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By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the 'drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By William G. Kegel

Apart from a usable product and good mining conditions, the greatest asset for a profitable coal mining organization is an effective mine maintenance program. The first step in achieving this is to have good mechanics-or men who want to be mechanics and are interested in knowing ,more about the design and control of the machines in their charge. A good mechanic's knowledge and ability result from ambition, curiosity, and determination. Starting with these qualities, the aspiring mechanic can launch his career by learning all he can about mechanics, electricity, and hydraulics. Though the path is rough, the end result is rewarding. Mining machinery probably receives as much, if not more, abuse as any other heavy equipment in use today. Considering the conditions under which much of the repair work must be done, it is essential that the mine operator has the best men and tools to perform the work. Mining machines, from their inception, have utilized the electric motor ; and down through the years of mechanization, this power source has undergone many changes to better adapt it to the job. The first motors used were direct-current (d-c) motors since d-c power was the most economical power source for mining at the time of early mechanization. These motors were large open-type machines which are seldom used in modern mining. Because of the mine environment, the d-c motor has been reduced in size to better suit the application in mining machines and is now manufactured with dust-tight or explosion-proof enclosures. The d-c motor is constructed with either (or both) series and shunt fields located on the stationary part of the motor (stator) and an armature coil wound on the rotating part of the motor (rotor). Power is supplied to the armature by brushes which are held stationary and make sliding contact with the armature. The brushes requires regular and careful maintenance because worn or defective brushes will cause heat or arcing which can destroy the motor. D-c motors can be used as d-c generators when mechanical power is supplied to them by the rotating

Jan 1, 1981

"The Midvale. Plant of the United States Smelting, Refining and Mining Company, situated twelve miles south of Salt Lake City, consists of mills for concentrating lead-zinc ores and a custom lead smelter.The milling department includes a 475-ton gravity mill for ores from the United States Mines at Bingham, a 100-ton Huff electrostatic zinc plant and a 60-ton pilot flotation mill for differential separation of lead and zinc. The gravity mill and electro¬static plant are being replaced by a 600-ton differential flotation plant, now under con¬struction, for differential separation of lead, zinc and iron. This new mill will have cap¬acity for treating custom ores in addition to ores from the company's mines at Bingham.The smelting department is equipped to handle 1600 tons of charge per day through six blast furnaces, 48 inches by 160 inches at the tuyeres. All gases from both blast furnaces and roasters are filtered through baghouses, which remove the dust from the gases so effectively that even when the plant is running at full capacity no smoke can be seen coming out of the 450-foot brick stack handling rca2ter gases, nor out of the two shorter steel stacks which take the blast furnace gases. On this account the Midvale plant has come to be known as the ""smokeless smelter.""The blast furnace gases are filtered through 832 woolen bags, 33 feet 6 inches by 18 inches in diameter, and 1200 woolen bags, 28 feet by 12 inches in diameter."

Jan 1, 1925

By Richard A. Queeney, Lance G. Peterson

ESTIMATES of the stacking fault free energy of copper reported in the literature show an extensive divergence of results. Based on measurements of dislocation node radii, Thornton et al.7 find the lower limit of stacking fault energy to be 60 ergs per sq cm: Jossang and coworkers4 estimate the same value should be less than 40 ergs per sq cm. Assuming stacking fault free energy to be twice the coherent twin boundary free energy, Valenzuela8 reports 72 ergs per cm, while Inman and Khan2 cite a value of 24 ergs per sq cm. which can no doubt be accounted for by almost complete absence of interstitials in solution. However, the minute concentration was sufficient to permit observable recovery of dislocation damping. Assuming a dislocation density of 1010 CM -2 and an average loop length of 0.5 , a concentration of interstitials as low as 0.01 at. ppm is sufficient to reduce dislocation damping by more than a factor of ten. The concentration of interstitial solute atoms in Ferrovac E-0.15 pct Ti was thus estimated at 0.01 at. ppm < (C + N) < 2 at. ppm. The absence at elevated temperature of strengthening due to interstitials, Fig. 1, was therefore anticipated in the titanium alloy. The temperature dependence of the flow stress below 300°K was unaffected by addition of either titanium&apos; or zirconium.&apos; Observed, however, was an initial difference in the absolute value of the flow stress below 320oK, Fig. 1. Grain size may account for the difference; the grain diameter of Ferrovac E was 30 to 45 µ and that of Ferrovac E-0.15 pct Ti 65 to 90 µ. Although second phase particles in the form of titanium carbides and nitrides precipitated in the Ferrovac E-0.15 pct Ti alloy, the spacing was too large to produce any strengthening effect. The mechanical properties measured, therefore, were inherent to the bcc lattice. 1W. C. Leslie and R. J. Sober: Trans. ASm, 1967, vol. 60, pp. 99-111. 2 H. Conrad: Journal of Metals, 1964, vol. 16, pp. 582-88. 3 A. S. Keh and W. C. Leslie: Materials Science Research. H. H. Stadelmaier and W.W.Austin, eds., vol. 1.pp. 208.50, Plenum Press, New York, 1963. 4A. S. Keh, Y. Nakada, and W. C. Leslie: Dislocation Dymmics, Rosenfield, Hahn, Bement, Jr., and Jaffe, eds., pp. 381-406, McCraw-Hill Book Co., New York, 1968. &apos;W. J. Bratina, J. T. McCrath, and H. E. Rosinger: Can. Met. Quart., in press. 6 W. J. Bratina, J. T. McGrath, and D. Mills: Suppl. Trans. Japan Inst. Metals. 1968, vol. 9, pp. 436-43. &apos;H. E. Rosinger and C. B. Craig: Can. Met. Quart., In press. %. Mills. J. T. McGrath. and W. J. Bratina: ScriptaMet,, 1968, vol. 2, pp. 311-13. The purpose of this note is to present the results of a direct measurement of the stacking fault free energy in copper. The present method avoids both the question of interaction forces of nodal dislocations and the assumption that the coherent twin boundary free energy is one-half that of a stacking fault. Fig. 1 shows a transmission electron micrograph of a stacking fault intersecting a high angle grain boundary in copper: Fig. 2 is a schematic representation of the intersecting interfaces. To produce the specimen, pure copper was rolled to 0.002 in. thickness and annealed for several hours at 875°C. These foils were strained in tension to l04 µ in. per in., and rean-nealed to 8 min. Recrystallization and/or grain growth were not observed during the second anneal, indicating that intersections such as Fig. 1 are equilibrium configurations. Many such stacking faults were observed, but few were noted as intersecting grain boundaries in well-illuminated areas. The intersection of Fig. 1 was well away from the specimen edge. Since similar defects have not been observed in fully recrystal-lized and annealed copper, it is felt that this defect is due to the tensile straining. Electron transmission

Jan 1, 1970

By E. A. Steigerwald

E. A. Steigerwald (Thompson Ramo Wooldridge, Inc.1— he authors&apos; results clearly indicate that cracking can be produced by the hydrogen pressure developed during a charging operation. This type of cracking or blistering has also been observed in polycrystalline materials24"28 when the charging conditions are sufficiently severe and is often referred to as irreversible embrittlement since it cannot be removed by a baking treatment. There are additional data, however, which must be considered before a pressure theory can be generally employed to account for all failures which occur as a result of hydrogen. In many cases, hydrogen embrittlement in a tensile test or in delayed failures under static loads is a reversible phenomena which cannot be simply explained on the basis of preexisting cracks generated by the charging operation. It is this aspect of the problem which has prompted many investigators to seek mechanisms other than hydrogen pressure to explain their results.24&apos;n728 Fig. 15 indicates an example where, under specific experimental circumstances, hydrogen embrittlement can occur at liquid nitrogen temperatures. In this case, which has been previously decribed,&apos;&apos; specimens were charged with varying quantities of hydrogen, immediately quenched, and tested in liquid nitrogen (-320°F). A companion set of identical specimens were charged, aged at 300°F to remove the hydrogen, and also tested at -320°F. When the current density was greater than lo-&apos; amp per sq in., embrittlekent occurred in both sets of specimens, indicating that cracking had occurred during charging and the embrittlement, as in the case of Fe-Si single crystals, was irreversible. At current densities between approximately 103 and lo-&apos; amp per sq in, the embrittlement was present only for those specimens which contained hydrogen during the testing sequence. The embrittlement was therefore reversible with respect to the aging and charging operations. Since extensive hydrogen movement would not be expected at -320°F, it is difficult to reconcile these data with a mechanism which requires pressure and pressure dependent growth of preexisting cracks. There are other features of hydrogen embrittlement such as the reversibility of the incubation time for delayed failure with respect to applied stressg0 and the influence of prestraining31 which are also difficult to explain using a pressure model. Any general mechanism of hydrogen embrittlement will have to consider the reversible aspects of the embrittlement data as well as the irreversible portion which has been clearly presented for the Fe-Si crystals and which is consistent with a pressure model. A. S. Tetelman and W. D. Robertson (authors&apos; reply)—he authors agree with Dr. Steigerwald that a general mechanism of hydrogen embrittlement must be applicable in all cases where embrittlement occurs. Dr. Steigerwald&apos;s experiments were performed on an iron alloy which has an extremely complex microstructure, and therefore does not lend itself to the direct and detailed observations that can be made in Fe-Si. The change in the characteristics of cracks as a consequence of annealing at 300°F is not really known in detail but it is probable that stress-relaxation (blunting) occurs, dislocations produced near the crack tips will be pinned by carbon atoms, and hydrogen will be lost to the atmosphere. Any, or all of these effects of annealing will alter the ease with which a crack subsequently propagates under applied stress. A quantitative treatment of the problem must take these effects into account. Since diffusional processes are presumably eliminated at -320°F, the general mechanism proposed by Dr. Steigerwald&apos;s colleagues cannot be operative at this temperature. A detailed discussion of the general&apos; inapplicability of this mechanism has been presented elsewhere. However, the data presented by Dr. Steigerwald in his discussion can be explained in terms of a pressure model. Crack propagation under internal pressure P and applied stress occurs when where is the total energy expended in creating new surface area and by plastic work at the crack tip. The total crack length increases with increasing current density, since we have shown that it systematically increases with hydrogen concentration and Dr. Steigerwald has shown that hydrogen concentration increases with current density. For large L (high current density) Eq. [I] can be satisfied even if P = 0 and the embrittlement process does not require the presence of hydrogen. Specimens charged at a lower current density will con-

Jan 1, 1963

By David Baker

A Discussion of the Paper of David Baker, read at the Lake Superior Meeting, September, 1904. (Washington Meeting, May, 1905.) MR. JOHN J. PORTER, Chicago Ill. (communication to the Secretary*) :-Mr. Baker&apos;s account of his experiences with stock-distribution has been particularly interesting to me, as it confirms the opinions which I had formed concerning the rapid failure of linings in several furnaces that have recently come to my notice. These furnaces, four -in number, are of modern construction, having been built or remodeled within the past two years, and are equipped with a well-known type of skip-hoist and double-bell charging-apparatus. In every case, a hot spot has developed within a few months after blowing-in, which has already compelled relining in two cases, and the probabilities are strongly against a long campaign in the other two. Since the hot spot in each case appeared in a position approximately opposite to the skip-hoist, and since the sizing, mentioned by Mr. Baker, is very apparent, it would seem as though there could be no doubt concerning the cause of the trouble. Nevertheless, there are some who cannot see it in that light; for the managers of two of these plants, at least, do not admit the existence of bad distribution, and have satisfied themselves by putting in cooling-plates, thickening the lining of the in-wall, and changing the brand of the fire-brick used for the construction of the walls. From observations of the clumping-action of the skip-hoist, and from subsequent inspection of the stock-distribution in the furnace itself, I arrived at the conclusion, some time ago, that no system of filling could be perfectly satisfactory where the stock is dumped into the hopper from one side, also that some

Mar 1, 1905

By P. Bolsaitis, L. Skolnick

A model of metallic solutions is postulated which explains the energy of formation of alloys on the basis of changes in electron density around solute and solvent atoms and changes in pairwise interactions between atoms. The model is based on the Wigner-Seitz cell model of metals, with the electronegativities of the metals as the parameter for the electron-attracting power of the constituent atoms. In contrast to models based on the description of cohesive energy in terms of pairwise interactions only, which require an empirical, adjustable correction parameter to the Berthe-lot relations in order to predict negative energies of formation, the electron cell model accounts for both negative and positive energies on the basis of parameters of the pure components. Calculated heats of mixing based on published parameters of the pure metals are found to compare favorably to experimental values, despite the absence of any adjustable parameters in the model. THE formulation of an "exact" quantum mechanical model for the energy of cohesion of metals reduces ultimately to the many-body problem and for a complete solution would require the knowledge of wave functions and energy levels of all the particles in the system. The case of alloys is further complicated by the fact that the potential fields around the constituent atoms are different and the matching of boundary conditions in terms of the resulting wave functions is still an unresolved mathematical problem. It appears that in spite of the numerous investigations that have led to an elucidation of many properties of the metallic state, the formulation of the Hume-Rothery rules in 1931 marks the lone accomplishment toward simple, qualitative prediction of the energy of formation of alloys. More recently Friedel&apos;&apos; and Arafa have utilized the modern concepts of the electronic structure in metals in combination with the Hume-Rothery rules to arrive at quantitative estimates of the energy of formation of alloys with low solute contents. The relative success of the Hume-Rothery rules and Friedel&apos;s and Arafa&apos;s studies encouraged broaching the subject of formulation of a model based on realistic physical parameters and of conceptual and mathematical simplicity that could be applied to alloys regardless of concentration. On the basis of the free-electron theory, the cohesive energy of pure metals can be expressed as a function of "valence" (number of free electrons per atom), lattice parameter (or density), and the ioniza-tion energy. In addition to the electronic contributions to cohesion, one has to consider the pairwise exchange interaction energy between neighboring ion cores and the contribution from van der Waals forces. The energy changes upon alloying are viewed as resulting primarily from a redistribution of electron densities around the ions (a simplification of the more basic concept of a change of the wave functions of the electrons in the presence of a perturbing potential field). In addition there is a change in the pairwise interactions between neighboring ions which is usually the only factor taken into account in commonly used adaptations of the quasichemical theory. The electronegativities of the metals forming the alloy are used as the measure of the electron-attracting power of the ions in the alloy and the difference in electronegativities as the driving force for changes in electron energy on alloying. The interplay of pairwise interactions and electronic forces results in positive or negative energies of formation of alloys. Results obtained for systems to which the free electron model is best applicable are in good agreement with experimental values. 1) COHESIVE ENERGY OF METALS IN TERMS OF THE ELECTRON CELL MODEL The simplest physical model of a metal is that of a lattice of positive charges immersed in a sea of uniform, negative charge distribution represented by the

Jan 1, 1969

By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,&apos;~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro&apos;~ suggested that the strain E can be deduced

Jan 1, 1970

By H. H. Podgurski, F. N. Davis

In silver alloys containing less than 0.2 wt pet Cu. the reaction 9 + 1/2 0, = CuO(s) was found to proceed to equilibrium between 700o and 808oC. From measurements of the equilibrium dissociation pressures of the CuO at several temperatures, the differential heat of solution and the activity coeflicients for copper in silver were calculated. These values were found to be in reasonable agreement with those calculated from data appearing in the literature. A metastable "copper oxide" with an atom ratio of oxygen to copper as high as 1.7 was formed by internal oxidation at 300°C of these same dilute Ag-Cu alloys. No anomalous behavior was noted in the temperature dependence of oxygen solubility in silver. The solubility minima between 300" and 800°C reported several years ago can be accounted for, at least in part, by reactions with trace impurities, such as copper. Cold-worked siloer exhibits an enhanced permeability to oxygen. THIS investigation was undertaken because of our interest in interactions between solute and lattice defects in metals. The reason for the choice of the O-Ag system for study is the anomaly in the solubility of oxygen in silver reported by Steacie and Johnson1 in 1926, specifically that isobars between 100 and 800 Torr show solubility minima at 400°C. It was also claimed that the copper impurity in the silver was not responsible for the minima. Recently, Eichenauer and Müller2 proposed that surface adsorption might have been responsible for this solubility anomaly, but no adsorption isotherms are available to check the pressure and temperature dependence observed at the low temperatures. Surface-tension measurements on silver made by Buttner, Funk, and udin3 suggest that a considerable fraction of a monolayer of oxygen exists on silver at 922°C and at an oxygen pressure of 150 Torr. To account for the pressure sensitivity reported by Steacie and Johnson1 at 300°C, the oxygen bound to the surface at 922°C cannot be considered relevant; the existence of a surface layer at 300°C characterized by a lower energy of binding would be required to explain the effect. All of our attempts to detect an interaction of this type with surface sites have failed. In this investigation we have not been able to associate the dissolution of oxygen in silver with a dislocation interaction. Evidently, severely cold-worked silver does not contain a sufficient number of trapping -sites for oxygen. Indeed, our work shows that oxidation of trace impurities in the silver was probably responsible for Steacie and Johnson&apos;s results. In addition, we have been able to establish the nature of the reaction with copper impurity in silver by thermodynamic considerations. EXPERIMENTAL PROCEDURE Measurements of both the internal oxidation rates and the solubility were made volumetric ally in a system equipped with a gas burette, a mercury manometer, a McLeod Gage, and a mass spectrometer. The silver and the silver-alloy samples were protected from contamination by mercury vapor from our pressure gages by suitably placed refrigerated (-78°C) traps. Silica reaction vessels were employed for experiments performed above 500°C. Spectroscopically pure gases were used in this investigation. The highest-purity silver used in the solubility measurements was 99.999 pet. By chemical analysis 2 ppm of Cu were found in this silver. The two Ag-Cu alloys used in this research were made up to 0.14 and 0.15 wt pet Cu starting with 99.999 pet Ag. An unexpected source of error was discovered in the course of the work. At temperatures near 800°C silver distilled from the hot silica reaction tubes into cooler regions of our system. Although the weight loss of silver from the sample was not important in itself, oxygen was being consumed by the silver distilled into the cooler part of the system to form a stable oxide phase from which the oxygen was not recovered. In a separate experiment conducted to determine the necessary correction, losses between 0.2 and 0.3 cu cm (stp) of 0, in 24 hr were measured at 810°C. On the assumption that the flux of silver from the vessel to form Ag2O de-

Jan 1, 1964

By R. E. Reed-Hill

A simple accurate graphical method for orienting fcc crystals using (111) slip traces on a single surface is described. Solutions placing the pole of the surface in a unit stereographic triangle are obtained using a Wulffnet, a (111) standard projection showing the four (111) planes, and a (111) standard projection ruled into unit stereogmphic triangles. The multiplicity of solutions is described in relation to this method. AN accurate, rapid single-surface technique for orienting fcc crystals, using (111) slip or twin traces, has been a matter of continuing interest, as evidenced by the periodic appearance of papers on this subject.&apos;-4 This note presents a new method possessing some advantages over those previously reported. It is an analog to the technique for hcp metals5 where the solution is based upon a stereographic rotation of the specimen surface on a (0002) standard projection that contains the planes of the possible features that might account for the observed traces. In the hexagonal solution, the axis of rotation is the basal-plane trace in the surface. In the fcc case, the axis of rotation is one of the observed ( 111) slip or twin traces. It has been observed that the solution is greatly facilitated if the indicated movements of the (111) traces during the rotation of the surface are plotted directly on a paper copy of a Wulff net as shown schematically in Fig. 1. The trace selected to represent the axis of rotation is assumed to fall at the north-south poles of the Wulff net. The directions of the other traces are then plotted as points at the proper angles around one-half of the basic circle of the net. The loci of points corresponding to the movements of these traces (directions) during a 90-deg rotation of the surface, about the polar axis of the net, are then easily and accurately drawn by following the appropriate small circles on the Wulff net. The solutions to the problem are obtained with the aid of a (111) standard projection of the (111) planes, see Fig. 2. This is normally a Xerox copy of a carefully drawn master made on high-quality tracing paper. The (111) standard projection is superimposed over the Wulff net and rotated about its center until the points of intersection of the loci of surface traces, drawn on the Wulff net, and the great circles representing the (111) traces, all lie along a common meridian of the Wulff net as demonstrated in Fig. 3. This latter great circle represents a possible position of the surface. The pole of this plane is then plotted on the (111) standard projection. Its location in a unit stereographic triangle may be readily obtained by superimposing (over the standard projection) another tracing paper (111) standard projection subdivided into unit stereographic triangles. The result of this last operation is shown in Fig. 4. MULTIPLICITY OF THE SOLUTIONS The maximum possible number of (111) traces on a single grain surface is four. Any one may be selected as the axis about which the surface is rotated. Corresponding to each such choice are three possible surface-pole orientations, related to each other by a simple 120-deg rotation about the pole of the (111) basic circle. This is a direct result of the threefold symmetry of the (111) standard projection. Since each of the four rotations will normally give a different set of three-pole positions, there are, accordingly, twelve possible solutions. Each of these twelve solutions places the surface pole in the same relative position in a stereographic triangle so that all are crystallo-graphically equivalent. Accordingly, only a single solution is required to obtain a basic orientation of the crystal. It should be noted, however, that the orientations obtained by reflecting* any of these twelve orien- *The reflected orientations may be obtained by a 90-deg rotation of the opposite sense to that shown in Fig. 1. This rotation places the correspond-ing trace loci in the lower hemisphere of the Wulff net rather than in the upper hemisphere. tations through the surface are also possible orientations that could account for the surface traces. Thus, a given set of four traces always corresponds to a pair of basic orientations related by reflection through the specimen surface. This ambiguity can only be re-

Jan 1, 1967

By R. A. Breitrick, J. N. Swinderman, J. J. Cooper, H. L. Bauer Jr.

The Robinson Mining District, near Ely, Nev., is one of the major porphyry copper districts in the world. Within the district is an eight mile long east-trending zone of altered porphyry, metamorphosed sedimentary rocks, and sulphide mineralization surrounded by Paleozoic limestone, dolomite, shale and sandstone, Tertiary volcanics, and Quaternary alluvium. Six major disseminated ore deposits have been exploited in this zone. About 20% of the district production has come from disseminated ore in metamorphosed sedimentary rocks found adjacent to altered quartz-monzonite porphyry. The following brief statements summarize some of the relations between porphyry alteration, metamor-phism, and mineralization: 1) Disseminated copper ore does not occur in unaltered porphyry or in m-metamorphosed sedimentary rocks. 2) Sedimentary rocks have been only weakly metamorphosed where intruded by unaltered porphyry. 3) Intensely metamorphosed sedimentary rocks are found only adjacent to altered porphyry. 4) Many hydrothermal minerals are common to both altered porphyry and adjacent metamorphosed sediments. 5) Disseminated ore is found in altered porphyry and adjacent metamorphosed sedimentary rocks. 6) In general, there is a direct correlation between grade of ore in porphyry and copper content in the adjacent rocks. 7) Chemical changes in the altered porphyry and metamorphosed rocks appear to be related. The foregoing relations support a hypothesis that the porphyry alteration, the metamorphism of the sedimentary rocks, and the ore deposition were all part of a continuous hydrothermal process which probably closely attended the porphyry intrusion. The Robinson Mining District, most often referred to as the Ruth or Ely District, is located in eastern Nev. and is one of the major porphyry copper districts of the world. Production from 1908 through 1962 was nearly 250 million tons of ore averaging a little over one percent copper with a total metal value of nearly one billion dollars. The ore has been produced from six major disseminated-type deposits with the Liberty Pit deposit accounting for 70% of the total district production. Less than one million tons of base metal and gold ores have been produced from the replacement-type deposits of the district. Approximately 20% of the district production has come from underground mining operations; the pit ore has been mined with shovels and removed by train haulage, truck-train haulage combinations, truck haulage, and presently by a combination truck-skip system. Many of the ore deposits formerly worked by underground methods have been and are being exploited by open pit methods. (See Fig. I.) Two co.&apos;s have accounted for virtually the entire production from the district. In 1958 Kennecott Copper Corp. acquired the district assets of Consolidated Coppermines Corp. and is now the sole ore producer in the district. Present operations are confined to the Liberty Pit where 22,500 tons of ore averaging a little less than 0.8% copper is mined per day. Cutoff grade is 0.4% copper, and the stripping ratio is three to one. The ore is hauled by rail 23 miles to the McGill Reduction Plant where it is concentrated to about 20% copper. Molybdenite is recovered as a by-product in the mill. The copper concentrates are smelted in McGill, and the blister copper is shipped for refining to Balt. where gold, silver, platinum and palladium are recovered. The Robinson Mining District has been well known as a porphyry copper district for the past fifty years, but many geologists are unaware of the fact that a large portion of the production has come from disseminated ore found in metamorphosed sedimentary rocks. The scope of this paper describes the occurrences of disseminated ore in the various metamorphosed sedimentary rocks, and presents evidence for the hypothesis that these ores are genetically, spacially, and coevally related to the disseminated ore in the porphyry rocks. Publication of this paper was granted by the management of Kennecott Copper Corp. A. H. James suggested and encouraged the writing of the manuscript. Special mineralogical and spectrographic analyses were performed by the Kennecott Research Center. The deposits of the district have been studied by many geologists since the turn of the century, and

Jan 1, 1964

By D. T. Peters, J. C. Bisseliches, J. W. Spretnak

The pain boundary relaxation phenomenon in high-purity copper, 0FHC copper, and a precipitation-hardenable alloy o-fCu-2 uit pct Co has been studied by internal ,friction and elastic aftereffect techniques. The data were analyzed by assuming the broad distribution of relaxation times observed obeys a lognormal distribution law which enables calculation of the relaxation strength. Grain size had no effect on relaxation strength, although the peak width increased with increasing grain size and decreasing temperature. A double grain boundary peak was produced in high-purity copper by annealing to produce secondary recrystallization. The activation energy measured for 99.999 pct Cu is 37.5 * 3 kcal per mol and 46.5 kcal per mole for OFHC copper. A small peak in the Cu-Co alloy at about 220°C at 1 cps was deduced to be the grain boundary peak. Its height increased and its activation energy decreased with increasing aging time. Except for erratic peak positions the observations were consistent with the theory of pain boundary sliding. BEFORE the mechanism of the grain boundary internal friction peak in metals can be satisfactorily explained, the detailed characteristics of the relaxation process must be documented. Of interest are the effect of grain size on relaxation strength, the high-temperature background, and peak width and position. The effect on the grain boundary peak of a precipitate at grain boundaries and of the change in distribution of the particles with aging time must also be explained by any existing or forthcoming theory. The model which has received the most attention was proposed by KG&apos; and zener2 and proposes that the anelastic strain results from sliding of adjacent crystals at grain boundaries. The sliding is limited by the interlocking of grain corners. It follows, according to this model, that the relaxation strength is independent of and the relaxation time is proportional to the grain size. The proportionality between grain size, D, and relaxation time, t, has been confirmed by K&&apos; and Bisseliches . In this case, the internal-friction peaks of various specimens can be superimposed by plotting Q-&apos; as a function of the parameter vD exp H/RT where v is the frequency and H the activation energy. However, the data of Starr et 01.&apos; and Leak6 fit better to a parameter containing D to an exponent near two. A meaningful relationship is not always deducible from the shift of peak temperature with grain size. KG7 demonstrated that a twofold variation in grain size obtained by varying the amount of cold work followed by identical recrystallization anneals will cause a peak shift that is too large to be accounted for even by an exponent of two. Since the decreased grain boundary area existing with a larger grain size is exactly compensated for by an increased sliding distance, the relaxation strength should not decrease with increasing grain size. The height of the internal-friction peak has generally been observed to be rather insensitive to grain size as long as the average grain diameter does not approach the specimen diameter. Exceptions have been reported by Koster, Bangert, and Lang8 for copper, and by Leak6 for iron. The observations for copper could well have been confused by the presence df 0.3 pct0. The possibility that the peaks may simply be increasing in width with increasing grain size and that the relaxation strength, which is proportional to the area under the peak, may remain constant was not examined. his point has been checked in this investigation using high-purity copper. Atomic mechanisms to account for damping by sliding at grain boundaries have been proposed by KG7 and Mott. KG predicts the activation energy to be identical to that for self-diffusion. Mott&apos;s "island" model suggests the activation energy is nL where n is the number of atoms in an island and L is the latent heat of fusion per atom. Other authors have felt that a value equal to the activa-

Jan 1, 1964

R. Schuhmann, Jr. (Purdue University)— Fulton and Chipman&apos;s results on rate of silica reduction from slags are analogous in many was to the results of Parlee, Seagle, and Schuhmann10 on rate of alumina reduction from alumina crucibles. Both investigations have given comparably low rates of reduction and slow approaches to equilibrium. Accordingly, we may hypothesize that the rate-determining step is the same in both kinds of experiments; that is, oxygen diffusion across the stagnant boundary layer on the liquid-metal side of the interface between the liquid metal and the oxide phase (slag or solid oxide). I suggest that silica reduction involves the following consecutive steps: I) At the slag-metal interface: SiO2(slag) Si+ 20 II) Transport of oxygen from slag-metal to gas-metal interface: a) diffusion across liquid-metal boundary layer at slag-metal interface. b) convection within the body of liquid metal. c) diffusion across boundary layer at metal-gas interface. 111) At the metal-gas interface: C +O- CO (gas) Iv) At the graphite-metal interface: C (graphite) -C At steelmaking temperatures it is reasonable to assume that equilibrium is attained in all three chemical reactions (I, 111, and IV) right at the respective interfaces. Convection within the stirred liquid metal (step IIb) is also rapid. Transport of Si and C should be orders of magnitude easier than transport of 0, because of the relatively high concentrations of Si and C. Accordingly, we might expect the overall reaction rate to be determined by boundary-layer diffusion of oxygen, either IIa or IIc. Fulton and Chipman&apos;s demonstration that bubbling CO through the system had no major effect on reaction rate indicates that IIc is not the slowest step. Therefore, it becomes logical to estimate the maximum rate for step IIa and to compare this theoretical estimate with Fulton and Chipman&apos;s experimental data. If oxygen diffusion across the liquid metal boundary layer at the slag metal interface (step IIa) is rate-determining, In this equation, dn sio, /dt is the rate of silica reduction in moles per sec,A is the area of slag-metal interface in sq cm, Do is the diffusivity of oxygen in sq cm per sec, 6, is the boundary layer thickness in cm, c,* is the oxygen concentration right at the slag-metal interface in moles per cubic cm, and co is the oxygen concentration in the body of the liquid metal, also in moles per cubic cm. Equilibrium data" on the silicon deoxidation reaction in liquid iron and steel at 1600°C indicate that the oxygen contents of the liquid metal in Fulton and Chipman&apos;s experiments at 1600°C probably fell in the range of 0.5 x10-3 x10-3wt pct. That is, the maximum conceivable value of co*-co for the system under consideration was on the order of 10"5 mole oxygen per cubic cm. On the basis of previously published data,1O,11 it is estimated that Do/0 will fall somewhere in the range from 10-3 to 10-1 cm per sec. The surface area A in Fulton and Chipman&apos;s experiments was approximately 20 sq cm, and the weight of metal involved was about 500 grams. Combination of all these figures with the above rate equation leads to an estimate that the rate of silica reduction should fall within the range from 0.002 to 0.2 wt pct Si per hr. This estimate is consistent with the experimental data. For example, Fulton and Chipman&apos;s Fig. 2 shows a change of about 0.3 pct Si in 10 hr, corresponding to an average rate of 0.03 pct per hr. According to the proposed hypothesis, increasing the temperature will increase the reaction rate ill two ways: 1) by increasing oxygen diffusivity and 2) by increasing the oxygen concentration (oxygen solubility) in the liquid metal. The combination of these two effects accounts for the high value of the observed activation energy. Summarizing, I propose that the rate of silica reduction, like that of the carbon-oxygen reaction, is diffusion controlled and that low oxygen concentration in the liquid metal is the major factor accounting for the very low observed rates of silica reduction. John Chipman (author&apos;s reply)—The authors thank Professor Schuhmann for his interesting contribution. His proposed explanation may well prove to be the correct one. There is clearly a need for much further experimental work on this problem, and further research is in progress.

Jan 1, 1961

By W. B. Gogarty

The reported decreases in water mobility do not seem unusual in view of non-Newtonian fluid properties. Shear stress vs shear rate diagrams have been reported for other solutions of water-soluble polymers. Some of these polymers are similar to the type mentioned by the author. Generally, the shear stress-shear rate is a non-linear function for these solutions. Data for plotting apparent viscosity vs shear rate can be obtained from this function. Apparent viscosity is defined as the ratio of shear stress to shear rate at a given shear rate. When plotted, the apparent viscosity decreases with increasing shear rate. This behavior is typical of a pseudoplastic fluid. For some water-soluble polymer solutions, the apparent viscosity decreases more than 50 times while the shear rate increases 1,000 times. Thus, viscosity of a pseudoplastic fluid only has meaning at a specified shear rate. Results of Fig. 1 could be explained in these terms. Viscosities measured in the Ostwald viscometer represent values at a given shear rate. Some average shear rate is affecting the polymer solutions while flowing through the core. This average value fixes the apparent viscosity as long as the flow rate remains constant. Viscosities measured by the two methods will be equal if shear rates are the same. The results indicate that shear rate in the core is lower (higher apparent viscosity) than in the viscometer. In the paper by Johnson, Bossler and Naumann, the relative permeability is independent of viscosity ratio. Thus, the relative permeability with respect to water flow at residual oil should be independent of the flowing phase viscosity. Polymer solutions will appear as Newtonian fluids The discussion emphasizes the nature of the "resistance factor effect" as discussed in the paper. Repeated anomalies arising in hundreds of experiments led us to the conclusion that non-Newtonian flow is not the only factor. Several of the key anomalies are as follows: 1. Measured viscosities over a range of shear rates from <1 sec-&apos; to 1,000 sec-&apos; do not account for but a minor fraction of the R observed in cores when compared in similar shear-rate ranges. 2. The slope of R vs flow rates in cores is always different from that expected from viscometer shear-rate measurements as shown in Fig. 2. in a core, the level of viscosity being fixed at a given flow rate. With these conditions, the definition of resistance factor R by Eq. 2 is simplified to Since , is constant with rate, R becomes a measure of the apparent viscosity in a core at a given flow rate. Variation in flow rate could easily account for the changes of R shown in Fig. 5. Also, this points to the fallacy of assuming R to be a unique parameter. The constant resistance factors at different flooding velocities appear to be in disagreement with the above discussion. The author furnishes Fig. 2 to support his arguments. As shown, the resistance factors remained substantially constant in the two cores over a considerable range of flooding velocities. However, in the 73-md core, the factor increases at lower rates. This behavior agrees with known characteristics of some pseudoplastic material. These materials act both as Newtonian and as non-Newtonian fluids in different regions of shear rate. Some exhibit first Newtonian, then non-Newtonian, finally, Newtonian character. Others are first non-Newtonian and then Newtonian. This latter type would explain the results with the 73-md core. The Fann-instrument results are not significant since shear rates in the core may be much different than with the viscometer. The higher resistance factor at high rates in the 150-md core is more difficult to explain. The greater resistance at increased flow rates could be attributed to what might be termed temporary bridging. As envisioned, changes in polymer configuration occur at the higher energy associated with the increased flow rate. These changes could cause less effective passage of polymer through the core. Correspondingly, increases in pressure drop will occur. These will be interpreted as higher resistance factors. 3. Most polymer solutions are non-Newtonian and many are more shear-rate sensitive than the polymers in question, yet only a very few polymers demonstrate useful R values. Gogarty&apos;s assumption that viscosities in cores and vis-cometers will be the same if measured at the same shear rate is only valid if non-Newtonian rheology is the only parameter. The experimental evidence does not validate this assumption. The anomalies observed in the equilibrium displacement experiment shown in Fig. 5 are not explained on the basis of varying flow rates since the rates were held constant. M

Jan 1, 1965

By J. S. Marsh

OPPORTUNITY to pay tribute to the memory of Professor Henry Marion Howe is a strenuous assignment as well as an honor. Upon recalling Howe lecturers and lectures of the past 25 years, glancing over the list of those earlier, and rereading Howe&apos;s books, I arrive at several conclusions: 1—Many lecturers either worked under or knew Professor Howe. 2—It is virtually impossible to pick a subject on which Professor Howe did not touch. 3—There is precedent for a technical paper based upon pursuit of a single subject. 4—There have been listening lectures and reading lectures. There is solid comfort only in 2: the subject field is wide open. I did not know, nor even ever saw, Professor Howe, so can supply no fitting reminiscence. As a college student I was dimly aware that he counted among the giants. Fuller appreciation of his stature came with reading his books and papers, growing acquaintance with some of his associates, and the intrinsic dignity of the climax of the Annual Meeting, beginning at four o&apos;clock of a Thursday afternoon in the auditorium of the Engineering Societies Building in New York. As for producing the technical paper sort of thing, it is my lot to have reached an age and assignment such that to do so would be to filch information from those who did the work and whose story is theirs to tell; for this I have no enthusiasm. As for the final conclusion, Professor Howe was one of the chosen few so highly expert at expository writing that he could produce a lecture or paper that reads as though it would also have listened well. One of his tricks was the free use of words not ordinarily part of the technical vocabulary, provided that such words were likely to communicate most precisely what he had in mind. How wonderful it would be for all who must read reports by the ton if ability at exposition could be taught with the effectiveness open, say to, differential calculus! Perhaps Professor Howe should be required college reading even if for no other reason than to prove that technical writing need be neither dull nor diffuse. My assignment is clearly still strenuous. Another point to consider is the fact that metallurgy is now so tremendously diversified that hope of finding a topic of universal appeal is negligible, even if one were competent enough to be permitted free choice. That which follows is, therefore, a compromise composed of necessity and of the obligation to attempt to avoid boring to slumber those of you who are not especially interested in the general subject chosen. The Iron and Steel Div. is now essentially a process metallurgy division, heavily concerned with the smelting of iron and the making of steel. The American Iron and Steel Inst. figure for present steel capacity of this country is 125,828,310 net tons; how this is divided among processes is indicated by the production totals for 1953, shown in Table I. The glamor girls and boys make the front page and so it is with steelmaking processes. If there is an Antarctic Daily Bugle, it undoubtedly has carried stories of revolutionary development, such as oxygen processes and vacuum melting, and stories of the incomparably rosy destiny of electric arc melting. All such certainly have their place and their future; meanwhile, it is the sturdy and old reliable open hearth that accounts for the bulk of production reported back on the financial page, and it is the old reliable that is most likely to continue to account for the bulk for some perfectly sound raw material, technologic, and economic reasons. This, plus the fact that next year marks a centennial (for it was in 1856 that Frederick and William Siemens conceived the regenerative open hearth), is reason enough to talk about open hearth furnaces, but is not the real one. The real reason is that in some years of association with open hearths, I have accumulated—in addition to a genuine liking and respect for them—certain odds and ends of fact and fancy that this lecture provides a unique chance

Jan 1, 1956

By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper&apos; that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By H. S. Thomsen, W. C. Duesterhoeft, R. E. Hartline

The attenuation and phase shift which formations produce in the electromagnetic field of an induction-type electrical well-logging instrument are great enough to substantially affect the response of the tool to formation conductivity under normal logging conditions. The application of the general equations for the propagation of an electromagnetic field in a conductive medium to the transmitter-receiver coil pair of an induction-logging-tool coil system gives an expression for the response which properly takes the propagation effects into account. A comparison of a calculation of this type with the response computed from the commonly used geometric factor concept, which does not include the propagation effect, leads to a factor Go representing the ratio of the responses computed by the two methods. The value of Go decreases not only with increasing formation conductivity, but also with increasing transmitter-to-detector coil spacing. For a single coil pair with a 40-in. spacing, the value of Go is 0.972 in a 20-millimho/m formation. The value is reduced to 0.915 and 0.812 for conductivities of 200 and 1,000 millimhos/m. As a result, the basic signal generated by the induction-logging coil system is not linearly related to formation conductivity as expected from the geometric factor concept. A uniform conductivity scale can be obtained only by adding a suitable nonlinear element to the recording system. The addition of auxiliary coils, having spacings less than the main-coil span, to achieve focusing results in an even greater departure of the basic signal from linearity with conductivity. The solution of the field equations near the interface between two formations of different conductivity gives the curve shape on an induction logging tool in crossing the interface. The addition of auxiliary coils to achieve focusing can add anomalous character to the curve shape in crossing the interface, which might be mistaken for lithological detail. Preliminary calculations which include the propagation effects in the determination of the conductivity correction for thin beds lead to correction factors which are substantially smaller than those obtained from geometric factor considerations. It is apparent that thin-bed corrections derived from geometric factor calculations are of doubtful validity. INTRODUCTION Although the electromagnetic induction type of electrical well log has been used for a number of years and has gained general acceptance in quantitative well-log interpretation, no technically complete investigation of the mechanism and of its operation has been published. The studies which have been presented are based upon the premise that neither the shape nor the intensity of the induction field of the logging tool is in any way affected by the electrical characteristics of the formation. From the inception of induction logging it has been recognized that under some formation conditions the performance of the instrument could be expected to be substantially different from that predicted by the simplified analysis. This anomalous performance has been called "skin effect" since it is the result of the same phenomenon which causes high-frequency alternating currents to flow only near the surface of metallic conductors. In the range of conductivities encountered in the sediments, the formation actually does not exhibit the sharply defined conducting "skin" shown by metals. The gradual modification of the distribution of the currents in the formation, produced by the induction field of the logging tool, is the direct result of phenomena associated with the propagation of the electromagnetic field through the formation. Therefore, it can be much more appropriately described as the "propagation effect". One purpose of this paper is to review the results of a solution of the equations for the performance of a single transmitter-receiver coil pair induction-logging system which takes into account the propagation effect, showing the manner in which the tool performance established by this analysis differs from that derived from the less comprehensive analyses currently in use. PRINCIPLE OF OPERATION OF THE INDUCTION LOGGING INSTRUMENT The high-frequency alternating current which is maintained at a constant value in the transmitter coil

By C. D. Stahl, S. M. Farouq Ali, W. E. Culham

One- and two-dimensional mathematical models have been developed that simulate transient, two-phase flow of hydrocarbon mixtures in porous media in a manner that accounts for interphase mass transfer. Numerical simulations of one-dimensional depletion-drive experiments using a two-component hydrucarbon fluid were used to establish the validity of the mathematical models. In addition, the experimental and numerical data were used to demonstrate that production rate had a relatively insignificant effect on the recovery of individual hydrocarbon components from the experimental system, and that attainment of equilibrium between phases is possible for a wide range of liquid and vapor velocities in reservoirs containing light hydrocarbon fluids. Results of some two-dimensional numerical simulations are also presented. INTRODUCTION This study was undertaken to develop a mathematical model that would simulate transient, two-phase flow of hydrocarbon mixtures in porous media under conditions that result in interphase mass transfer and to test the validity of the assumptions used to set up the model. In addition, the study was designed to determine if production rate influences the recovery of individual hydrocarbon components from reservoirs producing by depletion drive. Two-phase flow in porous media, with interchange of components between the two phases, is important in many petroleum recovery processes. Studiesl-5 conducted within the last 3 years have outlined methods of solving multiphase flow problems incorporating mass transfer. Some of these studies have also indicated the importance of accounting for mass transfer under various producing conditions. An earlier work6 first demonstrated the importance of combining relative permeability data with equilibrium ratios in compositional balance methods. The mathematical model presented in this paper is formulated so that a phase behavior package, as described in previous papers,5,17 is not required as an integral part of the routine employed to solve for the primary dependent variables. The finite difference formulation is designed so that all the primary variables can be solved for simultaneously. This is accomplished by utilizing one basic set of equations. These innovations, which are in contrast to other models2,3,5 but are similar in some respects to the approach used by Taylor,l render the total problem computationally simpler than any of the previously referenced formulations. The mathematical model was developed by combining Darcy&apos;s law with a continuity equation for each hydrocarbon component. The principal assumptions invoked in the formulation were (1) that capillary forces and diffusional effects are negligible, and (2) that thermodynamic equilibrium exists in the reservoir at all times. No assumption as to the type of vaporization process was made in formulating this model. Experimental data were required to complete this study. These were generated by conducting several depletion drive experiments. The experimental apparatus consisted of a sandstone core enclosed in a pressurized casing. The apparatus was designed in such a manner that the core could be charged with a liquid hydrocarbon mixture and depleted at different production rates. The experimental tests were designed to determine the effect of production rate on component recovery. In addition, direct comparison of experimental and mathematically predicted

Jan 1, 1970

By N. S. Stoloff, K. R. Jordan

The temperatwe and grain size dependence of the mechanical avoperties of ordered and disordered Fe-49 pct Co-2 Pct V were investigated. The yield and flow stresses obeyed the Hall-Petch relationship u = ai + kd-&apos;I2. Ohdering reduced the intercept stress cjj and raised the Petch slope, k, at all temperatures. Ordering also increased the temperatwe dependence of k. The ductile to brittle transition temperature increased with order and grair~ size. Cleavage fracture was nucleation limited and the fracture stress did not zlary linearly with d-&apos;". A quantitative test of the Cottrell-Petch fracture theory (and recent modifications which consider the influence of slip mode), demonstvated that this theory is not applicable to FeCo-V. COTTRELL&apos; and etch&apos; independently suggested that a criterion for cleavage failure at the yield point, a,, based on dislocation pileups at a grain boundary or other obstacle to dislocat.ion motion, is: aYYkd&apos;I2 1 opy [ll or, equivalently, aikz,d112 +k:)bpy [2] where a, and ky are the Hall-Petch intercept and slope, respectively, 2d is the grain diameter, P is a geometric factor dependent on the macroscopic ratio between shear and tensile stress, p is the shear modulus, and y is the true elastic surface energy. When the product of quantities on the left side of the equation is equal to or exceeds that on the right, cracks should be able to nucleate and propagate at the yield stress, as shown schematically in Fig. 1. Therefore a high intercept stress, high Petch slope, or coarse grain size favors brittleness. petch3 associated the existence of a ductile to brittle transition in ferrous alloys with the temperature dependence of ai. One of the earliest modifications of the Cottrell-Petch theory was presented by ~rmstrong,~ who derived an expression for transition temperature in terms of several measurable flow and fracture parameters. The latter paper was able to rationalize situations in which the transition temperature increases with decl-easing grain size, as in the case of molybdenum,&apos; and also suggested that Ppy should be a function of grain size as well as temperature. More recently Johnston et a1.6 and Smith and worthington7 have suggested that the temperature or composition dependence ol&apos; ky must also be taken into account if there is any cha.nge in deformation mode, as from wavy to planar slip, or wavy slip to twinning, with change in temperature or solute content. Armstrong %as suggested that for hcp metals changes in o;k,dw> o;k,d1/2< / is / ^^^^ / / y_______________________________________ d-"2 Fig. l—Schematic representation of grain size dependence of yield stress, cry, and fracture stress, CTF. Intersection defined by Cottrell-Petch equation. slip mode should be incorporated in the theory through changes in the critical resolved shear stress for the slip system which controls ky. The purpose of the present investigation was to critically test the modified677 Cottrell-Petch theory of fracture in the superlattice alloy Fe-49 pct Co-2 pct V, by studying the grain size dependence of the yield and fracture stresses over a range of temperatures, in conjunction with an investigation of slip mode and fracture behavior. Previous work has shown that long range order results in a sharp decrease in flow stress, a small increase in work hardening rate and a drastic upward shift in the ductile-brittle transition temperature of F~CO-V.~&apos;~ The only comprehensive study of slip character in this alloy has been reported in a preliminary account of the present investigation.10 EXPERIMENTAL PROCEDURE The experimental work was carried out on material produced from a 10 lb vacuum melted ingot, of composition 49.32 wt pct Co, 2.09 wt pct V, balance Fe. 30-mil thick sheet samples with a 1; in. gage section were machined from cold rolled stock. The degree of cold work ranged from 85 pct for the finest grained samples to 5 pct for the coarsest grain size. Details of ingot fabrication are reported elsewhere." Equi-axed grain sizes in the range 12.7 to 75.4 p were obtained by annealing for varying times at 850°C. (Re-crystallization annealing time, rather than temperature , was varied to control grain size to insure that samples of all grain sizes contained equivalent quenched-in vacancy and interstitial concentrations.) Grain sizes were measured by the line intercept method on several specimens of each grain size. Following recrystallization, all samples were disordered by quenching into iced brine.

Jan 1, 1970

By J. T. Norton, N. J. Grant, A. R. Chaudhuri

MOST of the recent work to establish the mech-anism of creep in metals at high temperatures has utilized aluminum as the experimental material. It was thought desirable to initiate an investigation of a hexagonal close-packed metal, because of the relatively simple slip system, and compare the observed deformation characteristics with those that have been observed for the face-centerd cubic metals. High-purity magnesium was chosen for this purpose, first, because its strength and other mechanical properties are similar to those of aluminum in the same temperature range, and second, because the existing equipment was ideally suited to observe magnesium during creep. It is proposed in this paper to present a pictorial and qualitative account of the changes that high-purity magnesium undergoes during creep at 500°F. The characteristics of deformation of aluminum described below have been observed by various workers and accounts of these may be obtained from the papers of Chang and Grant.&apos;- These characteristics are: slip, subgrain formation, grain boundary sliding and migration, fold formation, deformation bands, and kink bands. It is well known that in a flat magnesium specimen, slip on the basal plane (0001) in the [1120] direction results in the formation of straight bands on the surface of the specimen. Schmid and co-workers&apos; have shown that this system is operative in the temperature range of -185" to 300°C (-300° to 572°F). They have also shown that a second system, slip on the pyramidal planes {1071} or {1012} in the [1120] direction, is operative at temperatures higher than 225°C (437°F). Between 225° and 300°C (437" to 572°F), therefore, deformation by both these systems is expected. Bakarian and Mathewson5 confirmed the occurrence of pyramidal slip on the {1011} plane and found that it resulted in irregular markings on the surfaces of their specimens. Burke and Hibbard6 obtained evidence of pyramidal slip in single crystals of magnesium deformed at room temperature. Bakarian and Mathewson5 suggested that the irregular appearance of these bands was due to slip on both of the pyramidal planes occurring simultaneously but in the same direction, the close angular relationship between the planes making this process possible. Furthermore, since neither of these planes is close enough to the basal plane, slip on the latter does not exhibit the irregular appearance of slip bands resulting from pyramidal slip. Experimental Procedure High-purity magnesium, supplied by the Dow Chemical Co., was used in these experiments. The analysis was as follows: Al, 0.0002 pct; Mn, 0.0018; Fe, 0.0024; Cu, 0.0002; Sn, 0.001; Ca, 0.01; Ni, 0.0003; Zn, 0.01; Pb, 0.0005; Si, 0.001; and Mg, 99.972. The magnesium was supplied in the form of 1/2 in. diam rods. The specimens had an overall length of 21/4 in., the round ends being threaded to fit the specimen holders. The previously round 3/16 in. diam gage section of the specimen had two parallel flats machined on opposite sides for microscopic observation, yielding a test zone having the dimensions of lx3/16x7/64 in. The specimens were electrolytically polished (without prior mechanical polishing of the machined flats), in a solution composed of 375 ml of ortho-phosphoric acid and 625 ml of ethyl alcohol.&apos; The cathode was a stainless steel sheet bent so that the specimen was completely surrounded. The voltage for successful polishing was 1.5 v at 100 to 300 milli-amp current. Electropolishing for about 45 min sufficed to obtain a good metallographic surface on the specimens after they had been machined. The creep tests were performed under constant load, and two types of equipment were used. In the first, designed by Servi and Grant,V he specimens were beam-loaded, and a furnace could be lowered to surround the specimen. As the microstructural changes could not be observed during the course of the test, the tests had to be interrupted periodically by removing the specimen for microscopic examination. The second unit was a high temperature microscopy furnace designed by Chang and Grant.&apos; The furnace was fitted with an optically flat quartz window having area dimensions 1.25x0.5 in., so that the whole test portion could be viewed through it at magnifications up to x240. The metallurgical microscope had three mutually perpendicular axes of motion, and, in addition, it was possible to measure angular displacements by rotation of the eyepiece. It was thus possible to make precise observations of the specimen during creep, and micrographs could be taken by attaching a camera to the eyepiece of the microscope. The average grain size of the specimens that were tested was about 1 to 3 mm. This grain size could

Jan 1, 1954