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By W. H. Bassett, C. Davis

Although brasses and bronzes have been made for ages, a systematic study of their physical properties has been carried out only during the years of the present century. Among these properties may be included those which are to be detected by means of microscopic examination; in other words by the science of metallography. The earlier workers in this field, both in this country and abroad, gave their attention to steel. When the senior author explored the situation in 1902, there was little encouragement to be found in undertaking the study of the non-ferrous alloys. A start was made, and the metallography of the brasses and bronzes, as well as of the copper-nickel-zinc alloys developed materially under his direction. Annealing experiments were begun in 1902, and in the succeeding years the effect of temperature, and the influence of previous working, on the grain size of brass were studied. The conclusions so well known and widely published today were largely reached during those earlier years. In 1905 the first complete annealing series were made. By this it is meant that brass and copper sheet, 5 B & S Nos. hard, was machined into tensile test specimens, then annealed under accurate control for 30 min. at temperatures up to the melting point of the material. Various determinations were made, including tensile strength and elongation in 2 in. There rapidly followed similar series on all of the copper-zinc alloys from 100 to 60 per cent, copper, on the bronzes, cupronickels, and on copper-zinc-nickel alloys. At this point there was published by Grard, in October, 1909,' the very comprehensive and complete work on the tensile properties of cartridge brass, 90-10 copper-zinc, and electrolytic copper. The excellent photomicrographs in that paper illustrated the changes in structure produced by cold rolling as well as by annealing at different temperatures, but where Grard's work was confined to copper and to two alloys, the investigations in this laboratory have been over the entire fields of the commercial copper-zinc alloys, copper-tin alloys, representative copper-nickel and copper-nickel-zinc alloys as well as aluminum bronzes and others of a more special nature.

By S. Andrew Kulin, L. Kaufman

A general treatment of the broadening of X-ray double-crystal spectrometer rocking curves due to distributions of tilts and strains has been carried out. The results of this treatment have been applied to the case where dislocations in a crystal give rise to both tilts and strains. On this basis it is found that the rocking-curve halfwidth due to imperfections in the crystal, ßC , increases with increasing Bragg angle, 8. These considerations predict linear relationships between & and tan2 , and ßCand tan 8, for Gaussian and Cauchy distributions of dislocations, respectively. The zero intercept of the ßC us 8 curve, which is a measure of the degree of imperfection of the crystal, is found to depend directly on the distribution rather than the number of dislocations. In addition, the slope-intercept ratio for the ßc - ? curve has been calculated for both the Gaussian and Cauchy distributions. Experimental determination of the - 8 curves for a series of copper single crystals prepared by the Bridgeman and Czochralski methods yields results in agreement with the calculated slope-intercept ratio for a Cauchy distribution of dislocations. CERTAIN X-ray techniques have been used to study the perfection of single crystals. Gay, Hirsch, and Kelly have considered the spreading of spots into arcs on Debye-Sherrer rings due to imperfections. The Double-Crystal Spectrometer has also been applied to this problem.2 The characteristics of Double-Crystal Spectrometer Rocking Curves have been described in the literature by various workers.2-4 By assuming a random spacing of dislocations which give rise to a Gaussian distribution of misorientations relative to some mean orientation in a crystal Gay, et al.,1 arrive at the conclu- sion that the most probable misorientation is given by where h is the spacing between dislocations, and 8 and are the relative misorientations of neighboring regions. If ßC is the halfwidth of the rocking curve (the width at one-half the peak intensity) due to dislocations in the crystal then5

Jan 1, 1960

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

By A. Lubinski, J. E. Hansford

Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through Such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs. INTRODUCTION Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to unde-sired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated.' However, in wells where the maximum permissible dogleg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll.' The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in doglegs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures. FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffce to read only through the section Abrupt Dog-Legs. 1. Concept of the two extreme kinds of idealized doglegs: gradual and long dog-legs and abrupt dog-legs,' 2. Concept of why the bending moment in drill pipe un- der tension is the largest in the vicinity of the tool joint,' 3. Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension,' and 4. Definition of the rate of change of over-all hole angle (dog-leg severity)." Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.

Jan 1, 1967

By C. R. Johnson, R. A. Greenkorn, E. G. Woods

A new method of reservoir evaluation called pulse-testins has been developed for describing formation properties between wells. Pulse-testing utilizes a sensitive differential-pressure gauge at a responding well to measure and record the response generated by a series of flow rate changes (pulses) at an adjacent or pulsing well. Since the pulse-test instruments have a sensitivity of about 0.001 psi, pulses of several hours or less in duration will generate a measurable response in most reservoirs. For this reason, many well pairs can be tested in a short period of time with little interference in field operations. Comparison of pulse-test results to conventional testing methods shows that the pulses obey unsteady-state, compressible-flow theory and thus provide a measure of both transmissibility (kh/µ) and storage (Fch). In additian, the method can be used qualitatively to describe communication across faults and between zones, and direction and tnagnitude of fracture trends. INTRODUCTION To obtain maximum usefulness of new reservoir analysis methods as well as to aid the field engineer in understanding local reservoir anomalies, improved methods are needed to describe heterogeneities in specific reservoirs. Optimum well spacing, equipment specifications, well completion design and especially the economics of pressure maintenance and secondary recovery programs depend on the extent and location of the heterogeneities that affect flow behavior in the field. One method for obtaining a measure of areal reservoir heterogeneity is an interference test. In the simplest interference test. constant-rate production or injection is initiated at one well and the effect of this flow is measured as pressure vs time at another well. Thus, during interference tests the flow characteristics of the formation are determined in situ. Despite their obvious usefulness in reservoir delineation. interference tests have not enjoyed frequent usage. Reasons for this have been the weeks or months required in many fields to obtain a pressure response measurable with conventional gauges, and the interruption of routine field operation during the field-wide shut-in normally required during these long times. Also, only average properties of the relatively large volume of the reservoir disturbed during these long times can normally be obtained — variations in properties between individual wells cannot be delineated. To eliminate these drawbacks of conventional tests, a special reservoir description technique called pulse testing' has been developed. Pulse-testing has several advantages that make it more convenient and practical for field use than interference tests. Valid tests are more certain because use of a series of flow disturbances gives rise to a diagnostic pressure response that can more readily be distinguished from unknown trends in reservoir pressure and other "noise." The time required is only a fraction of that for an interference test because a special, high-sensitivity differential pressure gauge can detect a much smaller pressure change. Variations in properties between individual wells can be delineated because of the relatively small volume of the reservoir disturbed during these short times. Finally, wells other than the pulsing and responding wells do not have to be shut in or carefully regulated.

Jan 1, 1967

By S. F. Frederick, G. F. Pittinato

The deformation mechanisms operating in Ti-5Al-2.5Sn at 20°K under uniaxial and biaxial stress fields were determined by using both optical and electron microscopy. In the uniaxially stressed specimens, de-fu~rnation twins were found only in the immediate vicinity of the fracture. Twinning was, however, established as a deformation mechanism under biaxial stress conditions. The same slip systems were opera-tiz,e under both uniaxial and biaxial stress. Prismatic slip was identified as the major slip syslem; however, basal and first-order pyramidal slip also occurred, but to a lesser degree. The interaction of moving dis-locations on intersecting slip planes resulted in the formation of jogs and dipoles. Hexagonal dislocation networks were formed only under biaxial stress conditions. A discussion is given on the formation of hexagonal dislocation networks. IT has been shown that titanium alloys can exhibit unusually high strengths when tested in a biaxial stress field.'-" The high biaxial strengths are a consequence of a strong basal plane sheet texture which results in distinctly anisotropic flow properties. This texture strengthening appears to decrease with decreasing temperature2 and would seem to indicate a change in deformation modes. For example, in a uniaxial tensile test, Ti-5A1-2.5Sn yields isotropically at 20°K but is strongly anisotropic at room temperature. The increase in biaxial ultimate over uniaxial strength at 20°K is also much less than at room temperature. It is known that titanium car] form deformation twins more readily at cryogenic temperatures than at room temperature.4 Since the formation of deformation twins will reduce the degree of basal texture in sheet material,' an accompanying decrease in texture strengthening would be expected. To investigate more fully the nature of texture strengthening at cryogenic temperatures, the deformation modes of Ti-5A1-2.5Sn tested in uniaxial and 1:1 biaxial tension at 20°K were studied by optical and electron transmission microscopy. EXPERIMENTAL PROCEDURE The uniaxial and biaxial stress test specimens were prepared from 0.020-in. thick sheets of Ti-5A1-2.5Sn ELI having the composition shown in Table I. Uniaxial stress conditions were obtained by using flat tensile specimens machined from the sheet material. The longitudinal axis of the tensile specimens was aligned perpendicular to the rolling direction of the sheet. Tile biaxial test specimens were prepared by rolling precut, 19-in.-lengths of sheet into 4-in.-diam cyl- inders. Following longitudinal butt welding, the cylinders were stress relieved at 1000°F for 4 hr. A 9-in. sq "window" was then chemically milled into each cylinder's surface reducing the wall thickness in the milled area to approximately 0.006 in. The testing procedure consisted of pressurizing the cylinders while simultaneously applying a tensile load. Using this technique, a 1:l axial to hoop stress was obtained. Complete details of the specimen and testing procedures are given in Refs. 1 and 2. The biaxial and uniaxial stress specimens were all tested in liquid hydrogen. Specimens for electron transmission microscopy were prepared by first chemically milling to a thickness of about 0.001 in. followed by electrolytic polishing to electron transmission thickness. The chemical milling solution, consisting of 800 ml of water,

Jan 1, 1970

By Robert Maes, Robert de Strycker

The solidifzcation reactions in the Cu-Sn-As system were determined by microscopic examination, thermal analysis, and X-ray diffraction. The system presents no ternary compound. There is a quasi-binary section, of a simple eutectic type, between the compounds Cu5As2 and SnAs; the system presents, in addition, one ternary eutectic reaction, one ternary peritectic reaction, and seven transitional reactions. The temp-peratures corresponding to each of these reactions were determined, most of them with an accuracy of *lLC. The isothermal lines of the liquidus surface were also established for almost the entire diagram. NO reference was found in the literature relative to the Cu-Sn-As phase diagram and this is believed to be the first study on this subject. The Cu-Sn diagram was taken from Hansen and Anderko;' it is represented by Fig. 1, with the phase designation which will be used in the remainder of this work. For the Cu-As diagram, the solution proposed by Hansen and ~nderko' must be modified to take account of recent data, principally from Heyding and Despault~ and from Hume-Rothery and Burns; this yields the diagram represented by Fig. 2. As for the Sn-As diagram, it is not established with certainty, particularly so far as concerns the solid solubility of tin in arsenic and the solidification reactions near the compound SnsAsz. For this last point, Hansen and Anderko propose two solutions: congruent melting of Sn3Asz with a eutectic SnsAsZ + SnAs or incongruent melting implying a peri-tectic reaction L + SnAs = Sn3As2. Microscopic examination of the few binary alloys prepared in this composition range made us prefer the second of these solutions, which gives the diagram shown by Fig. 3. EXPERIMENTAL METHODS The experimental techniques used in this work were microscopic observation and thermal analysis; a few X-ray diffraction patterns were taken to verify the

Jan 1, 1967

By Nicholas J. Grant, William H. Ferguson, Bill C. Giessen

Ta-lr alloys have been examined over the complete range of compositions using metallographic and X-ray techniques. The terminal solid-solubility limits, solidus temperatures, and intermediate phases were determined. There are four inter-mediate phases: o, tetragonal, analogous to a (Fe-Cr); 0,. orthorhombic; az, tetragonal; and a TaZr,, cubic, AuCu, structure. Of these, o and a, melt peritecticaLly, a, decomposes peritectoidally, and a TaIrs has a congruent melting point. Three peri-tectic and one eutectic reactions occur. 1 HE Ta-Ir phase diagram has not been treated in the literature. Intermetallic phases and terminal solid solubilities have been described and estimated.'-4 The previous findings have been confirmed in this work. A complete diagram with additional phases and solidus curves is presented. EXPERIMENTAL METHODS Starting materials were tantalum powder of 99.8 pct purity, supplied by the National Research Corp., Cambridge, Mass., and iridium powder of 99.9 pct purity, supplied by the Bishop Co., Malvern, Pa. Both powders were -200 mesh. Table I lists the analyses as given by the suppliers. A standard procedure was employed in making the alloy buttons, which was described in detail in Refs. 5 and 6, and which included repeated arc-melting of powder compacts and determination of the composition by the weight-balance method. This is especially justifiable due to the similar vapor pressures of tantalum and iridium. In the critical parts of the diagram, a spacing of 1/2 at. pct was used, based on premelted master alloy material. The observed structures and X-ray spectra were consistent with the composition sequence of the alloys. Table II lists the final alloy atomic percentages with the calculated percent error of composition. Cross sections representative in grain size and composition were selected for the study, as described in Ref. 5. Based on prior experience, no contamination from the tungsten electrode was considered. Temperature measurements were obtained using a Leeds and Northrup optical pyrometer and have been described extensively in Refs. 5 and 6. All heat treatments were made in the high-vacuum tantalum tube furnace mentioned in Ref. 5. Samples annealed in tantalum containers cooled from 1800" to 1000"~ in 5 sec; those annealed in ceramic crucibles cooled over the same range in 15 to 30 sec. The thermal treatments are listed in Table 111. All specimens were homogenized at 1735°C for 24 hr. Tantalum-rich compositions were treated in tantalum buckets. Iridium-rich compositions were annealed in tantalum buckets below the eutectic temperature of 1950°C; up to 2200°C, tungsten-lined tantalum baskets were used; and above 2200°C thoria crucibles were used. It was found that refractory oxides (in early stages of the investigation alumina crucibles were used up to 1800°C and thoria crucibles were used to 2400"~) give off minute amounts of oxygen and thereby influence the microstructure considerably, or react directly with the alloys.

Jan 1, 1963

From the beginning to the end, the attendance and enthusiasm of the 119th meeting, which was held in New York, Feb. 17 to 20 surpassed all expectations. Besides the ten technical sessions, one of which was in conjunction with the American Institute of Electrical Engineering and one a session of the National Research Council, there were two memorial meetings, one for Dr. Raymond and one for the members who died in service; two joint sessions with the Canadian Mining Institute; and a meeting devoted to pictures of copper mining, milling, and smelting. Of the 732 persons registered, 119 registered in the Institute of Metals Division. Monday's sessions were devoted to the problems of industrial organization, the Institute of Metals Division, and to petroleum and gas. Among the special features of these sessions were the topical discussions on housing and. Americanization. Americanization, too, was the topic for discussion by the Woman's Auxiliary Wednesday morning. On Tuesday, nearly 100-members of the Canadian Mining Institute were present to discuss the possibility of bringing about uniform mining laws for the United States, Canada, and Mexico, to obviate the maintaining separate legal departments and managerial forces for the several countries; and to avoid the confusion which, it is said, has led to a duplication of effort and has sometimes created a barrier to international cooperation in mining. Among the Canadian delegation were D. B.

Jan 3, 1919

By E. M. Tory, P. T. Shannon

An analysis of batch and continuous thickening in terms of the movement of planes of constant concentration (i.e. continuity waves) is presented. Use of solids flux as a primary variable greatly facilitates the analysis and clarifies the relationship between batch and continuous thickening. An "ideal" slurry is defined as one whose settling rate is a function only of the local solids concentration. An analysis of continuous thickening of this ideal slurry in an ideal thickener explains many aspects of the steady — and unsteady — state behavior of real slurries, such as the main features of a thickener's "solids profile" (including the break attributed to rake action), the sudden appearance at abnormally high feed rates of a zone of constant concentration and the velocity with which it rises, and the effect of detention time at constant weight of sludge per unit area. Where deviations exist, they are explained in terms of the batch settling behavior of real slurries. The purpose of this paper is to interpret continuous thickening phenomena in terms of batch settling behavior. Both types of thickening may be considered as the process of propagating concentration changes, due to the downward movement of the solids, from the bottom of the settling vessel upward through the slurry.' These concentration changes may be either finite or infinitesimal as in the case of the propagation of a continuous concentration gradient. The slurry itself may be moving downward as in the case of continuous thickening. The downward velocity of the slurry may be such that the concentration changes being propagated up from below remain stationary relative to the thickener walls. This is the case for steady-state thickening. It seems appropriate to analyze continuous thickening in terms of the movement of planes of constant concentration. This has already been done for batch settling."3 Although our main interest is in real slurries, there are certain aspects of both types of settling which can be deduced from a theoretical analysis of highly idealized systems. To this end, an "ideal slurry" is defined as one for which the dimensionless settling rate at any point is a function only of the local solids concentration.1,2 An "ideal thickener" is one in which there is no radial variation in either the solids concentration or in the downward component of slurry velocity. The underflow outlet is a point sink. It is to be expected that the behavior of non-ideal systems will deviate in some measure from theoretical results. However, the same characteristics which cause deviations in continuous thickening should be evident in batch settling, permitting a rational explanation of the former in terms of the latter. PREDICTED RESULTS FOR AN IDEAL SLURRY IN AN IDEAL CONTINUOUS THICKENER General Theory: In continuous thickening, the downward solids flux (mass/area-time) relative to the thickener, G, results from two different

Jan 1, 1967

By Robert J. Linney

IN the latter part of the year 1943, it was decided to experiment with diamond-drill blast holes in the Old Bed magnetite mine at the Mineville mines of the Republic Steel Corporation, in sections of the ore body where vertical dimensions were large and where development for sublevel bench stopes had already been done. Other possibilities of application for this drilling method were in the reclamation of old floors and pillars in the pitching folds of the Lower Old Bed ore body and in the reclamation of large vertical pillars in the " 21 " Bonanza-Joker ore body. The cross sections and views of the two ore bodies will show the conditions to which the diamond-drill method has been applied. The Lower Old Bed magnetite ore body is lenticular and dips approximately 30° toward the southwest and strikes generally southeast and northwest. An intensely folded structure, which pitches generally on an axis approximately at right angles to the strike, is continuous from the uppermost old workings down to the present bottom of the mine, and probably continues with depth. On successively lower levels this folded structure becomes greater in vertical dimensions and the two folds are closer together in a horizontal dimension. As shown in Fig. 1, this folded structure gives to parts of the ore body considerable vertical dimensions, which provide areas that were developed for sublevel bench stoping above a slushing drift, as shown in Fig. 2. It was in one of these previously developed sublevel bench stopes, No. 26 on the 1185-ft. level, that the diamond-drill blast-hole method was applied for mining the upper sublevel. The lower sublevel was underhand-bench-drilled to the finger raises of the scram drift below. The roof of this stoping area began to break and spall on the lower sublevel, causing the roof to become inclined. Along the hanging wall of the stope this reached an elevation about half way between the two sublevels. A smooth schistose seam in the hanging wall causes the ore to break away freely. Therefore, if bench mining had been carried on in the upper sublevel, a dangerous condition of poorly supported benches would have resulted. When the drillers were slashing across the sublevel to footwall and hanging wall to make a bench, spalling roof of the opening below would probably have carried away part of the bench, and would have left a dangerous place in which to continue underhand benching. A 6 by 8-ft. raise had been driven between the lower stope and the upper sublevel about 200 ft. from a manway. It was decided to use this raise for a starting cut and to arrange holes as shown in Fig. 3, so that a slot would be opened across the ore body between the footwall and hanging wall. This slot would then be used for the purpose of breaking into the ore; by blasting vertical rings of holes drilled at right angles to the axis of the pitching folds as nearly as possible. Layouts of this slot drilling and the rings adjacent are

Jan 1, 1945

By Henry M. Rowe

Professor Ruff's most illuminating paper' describing his extremely valuable investigation of the carbon-iron equilibrium diagram assigns definite temperatures to certain very important lines in the diagram, viz.: the eutectic temperature EB (Fig. 1) and the " near-eutectic " temperature E'B', but without indicating clearly enough the reasoning which warrants these assignments. These temperatures are of such primary importance that it is well to indicate the apparent gaps in the reasoning, in the hope that they may be filled in. In his diagram, Fig. 1, the point X and the liues B'D'lII represent the experimental results reached by Ruff and Goecke;a AB, AEB, and SE represent the liquidus, the solidus, and the solubility of the carbon in solid austenite in the absence of graphite according to Gutowsky,3 AB being also in accordance with Spiecker's data; S'E' the solubility of carbon in solid austenite in the presence of graphite according to Ruer and Iljin;5 GS the line A3 after Ooerens and Meyer; 6 and EBC the true eutectic line as inferred by Prof. Ruff from Gutowsky's data. B'D' is the carbon content found in cast-iron which had apparently saturated itself with carbon in the presence of the graphite of the enclosing graphite crucibles in which the determinations were made. From its straightiiess and its sharp inflection near 6.67 per cent. of carbon, the carbon content of

Jan 1, 1913

By W. G. Bearden, P. P. Scott, G. C. Howard

This paper concerns the rupture or breakdown of rock formations as related to drilling, completing, and stimulating production of wells, and comprises data compiled from a study of literature and records of treatment of oil and gas wells. and from tests conducted in bores drilled into rock cores and outcrops of rock. Results of the investigation indicate that the internal pressure to rupture cylinders of rock and to breakdown rock formations surrounding a bore in the earth is dependent upon the extent of intrusion of fluids. the position of bedding planes. the ratio of internal to external diameter, the tensile strength of rock, and magnitude of confining pressure, and is independent of the size of bore, degree of fluid saturation. and temperature of rock within practical limits. It is concluded that the mathematical relationship of pressure in bores and stresses in the surrounding rock must not be limited by the simplifying assumptions of homogeneity. isotropy, and impermeability; that the incidence of lost circulation of drilling fluids to induced fractures may be reduced by preventing intrusion of fluids into the small intrinsic fractures along weak bedding planes; and that the magnitude of the breakdown pressure of wells to be treated may be lowered by removal of mud cake. INTRODUCTION The purpose of this paper is to present and discuss the results of tests which may serve to broaden the understanding of the phenomena of rupture or breakdown of rock and thus contribute to the improvement of the techniques for drilling and completing wells. including such operations as preventing lost circulation, stimulating production, and placing cement. Since the early recognition of the possibility of rupturing rock adjacent to a well by fluid pressure, the distribution and magnitude of stresses around a well and the internal pressure to cause failure have been expressed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of a homogeneous. isotropic, impermeable material. In either the elastic or plastic state, if the conditions of homogeneity. isotropy, and impermeability were the normal characteristics of rock. there would be no reason to question the validity of the above principles when applied to rock. However. since most rock formations are characteristically permeable to some degree, contain bedding planes and small intrinsic fractures. and are heterogeneous, rendering invalid the assumptions of homogeneity, isotropy, and impermeability, the application of the thick-walled cylinder theories to the behavior of rock formations penetrated by a bore appears illogical. Also the failure to consider the effect of the properties of the drilling fluids, which certainly intrude in various degrees into most rock formations. is further cause for questioning the application of these principles. Even in the case of cylinders of hardened chrome-nickel steel, which would he considered relatively homogeneous isotropic. and impermeable, as compared to rock, it has been observed that the internal pressure capable of being withstood by the cylinders varied with the sizes of molecules comprising the rupturing fluid used. Because of these apparent weaknesses in the theories of the behavior of thick-walled cylinders when applied to bores in rock, and the importance of knowing the true behavior of rock under the influence of fluid pressure when planning drilling and completing procedures for wells, tests were undertaken to determine by observation the actual rupturing pressure of cylinders of rock and the effects of such variables as environmental conditions and characteristics of rock formations, fluid properties, and bore dimensions. It was intended that by these tests the validity of the thick-walled cylinder theories when applied to rock would be determined and, if found invalid, mathematical expressions would be derived for predicting stress and rupturing pressure of rock formations under various conditions. Since the derivation of mathematical expressions has been only partially completed, all of the results of the latter phase are not included in this paper. PROCEDURE The investigation was initialed with a study of the theories pertaining to the rupturing of thick-walled cylinders of homogeneous. isotropic, impermeable material and a study of the

Jan 1, 1953

By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.' A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.' After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By Y. C. Kim, C. B. Manula

This paper is concerned with the details of the derivation of an operations research model, specifically linear programming, to solve production scheduling problems. While some results are presented for an actual study, the calculation of cases of a more general nature have not yet been completed. Production managers from those segments of the mining industry that experience a seasonal or highly variable sales demand find it rather difficult to develop overall producing plans for their organizations. In an attempt to solve this technical problem, demands are usually met by keeping production corresponding exactly to sales. This results in a fluctuating production schedule which is costly to maintain because of overtime premiums in periods of high requirements and because of costs associated with an idle mine plant during slack periods. An alternate solution may be to produce part of the desired amount and make up any deficiencies by using overproduction in previous time periods. This tends to smooth the production pattern through the use of a stockpile. However, because of associated storage costs, the solution may again be undesirable if it yields comparatively large surpluses. In general, this type of scheduling problem has an infinite number of solutions which satisfy the requirements. These are largely dependent on the extent to which an operation is geared to changes in production and on the size of its stockpiling facility. The determination of an efficient schedule is implied, therefore, as one lying between two extreme solutions, i.e., one that minimizes surpluses and one that minimizes output fluctuations. These conflicting objectives result in an economic balance problem between the costs of carrying surpluses forward from slack periods versus the cost of high production levels during peak demands. Various methods of operations research have been developed to handle problems whose genesis is explained above. It is very seldom, however, that these quantitative means are used in practice by the mining industry. Those who are familiar with mining operations know that most managers have not progressed satisfactorily in this area. Production planning systems which most mines employ today are often no more than rough records of management's mental planning. For small mines these means are normally sufficient; but as operations grow larger and become more complex, this type of planning ability is no longer adequate. Managers may find themselves losing control of cost relationships, taking longer to outline production sequences, and becoming forgetful of certain resource availabilities. ORIGIN AND SCOPE OF A SCHEDULING PROBLEM The more fundamental aspects of the production scheduling problem can be brought into focus by demonstrating how it exists in a bituminous coal mine* located in southwestern Pennsylvania. This mine, operating in the Pittsburgh seam, uses a definite room-and-pillar block system of mining, which is planned and carried out with only slight variations to meet local conditions. The coal seam, which is firm and varying in thickness from 8 to 9 ft with the bottom 6% ft being extracted, is under 500 ft of cover and opened by a shaft. The bulk of the coal (60%) is obtained from the pillaring activity with the mains and sections, which are considered primarily as development activities, contributing the balance of 12% and 28%, respectively. All coal is won by a ripper-type continuous miner in conjunction with shuttle-cars directly behind a loading machine. Track haulage is employed to move coal from these machine centers to the shaft bottom. The coal, thus mined, is shipped to one destination as part of a mixture of coals to be used in the making of steel. A material flow diagram of this distribution scheme is illustrated in Fig. 1. PROBLEM STATEMENT From the above types of shipments and mining limitations, the basic problem is to determine an economic means of producing and stockpiling a single coal product produced in three different machine centers (main, section, and pillar). Fig. 2 shows total demand for coal as a function of time. Because of the extremely high peak demands, slack period production must be stored and then distributed

Jan 1, 1969

By W. A. Anderson

Recrystallization of cold-worked metals has long been known to proceed by a process of nucleation and growth.' When a cold-worked metal is heated to a temperature at which recrystallization will ensue, nuclei of new grains, essentially strain-free, appear and grow. As the process proceeds, nuclei continue to appear and to grow, until the cold-worked matrix has been entirely consumed and recrystallization has been completed (Fig. I). Conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time, yields an isothermal recrystallization curve, showing the time course of the recrystallization process (Fig. 2).2 Evidently, then, the rate of recrystallization is determined by the rate at which nuclei form and the rate at which they grow. The rate of nucleation N is the number of nuclei that form in unit time in unit volume of the unrecrystallized matrix, and the rate of growth G is the increase in radius of the recrystallized grain per unit time. In recent years attempts have been made to determine N and G as these vary with the well-recognized variables affecting recrystallization: time, temperature, degree of deformation, etc.1 Such studies yield information that is more fundamental than that conveyed by the conventional recrystallization diagram,' since the rate of recrvstallization is thus analyzed into its two component rates3 Methods are now available by which N and G can be measured, and analytical expressions have been developed for the interrelationships among N, G, the isothermal recrystallization curve, and the final grain size, which greatly facilitate analysis.2-4 The application of these methods has been demonstrated recently for the recrystallization of silicon ferrite.2 Data on N and G in dependence upon the recognized recrystallization variables are, however, very fragmentary;" values of N and G have been determined for some metals, but the effect of temperature, which would yield the fundamentally important activation energies, has been too little studied. Thus far there has been no detailed study of the recrystallization of any one metal in terms of X and G ovcr appreciable ranges of the variables time, temperature, degree of deformation, and original grain size. It is the purpose of the present paper to provide such a study, employing aluminum.

Jan 1, 1945

By O. H. Eschholz

The electrostatic process of fume precipitation is an excellent example of the successful application of scientific knowledge to an industrial operation. Originally proposed for the precipitation of sulfuric acid mists, it has been extended until at present there is practically no fume-carrying gas to which the method cannot be applied. Among the more common applications are: the recovery of non-ferrous smelter flue-dust, iron blast-furnace dust, cement dust, and potash fume. It should be borne in mind that the process is restricted to the precipitation of suspended particles, either liquid or solid, and does not separate gaseous constituents. However, by proper temperature control, mixtures of vapors having different temperatures of condensation to either solids or liquids may be selectively precipitated. The process consists essentially of subjecting suspended particles, including those too minute to be effectively acted upon by centrifugal or gravitational forces, to such an electrical force that they are driven from the gas stream, acting as a conveyer, and deposited upon a suitable receiving surface. This directional impulse is obtained from the interaction of charged particles and an electrostatic field of definite intensity gradient existing between two dissimilar electrodes, known as discharge and receiving electrodes. In principle, the equipment is equally simple. As shown diagrammatically in Fig. 1, it consists of: (1) A source of high-potential direct, current,, requiring: (a) Source of alternating-current energy. (b) Means of transforming from low voltage to high voltage. (c) Means of converting alternating to direct current. (2) Precipitation chamber having: (a) Transmission tubes for fume-laden gases. (b) Suitably designed and disposed electrodes. (c) Means for affecting removal of deposited solids. Although Hohlfeld demonstrated, in 1824, that a smoke-laden atmosphere could be cleared by applying an electrostatic field, and while Sir

Jan 1, 1919

By P. H. Metzger, D. W. Fuerstenau

The activation of sphalerite was found to occur at a much lower rate with Pb++ then with Cut++ or Ag+. To prevent activation with Pb++, the ratio [m in solution must approximate 103. An example is given illustrating how this condition is met in practice through the addition of zinc sulfate and soda ash. In selective lead-zinc flotation, the mill operator, especially the one who is concentrating a partially oxidized ore, often must add zinc sulfate and/or soda ash for effective depression of the sphalerite. In the present paper the authors show how this practice prevents the activation of sphalerite in the presence of Pb++. A number of years ago Gaudin (1) postulated that Zn++ might control the activation of sphalerite with Pb++ through competitive adsorption. However, recent experimentation has shown the activation of sphalerite with Ag+ and Cut++ to be a chemical reaction in which silver or copper ions replace zinc in the sphalerite lattice through the formation of a more insoluble sul-fide (2,3,4) Thus, if activation with Pb++ is similar to that with Ag+ or Cu t+, zinc salts should control the activation of sphalerite not through competitive adsorption but because the ratio of [zn++/Pb++] in solution regulates the extent of the chemical exchange between Zn++ and Pb++ in the solid phase. The objective of this investigation has been to study the kinetics and equilibrium conditions for the uptake of Pb++ by sphalerite and to investigate the prevention of lead activation with zinc salts. BASIC PRINCIPLES Sphalerite activation has been shown to be a replacement reaction wherein a less soluble compound is formed at the expense of the more soluble zinc sul-fide (2,3,4) For example, if sphalerite is placed in an aqueous silver nitrate solution, ZnS gives to the solution more S= than can exist together with Ag+, and hence the following reaction takes place: ZnS + 2 Ag+? Ag2 S + Zn ++; k = [zn ++]/[Ag ++]2 = 10 26 (1) Therefore, ZnS will dissolve in the presence of Ag+ and activation of sphalerite with Ag+ will proceed after monolayer coverage by solid state diffusion until equilibrium conditions are reached in the system (2, 4) Because of the large difference in the solubility of ZnS and Ag2S, zinc salts cannot affect the reaction unless a complexing agent, such as cyanide ions, is present to complex Ag+ more tightly than Zn++ . By complexing Ag+ and Zn++ in solution, the uptake of Ag+ by sphalerite can be regulated by controlling the ratio m. . Experimentally (2) it was found that the activation of sphalerite by Ag+ could be prevented through the addition of NaCN if this ratio reached a value of approximately 10 26. The mechanism of sphalerite activation with copper salts is given by the following reactions: ZnS + Cu ++ ? CuS + Zn + + ; (2) k = [Zn++]/[Cu++] = 10 11 ZnS + Cu + ? Cu2S+ Zn++; (3) Experimentally Mao (3) found that the activation of sphalerite with Cu++ or Cu + was prevented if the ratios expressed in Equations 2 and 3 were approximately l09 and l022, respectively, with cyanide ions as the deactivator. Although zinc salts do not affect the activation of sphalerite with silver or copper ions in the absence of a complexing agent, activation with lead ions theoretically can be controlled by the addition of zinc salts because of the relatively small differences between the solubility of ZnS and PbS (5). Equilibrium

Jan 1, 1961

By Dr. O’Neil Thomas J., Donald W. Gentry

"We can easily represent things as we wish them to be..” -Aesop INTRODUCTION The first eight chapters of this book have primarily addressed the concepts and fundamentals associated with project valuation, particularly as they apply to mining-related projects. Specific emphasis was placed on the engineering and economic parameters and estimates necessary for quantifying line items in pro forma income statements and the subsequent calculation of net annual cash flows. Given these estimates of relative benefits, costs, and annual cash flows for a project, it then becomes necessary to convert these estimates into measures of relative desirability or attractiveness. The criteria and techniques typically utilized to determine project acceptability or desirability are, then, the topics of discussion in this chapter. Before proceeding it may be advantageous to put the problem of project evaluation into proper perspective by reiterating some of the fundamental concepts developed in Chapter 1. The basic premise set forth in this book is that the objective of the firm should be to maximize its value to its owners (stockholders' wealth). This value or wealth is represented by the market price of the firm's common stock; consequently, the primary objective of the firm can be restated as one of maximizing the value (price) of the firm's common stock in the marketplace over the long term. This price, in effect, is an indicator or index of the market's perception of the company's progress and a reflection of the investment, financing, and dividend decisions made by corporate management. These three major decisions are inter- related and jointly impact the market price of the firm's stock. Therefore, if the objective of maximizing the value of the firm to its stockholders is to be achieved, an optimal combination of the three decisions will be necessary. It is important to emphasize that maximizing stockholder wealth is not the same as profit maximization or even the maximization of earnings per share. Corporate managers making decisions based on the objectives of maximizing profits and/or earnings per share must recognize that these objectives do not consider: (I) the timing or duration of expected returns, (2) the business and financial risks of the promised earnings, or (3) the dividend policy of the firm. Obviously all of these factors are of concern to the company's stockholders and will have an effect on the market value or price of the firm's common stock. Maximizing market price per share, or wealth maximization, is therefore the appropriate corporate objective and

Jan 1, 1984

By R. F. Mehl, J. K. Stanley

THE recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are employed.1 Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystallization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress .4,5† The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed .27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert measurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now

Jan 1, 1942