear the concepts involved in magnetic torque measurements. Magnetic Torque Method It is fairly well known nowadays that single crystals of ferromagnetic substances have directions of easy magnetization and of hard magnetization. In Fig. 1 are reproduced typical magnetization curves for a single crystal of iron, which show that in a < 100 > direction saturation occurs at low fields compared to those required to saturate the same crystal in a <110> or a <111> direction. (The magnetization intensity I is defined by the equation B = H + 4pI.) At fields high enough to

Jan 1, 1939

By Leo P. Tarasov

Magnetic torque studies of ferromagnetic single crystals have been carried out in a number of laboratories during the last decade&apos;s2 and some work has been reported on polycrystalline material showing preferred orientation. Goss3 used the method extensively in developing electrical sheet with desirable magnetic properties, but he used it as a control rather than as a means of studying the texture. Bozorth4 made a quantitative correlation of a torque curve he obtained from some cold-rolled iron with the texture as determined from X-rays, but did not extend his studies beyond the one specimen. Other studies, which have been reported from time to time2,5 have also been incomplete in the sense that no effort was made to study a whole series of samples, differing only in degree of cold reduction or in the annealing temperature, in order to ascertain the effect of such treatments on the texture as revealed by torque measurements. It is the purpose of this investigation to make such a study, mainly in order to see how useful the method can be made when used under favorable circumstances and to find what kind of a correlation can be expected between magnetic and X-ray studies of texture. Before proceeding further, it is desirable to say a little about single crystals, so as to make clear the concepts involved in magnetic torque measurements. Magnetic Torque Method It is fairly well known nowadays that single crystals of ferromagnetic substances have directions of easy magnetization and of hard magnetization. In Fig. 1 are reproduced typical magnetization curves for a single crystal of iron, which show that in a < 100 > direction saturation occurs at low fields compared to those required to saturate the same crystal in a <110> or a <111> direction. (The magnetization intensity I is defined by the equation B = H + 4pI.) At fields high enough to

Jan 1, 1939