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By J. C. Martin

A theoretical analysis of steam stimulation is presented for single sands. The analysis includes the effect of steam production and most of the effects of heat conduction. The results show the effects of a number of important variables on the performance of an idealized well under steam stimulation. Calculated responses are presented which indicate the effects of steam production, amount of steam injected, water production, formation thickness and formation damage. Results indicate that steam production can cause large reductions in the heat contained in the formation. This effect can be eliminated by drawdown control. Water production reduces the amount of oil produced during stimulation. The optimum amount of steam to inject depends on economic factors as well as the well response. In many cases, the increased temperature resulting from stimulation reduces oil viscosity near the well sufficiently to overcome the effects of formation damage even if the damage is not removed during steam injection. Calculated responses for thin sands are more favorable than anticipated. INTRODUCTION Little has been published on the theory of steam stimulation'-' despite the interest it has created and the wide variation in well responses. The results of the present analysis provide an insight into steam stimulation, and the methods employed provide a foundation for future work. Analyses presented in Refs. 1 and 2 are very limited and apply to gravity drainage conditions. Ref. 3 contains an analysis similar to the one presented here. The idealized models used and the assumptions made in Ref. 3 are different from those used in this paper. The analysis assumes that after steam injection has heated a small portion of the volume within the radius of drainage of a single uniform sand, a shut-in soaking period is allowed before returning the well to production. The effects of gravity, capillarity, transient pressure and water-sensitive sands are neglected. The injection and soaking times are assumed short compared to the stimulated production time. The initial temperature is assumed uniform; thus, the results apply primarily to first-cycle stimulation. The effects of gas production other than steam are neglected, and the water-oil ratio during production is assumed constant. Steam stimulation involves the simultaneous variation of the temperature, pressure and saturations. General mathematical equations for these variations are complicated and can be very difficult to solve. Simplified equations based on idealized models are used to reduce the mathematics sufficiently to allow approximate solutions to be obtained. DISCUSSION INJECTION An idealized model for which heat conduction is neglected is used to represent the behavior of a well during steam injection. The mathematics for this model is presented in Appendix A which also contains an approximate solution for the behavior of the no-conduction model. SOAKING During soaking, the well is shut in. Only the temperature, pressure and saturation distributions at the end of soaking are needed in the analysis. During soaking the heat is considered to be conducted in a uniform medium from an initially uniformly-heated circular cylinder confined to the producing interval. At the end of soaking the saturations and pressures are assumed to correspond to the cold zone. Analysis of the heat flow during soaking is included in the next section. The radius of the heated cylinder is calculated from the following heat balance (for constant quality steam injection). At the end of the soaking period it is assumed that little or no free gas is present near the well, and that the soaking period has been sufficiently long that the steam zone has had time to expand and the steam has condensed. The condition where there is no soaking is considered in the next section. PRODUCTION In this section, an approximate method is presented for solving the equations of heat and fluid flow associated with the production of oil and water during steam stimulation. Where initial pressure drawdowns are sufficient to cause steam to flow into the wellbore, steam production is assumed to occur within a short initial adjustment period (Appendix B). The production practices followed soon after the well is returned to production can have a large influence on the amount of oil produced during the stimulation cycle. Under most conditions, there is a period of time in which some or all of the water in the heated zone is converted into steam and produced. This flashing of hot water is caused by the pressure in the heated zone dropping below

By Bruce Chalmers, D. C. Larson

Aluminum crystals with longitudinal-axis orientations of (111) . (110), and (100) were deforined in tension and annealed. The conditions of deformation were controlled so that the re crystallization nuclei originated in either the heavily deformed regions at saw cuts {artificial nucleation) or in the lightly deformed matrix (spontaneous nucleation). The artificial-nucleatioln experiments showed that in lightly deformed (110) and (100) crystals low-angle twist boundaries are most mobile, while in (111> crystals and heavily deformed (110) and (100) crystals high-angle tilt boundaries with near (111) rotations are favored. The spontaneous-nucleation experiments showed the existence of preferred orientations in the (111) crystals. The nonrandomness of the grain orientations is quantitatively determined through a comparison with the results which would he obtained from a randowl set of grain ovientations. PREVIOUS recrystallization studies have been performed on single crystals deformed in tension.1 7 The crystals used in these studies usually had random tensile-axis orientations and the extent of deformation was not a primary consideration. The present study concerns the recrystallization of single crystals with tensile-axis orientations of (Ill), (110), and (100). The emphasis of this work is on the influence of the tensile-axis orientation and the degree of deformation on both the nucleation and growth processes. The multiple-slip orientations were chosen because secondary slip or slip intersection promotes nucleation.1,5,8 These crystals recrystallize at lower strains than the crystals which are oriented for single slip. Also, the greatest variation in deformation behavior is exhibited by the multiple-slip orientations. The stress-strain curves for crystals with tensile-axis orientations of (111) are higher than the stress-strain curves for poly-crystals, and the stress-strain curves for crystals with tensile-axis orientations of (100) are lower (at large strains) than the stress-strain curves for the crystals which deform initially in single slip.g The recrystallization nuclei originated in either 1) the homogeneously* deformed matrix of the crys- tals or 2) the heavily and inhomogeneously deformed regions at saw cuts. The nuclei will be referred to hereafter as spontaneous and artificial nuclei, respectively. The two terms do not imply a difference in the nature of the nuclei; they imply simply a difference in the mode of introduction of the nuclei. During spontaneous nucleation very few (always less than ten) grains nucleate, while during artificial nucleation large numbers of grains nucleate. Only a fraction of the artificially nucleated grains penetrate very far into the deformed matrix during annealing. The grains that penetrate the farthest into the deformed matrix will be referred to as the dominant grains. EXPERIMENTAL PROCEDURE The thirty-five crystals used in this investigation were grown from the melt in milled graphite boats at a rate of 1.6 cm per hr. The crystals had dimensions of approximately 6 by 12 by 80 or 6 by 6 by 80 mm and the aluminum was of 99.992 pet purity. The as-grown crystals were annealed at 610°C for 24 hr and furnace-cooled. They were then heavily etched and electropolished in a solution of five parts methanol to one part perchloric acid. The crystal orientations were obtained by back-reflection Laue photographs and were accurate to ±2 deg. The tensile-axis orientations were (loo), (110), and (111). Two of the side faces of the (111) crystals were (110) lanes. The (110) crystals had both {100) and {110) side faces and the (100) crystals had (100) side faces. The crystals were deformed at a strain rate of 0.003 per min. Shear stress and shear strain were obtained by multiplying and dividing the tensile stress and strain, respectively, by the Schmid factor, m. For the (111) crystals m = 0.272 and for the (110) and the (100) crystals m = 0.408. The Schmid factor is effectively constant during deformation for all orientations. The deformed crystals were sawed into 1-in.-long specimens while the crystals were totally enclosed in a graphite boat. The sawing was performed very carefully in order to limit the plastic deformation to the sawed regions. The specimens were electropolished in the solution mentioned above to remove the sawed-end deformation as well as controlled amounts of surface material. A special stainless-steel grip was used to hold the specimens during the electropolishing treatment. The gripping faces were flat, with no teeth, to prevent the introduction of extraneous de-

Jan 1, 1964

By Robert W. Hendricks, John B. Newkirk

A simple method is described for determining the orientation of a single crystal by means of a cylindr cal X-ray camera. Orientation setting to within ±1 deg is attainable by a stereographic analysis of a single cylindrical Laue pattern produced by the originally randomly mounted crystal. Final precision adjustments which permit orientation of the crystal to within ±5 min of arc from the desired position can be made by the method of Weisz and Cole. A chart, originally Presented by Schiebold and schneider7 and which allows a direct reading of the two stereographic polar coordinates of the corresponding pole of a given Laue spot, has been recomputed to aid in the stereographic interpretation of the cylindrical Laue X-ray photograph. Detailed instructions for the use of the chart, a simple example, and a comparison with the conventional flat-film Laue Methods, are presented. 1 HE problem of determining the orientation of the unit cell of a single crystal relative to a set of fixed external reference coordinates is fundamental to most problems of X-ray crystallography and to many experimental studies of the structure-sensitive physical properties of crystalline materials. Several techniques for measuring these orientation relations have been developed which correlate optically observable, orientation-dependent physical properties to the unit cell. Examples of such procedures include the observation of cleavage faces or birefringence, as discussed by bunn,1 or the examination of preferentially formed etch-pits, as discussed by barrett.2 Each of these methods is limited, for various reasons, to an orientation accuracy of approximately ±1 deg—a serious limitation in some experimental studies. Several other limitations decrease the generality of these methods. Of these, perhaps most notable is the absence in many crystals of the physical property necessary for the orientation technique. The most widely used methods for determining crystal orientation are variations of the Laue X-ray diffraction method. Because of the indeterminacy of the X-ray wavelength diffracted to a given spot, the interpretation of Laue photographs is now limited almost exclusively to the procedure of using a chart to determine the angular coordinates of the corresponding pole for each spot. For the flat-film geometries, either a leonhardt3 or a Dunn-Martin4 chart is used in interpreting transmission patterns, whereas a greninger5 chart is used for interpreting back-reflection patterns. A less common method of interpreting flat-film transmission Laue photographs is by comparing the Laue pattern with the Majima and Togino standards,6 or with the revised standards prepared by Dunn and Martin.4 Although this last method is applicable only to crystals with cubic symmetry, it can be very rapid and just as accurate as the graphical methods. The primary limitation of all the X-ray methods mentioned is the relatively small number of Laue spots and zones which are recorded on the flat film. Often, few, if any, major poles appear, thus making interpretation tedious and sometimes uncertain. The use of a cylindrical film eliminates this problem. Schiebold and schneider7 prepared a chart by which the orientation of the specimen crystal could be determined from a cylindrical Laue photograph. However, it was only drawn in 5-deg intervals of each of the two angular variables used to identify the Laue spots, thus limiting the accuracy of orientation to about ±3 deg. An examination of this chart indicated that if it were drawn in 2-deg intervals, crystal orientations to ±1 deg would be attainable. Subsequent use of the replotted chart has confirmed this accuracy. It is the purpose of this paper to describe the redevelopment and use of this chart, and to point out its advantages and limitations. I) CAMERA GEOMETRY AND CHART CALCULATIONS The geometry of the cylindrical camera with a related reference sphere is shown in Fig. 1. The X-ray beam BB&apos; pierces the film at the back-reflection hole B, strikes the crystal at 0, and the transmitted beam leaves the camera at the transmission hole T. One of the diffracted X-rays intersects the film at a Laue spot L. The normal OP to the diffracting plane bisects the angle BOL between the incident and diffracted X-ray beams. The point P on the reference sphere can be located uniquely by the two orthogonal motions 6 and 8 on the two great circles ENWS and BPQT respectively. Because the Bragg angle 8 (= 90 - < BOP) is always less than 90 deg, P always remains in the hemisphere BENWS. Therefore, if every possible pole P is to be recorded on the same stereographic projection, it is necessary that the projection reference point be at T with the projection plane tangent to the sphere at B.* The great

Jan 1, 1963

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.&apos; The U. S. Bureau of Mines2-&apos; described and later improved the apparatus for a now widely used method generally known as the "Boyle&apos;s law" method. In the present form of the Washburn-Bunting method,&apos; the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle&apos;s law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle&apos;s law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle&apos;s law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

By B. Ramaswami, U. F. Kocks, B. Chalmers

The latent hardening of silver and an Ag-Au alloy was investigated by lateral compression, overshoot in tension and cormpression, and the stability of multiple-slib orientations. The latent hardening of a secondary slip systenz depends on its relation to the primary slip system. For most secondary slip systems the latent hardening is larger for Ag-10 at. pct Au than for pure silver. The maximum increase in. flow stress on a secondary slip system over that of the primary slip system was 40 pct. The work hardening during the lateral-compression test on the latent system after prestress on the primary system is iuterbreted in terms of the preferential distribution of barriers to dislocation movement with respect to the active slip system in work-lzardened fcc crystals. The work-hardening in fcc crystals is mainly due to the dislocation interactions and the barriers to dislocation movement formed as a result of reactions between dislocations of different slip systems. The operation of sources on the latent system depends on the flow stress of those systems; hence, the increase in flow stress of a latent system due to glide on an active system, which is called latent hardening, is an important element in understanding the phenomenon of work hardening. The problem of latent hardening has attracted the attention of many investigators in the past. For example, a theoretical study of the elastic latent hardening of the latent systems due to glide on an operative system has been made by Haasen&apos; and ~troh. These calculations, however, neglect the stress required for the intersection of forest dislocations by the glide dislocations, a factor which would be important for producing macroscopic strains on the secondary slip systems. The importance of this factor will become evident from the results presented here. Attempts have also been made to determine the latent hardening of different slip systems by experimental means by the methods summarized in Table I.3-9 The experimental methods used have been subject to certain limitations. For instance, in the method used by Hauser,9 frictional constraints between the specimen and the compression platen were not eliminated by proper lubrication (see Hos- ford10). Secondly, with the exception of Kocks,6 Hauser,9 and Rohm and Kochendorfer,11 latent-hardening studies have been made on only one of the slip systems, i.e., on either the conjugate or the coplanar slip system; hence, extensive results are not available on the latent hardening of different slip systems in the same materials, with the exception of aluminum.6 It was therefore decided to study the latent hardening of the conjugate, critical and half-related slip systems in silver. Similar experiments were done in Ag-10 at. pct Au to study the effect of solute (gold) on the latent hardening of silver. Lastly, indirect evidence can be obtained by a study of the orientation stability of crystals of multiple-slip orientations in tension and compression. This method has been used by Kocks6 to supplement his studies of latent hardening in aluminum. Similar studies were made at room temperature in single crystals of silver. EXPERIMENTAL PROCEDURE The single crystals of the desired orientations were grown and the tensile test specimens were prepared as described in Ref. 12. The compression tests were made on 1/4-in.-cube specimens. The specimens were cut from single crystals, in the Servomet spark-erosion machine.13 The two cut surfaces were planed using the lowest available planing rate in the machine to minimize the deformation layer. A brass strip was used as the planing tool. This method of preparation ensured plane parallel faces for the compression tests. The deformed material was removed by prolonged etching in a weak etching solution. A weak etching solution was used to prevent pitting of the surfaces and to ensure uniform etching. About 25 to 50 µ of material were removed from all faces by the etching treatment. The specimens were then annealed for 24 hr at 940°C in oxygen-free helium and cooled in the furnace to room temperature over a period of 7 hr. After annealing, the orientation of the specimens was determined by Laue back-reflection technique to make sure that no recrystallization had occurred on annealing. The compression-test technique and setup are described in Ref. 14. The Laue back-reflection technique was used to study the overshoot in tension, the overshoot in compression, and the stability of the axial orientation in tension and compression. The tests were interrupted after every few percent strain to determine the axial orientation. In investigating the overshoot in compression, the operative system was determined by studying the asterism of the Laue spots.

Jan 1, 1965

By D. E. Spiller

Introduction Precious metals recovery from ore can generally be accomplished using gravity concentration, flotation, and/or hydrometallurgical (leaching) techniques. The objective of this paper is to show why gravity concentration can be an important part of recovery systems that employ leaching as the primary unit operation. A brief discussion of modem gravity concentration equipment is also presented. Discussion Gravity concentration of ores has generated increasing interest in recent years. Reasons for this interest include: • Gravity concentration is environmentally attractive. There is little or no use of reagents. Hence, it is relatively nonpolluting. • The cost of cyanide has continued to increase. Therefore, cost savings may be realized whenever leaching feed tonnage can be reduced by preconcentration. • Compared to flotation and leaching, gravity equipment costs are low per processed ton. Field installation costs for gravity circuits usually are less because many&apos; units are supplied as self-contained modules. Also, the cost required to supply services, particularly power, to a gravity plant site are also less. In situations where preconcentration at coarse particle size is applicable, significant grinding equipment savings may be possible. • Gravity circuit operating costs are also relatively low compared to typical flotation and leaching circuits. Reagents, power, maintenance, and manpower savings in a well-engineered gravity plant may be realized. Again, if grinding is reduced, significant power and steel (media and liners) savings are possible. •In recent years, more efficient gravity concentrating devices have been developed. Benefits to Precious Metal Leaching Gravity beneficiation can complement precious metal leaching in two ways. First, the recovery of coarse liberated values before leaching may reduce leach time requirements and may reduce reagent consumption. Second, gravity preconcentration can reduce the size of a leach plant by decreasing the quantity of material to be leached. Coarse gold and silver have been shown to leach rather slowly. Kameda (1949) and Habashi (1967) have investigated the kinetics of cyanide leaching systems. They concur that in a heterogeneous reaction, the rate of gold and silver dissolution is directly proportional to the surface area. Thus, the instantaneous rate of dissolution for spherical 0.37 mm (400 mesh) gold is theoretically -25 times faster than for the same amount of gold at .841 mm (20 mesh), based on data from Fuerstenau, Chander, and Abouzeid (1979). Conversely, coarse liberated, +.841 mm (20 mesh), gold is more readily recovered by gravity concentration than is fine, -.037 mm (400 mesh) gold. Therefore, it is apparent that the two recovery systems complement one another. Figure 1 data demonstrates the potential synergism. A sample of - 3.327 mm (6 mesh) Nevada gold-bearing ore was cyanide leached using conventional bottle-roll test procedures. Gold extraction was determined as a function of leaching time. A second sample split from the same leach feed material was hand jigged to remove a coarse heavy mineral fraction, including virtually all of the +.210 mm (65 mesh) liberated free gold. This second sample, with the coarse gold and heavy minerals removed, was subjected to an identical cyanide leach procedure. Figure 1 presents the resulting comparative extraction data. Note that the percent gold extraction for the sample containing no +.210 mm (65 mesh) free gold includes the coarse gold recovered by gravity. The data show that the sample containing coarse gold required about 72 hours of leaching time to achieve 80% extraction. This compared to about 22 hours of leaching time for 80% gold recovery from the sample that contained only -.210 mm (65 mesh) free gold. Thus, there was a 69% reduction in leaching time. The improved extraction data is not wholly attributable to coarse gold removal, but rather it was the combination of gold removal and rejection of other heavy mineral cyanide consumers or leach retardants. Further investigation was not warranted at this time. Preconcentration is the second manner in which leaching systems can benefit from gravity concentration. The premise is that preconcentration can reduce the quantity of leach feed, which, in turn, may reduce leaching costs. Figure 2 presents preliminary data developed by CSMRI for US Minerals Exploration (USMX). Centennial Exploration Inc., in agreement with USMX, is proceeding with evaluations to determine the suitability of various processing schemes for recovery of gold values from the Montana Tunnels property. The data shows how the ore can be preconcentrated by gravity techniques to result in a reduced feed tonnage to secondary extraction techniques, presumably flotation or cyanide leaching. Testing has shown that Reichert cones, followed by treating the cone concentrate on spirals, can deliver about 88% gold recovery in about 13% weight, that is, 87% weight rejection. Consequently, fine grinding and reagent costs are attributable to only 13% of the plant feed rate. Cost data is not yet available, but the potential exists for significant cost savings.

Jan 1, 1985

By J. W. Rutter, K. T. Aust

The migration of individual, large-angle grain boundaries has been studied as a function of tempereature and solute concentration in specimens of zone i.e filled lead containig very small additions of silver and of gold. Tile results are compared with various the-ories of grain boundary migration and with observations made prev.iorlsly of grain boundary migration in similar specimens of zone-refined lead containing tin additions. A previous investigation by the authors dealt with [he temperature dependence of grain boundary migration in bicrystals of zone-refined lead containing small additions of tin.&apos; It was shown that tin additions as low as a few parts per million cause a large decrease in the grain boundary migration rate at any given temperature, as well as a marked increase in the temperature dependence of the migration rate. It was found that existing theories of grain boundary migration. based on the motion of dislocations. or upon the concept of atom transfer in groups across the boundary (group process theory). or upon the control of grain boundary motion by volume diffusion of impurity atonls along with the boundary. are incapable of accounting for the observations. The single process theory of grain boundary migration. which is an absolute reaction rate calculation based on the transfer ui atoms singly across the moving boundary, was found to predict the migration rate reasonably well for a number of boundaries whose motion was shown to be very little influenced by impurities, but not for boundaries whose illation was influenced markedly by impurities. It was concluded that the elementary process of grain boundary migration involves the activation of single atoms during transfer across the boundary. and that inadequate knowledge is available to permit the influence of impurities to be properly taken into account. The present study was initiated to check the validity of the above conclusions with other alloy systems, namely high-purity lead with small additions of silver and of gold. Both silver and gold diffuse faster. and with a lower activation energy of volume diffusion. than does tin in lead;&apos; consequently, a study of the effects of silver and gold on grain boundary migration in high-purity lead offered a means of testing theories of boundary migration based on bulk diffusion of the solute (eg. ref. 3). In addition. it was hoped that the present work, in comparison with the results for tin in lead, would provide information concerning which factors are important in determin- ing the interaction between solute atoms and a grain boundary. EXPERIMENTAL PROCEDURE The preparation of bicrystals of zone-refined lead, with various silver or gold additions, was identical to that previously described for the lead-tin alloys.&apos;&apos;4 Each bicrystal consisted of a striated crystal which was grown from the melt. and an adjacent striation-free crystal which was introduced by artificial nucleation and growth.&apos;&apos;4 The striation or lineage substructure in the melt-grown crystal provided the driving force for grain boundary migration. During the preparation of striated single crystals by growth from the melt, it was found that silver or gold concentrations as low as 2 or 3 ppm by atoms were sufficient to cause formation of the hexagonal cell structure. which is due to the presence of impurity, during freezing. This structure is revealed on the solid-liquid interface by decanting the liquid during freezing. The hexagonal cell structure was observed previously4 in zone-refined lead crystals with tin contents above approximately 200 ppm by atoms. These concentrations of silver, gold, or tin are in agreement with the predicted amounts required for cell formation in lead,5&apos;6 under the present conditions of freezing.4 The absence of cell structure at decanted interfaces, therefore, served as a useful indication that the silver or gold contents were less than 2 or 3 ppm by atoms in the specimens as grown. It was found that grain boundary migration occurred only very slowly when the solute content approached that necessary for cell formation. As a result, the present experiments were conducted with silver or gold additions less than 1 ppm by atoms. This impurity level is well within the solid solubility limits for silver and gold in lead.7 The annealing treatments, measurements of grain boundary velocities, and orientation determinations were carried out as described previously.&apos; However. each bicrystal was also chemically polished in a solution consisting of 8 parts glacial acetic acid and 2

Jan 1, 1961

By B. B. Rath, Hsun Hu

In wedge-shaped bicrystals of zone-refined aluminum it is observed that (111) pure tilt boundaries migrate under the driving force of their own inter-facial free energy. The boundary velocity is a power function of the driving force. The driving force exponent decreases with decreasing angle of misorien-tation. For example, at 64O°C, the exponent decreased from 4.0 for a 40 deg to 3.2 for a 16 deg tilt boundary. An evaluation of the driving force acting on the boundaries during their motion indicates that for low driv-forces, up to about 2 x l03 ergs per cu cm, the velocity is relatively independent of misorientation, whereas at higher driving forces a 40 deg tilt boundary exhibits the highest velocity. The measured activation energy for boundary migration approaches that for bulk self-diffusion at low driving forces, decreasing from 33 to 27 kcal per mole as the driving force is increased from 1 x l0 to 5 x l03 ergs per cu cm. These results are compared with current theories of grain-boundary migration. In previous experimental studies of grain boundary migration the driving force has been limited to a difference in stored energy across the boundary. This stored energy has been introduced into the crystal either by prior deformation1-3 or by grown-in lineage structure. A part of the energy stored in the deformed crystal is released by recovery either prior to or concurrently with grain boundary migration, thus introducing an uncertainty as to the magnitude of the driving force responsible for grain boundary migration. The grown-in lineage structure, though thermally stable during annealing, neither provides conditions under which different levels of energy may be stored in the imperfect crystal nor provides a control of orientation difference across the migrating boundary of a growing grain. Furthermore, because of variation in the lineage structure, it is difficult to determine accurately the energy stored in the imperfect crystal. Several investigations of grain boundary migration during normal grain growth have also suffered from difficulties in estimating the driving force because of uncertainties in the principal radii of curvature.~ In the present investigation the velocity of pure tilt boundaries in zone-refined aluminum bicrystals of selected orientation (40, 30, and 16 deg around the [Ill] tilt axis) has been measured in the absence of a dislocation density difference across the moving boundary, thus eliminating the previous experimental difficulties. The driving force for boundary migration is derived from a gradient of the total interfacial free energy of the migrating boundary in wedge-shaped bicrystals. A similar method was attempted by Bron and Machlin in a study of grain boundary migration in silver. However, they found that one of the crystals was deformed and consequently the motion of the boundary was partly due to a difference of stored energy across the boundary. The observed behavior of boundary velocities as affected by the driving force is examined in the light of the predictions of the current theories of grain boundary migration.7"10 The effect of boundary misorientation on velocity is compared with the theory of " which is based on a dislocation core model for high-angle boundaries. EXPERIMENTAL METHOD Seed-oriented bicrystals of zone-refined aluminum, 2.5 cm wide, 0.5 cm thick, and 12 cm long, containing tilt boundaries with a common (111) axis, were grown from the melt in the direction of this axis. Spectro-graphic analysis, reported earlier,&apos;&apos; indicated the purity of the crystals to be 99.999+pct. Three such bicrystals containing 16, 30, and 40 deg tilt boundaries were used. Wedge-shaped specimens were prepared from these bicrystals by spark cutting followed by electrolytic polishing. The angle of the wedge was usually 40 deg and the specimens were usually 0.25 cm thick. The intercrystalline boundary was located within 0.2 to 0.5 cm from the tip of the wedge. Fig. 1 shows a section of an oriented bicrystal containing an outline of a wedge-shaped specimen. The crystallographic directions shown in Fig. 1 represent the orientation of one of the crystals (the larger section of the bicrys-tal); the orientation of the other crystal differs only by rotation around the common [lil] axis. The parallel faces of the wedge always corresponded to the common (171) planes in both crystals, whereas the orientation of the side faces varied, depending on the misorientation angle. The bicrystal orientations were determined

Jan 1, 1970

By R. V. McAfee

The fundamentals of vertical-lift performance are examined with the aid of computer-calculated flowing gradient charts. Flowing and gas-lift well performance characteristics are determined from available well test data. The effect of tubing size, gas-liquid ratio and wellhead pressure is discussed for both flowing and gas-lift wells. The effect of gas-injection pressure, formation gas, bottom-hole pressure and valve spacing is also discussed for gas lift wells. From these studies conclusions may be reached for improving or prolonging natural flow, obtaining optimum lift efficiency when natural flow ceases and improving existing gas-lift systems. The techniques perfected satisfy the requirement that the time involved to conduct an evaluation be practical for operating personnel. INTRODUCTION Flowing pressure gradients furnish the key to successful evaluation of vertical-lift performance in producing wells. Command of multiphase flow gradients in some readily usable form is a necessity before operating personnel can competently include vertical-lift performance evaluation of both flowing and artificial-lift wells in their over-all consideration of production efficiency. A readily usable form cannot be overemphasized since most of the decisions which confront the production engineer with a problem well must be made quickly. In moving a barrel of oil from the reservoir to the stock tank, the major portion of energy generally is expended in the vertical-lift phase. This may or may not be of concern during the flowing life of a well, depending upon the production requirements. It becomes of some concern when the flow performance of the well becomes erratic, and a conscious effort must be made to maintain natural flow. It is at this time that the first steps may be taken to modify existing conditions to relieve unnecessary limitations to proper flow. When natural flow ceases and some form of artificial lift must be installed, the amount of energy expended in lifting liquids becomes quite obvious. It is at this time, if no other, that lifting efficiency becomes important because that part which must be supplied from an outside source is now related directly as a cost per barrel of oil produced. Ten years ago, the majority of gas-lift wells were produced with gas-well gas. Today, the majority are produced by closed rotative gas-lift systems. This permits a direct evaluation of well performance in terms of horsepower requirements and has resulted in mixed conclusions as to the success of gas lift based upon the relative efficiency of a particular system. An increased awareness of the need to resolve vertical-lift performance on a readily usable, scientific basis was inevitable. An indication of the need for better applied science in this field is the often-asked question of whether or not gas-lift can efficiently deplete a given well or reservoir. This question cannot possibly be answered without first evaluating reservoir, surface and vertical-lift performance both as encountered today and as anticipated throughout the life of the well or wells. The technique presented in this paper was originally developed to upgrade gas-lift installation design from an applied art to an applied science. It has since been successfully used not only for this purpose, but also for the whole field of vertical-lift performance in its broadest sense. Lift efficiency should be considered important while the well is still flowing, as well as after natural flow ceases. Correct interpretation and proper modification of the vertical-lift performance of a producing well can provide dramatic improvement in production performance and/or efficiency. STATEMENT OF THEORY AND DEFINITIONS Fig. 1 illustrates the three divisions of production which will be used in this paper. The terms are a modified version of those presented in the very fine paper by Gilbert.&apos; The fields of reservoir and surface performance both have been greatly improved over the years. A study of those writings which may be found indicates that the field of vertical-lift performance has not progressed as well. There are two possible reasons for this lack of progress. 1. It has not been recognized as a scientific field in itself by the oil companies, as has reservoir engineering. 2. The equipment companies have confined their efforts to mechanical design research rather than the more basic study of vertical-lift performance of producing wells. Both organizations must have an economic stimulus for doing research in this field, and most of the results obtained in past work has been so erratic as to arouse little enthusiasm. The basic purpose of interpreting vertical-lift performance is to predict operating conditions below the surface of the ground from available data. The success of the interpretation depends upon the accuracy with

By R. I. Garrod, R. A. Coyle

The shapes and positions of X-ray reflections from specimens of copper, steel, and aluminum alloy haue been examined in the elastic and plastic ranges both while the specimen was under stress and in the unloaded condition. For the aluminum alloy the shape was unaltered by the application of stress either within the elastic limit or in the plastic range provided that no additional plastic strain was induced. In copper the broadening accompanying plastic deformation was very slightly reduced when the specimen was unloaded. A similay but more marked elastic component of broadening was also found for steel, but in this case below the yield stress. Line profiles corrected for instrumental and particle-size broadening indicate very large internal stresses in local regions of the plastically deformed metals. The results are discussed in terms of a recent suggestion that the heterogeneous dislocation distribution between the cells and their boundary walls plays a major role in the peak shifts and broadening of the X-ray reflections. STUDIES of the X-ray line profiles from strained polycrystalline aggregates concentrate usually on one or the other of two main parameters: a) the displacement of the peak of the intensity contour from its position for a strain-free aggregate, or b) the shape of the profile. From peak shifts data can be obtained either on the relation in both the elastic and plastic ranges between applied external stress and average lattice strains in a given (hkl) direction, or, alternatively, on the residual lattice strains which are present after a plastically deformed specimen is unloaded.&apos; On the other hand, the shapes of the broadened profiles from cold-worked metals can be analyzed to separate the broadening produced by small particle size and by heterogeneous lattice strains.&apos; In this paper the terms "size broadening" and "strain broadening&apos;&apos; are used in the general sense adopted by warren.&apos; In the past, apart from two early qualitative observation, it has been customary to examine only the movements of the peaks of the profiles while the specimen is actually under load, since the line broadening induced by plastic strain remains after removal of the external stress. Consideration of the implications of existing data of this type suggests, however, that fruitful additional information on a number of fundamental aspects might be gained by careful examination of whether the X-ray line profile is in fact different in the loaded and unloaded states of the specimen. By taking advantage of the sensitivity and convenience of modern diffractometer techniques it is possible to explore with relative ease the magnitude and importance of any elastic effects which may be superimposed upon the well-known permanent changes in profile. The main aim of the work to be described was thus to investigate this point for typical metals and alloys. For this purpose annealed specimens were extended first elastically and then plastically and the positions and shapes of X-ray reflections were recorded. Initially it was anticipated that prime interest would center on observations within the plastic range; it has been found, however, that small changes in profile sometimes occur both before and after the nominal elastic limit of the material is reached. It is shown that the results obtained have important implications in relation to the structural changes and processes associated with deformation. I) EXPERIMENTAL To enable the diffraction lines to be recorded while the specimen was under uniaxial-tensile stress, a small hydraulic testing machine was designed and constructed for direct attachment to the goniometer of a Philips diffractometer. The specimens, which were machined from 1/2-in.-diam rod and had a central rectangular section 3/8 by 1/16 in. over a gage length of 1 in., were held in the machine by split collets mounted in grooves in the cylindrical ends of each specimen. No special precautions were taken to ensure precise axiality of loading. Constant oil pressure was maintained by a lever and weights system and transmitted to the loading rig by flexible pipe. The actual load on the specimen was measured by a load cell in the machine to an accuracy of * 1 pct. To enable smooth X-ray profiles to be obtained the specimen and machine were oscillated continuously during recording through *7-1/2 deg about the normal half-angle position of the goniometer. The three materials chosen for the investigations were high-purity copper as representative of a ductile fcc metal, a low-carbon steel for a bcc metal, and an aluminum alloy as a material in which the proof stress/ultimate strength ratio is high. Details are as follows. a) Copper. 99.999 pct purity. After machining the specimen surface was polished mechanically and

Jan 1, 1964

By A. M. Johnson, M. M. Singh

The mechanism of failure under a drill bit is still improperly understood in spite of several investigations of the subject. Generally, the cratering process under static loading conditions is considered to be similar to that achieved dynamically by impact. This paper attempts to indicate that, although the sequence of fracturing in the two cases appear to be identical, at least some dissimilarities exist. For example, the width-to-depth ratios of the craters vary to some extent, and the amount of energy consumed per unit of volume of craters is unequal for the two different loading conditions. Prevalent rock penetration processes are dominated by methods utilizing mechanical attack on rock. It is, therefore, generally accepted that a better comprehension of the mechanism of rock failure under a wedge would prove beneficial towards improving present drilling techniques. Several attempts have been made in recent years to explain how craters are formed under a drill bit, but the mechanism of failure beneath a bit is still improperly understood. 1-11 Most investigators, to date, have inferred the sequence of events occurring during crater formation from analyses of force-time diagrams,1"6 from theoretical considerations,7 or from a study of the configurations of final craters.8-l0 These analyses have led to the presentation of widely divergent models for rock failure beneath a drill bit, ranging from brittle to viscoelastic. The cratering process under dynamic loading commonly is regarded as being similar to that obtained under gradually applied, or &apos;static&apos;, loads. But the effect of rate of loading on the action of a bit is still disputed. Some investigators11-12 maintain that there should be no such effects, whereas others have demonstrated experimentally that these exist.13-17&apos; The purpose of the investigation reported in this paper was to examine petrographically the damage done to rock under the action of a chisel-shaped wedge, both with &apos;static&apos; and dynamic loading, and to determine if rate-of-loading effects could be detected. Significant quantitative differences in crater volumes and depths were found to exist for a given consumption of energy. On the basis of this data, an attempt was made to indicate some of the rheological properties that a proposed model should possess. All the work reported herein was conducted at atmospheric pressures. EXPERIMENTAL APPARATUS AND PROCEDURE Two types of rocks were employed for most of the experiments reported in this paper, viz. Bedford (Indiana) limestone and Vermont marble. The mechanical properties of these rocks are given in Appendix A. Actually two types of Vermont marble were used, but since no marked difference could be discerned between the two varieties (as seen in Fig. 10) the data was used collectively for the analysis. Stronger rocks were not employed owing to difficulty in generation of observable craters without damage to the equipment. Six-in. diam cores were drilled from the rock samples and embedded in 8-in, diam steel pipe with 3/8-in. wall thickness, using hydrostone to fill the annulus between the core and the pipe. This procedure was adopted to confine the rock specimen so that fractures would not propagate to the edges of the cores. This goal was achieved satisfactorily for these tests because no cracks were observed to extend into the medium surrounding the rock, even when craters were formed only 1 in. from the rock core periphery. Three to four craters were formed on a core face, because the rock damage from any one crater generally did not appear to extend into the others. Whenever, interference between damaged areas around adjacent craters was suspected, the data was rejected for purposes of the analysis. The limestone and marble samples were tested with a 60-degree, wedge-shaped bit, 1 5/8-in. in length, made of tool steel. The bit shank had two SR-4 type electrical resistance strain gages, mounted axially, to record the force-time history during the loading operation. The static indentation tests were conducted using a 50-ton capacity press fitted with an adapter for drill bit attachment. See Fig. 1. The force exerted by the bit at any instant was measured with strain gages affixed to the bit shank. An aluminum cantilever, with two SR-4 strain gages mounted near its clamped end, was employed to measure bit displacement. Both sets of gages were included in Wheatstone bridge circuits,

Jan 1, 1968

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By J. H. Moran, E. E. Finklea

The pressure build-up technique is a recognized method of determining permeability from conventional drillstem tests. In this paper an effort is made to extend such techniques to the interpretation of data obtained from the wireline formation tester. Such a study is necessary because of the differences, for this case, in the magnitude of the flow parameters (rate of flow, amount of recovered fluids) and in the flow geometry (flow through a perforation vs flow across the face of the wellbore, etc.) involved in the solution of the equations of flow for compressible fluids. The perforation is replaced by a spherical hole, and the effect of the borehole is neglected, so that the flow can be considered to be radial in a spherical co-ordinate system. Arguments are presented to justify this idealization. Assuming single-phase flow, general relations between pressure and flow rate are developed for a homogeneous medium. The study is then extended to permeable beds of finite thickness. It is shown that the early stages of pressure build-up tend towards spherical flow, while the later stages tend towards cylindrical flow. The thinner the bed, the more quickly flow approaches the cylindrical model. The prevalence of thin beds in practical work makes this analysis quite important. Cases involving permeability anisotropy are treated. INTRODUCTION From wireline formation tester operation, two types of data are obtained: (1) the nature and amount of recovered fluids, and (2) the pressure history recorded during the test. A number of papers have been written dealing with the interpretation of formation production on the basis of the recovered fluids.&apos;.&apos; In general, the methods described have been quite accurate for both high- and low-permeability formations. The present paper will deal with an analysis of the pressures observed. An analysis of the pressure build-up curves obtained in hard-rock country has already been attempted on the basis of the formula proposed by Hor-ner. Although this approach has met with success in many instances, some questions have been raised as to its validity. It is the aim of the present study to place the analysis of pressure build-up in the formation tester on a firmer basis, from which more detailed methods of interpretation can evolve. Because of the great differences between the operation of the wireline formation tester and the conventional drillstem test, modifications are necessary in the interpretation. The major difference relates to the flow geometry. Once the flow geometry has been established other features such as multiphase flow, skin effect, afterflow, etc., well described in the literature, can be introduced. It will be assumed that the mechanical operation of the formation tester is already known to the reader.6 t will suffice here merely to state that the tester provides the means for taking a relatively small sample of the fluid immediately adjacent to the borehole, and for recording the subsequent pressure response. In comparison with conventional drillstem tests, the time required for a satisfactory pressure build-up response is much shorter, because of the relatively small quantity of fluid withdrawn by the wireline tester. This feature is highly desirable in the case of low-permeability formations. For an analysis of the pressure response within the formation, three simple flow geometries are considered— linear, cylindrical and spherical. The spherical and cylindrical flow geometries are most pertinent to the formation tester; therefore, they will receive the major emphasis. Since the configuration of the borehole and the perforation made by the tester complicate the flow geometry, it is necessary to allow for them in the drawdown response. However, because of the volume of formations contributing to the pressure-response, the details of the perforation shape are unimportant in the build-up period. Since relatively small amounts of fluid are withdrawn from the formation, in contrast to a conventional drill-stem test, a study of the "depth of investigation" and the significance of drawdown as well as build-up data will be included. Because the "depth of investigation" will be shown to be rather large, the effect on the build-up curves of the finite thickness of the permeable bed is considered. It is this consideration that leads to the importance of cylindrical flow geometry. Also included is a discussion of permeability anisotropy and its effect on the interpretation of the tester results. The pressure curves recorded by the formation tester will follow two general patterns, depending upon whether the formation is of high or low permeability. Fig. I (a and b) schematically illustrates these two responses. In Fig. 1(a), the high pressure recorded during fill-up of the tool is essentially the pressure differential across the choke in the system. In Fig. l(b), the flow rate is

By R. O. Williams

It is shown that Ni3Al precipitates homogeneously from nickel-rich alwminum alloys as plates on the (100) planes. Prior to actual precipitation a process occurs which is believed to be one of increasing short-range order. After precipitating the Ni3Al plates enlarge through competitive growth. Discontinuous precipitation can occur simultaneously with the above processes. Recent ideas of the origin of precipitation strengthening appear adequate to explain the hardness changes. REMARKABLY little appears to be known about the precipitation process in Ni-Al alloys in spite of their technical importance. This investigation originated to supply additional information about precipitation in general, this system in particular. Information on the structures and kinetics have been obtained through the use of hardness, X-rays, microscopy, calorimetry, and resistivity on high-purity alloys. PROCEDURES Six alloys, Table I, were prepared by melting carbonyl nickel and high-purity aluminum in alumina crucibles in vacuum and casting into 1-in. graphite molds. All rods were homogenized at least once at 1300°C for 24 hr prior to swaging and this was repeated on the first three alloys after 75 pct reduction. Alloy 4 could be reduced only 10 pct at 1000°C (probably in two-phase field) prior to fracture but 1/4-in. samples quenched from 1100°C were readily reduced cold. Alloy 5 was reduced 15 pct cold but failed on the next pass while alloy 6 of essentially the same aluminum content failed inter-granularly without apparent flow up to 1000°C. The alloys were heated in hydrogen at the elevated temperatures and formed thin, coherent aluminum oxide coatings which provided excellent oxidation resistance at lower temperatures. However, freshly prepared surfaces showed considerably less resistance at 500"to 700°C in air and apparently resulted in internal oxidation. As a consequence, low-temperature agings were carried out in evacuated tubes. RESULTS The isothermal hardening behavior of these alloys at 500"and 565C is given in Figs. 1 and 2. These results were obtained from samples cold worked 75 pct, recrystallized at 1000°C (1100°C for the 7.8 pct Al) and quenched in water. This recrystallization was used to give smaller grain sizes so as to obtain more uniform hardness values and the points represent an average of five readings. The electrical resistivity was measured on 1/16-in. wires quenched from 1000°C during aging at 495°C to give Fig. 3. The energy release and its rate are given in Fig. 4 for the 6.9 pct Al alloy during aging around 500°C. Inasmuch as this was a single run, its accuracy is not known but certainly the general shape and magnitudes are correct. The method used to obtain these results is described elsewhere.&apos; Data for the aging at 600°, 700°, and 800°C of these alloys cold worked 50 pct are given in Fig. 5. Supplementary information from microscopy and X-ray diffraction have been included to indicate recrystallization, discontinuous precipitation and the appearance of superlattice lines from the Ni3Al. The hardness of these alloys as annealed, aged, cold worked, and cold worked and aged is given vs composition in Fig. 6. Those samples which were isothermally aged, Figs. 1 and 2, were reaged at 532°C and at successively higher temperatures for the indicated times to give the data of Fig. 7. These results as well as certain others, support the idea that the level of hardness reached for temperatures above 600°C are equilibrium values more or less independent of path. This being the case, the breaks in the curves would be the complete solution of the Ni,Al. The electrical resistivity versus temperatures for some of these alloys, both aged and unaged, is given in Fig. 8 along with those data from heating slowly (10 deg per day) to high temperatures. Interesting points include the lowering of the Curie temperature (the change in slope), the lack of any indications of a solubility limit and the large temperature coefficient for the Ni3Al. A slight break for Ni3Al around 100C shows up but this is not a Curie temperature as Ni3Al is not ferromagnetic down to -190°C. Metallographically both the nickel-rich solid solution and the Ni3Al appear very much like pure nickel. Profuse twin boundaries are present both

Jan 1, 1960

By G. R. Leverant, C. P. Sullivan

To evaluate the effect of a dispersion of nondeform-able, incoherent, second-phase particles on high-strain cyclic deformation and fracture, recrystallized TD-nickel (Ni-2ThO2) and a commercially pure nickel, Ni-200, were fatigued under strain control at total strain ranges varying from 0.009 to 0.036. Relative to the Ni-200, the slip at the surface of the TD-nickel was more wavy and discontinuous due to the presence of the thoria particles. This made crevice formation (incipient cracking) within slip bands more difficult in TD-nickel than in Ni-200. Both materials cyclically hardened to a constant (saturation) flow stress which increased with increasing plastic strain amplitude. Cellular substructures were developed in both materials during cycling. The cell size in TD-nickel was controlled by the thoria particle distribution and was independent of plastic strain amplitude over the range investigated. The cell size in Ni-ZOO was larger than that in TD-nickel at similar plastic strain amplitudes and was a function of plastic strain amplitude. These results, together with the cyclic stress-strain curves for both materials, are discussed in terms of a model for fatigue strain accommodation at saturation recently proposed by Feltner and Laird. NUMEROUS fatigue investigations have considered the interrelation of slip character, dislocation substructure, and cracking in pure metals and solid-solution alloys. However, except for the studies of the low-strain fatigue of internally oxidized copper alloys1 and cast, dispersion-strengthened lead,&apos; little is known about the effects which small, incoherent, nondeform-able, second-phase particles have on cyclic deformation and cracking processes. Effects due to the particles alone are often obscured by a dislocation substructure introduced during thermomechanical processing of dispersion-strengthened metals. In the present study, recrystallized TD-nickel and a commercially pure nickel, Ni-200, were employed to evaluate the effect of a thoria dispersion on high-strai fatigue deformation and cracking at room temperature. I) MATERIAL AND EXPERIMENTAL PROCEDURE The TD-nickel was supplied by DuPont as a 5/8-in.-thick stress-relieved plate which had been subjected to a proprietary schedule of thermomechanical treatments, and the Ni-200 as 3/4-in. bar which was subsequently annealed for 2 hr at 850°C in argon resulting in an average grain diameter of 0.05 mm. The compositions of these materials are given in Table I. The microstructure of the TD-nickel consisted of elongated grains parallel to the primary working direction with an average width of 0.16 mm, Fig. l(a). Many fine annealing twins were present indicating that the starting material was in a recrystallized condition; this supposition was confirmed by the absence of of any extensive dislocation substructure, Fig. l(b). Sheetlike stringers parallel to the rolling direction were occasionally seen both within grains and at grain boundaries. Some approximately spherical particles about 2 in diam, which may correspond to exceptionally large thoria particle aggregates, were also present. The average Young&apos;s modulus of the plate material in the rolling direction was 21.8 X 106 psi which is consistent with a {100}<001>recrystalliza-tion texture3&apos;* being prominent. In transmission microscopy, the 2.3 vol pct of thoria particles generally appeared to be uniformly distributed although some clusters, 0.1 to 0.3 in diam, of larger particles were observed as previously reported for TD-nickel sheet,5 and stringering of particles was present in some areas as welt. The average diameter of the thoria particles was 450A with a calculated mean planar center-to-center spacing of 2100A, as determined by quantitative metallographic analysis.= The 0.2 pct offset yield stress was 36,000 psi which agrees with the value predicted by the modified Orowan relation7 for edge dislocations bowing between thoria particles of the size and spacing observed in the present investigation. Fig. 2 illustrates the specimen design employed for the axial high-strain fatigue testing. Adapters were screwed onto the threaded portions of each specimen so that testing could be performed in the same manner as that reported for buttonhead specimens.8 Stressing was coincident with the working direction for both materials. The gage section of each specimen was electropolished and lightly etched prior to testing. The total strain was controlled, being varied between zero and a maximum tensile strain ranging from 0.009 to 0.036. In addition to these tests, a circum-ferentially notched TD-nickel specimen was cycled over a total strain range of 0.0075. The same strain

Jan 1, 1969

By George S. Ansell, Thomas E. Davidson

It has been known for a considerable period of time that the ductility of even quite brittle materials can be enhanced if they are deformed under a superposed hydrostatic pressure of sufficient magnitude. The response of ductility to pressure, however, has been shown to vary considerably between materials. Prior work has shown that the effects of pressure upon the tensile ductility of Fe-C materials depend upon the amount, shape and distribution of the brittle cementite phase. In this current investigation, the effects of pressure upon the fracture mechanisms in a series of annealed and spheroidized Fe-C materials were examined. It was observed that the principal effect of pressure is to suppress void growth and coalescence, retard cleavage fracture and to enhance the ductility of cementite platelets in pearlite. Based upon the observed effects of pressure upon the fracture mechanisms, a proposed explanation for the enhancement in ductility by pressure and for the structure sensitivity of the phenomena is presented and discussed. THE effect of superposed pressure upon the tensile ductility of a variety of metals has been well documented.&apos;-&apos;&apos; Some of the results from several investigators are summarized in Fig. 1 where tensile ductility in terms of true strain to fracture (ef) is plotted as a function of the superposed pressure. As can be seen, a pressure of sufficient magnitude can significantly enhance the ductility of metals. However, Fig. 1 also demonstrates that the response of ductility to pressure and the form of the ductility-pressure relationship varies considerably between materials. Several explanations have been offered for the observed enhancement in ductility by a superposed pressure. Although no experimental evidence was provided, Bridgman13 and Bobrowsky10 proposed that the observed effect was due to the prevention or healing of microcracks or holes. Bulychev et a1.14 observed that cracks and voids in initially prestrained copper were healed in the necked region of a tensile specimen upon further straining while under a superposed pressure. Also, pugh5 observed that large cavities were suppressed in copper fractured in tension while under pressure. A second proposal has been forwarded by Beresnev et at al.6 This proposal is based upon the hypothesis that a material fails in a brittle manner because the normal tensile stress reaches a critical value before the shear stress is of sufficient magnitude to cause plastic flow. Since a superposed hydrostatic pressure will increase the ratio of shear to normal tensile stress, a sufficiently high hydrostatic pressure should favor plastic flow while retarding brittle fracture. Galli15 reported that a superposed pressure shifts the ductile-brittle transition temperature of molybdenum. This was explained based upon the reduction of the normal tensile stress by the superposed pressure. Pugh5 explained the occurrence of the observed pressure induced brittle-to-ductile transition in zinc in the same manner. Davidson et al.12 proposed an explanation for the enhancement of ductility by pressure based upon the effects of pressure upon the stress-state-sensitive stages of various fracture propagation mechanisms. Basically, they proposed that pressure will retard cleavage and intergranular fracture by counteracting the required normal tensile stress or will suppress void growth. They observed suppression of intergranular fracture and void growth in magnesium by pressure. Davidson and .Ansell16 reported ductility as a function of pressure for a series of annealed and spheroidized Fe-C alloys. Fig. 2, from this prior work, demonstrates that the effect of pressure upon ductility is structure sensitive in terms of the amount, shape and distribution of the brittle cementite phase. As shown in Fig. 2, in the absence of cementite or when the cementite is in isolated particle form (spheroidized), the ductility-pressure relationship is linear and the slope decreases with increasing carbon content. In the annealed carbon-bearing alloys wherein the cementite is in the form of closely spaced platelets (pearlite) or in the form of a continuous network along prior aus-tenite boundaries (1.1 pct C material), ductility as a function of pressure is nonlinear (polynomial relationship) in which the slope increases with increasing pressure. At the highest pressures studied (22.8 kbars), the slope of the curves for these materials tends to approach those for the spheroidized material of the same carbon content. In this current investigation the change in fracture mechanisms as a function of pressure for the materials shown in Fig. 2 has been examined. The possible connection between the observed effects of pressure upon the fracture mechanisms and the effect of pressure upon ductility is discussed.

Jan 1, 1970

By K. G. Davis

Dilute alloys of silver and of thallium in tin have been solidijzed unidirectionally under controlled conditions, to study the segregation associated with a cellular interface under conditions where both thermal and solute convection are present. Autoradiography and radioactive tracer counting techniques were combined with electron-probe microanalysis to study both macro- and microsegregation. It was found that, for concentrations giving only small amounts of constitutional supercooling, cell formation had little effect on the macroscopic distribution of solute along the specimen. At higher concentrations the effective distribution coefficient was higher than that expected for a smooth interface. Node spacing was independent of initial solute content at lower concentrations, becoming greater as keff increased. Silver content at the segregation nodes of silver in tin alloys was independent of initial concentration and considerably in excess of the eutectic composition. SINCE the investigation of cell formation at advancing solid-liquid interfaces by Rutter and Chalmers,&apos; a large volume of work has been dedicated to the determination of solidification conditions under which a planar interface will break down into cellular form. Early experiments were explained satisfactorily by the concept of constitutional supercooling,2 but, due to poor measurement of temperature gradients in the liquid, lack of accurate data on liquid diffusion and equilibrium distribution coefficients, and uncertainty about the effects of thermal and solute convection, these experiments cannot be used as proof for the theory. More recent work, however, has shown that under conditions where convection is eliminated or can be ignored good correlation is observed.3,4 Investigations into segregation at cell caps5 and at cell nodes6-&apos;&apos; have been made, but no measurements appear to have been done on the overall, macroscopic segregation down a unidirectionally solidified rod of material which has solidified with a cellular substructure. This has practical importance in casting, where regions of material with cellular substructure are often encountered, and also in zone refining where the thermal conditions necessary for a planar interface are unattainable. Further, as will be shown, the macroscopic segregation can give information on the following question. Granted that a cellular solid-liquid interface develops from a planar one when the conditions for constitutional supercooling are exceeded, how much supercooling is present after the cells have formed? EXPERIMENTAL PROCEDURE AND RESULTS Specimen Preparation. Specimens 25 cm long with a square cross section 0.6 by 0.6 cm were grown in graphite boats by solidification from one end. Alloy compositions are given in Table I. Two specimens of each composition were grown. The tin was 5-9 grade and the silver and thallium both 4-9 grade. Ag110 and Tl204 were used as tracers. Each composition had the same quantity of tracer so that auto radiographs of specimens containing different concentrations of the same element could be easily compared. Thermocouples inserted through the lid of the boat into a dummy specimen showed that, over the first 10 cm of growth, thermal conditions were quite steady, with a rate of interface advance of 5.8 cm per hr and a temperature gradient in the melt ahead of the interface of 3.0°C per cm. The specimens were seeded from tin crystals of a common orientation to eliminate orientation effects. Dilution of the specimen by seed material was minimized by the provision of a narrow neck between specimen and seed crystal. Macrosegregation. After growth, the specimens were sectioned with a spark cutter. The rods of silver alloy were cut into 1-cm lengths and analyzed for Ag110 using a y -ray counter with fixed geometry. The specimens containing thallium were cut into 2-cm lengths and analyzed for T1 204 by taking 13 counts from each end of the cut lengths through an aperture in lead sheet approximately 0.4 cm square. The results are summarized in Figs. 1 and 2. To find the effective distribution coefficient for the silver in tin alloys under smooth interface conditions, the region of substructure at the bottom surface of one of the 10 ppm specimens, see Fig. 3, was removed by spark machining before counting. Autoradiography. For both alloy systems the samples were polished on sections taken alternately parallel and perpendicular to the growth direction, and autoradiographed by placing the polished surfaces in contact with Kodak "Process Ortho" film. Figs. 3 and 4 show the structures revealed. The alloy containing 10 ppm Ag showed substructure only after a few centimeters of growth, and then substructure was limited to a narrow layer at the base. The "speckled" substructure reported previously in this system4 is here clearly seen to be an intermediate stage between planar and cellular interface conditions. The other samples show a remarkable similarity considering

Jan 1, 1969

By W. A. Oates, J. A. Lambert, P. T. GaIIagher

Monte Carlo methods have been used to compute the arrangements of interstitial atoms dissolved in tetrahedral sites in bcc lattices. It is assumed that the presence of an interstitial atom "blocks " a certain number of neighboring sites and prevents their occupancy. Sites "blocked" by more than one filled site are allowed for. The computed values of. the mean occupation number (defined as the ratio of the total number of sites blocked to the number of solute atoms are used to calculate the configurational entropies of the solutions. These entropies are compared with those resulting from previous theoretical studies of this problem and also with available experin~ental data for the p Zr-H, Nb-H, V-H, and Ta-H systems. Evidence is also given that the "blocking" explanation of low limiting compositions in these systems, rather than this being due to initial limitations on the number of sites available, is probably correct. THE ideal partial configurational entropy of mixing of an interstitial solute in a metal is given by: where p is the number of interstitial sites per metal atom and Xi is the atomic fraction of the interstitial. For the bcc lattice. which we shall be concerned with in this paper, the interstitial positions are shown in Fig. 1. It can be seen that for the tetrahedral sites, p=6. whereas for the octahedral sites, p = 3. Different emphasis has been placed on the relative importance of energy and entropy effects in determining deviations from ideality in interstitial solid solutions. In some cases the same system, e.g., Fe-C, has been described by the contradictory regular and athermal solution models indicating that the enthalpy and entropy functions, derived from equilibrium data, are frequently not accu.rate enough to differentiate between these treatments. However, for certain metal-hydrogen solutions the equilibrium data is available over sufficiently wide ranges of temperature and composition to permit a reasonably accurate determination of the compositional variation of the heats and entropies. Hoch&apos; has attempted to interpret the results of interstitial solid solutions in terms of a regular solution model. In the case of the Ta-H system where 13 = 6, this model entails fitting the experimental relative partial entropies of solution, asH, to the equation: where ASgs is the relative partial excess entropy of solution of hydrogen. Hoch found that the results of Mallett and Koeh1 could be fitted to this equation with an approximately constant value of AF up to XH = 0.25. However, it is apparent from the solubility isotherms in this system which become asymptotic to the composition TaH that, since (Xh /6 - ~Xh ) becomes infinite only at TaH6, it is necessary that AS<&apos; tends to infinity at TaH. In other words, the low saturation composition of TaH, instead of the anticipated TaH,, eliminates the possibility of applying regular solution theory to such systems. Rather large negative excess configurational entropies must exist at higher hydrogen concentrations in order to explain the lower saturation values. To account for these low limiting compositions and excess entropies two distinctly different approaches have been followed. Rees and many others1-l2 have assumed that not all interstitial sites are crystallographically equivalent with respect to the interstitial addition; that is, in Eq. [I] p is less than the value anticipated from geometrical considerations. To describe, say, a bcc metal-hydrogen system with a limiting composition of MH by this approach one would consider that p = 1 in the first instance instead of p = 6.&apos;j3 In some cases, nonintegral values of B have been taken in order to improve the fit with the experimental data over limited ranges of composition. The other approach which has been used to explain the low saturation compositions is to assume that, although all sites are available for occupancy, strong repulsive interactions exist between the neighboring interstitial atoms, and hence occupancy of any site excludes or blocks a certain number of neighboring sites from being occupied. Earliest treatments of this concept considered the exclusion of an integral number, of nearest-neighbor sites from being occupied at all concentrations. In this case, the partial configurational entropy is given by: These early treatments failed to allow for the overlap of the blocked sites which will arise at all but the very lowest concentrations. More recently attempts have been made to calculate the effect of this decrease in the number of blocked sites on the configurational entropy. Using the quasichemical treatment of interstitial solid solutions as given by Lacher and assuming that an infinite repulsive interaction energy existed between the solute atoms. atom obtained an approximate configurational entropy applicable to the blocking with overlap case:

Jan 1, 1970

By C. J. Guntner, R. P. Reed

A commercial 18Cr-8Ni iron alloy (AISI 304L) was examined in tension at 300°, 76°, 20°, and 4°K. Continuous stress-strain recordings were made, X-ray analyses at periodic stress (strain) intervals were obtained, and the magnetic measurements were taken. From this data the percentage of martensitic products [bcc(a) and hcp (E)] was computed as a function of stress (strain). It was found thatup to 15 pct E phase forms at low temperntures. The amount of E formed increases to a maximum at about 5 pct strain, then decreases. This decrease indicates the additional transformation of E to a&apos;. The total amount of E and a&apos; was suppressed at constant stress (strain) at 4°K as compared to 76°K. It is proposed that the suppression of E and a&apos; is associated with the decreased mobility of extended dislocations at very low temperatures. The yield strength decreased as the temperature was depressed below room temperature and then increased rapidly near 4°K. SOME ferrous alloys which are austenitic (fcc ?) at room temperature appear to be unique in that two martensitic products (hcp e and bcc a&apos;) may form on cooling to lower temperatures or on application of mechanical stress. The most common room-temperature austenitic ferrous alloys are 18Cr, 8Ni stainless steels. Most aspects of the spontaneous transformations have been previously described for these steels.&apos; Several previous papers have described special aspects of the stress-induced transformations at low temperatures for the stainless steels, such as the existence of the hcp phase (c) after straining at 76oK,2-7 the morphology after straining using electron microscopy,7 and the decrease in E at higher strains at 76oK.4 However, for a complete representation, one must know the stress-strain characteristics and the dependence of both martensitic products on applied stress and temperature. It is the intention of this paper to provide that documentation. To accomplish this, continuous stress vs strain recordings were made at four temperatures: 300°, 76", 20°, and 4°K for annealed AISI 304L (a commercial 18Cr-8Ni alloy). At periodic stress intervals at each temperature the integrated X-ray line intensity of a selected peak for each phase (y, E, and a&apos;) was measured. In addition, photomicrographs of the strained surfaces were taken and magnetic measurements were made. The magnetic readings can be directly converted into percent a&apos;.&apos;,e With these measurements the percentage of each phase may be plotted as a function of stress (or strain) and test temperature. It was found that up to 15 pct E phase forms upon stressing the AISI 304L alloy at low temperatures. The E percentage increases abruptly after the alloy yields, but then decreases gradually at higher stresses. The rapid increase in e at 76°K is associated with an "easy-glide" portion of the stress-strain curve. The total amount of a&apos; + .G is suppressed below 76°K at a constant stress or strain. The yield strength decreases down to 76°K but increases rapidly below 20°K. EXPERIMENTAL PROCEDURE Tensile test specimens were cut parallel to the rolling direction from 0.1-in.-thick sheet. Continuous stress vs strain recordings were obtained at each test temperature (300°, 76o, 20°, and 4°K) using equipment and methods described elsewhere.&apos; The specimens which were used in the X-ray analysis were stressed to successive increments of strain at each temperature, analyzed at room temperature, then restressed at the test temperature. This procedure was repeated until approximately ten X-ray analyses had been performed with approximately 1.0 pct strain increments. The specimens had a reduced section 1 in. long, 1.2 in. wide, and 0.1 in. thick. They were electro polished prior to testing and after each strain increment. Table I lists the chemical composition, grain size, and hardness for the alloy which was used. This is the same alloy for which extensive mechanical-property tests3 and morphological studies of the spontaneous transformations&apos; have previously been made. For the low-temperature tests (76o and 4°K) below the Ms temperature the specimens were initially cooled to the test temperature, held for 1/2 hr, then warmed and X-rayed at room temperature. The results are listed in Table 11. From earlier work8 it was known that additional transformation on the second cycle would be considerably less (-0.1 pct

Jan 1, 1964

mean to say that these explosions are mechanical, but that the ejectment of the stock, throwing out of tops, etc., are mechanical. I see no reason at present, although I have had almost no experience in the use of large quantities of Mesabi ore, to change my ideas on the subject. That these explosions should follow irregular working or slipping in the furnace, I think can be explained. I have noticed that immediately following slips there is little or no settling of the stock on top, although there is no lessening of the volume of gas passing into the stoves and boilers. Supposing that, after a slip of 3 or 4 feet, the filling continues, but for some distance from the &apos;top the stock fails to move: there would be a much better chance for the deposited carbon to clog interstices in the stock, and for the additional effect in the same direction of the fine ore in the charge, than if the stock were properly settling. Under such conditions it is easily supposable that the openings would be entirely closed, or closed so tightly that the pressure below the obstruction would be raised to a point approaching the blast-pressure, or to a point high enough to force a passage or an enlargement of the small passages which may remain. When this occurs, gas from below under pressure carries with it large quantities of deposited carbon and fine ore; if the case is aggravated, coke, stone, bell, etc. As soon as the red-hot deposited carbon meets the air there are perfect conditions for a dust explosion, which naturally follows, the same as in a coal-mine or flour-mill.

Jan 1, 1899