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By Nicholas J. Grant, H. C. Chang

Microscopic observations during creep tests were made on AI-20 pet Zn, 80 pet Ni-20 pet Cr, and 25 and 3S aluminum specimens. All these materials failed in an inter-crystalline manner under certain stress and temperature conditions. Particular atten-tion was given to the initiation and propagation of intercrystalline cracks in coarsegrained AI-20 pct Zn specimens. The geometry of the grains and grain boundaries in these specimens was known before the tests. On the basis of the observations and a knowledge of the interaction between grains and grain boundaries, a mechanism of intercrystalline fracture and propagation of the fracture has been proposed. METAL, and alloy fracture occurs essentially in two ways: transcrystalline and intemrystalline. In the past most of the work done in this field was centered on the determination of stress criteria for fracture. The specimens used for these studies were tested under varying conditions of stress state, temperature, and strain rate. Unfortunately, very little attention was given to the initiation and propagation of the fracture, whereas the nature of fracture was examined closely only after failure. Several extensive reviews of these studies have been published by Orowan, Smith, Barrett, and Petch.1, 4 It is well known that a material which exhibits a ductile and transcrystalline fracture can be made to exhibit a brittle and intercrystalline fracture by modifying its composition and by heat treatment. This modification may or may not result in microscopically observable precipitation in the grain boundaries." In the creep of any one alloy the transition of transcrystalline to intercrystalline fracture is a function of stress, strain rate, and temperature." The tendency for intercrystalline fracture to occur increases as the strain rate decreases and the testing temperature increases. Extensive work on high purity aluminum (99.995 pet) under creep conditions showed the importance of the interaction between grains and grain boundaries, and the different responses of grain and grain boundaries to the variables: stress, strain rate, and temperature.7, 8 It was also shown that grain boundary deformation necessarily has to be accommodated in the grains by various deformation means as. for example, fold formation. The type of fracture resulting from the creep of high purity aluminum was invariably found to be transcrystalline. On the other hand, 2S and 3s aluminum were, under certain conditions, found to fracture in an intercrystalline manner." One reason given for this was that the grains could accommodate to a lesser extent the deformation of the grain boundaries.19 It was decided to examine this line of reasoning in greater detail and to investigate the particular interactions between grains and grain boundaries that result in the incidence and progression of inter-ct,ystalline fracture. It is also the purpose of this paper to show where and how intercrystalline cracks start and how they propagate to result in fracture. Several alloys—Al-20 pct Zn, 80 pet Ni-20 pet Cr, 2S and 3s aluminum-— were used for this study, but attention was paid mainly to the behavior of an A1-20 pet Zn alloy, since its general creep behavior has been established." From the results of this study a mechanism of intercrystalline fracture is proposed. Experimental Procedure The experimental procedure was similar to that used in previous work and has been detailed elsewhere.' Two parallel flat surfaces were milled from an originally round specimen, giving a gage portion which was 1x0.09X0.17 in. Some round specimens, 1/4 in. round by 1 in., were also tested. The A1-20 pet Zn specimens. which were annealed at 1030°F for 24 hr, showed two to four grains across the width of the test bar, and most of the grains occupied the whole thickness of the specimenu. Before some of the specimens were subjected to creep, the grain arrangement was mapped out in a development drawing, Fig. 1. The initiation and

Jan 1, 1957

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By K. H. Coats

This paper describes an approximate technique for handling the problem of percolation of evolved gas upwards through the oil column in computer simulation of natural depletion. This technique has been incorporated into a general model for simulating three-phase flow in one, two or three dimensions. The mathematical model for perfonning these calculations is described in detail in a separate article. 1 While vertical gas percolation occurs during natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle reel or bioherm. The reel may have an areal extent less than one section with a thickness of up to 800 It. The upward percolation of evolved gas often limits the time step in calculations as little as one day. Using this small time step, computer expense for a single 30- to 40-year simulation on even a one-dimensional basis has exceeded 92,000. The method described here for handling the percolation allows time steps of 60 days or more (depending on reservoir size and production rate), resulting in a considerable reduction in computing expense. The method also allows calculations in which secondary gas caps build up in tight zones of the oil column below the main gas cap. The validity of the method is indicated in connection with an example pinnacle reef field. Calculated results using a 2-day time step (where the method in question is not needed and not invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results from one- and two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was also performed and the required computing time is given. INTRODUCTION A general analysis for simulating three-dimensional, three-phase flow in reservoirs has been developed. 1 In applying this model to reservoirs undergoing natural depletion, a time-step restriction was encountered due to the flow of evolved gas upwards through the oil column and toward the gas cap. A remedy for this problem has been incorporated in the analysis and is described here. The time-step restriction is encountered only in calculations which include flow in the vertical or near vertical direction. The restriction occurs to some extent in reservoirs of any geometrical configuration, but it is especially pronounced in the pinnacle reef or bioherm where the ratio of thickness to areal extent is unusually large. This paper describes the problem, a method of handling it, incorporation of the method in the three-dimensional, three-phase model, and, finally, a test of the method's validity in an application to an example pinnacle reef reservoir. THE PROBLEM During the early stages of reservoir depletion, pressure falls below bubble point in progressively lower regions of the oil column. Continuing production results in evolution of dissoived gas throughout the oil column. This gas then percolates upwards toward the top of the reservoir. If the gas encounters a sufficiently low permeability zone in its travel upward, then it can accumulate and form a secondary gas cap. If no zones are encountered which are tight enough to hold gas against the gravity forces, then the gas travels on until it reaches the top of the sand or the main gas cap. Numerical simulation of multiphase flow in reservoirs is generally performed with time steps such that the flow of a fluid into or out of a block in one time step is a fraction (considerably less than one) of the total amount of that fluid present in the block. Use of a time step where the time step's

Jan 1, 1969

By Attilio Ligasacchi

The production of magnetite in copper smelting has been the subject of wide investigation in the past.1-9 It is accepted that most of the magnetite is produced in the converters and returned to the re-verberatory furnace with the converter slag. Part of this magnetite is circulated back to the converters in the matte. As a result, if proper fluxing practice is not followed, and temperatures in the converting process are not strictly controlled, an undesirable circulating load of magnetite may occur. This might ultimately lead to saturation in the reverberatory bath with consequent settling of the magnetite at the furnace bottom. This paper contains the cumulative results of a series of investigations on the formation and control of magnetite presently being conducted by the metallurgical department of the Chino Mines Division of Kennecott Copper Corp. THE METHOD USED FOR THE DETERMINATION OF MAGNETITE AND OTHER MAGNETIC MATERIALS Conventional wet chemical magnetite analyses are neither reproducible nor theoretically sound. These analyses are sensitive to time, temperature, and heating rate-all factors which tend to decrease their accuracy and reproducibility. To overcome the unreliability of the above method, H. W. Mossman1 developed an inductance bridge magnetite "meter" which completely replaces the wet chemical analysis with the advantage of quicker and reproducible results. Fig. 1 is a schematic diagram of the meter in use in the Chino metallurgical laboratory. When a pulverized specimen with magnetic properties is placed in coil A of the inductance bridge circuit, the permeability of the core is increased, causing a voltage drop across the coil. The unbalance is amplified to operate the balancing motor which adjusts the movable iron core in coils C and D to bring the bridge back to balance. An indicator arm connected to the movable iron core indicates directly the percent, or weight, of the magnetic material in the specimen. Coil B acts as a reference coil and a zero adjustment. The meter is standardized with a set of various amounts of -100 mesh pure magnetite crystals (99.8 pet Fe3O4) thoroughly mixed in a test tube with -100 mesh quartz sand. These mixtures are combined with inert transoptic powder and heated to 140° to 160°C (melting point of the powder) and subsequently cooled to room temperature, solidifying the whole mixture, in this manner eliminating any possible preferential orientation of the magnetite grains. In order to determine the effect of the particle size" of the magnetite and other magnetic materials on the meter determinations, five size fractions were obtained by wet screening of the 99.8 pet pure magnetite and several reverberatory matte and slag samples. The following size fractions were investigated: -80 + 100; -100 + 150; -150 + 180; -200 + 250; -250 + 300 and -100 mesh. The deviation of the meter readings for the various sizes of each sample never exceeded ±0.3 pet. This deviation is considered well within the accuracy needed for common smelter operation procedures. Further investigation proved also that grinding slag and matte samples in our laboratory disc grinder normally produced a powder constituted of 95 pet -200 + 300 mesh. For practical purposes a - 100 mesh size was used as standard for our studies. It was also found that for rapid determinations tamping of the sample in the test tube was sufficient and gave comparable results with those samples solidified with transoptic powder. For the purpose of this study we define the magnetite content in copper smelter slags and matte as the equilibrium amount of crystalline Fe3O4 existent in the specimen at a given reference temperature, excluding any secondary magnetite precipitated in the specimen during nonequilibrium conditions. MAGNETITE DETERMINATION IN SLAGS Since it is impossible to ascertain the status of equilibrium of a conventional slag sample, due to

Jan 1, 1965

By S. K. Mitra

A refinement of the Seeger model for intersection process is investigated which is in better agreement with experimental observations than the original. It is shown that, in single crystals, the strain hardening in Stage II is mainly due to the short-mnge interactions when intersection is the rate-controlling process. It is also demonstrated that the creep curves, as predicted by this theory, are in good agreement with the experimental observations. MOTT: Cottrell? and Seeger have developed an approximate theory for plastic deformation of single crystals over the range of variables where the strain rate is controlled by the rate of intersection of dislocations. Although it is now generally agreed that the low temperature deformation of many pure metals is controlled by the intersection mechanism, various dictates of the over-simplified Seeger model are not in good agreement with all the experimental facts. It is the purpose of this paper to reveal that by appropriate extensions of the Seeger model, particularly those suggested by Basinski: a much more reliable theory results. The refined model to be presented here will be shown to account, in a satisfactory way, for the effect of stress, temperature, and strain on the creep rate under constant stress and for the effect of temperature and strain on the flow stress in constant strain-rate tests. EXPERIMENTAL METHOD To Check the theoretical deductions, both creep and tension tests were conducted on single crystals of high-purity Al (99.994 pct Al) so oriented that both the active slip plane and the Burger's vector of the operative dislocations on that plane made angles of about 45 deg to the tension axis. Single crystals of aluminum (5/8 in. by 1/10 in. by 8 in.) were grown in a graphite mold under an inert atmosphere using the Bridgman method. The chemical composition of the aluminum is given in Table I. A common seed was used for all crystals and their orientation is shown in Fig 3. The extensometry consisted of two differential transformers with matched outputs mounted so as to measure the extension in a 2 in. gage length. The amplified difference in output of the two transformers was recorded by a potentiometer. The amplification was calibrated before each run so that one chart division of the recording potentiometer indicated a 105 shear strain on the specimen. Stresses were measured to the nearest 1 x l04 dynes per sq cm. ACTIVATION VOLUME The concept of Basinski that the activation volume is not constant but is a function of the force that aids thermal fluctuation in effecting the cutting of dislocations will be adopted in this section. The force acting due to an applied shear stress on the dislocation being intersected is where L is the mean spacing between the forest dislocations, is the Burger's vector and T is the back stress. A detailed discussion about the origin of back stress will be taken up later in this report. As shown by Basinski, the activation energy, U, that must be supplied by a thermal fluctuation in order to effect intersection, is equal to where x is the distance through which the dislocation must be translated for complete intersection, and Fm is the maximum force encountered in intersection. When the applied stress is decreased abrupt ly F also decreases and the activation energy increases correspondingly as documented in Eqs. [ 1 ] and [2]. The Seeger equation for the strain rate when the deformation is controlled by rate of intersection of where the shear strain rate (per sec) N = the number of points per unit vol at which intersection can take place

Jan 1, 1962

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study' that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,' flow in packed columns,' fracture flow capacity' and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By C. Gatlin, M. E. Chenevert

The effects of bedding plane orientation on the elastic constants and the yield strengths of three laminated rocks (one sandstone and two shales) and one isotropic rock (a limestone) were studied. The directional dependence of the elastic properties of these rocks was experimentally evaluated using a triaxial compression cell and auxiliary stress-strain measuring equipment. Symmetry of Poisson's ratios within the bedding plane suggested that horizontal isotropy exists, but the bedding planes do give rise to an appreciable difference between properties in the horizontal and vertical directions. For the three bedded rocks studied, Young's modulus was lower normal to bedding than along bedding. Yield strengths were determined at confining pressures from 0 to 12,000 psi in a triaxial compression cell. The rocks studied showed strength reductions as high as 40 per cent when the test specimen was oriented at 20°-30° to the bedding planes. The mechanical behavior of these rocks suggested that the rock properties of shear strength and/or coefficient of internal friction can vary with direction, depending on the particular rock tested. Tensile strengths were also measured and found to be lowest when failure occurred along bedding. This work shows that bedded formations exhibit sizable directional variations in both their elastic constants and yield strengths. It is suggested that these variations may be accounted for by using the "elastic laminate" model and the "variable coefficients" failure model. INTRODUCTION The nature of rock deformation at elevated pressures has been studied by many workers; papers by Handin,l,2 and Robinson3 illustrate the present state of knowledge. Most investigators have either chosen rocks which were as isotropic as possible (in order to avoid complications of data interpretation and analysis) or they have oriented their samples so that the effects of anisotropies (such as bedding planes) have been avoided. Of the studies performed, few were concerned specifically with mechanical anisotrop-ies. Griggs4 has presented limited data for specimens cut parallel, normal, and 45° to the bedding plane; he relates the strength anisotropy observed to the fabric (bedding) anisotropy. His tests were primarily concerned with large deformations (20 per cent strain); thus, no directional values of the elastic constants were reported. Handin has reported the results of similar experiments. Bott5has discussed rock strength anisotropies due to faults, cleavage, or bedding. He was concerned primari ly with determining the shear stress on such planes and did not mention the effect of friction. Jaeger6 later generalized Bott's work by taking friction into account and presented a limited theory for the failure of rocks having a "single plane of weakness", and also for rocks having a constant coefficient of friction, and a shear strength which varies with bedding plane orientation. Donath and Cohen,7 and Donathg have evaluated rock strengths from shale and slate specimens cut normal and parallel to bedding. A dependence of cohesive strength (7,) on the specimen orientation was also shown. Adler9 has also studied this problem and lists similar results. He assumes that all bedded rocks behave according to Jaeger's single-plane-of-weakness theory. Kalinin and Belorussov10 list results for strength tests parallel and perpendicular to bedding and use this information as a basis for hole deviation analysis. From the literature it is apparent that sedimentary rocks have been tested under widely varying conditions of stress; however, the assumption of isotropy is generally, but not always, made. Since geologic sedimentation often deposits sediments in very definite lavers.,. it seems that more svstema tic attention should be given to the possible effects of this natural bedding. Bedding, as used here, refers to visible regularities of grain size or orientation resulting from depositional processes. The mechanical strength anisotropies, which bedding may present, is not the only anisotronic property to be considered, since the elastic

Jan 1, 1966

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967

Sec. 1. This Division shall be known as the Institute of Metals Division of the American Institute of Mining and Metallurgical Engineers. Sec. 2. The object of the Division shall be to furnish a medium of cooperation between those interested in the metallurgy, fabrication and uses of the nonferrous metals and their alloys; to represent the A. I. M. E. in so far as nonferrous metallurgy is concerned, within the rights given in A. I. M. E. By-law XI., Sec. 1, and not inconsistent with the Constitution and By-laws of the A. I. M. E.; to hold meetings for social intercourse and the discussion of nonferrous metallurgy; to stimulate the writing, presentation and discussion of papers of high quality on nonferrous metallurgy; to reject or accept such papers for presentation before meetings of the Division. Article II—MembeRs Sec. 1. Any Member, Associate, or Junior Associate of the A. I. M. E. in good standing may become a Member, Associate or Junior Associate of this Division upon registering in writing a desire so to do, but without additional dues. Sec. 2. But no one who has been continuously indebted to the A. I. M. E. or to this Division for more than three months shall be entitled to vote or to receive publications to which, as a member of the Division, he would be entitled. Article III—Funds Sec. 1. The expenditure of the funds reccived by the Division shall be authorized by the Executive Committee of the Division. Article IV—Meetings Sec. 1. The Division shall meet at the same time and place as the annual meeting of the A. I. M. E., and at such other times and places as may be determined by the Executive Committee subject to the approval of the Board of Directors of the A. I. M. E. Sec. 2. The annual business meeting for election of officers shall be held within a few days before or after the annual business meeting of the A. I. M. E. Sec. 3. At any meeting of the Division for which notice has been sent to the members of the Division through the regular mail at least one month in advance, a business meeting may be convened by order of the Executive Committee, and any routine business transacted not inconsistent with these By-laws or with the Constitution or By-laws of the A. I. M. E. Sec. 4. For the transaction of business, the presence of a quorum of not less than 25 members of the Division shall be necessary. Article V—Officers and Government Sec. 1. The officers of the Division shall consist of a Chairman, two Vice-chairInen, Secretary and Treasurer. The office of Secretary and Treasurer may be combined in one person, if desired by the Executive Committee. Sec. 2. The government of the affairs of the Division shall rest in an Executive Committee, in so far as is consistent with the By-laws of the Division and the Constitution and By-laws of the A. I. M. E. Institute of Metals Divisiori

Jan 1, 1931

By J. D. Meakin

J. D. Meakin (The Franklin Institute Laboratories)— In a recent paper Garofalo12 has shown that a number of experimental creep results can be represented by the empirical relation In this expression ? is the steady creep rate, s is the applied stress, and A is a constant at a given temperature; a and n are adjustable parameters. Garofalo has shown that Expression [6] approximates to a power function at low stresses and a simple exponential function at high stresses. Among the data used by Garofalo are the results we published for creep of copper." For these results we found that the best correlation was an exponential law with different parameters in the low-and high-stress region, respectively. That is, i = A exp qs where A and q have different values above and below a critical stress a,. In Ref. 13 are listed a variety of observations which support the proposal that different mechanisms are operative at stresses above and below a,, and it is not felt appropriate to repeat those observations here. The purpose of this note is to demonstrate that, although the representation used by Garofalo does fit the experimental data very well, this fit cannot be used to conclude that only one mechanism is rate-controlling. The argument is best made graphically and is illustrated in Fig. 9. The continuous curves 2 and 3 represent pairs of simple exponential functions which intersect at i = 10-5. The curve 2 closely resembles the copper results in that a change of slope of 2:1 occurs at i = 10-5; the two functions shown are in fact: e = 10-7 exp (1.150) and ? = 10-6&apos; exp (0.576s) For purposes of comparison, curve 3 represents two exponential functions with a change of exponent of 3:1 and curve 1 has the exponent 1.150 throughout. It is quite clear that a satisfactory straight-line fit is obtained on a Garofalo plot for all three curves. The curves represent processes which have either a single stress exponent or two ex- ponents in a ratio as high as 3:l. It must, therefore, be concluded that the ability to obtain a linear dependence between log i and log (sinh cyo) cannot be taken as evidence for a single activated process. In fact, to some extent the way the experimental points quoted by Garofalo lie about a best fit straight line on the log (sinh as) plot indicates that two processes are indeed occurring. This is seen in Figs. 7(c) and 8(c) of Ref. 12 where it is particularly evident that the experimental points deviate from the straight line in a manner similar to curves 2 and 3 of Fig. 9. It is, of course, recognized that the generally used exponential form is an approximation to the hyperbolic sine function which is not valid for exponents of less than 1.2, e.g., qs < 1.2. The only curve in Ref. 12 which is affected by this restriction is Fig. 6(b) where the deviation from a In ? vs s

Jan 1, 1964

By M. T. Hepworth, A. K. Stewart

Iron containing 0.1 pct A1 and -0.9 pct P by weight was internally oxidized in the temperature range 900° to 1300° C, where the bcc structure is stabilized by phosphorous. By measuring the depth of penetration of oxygen with time in an internally oxidized zone for an imposed surface oxygen potential, oxygen permeability was determined. The dgfusion coefficient of oxygen in iron was then calculated using known solubility data, yielding the expression: where Do is the diffusion coefficient of oxygen in bcc iron in sq cm per sec and T is temperature in OK. RECENTLY Hepworth, Smith, and Turkdoganl measured the diffusivity of oxygen in bcc iron and reported the temperature dependence of diffusivity from data determined in the a, and 6 temperature ranges. Subsequently Swisher and Turkdogan&apos; have measured the diffusivity of oxygen in fcc iron. Internal oxidation techniques were employed by these investigators and in this current study. The analysis of this technique is developed by wagner3 (presented in English by Hauffe4 and Rapp 5). In this present study bcc iron stabilized by phosphorous was used to determine oxygen diffusivity in the temperature range 900° to 1300°C. Meijerin 6 has studied oxygen permeability in this temperature range using bcc iron stabilized with 5 pct Sn. Other inves- tigators who have studied oxygen permeability in bcc iron at other temperatures are Schenck et al., 7 Bohen-kamp and Engell, 8 and Bradford. EXPERIMENTAL Electrolytic iron of 99.99 pct purity was alloyed to contain 0.897 pct P and 0.093 pct Al. The maximum weight percent phosphorous required to stabilize bcc iron between 910" and 1392°C is 0.51 pct as determined by Haughton,10 0.42 pct by Roquet and jegaden," and 0.58 pct by vogel,12 with the latter value preferred by Hansen.13 Microprobe analysis indicated that there was no segregation of the phosphorous either before or after permeability studies; therefore, the quantity of phosphorous added was assumed to be sufficient to stabilize the bcc structure. Furthermore, the permeability results of studies on this alloy agreed substantially with interpolated values from previous data on bcc iron.&apos; An ingot of the Fe-P-A1 alloy was hot-rolled to a l-in.-thick slab. Specimens were machined to dimensions: 13/8 by $ by 1/4 in. The experimental apparatus and procedure used have been described before.&apos; A constant oxygen potential was established by passing argon and hydrogen through a column of oxalic acid dihydrate, which has a water vapor pressure which is well-known as a function of temperature. Slab specimens were exposed to a gas mixture sufficiently lean in oxygen to prevent the formation of a surface oxide for predetermined temperature for selected times. The specimens were then quenched, sectioned, and examined metallo-graphically. All quenched specimens were iron-plated to provide protection from the outside sample edge during polishing. Fig. 1 shows a typical microstruc-ture for a specimen oxidized at 953°C for 48.00 hr at a water vapor-to-hydrogen pressure ratio of 0.20. DISCUSSION AND RESULTS The following equation was derived by Hepworth et al.&apos; from Wagner&apos;s kinetic expressions for internal oxidation:

Jan 1, 1969

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author&apos;s suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By S. I. Liu

THE effects of strain histories, consisting of several prestrains in opposite directions, on the flow and fracturing characteristics of metals determined in a final test have been investigated previously.&apos;" Such strain histories vary from a single prestrain in tension or compression to the number of strain cycles leading to fatigue failure.&apos; Between these two limits, various strain histories could be visualized and some can be attained readily. One such example is a strain history consisting of a first prestrain in tension of various magnitudes and a second prestrain in compression also of various mag-nitude. In this investigation the strain history was extended to the combination of these two limits, i.e., a single prestrain in tension or compression followed by balanced strain cycles of a selected magnitude e, = k0.12. It was found in this case that only compressive initial prestrains could be investigated with sufficient accuracy.* Such strain histories can be considered also as (low cycle) fatigue tests of a metal subjected to various amounts of cold working. It appears from previous publications that cold working within a wide range of reductions usually raises the un-notched fatigue strength of many metals.&apos;-&apos; This effect, however, has been found to be inconsistent and sometimes reversed for other metals?.7 Furthermore, Ludwik reports that the yield strength of cold-worked specimens may be reduced by cyclic strains, while that of materials without cold work is generally increased in the initial cycles." " In addition to the above tests, a study was made of the effect of intermediate re-solution heat treatment on low cycle fatigue behavior. Such anneals should eliminate the strain hardening induced by the cyclic strains. As far as their effect on the fracture characteristics is concerned, a few previous tests seemed to indicate that the damage resulting from cyclic strains is retained only partially after heat treatment." A further investigation was made in which one specimen was subjected to repeated unbalanced tension cycles in which the strain interval was approximately $ 0.013. This repetition of plastic tension damages the material slightly. This result appears to confirm Ludwik&apos;s observations." " Commercial 3/4-in. rod of the aluminum alloy 24ST4 was selected for this investigation. The material was subjected to the following treatments before machining: 1—Re-solution treatment at 920" ± 10°F for 45 min, 2—water quench at room temperature, and 3—aging for four days at room tem-perature.? The treated material then was machined to desired specimen contour and tested. A coolant was used during machining to minimize any artificial aging effects of heating during machining. In some cases the 24ST4 specimens were reheat treated after having been strained. In these cases, the heat treatment was the same as the re-solution heat treatment described above. Procedure As shown in Fig. 1, threaded end specimens with a minimum diameter of 0.266 in. and a contour radius of 2 in. were used for prestraining to an axial compressive strain ranging from 6, = —0.10 to E, = —0.48. For large prestrains, two consecutive corn-

Jan 1, 1952

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author&apos;s suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By N. F. Schulz

The purpose of this investigation was to evaluate the effects of variables in equipment and procedure on tube test results. This information was then to be used to formulate specifications, preferably within the practical ranges of existing machines, for test procedures capable of yielding precise and meaningful data concerning the magnetic separation of any magnetite ore, regardless of its origin. A survey of current practice was conducted among laboratories using the Davis tube test. Many tube tests were performed to experimentally evaluate the variables most likely to affect test results. A simple method was then sought for adequately interpreting tube test results. The Davis magnetic tube concentrator is a laboratory machine designed to separate a small sample of pulverized magnetic iron ore into magnetic and non-magnetic fractions. It was developed in 1921 by mechanization of a test previously performed manually No significant changes have been made in the design of the apparatus since that time. The Davis magnetic tube test continues to serve as a practical basis for judging the amenability of an ore to magnetic separation and for controlling magnetic separation plant operations. The apparatus consists of an inclined cylindrical glass tube supported adjacent to closely spaced pointed poles of a powerful C-magnet. (Fig. 1). To conduct a tube test, a sample of suitably prepared ore is poured into the water-filled tube. With wash water flowing through, the tube is oscillated to gradually reject the non-magnetic and weakly magnetic ore particles until the desired degree of separation is attained. Both the magnetic concentrate and the tailings may be recovered for examination. MAGNETIC SEPARATION BY THE DAVIS TUBE Mechanical separation of a specified mineral component from an ore usually requires comminution to fine sizes for sufficient liberation. Some distinguish- ing property of the mineral is then exploited to sort the desired mineral particles from the gangue particles. The magnetic separation of iron ores is based on the fact that magnetite, Fe3O4, is strongly attracted by a magnetic field while the gangue minerals are not. Maghemite, ?-Fe2O3, which may occur in certain chemically processed ores, responds similarly to magnetite. The magnetic process is practical only when the loss of iron in the form of relatively nonmagnetic hematite, Fe2O3, goethite, Fe2O3.nH2O, or other iron mineral can be tolerated. In the Davis magnetic tube concentrator, magnetic attraction holds magnetically susceptible particles in a magnetic field. Forces due to gravity, inertia, and fluid-solid friction tend to remove the less susceptible particles from the field. The probability that a given middling particle will be rejected from the tube in a given period of time is an inverse function of its magnetite content, with some modification due to particle size and mineral specific gravities. The net result is that ore particles tend to be rejected in their order of increasing magnetite content, while the retained portion or magnetic concentrate increases in grade continuously during the process. MAGNETIC SEPARATION CHARACTERISTIC The magnetic separation characteristic or MSC of a magnetite ore is the correlation between concentrate

Jan 1, 1964

In the 100&apos; years since AIME was founded in 1871, the Institute has issued a great many publications in a variety of forms: periodicals, Transactions volumes, and special volumes or books. The following is a brief history of AIME publishing with some suggestions for proper referencing. TRANSACTIONS AIME Transactions volumes have been numbered consecutively since No. 1 was issued in 1873, including papers for the period 1871-1873. One or more volumes have been issued each year and may be divided into three general time periods: General Volumes (1873-1927), Volumes classified by subject matter (1928-1949), and the present practice, begun in 1949, of issuing three volumes per year, one each in the fields of mining engineering, metallurgy, and petroleum technology. The broad divisions of subject matter in each of these volumes correspond to the technical areas of the three constituent societies of AIME. AIME&apos;s Technical Publications, usually designated by TP number&apos;s (until the change in numbering system by the Society of Mining Engineers in 1958), may, with some exceptions, be referenced to an AIME Transactions volume. Reference to a specific volume, rather than paper number, is the preferred reference, since the volumes are the form of publication most commonly available in libraries. In many cases, over the years, the Technical Publications may also have been available in some other form, either as separates or in a periodical. General. Volumes (Vols. 1-78, 1873-1927): Until 1927 all papers eligible for Transactions were published in general volumes with no systematic attempt made to segregate the material on the basis of the technological fields to which the papers related.. One volume per year was issued from 1873 until 1912; from 1912 until 1927 from two to four volumes were issued annually. In addition to the Transactions papers, these volumes carried some of the proceedings of the business meetings of AIMS. Subject Volumes. (Vols. 79-183; 1928-1949): The material for these volumes was segregated according to subject matter, and up. to seven volumes were issued a year. In the latter part of the period, from 1934 on, there was one volume each&apos; year for the Petroleum, Institute of Metals, and Iron and Steel Divisions and-the remaining papers were grouped in various ways and is sued whenever sufficient numbers of papers had accumulated: The subject volumes containing mining engineering papers are listed in Table 1. The volumes for the period, 1936-1949 are included in this Cumulative Index. Each of the Transactions volumes carries on the binding the year of publication; this date does not give an indication of when the papers included were originally presented at meetings. The contents of the volumes usually list the meetings at which. the papers were presented. Not all papers from a given meeting necessarily are in one Transactions volume. Some of the earlier volumes do not have a number on the binding or within the volume. In 1934 numbers" were assigned to all Transactions volumes, commencing with the 1871-1873 volume as No. 1. Many of the papers published [ ]

Jan 1, 1972

By H. K. van Poollen, H. C. Bixel

A treatment is given of the transient pressure behavior of a well located at the center of a circular region surrounded by a radial discontinuity. On either side of the discontinuity, the values of permeability, viscosity, compressibility and porosity are uniform but may be different from those on the other side of the discontinuity. The results are obtained by solving a pair of finite difference equations. The numerical solution to these equations is obtained using a digital computer. The results are compared with previously published, approximated analytical solutions to the same problem. Solutions, presented graphically, show pressure decline for constant rate fluid production. The range of variables studied include dimensionless time from &apos;0.001 to 100 and storage capacity ratio from 0.001 to 1,000. The well behaves as if it were in an infinite reservoir for dimensionless times less than 0.25. Reservoir properties near the well can be estimated in the usual manner. An overlay technique is used to match an experimental curve with one of the theoretical curves. It is possible to estimate the distance to a discontinuity by substituting the actual time t and the corresponding dimensionless time tD at which a match occurs into the equation a = (0.000264 tk1/tD , µ1 cI)I/2 where kI/ I µI cI is the diffusivity near the well, and may be estimated from data taken at early time. Several buildup curves are computed. These curves show that for early shut-in times, correct values for transmissibility are obtained from conventional analysis. However, erroneous values of static reservoir Pressure are obtained unless data at large shut-in times are taken. INTRODUCTION A mathematical treatment of the transient pressure response of a well located at the center of a region bounded by a circular discontinuity is given. Within a region (Fig. 20) the properties of both the rock and the fluid are considered to be constant on either side of the discontinuity. While these properties are considered constant, they may be different on opposite sides of the discontinuity. A discontinuity of this type could be a fluid-fluid contact or a sudden change in rock characteristics such as thickness, porosity or permeability. Analytical solutions to this problem are available. 1-3 However, they are so involved that they are of little practical use. An approximate solutionl is available but the range of times over which it is valid has not been specified. A numerical solution to a pair of finite difference equations is used to obtain the solution given in this paper. PREVIOUS WORK One of the first solutions to the problem was published by William Hurst.1 Hurst considered unsteady-state flow of fluids through two sands in series with different mobilities in each sand. He used Laplace transforms to obtain a solution for a single well located at the center of the circle enclosing the first of the two sands. In this case, the solution for the pressure change in Region I (Fig. 20) is2

By M. J. Pool, P. J. Spencer

Using liquid tin as the solvent metal, the heats of solution of silver and gold in dilute Ag-Au-Sn alloys have been determined at 723°K by solution calorimetry. From the values obtained, the various enthalpy interaction coefficients in the liquid solutions have been calculated. The self-interaction coefficients Au and Ag values of 2413 and -6322 cal per g-atom in binary Au-Sn and Ag-Sn alloys, respectively. For an alloy containing 0.04 mole fraction Ag, Au is equal to 2443 cal per g-atom, and in an alloy containing 0.04 mole fraction Au, Ag has a value of —8883 cal per g-atom. Ag Au has been determined as —2650 cal per g-atom. ADDITION of a second solute to a dilute binary alloy may cause striking changes in the thermodynamic characteristics of the alloy. As yet, such influences cannot be reliably predicted and it is only by accumulation and critical assessment of data that definite patterns can be established. Solute interactions in dilute solutions were first treated mathematically by Wagner,1 who derived expressions for the Gibbs energy interaction coefficients. For an alloy consisting of. two dilute solutes, i and j, in a solvent s, these coefficients are given by: where yi is the activity coefficient of component i and x represents the mole fraction of solute or solvent. Other interaction coefficients have since been established in terms of the various partial molar thermodynamic properties of an alloy; the definitions of these are summarized in a recent paper by Lupis and Elliott.2 Mathematical and experimental studies of such coefficients have received much attention recently, providing a very useful theoretical background to an understanding of the nature of solute interactions taking place in dilute solutions. One of the definitions to arise from such work has been the extension of Wagner&apos;s treatment by Lupis and Elliott4 to include an enthalpy interaction coefficient, defined as. where ?Hi is the relative partial molar enthalpy of component i. ?Hi is related to the relative partial molar enthalpy at infinite dilution, ?Hio, and to the enthalpy interaction coefficients by the expression: Values of ?Hi can often be obtained with a high degree of accuracy by calorimetry, and, if the composition of the alloy is carefully controlled by making calculated solute additions throughout a series of measurements, application of Eq. [2] will enable reliable enthalpy interaction coefficients to be determined. Partial heats of solution must be investigated as a function of solute concentrations down to xi = 0, and, since ? values are obtained from the slope of mi plotted against x, great care must be taken to obtain precise data. The data for binary systems which are presently available often require extrapolation of ?Hi values from compositions as great as xi = 0.05 or even 0.1 to obtain limiting heats of solution. Reliable enthalpy interaction coefficients are thus impossible to obtain from published data for most of the alloy systems already investigated. The aim of the present work was to determine values of Au, Ag, Ag, and Au in the limit xsn -1 for the relatively simple Ag-Au-Sn system and from these results to gain some insight into the possible influence

Jan 1, 1969

By P. Marier, T. R. Ingraham

When anhydrous cupric sulfate is heated in a stream of nonreactive gas, cupric oxysulfate is formed. When this reaction is complete, the cupric oxysulfate then decomposes to cupric oxide, which is the normal end product of reaction. The kinetics of each of these reactions has been studied using pellets prepared from finely divided cupric sulfate and from finely divided cupric oxysulfate. In each case, the reactant-product interface within the pellet is well-defined, and by normalizing the decrease in inter facial area with the weight fraction of the pellet decomposed it has been shown that the interface migrates into the pellet at a uniform rate at constant temperature. The activation energy estirnated for the decomposition of cupric sulfate is 57 ± 7 kcal per mole and that for cupric oxysulfate is 67 ± 8 kcal per mole. The rate of interfacial reaction is flow-sensitive, increasing with increasing flow of a sweep gas in the range from 50 to 2000 cu cm per min. The rate of decomposition is retarded by sulphur trioxide in the sweep gas. The relationship between sulfur trioxide Partial pressure and rate is consistent with the Langmuir Adsorption Isotherm governing the retention of sulfur trioxide in the interfacial layer. MOST of the work reported on the thermal decomposition of cupric sulfate and of cupric oxysulfate is related to the thermodynamics of the individual decompositions.&apos;-4 No information is available on the rates of the individual reactions, on their activation energies, or on the effects of gas flow or of partial pressure of sulfur trioxide on the reaction rates. Some dubious conclusions based on relative reaction rates have been drawn from studies on the oxidation of sulfides. For example, on the basis of the products observed in a quenched system, it has been suggested5" that, when copper sulfide is roasted, the cupric oxide which is formed arises from the decomposition of either cupric sulfate or cupric oxysulfate. This is very difficult to reconcile with the thermodynamics of the C-S-O System,3 which support the probability that both cuprous oxide and cupric oxide precede cupric oxysulfate and cupric sulfate in the sequence of products formed during the oxidation of cuprous sulfide. In this paper the individual sulfate decomposition reactions will be examined and suggestions will be advanced for the mechanism of reaction. This will be based on the effects on reaction rate of changes in interfacial area, flow rate, and back-pressure of sulfur trioxide. EXPERIMENTAL Materials. The copper source material used in all experiments was Fisher Certified Reagent Grade anhydrous cupric sulfate, for which the following analysis was supplied by the manufacturer: chloride, 0.002 pct; alkalies and earths, 0.2 pct; insoluble, 0.002 pct; iron, 0.020 pct. Cupric oxysulfate was prepared by roasting cupric sulfate for 48 hr, with frequent rabbling, in an open tray in a muffle furnace maintained at 725°C. At this temperature, cupric sulfate develops about 0.16 atm pressure of combined sulfur trioxide, sulfur dioxide, and oxygen. Cupric oxysulfate develops only about 0.05 atm pressure, and is stable until

Jan 1, 1965

By D. B. Jugle, J. B. Darby

The equilibrium solubility limits of the transition elements Ti, V, Cr, Fe, and Co in liquid tin were determined in the temperature range from 827" to 1211°K. Since the equilibrium concentration of Ti, V, or Cr in liquid tin is moderately dilute in the temperature range investigated, the solubility data were employed to estimate the partial molar enthalpy and the partial molar excess entropy of solution for the three solutes in liquid tin. The reference state s for titanium or vanadium were selected relative to the solute in an intermetallic compound. The thermodynamic quantities for chromium were calculated relative to pure chromium. RECENT experiments1 have shown that the rate of solution of several transition elements in liquid aluminum can be qualitatively predicted from a knowledge of the temperature dependence of the solvent-rich liquidus. In order to extend the analysis to binary tin systems,&apos; it was necessary to know the equilibrium solubility of several of the first-long-period transition elements in liquid tin. Since solubility data for the tin-rich portion of binary systems are meager, the present investigation was undertaken to determine the equilibrium solubility limit of Ti, V, Cr, Fe, and Co in liquid tin in the temperature range from 850" to 1200°K. EXPERIMENTAL PROCEDURE A useful technique3 to determine the equilibrium solubility of a solute in a liquid-metal solvent consists essentially of placing a pure solute in contact with a pure solvent and allowing sufficient time for equilibrium to be attained at the temperature of interest. Subsequently, the solvent is removed and the equilibrium solute concentration in the solvent is determined by an appropriate analytical procedure. The technique can be applied very successfully to relatively simple systems such as the copper-germanium system.3 However, in many binary systems of transition elements with tin, several intermediate phases are known to exist and precipitation of the phases from solution, in solubility experiments, can lead to an erroneously large solubility. The difficulty was avoided in the present work by equilibration of the most solvent-rich intermediate phase with the pure solvent over a range of temperatures. The compounds employed in this investigation, and the temperature range over which each compound is in equilibrium with liquid tin are listed in Table I. No stable intermediate phases are reported in the chromium-tin system4 and, therefore, pure chromium was utilized as the solute. The stoichiometric compounds were prepared by arc-melting on a water-cooled copper hearth in a helium-argon atmosphere. The elemental tin employed in.this investigation was 99.998 pct pure, and typical lot analyses of the transition elements were reported elsewhere.&apos; A sample of an appropriate solute, in the form of a button and in sufficient quantity to exceed the equilibrium solubility, and the pure tin solvent were placed in a high-purity recrystallized-alumina crucible. The crucible and contents were placed in a horizontal furnace under a high vacuum (10-6 torr) and held at temperature for periods varying between 24 and 72 hr. A water-cooled quench tank, partially filled with diffusion-pump oil, was attached close to one end of the

Jan 1, 1970