Search Documents

By A. E. Kurie

The Great Salt Lake occupies about 1000 square miles whereas its predecessor, Lake Bonneville occupied 20,000 square miles and its shoreline reached 1000 feet above the present lake level. The sediments of Lake Bonneville range from peripheral gravel and sand deposits to central basin calcareous clays and silts, gypsum sands, and saline precipitates. The drilling and engineering tests conducted by the Utah State Department of Highways for many highway structure sites and the construction of Federal Interstate freeway provided engineering and hydrologic properties of Lake Bonneville sediments. Ground water and surface brine exploitation have contributed hydrologic and chemical data; the geologic and mineralogical data are scientific research contributions.

Jan 1, 1967

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By W. H. Eddy

The Bureau of Mines made small-scale continuous tests and large-scale commercial plant tests of a calcareous fluorspar ore near Cave-In-Rock, Ill., to determine if the application of the lignin-fluoride process of fluorspar flotation would be industrially feasible for treatment of fluorspar ores, and also to compare the lignin-fluoride process with the quebracho process, which is the method currently used for concentrating calcareous fluorspar ores. The small-scale continuous tests yielded fluorspar concentrates analyzing 93.6 percent CaF2 with a recovery of 87.6 percent of the total fluorspar in the ore. In large-scale commercial plant tests, a fluorspar concentrate analyzing 93.3 percent CaF2 with a recovery of 78.0 percent was produced by the quebracho method. About 86.0 percent of the fluorspar was recovered in a metallurgical-grade fluorspar concentrate from the lignin-fluoride circuit which analyzed 89.9 percent CaF2? with a much simpler flowsheet than that in the current commercial application.

Jan 1, 1967

By H. Y. Jennings

An extensive field and laboratory experimental program was carried out to compare the waterflood behavior of carefully preserved soft and unconsolidated cores with measurements on the same cores after extraction. Results obtained from using idealized consolidated and unconsolidated porous media in which wettability could be carefully controlled were contrasted with the preserved core data. The controlled tests on idealized porous media investigated the effect of wettability, flood rate, core length, core permeability and consolidation on the displacement of high viscosity oils. It was concluded from these studies that waterfloods are more favorable when carried out with crude oil in preserved soft and unconsolidated cores than with the same cores after they have been extracted and re-saturated. Waterfloods are usually more favorable when carried out with crude oil in extracted .soft and unconsolidated cores than with refined oil of the .same viscosity in the same cores. The less favorable behavior of extracted soft and unconsolidated cores compared to preserved cores is due to alteration of the core by extraction. Preserved cores saturated with native water and oil should be used for laboratory displacement experiments because they more accurately reflect true reservoir behavior INTRODUCTION The demand for low gravity crude oil created by refinery modernization has focused attention on increasing the production of this viscous crude oil. Billions of barrels are in place in fields that are depleted, or nearly depleted, by primary production mechanisms. Since low gravity reservoirs are relatively recent, geologically, the solid matrix material is usually soft and unconsolidated sand. Such formations are also characterized by a high clay content. Evaluation of sophisticated oil recovery processes with the associated high capital investments has increased the demand for special core analysis tests on material from these soft and unconsolidated sand reservoirs. Data in this paper have resulted from an extensive field and laboratory experimental program. The initial objective vras to provide soft and unconsolidated sand cores for laboratory measurements with as little alteration as possible from their reservoir condition. A secondary objective was to compare the waterflood behavior of these carefully preserved cores with measurements on the same cores after they had been extracted and resaturated. When the comparison showed markedly different behavior the final objective was to attempt to explain the difference by making measurements on idealized porous media free of clay in which initial wettability could be carefully controlled. EXPERIMENTS MATERIALS Core Material The preserved cores used in this study were obtained with as little alteration as possible from their reservoir conditions. Special techniques were developed to satisfy this objective. The cores were cut with native crude whenever the crude had the necessary properties to satisfy the minimum drilling fluid requirements. A pure hydrocarbon chromatographic tracer was added to the crude to provide a simple, safe and inexpensive method to distinguish between oil filtrate and formation oil. Details of the tracer technique used in this study and the procedures used to handle and process the soft, unconsolidated cores have been published.' The core samples were then preserved and packaged at the well site with a dip-applied strippable plastic, or by using a rubber sleeve from a rubber-sleeve core barrel. The final step was to insure that the carefully taken and preserved samples were not altered by processing in the laboratory. Some soft and poorly consolidated sands were carefully shaped in the lab and encased in a protective mounting without disturbing their three-dimensional integrity. Many samples were so poorly consolidated that they literally flowed from the package when the seal was broken. A technique was developed to obtain cylindrical plugs from these samples by using liquid nitrogen as the drilling fluid in a conventional core-drill, drill-press assembly. The idealized porous media consisted of sintered rods of Alundum RA 139, outcrop sandstone identified as Al-hambra sandstone and packs of No. 130 Nevada sand. This sand is 95 per cent 140-200 mesh. (Physical properties of these porous media with those representative of preserved cores are in Table 1.) The natural cores and most of the idealized porous media were 1 1/2-in. in diameter and 3-in. long. The samples used to study the effect of core length were 1 1/2-in. in diameter and 12-in. long. Liquids Water and oil produced from the formations being studied were protected from the atmosphere and collected in carefully cleaned glass or plastic-lined containers. The production was free of chemical additives such as emulsion breakers and corrosion inhibitors. The crude oil was

Jan 1, 1967

By A. M. Adair

The effect of cathodically charging zone-refined iron with hydrogen and the resultant yield stress-grain size relationship has been investigated by tensile testing at -31°C. The resulting Petch plots (using a least-squares analysis) reveal a significant reduction in the slope and an increase in the intercept for specimens cathodically charged with hydrogen, regardless of whether the hydrogen is present during testing or is removed by evacuation. Other than surface blistering, the major effect of cathodically charging this material is to create occasional grain boundary cracks and thus presumably a large number of free dislocations at grain boundaries. These results are consistent with the hypothesis that the slope of the Petch plot is related to the stress required to activate dislocation sources at or near pain boundaries. While there is no significant effect of the presence of hydrogen on the lower yield stress of this material, the ductility is considerably reduced. After hydrogen removal by evacuation, the ductility recovers substantially and almost complete recovery of ductility is experienced by the smaller grain size specimens. THE influence of hydrogen on the mechanical properties of ferritic materials has received much attention throughout the history of the metallurgy profession. This interest has stemmed from the obvious importance of preventing the catastrophic failure of parts in service, and from the desire to determine what mechanism is responsible for the observed behavior. The various mechanisms proposed for hydrogen em-brittlement have been discussed in detail by Tetel-man,'who concludes that a combination of the applied stress and hydrogen pressure within voids best accounts for the many experimental observations reported. From a quite reasonable correlation of the strain aging and delayed-failure behavior of a variety of materials,2-7 Troiano and coworkers are of the opinion that the delayed-failure mechanism (slow strain rate embrittlement as well) is better explained as a lattice effect; solute elements diffuse to regions of high triaxial stress, form uncondensed atmospheres there, and effect a reduction in the cohesive strength of the lattice. Since hydrogen yield points8,9 have been observed in ferritic materials, and since the hydrogen embrittlement process may be related to strain aging, one further contribution to embrittlement could be hydrogen-dislocation interactions which make crack blunting by plastic deformation a more difficult process. The etch" relationship offers a means of comparing the relative ease of initiating and propagating plastic deformation in metals and alloys. In the present study, this relationship was used to compare the behavior of zone-refined iron in three conditions: uncharged, cathodically charged with hydrogen, and cathodically charged with hydrogen and evacuated. These Petch plots and the observed ductility parameters allowed a separation of the effects of the very presence of hydrogen and the act of cathodically charging hydrogen into this material. MATERIALS AND EXPERIMENTAL PROCEDURE An ingot of zone-refined iron was obtained from Battelle Memorial Institute which contained the following (typical) interstitial impurities in ppm: carbon, 10 * 5; nitrogen, 1; oxygen, 22; hydrogen, 0.9. The ingot was cold-reduced to a 1/2-in.-sq cross section, recrystallized 1 hr at 575°C, and then straight-rolled to a thickness of about 0.105 in. Tensile specimens were milled from the strip having a 1-in. gage length

Jan 1, 1967

By J. C. Uy, A. A. Burr

A quantitative relationship between the allotropic phase boundaries of zirconium-base binary systenzs and the solute metallic valence is shown through an intermediate thermodynamic parameter. A simplified equation relating this parameter to the phase boundaries is briefly reviewed, and data from the literature are used to show the relationship of this parameter to the solute metallic valence. It has been reported that the solute metallic valence can be used as an index of phase stabilization in zirconium-base binary alloys.' It was shown that the algebraic sign of the slopes of the hcp/bcc phase boundaries of zirconium alloys correspond to the algebraic sign of the metallic valence of zirconium minus the metallic valence of the solute, or, in other words, a solute whose metallic valence is higher than that of the solvent tends to stabilize the high-temperature phase while one whose metallic valence is lower than that of the solvent tends to stabilize the low-temperature phase. Further analysis of the zirconium binary systems has revealed a quantitative relationship between the solute metallic valence and the relative slopes of the two-phase allotropic boundaries. This relationship involves a thermodynamic quantity whose significance can be seen in the following section. PHASE-STABILIZATION PARAMETER Let Qb be the difference between the partial molar heats of mixing of a given solute in the two allotropic phases of the solvent which are in equilibrium with each other at a given temperature, thus A relationship between this term Qb and allotropic phase boundaries has been employed by several au-thors'-= in the evaluation of phase diagrams, and can be briefly derived as follows. Referring to Fig. 1, consider the general case of two allotropic phases, each having a small mole fraction (Xa,Xb) of the solute, in equilibrium at temperature T and atmospheric pressure as represented by the reaction. solute in ß phase =solute in a phase If now a reaction occurs such that an infinitesimal amount of the solute is removed from the ß phase and added to the a phase, there would be a partial molar

Jan 1, 1967

By Alla D. Mah

Heat content and entropy data at high temperatures were obtained for cuprous oxide (Cu2O) and cupric oxide (CuO). Experimental results and smooth values are reported. Equations are given for heat content increments and heat capacities above 2980 K. Low-temperature heat capacity data were obtained for cuprous oxide. Evaluation of the 2980 K entropy gave, S°298.15(Cu2O) = 22.08 ± 0.10 cal/deg mole. Heat of formation values were determined for cuprous and cupric oxides. The values are: AH°298.15(Cu2O) = -40,830 ± 300 cal/mole, and AH°298.15(CuO) = -37,230 ± 150 cal/mole.

Jan 1, 1967

By Stephen D. Cramer

The objective of the present studies was to develop thick adherent and coherent coatings of platinum and palladium on refractory metals and other substrates of industrial and engineering importance. Existing platinum and palladium electrolytes were modified to make them suitable for the electrodeposition of thick deposits. The optimum operating conditions for these electrolytes were established. Pretreatment procedures for columbium, copper, graphite, molybdenum, nickel, stainless steel, tantalum, titanium, tungsten, vanadium, and zirconium substrates were studied. New pretreatment procedures for columbium, molybdenum, stainless steel, tantalum, tungsten, and nickel were developed. The internal stress and hardness of selected electrodeposits were measured. The effects of heat treatment upon the properties of electrodeposits were studied.

Jan 1, 1967

By Arcy R., D&apos George

A process for removing sulfate from Great Salt Lake brines and other natural brines, including sea water, has been developed. Sulfate is quantitatively removed by precipitation as barium sulfate in a cyclic process employing ion-exchange techniques. Barium is continously recovered and recycled, and sodium carbonate and sulfur or sulfuric acid are produced as byproducts in quantities sufficient to more than defray the cost of desulfation.

Jan 1, 1967

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By G. S. Cole, H. Biloni, G. F. Bolling

An experimental investigation of sovlze low .melting point alloys sJtows that a substvucture of isolated depressions can be the first manvestation of constitutional supercooling on solid-liquid interjaces veuealed by decanting. Electron-tni cvop vobe and wletallo gvaplic esanzinations, in tlze bulk belzind the interjace, oj the segregation associated with these isolated areas substantiate tlzei&apos;v depressed nature, since a solute of ko < 1 is enriched, and a solute of ko > 1 depleted. In contrast, the pox structuve, a set of projections often veported in the literature, leaves no trace oj. segvegation. These obserl;atims, accovlrpanied by a brief review of recent literature, point to inconsistencies between experirrental obsevvation and the idea that the fornzation of a projection is a causal step in the development of a cellular substructure. An argument is presented to show instead how it is plausible for substantial depvessiom to form in the pvesence of constitutional supercooling at dislocations threading the solid-liquid interjace. THE development of constitutional supercooling during growth from the melt leads to the formation of the cellular solidification substructure. This well-founded association between structure and instability has been basic in understanding cellular substructure and micro segregation; however, the initial formation of structure seems unclear. Rutter and Chalmers,&apos; in definitive experiments and theory, noted that in the presence of constitutional a planar interface might break down: "resulting in the formation of a small projection on an initially plane or uniformly curved interface." That is, the breakdown from a planar to a cellular interface was implied to be initiated via a projection into the unstable liquid. Later, Walton et (11. found that a structure of isolated projections, termed "pox", appeared at solid-liquid interfaces decanted under growth conditions near the onset of constitutional supercooling; the pox were taken as the indication of the instability promoted by the supercooling. Tiller and Rutter4 in their extensive work studied the shape transitions at decanted interfaces which were generally observed to proceed as— pox, "irregular cells", elongated cells, regular (hexagonal) cells, and so forth. The pox varied in size from lo-&apos; to 1CT4 cm, and tended to disappear as cells increased in number and regularity, but as noted,4 the first real array of cells did not seem to be a development from the pox. In fact these authors implied a lack of connection because they stated that the pox are denser on "irregular cells", and as cell boundaries increase in number (i.e., the cells become smaller) there is less need for the pox which do dis- appear. Thereafter, most authors dealing with either experiment or theory have accepted the reality of pox and have used them as a criterion for the onset of constitutional supercooling. In contrast, Spittle, Hunt, and smiths have now suggested that pox are irrelevant artifacts comprised of such things as entrapped oxide. This proposal invokes the observations of weinberg6 and chadwick7 each of whom have shown that the act of decanting leaves a residual liquid on a decanted interface; the remnant solid layer of the order 10 p may thus contain particles that might have been transported from the external surfaces, or elsewhere, during decanting. With the incentive of this suggestion,= some further experiments and a reexamination of the literature have been conducted, in order to question the validity of pox as evidence of an instability and to examine the initial development of the cellular substructure. 1) EXPERIMENTS Single crystals of zone-refined tin (-99.9999 pct) were grown from the melt in a controlled fashion with various, small concentration additions of lead and antimony, for which ko < 1 and > 1, respectively. The crystals were decanted at conditions near the onset of constitutional supercooling and were thus appropriate for observation of slight perturbations. It was possible to observe two types of small departure from smooth or "planar" interfaces in both cases of lead or antimony additions. Some were projections and others, if in regular array of any type, were depressions. The crystals were etched with suitable reagents progressively dissolving the decanted interface surface; projections left no record, but depressions were continuously associated with spotlike areas contrasting with the rest of the interface. Traverses were made with the beam of an electron microprobe across the regions of contrast; with lead addition the persistent spots were lead-rich, and with antimony addition the persistent spots were antimony-poor. This is consistent only with a dominant role for depressions, because if the projections had left spots but were incorrectly catalogued, a reversed observation should have been made; that is, the Pb(ko < 1) should have been depleted and the Sb(ko > 1) enriched. In the work of Cole and inegard, and elewhere, regular arrays of structure associated with the initial stage of instability have been shown, in photographs and represented as pox or projections. We believe this to be erroneous, by inference, since whenever a regular array was observed, in the present examination, it consisted of depressions, regardless of the nature of the solute, ko 1. Fig. 1 is reproduced8 as an ideal example of the possible optical illusion involved; the observer can satisfy himself from the distribution of illuminated areas that the markings are depressions. Fig. 2 from the present investigation is an interference photograph of an interface similar to that in Fig.

Jan 1, 1967

By Russell E. Griffin

Dielectric constants and dissipation factors were measured for six rocks over the 20-to 100-megahertz frequency range by means of the susceptance-variation method. Results for both dry and moist specimens are presented and compared with data reported by others. Loss factors calculated from the data presented are important to the Bureau&apos;s study of rock fragmentation by means of dielectric heating.

Jan 1, 1967

By J. Gurland

The wmk is concerned with the estimate of the degee of continuity of a particulate phase dispersed in a matrix. The first section is a verieu: of the parameters nzeasurable by quantitative rnetallogvaphy, namely the contact area and, under certain conditions, the number of contacts between particles of one phase. In the second section, the frequency of particle contacts is related to the degee of continuity of a randomly embedded phase orz the basis of the lattice-percolation model of Hamrnersley and others. THE extent of continuity of the constituent phases may greatly influence the structure-sensitive properties of phase mixtures, particularly if the phase properties differ significantly. An example from the literature1 is shown in Fig. 1. The marked decrease of the electrical resistivity of sintered silver-alumina bodies near 25 pct by volume of silver presumably occurs because the more conductive phase changes from a discontinuous to a continuous structure. Other example of electrical- and thermal-conductivity transitions are cited by kingery In view of these observations, a knowledge and understanding of the connectivity of the microstructure may be of considerable practical importance. This study is concerned with one aspect of the genera1 problem, namely the estimate of the degree of continuity of a particulate phase dispersed in an opaque matrix. The first section reviews the parameters measurable on a polished cross section by auantitative metallography, such as the contact area and under certain conditions, the number of contacts between particles of one phase. In the second section, an attempt is made to relate the frequency of particle contacts to the degree of continuity of a randomly embedded phase. For the purpose of this discussion, the aggregate has two constituents: the particulate phase and the matrix. The latter is considered to be homogeneous. The term "particle" is used with the meaning of "grain", i.e., a minute unit of matter which is usually a single crystal of a readily distinguishable substance within the confines of a simply connected boundary. While many of the concepts which are used here to describe the structural variables characterizing the microstructure of phase mixtures are qualitative and ill-defined, they are presented with the intent of stimulating further work of a more general and rigorous nature. I) PARTICLE CONTACT, CONTIGUITY, AND MEAN FREE PATH 1) Measurement of Contiguity. The fraction of the total internal surface of a phase a shared with particles of that same phase in a two-phase mixture of and $ is indicated by the contiguity ratio:3 whereis the area of the interface between o particles, and Sap is the area of the interface between a particles and matrix P, per unit volume of mixture. The contiguity ratio ranges from 0 to 1 as the distribution of the a phase changes from a completely dispersed to a completely agglomerated structure. The interfacial areas may be obtained from simple intercept measurements on a random plane, after Smith and Guttman where and N are the numbers of intercepts between a random line of unit length on a plane of polish and the interparticle and interphase interfaces, respectively. The equations are valid for any distribution of particle sizes and shapes.

Jan 1, 1967

By P. H. Thornton

MaNY intermediate phases are solid solutions which have a solute-solubility range greater than 3 at. pct. These phases, which are generally very strong and often have simple crystal structures, are usually extremely brittle so that specimens of simple shape cannot be produced by the usual mechanical-deformation techniques. Furthermore, single crystals of reasonably uniform composition are difficult to grow by the Bridgman technique because the phases generally form by a peritectic reaction, which causes pronounced segregation. In this note, a technique is described for the preparation of thin-rod specimens of brittle intermediate phases, which may be used for physical-property studies such as resistivity changes&apos; and for the conversion of such rods into single crystals. The method has been used for the preparation of rod single crystals of the phases and Ingots, of about 100 g weight and 11 mm diam, were made by melting together the appropriate amounts of high-purity materials (usually 99.999 pct) in sealed

Jan 1, 1967

By M. S. Burton, B. W. Christ, G. V. Smith

Evidence of the effects which high-angle grain boundaries and veining subgrain boundaries have on the yield phenomenon of zone-refined iron is reported. Room-temperature tensile tests on 50-mil wive at several gram sizes produced upon recrystallization at diffevent temperatures below 910C (a-y phase-transfornzatzon temperature) show that upper and lower yield stress decrease with increasing grain size. The upper yield point effectively disappears at grain sizes of 81 and 102 u in samples of this diameter. However, samples of 129 p grain size. produced during recrys-tallization at 950°C, exhibit a pronounced upper yield point and an increased lower yield stress. Possible causes of the reversal in the grain-size dependence of yielding are discussed. Veining substructure, detected with picval-HC1 etchant, but not with 2 pct nital, is formed during the a-y transformation, and is believed to account for the observed effecls. The strengthening associated with high-angle boundaries in zone-refined tron is discussed in terms of: 1) the stress dependence of slzp multiplicity, and 2) the stress dependence of dislocation emission from grain boundaries. WIDE use of transmission electron microscopy and dislocation etch-pitting techniques has led to a growing awareness of the presence of dislocation substructures in annealed pure metals. Whereas much speculation&apos;-4 has developed about the influence which subgrain structures have on the mechanical behavior of metals, particularly the yield strength, only limited experimental evidence correlating subgrain structures with lower yield strength has been presented. 2,3,5-7 It is the purpose of this note to present experimental evidence of the effects which grain boundaries and subgrain boundaries have on both the upper and lower yield strength of zone-refined iron. Effects due to high-angle boundaries formed upon recrystallization below the a-y phase transformation are compared with effects due to veining subgrain boundaries formed upon "recrystallization" above the a-y phase-transformation temperature. These effects are further compared with the reported influence 2,3,5-7 which low-angle boundaries have on the lower yield strength of bcc transition metals. EXPERIMENTAL PROCEDURE The starting material for these experiments was a 1-in.-diam zone-refined ingot prepared at Battelle Memorial Institute. Initial purification of electrolytic iron by vacuum-induction melting was improved by a floating zone-melting treatment in ultrapure hydrogen.&apos; Chemical analysis of this zone-refined iron appears in Table I. Tensile samples of 50-mil wire were prepared by rolling and drawing portions of the ingot. An intermediate recrystallization anneal at 625°C after rolling to a reduction in area of 85 pct was carried out in an evacuated Vycor capsule (10-=5 mm Hg). Further reduction in area of 91 pct was followed by recrystallization in evacuated Vycor capsules at temperatures between 600" and 950°C, see Table 111. All samples

Jan 1, 1967

By S. E. Szasz, E. J. Moore, B. F. Whitney

An accurate value of formation water resistivity R, is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where R, has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate R, from the chemical analysis of the formation water. INTRODUCTION It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating R, from the chemical anaylsis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ions, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na&apos; and C1-. Dunlap and Hawthorne&apos; have proposed to convert the concentration of all other ions to equivalent Na&apos; and C1-concentrations by means of constant multipliers; e.g., 0.95 for Ca"; 2.0 for Mg"; 0.27 for HCO 3-; 0.5 for SO, -, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. The Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of R, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp.&apos;s Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples. FUNDAMENTAL CONSIDERATIONS The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na&apos; or C1- always carry the same charge. Compounds of polyvalent ions, however. may show incomplete dissociation, e.g., NaSO; + Na&apos; instead of SO,-- + 2Na&apos;. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaC1, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy. The Dunlap method, on the other hand. is too simple because it askmes that at any concentration the contrih-

Jan 1, 1967

By Wilbur I. Duvall

In this report, the Bureau of Mines presents a theoretical solution for the stresses and displacements in an infinite elastic plate containing a circular hole the boundary of which is loaded by applied radial stresses over four separated arcs. The problem solved is a two-dimensional approximation of the stresses and displacements developed by a large tunnel-boring machine anchored in a circular tunnel. Analysis of the solution shows that the tangential tensile stresses induced on the boundary of the circular opening can be minimized in the roof and maximized in the floor of the opening by proper spacing and loading of the four arcs.

Jan 1, 1967

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,&apos; at 0.6 to 0.9 of included to see whether Mullins&apos; theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.&apos;-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann&apos;s constant, and the vacancy formation entropy, respectively. After applying Stirling&apos;s approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling&apos;s approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling&apos;s approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By R. J. McLeod

"Grinding at Giant Yellowknife is done in two stages. The first stage consists of two ball mills in closed circuit will: mechanical classifiers, the classifier overflow goes to flotation. The tailings from this flotation circuit are separated into slime and sand portions, the slimes go to an additional flotation circuit while the sand portion goes to the secondary grinding mills.Milltronic automatic sound control units were installed on each of the two primary ball mills and put into operation September 3, 1966. After about two months adjustments to the control units the operators were taken off the grinding circuit on November 1, 1966. The operators duties were taken over by the automatic control units while miscellaneous work was taken over by the helpers in the mill. The labour saving by the installation is approximately $2250.00 per month.After a short period of operation it was apparent there was a slight change in grind. The screen analysis of the primary classifier overflows for the period May to August 1966 averaged 62.23% minus 200 mesh while for the period September to December 1966 averaged 62.0% minus 200 mesh. This is a slight coarsening of the grind. The change in the primary grind has manifested itself also in the screen analysis of the final grind. Before automation the final grind was 80% minus 200 mesh, while after automation it was 7 5% minus 200 mesh. A change of grind was also noted in the flotation concentrates. Before automation the screen analysis of the concentrates was 35% plus 200 mesh and 50% minus 3 25 mesh. A ft er automation it was 35% plus 200 mesh and 47 .5% minus 325 mesh. In other words the grind got coarser or perhaps we should say there was less overgrinding. Another significant change took place in the assays of the slime and sand portion of the primary flotation tailings. It was usual under manual control for the slime portion to assay higher in gold than the sand portion. The reverse is now true."

Jan 1, 1967