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By Richard Miller

RECENT studies of creep have made it apparent that plastic deforma-tion may occur in metals under stresses less than the elastic limit as deter-mined from short-time tests. In summarizing conclusions drawn from creep tests by various investigators, Tapsell1 said: "It is evident that if a material has a true elastic range, the elastic limit must represent the maximum stress for no creep." The presence of a. definite elastic limit, represented in single crystals by a critical or threshold shearing stress, is claimed by Schmid2, Elam3 and others who have investigated the plastic deformation of single crystals. However, this "law of critical shearing stress" was deter-mined2 from short-time tests, and the measurement of the deformation was made with apparatus primarily designed to observe large amounts of plastic deformation, not to detect elastic changes. Experimental data recently obtained with highly sensitive instru-ments by A. W. Hanson4 on zinc and by Podaschowsky5 on rock salt indicate that the elastic range in single crystals is considerably narrower than formerly was supposed. Moreover, a theoretical possibility of permanent deformation, under the influence of even the smallest shear stress in single crystals above a certain temperature (Td), has been developed by G. I. Taylor6. This evidence seemed to warrant an examination of the elastic limit in large single crystals by means of creep tests. The first metal chosen for examination was zinc.

Jan 1, 1936

By Edward Capillon

THE problem of scrap is probably of greater importance inn the production of gold, silver and other precious metal alloys than is the case for base metals and alloys. Remelting of gold and silver scrap in the shop is always a costly process because it involves losses by oxidation of the base metals in the alloy with a consequent increase in the percentage of precious metal. This is most marked in the case of alloys containing the low-boiling and easily oxidized metals zinc and cadmium. Since it is. not generally feasible to assay every shop remelt it follows that the possibilities of lost values are large. So-called rolled gold and silver plate is made by soldering or welding the precious metal alloys onto base, metal. Such plate when defective must be sent to the refinery to recover the gold and silver values, thereby involving additional expense in the form of refining charges. It is obvious therefore that gold and silver alloy scrap is an important item in manufacturing cost and must be reduced to a minimum. The amount of scrap resulting from poor metal will depend on a number of factors in the manufacturing operations, not least among which is the melting and casting practice. The notes which follow are a summary of experiments performed at various times to determine what variables in melting and casting are influential in the production of sound alloys.

Jan 1, 1930

By J. M. Dahl, L. H. Van Vlack

STAFF: Editor, Gerhard Derge Associate Editor, Paul G. Shewman Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Post-President; Harold B. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. B. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of monuscripts is under the supervision of the following Publications Committees: Extractive Metollurgy Division: R. E. Grace, Chairman; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Healy, T. A. Henrie, R. D. Holli-day, C. E. O'Neill, C. S. Sami s, A. W. Schlech-ten, and Charles Shull . Iron and Steel Division: R. D. Pehlke, Chairman; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Tuckdogon, L. H.Von Vlack, and J. M. Uys. Institute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Chairman; M. R. Achter, G. F. Bolling, J. O. Brittain, G. P. Conard, II, L. A. Girifolco. G. T. Hahn, J.P. Hirth, L. Himmel, G. T. Horne, George Krauss, C. F. Leitton, Jr., J. D. Livingston, R. D. Monning, H. M. Otte, S. V. Radcliffe, R. E. Reed-Hill, H. C. Rogers, O. Sherby, M. T. Simnod, G. R. Speich, E. A. Steigerwold, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Walton, H. W. Weart, W. W. Webb, and D. WiIsdorf. Published monthly by the American lnstitute of Mining, Metollurgicol, and Petroleum Engineers, Inc., 345 East 47th Street, New York, N. Y. 10017. Telephone PLAZA 2-6800. Subscription $30 per year for non-AIME members in United States and North, South, and Central America; $32, foreign; $7.50 for AlME members. Single copies, $6.00, single copies foreign, $6.50. The AlME is not responsible for any statement mode or opinion expressed in its publications . . . Copyright 1965 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AlME New York . . . Indexed in Engineering Index, lndustrial Arts Index, and Chemical Abstracts . . Second class postage paid at New York, N. Y., and Ann Arbor, Mich. Volume 233, Number 1.

Jan 1, 1965

By Nicholas J. Grant, H. C. Chang

TRANSCRYSTALLINE fracture surfaces of the cleavage type have been examined by microscopy and X-rays for several metals.' These investigations revealed that the fractured surfaces were not flat and invariably had cleavage and other deformation markings on them. On the other hand, the study of inter crystalline fracture surfaces has been limited. Perryman, in a recently published paper on the inter crystalline fracture of ß-brasses,' found that a thin layer of heavily deformed metal was invariably associated with these surfaces. Furthermore, the thickness of this layer was found to depend on the orientation of the grain boundary surface with respect to the applied stress. The mechanisms of grain boundary sliding and intercrystalline fracture have been presented in two previous papers,which described certain aspects of the deformation of a 20 pct Zn-A1 alloy. It is the purpose of this paper to present some observations on the structure of intercrystalline fracture surfaces and to correlate the structure of such surfaces with the mechanism of intercrystalline fracture. Experimental Techniques—The high purity 20 pct Zn-Al alloy was generously supplied by the Research Laboratories of the Aluminum Co. of America. Two sizes of specimen were used; the first had two parallel flat surfaces of dimensions 1x0.17x0.09 in. and the second was round with a 0.25 in. diam. A grain diameter of 1 to 3 mm was obtained by annealing the specimens at 1000°F for 24 hr. The specimens were then air cooled. The specimens were subjected to creep at 500°F and 2300 psi. The rupture times ranged from % to 3 hr, with one room temperature tensile test. It has been mentioned previous1y" that the intercrystalline fracture surfaces of this alloy, when tested under the conditions given above, are sharply defined. In the optical examination of the fracture surfaces, whenever possible, magnifications of at least X250 were used. The locations of the regions examined, both optically and by X-rays, were selected to give several fracture surface orientations with respect to the stress axis and to the specimen surfaces. This was possible for the X-ray studies since the grain diameters were large compared to the X-ray beam. A film to specimen distance of 3 cm, a 1 mm pinhole and Cr radiation were used for the Laue back reflection pictures.

Jan 1, 1957

By Fulton Flick

THE micrography and macrography of aluminum and its alloys present certain difficulties. Many of the difficulties attendant on the micrography have been removed by methods developed during the past few years, notably those of E. H. Dix, Jr.1 The development of grain size in aluminum and its alloys may be equally troublesome, yet comparatively little detailed attention appears to have been given to it. Satisfactory reagents. are available for the development of such structures in ferrous and most non-ferrous metals, but those applied to aluminum and its alloys, i. e., alcoholic or aqueous solutions of sodium hydroxide or hydrofluoric acid are not entirely satisfactory. Hanson and Archbutt,2 in speaking of these two reagents, state that "These two reagents give fairly satisfactory results, but they sometimes produce badly tarnished surfaces from which the surface deposit is difficult to remove." It has been our experience that neither of these reagents is to be entirely relied on for developing structures suitable for study or photography. This means that when the etch fails to produce satisfactory results the, specimen must be repolished, through the 000-paper at least, and then etched with another reagent. This procedure entails a con¬siderable loss of time, and the final results may not be all that might be desired. However, the reagent to be described, although not a panacea for all etching troubles, has improved results so markedly that it is felt that it is worth offering as a grain-size etch generally applicable to aluminum and aluminum alloys. Czochralski3 in 1915 mentioned the application of a solution of 10 to 20 c. c. concentrated hydrofluoric acid in 100 c.c. absolute alcohol, etching in this reagent being followed by dipping in concentrated hydrochloric-acid solution.

Jan 2, 1925

By A. U. Seybolt

The pressure-temperature relations required to maintain the existence of Si3N4 in silicon-iron of 0.44-11.7 pet Si have been partially explored. The critical data obtained have allowed the calculation of some thermodynamic quantities, and have shown evidence of an order-disorder two-phase field extending at 800°C from about l pet to 5.5 pet Si. THE presence of silicon nitride in electrical sheet, nominally about 3 1/4 pet silicon, balance iron, has been described by several authors'" but there has been some discrepancy among them regarding the identity of the nitride. Also, little has been reported on the quantitative thermodynamic prop- erties. In the work to be reported here, the nitride has been found to be more stable than described by Corney and Turkdogan." Several silicon nitrides have been described in the past, including SiN, Si3N4 and Si2N4 (see, for example, Abegg6 and Pascal7). However, the literature on nitrides other than Si,N, is all very old. No recent investigators using the more powerful tools available today have reported the presence of any nitride other than S3,N4. W. B. Hicke and L. R. Brantley8 in 1930 determined the dissociation pressure of Si3N4 which they made by reacting nitrogen

Jan 1, 1959

By R. S. Olson

An analysis of the wash thickener-two stage filtration circuit was undertaken to quantitatively describe the circuit performance. On the basis of information developed in this study, the factors of major importance in reducing soluble loss are: filter wash, wash zone size, filter capacity, filter feed pulp dilution, blow back, filter cloth, water to repulp, water to primary wash, water to feed pulp and thickener underflow. The wash thickener-two stage filtration circuit has been used in many hydrometallurgical plants to separate solute from leach solids. As many as 20 to 30 plant operating variables determine the performance of the wash circuit and hence the soluble loss. The complex relationships of these variables, with each other and with soluble loss, make the evaluation of their effect on mill performance difficult. An analysis of this type of circuit was undertaken to quantitatively describe the circuit performance. THE CIRCUIT The diagram in Fig. 1 represents the operation of the wash thickener-two stage filter circuit. This circuit provides for counter current, cross current or for a combination of countercurrent-cross current operation. The feed pulp stream, J, is intended to include any solution or water, other than primary and secondary filtrate, which enters the wash thickener. Except for filter washing, the operations in the circuit are simple mixing operations which can be described by material balance. The concentration of solute in the filtrate and cake solution after application of wash liquor cannot be described by simple material balance. The displacement washing equation, derived by Rhodes1 and extended by Choundhury and Dahlstrom,2 appears to best describe this case of miscible displacement in porous media. In a useful form, it is

Jan 1, 1963

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy's law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy's law as a premise and other papers4-7,16-10 which recognize that Darcy's law may not hold for flow into gas wells. Miller8 compared theory based on Darcy's law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy's law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy's law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy's law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy's law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy's law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy's law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By M. R. TECK, N. Rudd, L. K. Thomas, D. L. Katz

The authors are to be congratulated for presenting the first comprehensive paper on the theory and practice of threshold pressure determination in connection with underground gas storage. It is of particular value since most previous experimental work on this subject has been proprietary to the commercial laboratories engaged in such testing and to their clients. This dlscussion is presented in amplification of the subject paper, not in criticism, and is based upon our experience with approximately 5,000 threshold pressure determinations. Our comments are directed primarily to the experimental procedures as described by Thomas et al. It should be noted that, while clay mineral-rich lithologies are the most common caprock materials, the samples used (Table 1) include low permeability sandstones and carbonates, but do not include shales or other formations in which clav minerals exert a dominant effect. While our experience on samples analogous to those investigated by the authors generally confirms their findings, we have found that even more rigorous experimental conditions must be imposed where clay minerals are the controlling factor. These additional conditions result from the well-known molecular character of the clay minerals themselves in which water is interlaminated with, and bonded to, silicate sheets, thus becoming an essential component of the molecule. In many clay minerals the character of the intersheet bonding, and thus the dimension of the lattice, is strongly affected by variations in the identity and concentration of cations present in the intersilicate water. On a supermolecular scale, adsorbed water films on particle or "flakes" of shale provide much of the cohesive force necessary to maintain mechanical strength. The thickness of these films is variable and inversely proportional to intergranular pressure within the dimensional limits involved in caprock investigation. The thickness of the intersilicate water layers may also be subject to pressure under some conditions. These considerations are reflected in several necessary modifications of the experimental procedures described by the authors. Two of these are, in our judgment and experience, of such importance that they cast real doubt on the validity of data obtained on argillaceous materials without their application. The very careful resaturation procedures proposed by the authors should give good results in connection with the relatively "inert" lithologies used in their experiments. Our experience suggests, however, that they would create more problems than they would eliminate if applied to argillaceous materials. 1. Drying of the sample at the temperature and for the duration indicated by the authors not only will dessicate the sample with consequent shrinkage cracking, parting along bedding planes, and even total disassociation in the case of fissile shales, but it may also alter the character of the clay minerals themselves — in some cases irreversibly. 2. Prolonged evacuation to 2 microns Hg further dessicates the sample and is even more effective in reducing the intersilicate water content. 3. Resaturation with water differing in pH or chemical content from that existing originally in the sample also serves to alter the nature of the sample, particularly its structure and strength. 4. Our experience has been that, even with the thorough precautions proposed by the authors, complete resaturation of very fine grained materials is rarely obtained. Yet our experience confirms the

Jan 1, 1969

By Lawrence H. Van Vlack, Alfred S. Keh

The distribution of sulfur in iron was found to be dependent upon the time and temperature of the treatment as well as the chemical composition of the sulfide. With higher temperatures, the sulfide phase spreads more extensively between the iron grains. A complete network, however, does not form until approximately 1300°C (2372°F), ot which temperature the dihedral angle approaches zero. Silicon has little effect on this change. Aluminum, oxygen, and manganese all modify the temperature of sulfide network formation to a higher value. The microstructures which result and have significance in relation to hot-shortness are discussed. SULFIDE inclusions in steel were recognized by metallurgists before the turn of the century. Considerable attention has been paid to them, and numerous studies have been made on the working properties of steel as affected by them. It has been suggested that ho t-shortness of steel is due to the presence of an enveloping liquid sulfide film at the grain boundaries of the steel in the range of the hot-working temperatures. However, several facts have been observed in commercial steels which do not seem to be completely consistent with this explanation: 1) the frequent absence of continuous films of sulfide as observed under the microscope, 2) the absence of hot-shortness in some high sulfur and resulfurized steels, and 3) the limitation of hot-shortness to a definite temperature range. The role that manganese plays in steel to eliminate hot-shortness is well known, but the theory behind it is still under question. Moreover, the effect of de-oxidizers such as aluminum and silicon, and the effect of oxygen are still not clearly known. In this study, the effect of heat treatments and of additions of manganese, aluminum, silicon, and oxygen upon the distribution of sulfide inclusions in iron was investigated. Both the as-cast and the heat treated structures were studied, using microscopic and autoradiographic techniques. Part of the results were interpreted in terms of Smith's' concept of microstructure. Review of Literature Metallurgists used to consider sulfide inclusions as suspended particles. It was Wohrman' who first pointed out that sulfide inclusions are soluble in liquid iron. Many observed facts may be understood on the basis of this concept of solubility. Wohrman found that small castings contain small inclusions. and larger castings contain larger ones. Also, inclusion sizes are smaller near the chilled surface. For the same size ingot, the average inclusion size in a given heat of steel depends upon the rate of solidification. That is, with slow solidification, enough time for precipitation and agglomeration of these

Jan 1, 1957

By J. B. Clark

In multiphase ternary diffusion studies, plots of the variation bf the composition on the isotherm constitutes one of the most effective methods of presenting experimental results, especially if such plots are made in a manner which relates the composition path on the isotherm with the diffusion layer structure in the couple. Unfortunately, if different conventions for plotting are used serious misinterpretations occur readily, causing apparent disagreement between investigators who actually share the same viewpoint. A common convention for mapping these diffusion paths is needed at this time because with the increasing use of the electron-probe X-ray microanalyzer, a much greater number of ternary diffusion studies can be expected in the near future. In an effort to prevent unnecessary confusion in the future litera- ture, a convention for these plots is proposed, as outlined below. A hypothetical example of the use of these conventions is given in Fig. 1 where the path of composition through the diffusion structure of the 100 pct A/50 pct B, 50 pct C couple is plotted on the appropriate isotherm of the ABC system. The lower case letters relate the region in the diffusion layer structure to the appropriate composition on the ternary isotherm. 1) The diffusion path is plotted on the isothermal section corresponding to the diffusion temperature of the couple. 2) The terminal compositions of the plotted diffusion path are the initial compositions of the couple halves—provided infinite boundary conditions are maintained. If, in either couple half, infinite conditions are not maintained, then the path terminates at the composition of the exterior surface of the couple. If, at this surface, the composition varies with time or if the plotted path is time dependent, then the diffusion time should be noted beside the plotted path. 3) A solid line crossing a single phase field (e.g., line a-b in Fig. 1) denotes an existing layer of that phase in the diffused couple. 4) A dashed line crossing a two-phase field parallel to the tie lines (e.g., line g-h) represents an interface between the two phases with interfacial compositions designated by the ends of the tie-line. The line represents no spatial extent. 5) A solid line crossing a two-phase field so as to cut tie lines (e.g., line b-c or line j-k) represents a locally equilibrated columnar two-phase layer. The solid line should cut those tie lines which correspond to the lateral interfacial equilibria along the columnar

Jan 1, 1963

By J. B. Fletcher

The Miami mine first started operations in 1910. For convenience, the history of the orebody can be divided into the following categories (Fig. 1): 1) 1910 to 1925: 24.4 million tons of high grade ore, mined by top slicing, sublevel caving, etc. 2) 1926 to 1954: 102 million tons of low grade ore, mined by block caving.

Jan 1, 1961

By D. G. Westlake

Alloys of poly crystalline Nb-H have been tensile tested at 77" and 120°K after slow-cooling and after quenching from room temperature. A rationale has been developed to explain the effect of cooling rate on ductility in terms of microstructure. The inferior ductility of the slow-cooled alloys in this temperature range can be attributed to the precipitation of coarse hydride particles that fracture in the early stages of plastic deformation. Quenching Produced much smaller hydride particles and a decreased tendency for initia-tion and popagation of cracks. Prismatic dislocation loops, punched into the matrix of quenched alloys, eliminate the yield point and may Play some role in the low temperature ductility of the quenched alloys. The difference in ductility between quenched and slow-cooled V-H alloys was even greater than that observed in the N b-H alloys. It is well known that the ductility of Nb-H and V-H alloys decreases with increasing hydrogen concentra-tion and with decreasing temperature.1-l1 The follow-ing are some of the numerous mechanisms that have been adopted in attempts to explain these observations: 1) hydrogen-dislocation interarction,4'6 2) lowering of the crack surface energy by adsorbed hydrogen,9'10 3) localized lowering of the niobium bond strength,9 and 4) exertion of pressure inside voids by molecular hydrogen.6 A recent study1' indicates that, in some way, the embrittlement is related to the precipitation of a hydrogen-rich phase, because embrittlement and hydrogen solubility have the same temperature dependence. Most of the investigators observed that at very low temperatures there was a return of the ductility. Thus, hydrogenated niobium and vanadium may be said to exhibit a low temperature ductility minimum."1'8'9 It has been reasoned by most observers that diffusion is required for the embrittlement mechanism to be operative, and that as hydrogen becomes immobile at very low temperatures, the ductility increases. This investigation of the mechanical behavior of Nb-H al-loys under various conditions is an attempt to gain a better understanding of the low temperature ductility minimum. EXPERIMENTAL Tensile specimens, with gage length dimensions 20 by 3 mm, were machined from sheet stock" and both faces were ground on wet 600 grit Sic paper to obtain a final thickness of 0.5 mm. Annealing as described earlier12 resulted in average grain diameters of 0.3 mm. The recrystallized niobium tensile specimens were electropolished in 90 parts H2S04, 10 parts HF (48.9 pct) by volume, at 287°K and 30 v. Hydrogen, which may have been present in the starting material and/or added during specimen preparation, was removed by annealing at 1073°K in a dynamic vacuum of 2 X 10-6 torr. Hydrogenated specimens (1.15 at. pct H) were prepared by reaction with a known quantity of pure hydrogen (obtained by thermal decomposition of UH3) at 1073oK, followed by cooling at the rate of 100" per hr. These were vacuum encapsulated, homogenized at 573°K for 3 to 5 hr, and furnace-cooled. Tensile tests were conducted on an Instron machine at a strain rate of 4 x l0-5 per sec. The gripping device was such that the specimen was positioned below the crosshead. Thus, subambient test temperatures could be obtained by immersion of the device in a cooling bath of either liquid nitrogen or Freon-12. The temperature of the Freon-12 was controlled within ± 0.1°K of the desired temperature by automatically monitoring the flow of liquid nitrogen through a copper coil in the bath. Slow-cooling to 77°K was accomplished as follows. The testing device was surrounded by a rubber jacket, open at the top and with small holes in the bottom. Liquid nitrogen, brought up to the bottom of the jacket, entered the holes and vaporized quickly. The temperature was monitored at the specimen with a copper-constantan thermocouple, and a constant cooling rate of 2 deg per min was easily achieved by controlling the level of the liquid nitrogen outside the jacket. RESULTS AND DISCUSSION Low Temperature Ductility Minimum. Resistometric studies of both Nb-H12 and V-H13 indicated that at tem-peratures less than 150°K, virtually all of the hydrogen

Jan 1, 1970

By J. Buchwald, R. W. Heckel

THE DeHoff method' of analysis of ellipsoids of constant shape provides a quantitative metallo-graphic technique whereby the actual size distribution of the ellipsoids may be determined from polished and etched random planar sections. This method provides a useful metallographic tool since it appears to be the only method available for determining the size distribution of nonequiaxed second-phase particles. This method, however, assumes that the type of particle being studied is known to be either oblate or prolate of a fixed minor to major axis ratio, q. This, in general, means that one assumes either oblate or prolate ellipsoids of a given q and checks the total volume and surface area of the second phase as determined from the particle size distribution to values of these quantities determined by other techniques. Suitable check methods may be point counting, lineal fraction, and areal fraction methods for obtaining the total volume and the Smith and Guttman2 method of intercepts for obtaining the total surface area. If the initial guess at particle shape and q were incorrect, i.c., the volume and surface information obtained from the particle size distribution data does not agree with those values obtained by other techniques, another assumption must be made and the particle size dist distribution must be recalculated. A current study in this laboratory has involved a large number of these calculations. To facilitate the handling of the calculations, the DeHoff method was programmed in the FORTRAN language for an IBM 1620 computer. The purpose of this note is to briefly describe this program. The complete program along with a list of variable names, a sample input, and a sample output may be obtained from the senior author. Basically, the program provides for the calculation of particle size distributions for a series of q values for both oblate and prolate ellipsoids for each set of input data. The total volume of second-phase particles per unit volume are calculated for each calculated particle size distribution. The output of the program is arranged to allow a rapid comparison of the calculated volume and surface values to data obtained by independent check measurements. A condensed flow chart of the program in the notation of DeHoff1 is given in Fig. 1 The calculation of the number of particles per unit volume in the jth size class, Ni, according to the DeHoff method' is: where k(q) is the shape-correction factor given by DeHoff as a function of q for both oblate and prolate ellipsoids, A is the size-class increment, k is the number of size classes, ni is the number of particles in the ith class on the planar measurement surface, and B(j,i) are the saltykov3 coefficients which correct for measurement surfaces which do not pass through the major and minor axes of the particles. The values of /3(j,i) are included as a two-dimensional array in the program. Particular values of k(q) are included in the program in increments of q of 0.05. The first calculation is carried out for q = 1 (spheres), the second for q = 0.95 oblate, the third for q = 0.95 prolate, and so forth. The number of q values chosen for the calculation is determined by a control card in the input for each set of data.

Jan 1, 1965

By H. T. Kennedy, S. M. Avasthi

An equation developed for gaseous hydrocarbon mixtures predicts molal volumes with an average absolute deviation of 0.73 percent when applied to 264 natural gas and condensate systems including 2,043 PVT points. Another equation developed for liquid hydrocarbon mixtures predicts molal volumes with an average absolute deviation of 1.12 percent when applied to 346 crude oil systems including 1,759 PVT points. Both equations require composition of the mixture to be expressed as mole fraction of methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide, together with the characteristics of the heptanes-plus fraction in addition to the temperature and pressure. The equations cover wide ranges of the variables involved, and their accuracy is considerably better than that of other available methods. The equations were differentiated to allow calculation of the coefficients of isothermal compressibility and isobaric thermal expansion. (In this paper the coefficient of isothermal com-pressibility and the coefficient of isobaric thermal expansion will be expressed as compressibility and thermal expansion coefficient, respectively.) Equations to calculate these quantities are presented. INTRODUCTION Calculations of reservoir performance for petroleum reservoirs require accurate knowledge of the volumetric behavior of hydrocarbon mixtures, both liquid and gaseous. Compressibilities are required in transient fluid flow problems, and thermal expansion coefficients are important in thermal methods of production. An accurate laboratory investigation of the PVT behavior of each reservoir fluid encountered would be costly and time consuming. For this reason various correlations for predicting fluid properties have been developed and recorded in recent literature. Correlations have been presented in the form of graphs, tables and equations. Since an increasing number of studies are being conducted with the aid of electronic computers, recent efforts have been directed toward development of correla-tions suitable for computer programming. Application of computers permits the use of more complex correlations which otherwise are not feasible. Moreover, methods for predicting reservoir performance, particularly those based on the compositional material balance, depend upon the capability of accurately expressing the molal volumes and other fluid properties as functions of pressure, temperature and composition. The coefficient of isothermal compressibility c is defined by

Jan 1, 1969

By Henry G. Granger

I. INTRODUCTION. REPEATED failures in attempts to work gold-bearing gravels by means of suction-dredges have created the impression that this method is impracticable. The suction-dredges have failed from three special causes excessive wear and frequent breakage of pump-shell, runners and liners; inability to dredge compact gravel which would ,not. readily move towards the intake; and, most important of all, closing. of the suction-pipe by stones too large to enter it. In my opinion, all three causes of trouble may be remedied: the first, by making stronger the parts most liable to wear and breakage; the second, by means for loosening the gravel at the intake; and the third, by sufficiently... Increasing.. the diameter of the suction-pipe. In suction gold-dredges, this diameter has not usually exceeded 10 or 12 in.; whereas there are few profitable gold-fields which can bee considered dredgeable, in which stones more than' 12 in. in diameter, are-.not frequently encountered. II. AN EFFECTIVE SUCTION-DREDGE. In harbor-operations, much larger stones are handled by suction-dredges.., The large dredge of the Henry Steers Contracting Co. worked for nearly four years at League Island, Philadelphia, where it sucked up, passed through the pump, and forced through 3,700 ft. of discharge-pipe; gravel containing boulders up to 200 lb. in weight. This was done with no bad breaks and few shut-downs. The cutter; and liners were the only parts liable to damage, and these were easily replaced with brief interruption of work. The chrome-steel liners are said to have lasted from six to nine months. I am informed that this dredge worked continously for nine

Apr 1, 1909

By R. Schuhmann

Jan 1, 1965

By F. H. Buchella, J. F. Buchanan

The San Manuel copper deposit is located about 45 miles northeast of Tucson. The concentrator, smelter, administration building, and other plant facilities are located about seven miles southeast of the ,nine area at the new town of Sari Manuel as shown on Figure 1 (Sketch).

Jan 1, 1961

By T. R. A. Davey

The fundamental principles by which bismuth may be removed from lead by pyrometallurgical processes are enumerated. Qualitative discussion of the phase diagrams concerned is followed by presentation of quantitative diagrams. Brief mention is made of the practical aspects. Data presented show how chemical lead (<0.005 pct Bi) may be produced by the Jollivet, Dittmer, and Kroll-Betterton processes. BISMUTH is an element whose properties are very similar to those of lead, and its minerals are associated to a greater or lesser extent with nearly all the major lead ore deposits of the world. In consequence, the lead produced contains bismuth unless a special debismuthizing process is practiced. There does not appear to be any published comprehensive review of the effect of bismuth as an impurity on the properties of lead, and there is some uncertainty as to the beneficial or detrimental effects of small amounts of bismuth in lead used for particular applications. Standard specifications of most countries stipulate a maximum bismuth content of 0.005 pct for chemical lead. With one exception, this specification is met only by lead producers whose ores are relatively bismuth-free, or whose refineries are electrolytic. In lead for certain applications a higher bismuth content is preferred by some fabricators.&apos; In contrast to the refining for silver, copper, and antimony, the refining for bismuth does not usually result in a large overalil economic gain from the sale of byproduct. Thus, debismuthizing is customarily practiced only if market conditions demand a lead with a bismuth content lower than that produced by classical refining; i.e., softening, desilverizing, and zinc refining. Until this century, debismuthizing was carried out only a:; an incidental result of desilverizing, as later described. This century has seen the development of the Betts electrolytic process—the only successful one of many electrolytic processes proposed and patented —and a number of precipitation processes based on the pioneering work of Kroll,&apos; although only one of these, the Kroll-Better ton process,&apos; is in wide commercial use today. It is proposed in this paper to deal only with the pyrometallurgical processes, excluding those based on aqueous electrolysis. Historical Background Prior to 1833 silver (and incidentally bismuth) could not be removed from lead. To recover silver from rich bullion, the only course available to lead refineries was to cupel the bullion, forming a slag of litharge. The first slag tappings or skimmings, on reduction, yielded soft lead of very low silver and bismuth contents. Intermediate skimmings yielded a lead of somewhat higher silver and bismuth contents, which could if desired be recupelled. The last skimmings yielded a litharge very high in bismuth, which could by successive oxidation and reduction cycles be separated into high purity bismuth, and lead returns. This oxidation reduction process, with modern operating techniques, can still be used today to produce a portion of a lead refinery&apos;s output of very low bismuth content, as discussed later. In 1833 Pattinsone discovered that lead bullion could be purified of silver and bismuth by fractional crystallization, the primary lead crystals formed by partial freezing being purer than the melt. Repeated processing in pans produced a lead containing as little as 0.02 pct Bi. The simple explanation of this

Jan 1, 1957

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970