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By J. R. Long, T. R. Graham, R. S. Dean

ALTHOUGH considerable information has been published concerning manganese additions to the aluminum bronzes, these data refer principally to the two-phase alloys containing 8 to 11 pct aluminum, with some incidental information on the single-phase alpha solid solution alloys. Strauss1 gives an excellent review of the literature on aluminum bronzes up to 1927 and a bulletin2 of the Copper Development Association brings the bibliography up to 1938. The most extensive work on manganese addition is that of Rosenhain and Lantsberry,3 who investigated alloys ranging up to 10 pct aluminum and up to 10 pct manganese, and presented data on the physical properties of sand-cast, chill-cast, and several wrought alloys. The greater portion of the work, however, concerns alloys ranging from 7 to 10 pct aluminum in the cast condition and sheds little light on the properties of wrought single-phase alloys. Corson4 notes that alloys containing 10 pct manganese and 4 pct aluminum are not hardenable by heat-treatment, while one with 15 pct manganese and 5 pct aluminum can be hardened, but he gives no tensile data on it. In fact, no systematic study of the properties of single-phase wrought alloys containing substantial amounts of manganese has been reported. It should also be noted that most of the investigators worked with alloys containing significant amounts of iron and silicon, and that these impurities, whether intentionally added or accrued from the raw materials used in the preparation of the alloys, may be expected to have a direct bearing on the resultant properties. In the work on alloys made with electrolytic manganese, the Bureau of Mines has undertaken an investigation of the copper-manganese-aluminum system for the purpose of establishing the constitution and properties of high-purity alloys. In a recent paper5 the authors reported a metallographic investigation of the alpha solid solution area and the adjoining fields of the copper-manganese-aluminum system up to 50 pct manganese. This study established the alpha-phase boundaries at 50° temperature levels from 400° to 850°C. It was found that the addition of manganese to copper-aluminum alloys decreases the solubility of aluminum in the alpha phase (Fig I), curving the boundary toward the copper-manganese base line. The greatest change occurs in the first 20 to 25 pct manganese, which decreases the solubility of aluminum to approximately 4 pct. With larger amounts of manganese the alpha boundary tends to parallel the copper-manganese binary. At 1300°F and higher,

Jan 1, 1947

By R. W. Ludt, C. C. DeWitt

The use of froth flotation for the separation of minerals has become one of the most important of ore dressing processes. Its particular adaptability to the enrichment of low grade ores has made the process an important factor in the national economy. The methods have been extended to the recovery of a great number of minerals. Among the few minerals which have resisted efforts toward industrial flotation is chrysocolla, a hydrated partly colloidal copper silicate. Chrysocolla, being a product of natural oxidation, has been found to occur in small quantities with many ores which are recovered by flotation methods. In present practice, these small quantities of copper silicate pass off with the tailings and are lost. The advantages to be gained by a satisfactory process for the recovery of chrysocolla is apparent. Any application of principles which points a way toward the satisfactory industrial flotation process for copper silicate would be of advantage. This paper presents an attack on this problem. Two methods for the recovery of chrysocolla have been developed by the United States Bureau of Mines.1,2 They have been successful on a laboratory scale but have been seriously restricted in industrial application by critical requirements in the procedure. In one of the Bureau of Mines methods,' the ore is activated with sodium or hydrogen sulphide in an aqueous solution at a pH of 4. Amy1 xanthate is then used as a collector with pine oil as a frother in the flotation process. An excess of sulphide acts as a depressant and the state of optimum conditions is difficult to control industrially. In the second Bureau of Mines method,2 soap is used as the collector at a pH of between 8 and 9. The diffi- culties with this process are that soap is not a specific collector, that heavy metal or alkaline earth ions cause the formation of insoluble soaps, and that a more acid solution causes the formation of a free acid which does not act as a collector for chrysocolla. The problem of recovering chrysocolla by flotation involves the selection of a suitable collector. The collector molecule must be composed of an active polar group that has an attraction for chrysocolla, and of a hydrocarbon chain. Certain dyes have been shown to have an attraction for certain minerals. Suida3 found that hydrated silicates are colored by basic dyes. Dittler4 showed that chrysocolla, among other colloidal minerals of acid reaction, preferentially takes up such basic dyes as fuchsin B, methylene blue, and methyl green. Endell5 gave information to show that the colloidal material in clay may be determined by its selective adsorption of fuchsin. A simple experiment, likewise, illustrates the difference in the adsorptive power of chrysocolla and of silica for the basic triphenyl methane dyes. When a mixture of chrysocolla and silica is immersed in a very dilute dye solution, less than 5 ppm, the chryso-colla is rapidly dyed and the silica is dyed more slowly. The difference is substantial but one of degree. Dean2 showed that the dyes, crystal violet and toluidine blue, are taken up by quartz in an adsorption type process. The difference in the adsorptive power, however, offers the means by which a new collector may act. To form such a collector, a hydrocarbon chain must be attached to the dye molecule. This involves a process of organic synthesis. Butyl, hexyl, and octyl hydrocarbon chains were selected for substitution in the malachite green molecule. For the purpose of identification, the alkyl-substituted dyes formed are called: butyl-malachite green; hexyl- malachite green; and octyl-malachite green. An outline of the procedure for their synthesis is given in the appendix. It is generally recognized in the preparation of this type of dye that the chemical structure of some of the dye molecules varies. However, a uniform formula is attributed to the dye. Such a procedure has been followed in specifying the structure of these alkyl-substi-tuted malachite green dyes. The structure is given on the basis of their properties as an homologous series of dyes, on their method of preparation, and on the purity of intermediates used. Structure of substituted alkyl malachite green is: C6H4 N(CH3)2 p-R C6H4 CH C6H4 N(CH)2 Procedure The flotation cell is a Bureau of Mines 100-g, batch unit provided with an air inlet at the bottom above which is a variable speed agitator. The agi-

Jan 1, 1950

By P. R. Swann, R. M. Fisher, W. R. Duff

Observations by transmission electron microscoPy of the microstructures in quenched Fe-A1 alloys provide the basis for revision of the Fe-A1 phase diagram. The diagram is characterized by first-order transitions between the disordered ferromagnetic a! solid solution and the two ordered phases FeAl and Fe3Al. However, second-order transitions showing corre-luted fluctuations in the degree of order near the critical temperature occur between the paramagnetic a! and FeAl and the FeAl and FeAl phases. ELUCIDATION of the true nature of the Fe-A1 equilibrium diagram has proven to be an extremely challenging problem as evidenced by the fact that six quite different versions of the iron-rich portions have been published since 1958.&apos;-6 The most recent diagram shown in Fig. 1 was proposed by Rimlinger6 based on X-ray diffraction analysis and dilatometry. He shows the single-phase fields of the ordered phases of the types FeAl(L20) and Fe3A1(D03) and the disordered bcc Fe-A1 solid solution, a, separated from one another in every case by large two-phase regions. Thus, he implies that in Fe-A1 alloys ordering always occurs via a classical phase transition. In contrast to this view, theoretical studies3&apos;" have concluded that the transitions a — FeAl and FeAl — Fe3A1 should be second- or higher-order in character. A further revision of the Fe-A1 diagram of state is presented in Fig. 2 based on our previous8,9 and current observations by transmission electron microscopy of the microstructures found in quenched specimens. The average quenching rate was 50,000°C per sec and although this was sufficiently rapid to prevent Fe3A1-type ordering below -550°C it was not sufficient to suppress ordering of the type FeAl in the temperature range -650" to 800°C. However, ordering during the quench is easily recognized since the FeAl phase formed during holding at temperature rapidly develops large antiphase domains whereas FeAl formed during quenching has a very fine domain size, -50Å diam. Each symbol in Fig. 2 indicates the result of a micro-structural examination of specimens heat-treated (-1 hr) until equilibrium was established. The results will be discussed in the order of the points, A - Dl marked on both diagrams with reference to the phase fields, critical temperature, and "transition" ranges, respectively. The dark-field micrograph corresponding to point A is shown in Fig. 3 and was obtained using a 111 reflection of the Fe3A1 structure which reveals both a&apos;/4<111> and a&apos;/2<100> antiphase domain boundaries.10 The structure observed in this specimen is typical of single-phase Fe3A1 and shows no evidence for FeAl or any other additional phase. The dark-field micrograph shown in Fig. 4 corresponds to point B on the two diagrams. It was taken with a 100 FeAl reflection which reveals a/2(111) domains and exhibits the typical structure of single-

Jan 1, 1970

By A. R. Troiano, A. B. Greninger

There is need for an adequate working hypothesis that would describe at least qualitatively the crystallographic mechanism for the transformation from austenite to martensite in steel. A general theory would not only be of great assistance in the correlation of existing data and in planning future experimentation, but would also form the basis for an eventual explanation of the property changes that accompany lattice transformations. The mechanism of martensite formation described in the following pages is the outcome of two new experimental determinations: (1) the accurate evaluation of the lattice relationship between austenite and individual crystals of martensite, and (2) the measurement and analysis of the change in position that a volume of austenite undergoes when it transforms into a crystal of martensite. For this latter study, the stereographic analysis of shear was employed; this method greatly simplifies the solution of lattice-shear problems, and some space is devoted to its description. Lattiice Relationships and Habits PREVIOUS WORK The lattice relationships between austenite and martensite in carbon steels have been studied by Kurdjurnow-and Sachs,&apos; and by Wassermann;2 and in iron-nickel alloys by Nishiyama.3 Wassermann,2 and Mehl and Derge.4 The studies by Kurdjumow and Sachs and by Wassermann were made on single (austenite) crystals of quenched 1.4 pct carbon steel, and the results of these two independent studies agree closely with the postulated lattice relationships: (III)r||(0ll)a [101]r [111]a [1] Both Nishiyama and Wassermann worked with an alloy of iron plus 30 pct nickel (all austenite at room temperature), and "martensitic alpha" was formed by cooling in liquid air. They agree that the lattice relationships for these conditions are: (lll)r||(011)a [112]r[011]a [2] Mehl and Derge worked with a range of iron-nickel alloy compositions centered about 30 pct nickel. They concluded that when the transformation takes place near room temperature or above, relationship [l] holds, but if the same specimen is made to transform at -195°C, relationship [2] obtains;intermediate temperatures evidently produced a combination of these two relationships. Sachs and co-worker~,1,7 as well as Nishiyama,3 have proposed transformation mechanisms for martensite formation.* Both of the mechanisms picture the transformation as initiated by shearing movements along the octahedral [Ill] plane of austenite, followed by suitable expansion and contraction to complete the transformation. These mechanisms have been described and commented upon by Mehl, Barrett, and Smith,8 Mehl and Derge,4 Wassermann,2 and others, and generally accepted by investigators in this field. Greninger and Troiano9 have recently published the results of a detailed study of the shapes and orientation habits of martensite crystals in plain-carbon and nickel steels. They found that, contrary to previous assumptions, martensite plates form not along the octahedral planes but along austenite planes of very high indices; these results were in line with those of previous studies of martensite reactions in nonferrous alloy systems by Greninger and coworkers.6,10 Greninger and Troiano concluded that the transformation theories of Kurdjumow and Sachsl and of Nishiyama3 are untenable. Phragmén11 reached a similar conclusion. EXPERlMENTAL METHODS The object of this particular study was the evaluation of (1) lattice relationship between austenite and martensite, and (2) relationship between the martensite lattice and the martensite plate. The technique used for solving these problems was similar to that used by Greninger6 on martensitic structures in 8 copper-aluminum alloys. Briefly, the method consists of grinding and polishing a specimen on a surface parallel to an individual martensite plate and thus exposing a single martensite crystal for an area of l to 3 mm. The orientation of this exposed martensite crystal is then determined by means of a back-reflection Laue X ray pattern.12 Another pattern is obtained from the matrix crystal, and a stereo-graphic plot of data from these two patterns then provides the solution to the problem. It is necessary to repeat this process on several crystals in order to determine whether or not the solution is unique.

Jan 1, 1950

By L. L. Handy

The development of a theory for miscible liquid displacement requires evaluation of the variables which affect growth of the mixing zone between solvent and displaced oil. Factors which appear to be important are individual fluid viscosities, viscosity ratios, flood rate, fluid densities, flow characteristics of the porous medium and molecular diffusion coefficients of the fluid components. The primary purpose of this paper is to evaluate diffusion effects. Theoretical treatments to date have been limited to floods for which the viscosity ratio is one. Two principal theories have been proposed. Von Rosenberg adapted for porous media a theory derived for capillary tubes by G. Taylor.&apos; ,&apos; In this theory molecular diffusion perpendicular to the direction of flow is a primary factor in sharpening the flood front. Slow floods give sharper fronts for a given distance traveled than fast floods. An alternative theory considers miscible liquid displacement as a statistical problem.3,4,5 Diffusion is not an important factor in this theory, but it leads to the same general type of equation as von Rosenberg&apos;s. Both theories predict S-shaped concentration profiles with the same dependence on distance traveled. The statistical or "dispersion" theory predicts rate independence, however. To supplement rate studies a direct measurement of a diffusion effect would be helpful in evaluating which of the two proposed mechanisms best describes miscible liquid displacement for one-to-one viscosity ratio systems. No quantitative theory has been proposed for floods in which a low-viscosity fluid displaces a high-viscosity fluid. It might be anticipated, however, that the extensive fingering observed in floods with adverse viscosity ratios would increase opportunities for an exchange of components between displaced and displacing liquids by a diffusional process. Even if molecular diffusion were not an important mixing mechanism for one-to-one viscosity ratio systems, it could be significant in systems with adverse viscosity ratios. METHOD FOR EVALUATING DIFFUSIONAL MIXING In solvent flooding the displacing liquid can become mixed with the displaced liquid by a number of processes; in general, either mechanical or diffusional in character. To evaluate the contribution of diffusion, a method was sought that would distinguish diffusional mixing from mechanical mixing. Suppose two soluble tracers are added to the displacing liquid and that one tracer has a diffusion coefficient much greater than the other. Then, if diffusion is important during miscible liquid displacement and if diffusional transport is primarily transverse to the direction of flow, substances with high diffusion coefficients will have sharper concentration profiles than those with comparatively low molecular diffusion coefficients. In order to have material balance the profiles for the two tracers must intersect. For one-to-one viscosity ratios the intersection would occur at the 50 per cent concentration point. It is generally assumed that diffusion in the direction of flow is negligible. This assumption appears reasonable because flow velocities are ordinarily orders of magnitude greater than diffusional velocities. If this is not a valid assumption, however, the shapes of the fronts will be further degraded by longitudinal diffusion. The effects of rate and molecular diffusion coefficients are the opposite for longitudinal diffusion to those for lateral diffusion. Higher rates or lower diffusion coefficients would tend to give sharper fronts. The double tracer method offers several unique advantages in evaluating effect of molecular diffusion. First, the method gives a direct measure of the effect of diffusion on mixing zone size. Second, the effect of a difference in diffusion coefficients is determined from a single experiment. Comparison of several experiments at different rates is not required. Third, the method is applicable for any viscosity ratio. Fourth, the method is unaffected by density differences between the two fluids which might result in rate dependent gravity effects. EXPERIMENTAL PROCEDURE Suitable tracers are substances whose diffusion coefficients differ as widely as possible, but whose adsorptions on rock surfaces is negligible. The two tracers selected were methanol and sucrose in water solutions. The approximate diffusion coefficients for methanol and sucrose, as given in the International Critical Tables, are 1.3 X 10-5 and 0.3 X 10-5 m2/sec, respectively. Concentrations in the water solutions were 200 gm/liter of solution for both methanol and sucrose. These high

By J. E. Fox Jr., J. L. Lummus, J. P. Gallus

Fresh water or brine drilling fluids may be kept free of suspended drilled solids by the addition of a water soluble acrylamide-carboxylic acid copolymer at the flowline. Addition of from .01 to 0.2 lblbbl of the polymer solution to drilling fluids containing less than 5 per cent clay solids by weight causes the solids to flocculate and settle rapidly to the bottom of the pits. Solutions of the polymer injected at the pump suction reduce the loss of water to permeable formations without impairing the permeability to oil. The use of drill-itlg fluids clarified with the polymer has resulted in increased drilling rates, extended bit life, and lower drilling fluid costs. INTRODUCTION Field experience and the results of a number of investigations have established that the accumulation of solids in drilling fluid reduces drilling rate.&apos;-&apos; Drilling with water makes possible higher drilling rates than can be achieved with mud but in many areas drilling with water may not be feasible because of the possibility of encountering high formation pressures or by-dratable formations. To combat these conditions, the drilling fluid must possess certain physical properties such as viscosity, density, fluid loss, etc., which require the presence of solids. The current trend in drilling fluid treatment is to maintain as low a percentage of solids as is possible without harmfully affecting the mud properties needed for drilling. Mechanical separating devices such as wet cyclones and decanting-type centrifuges are proving to be an economical means of controlling the percentage of solids and thereby maintaining low solids muds. Also: special muds have been developed for the purpose of retarding the hydration of drilled solids so that they may be more easily removed by shale shakers or settling pits. In some areas, such as West Texas, the characteristics of some formations will permit drilling with water. However, because of the dispersion of drilled solids, it is usually not possible to maintain clear water even with the aid of mechanical separators, or by utilizing large settling pits. For this reason the commonly used term "water drilling" is a misnomer since the water usually contains some solids. Because of the improved drilling rates and other benefits which might be effected, a laboratory and field study was made of the use of flocculating agents for maintaining clear water for drilling. PROCEDURE Laboratory—Solids Settling Two techniques were employed to determine the effectiveness of flocculating agents in settling solids from drilling mud. First, the rate of fall of solids was measured in graduated beakers containing mud treated with various flocculating agents. Natural gum, oil-in-water emulsions prepared with ethoxylated nonyl phenols and diesel oil. and a powdered synthetic acrylamide-carboxylic acid copolymer* (hereinafter referred to as "polymer") were tested as flocculating agents in both fresh water and salt saturated muds containing 4 per cent solids. The polymer was not added in the powder form directly to the muds but was first dissolved in water in a concentration of 3.5 lb/bbl. The polymer solution was then added directly to the mud. The concentration of the flocculating agents, including the polymer, was varied. High rates of fall of the solids indicated high flocculating efficiency. A second technique consisted of measuring the time in minutes required to obtain clear water at the pump suction after addition of the various flocculating agents at the flowline. These tests were made using a model mud circulating system having a total volume of approximately 10 gal. The natural fresh water and brine muds used contained 4 per cent solids. A sketch of the circulating system appears in Fig. 1. The circulating rate

By R. R. Harvey

Recent evidence has indicated that the films forming at crude oil-water interfaces are the result of naturally occurring su,rface-active components in the crude oil rather than oxidation products resulting from exposure of the oil to air. Since the presence of such films may strongly affect the displacement of oil from porous media, a knowledge of their composition and formatiorz is of fundamental importance. In this study, without the assumption of a specific mechanism, film formation is considered to involve the transfer of a weakly surface-active species in solution in the oil to the oil-water interface. The film gas law and the Gibbs adsorption equation may thus he applied to the system. The rigid films which form upon decrease of the oil-water interfacial area are considered a result of the very slow rate of re-solution of the film material into the oil. When the shrinkage of the interface is very rapid, the amount of film material leaving the interface is negligible, and the system may then be treated in the same manner as an insoluble film. The combination of these treatments leads to a new concept of the film factor in which it may he quantitatively related to the concentration of film-forming material at the interface. Suitable experiments can then yield the following information. 1. Original concentration of surface-active species in the oil. 2. The change of concentration with time. 3. Concentration of surface active species at the interface. 4. The change of this concentration with time. 5. Interfacial tension of the system at any time and its variation with time. 6. Equilibriunz concentrations for a given set of conditions. 7. Concentration requirements for solid film formation. 8. Molecular diameter of the adrorbed species. These calculations may be made solely from data taken from measurements on the original oil. While using the pendant drop method of interfacial tension measurement of crude oil-water systems, Bartell and Niederhauser&apos; remarked on the thin, transparent, pliable, solid films or membranes which were often formed at the interface between crude oil and water. As a result of their observations of these films, Bar-tell and Niederhauser concluded: 1. The films are formed by material from the oil adsorbed at the interface rather than by a reaction at the interface. 2. The adsorption of the film-forming material is a rather slow process. 3. There are good indications that the process is reversible; i.e., the film constituents may re-dissolve into the oil. 4. The film will spontaneously spread over any new surface formed. 5. The process of adsorption at the interface is accompanied by a decrease in the interfacial tension of the system. Although they had proved that film formation was not due to a reaction at the interface, Bartell and Niederhauser were unable to demonstrate conclusively whether these film-forming constituents were present in the original reservoir oil or whether they were formed as oxidation products after exposure of the oil to air. Recent evidence seems to point to their presence in the original oil. Although the true nature of the film-forming constituents is still uncertain, these conditions would be fulfilled by the assumption of the presence of a slightly soluble surface-active component in the original oil. This component would migrate to a freshly formed interface because it would thereby lower the free energy of the system. The component at the surface constitutes an expanded monolayer which would become compressed, upon retraction of drop, due to the slow rate of re-solution of the film components into the bulk of the oil. It is possible, by involved extraction processes, to separate or at least concentrate this film-forming fraction. However, using the assumptions made above, the technique of monolayer film study may be applied to reveal much of the nature of the adsorbing material without resorting to an actual separation of the film-forming constituents.

By T. P. Chen, F. W. Bowdish

Studies made with a captive bubble apparatus on the sulfidization and collection by amyl xanthate of true chrysocolla specimens have defined the ranges of pH value and sulfide concentration which permit contact between the bubble and the mineral surface. Titanium compounds were the most effective of the materials found to activate the sulfidization of chrysocolla. With titanium activation, the contact angles and the ranges of pH value and sulfide wncentration giving bubble contact were all increased. Chrysocolla ores were concentrated by flotation. Chrysocolla ores occur at many localities in grade and quantity sufficient to make mining and millin feasible, but no satisfactory method of concentratio has been found. Although chrysocolla may be leached with acid, only those ores without acid-consuming gangue may be leached economically. Because of its potential importance, a study of the conditions nece sary for flotation of chrysocolla has been carried ou The literature contains a few references to flotation of chrysocolla. Two methods were developed by the U. S. Bureau of Mines.1,2 The first consisted of a fatty acid soap and a high xanthate as collectors of chrysocolla from a synthetic ore, while the second involved the use of hydrogen sulfide and xanthate. Ludt and DeWitt3 demonstrated the difference in adsorptive powers of chrysocolla and quartz for bas triphenyl methane dyes and suggested the use of butyl, hexyl or octyl-substituted malachite green as collector. Jackel4 emphasized the effects of combin tions of reagents such as Aerofloat 31, pine oil, and Reagents 404 and 425 with sodium sulfide and zinc hydrosulfite as conditioning agents. Although he reported recoveries of 89% from a synthetic ore and 98% from a natural ore containing azurite, malachite, chalcopyrite and chrysocolla, careful application of Jackel&apos;s method to chrysocolla from Tyrone, N.M., failed to give a high recovery. MATERIALS AND TECHNIQUE Samples from Inspiration, Ariz., and Tyrone and Magdalena, N. M., were used for experimentation and verified as true chrysocolla by leaching tests, specific gravity tests and X-ray diffraction. Chrysocolla does not dissolve at pH 4, although malachite and azurite do. Chrysocolla is about half as dense as the copper carbonates. X-ray diffraction analyses by the powder camera method confirmed the samples as true chrysocolla. A captive bubble apparatus, which cast an enlarged image of the air bubble and the mineral surface upon a screen, was used to check on the character of the surfaces. The specimens were prepared by grinding a flat surface on a glass plate using fine abrasive; then they were washed and kept in distilled water until they were to be treated with reagents. Before each reagent treatment, the specimen was carefully checked for cleanliness in the captive bubble apparatus. It was assumed that the surface was clean if, after fine grinding and washing of the specimen, the bubble would not stick. Specimens were handled with glass forceps, and precautions were taken to avoid contamination of the mineral surfaces. Contact angle measurements were carefully made several times on each treated specimen to obtain reliable average values. EFFECT OF pH VALUE AND SODIUM SULFIDE CONCENTRATION In each experiment, a specimen with a freshly ground surface was immersed for 10 min in a solution of sodium sulfide, washed and immersed for 15 min in a solution containing 30 mg per 1 of potassium amyl xanthate. The specimen was then washed again in distilled water and tested for contact angle in the captive bubble apparatus while submerged in distilled water. In this series of experiments, the pH of the sulfidizing solution was varied from 3 to 7, and the concentration of sodium sulfide, containing 60% Na2S, was varied from 50 to 650 mg per 1. Many combinations of pH value and sulfide concentration resulted in no contact between the bubble and the surface, but over a limited range of conditions, contact angles varying from 24ºto 52ºwere obtained. The data in Fig. 1 show sulfidization conditions that lead to bubble contact and those that do not. The region of contact is surprisingly small, which may indicate why flotation of chrysocolla involving sulfidization has proven so difficult in practice. Several features of the system are illustrated in Fig. 1. In the region between pH values of 4 and 6 with sodium sulfide concentrations below about 350

Jan 1, 1963

By R. D. Daniels, T. W. Wood

The tensile properties of columbium and Cb-H alloys containing up to 455 ppm H were studied as a function of temperature and strain rate. Hydrogen, introduced into columbium at elevated temperatures, using a thermal -equilibrium technique, embrittled columbium most severely at about —77°C. This elnbrittle ment occurred even at hydrogen concentrations of an order of 20 ppm. At higher temperatures, the hydrogen tolerance of columbium increased in relation to the increased solubility of hydrogen in tile metal. Below this temperature hydrogen tolerance, as determined by ductility and fracture stress, increased slightly. Strain rate had little effect on the tensile results for cross-head speeds over the range 0.002 to 2.0 in. per min. Strain aging during the tensile test appears to explain the ductility mininmum at —77°C. The apparent increase in hydrogen tolerance at lower temperatures is attributed to the low mobility of hyhogen. Experiments were performed in which samples were prestrained in tension at room temperature and tested to failure at —196°C. Results suggest that hydrogetz segregation to preformed crack nuclei can cause subsequent embrittlement even at temperatures where hydrogen mobility is too low to cause embrittlement in a normal tensile test. COLUMBIUM is an example of the class of bcc metals with ductile-brittle transition temperatures sensitive to the presence of interstitial atom contaminants. Hydrogen is one of these embrittling contaminants. The embrittling effect of hydrogen is less potent, perhaps, in columbium than in some of the other bcc refractory metals, but it is still a problem of both theoretical and practical interest. Unlike hydrogen in iron and steels, hydrogen in columbium is exothermically rather than endo-thermically occluded. The embrittlement process in exothermic systems has not been studied as extensively as that in endothermic systems, especially at hydrogen concentrations below the limit of solubility. The purpose of this investigation was to evaluate the embrittlement process in initially pure columbium as a function of hydrogen content, temperature, and strain rate. The Cb-H phase diagram, according to Albrecht et al.,1 is shown in Fig. 1. Columbium reacts exothermically with hydrogen producing a solid solution at concentrations of less than about 250 ppm (parts per million by weight) H at room temperature. At concentrations above the highly temperature-dependent solvus a second phase is formed. Like many similar hydrogen-metal systems,2 his system exhibits a miscibility gap with respect to hydrogen solution. Albrecht found the critical temperature of the miscibility gap to be about 140°C, the critical concentration to be 0.23 atom fraction hydrogen, and the critical pressure to be 0.01 mm Hg. Above 140°C there is a solid solution of increasing lattice constant extending across the phase diagram. Hydrogen concentrations of particular interest in this investigation were those below the limit of solubility in columbium. At hydrogen concentrations above the limit of solubility, columbium will contain the hydrogen-rich second phase and will be brittle under most testing conditions because the hydride generally precipitates as platelets with coincident matrix lattice strains.1&apos;3 At hydrogen concentrations below the limit of solubility, the tensile behavior of columbium is expected to be more sensitive to the interrelationships between hydrogen concentration and mobility and the testing variables such as temperature and strain rate. Literature references to the hydrogen embrittlement of metals, especially ferrous alloys and titanium alloys, are too voluminous to mention. It is only recently, however, that detailed studies of the hydrogen embrittlement of columbium have been undertaken. Wilcox et a1.4 studied the strain rate and temperature dependences of the low-temperature deformation behavior of fine-grained are-melted columbium (1 ppm H) and the effect of hydrogen content (1,9, and 30 ppm H) on the mechanical behavior of columbium at a series of temperatures for a single strain rate. A strain-aging peak was ob-served at about -50°C which was attributed to the presence of hydrogen in the metal. Eustice and carlson5 studied the effect of hydrogen on the ductility of V-Cb alloys at a series of temperatures over the range -196° to 25°C. Pure columbium was embrittled by 20 ppm H which produced a ductility transition at approximately -70°C. Ingram et al.6 studied the effect of oxygen and hydrogen on the tensile properties of columbium and tantalum. A minimum in the notched-to-unnotched tensile ratio of hydrogenated columbium was obtained at about -75°C, but because of the relatively large hydrogen content employed (200 and 390 ppm) the ductility

Jan 1, 1965

By H. L. Stone, A. O. Garder

A numerical method of solving the partial differential equations which describe the one-dimensional displacement of oil by gas has been presented. Possible extension of the method to treat multidimensional flow is discussed, and the limitations of this extension are indicated. Using this method, it is possible to allow for the existence of a gas cap, the presence of any number of gas-injection or oil-production wells and the evolution of dissolved gas from the oil. It is also possible to allow for variation in the cross-sectional area, elevation, porosity and permeability of the reservoir. The influence of relative permeability and the force of gravity in the direction of flow upon the displacement is considered. The influence of capillary pressure upon the flow and the effect of gravity in the direction perpendicular to flow are neglected. The physical properties 01 the fluids are considered to be Junctions of pressure only, and equilibrium between contiguous phases is assumed. The numerical calculations can be readily carried out by the use of a digital computer. Several example analyses have been performed using the IBM 704 computer, and about one-third of an hour of computing time was required per case. Reservoir behavior predicted by use of this numerical method was compared to data obtained by other methods for three cases — complete pressure maintenance, dissolved-gas drive and gas-cap drive. The independent solutions to these problems were obtained by analytical solution, laboratory experiment and field data, respectively. Agreement of the numerical solution with data from these sources was good; this agreement establishes the convergence and accuracy of the numerical method. INTRODUCTION Most petroleum reservoirs can be produced by any one of several alternative programs. When a reservoir is produced by primary methods, production economics can be influenced by controlling the number and location of wells and the flow rate of each well. An even greater influence may be achieved by augmenting the recovery of oil obtainable by primary methods. This can be accomplished by injection of fluids such as water, natural or enriched gas or a bank of light liquid hydrocarbons. Selection of the most desirable operation requires a means of predicting the reservoir behavior which will result from each of the several alternative programs. The purpose of this paper is to present a mathematical method for predicting the behavior of reservoirs produced by gas-cap drive, dissolved-gas drive or pressure maintenance by gas injection. The method described herein takes cognizance of phase changes caused by a decline or an increase (due to gas injection) in reservoir pressure, of the presence of a gas cap and of the effect of gravity on the flow of gas and oil. Relative permeability relationships are used to define the flow properties of the rock. Allowance is made for variation in cross-sectional area, elevation, permeability and porosity of the reservoir. Both the influence of capillary pressure upon the flow and pressure gradients in the gas cap are neglected. Whenever a liquid phase and a gas phase are in contact, they are assumed to be in equilibrium. The physical properties of the fluids are considered to be functions of pressure only. Therefore, if the method is to be used to predict the effects of a gas-injection program, mixtures of the injected gas and formation crude should-have the same physical properties as mixtures of formation gas and crude. The equations to be presented in this paper apply only to a one-dimensional case; therefore, they neglect the influence of gravity in the direction transverse to the flow. As is well known, this gravitational influence may lead to overriding of oil by gas. Consequently, this procedure as presented is most applicable to long, thin reservoirs for which gravity overriding is not important. On the other hand, the equations presented can be generalized to treat multidimensional flow and, hence, to consider gravity overriding, if desired. A word of caution on two points is advisable here, however. First, the authors have not demonstrated the accuracy of the numerical technique for multidimensional flow. Second, and more important, capillary pressure will often be of importance in multidimensional problems. Obviously, in such cases a generalization of the

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"&apos; and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7&apos;8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965

By A. M. Gaudin, C. S. Chang

Adsorption was measured for barium ion and laurate radical, using radioactively marked agents, over wide range of concentrations. Laurate adsorbed in absence of barium fails to float. With barium, flotation-effective laurate coating needs not exceed 5 pct of monolayer. Barium adsorption then is several fold larger. No barium laurate coating is obtained. IN general, fatty acids or their alkali salts do not cause clean quartz to float. However, the presence of multivalent ions, such as the alkaline-earth metal ions and heavy-metal ions, can activate quartz and thus make it respond to soap flotation. The mechanism of activation and soap flotation of quartz has been studied.&apos;-&apos; The problem was attacked by making flotation tests rather than by careful adsorption measurements on suspensions of ground quartz in solutions containing the activator and the collector. Attempts have been made to determine the adsorption of barium ion and calcium ion on quartz. The results have only qualitative value as the analytical methods were not adequately precise. Artificial radioactivity and progress in radioactivity detection have introduced a new analytical tool, which can have a sensitivity several orders of magnitude greater than that of other methods."-" In the experimental work described in this paper the radioactive tracers, barium 140 and carbon 14, were employed. Lauric acid was synthesized, having a radioactive carbon atom and was used with Ba" to study the adsorption of barium and laurate ions from aqueous solution on ground quartz. Flotation tests, using the vacuum flotation technique,&apos; were run in conjunction with the adsorption experiments. The object of this investigation was to understand better the reaction mechanism of barium activation and soap flotation of quartz. Methods and Materials Quartz Sample Preparation: Lumps of hand-picked quartz, washed free of stains, were reduced in size to —20 mesh in laboratory crushers. The product was boiled in concentrated hydrochloric acid to remove the abraded iron. The cleaned product then was ground dry in a laboratory porcelain mill, using siliceous pebbles, to pass through a 200 mesh screen. The ground product was deslimed by sedimentation at 37 microns. This —200 mesh +400 mesh material was subjected again to boiling with concentrated hydrochloric acid, followed by washing with distilled water and further desliming. The cycle was repeated until no trace of iron could be detected in the wash liquor. During the final washing, the pH of the wash water was checked to insure the complete removal of the acid from the mineral. The quartz then was rinsed with conductivity water. The resulting product was dried in a drying oven and stored in mason jars. The impurities (spectrographic) were as follows: Al, 0.01 to 0.001 pct; Li, Mg, Mn, Na, each less than 0.001 pct; Fe and Cu not detected. The specific surface of the quartz sample was determined by the krypton gas adsorption method.&apos; The average of two measurements was 881 sq cm per g. The calculated specific surface for 37/74-micron quartz particles, using a surface factor of 1.96; is 900 sq cm per g. This is in good agreement with the measured value of 881 sq cm per g. Beta-Counting Method: The radioactive isotope of barium used in the experimental work was barium 140. It has a sufficiently long half-life, 12.8 days, emits high-energy beta particles (up to 1.0

Jan 1, 1953

By A. M. Gaudin, C. S. Chang

Adsorption was measured for barium ion and laurate radical, using radioactively marked agents, over wide range of concentrations. Laurate adsorbed in absence of barium fails to float. With barium, flotation-effective laurate coating needs not exceed 5 pct of monolayer. Barium adsorption then is several fold larger. No barium laurate coating is obtained. IN general, fatty acids or their alkali salts do not cause clean quartz to float. However, the presence of multivalent ions, such as the alkaline-earth metal ions and heavy-metal ions, can activate quartz and thus make it respond to soap flotation. The mechanism of activation and soap flotation of quartz has been studied.&apos;-&apos; The problem was attacked by making flotation tests rather than by careful adsorption measurements on suspensions of ground quartz in solutions containing the activator and the collector. Attempts have been made to determine the adsorption of barium ion and calcium ion on quartz. The results have only qualitative value as the analytical methods were not adequately precise. Artificial radioactivity and progress in radioactivity detection have introduced a new analytical tool, which can have a sensitivity several orders of magnitude greater than that of other methods."-" In the experimental work described in this paper the radioactive tracers, barium 140 and carbon 14, were employed. Lauric acid was synthesized, having a radioactive carbon atom and was used with Ba" to study the adsorption of barium and laurate ions from aqueous solution on ground quartz. Flotation tests, using the vacuum flotation technique,&apos; were run in conjunction with the adsorption experiments. The object of this investigation was to understand better the reaction mechanism of barium activation and soap flotation of quartz. Methods and Materials Quartz Sample Preparation: Lumps of hand-picked quartz, washed free of stains, were reduced in size to —20 mesh in laboratory crushers. The product was boiled in concentrated hydrochloric acid to remove the abraded iron. The cleaned product then was ground dry in a laboratory porcelain mill, using siliceous pebbles, to pass through a 200 mesh screen. The ground product was deslimed by sedimentation at 37 microns. This —200 mesh +400 mesh material was subjected again to boiling with concentrated hydrochloric acid, followed by washing with distilled water and further desliming. The cycle was repeated until no trace of iron could be detected in the wash liquor. During the final washing, the pH of the wash water was checked to insure the complete removal of the acid from the mineral. The quartz then was rinsed with conductivity water. The resulting product was dried in a drying oven and stored in mason jars. The impurities (spectrographic) were as follows: Al, 0.01 to 0.001 pct; Li, Mg, Mn, Na, each less than 0.001 pct; Fe and Cu not detected. The specific surface of the quartz sample was determined by the krypton gas adsorption method.&apos; The average of two measurements was 881 sq cm per g. The calculated specific surface for 37/74-micron quartz particles, using a surface factor of 1.96; is 900 sq cm per g. This is in good agreement with the measured value of 881 sq cm per g. Beta-Counting Method: The radioactive isotope of barium used in the experimental work was barium 140. It has a sufficiently long half-life, 12.8 days, emits high-energy beta particles (up to 1.0

Jan 1, 1953

By E. V. Kleber, V. F. Novy, R. C. Vickery

The constitutional diagram has been determined in part for the sgstem Gd-Fe. Seven intermetallic compounds have been found at compositions corresponding to the following Gd-Fe ratios; 2:3, 1.2, 1:3, 2:7, 1:4, 1:5, and 2:17. The GdFe, com-pound has a congruent melting point above 18000C, whereas all of the remaining compounds melt incongruently, A eutectic exists at 13 wt pct Fe at a temperature of 860°C. ALTHOUGH an increasing amount of information is becoming available on the metallurgy of pure rare earth metals, relatively few studies have been made on alloy systems of the rare earths with the transition metals; iron, nickel, and cobalt. Even less data are extant on gadolinium alloys although it could be expected that such alloys might possess interesting structural and magnetic properties. In this paper, we report investigation of the gadolinium-iron alloy system. Studies on systems containing nickel and cobalt will be presented in subsequent papers. Previous data on gadolinium-iron compounds have been reported by Endter and Klemm1 and Jep-son and Duwez.2 Both reports agree on the existence of the GdFe2 phase, which crystallizes with the C-15type structure (face-centered cubic). This is in accord with results of the present work. EXPERIMENTAL The gadolinium metal used was prepared by met-allothermic reduction of high purity gadolinium fluoride. A typical analysis of the metal thus produced indicated the principal impurities to be oxygen, 0.24 pct, and tantalum, 0.2 pct. The iron metal used for alloying was a reagent grade material. Alloys were prepared by arc melting mixtures of the respective metals. Appropriate quantities of the two component metals were carefully weighed, blended and compacted. The compacts were then melted in an arc furnace consisting of a water-cooled copper hearth plate and a water-cooled tungsten-tipped counter electrode contained in a brass vacuum chamber. The furnace was evacuated to an absolute pressure of less than 1 with the leak rate established as being less than 20 per min. The furnace was then back-filled to a pressure of 25 mm of Hg, with a 75 pct He-25 pct Ar mixture. Arc melting at 25 v and 300 amp was maintained for about 30 to 60 sec until the entire visible area of the sample became molten, by which time surface tension had drawn the molten metal pool into a large bead. After allowing the furnace to cool, the alloy button was inverted and the melting process repeated. A series of melts was made covering entire composition ranges from 100 pct Gd to 100 pct Fe. All samples were examined metallographically in the as-melted condition. As the phase diagram became rationalized, and differential thermal analysis had given indications of temperature arrests, annealing was carried out in vacuo or in argon. Generally, compositions containing more than about 60 pct Gd were heat treated at 750°C and alloys containing less than this quantity of gadolinium were annealed at 1000°C. Prolonged annealing times were of the order of 100 to 200 hr. Metallographic examination was repeated on the annealed materials. Although little material loss was noted during alloy preparation, chemical analyses were made on all specimens prepared. The following standard, analytical techniques were used. Samples were dissolved in hydrochloric acid; insoluble material was filtered off, ignited and fused with potassium pyro-sulfate. The cold melt was leached with dilute acid and the solution thus obtained added to the main sample solution. Gadolinium was always determined gravimetri-callv as oxide from oxalate ignition. Iron was removed from an aliquot sample by electrolysis on a mercury cathode at approximately six volts. Gadolinium in the iron-free electrolyte was then precipitated as oxalate which was subsequently ignited to oxide. Iron was determined volumetrically in an aliquot solution by reduction with stannous chloride fol-

Jan 1, 1962

By A. M. Gaudin, C. S. Chang

IN general, fatty acids or their alkali salts do not cause clean quartz to float. However, the presence of multivalent ions, such as the alkaline-earth metal ions and heavy-metal ions, can activate quartz and thus make it respond to soap flotation. The mechanism of activation and soap flotation of quartz has been studied.1-4 The problem was attacked by making flotation tests rather than by careful adsorption measurements on suspensions of ground quartz in solutions containing the activator and the collector. Attempts have been made to determine the adsorption of barium ion and calcium ion on quartz. The results have only qualitative value as the analytical methods were not adequately precise. Artificial radioactivity and progress in radioactivity detection have introduced a new analytical tool, which can have a sensitivity several orders of magnitude greater than that of other methods.5-6 In the experimental work described in this paper the radioactive tracers, barium 140 and carbon 14, were employed. Lauric acid was synthesized, having a radioactive carbon atom and was used with Ba140 to study the adsorption of barium and laurate ions from aqueous solution on ground quartz. Flotation tests, using the vacuum flotation technique,4 were run in conjunction with the adsorption experiments. The object of this investigation was to understand better the reaction mechanism of barium activation and soap flotation of quartz. Methods and Materials Quartz Sample Preparation: Lumps of hand picked quartz, washed free of stains, were reduced in size to -20 mesh in laboratory crushers. The product was boiled in concentrated hydrochloric acid to remove the abraded iron. The cleaned product then was ground dry in a laboratory porcelain mill, using siliceous pebbles, to pass through a 200 mesh screen. The ground product was deslimed by sedimentation at 37 microns. This -200 mesh +400 mesh material was subjected again to boiling with concentrated hydrochloric acid, followed by washing with distilled water and further desliming. The cycle was repeated until no trace of iron could be detected in the wash liquor. During the final washing, the pH of the wash water was checked to insure the complete removal of the acid from the mineral. The quartz then&apos; was rinsed with conductivity water. The resulting product was dried in a drying oven and stored in mason jars. The impurities (spectrographic) were as follows: Al, 0.01 to 0.001 pct; Li, Mg, Mn,, Na, each less than 0.001 pct; Fe and Cu not detected. The specific surface of the quartz sample was determined by the krypton gas adsorption method.7 The average of two measurements was 881 sq cm per g. The calculated specific surface for 37/74 micron quartz particles, using a surface factor of 1.96,8 is 900 sq cm per g. This is in good agreement with the measured value of 881 sq cm per g. Beta-Counting Method: The radioactive isotope of barium used in the experimental work was barium 140. It has a sufficiently long half-life, 12.8 days, emits high-energy beta particles (up to 1.0

Jan 1, 1952

By J. T. Williams

The equilibria in the V-Zr alloy system were investigated by solidus temperature determinations, thermal analysis, dilatometry, electrical resistance measurements, microscopic examination, and X-ray diffraction analysis. There is a eutectic reaction at 1230°C between a compound, V2Zr, and a solid solution containing 10 pct V in ß zirconium. V2Zr decomposes at 1300°C into liquid and a solid solution containing about 10 pct Zr in vanadium. The eutectic composition is probably about 30 pct V. A eutectoid reaction between V2 Zr and a zirconium takes place at 777°C at a very high rate. The eutectoid composition is 5 wt pct V. The limit of solubility of zirconium in vanadium was estimated to be 5 pct at 600°C. No attempt was made to determine the liquidus for the system. THE recent availability of large quantities of high purity zirconium has stimulated the study of zirconium binary systems. The equilibrium diagram for the V-Zr system has received little attention, however. Wallbauml appears to have made the first report concerning the equilibria in these alloys. He reported the existence of a compound, V2Zr, having the MgZn2 ((214) type of structure with a, = 5.277 kX and c° = 8.647 kX. Anderson, Hayes, Roberson, and Kroll2 made a survey of some potentially useful zirconium binary alloys and found that zirconium probably dissolves a small amount of vanadium. They reported the probable existence of a compound between the two elements and suggested that the zirconium-rich solid solution undergoes a eutectic reaction with this compound. Pfeil," in a critical review of the existing information, estimated that the solubility of vanadium in zirconium is less than 4.7 pct and probably less than 1.8 pct. Rostoker and Yamamoto&apos; proposed a partial diagram for the V-Zr system in a survey paper on vanadium binary alloys. Their diagram indicates the compound, V,Zr, a eutectic reaction at 1360°C, a peritectic reaction at 1740°C, and a limit of solubility of zirconium in vanadium of about 3 pct. They obtained no information on the equilibria in the zirconium-rich alloys. In view of the potential utility of the V-Zr alloys and the incomplete knowledge concerning the equilibria in the system, an attempt was made to establish the constitutional diagram. Preparation of the Alloys Raw Materials: The vanadium for making up these alloys came from the Electro Metallurgical Corp. Zirconium came from two sources. In the beginning of the investigation, sponge zirconium from the Bureau of Mines was used in making some of the alloys. Later, iodide metal made at the Westinghouse Atomic Power Development Laboratories became available. This material was used in the preparation of all the dilatometric and resistance specimens and about two-thirds of the solidus temperature specimens. A typical manufacturer&apos;s analysis of the vanadium is shown in Table I. No other analysis of the vanadium was made. The metal contained a dispersed second phase and did not have a sharp melting point. Typical results of spectrographic analysis of the Westinghouse zirconium are shown in Table 11. These data indicate a very high purity. The Bureau of Mines sponge metal was probably less pure but had good ductility. Melting: All of the alloys used in the investigation were made by melting pieces of vanadium and zirconium together in a dc electric arc furnace similar to those of Geach and Summers-Smith, craighead, Simmons, and Eastwood," and others. Melting was done in an atmosphere of helium scavenged of residual air by the preliminary melting of a separate charge of zirconium. Each ingot was turned over and melted at least three more times before removal from the furnace to aid in the attainment of homogeneity. Alloys prepared for use in the investigation are listed with the results of solidus determinations in Table III with the exception of the following compositions upon which no solidus determinations were made: 0.29, 0.54, 4.57, and 5.55 pct V. Analysis: The weight of each ingot made from iodide zirconium was within 0.1 g of the total weight of the initial charge, about 90 g. Since each component of each charge was weighed to the nearest 20 mg for amounts less than 10 g and to the nearest 0.1 g otherwise, the gross composition of an ingot could be calculated accurately. Chemical analysis for the vanadium content of several alloys agreed

Jan 1, 1956

By Paul A. Farrar, Sanford Adler

The Tz-Zr system was reinvestigated using both metallographic and X-ray diffraction techniques. It mas found that titanium and zirconium are soluble in all proportions in both the a and 0 phases. The minimum in the transformation was found at 50 at. pct and 535°C. THE Ti-Zr system has previously been the subject of several investigations.1-6 A study by Hayes et al.5 using magnesium-reduced titanium and zirconium melted in graphite crucibles indicated that the system was a continuous series of solid solutions in both a and 0 phases with a minimum at approximately 545°C and 65 pct* Zr. These conclusions were substantiated by the work of Duwez4 as well as by the limited data of Craighead et al.,3 Fast,2 and deBoer.1 However, a more recent investigation of the titanium-rich region by Ence and Margolin6 indicated that the solubility of zirconium in a, titanium at 500°C is approximately 22 pct with the a + 0 field extending to approximately 47 pct Zr. Therefore in order to resolve this discrepancy the following investigation was initiated. EXPERIMENTAL PROCEDURES The alloys used in this investigation were prepared as 20- to 30-g buttons by nonconsumable electrode melting in a helium atmosphere. The starting materials were Bureau of Mines titanium BHN 71 and Foot Mineral iodide crystal bar zirconium. The titanium was premelted before the alloys were prepared to avoid excessive weight losses in the final melting. The compositions of the alloys prepared were as follows: Ti-12.0, 22.2, 29.0, 39.6, 50.0, 58.0, 72.4, 83.5. and 90.8 pct Zr. Prior to heat treatment the alloys were cold-worked 10 to 20 pct, stopping at the first signs of cracking. Specimens for heat treatment were wrapped in molybdenum sheet and annealed in argon-filled quartz capsules for the following times and temperatures: 750°C-40 days, 675°C-61 days, 600°C—109 days, 575°C-112 days, 550°C-112 days, 525°C—127 days, and 450°C —153 days. Quenching was accomplished by breaking the capsules in an iced-brine solution. The standard techniques used for polishing the specimens involved belt grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch7 or "R" etch 8 Debye-Scherrer X-ray powder photograms were obtained for a number of samples using a 114.6-mm camera and CuK, radiation. Exposure times were from 19 to 23 hr. The powder samples were obtained by filing to 270 mesh size. After filing the samples were wrapped in molybdenum foil capsuled in quartz and reannealed at the temperature of original heat treatments; following the heat treatment the samples were quenched into iced brine without breaking the capsules. RESULTS AND CONCLUSIONS On the basis of the microstructural examinations of the heat-treated samples and of the X-ray diffraction data, the Ti-Zr system shown in Fig. 1 was constructed. The data indicate that a, and 0 titanium form a complete series of solid solutions with a, and ß zirconium. The minimum was found to occur at 65 pct (50 at. pct) Zr and 535°C, in excellent agreement with the earlier investigations,1-5 see Fig. 2. Typical microstructures are shown in Figs. 3 to 7. Figs. 3, 4, and 5 show the 22.2, 39.6, and 50.0 pct Zr alloys after heat treatment at 675°C for 61 days with the 22.2 pct Zr showing equiaxed a, and the 39.6 pct Zr alloy a + transformed ß, while the 50 pct Zr alloy shows only transformed B. Figs. 6 and 7 show the 29.0 and 39.6 pct Zr alloys after heat treatment for 109 days at 600°C. The 29 pct Zr alloy has an equiaxed a structure while the 39.6 pct alloy has a partially recrystallized a+ß structure. X-ray diffraction data obtained from the 50 pct Zr alloys after heat treatment at 525° and 450°C as well as from the as-cold-rolled material showed only those lineos which couid be indexed a: a titanium, good agreement with the previously published values. 2,4,5,9 Chemical analysis* of the 50 pct Zr alloy

Jan 1, 1967

By G. R. Speich

The age-hardening of Fe-18 to 21 pct Ni marten-sites containing small amounts of titanium, aluminum, copper, or molybdenum has been studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electyon-probe microanaly-sis of the extracted precipitates was also performed. The effects of temperature and composition on the aging kinetics have been studied in detail for Fe-20 pctNi-Ti martensites. All the martensites hardened on aging at 400" to 500 "C with a single aging peak. In the Fe-20 pct Ni-Ti martensites hardening was associated with the formation of a fine dispersion of NisTi. No precipitation was observed in an Fe-21 pct Ni-2.6 pct A1 alloy, although the hardness increased from 327 to 545 Dph during aging at 500°C. Copper was precgitated from an Fe-20 pct Ni-10.7pct Cu alloy, at least during the later stages of age-hardening. Hardening in an Fe-18 pctNi-5pct Mo alloy was associated with the precipitation of an intemzetallic compound tentatively identified as NisMo. The formation of austenite and the recovery of the defect structure of the martensite occur simultaneously with the normal precipitation processes &ring aging of these alloys. THE age-hardening of substitutional iron-base martensites is an important subject for study since age-hardening is one of the principal means of strengthening the substitutional iron-base martensites in precipitation-hardening stainless steels1 and maraging steels.a~4 In contrast to Fe-C martensites, these martensites are relatively soft and ductile in the as-quenched condition, due to the low solid-solution hardening effect of the substitutional elements as compared to carbon. Also, these martensites are hardened by aging at low temperatures in contrast to Fe-C martensites which generally soften on tempering. Titanium and aluminum, singly or in combination, as well as copper and molybdenum, have been the principal alloying additions to stainless steels to obtain an age-hardening reaction.&apos; Ti-A1 or Co-Mo-Ti combinations have been used in the case of maraging steels.3"4 The present work has been confined to a study of the age-hardening characteristics of an Fe-18 to 21 pct Ni martensite to which small amounts of titanium, aluminum, copper, and molybdenum were added in order to study the effects of each alloying element separately. The age-hardening characteristics of these alloys were studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electron-probe micro-analysis of the extracted precipitates was also performed. The types and dispersion of precipitates, the formation of austenite, and the recovery of the defect structure of the martensite all were studied. EXPERIMENTAL PROCEDURE Alloys. The compositions of the alloys studied are listed in Table I. The level of 18 to 21 pct Ni was chosen to assure complete transformation to martensite on quenching and is the same nickel level used in maraging steels. The concentrations of titanium, aluminum, copper, and molybdenum were chosen after a study of the and Fe-Ni-MO&apos; ternary diagrams indicated how much of each alloying element could be dissolved in austenite. Alloys with 2 and 4 pct Cu were also studied, but these did not show precipitation hardening at the nickel levels studied and will not be discussed further. The alloys were prepared from electrolytic iron and high-purity* nickel, titanium, aluminum, copper, and molybdenum by vacuum melting of 20-lb heats. These were vacuum-cast into two 8-lb ingots. The ingots were hot-rolled at 1100°C to 1/2-in. plate and subsequently cut into 3/8-in. cubes. The cubes were sealed in evacuated quartz capsules and solution-treated for 16 hr at 1100°C, except for the Fe-20 pct Ni-10.7 pct Cu alloy and Fe-21 pct Ni-2.6 pct A1 alloys which were solution-treated for 16 hr at 1300" and at 1250"C, respectively. Metallographic examina-

Jan 1, 1963

By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,&apos;.&apos; who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy&apos;s law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy&apos;s law, as extended to two-phase flow including the effect of capillary pressure,&apos; is as follows:

By L. S. Richardson, N. J. Grant

Iodide-grade titanium, two oxygen alloys, and two aluminum alloys were studied by means of creep-rupture tests from 1000° to 2000°F. From the test information an evaluation was made of, 1) the relative creep-rupture strengths of the u (hexagonal-close-packed) and 0 (body-centered-cubic) forms of titanium and some of its alloys; 2) the effects of solid-solution strengthening by oxygen and aluminum on the u and 0 structures; and 3) the extent and effect of atmospheric oxygen alloying on rupture life in tests above about 1000°F. THE use of titanium alloys at temperatures above 1000° F has been considered unlikely by most investigators because of low creep strength (based on a requirement for room-temperature ductility, formability, and weldability) and low oxidation resistance. The results of this testing program do not entirely uphold this pessimism in terms of strength and oxidation resistance. The observations described below are based entirely on stress-rupture results, although some creep tests were also carried out on these alloys. Three items of primary importance are covered: 1) Stress-rupture data in the form of the Larson-Miller parameter curves for several titanium alloys at temperatures up to 2000°F; 2) The relative strengths of the hexagonal-close-packed a structure and the body-centered-cubic 0 structure; 3) The effects of solid-solution alloying on the creep-rupture properties of titaniu&apos;m at elevated temperatures. Only two investigatons have reported the creep- rupture properties of titanium at temperatures above 1000° F. Lunsford and rant&apos; tested iodide titanium; their values are also utilized in the paper. EXPERIMENTAL PROCEDURE After a few tests had been made in a conventional creep-rupture test machine, it became clear that some sort of atmospheric protection would be necessary for short-time tests conducted at temperatures above 1600°F, or for times greater than 100 hr at 1200°F or above. Several furnace units and test machines were constructed, the most successful of which is shown in Fig. 1. Certain experimental difficulties peculiar to titanium were encountered; for example, the use of molybdenum holders was dictated because titanium forms low melting-point eutectics with conventional high-temperature alloys containing appreciable amounts of iron, nickel, or cobalt. This same difficulty made the use of chrome l-alumel thermocouples in direct contact with a test specimen impossible, above about 1500" F. The high-temperature high-vacuum furnace shown in Fig. 1 was capable of maintaining a vacuum of better than 10"5 mm of mercury at 2000°F (pressure measured in cold part of system) and 5 X lo-&apos; mm at room temperature. Most of the tests eonducted in vacuum were at temperatures

Jan 1, 1960