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By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By Pradeep K. Rohatgi, Clyde M. Adams

Structures produced upon solidification of the eu-tectic composition (33 wt pct Cu) aluminum copper alloy have been examined as a function of freezing rate dfs /d? , the rate of change of fraction solid (fs) with time (8). Slow (dfs/d? = 0.0016 sec-1), intermediate (dfs/d? = 0.02 sec-1) and rapid (dfs/d? = 0.4 to 7.30 sec-1) freezing rates were used. The lamellar Al-Cual2 eutectic is arranged in the form of rod-shaped colonies at rapid freezing rates. The colonies are aligned parallel to the direction of heat flow, whereas the lamellae within the colonies are aligned at various angles, as high as 90 deg, to the direction of heat flow. The colony spacing (C) is proportional to the square root of inverse freezihg rate. The relationship is C = 15.5(dfs/d?)-1/2 where C is in µ and 8 is in sec. The ratio of colony spacing to lamellar spacing is greater than 20.0 and increases with a decrease in the freezing rate. A duplex dendritic structure is produced at intermediate freezing rates. A fine lamellar eutectic is arranged within the dendrites (exhibiting side branches at an angle close to 60 deg from the main stem) and a coarse irregular eutectic appears in the interdendritic regions. The duplex eutectic structure is also produced at slow freezing rates. However, at slow freezing rates there is a Platelat of CuAl2, along the center of the main stem of each dendrite and the other lamellae are arranged perpendicular to the central platelet. THE eutectic between CuA12 and a! aluminum has been reported to freeze in a lamellar form by several workers.'-3 chadwick4 has measured the interlamel-lar spacing as a function of growth rate. Kraft and Albright2 have reported on irregularities in the lamellar structures, and have proposed growth models which account for the formation of faults during solidification. In certain instances the lamellar eutectic has been found to exist in colonies. The colony formation315 has been attributed to the breakdown of a planar liquid-solid interface due to rejection of impurities. The aim of the present work is to study the structures produced from the eutectic aluminum-copper alloy under relatively fast solidification rates, such as encountered in casting and welding operations. The solid-liquid interface presumably remains planar under conditions of slow unidirectional freezing which produce lamellae aligned parallel to the direction of heat flow. The local growth velocities are the same over the entire interface and are equal to the rate of growth of the all-solid region. The spacing between the eutectic lamellae is inversely proportional to the square root of the growth rate of the all-solid region. Under the freezing conditions used in the present study, the solid-liquid interface is cellular or dendritic and the local growth velocities are different in the different regions of the interface. The relationship between the growth rate of the all solid region and the local growth velocities varies with the location and the shape of the interface. The growth rate of the all-solid region is, therefore, an inadequate parameter to describe the eutectic micro-structures which depend upon the local growth velocities. For this reason the structures have been examined as a function of freezing rate, dfs/d?, where fs is the fraction solidified at time 0. The freezing rate was varied by a factor of 4000. The relationship between the freezing rate, dfs/d?, and the growth velocit of the all solid region depends upon the specimen geometry and the shape of the interface. EXPERIMENTAL PROCEDURES The A1-33 pct Cu alloy used throughout this study was made in an induction furnace, using electrolytic copper and aluminum of commercial purity (99.7 pct), the primary impurities being silicon (0.12 pct), iron (0.14 pct), and zinc (0.02 pct). Three ranges of freezing rates were investigated: 1) A spectrum of rapid freezing rates (ranging from 0.40 to 7.30 sec-1) was obtained in arc deposits made on 2-in. thick cast plates of the eutectic alloy. The arc was operated at constant power and was made to travel at constant velocity on the surface of the plate that was in contact with the chill surface during solidification. The pool of liquid metal formed under the moving tungsten arc solidified rapidly by heat extraction through the unmelted plate. Conditions of unidirectional heat flow were achieved near the fusion zone interface, especially in the center of the arc deposits. The great advantage of the arc technique is that rapid cooling and freezing rates can be varied in a qualitative way. The correlation between the arc parameters and the solidification rate is given by the following relationship:6-8

Jan 1, 1970

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By R. E. Cech, T. D. Tiemann

It has been shown that hydrogen may be made to serve as a rapid and eflicient reducing agent for Cu, Ni, Co, and Fe sulfides if a scavenging agent for hydrogen sulfide is intimately mixed with the sulfide particles being reduced. Accelerated reduction kinetics are demonstrated for nickel sulfide. Copper, nickel, and cobalt sulfides, when treated at certain temperatures in a combined reducing agent-scavenging agent system, are converted to voluminous masses of fibrous metal product. Studies have been carried out to determine the conditions which lead, on the one hand, to irregular poly crystalline fibers and, on the other, to long single crystal filaments a few microns in diameter. A mechanism is proposed to account for the formation of single crystal filuments. The sulfide minerals of Cu, Ni, Co, and Fe are an important source of these metals yet there has been comparatively little scientific effort devoted towards understanding reduction mechanisms of these minerals. This may be, in part, due to the fact that the most convenient reducing agents for carrying out such studies, viz., hydrogen and carbon, do not react appreciably with sulfides. We have found that the reaction of hydrogen with metal sulfides can be markedly accelerated by placing a scavenging agent for hydrogen sulfide in close proximity to the metal sulfide. A brief series of experiments demonstrating relative reduction rates is reported in this paper to illustrate the effect. With the reduction process thus accelerated we have observed an unusual type of reduction behavior on some of the sulfides investigated. Under certain conditions the metallic product of the reduction reaction takes the form of filaments growing outward from the sulfide particles. The present paper deals largely with efforts to classify the various types of growth forms observed. This study has shown that filamentary growths from sulfides take a much greater variety of forms than has heretofore been reported by Ercker,1 Hardy,2 and Nabarro and Jackson3 in their reviews of metallic growths from copper and silver sulfides. THERMODYNAMIC CONSIDERATIONS The thermodynamics for hydrogen reduction of metal sulfides is quite unfavorable. For the sulfides considered here equilibrium constants typically range from 10-3 to 10-5. These low equilibrium constants impose severe kinetic limitations on reduction since hydrogen sulfide must be transported out of the system at concentrations of only a few hundred ppm. Unless extremely high gas flow rates are employed the atmosphere surrounding any sulfide particle will always be essentially in equilibrium with the sulfide. If, however, one places an efficient scavenging agent for hydrogen sulfide in close proximity to the metal sulfide particles the concentration of H2S near the metal sulfide will be held to a very low value. This would permit the reduction reaction to proceed with little or no inhibition from a buildup of reaction product gas. It is well known that calcium oxide is capable of removing hydrogen sulfide from a hydrogen gas stream of low dew point.4 If a sufficient quantity of calcium oxide is mixed with the metal sulfide particles the reaction: CaO+H2S=CaS+ H2O [l] will substitute moisture in place of hydrogen sulfide in the gas stream and this will not affect, in a direct manner, the reaction: MeS +H2=Me + H2S [2] A convenient method of considering the thermodynamics of the combined reducing agent-scavenging agent system is to consider the atmosphere when the partial pressure of hydrogen sulfide is the same over both the metal sulfide and the scavenging agent, i.e., pH2S (1) =pH2S (2). As a consequence: pH2O (1) pH2(2) =K1K2 The chemical driving force for reduction will depend inversely upon the moisture content of the gas and will be 0 when, in the system, pH2O = pH2.K1K2. Table I lists values of the equilibrium constants for reduction and H2S scavenging reactions for a number of sulfides at several temperatures. Data are taken from Rosenqvist4,5 and Kelly.6 The equilibrium constant products calculated from this data show that the limiting level of gaseous reaction product has been increased by a factor of 10' to l04 as a result of substituting a reducing agent-scavenging agent system for a simple reducing agent system. One possible side effect which must be considered is the possibility that the moisture evolved in the scavenging reaction might cause the atmosphere in the system to be sufficiently oxidizing to favor the formation of oxide rather than metal. This possibility was examined by comparing the equilibrium constant products listed in Table I with equilibrium constants for hydrogen reduction of the respective metal oxides. It was found that for copper, nickel, and cobalt the combined reduction-scavenging reactions could not develop a sufficiently high oxidizing potential in the

Jan 1, 1970

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By W. L. McMorris, A. H. Brisse

IN the last several years the coal industry has intensified its effort to solve the growing problem of cleaning and recovering fine mesh coals. On one hand these has been increasing civic pressure for cleaner streams, and on the other hand there has been increasing production of fine mesh coal, resulting directly from adoption of the modern mining methods so essential to the economy of the coal mining industry. Cleaning fine coal with the same precision possible with coarser coals is a difficult task, and for coals finer than 200 mesh it has been impractical. Furthermore, the inclusion of —200 mesh material in the final product markedly increases costs of de-watering and thermal drying, which are necessary steps if coal is to meet market requirements. Consequently these extreme fines have generally been wasted. As a result, problems have been created in many districts because there has not been enough area for adequate settling basins. Wasting of coal in the -200 mesh slimes may account for a loss in washer yield equivalent to 2.0 to 2.5 pct of the raw coal input. With rising mining costs the value of such a loss is constantly increasing and a need for a better solution to the fines problem becomes more pressing every day. From an operating viewpoint, also, continuous removal of extreme fines from the washing plant circuit permits good water clarification practice, improving significantly the overall cleaning efficiency. The obvious desirability of recovering a commercially acceptable coal from washery slimes prompted U. S. Steel Corp. to investigate the merits of the Convertol process developed in Germany." Although this process has been used commercially in Europe for some time, little if any consideration has been given to its possible adoption in the U. S. until very recently. Fundamentals of the Convertol Process: In the Convertol process, droplets of dispersed oil are brought into intimate contact with the solids suspended in the coal slurry to be treated. This contact causes oil to displace the water on the surface of the coal by preferential wetting, or phase inversion, after which the coal particles are allowed to agglomerate in a manner permitting their re- moval from the slurry by centrifugal filtration. The clay and other particles of mineral matter suspended in the slurry do not have the affinity for oil the coal particles have. Consequently the oil treatment is preferential to coal to the extent that more than 95 pct of the oil used reports with the clean coal recovered. Figs. 1 through 3 will clarify the steps involved in the process. Fig. 1 shows the suspended material in the slurry to be treated, which is a thickened product containing 40 to 45 pct solids. Oil is now injected into the slurry under vigorous agitation to produce good oil to coal contact conditions, which result in preferential oiling of the coal particles. These coal particles are then permitted to agglomerate by gentle stirring in a conditioner to form flocs, as shown in Fig. 2. At this point in the process the agglomerated oiled coal can be washed and partially dewatered on a vibrating screen, as shown in Fig. 3. Finally, the washed flocculate can be further dewatered in a high-speed screen basket centrifuge or in a solid bowl centrifuge. Commercial Application of the Convertol Process in Germany: The original Convertol process was developed by Bergwerksverband zur Verwertung von Schutzrechten der Kohlentechnik, G.m.b.H., a German research organization controlled by the Coal Operators Assn. of the Ruhr Valley. The process as reduced to commercial practice in Germany' is shown in Fig. 4. In this process a thickened slurry (40 to 45 pct solids) mixed with a predetermined percentage of oil is fed from a surge tank to the phase inversion mill. After the phase inversion step, the slurry is usually discharged directly to a highspeed screen centrifuge. From 3 to 10 pct oil is used, depending on type of oil, size consist of coal to be recovered, and operating temperature. The top size of fine coal cleaned in Germany by the Convertol process is limited by the size of the openings in the centrifuge screen basket. Any mineral matter coarser than the basket opening, which is generally 60 to 80 mesh, must remain with the oiled coal. If the coal fines have been effectively cleaned down to about 80 mesh, the cleaning performance of the process is practically unaffected by the presence of coarse coal particles. However, since recovery of coal much coarser than 80 mesh is mow economical by conventional methods, it normally becomes more costly to allow substantial percentages of this coarse coal in Convertol process feed. Where the general plant layout does not permit effective cleaning of coal sizes down to 80 mesh or lower. there is some justification for a coarser Con-

Jan 1, 1959

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By Ralph B. Stevens

INTRODUCTION Underground fires continue to be one of the most serious hazards to life and property in the mining industry. Although underground mines are analogous to high-rise buildings where persons are isolated from immediate escape or rescue, application of technology to locate and control fire hazards while still in their controllable state is slow to be implemented in underground mines. Even in large surface structures such as hotels, often only fire protection systems which meet minimal laws are implemented due to the high cost of adding extensive extinguishing systems, isolation barriers, alternate ventilation, escape routes and alarm systems. Incomplete and ineffective protection occasionally is evidenced where costs would not seem to be a factor, such as the $211 million MGM Grand Hotel fire November 21, 19801. Paramount in increasing fire safety and decreasing the threat of serious fire is early warning followed by proper decision analysis to perform the correct action. However, very complex fire situations can be produced in structures such as high-rise buildings and underground mines simply because of the distances between the numerous fire-potential locations and fire safe areas. Other complexities arise when normal activities occur that emit products of combustion signaling a fire condition to a sensitive fire/smoke sensor. For example, the operation of diesel equipment or the performance of regular blasting can produce combustion products that reach the sensitive alarm points of many sensors2. Smoke detectors for surface installations provide fire warning when occupants are at a distant location or when sleeping, thus greatly reducing injuries and property damage. However, when installed in the harsh environments of underground mines, fire and smoke detection equipment soon becomes inoperative, unreliable, or requires excessive maintenance. The U.S. Bureau of Mines has performed many studies and tests to improve fire and smoke protection for underground mine workers3. This paper describes several USBM safety programs which included in-mine testing with mine fire and smoke sensors, telemetry and instrumentation to develop recommendations for improving mine fire safety. It is hoped that the technology developed during these programs can be added to other programs to provide the mining industry with the necessary fire safety facts. By recognizing fire potentials and being provided with cost-effective, proven components that will perform reliably under the poor environmental conditions of mining, mine operators can provide protection for their working life and property equal to that which they provide for themselves and their families at home. The basis of this report is two USBM programs for fire protection in metal and nonmetal mines4,5 and one coal program6. The data was collected beginning in May 1974 and continuing through the present with underground tests of a South African fire system installed at Magma Mine in Superior, Arizona, and a computer-assisted, experimental system at Peabody Coal Mine in Pawnee, Illinois. The conduct of each program was as follows: • Define the problem and its magnitude in the industry • Develop concepts to solve or diminish the problem • Review available hardware or systems approaches to fit the concepts • Install and demonstrate the performance of a prototype system through fire tests in an operating mine. MINE FIRE FACTS Whether in coal or metal and nonmetal mines, the potential severity of fire hazard is directly related to location. As shown in Figure 1, fire in intake air at zones A, B, C or D can cause contamined air to route throughout the mine quickly if not detected, isolated or rerouted. Causes and location of former metal and nonmetal fires are represented in Table 1; the cause and location of fatalities and injuries is shown in Table 2. Coal-related fires and their impact on deaths and injuries are graphed in Figure 2; their locations are described in Table 37. Significantly the table shows that the hazard to personnel was three times greater for fires occurring in shaft or slope areas, and the percentage of deaths and injuries was four times that of other areas. Number of Persons Affected A 129-mine sample indicated that from 8 to 479 employees per shift work in underground metal and nonmetal mines, and that deeper mines have larger populations, as shown in Figure 3. Coal mining relates similar employment, and a 16-state sample of 670 mines employing at least 25 persons shows the distribution in Figure 4. Drift mines accounted for 58 percent of the sample but employ only 45 percent of the underground workers.

Jan 1, 1982

By W. H. Herrnstein, J. B. Clark, E. C. Utley, A. J. McEvily

The ratio of the endurance limit (10' cycles) to tensile strength of age-hardened aluminum alloys is approximately 0.3, whereas the ratio for annealed alloys is about 0.5. The lower value for the age-hardened alloys has been associated with the instability of coherent precipitate during cyclic loading, but it has not been definitely established whether this instability is due to overaging or reversion during cyclic loading. The results of the present investigatzon support the reversion viewpoint. In this work specimem of 2024-T4 aluminum alloy were aged for 16 hr at 150°C after cycling for 10 pct of the life at 25.000 psi. These specimens were then tested to failure and exhibzted a marked increase in fatigue life. It is proposed that during the early stages of fatigue in this alloy dislocations cut through the coherent precipitate and bring about the reversion of the precipitate. Subsequent aging at 150ºC induces reprecipitation in the precipitate-free zones so that the weakened regions are strengthened and the fatigue life is extended. It Is recognized that the fatigue strengths of precipitation hardened aluminum alloys are unusually low relative to their tensile strength.'-= This feature is illustrated in Fig. 1 where it can be seen that age-hardened alloys have lower fatigue ratios (the ratio of the fatigue strength to the tensile strength) than those in the annealed or cold worked state. Further, as shown in Fig. 2, the more an alloy is dependent upon precipitation hardening for its total strength, the lower is the ratio of the fatigue strength to the tensile strength. This state of affairs has been associated with an instability of the metastable metallurgical structure of precipitation hardened aluminum alloys during cyclic loading. Evidence2 in support of this view is that the fatigue ratio increases in these alloys as the test temperature is lowered, thereby indicating that thermo-mechanical instability, rather than some other factor such as a non-uniform distribution of precipitate, is the factor responsible for the low fatigue ratio at room temperature. Two mutually exclusive proposals have been ad- vanced to account for this instability. Hanstock has proposed that overaging takes place during cyclic loading, and in support of this view, Broom et a1.2 have indicated that an overaging process might be promoted by the large numbers of vacancies which are created during cyclic loading. The creation of vacancies by radiation4 has been shown to lead to rapid overaging. Hanstockl obtained visual evidence of overaging in an aluminum alloy after cyclic loading, but in this instance it has been pointed ou? that because of the high frequency used (60,000 cpm) the observed effect may have been due to normal high temperature precipitation around energy dissipating cracks. Efforts to discern visual evidence of overaging in this alloy at lower test frequencies were not successful.3 The alternative postulate3 is that reversion takes place during cyclic loading and leads to localized soft spots at which fatigue cracks are readily initiated. Evidence for this process has recently been provided by Polmear and Bainbridge5 who demonstrated metallographically that regions depleted of precipitate were created during cyclic loading of an aluminum alloy. Inasmuch as precipitate particles bordering the depleted region had not grown in size, it was concluded that the solute atoms which had constituted the missing particles had gone back into solution. No mechanism for the reversion process was presented. The present study was undertaken to investigate further the conditions leading to instability during cyclic loading, and to determine whether reversion or overaging had taken place as a result of cyclic loading. BACKGROUND AND TEST PROCEDURE In order to differentiate between the processes of reversion and overaging, rest periods at an elevated temperature, which ordinarily would insure additional precipitation, were used in this investigation. It was expected that after a period of cyclic loading an elevated temperature rest period would result in a decrease in the remaining life of the specimen if overaging were occurring during cyclic loading, whereas in the case of reversion, reprecipitation would occur and the fatigue life would be extended. Such an expectation is based on the assumption that the crack-nucleation phase is a significant portion of the total fatigue life, and that such a treatment is of influence in the crack-nucleation stage and is relatively unimportant thereafter.

Jan 1, 1963

By C. S. Matthews, H. C. Lefkovits

Drilling progress is often delayed by sticking of the drill string. The development of preventive and remedial methods has been hampered by incomplete understanding of the sticking mechanism. A recent lahorntory investigation hns indicated that one type of sticking may be attributed to the difference in pressure between the borehole and formation. This paper shows, by means of soil mechanics, that the primary cause for differential pressure sticking is cessation of pipe movement, whereas diflerential pressre and stanrtding time determine the severity of the sticking. The analysis stresses the importance of using low-weight muds with low solids content and low water loss to alleviate diflerential pressure sticking and describes why packed hole drilling, long strings of drill collars, and a large deviation from the vertical are conducive to sticking. Finally, preventrve and remedial methods ore evaluated, and a theory is presented on the release of stuck pipe by spotting oil. INTRODUCTION Since drilling with long strings of oversize drill collars has become standard practice in many areas, the incidence and severity of the stuck pipe problem has increased. It has been noticed that in the majority of these cases the sticking could not possibly be attributed to key seating or caving of shales. It appeared that, due to the differential pressure between the mud column and the formation fluid, the collars were pressed into the wall and so became "wall stuck". Points to note about differential pressure sticking are: (1) sticking is restricted to the drill collars, (2) the collars become stuck opposite a permeable formation, (3) the sticking occurs after an interruption of pipe movement, (4) circulation, if interrupted, can be restarted after the sticking is noticed, and (5) no large amounts of cuttings are circulated out after restarting circulation. Helmick and Longleyl investigated pipe sticking by differential pressure in the laboratory and found an empirical relationship between the differential pressure, the sticking time and the required pull-out force. In this paper an explanation of the mechanism is given based on Terzaghi's theory of clay consolidation. A qualitative description is given in the following paragraphs while the derivation of fonnulas is given in Appendices. This paper is a first attempt to explain pressure differential sticking and many points will require additional theoretical and practical investigation before the problem can be fully understood. PRESSURE DIFFERENTIAL STICKING AS A CONSOLIDATION PROBLEM In any borehole, where the mud pressure is higher than that exerted by the formation fluids, a mud cake is formed opposite the permeable sections of the hole and a continuous flow of filtrate takes place from the mud, through the cake and into the formation. This radial flow pattern requires a certain distribution of the hydraulic and the effective (grain-to-grain) stresses inside the mud cake. Any quantitative or qualitative change in the external pressure conditions will produce a change in the flow pattern and, consequently, also in the internal stress distribution inside the cake. In view of the low permeability and the high compressibility of a clay mud cake, the adjustment of the internal stress distribution is slow and is accompanied by a change in volume. Time dependent stresses are thus created which gradually diminish as the new state of equilibrium between internal and external pressures is approached. Some 30 years ago, Terzaghi developed his "Theory of Consolidation" to account for the time-dependent stresses and settling of clay formations under the influence of external loads. He derived a differential equation by which the time-dependent hydraulic stress and the consolidation can be computed for any point inside the layer during the consolidation process. His theory is based on the assumption that the change in stress is solely due to a change in water content and it may only be applied to one-dimensional consolidation phenomena. Other investiga-tors5,10 have expanded his theory to include processes of more than one dimension. The difference between the external pressures on the mud cake before and after sticking is a qualitative one (isolation of part of the cake by the static contact with the drill collars after pipe movement has been stopped)', and the time-dependent stresses thus created may be investigated by means of Terzaghi's theory. By this analysis the changes in the nature of the contact surface between the drill collars and the mud cake during the sticking can be explained; and the friction force between the two may be computed as a function of the sticking time, the borehole dimensions and the mud cake characteristics.

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole'') and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-') is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-' using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- ' torr, Maiya and lakel measured y as 39 kcal mole-' using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-': there is evidence also for a low temperature value of about 20 kcal mole-'. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.'-'' Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A', C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2'3 M = mass of an evaporating molecule

Jan 1, 1970

By David W. James, Howard Jones, George M. Leak

Conditions are described for producing, by primary recrystallization, a matrix suitable for the growth of large grains near (110)[001] orientation in silicon iron strip by secondary recrystallizaliun in a steep temperature gradient. The orientation distribution of these large grains is expressed in terms of rotational deviations about the cross-rolling direction, the rolling direction, and the normal to the sheet, the deviational spread increasing in that order. With the aid of cowplenientary published data on the orientation dependence of growth rate, it is shown that this observation is consistent with the oriented-growth theory of recrystallization lextures. It is conclutled that growth-rate and orientation-distribution data obtained in a steep thermal gradient should be used with caution to account for isothermally Produced recrystallization textures. SEVERAL authors have reported methods of growing large grains by re crystallization of a small-grained matrix in silicon iron 1- B and pure a cr The present study was a preliminary in the growth of single crystals and bicrystals for surface relaxation," grain boundary mobility, and grain boundary diffusion studies. The method was to control the growth of a seed crystal into a suitable primary re crystallized matrix by feeding through a steep temperature gradient. The driving energy for growth derived from the grain boundary energy released as the seed crystals grew into the matrix. Thus, stability of the matrix against normal grain growth was considered to be essential for success. It was known that the manganese sulfide dispersion present in commercial silicon iron performs this function during secondary recrystallization to the (110)[001.] texture.12 Hence commercial, rather than high-purity, material was used throughout. The paper describes the growth conditions for grains large enough to be used as seed crystals for further growth into single crystals. The orientation distribution of the seed crystals is analyzed and its significance for the theory of recrystallization textures is discussed. EXPERIMENTAL PROCEDURE Strip material was supplied by the Steel Co. of Wales, Ltd. The chemical analysis in weight percent was Si, 2.90; C, 0.015; Mn, 0.059; P, 0.011; S, 0.027; Ni, 0.032; 0, 0.009; Fe, balance. A gradient furnace of similar design to one described previously4 was loaned from B.I.S.R.A. It consisted essentially of a vertical water-cooled copper slot projecting downwards into the hot zone of a molybdenum furnace. Hydrogen was passed through the furnace to protect both heating element and specimen from oxidation. Strip specimens up to 8 cm wide and 0.2 cm thick were sealed into the furnace at the mouth of the copper slot. A coating of light oil on the strip surface maintained the seal during translation of a specimen. The maximum temperature gradient in the region just below the copper slot was 500°C per cm over 1 cm, with the hottest point controlled at 1175°C. Several large grains would usually grow by secondary recrystallization from the primary matrix when a specimen was immersed in the hot zone for about 30 min. A back-reflection X-ray camera was constructed to facilitate rapid and accurate orientation determinations of the large grains produced. It was possible to reproduce a standard geometry, with regard to strip and camera, without the tedium of careful alignment on each occasion. Specimens, typically 4 cm wide and 75 cm long, were cut with the longitudinal axis parallel to the rolling direction of the original strip. The surfaces were cleaned by immersion alternately in a hot aqueous solution containing 2 pct hydrofluoric acid plus 10 pct sulfuric acid and in cold 10 pct nitric acid. The nitric acid etch was just sufficient to reveal the grain structure. Rolling and annealing treatments to prepare the matrix (discussed below) were followed by growth of seed crystals in the gradient furnace. The matrix was transformed to a single crystal by growth of a selected seed crystal connected to the matrix by a thin neck. 4,5 Growth was promoted by controlled feeding into the gradient furnace. Several single crystals of controlled orientation were grown successfully from seed crystals by twisting the interconnecting neck in a reorien-tation jig.4 EXPERIMENTAL RESULTS AND DISCUSSION Growth Conditions. A suitable matrix for growth of large grains was prepared starting from primary re-crystallized strip 1.9 mm thick. This was cold-rolled in two stages each being followed by a recrystallization anneal at 800°C for a few minutes. Such treatment gave the required growth matrix only if the two cold-reduction stages were each performed in several passes and in the following ranges: the first, 30 to 70 pct; the second, 10 to 50 pct. Immersion in the temperature gradient otherwise resulted in an equiaxed

Jan 1, 1967

By N. A. Gokcen, John Chipman

SILICON is the most commonly used deoxidizer and an important alloying element in steelmak-ing; hence a detailed study of this element in liquid iron containing oxygen is of considerable interest. The equilibrium between silicon and oxygen in liquid iron has been studied by a number of investigators but generally with inconclusive or incomplete results. The variation of the activity coefficients of silicon and oxygen with composition is entirely unknown. Published investigations deal with the reaction of dissolved oxygen with silicon in liquid iron and the results are expressed in terms of a deoxidation product. For consistency and convenience in comparison of the published information, the deoxidation product as referred to the following reaction is expressed in terms of the percentage by weight of silicon and oxygen in the melt in equilibrium with solid silica: SiO (s) = Si + 2 O; K'l = [% Si] [% 012 [I] Theoretical attempts to calculate the deoxidation constant for silicon in liquid iron from the free energies of various reactions yielded results which were invariably lower than the experimental values. Thus, the deoxidation "constants" calculated by McCance,1,2 Feild,3 Schenck, and Chipman were of the order of 10, which is below the experimental values by a factor of more than 10. Experiments of Herty and coworkers" in the laboratory and steel plant resulted in an average deoxidation constant of 0.82x10 ' at about 1600°C. The technique employed in their investigation was crude and the reported temperature was quite uncertain. The concentration of silicon was obtained by subtracting silicon in the inclusions from the total. Since at least some of the inclusions resulting from chilling must represent a fraction of the silicon in solution at high temperatures, such a subtraction is not justifiable. Results of Schenck4 for K'1 from acid open-hearth plant data yielded a value of 2.8x10-5, which was later revised as 1.24x10 at 1600°C. Similarly Schenck and Bruggemann7 obtained 1.76x10-5 at 1600OC. The discrepancies and errors involved in the acid open-hearth plant data as compared with the results of more reliable laboratory techniques were attributed by these authors to the lack of equilibrium and the impurities in liquid metal and slag, and are sufficiently discussed elsewhere." Korber and Oelsen" investigated the relation between dissolved oxygen and silicon in liquid iron covered with silica-saturated slags containing varying concentrations of MnO and FeO. The deoxidation products obtained by their method scatter considerably, and their chosen average values of 1.34x10, 3.6x10-5, and 10.6x10-5 1550°, 1600°, and 1650°C, respectively, represent the best experimental results which were available until quite recently. Darken's10 plant data from a steel bath agree approximately with their data at 1575° to 1625°C. Zapffe and Sims" investigated the reaction of H2O and H2 with liquid iron containing less than 1 pct Si and obtained deoxidation products varying by a factor of more than 20. Inadequate gas-metal contact and lack of stirring in the metal bath should require a longer period of time than the 1 to 5.5 hr which they allowed for the attainment of equilibrium. Furthermore, their oxygen analyses were incomplete and irregular and confined to a few unsatisfactory preliminary samples. Their results did indeed indicate that the activity coefficient of oxygen is decreased by the presence of silicon, although they made no such simple statement. They chose to attempt to account for their anomalous data by the unlikely hypothesis that SiO is dissolved in the melt. Hilty and Crafts" investigated the reaction of liquid iron with acid slags under an atmosphere of argon, making careful determinations of silicon and oxygen contents at several temperatures. Despite erroneous interpretation of the data at very low silicon concentrations, their data represent the most dependable information on this equilibrium that has been published. In the range 0.1 to 1.0 pct Si, their data yield the following values for the deoxidation product: 1.6x10-5, 3.0x10- ', and 5.3x10 at 1550°, 1600°, and 1650°C, respectively. The purpose of the work described herein was to study the equilibrium represented by eq 1 as well as the following reactions, all in the presence of solid silica: SiO2 (s) + 2H2 (g) = Si + 2H2O (g);

Jan 1, 1953

By H. H. Hausner, H. S. Kalish

M. Hansen—This paper certainly is an interesting study. Although I have not had too much experience in the powder metallurgical methods of studying phase equilibria, I would like to say the following concerning the interpretations of the results obtained: 1. The existence of a zirconium-rich eutectic having a melting point close to 950°C and containing approximately 5 pct beryllium is well established. 2. Undoubtedly sintering of the original compacts (i.e., without repressing and resintering at 1350°C) resulted in a condition being far from equilibrium, even in the low-melting point zircon-rich region where undissolved zirconium particles have been observed. This means that only partial reaction between the component powders has taken place. 3. In preparing and handling powder mixtures for pressing and sintering, we have found that with powders differing considerably in density, and also in particle size, separation in layers of different composition may occur. This means that a concentration gradient would exist within such samples. This phenomenon may, at least to some extent, account for the difference in microstructure of the top and bottom regions of some of the sintered samples. If this is the case, density figures for some of the nominal compositions would not represent actual densities of those mixtures. 4. Fig. 1 shows that the low densities of mixtures with 40 and 60 pct beryllium sintered at 1350°C are changed to much higher densities if the products sintered at 1100°C are repressed and resintered at 1350°C, whereby an approach toward equilibrium takes place. This would mean that the low density and growth in volume is due to nonequilibrium conditions. If this is true, would it be justified, then, to conclude that "the remarkable growth of the alloys in the vicinity of 40 to 60 pct Be indicates the formation of a high-melting point phase, probably accompanied by a considerable change in volume due to a large alteration of the crystal structure from that of the original compounds"? If some compound formation has taken place already during the first sintering at 950" to 1350°C, more compound would be formed by repressing and re-sintering of the 1100" samples. This treatment, however, results in higher, rather than lower, densities. In general, the density-composition curve of alloy systems containing one or more intermediate phases is characterized by a more or less defined contraction (decrease in specific volume, increase in density) over the "theoretical" density. Does not discrepancy exist between the two statements that "growth of the alloy indicates the formation of a high-melting phase . . ." and "even at 1350°C, no indications of sintering have been observed"? 5. I am not sure that the explanation given for the fact that fig. 4 did not reveal as much eutectic as the top portions of the mixture with 2 pct Be, is correct. The density of the melt containing only 5 pct Be or even perhaps less, is not too much different from that of the nominal composition. The reason might be also that there was already some separation of the components in the pressed compact. 6. I do not understand why the microstructure of the bottom regions of the compact with 5 pct Be (fig. 6) is so different from that of the top regions (fig. 5). The compact was melted on sintering at 1100°C. Its composition lies close to the eutectic point. There should be at least some lamellar structure in the bottom regions too; otherwise, the composition of top and bottom must have been very different after sintering, because the eutectic is said to extend as far as the composition ZrBe2. In case the white and gray areas of fig. 6 are both gamma, and the black areas undissolved zirconium, this composition would be close to the phase coexisting with zirconium, that is, ZrBe2, according to the hypothetical diagram, or a compound richer in zirconium. 7. Figs. 9 and 10 are not mentioned in the text. 8. The great difference in microstructure of the composition 20 pct Be of figs. 8 and 14 on one side and fig. 15 on the other side proves that sintering at 950" and 1100°C results only in partial reaction of the powers. 9. The mixture with 60 pct Be (fig. 19) seems to consist of two phases, rather than one phase, one interspersed in a matrix of another. 10. The statement that the eta phase "may be an intermetallic compound or the product of a peritectic or monotectic reaction" seems to be misleading, because the product of a peritectic or monotectic reaction in this region of the system must be an intermetallic compound. 11. If there is some solid solubility of Be in alpha and beta-Zr, it would be expected to be higher in beta-Zr (b.c.c.) than in alpha-Zr (h.c.p.). The temperature of the polymorphic transformation of zirconium then would be lowered, rather than increased. In accordance with this, Battelle has found that the transformation point of titanium is decreased by beryllium. 12. In case the phases present in alloys with 80, 90, and 95 pct Be are identical (which appears to be correct), it is striking that the relative amounts of both phases (eta and beryllium) are not too different within this wide range of composition. With 60 to 65 pct Be

Jan 1, 1951

By Lo-Ching Chang, J. Chipman

The perennial and increasing interest in the chemical behavior of steelmaking slags has led to numerous attempts to formulate the thermodynamic properties of these solutions. The classical view is that of a solution of the component oxides in which certain acidic oxides are more or less completely held in combination with basic or metallic oxides, the nature of the interoxide compounds being derivable from the chemical behavior of the slag or from the mineralogy of a solidified specimen. The known electrical conductivity of slags has pointed to the existence of ions in the solution and a number of attempts have been made to account for the observed facts of slag behavior on the basis of a theory of complete ionization of the solution. It is the purpose of this paper to examine, in the light of ionic theory, a number of recently published series of data on slag-metal and slag-gas equilibria, with the purpose of obtaining a more complete or more satisfactory generalization than has been possible on either of the single bases of simple compound formation or complete ionization. The attempt to formulate the ionic constitution of a complex solution is fraught with many uncertainties. An ion is not something that can be plucked from the solution and examined in detail, nor can its true formula be determined with certainty by any single experimental method. In attempting to express the composition of a slag by various ionic formulas it can be expected that alternative hypotheses of essentially equal merit will present themselves. In the present state of early development of the ionic theory of slags, it may be necessary to make some rather arbitrary choices of ionic formulas in the absence of su- cient information to yield complete certainty. Acids and Bases The classification of slag-forming oxides as acidic or basic apparently dates back into the days of Berzelius. It is difficult to see how the concept could have originated in the early twentieth century when it was fashionable to define an acid or a base as an aqueous solution containing hydrogen or hy-droxyl ions. It is, however, entirely consistent with the modern and more general theory of acids and bases. In this theory, as originally formulated by G. N. Lewis,' a basic molecule is one that has an electron pair which may enter the valence shell of another atom thus binding the two together by the electron-pair bond. An acid molecule is one which is capable of receiving such an electron pair into the shell of one of its atoms. The acid, the base, and the product of neutralization may be either ions or neutral molecules. The product of such a reaction may itself be a base or an acid if it is further capable of giving or accepting an electron pair. Thus a base is a donor of electrons, an acid, an acceptor. In oxide slags the typical and ever-present base is oxide ion, 0-—. In behavior and in importance it is analogous to hydroxyl ion, OH-, which is the typical base of aqueous solutions. There is nothing in the chemistry of slags which is quite analogous to the acid H30+ in aqueous solutions. This is not surprising for in slag systems there is nothing which can be designated as a solvent and no ubiquitous positive ion. The chemistry of slags is in fact more complex than the chemistry of aqueous solutions and the concepts which must be evoked in its study are correspondingly broader. In seeking a basis for a classification of slag-forming oxides as basic or acidic it must be remembered that these terms are not absolute but relative. A substance which acts as a base toward a second substance may act as an acid toward a third. This is less likely to happen among strong bases or acids than among the weak ones; there are numerous examples of weak acids which under the influence of a stronger acid behave as weak bases. Such substances are called amphoteric. A classification of the glass-forming oxides has been proposed by Sun and Silverman² and further developed by Sun3 in which the oxides are arranged in order of decreasing acidity or increasing basicity, each substance being potentially capable of acting as an acid toward substances below it in the list and as a base toward those above it. It is based upon the relative strengths of the metal-to-oxygen bond as determined by the energy required to dissociate the oxide into its component atoms.' Data are available for computation of this energy, at least approximately, for the oxides of slags and glasses. In general those oxides from which it is most difficult to remove the positive atom are the strong acids while those in which it is most loosely held are the strong bases. It is in the latter, of course, that formation of oxide ion occurs most readily as, for example, in CaO which in solution ionizes to form the weak acid Ca++ and the strong base O—. The order of arrangement found by Sun is shown in the first column of Table 1, to which have been added the data for

Jan 1, 1950

By James H. Courtright, Kenyon Richard

SILVER Bell is situated 35 airline miles northwest of Tucson, Ariz., in a small, rugged range rising above the extensive alluvial plains of this desert region. Its geographical relation to other porphyry copper deposits of the Southwest is shown on the inset map in the lower left corner of Fig. 1. The climate is semi-arid. Altitudes range within 2000 and 4000 ft. Opening of the Boot mine, later known as the Mammoth, in 1865 was the first event of note in the district's history. Oxidized copper ores containing minor silver-lead values were mined from replacement deposits in garnetized limestone and treated in local smelters. Copper production had approached 45 million pounds by 1909 when the disseminated copper possibilities in igneous rocks were recognized. Extensive churn drill exploration carried out during the next three years resulted in partial delineation of two copper sulphide deposits, the Oxide and El Tiro. Although the then submarginal tenor discouraged exploitation of these disseminated deposits, selective mining of orebodies in the sedimentary rocks continued intermittently until 1930, providing a production total of about 100 million pounds of copper. The American Smelting & Refining Co. began exploratory and check drilling in 1948 and subsequently made plans for mining and milling the Oxide and El Tiro orebodies at the rate of 7500 tons per day. Production began in 1954 at a rate of about 18,000 tons of copper annually. Formations ranging in age from Pre-Cambrian to Recent are exposed in the Silver Bell vicinity. The more erosion-resistant of these, Paleozoic limestone and Tertiary volcanics, predominate in the scattered peaks and ridges comprising the Silver Bell mountains. The porphyry copper deposits are located along the southwest flank of these mountains in hydrothermally altered igneous rocks. These are principally intrusives which cut Cretaceous and older sediments and are considered to be components of the Laramide Revolution. For three-fourths of its length the zone of alteration strikes west-northwest, Fig. 1. There now is no single structure that accounts for this alignment. However, indirect evidence suggests that a fault representing a line of profound structural weakness existed in this position prior to the advent of Laramide intrusive activity. This line will be referred to as the major structure. It was obliterated by the Laramide intrusive bodies but exerted a degree of control on their emplacement, as evidenced by their shapes and positions. The influence of fault structures on the shapes of intrusives in other porphyry copper districts has been noted by Butler and Wilson' and by others. As shown on the inset map on Fig. 2, a fault of parallel trend and considerable displacement lies to the north. This fault is now marked by a line of small Laramide intrusive bodies. To the south is a third fault of large displacement. Evidence of its age in relation to the Laramide intrusions and mineralization is not recognized, but its conformance in strike with the other two major faults is significant. These three breaks establish a pronounced trend of regional faulting. They are high-angle, and the southerly one may be reverse, Stratigraphic separations on these faults are of the order of several thousand feet. The local Paleozoic section is about 4000 ft thick. It is composed predominantly of limestone with a basal quartzite member. The Cretaceous section appears to exceed 5000 ft. Conglomerates, red shales, and arkosic sandstones (the youngest) characterize the three principal members. Intrusion of alaskite marked the beginning of Laramide igneous activity. It was emplaced as an elongate stock with one side closely conforming to the major structure line throughout a distance of nearly 4 miles. The alaskite was at one time regarded as a thrust block of pre-Cambrian rock'; however, its intrusive relationship and consequent post-Paleozoic age has been established by inclusions of limestone found in outcrops north of El Tiro. The next event was the intrusion of a large stock of dacite porphyry into Paleozoic sediments and alaskite. The stock was some 3 miles wide and at least 6 miles long in a northwesterly direction. It was sharply confined along its southwest side by the major structure line. A number of large pendants of moderately folded Paleozoic sediments occur within and along its southwest edge. Thus the inferred, original major fault between Paleozoic and Cretaceous sediments became a contact between alaskite and Paleozoic sediments and then a contact between dacite porphyry and alaskite. Andesite porphyry may have been intruded later than the dacite porphyry, but relationships are not clear; it may be simply a facies of the latter. The intrusive activity was at this stage interrupted by an interval of erosion. The erosion surface probably was rugged, as there were local accumulations of coarse, angular conglomerate. Subsequently a series of volcanic flows and pyroclastics several thousand feet thick was deposited. A similar unconformity has been recognized elsewhere in the Southwest, particularly in the Patagonia Mountains near the Flux mine some 75 miles southeasterly. Here, as at Silver Bell, volcanics were deposited on an erosion surface cut in Cretaceous and older sediments which had been intruded by alaskite. Though no evidence is offered that closely defines the age of this unconformity, and proper analysis of the problem is beyond the scope of this paper, it is

Jan 1, 1955

By Arnt Solbu, Jomar Thonstad

The reaction between CO, and aluminum in cryolite-alumina melts in contact with aluminum has been studied by passing CO2 over the melt. In unstirred melts a homogeneous reaction between dissolved metal and dissolved CO2 was observed. In stirred melts in which convection was induced by bubbling argon through the melt, the dissolved metal apparently reacted mainly with gaseous CO2. The rate of formation of CO increased slightly with increasing depth of the melt, and it did not depend on whether CO2 was passed over or bubbled through the melt. The rate of formation of CO increased with increasing area of the metal/melt interface and with the application of anodic current to the metal. It is concluded that the dissolution of metal into the melt is the rate-determining reaction. THE current efficiency in aluminum electrolysis is determined by the rate of the recombination reaction between the anode gas and the metal: 2A1 + 3CO2—A12O3 + 3CO [1] as originally stated by Pearson and waddington.1 The occurrence of this reaction in cryolite-alumina melts in contact with aluminum was first verified experimentally by Schadinger.2 Thonstad3 has shown that the reaction may proceed further to give free carbon: 2A1 + 3CO— A12O3 + 3C [2] Normally only a few percent of the CO formed undergoes such reduction. The mechanism of these reactions has not yet been clarified. Aluminum, as well as CO,, is soluble in the melt. The solubility of aluminum in cryolite-alumina melts at around 1000°C corresponds to 75 x 10- 6 mole A1 per cu cm,4 while that of CO2 is only 3 x 10-6 mole CO, per cu cm.5 Taking into account the stoichiometry of Reaction [I], the ratio between dissolved aluminum and dissolved CO2 available for the reaction in a saturated melt is about 40. Therefore, as will be shown in the following, the reaction probably mainly occurs between gaseous COa and dissolved aluminum. The dissolved aluminum presumably consists of subvalent ions of aluminum and sodium.4'6 Since the interpretation of the present results is not dependent upon the nature of this solution, the dissolved metal will be designated solely as Al+ in the following. The reaction can then be divided into four steps: A) dissolution of metal, e.g., 2A1 + Al3 — 3A1+ [3] B) diffusion of dissolved metal through a boundary layer; C) transport of dissolved metal through the bulk of the melt; D) Reaction [1]. If dissolved CO, takes part in the reaction, three additional steps embodying the dissolution and transport of CO2 must be added. schadinger2 observed, when bubbling CO2 through the melt, that the rate of formation of CO (in the following designated rfco) did not depend on the distance from the metal surface. The results also indicate that the rate of bubbling did not affect the rfco. When passing CO, over the melt, Revazyan7 found that the loss of metal did not depend on the depth of the melt above the metal or on the flow rate of CO2, and concluded that Step A is rate-determining. In an unstirred melt, however, Gjerstad and welch8 found that the rfCo decreased with increasing depth of the melt, indicating that step C was rate-determining. It thus appears that the rate control of the process depends on the experimental conditions, particularly on the convection. In the present measurements the reaction has been studied in unstirred as well as in stirred melts. EXPERIMENTAL AND RESULTS The experiments were carried out at 1000°C in a Kanthal furnace with a 10-cm uniform temperature zone (±0.l°C). The melts were made up of "super purity" aluminum (99.998 pct), hand-picked natural cryolite, and reagent-grade alumina. In experiments where alumina crucibles were used, the alumina content in the melt was close to saturation (13.5 wt pct9); otherwise it was 4 wt pct. Pure Co2 (99.85 pct) was passed over the melt, and the exit gas was analyzed for CO2 and CO by the conventional absorption method.3 From the weighed amount of CO (as CO2) the rfco was calculated as the number of moles of CO formed per min per sq cm of the surface area of the melt. The amount of carbon formed by Reaction [2] was not determined. As already indicated the rfco is much higher than the rfC, by Reaction [2]. Since the rfC probably is proportional to the rfco, the measured rfco should then the proportional to, but slightly lower than, the total rate of Reactions [I] and 121. In general the scatter of results obtained in duplicate measurements was ±5 to 10 pct, while within a given run a precision of ±3 to 5 pct was obtained. The various crucible assemblies that were used will be described below. Measurements in Unstirred Melts. When carrying out aluminum electrolysis in small alumina crucibles. Tuset10 observed that after solidification the lower part of the electrolyte was gray and contained free metal, while the upper part near the anode was white and contained no metal. One may test for the presence of free metal by treating with dilute hydrochlorid acid.

Jan 1, 1969

By James R. Stuart

AS the available remaining properties of iron ore reserves on the Mesabi Range are opened up for mining, the various properties located under lake beds are brought nearer an active status. The actual physical problems involved in stripping these properties do not act as a deterrent so much as the legal and political problems that are encountered. When it is proposed to destroy a natural lake that has been used by the public for many years, much local as well as state opposition may be encountered regarding its destruction. Public hearings must be held and some adverse publicity is likely to result. The ownership of the ore under the lake and the rights of the abutting property owners must be settled, and protection from damage caused by a disturbance in surface and subsurface drainage is likely to be demanded by property owners some distance from the proposed mine area. The Embarrass Mine, located near Biwabik, Minn., falls into this classification. A portion of the orebody lies under what was formerly Syracuse Lake, this body of water having been removed in the process of stripping the mine. An additional problem in the case of a meandered body of water is the establishment of a meander line that can be projected downward as mining progresses to form the basis for a satisfactory division between lake bed and upland ore shipments for royalty purposes. Fig. 1 illustrates the complications encountered in maintaining these divisions. A balance point was agreed upon in the center of the lake to make an equable division of lake bed ore to the abutting properties. The entire lake bed has since been adjudged the property of Minnesota. Lake Characteristics Lake bed stripping problems with which this paper is concerned necessarily are limited to a specific type of lake, namely the glacial lakes of the Lake Superior region. One characteristic common to these bodies of water is a deposit of fine black mud or silt on the bottom, frequently underlain by a layer of impervious blue clay. This is also true of the muskeg areas of the region, which present almost identical problems as lakes in stripping. The actual removal of the water and the lake bed material is a routine matter more or less standardized as to equipment, and the period of time required can be estimated easily on the basis of volume and capacity. More important than the foregoing is the execution of preliminary work, and above all, the timing involved. An account could be prepared based entirely on statistical and cost data which would give a very fair picture of the time required and cash outlay needed to effect the removal of a body of water preliminary to stripping the orebody. However, the real interest from the standpoint of the operator and the engineer who carry responsibility for completion of the job lies in the unexpected emergencies and the action of various materials involved in the stripping when the balance has been upset through diversion of water courses and the reduction of the lake level. Runoff and Drainage Lakes are located in natural basins that catch all the rain water and runoff water for a considerable area. Where a lake is involved having an inlet and outlet or a sizeable water course running through it, the drainage area may include a watershed covering many square miles. All available data then must be collected to supply a history extending over as many years for which information can be gathered on the flow of streams, annual rain and snowfall, and most important, the peak flows to be expected. Where the diversion of a stream around the stripping area is a part of the problem, this last factor is of great importance since it controls the cross-section to be selected for the diversion channel and the volume to be removed in its excavation, as well as affecting the hydraulic considerations to be met in the design of the completed channel. Characteristic material in the overburden found at the Embarrass Mine is illustrated in Fig. 2. Well Pumping Pumping from the well holes was started well in advance of the draining of the lake. Fig. 3 shows a gradual lowering of the water table with no noticeable fluctuations during the period in which the lake was being dewatered. Unfortunately, because of tight ground, a maximum flow to the wells was not maintained. This retarded the rate at which the water table was reduced so that in the course of stripping the excavation soon extended below the water table, and the great bulk of the pumping was handled from a system of sumps in the pit itself. Any dewatering program projected by prepumping from wells, a glorified well point system, would have to be started well in advance of the stripping to be of any great advantage. Preliminary drainage of the surface over the mine area is entirely apart from the actual elimination of the lake bed itself. Since the lake is what is called a perched water table because of the impervious character of the lake bottom, the adjoining surface may be dewatered below the surface of the existing lake and the flow will not be affected by the proximity of that body of water. This condition actually has been demonstrated through the establishment of a number of observation holes where a small churn drill was used to put down the holes and a 3-in. pipe was installed for taking water level

Jan 1, 1952

By M. G. Corson

Until recently, the characteristics of cast copper have seldom been studied and such study as has been made has been inadequate. The prevailing idea seems to be that since pure copper is infrequently used in the cast stlate, there is no reason for trying to establish precise data regarding the properties of the metal in that condition. On the other hand, wrought copper either in the shape of sheets or wire rarely fails in service, except as a result of the action of reducing gases at the annealing temperatures, so there is little incentive to study the properties of the cast shapes —cakes, bars, ingots and billets—for the sake of tracing the causes of failures of the wrought metal to the cast stock. However, about a decade ago, wirebars of American origin often cracked badly while being hot-rolled in mills in Germany. This Icd to four investigations: by E. Seidl and E. Schieboldll by P. Siebe12 by 0. Bauer and G. Sachs,3 and by G. Welter.4 These authors came to the conclusion that failures in hot-rolling were due essentially to the presence of a wide zone of columnar crystals between t'he thin layer of fine crystal5 near the surfaces of the bars and the large but more nearly equiaxed grains of the central core. This macrostructural defect was explained in turn by the probable upward deviation in the temperature of the metal while it was being poured into the molds of the castling machine. More recently, cast shapes of copper were investigated by X. 1'. Allenh and by C. Blazey. Allen examined vertically cast wirebars and hori-zontally cast wedge cakes of electrolytic tough-pitch copper, but only for the distribution of densities; i.e., porosity. Blazey was interested mainly in the mechanism of the variations in electrical conductivity due to cold-work and anneal, but gave introductively an account of the composi-tion and average densities of the tough-pitch horizontally cast Wirebars used. As far as the present writer can tell, no investigation mas under-taken for the sake of presenting a picture of the distribution of mechanical characteristics in the wirebars of copper, or otherwise.

Jan 1, 1938

By M. G. Corson

Until recently, the characteristics of cast copper have seldom been studied and such study as has been made has been inadequate. The prevailing idea seems to be that since pure copper is infrequently used in the cast stlate, there is no reason for trying to establish precise data regarding the properties of the metal in that condition. On the other hand, wrought copper either in the shape of sheets or wire rarely fails in service, except as a result of the action of reducing gases at the annealing temperatures, so there is little incentive to study the properties of the cast shapes —cakes, bars, ingots and billets—for the sake of tracing the causes of failures of the wrought metal to the cast stock. However, about a decade ago, wirebars of American origin often cracked badly while being hot-rolled in mills in Germany. This Icd to four investigations: by E. Seidl and E. Schieboldll by P. Siebe12 by 0. Bauer and G. Sachs,3 and by G. Welter.4 These authors came to the conclusion that failures in hot-rolling were due essentially to the presence of a wide zone of columnar crystals between t'he thin layer of fine crystal5 near the surfaces of the bars and the large but more nearly equiaxed grains of the central core. This macrostructural defect was explained in turn by the probable upward deviation in the temperature of the metal while it was being poured into the molds of the castling machine. More recently, cast shapes of copper were investigated by X. 1'. Allenh and by C. Blazey. Allen examined vertically cast wirebars and hori-zontally cast wedge cakes of electrolytic tough-pitch copper, but only for the distribution of densities; i.e., porosity. Blazey was interested mainly in the mechanism of the variations in electrical conductivity due to cold-work and anneal, but gave introductively an account of the composi-tion and average densities of the tough-pitch horizontally cast Wirebars used. As far as the present writer can tell, no investigation mas under-taken for the sake of presenting a picture of the distribution of mechanical characteristics in the wirebars of copper, or otherwise.

Jan 1, 1938