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By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

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' 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 Norman D. Fitz, Gerald

BOTH physical and economic factors are concerned in determining the optimum rate of depletion of a mineral deposit. The physical limitations are, in a large measure fixed by nature. Economic influences on the other hand, are man-made and subject to wide changes. Analyses of the interrelations of these two groups of factors are of major importance in selecting the optimum rate of production of petroleum and mining properties and in their valuation. Physical Influences PRIMARY limitations on the rate of mining are the rate of shaft sinking and underground development, the rate of hoisting, and the rate of sloping. These rates are largely determined by the physical features of a property. Technical methods which may be employed, and consequently the length of time required, are governed by the dimensions of the deposit, its attitude, depth, regularity, the unit value and character of the ore, the nature of the wall rocks, and similar factors.

Jan 1, 1938

By C. C. Herrick

The vapor pressure of indium has been measured by the torque-effusion technique, as a function of temperature between 1102o and 1422oK. For liquid indium, the vapor pressure (in atmospheres) can be represented by the equation -R In P = 5.782 x104/T - 25.29from 1000o to 1422oK. Extrapolation yields a calculated normal boiling point of 2329°K and a heat of vaporization at 298 oK of 58.09 kcal per mole by the third-law method and of 58.39 kcal per mole by the second-law method. Calculations indicate that the free-energy functions of Hultgren are to be preferred to those of Guruich. BECAUSE of the potential uses of liquid metals, it is important that convenient experimental methods be developed which will lead to a sufficient body of thermodynamic data so that reasonable estimates of properties of liquid metals can be made. Indium is particularly well-suited to investigation, since it remains liquid over a long temperature interval, it alloys readily, suitable containers for it are easily procured, and relatively few investigations of its thermodynamic properties in the region above 1000°K have been made. PREVIOUS RESEARCH The first determination of the vapor pressure of indium was made by Anderson,' using the Knudsen method and silica-lines stainless-steel cells. Kohlmeyer and spandau2 determined the normal boiling point, and a mass-spectroscopic investigation has been made by Lyubimov and Lyubitov.3 (Unfortunately, only an equation representing the data of the latter investigators has been available to us.) Hultgren et al.4 and Gurvich5 have published discordant tables of the free-energy functions for indium. EXPERIMENTAL METHOD The torsion-effusion principle has been described amply in the literature.8,7 With this method, one observes the angular deflection induced by effusion of vapor from a multihole effusion cell which is suspended from a filament producing a small rotational restoring force. The pressure within the effusion cell can be computed from the relation ziaifiai where k is the torsion constant of the filament, 6 is the observed angular deflection, and ai, fi, and qi are the area, force factor, and moment arm of the ith effusion orifice. The force factor f is analogous to the Clausing factor,' and corrects for the reduction in effusive force attributable to the finite geometry of the effusion orifice. Schultz and Searcy' have tabulated the force factors for various tube geometries. EXPERIMENTAL APPARATUS The physical arrangement employed in this study is shown in Fig. 1. The furnace elements are six Globar heat rods with 15-in. hot zones. Temperature is maintained to * 1°K by a Beck mechanism driving two 26-amp Powerstats in parallel. A Pt (Pt, Rh 10 pct) thermocouple serves as the sensing element. Four inner tubes act as vibration isolators; the air pressure required for maximum isolation was determined empirically, and is maintained by a solenoid valve. The tungsten fiber, 9 by 0.002 in., is joined to an 0.008-in. tungsten wire or graphite rod via a machined lightweight chuck.

Jan 1, 1964

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By J. W. Wolfe

The Benedict-Webb-Rmbin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predrcted component K-vallles, mixture enthalpies and phase aensities within tile accuracy of available correlations for rune-component mixtures: significant deviations were noted when mixtures contained components heavier than heptune. INTRODUCTION Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas proccssing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently. the best equation of state for describing the behavior of pure, light hydrocarbons over single-and two-phase regions, both below and above critical pressure, is that of Benedict. Webb and Rubin.' The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the clevelopment of their equation as early as 1940.2 The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a serics of articles in 1951,' showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed,'-',"'-':' the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state." Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases. Consequent-

Jan 1, 1967

By W. C. Hagel, H. J. Beattie

Variations in the secondary phase reactions of six nickel-and cobalt-base alloys were determined as a function of solu-tioning from 1700" to 2200°F and aging at 1200" to 1800° F for times up to 1000 hr. Room-temperature impact energies and hardnesses were also measured. Precipitation hardening of these alloys results mainly from the grain-interior formation of ? '; M23C6 appears principally as grazn-boundary cells which can be eliminated by intermediate high-temperature aging treatments. Cellular precipitation of ?' occurs up to 1500°F in cobalt-nickel alloys devoid of chromium, where precipitation by this mode can be attributed to a large degree of lattice disvegistery. THE usefulness of nickel- and cobalt-base alloys is dependent on balancing the strength and ductility provided by the solid-solution matrix, dislocation-type subboundaries, grain-boundary phases and genera1 precipitation within individual grains. Since equilibrium relationships for complex austenitic alloys are not easily fixed, a satisfactory balance

Jan 1, 1960

By Charles M. Cooley

With explosives representing over 10 pct of the cost of operating the entire company, the Maumee Collieries Co., Terre Haute, Ind., inaugurated a program to develop a low-cost blasting agent. Results of more than two years' work were announced on May 1 by Hugh B. Lee, president of the company. Utilizing a mixture of commercial-grade ammonium nitrate and carbon black packed in polyethylene bags, Maumee has been able to reduce blasting costs by 50 pct. The lower costs are brought about principally by elimination of high transportation charges on fixed explosives and use of low-cost material (commercial NH,NO, and carbon black). The Akremite blasting method incorporates a 20-lb cap-sensitive primer to detonate the stable explosive. Maumee now uses Akremite exclusively in its stripping operations producing more than 2 million tons of coal per year. The explosive is employed to break about 25 million cu yd of overburden that covers the coal

Jan 5, 1955

By E. P. Peleider

DIAMOND drill research work was initiated at the School of Mines, University of Minnesota, in late 1949. The Drilling Symposium held in Duluth that spring highlighted the problem of high cost and core recovery and the need for controlled testing. An advisory committee made up of informed representatives of both mining companies and drilling companies was formed to suggest and advise on a program of drill research. A Hy-Mac hydraulic drill unit, see Fig. 1, especially designed for experimental testing, was obtained for this work by the School of Mines through the courtesy of the Carboloy Co. It is an extremely flexible unit, capable of exerting a forward thrust of about 1750 lb and turning at speeds from 650 to 2200 rpm. The feed arrangement is so designed that the advance can be set either at a constant rate or permitted to vary at a fixed Pressure, see Fig. 2. The

Jan 1, 1953

By E. P. Peleider

DIAMOND drill research work was initiated at the School of Mines, University of Minnesota, in late 1949. The Drilling Symposium held in Duluth that spring highlighted the problem of high cost and core recovery and the need for controlled testing. An advisory committee made up of informed representatives of both mining companies and drilling companies was formed to suggest and advise on a program of drill research. A Hy-Mac hydraulic drill unit, see Fig. 1, especially designed for experimental testing, was obtained for this work by the School of Mines through the courtesy of the Carboloy Co. It is an extremely flexible unit, capable of exerting a forward thrust of about 1750 lb and turning at speeds from 650 to 2200 rpm. The feed arrangement is so designed that the advance can be set either at a constant rate or permitted to vary at a fixed Pressure, see Fig. 2. The

Jan 1, 1953

"WELFARE…Welfare endeavor in connection with both the metal and the coal mines of Utah has shown gratifying progress during recent years and both the operators and their employees are deserving of much credit for the efforts put forth to better living, working, educational and receational conditions in most of the mining camps of the state.In the older metal mining camps of Utah, where the towns are incorporated and independent of the mining properties operating in the vicinity, less opportunity is pre¬sented for the companies to exercise efforts looking towards improved welfare conditions than is the case of camps located on company ground and under the full control of operators.Even in such camps, however, as illustrated in Bingham, the companies can do much to better welfare conditions. In this camp the Utah Copper Company has spent $800,000 since 1 920 in the erection of modern brick cottages, apartment houses and the Gemmell Memorial Club. The cottages and apartments have every convenience to be found in up-to-date city homes. The Gemmell Memorial Club, erected and equipped at a cost of $1 75,000, was provided by the company for the benefit of the Utah Copper Company employees living in the canyon and has been made the recreational center for the camp."

Jan 1, 1925

By G. J. Harmsen

is shown that in any isotropic porous medium there is a fixed ratio, : , between the numerical valrles of the total pore perimeter per unit of cross-section and the specific surface area per unit of bulk volume. The consequences of this fact on the use of the concept "hydraulic radius" in the case of porous media are examined. The validity for consolidated sands of Kozeny's rela- tionship and of the formula derived by Carman for capillary rise are discussed. INTRODUCTION In the course of time several quantities and relations have been put forward in order to describe the texture of a porous medium and the flow of fluid through it. Among these relations the so-called Kozeny formula and a formula for capillary rise, for both of which Carman',' has given a derivation, will be specially considered here. These relations are of a semi-empirical nature and the derivations must be considered to have a heuristic significance only. For unconsolidated mate-

Jan 1, 1956

By Samuel G. Bonasso

The article by Benavides and Schuster provides an in-depth study of this transportation alternatives for a four-mine complex in western Kentucky. The examination of aerial tramways was not undertaken as an alternative solution. We feel this is an oversight since industrial ropeways are competitive with both belt conveyance and overland truck hauling. In fact, there are aerial tramway system, operational today, which are 100 years old and operating with some original components. Maybe unfortunately, there are no fixed rules or guidelines whereby the most cost-effective means of transporting and handling material for a given situation may be selected. Each situation must be evaluated m the variables that influence the selection of the desired alternative can be clearly defined. However, there are in-place industrial ropeway system that have proven economically feasible over a range of 1.6-50 km (1-31 miles). The more difficult the terrain, the greater the cost efficiency.

Jan 1, 1984

By Harlowe Hardinge

[Crushing Tests by Pressure and Impact (T.P. 1895, by F. C. BOND,, Min. Tech. Jan. 1946). Discussion by H. HARDINGE and the author 1 Pumping Sands, Slurries and Slimes and Installation and Performance of Sand Pumps (T.P. 2013, by W. B. STEPHENSON, Min. Tech., May 1946 and T.P. 1978, by C. G. SOUTHMAYD, Min. Tech., March 1946). Discussion by OSCAR LEE, G. J. HOLT, L. D. ANDERSON, and the author 2 Rapid Polarographic Method for Determination of Copper, Zinc and Lead in Flotation Tailings (T.P. 2010, by G. A. CROWE and W. T. BISHOP, Min. Tech., March 1946). Discussion by E. H. ROSE and the authors 4 Ball Wear and Functioning of the Ball Load in a Fine-grinding Ball Mill (T.P. 1984, by W. I. GARMS and J. L. STEVENS, Min. Tech., March 1946). Discussion by J. F. MYERS, E. W. DAVIS, F. M. JARDINE, H. HARDINGE, F. C. BOND and the authors 5 Correlation between Mineral Behavior in Cataphoresis and Flotation (T.P. 2005, by A. M. GAUDIN and S. C. SuN, Min. Tech., May 1946). Discussion by 0. C. RALSTON, G. L. SIMARD and D. J. SALLEY 7 Accident Experience in Milling (T.P. 1981, by J. F. MYERS and S. E. SHARP, Min. Tech., May 1946). Discussion by C. E. MCKNIGHT, C. H. BENEDICT, T. S. WILSON and S. POWER WARREN9 Mill Design for Labor Economy (T.P. 1997, by NORMAN WEISS, Min. Tech., May 1946). Discussion by R. S. HANDY and the author13] Crushing Tests by Pressure and Impact (0.C. Ralston presiding) HARLOWE HARDINGE.*-Has the impact method described in the paper been used to compare the resistance to reduction in size of various materials with actual operation results of mills in the field? Is this impact method a better index of the true resistance to grinding under actual field conditions than other methods the author has reported in the TRANSACTIONS? F. C. BOND (author's reply).-The impact crushing device was designed to measure relative resistance to crushing, or what may be called the crushability, and is not used for comparing the resistance to grinding, or grindability. The correlation between crushability and grindability of different materials is not at all close, since fractures, zones of weakness, and structural features of rock have a much greater effect upon the crushability than upon the grindability. We still depend upon our standard grindability tests for measuring resistance to grinding, and use the impact crushing tests only in relation to crusher installations. The impact crushing device has several advantages over the measurement of crushing strength in pounds per square inch as an index of crushing resistance.

Jan 1, 1946

By D. J. Mack, R. E. Reiswig

Six examples of the peritectoid transformation were selected from the literature and studied by the method of isothermal transformation. The kinetics and mechanisms of five of the examples are presented as TTT diagrams and photomicrographs. The exist-enc- of a peritectoid in the sixth case is doubtful. ALTHOUGH the peritectoid transformation per se has been known for many years, no precise published data exist concerning the kinetics or mechanisms involved in transformations of this type, except for the brief treatment by Rhines, et al. 1,10 Bearing in mind the fact that investigations of recent years are uncovering more and more peritectoids and suspected peritectoids, a thorough study of the well-established peritectoids appeared to be in order. It was for this reason that a study of the kinetics and morphological mechanisms of six binary peritectoids was undertaken. The six peritectoids selected from the literature for study were those reported at 7.02 wt pct Al-Ag, 26.0 wt pct Sb-Cu, 30.5 wt pct Sb-Cu, 32.3 wt pct Sn-Cu, 8.35 wt pct Si-Cu, and 21.2 wt pct Al-Cu. These selections were based on availability and purity of components, ease of preparation and heat-treatment, and estimated reliability of the available equilibrium diagrams in the regions of interest. EXPERIMENTAL PROCEDURE The alloys used in this investigation were induction melted in electrode-grade graphite and chill-cast in cast-iron split molds. In all cases, the alloys were so brittle that they could easily be broken into samples weighing 1 or 2 g. Chemical analyses showed that the alloys used were close to the respective peritectoid compositions reported in the literature and that the impurity levels were low in all cases. Metallographic examination showed uniform distributions of phases in all samples, indicating uniformity of composition in the samples studied. Isothermal transformation studies were carried out in fused-salt media, using the familiar inter-rupted-quench method. Uniformity of temperature in the salt baths was maintained by continuous stirring with a stainless-steel agitator. On the basis of actual observations of the temperature fluctuations, the estimated temperature control was + 10C for the Ag-Al and Cu-Sb alloys and ±30C for the Cu-Sn, Cu-Si, and Cu-Al alloys. The accuracy of all temperature measurements was estimated to be ±1°C. It was found necessary to mount metallographic specimens of the Ag-Al alloy in cold-curing methyl methacrylate, since the temperatures encountered in mounting in bakelite or lucite caused an appreciable degree of transformation to the ß phase. For the other alloys, wood-flour-filled bakelite mounts were used to avoid extraneous X-ray diffraction lines during the later examination of the metallographic specimens on a Norelco Geiger-counter d if f r ac tomete r. In the X-ray diffraction procedure, agreement between the published diffraction patterns and those obtained in this study was good. This was particularly important for phase identification, since the literature contained little in the way of micrograph description in some cases. Etching of the silver-aluminum alloy for metallographic examination was done by swabbing with either of the following reagents: 1) 10 g CrO3, 1 g (NH4), SO2, 0.5 g NH4NO3, 100 ml H2O, or 2) 10 ml NH4OH, 1 ml 20 pct KOH, 4 ml 3 pct H2O2, 5 ml H2O. The other alloys were etched with the usual bichromate etchant: 2 g K2Cr2O7, 1.5 g NaC1, 8 ml conc. H2SO4, 100 ml H20 (swabbed vigorously). EXPERIMENTAL RESULTS A) The Ag-Al peritectoid at 7.02 wt pct Al— The phase equilibrium involved in this peritectoid is shown in Fig. I.2 The phase boundaries in the vicinity of the peritectoid were most comprehensively established by Hume-Rothery, et al,3 who placed the equilibrium temperature at 448 °C and the equilibrium compositions of the a ß' and y phases at 6.11, 7.02, and 7.24 wt pct Al, respective The alloy used in this study analyzed4 6.95 wt pct A making it slightly hypoperitectoid according to the accepted equilibrium diagram. The rate of the transformation a+ y — ß' varies rapidly with degree of undercooling below the equilibrium temperature, passing through a maximum in the vicinity of 350°C. Thus the TTT dia-

Jan 1, 1960

By A. M. Beebee

IN the present century the coal and manufactured gas industries have been eclipsed in public interest by oil, natural gas, and hydro- electric energy, which have had the benefit of rapid development and novelty. I sometimes wish that our social- order were such that hydro power had been developed first, that the use of gas from coal had never been seriously considered, and that our domestic energy requirements were supplied by other fuels. Sup- pose the manufacture of gas from coal should then come on the scene at the present time with the current plight of the railroads, coal regions, and labor generally, presenting the fact that it could increase the amount of coal mined and shipped by the railroads by some 16,000,000 tons, and increase the coal used at existing u plants five times. Imagine the great public interest that would be manifested; it would supply the cooking and water-heating requirements of a community with a superior character of service at a cost to the customer approximately half that which had obtained previously. Would not such a situation be heralded as the salvation of our country and all help be given it?

Jan 1, 1940

By Finney, W. R.

MUCH has been said and written of the "Big Inch," of the terrific obstacles encountered in its construction, of the colorful and tough men engaged in its building, but little has been publicized of the engineering and economic problems behind the scenes. Long before Pearl Harbor it was apparent to the petroleum industry that a critical oil shortage could be expected along the Atlantic seaboard, owing to delay in tanker deliveries as a result of convoy movements, and to allocation of vessels for foreign shipments. This area, with a normal consumption of approximately 1,800,000 barrels per day of oil and products, was almost entirely supplied by tanker. Pipe lines supplied an average of only 20,000 barrels per day in 1939, 40,300 barrels per day in 1940, and 55,000 barrels per day in 1941. A small amount of oil and products was also delivered via barge.

Jan 1, 1943

By D. P. Kedzie, R. A. Dodd

The fatigue strength, fatigue hardening, and effect of fatigue deformation on subsequent age hardening of supersaturated Al(Cu) solid solutions have been determined as functions of alloy composition and temperature. The fatigue strength/tensile strength ratios, determined at 150°, 25°, and -195°C, decreased with increase in alloy content for all temperatures, but the F.S./U.T.S. ratios at -195°C decreased much more rapidly than did the ratios for 150" and 25°C. This suggested that strain aging and/or age hardening occurred during tests at higher temperatures. Additionally, the F.S./U.T.S. ratios at 150°C exceeded those at 25°C for all compositions, indicating greater strengthening during fatigue at 150°C. The effect of fatigue or tensile deformation at 150°, 25°, and -195°C on subsequent age hardening showed that the deformatzon increased the rate of precipitation and indicated that mechanically produced vacancies were probably formed during deformation. Fatigue hardening was studied at 150°, 25°, and -195°C, and the effect of room-temperature rests after 10 and 100 cycles was examined. The results confirmed that strain aging occurred at the higher temperatures . DURING the last 15 years various mechanisms of fatigue crack nucleation and growth based on dislocation and vacancy interactions, operating singly or collectively, have been proposed. The probable consensus of present opinion is that the fatigue process in pure metals essentially involves dislocation interactions, and that vacancies formed by such interactions play a minor or inconsequential role. However, there is some evidence that age-hardened alloys tend to overage during fatigue, probably by local vacancy-enhanced diffusion, and strain aging also might be important in selected cases. Furthermore, it has been established that the behavior of quenched-in vacancies in Al(Cu) and other solid solutions is composition-sensitive. Therefore, it seemed worthwhile to investigate various aspects of the fatigue behavior of supersaturated Al(Cu) alloys and to examine the results in terms of vacancy-enhanced effects. EXPERIMENTAL The alloys used in this investigation were prepared from 99.994 wt pet A1 and OFHC copper, the latter containing 0.04 pet 0 as the principal impurity. Six alloys were made, containing, by actual analysis, 0.58, 0.96, 1.96, 2.85, 4.45, and 5.51 wt pet Cu. They were induction-melted in air in graphite crucibles, cast as 7-in. by 7/8-in.-diam rods in graphite molds, and hot-rolled to 5/8 in. diam. The experimental work was a three-part program involving the determination of a) 10' cycle fatigue stresses as a function of alloy composition and temperature; b) the effect of fatigue deformation on subsequent aging of the supersaturated alloys; and c) fatigue hardening as a function of alloy composition and temperature. For determining the 105 cycle fatigue stresses, a portion of the 5/8-in. stock was machined into Krouse rotating cantilever beam fatigue specimens, 2 in. in length by 1/4 in. minimum diameter. These were tested at +150°, 25°, and -195°C (liquid nitrogen) on a Krouse high-speed machine, with special weights to provide lower -than-normal loading ranges, this being necessitated by the small load requirements of those alloys of lower copper content. For the high-temperature tests a small resistance heater was designed to clear the collets and fit in between the chucks, while for the low-temperature tests a hollow nylon cylinder was used, having closed ends drilled to pass a fatigue specimen, and positioned similarly to the heater. A plexiglass container completely enclosed the fatigue machine; rubber gloves fixed to ports in the walls enabled the machine to be operated from outside the box. A tray of magnesium perchlorate dried the air in the container and prevented both atmospheric corrosion fatigue at room and elevated temperatures and troublesome ice build-up at low temperatures. A total of ten to fifteen specimens was used for each combination of alloy composition and temperature. The result of each test was plotted on a standard S-N diagram, and the next stress was selected on the basis of the trends indicated by previous specimens. In this manner a small portion of the S-N diagram was constructed, and the 105 cycle fatigue stress obtained. Small Krouse fatigue specimens were also used to study the effect of cyclic prestrain on subsequent

Jan 1, 1964

By E. T. Turkdogan, W. L. Worrell

The rate of reaction of hydrogen sulfide with ferrous sulfide was studied by measuring the initial rates of sulfidation of iron strips in hydrogen sulfide-hydrogen-argon mixtures at 670°, 800°, and 900" C. The time-dependent surface sulfur activity is derived from the instantaneous rate of sulfidation with the assumption that diffusion in the sulfide layer is in a pseudo-steady state with the gas-sulfide chemical reaction. The rate of sulfur transfer from hydrogen sulfide to the surface of iron sulfide is proportional to the partial pressure of hydrogen sulfide and inversely proportional to the activity of sulfur at the surface of the sulfide layer. The derived rate equation is based on the assumption that most of the surface sites on the chemisorbed layer of iron sulfide are occupied by sulfur atoms and that the slow rate-controlling reaction is the dissociation of hydrogen sulfide on the chemisorbed layer. The experimental results are in reasonable accord with this reaction model. 1 HE slow approach to parabolic growth rate in the sulfidation of iron in hydrogen sulfide-hydrogen mixtures is a manifestation of slow approach to surface equilibrium between the gas and the surface of the sulfide layer. For example, at 800°C and Fig. 7 in Part I, the parabolic growth rate begins after approximately 1 day of sulfidation time. With decreasing temperature and decreasing partial pressure of hydrogen sulfide, the time necessary to reach gas-sulfide surface equilibrium is much longer. These observations are similar to those reported previously by Turkdogan et al.' on the oxidation of iron to wustite in hydrogen-water vapor mixtures. The slow approach to gas-sulfide equilibrium is well-demonstrated by the results in Fig. 1 where the square of the weight gain per unit area, ( g S per sq cmI2, is plotted against time for gas mixtures having PH g//>H = 1.0 with 0, 25, 50, and 67 pct Ar at 800°C. The value of 1.5 X lo-' (g S per sq cm)' corresponds to almost complete sulfidation of the iron strip (- 0.05 cm thick) to iron sulfide. The points fall on S-shaped curves. If the inflection parts of the curves are considered to be linear, thus indicating parabolic growth rate and the establishment of gas-sulfide equilibrium, their slopes would have to be the same for a fixed ratio in the gas mixture. Such is not the case, and the slopes for the "linear" parts of the S-shaped curves are lower than the value when gas-sulfide surface equilibrium is established. The subject matter of this paper is the kinetics of the surface reaction of hydrogen sulfide with iron sulfide during the early stages of sulfidation of an iron strip. EXPERIMENTAL RESULTS The apparatus and materials used were the same as those discussed in Part I. In the present experiments of relatively short duration, a purified iron strip, 5 by 2 by 0.05 cm, which was suspended in the uniform hot zone of a vertical zircon tube, reacted with a flowing gas mixture of hydrogen sulfide-hydrogen-argon. The sample was suspended from a gold chain attached to a calibrated silica spring. The amount of sulfur picked up by the iron, which formed a layer of iron sulfide, was determined by measuring the displacement of a reference point on the silica spring, using a cathetom-eter. In all cases, the degreased sample was first annealed in a stream of oxygen-free dry hydrogen for several hours to remove any impurities such as oxygen, nitrogen, or carbon which might have been present on the surface of the sample.' The rate measurements were carried out at 670°, 800°, and 900° C in hydrogen sulfide-hydrogen-argon mixtures with pH2 s/Ph2 ratios from 4 to 0.1. In a few experiments of short duration no sulfur deposition was observed in gas mixtures with (comments concerning sulfur deposition at high pH s/ph ratios were made in Part I.) Typical examples of the results obtained are shown in Fig. 2 for two temperatures and two gas compositions. With the present experimental technique, reproducible rate data could be obtained only after a uniform

Jan 1, 1969

By Dilip K. Das, Douglas T. Pitman

ONE of the major uses of barium in metallic form is as a getter material in vacuum tubes. Because of the high chemical reactivity of the metal, Ba-Al alloys are extensively used. Numerous methods for the preparation of Ba-Al alloys have been published, a few of which1-4 are cited here. Most of these methods were found to be quite elaborate, involving the reduction of BaO, and not too well adapted for the close control of the final composition of small amounts of alloys prepared for laboratory use. A simple laboratory method for the preparation of Ba-A1 alloys in small batches starting from pure metals was devised, so that it was possible to control the desired compositions to within 1 pct. The pertinent features of the alloy system Ba-Al5 are 1) an intermediate compound BaAl, with the melting point of 1050°C, and 2) a eutectic between aluminum and BaAl4 at 98 pct Al. The accompanying sketch shows the experimental arrangement for the preparation of the alloys. Weighed amounts of aluminum and barium were placed in an alumina and a stainless steel crucible, respectively. According to the supplier's specification, the purity of the metals used in the alloys is as follows: a) aluminum rods—99.9 pct Al, and b) barium rods—99.5 pct Ba. The stainless steel crucible, tapered at the bottom and having a 1/16 in. diam hole, rested on top of the alumina crucible. The assembly was placed inside a graphite sleeve which rested on a refractory platform. The platform moved the assembly up and down through the field of a radio frequency coil. A glass bell jar was placed between the crucible assembly and the radio frequency coil to maintain a steady flow of helium around the melt. A small window was cut out on the wall of the alumina crucible to observe the progress of the re- action and to record the temperature with an optical pyrometer. The platform was first raised high enough to move the barium out of the radio frequency coil field in order to allow only the aluminum to melt. The assembly was then lowered so that the barium began to melt and flow out through the small orifice into the molten aluminum. In order to keep the violence of the exothermic reaction under control, the rate of flow of barium was carefully regulated by raising or lowering the crucible assembly. All the samples prepared by this technique were examined by a Norelco X-ray diffractometer using CuKa radiation, The diffraction specimens were prepared by placing the finely powdered samples in flat specimen holders. The Ba-Al alloys prepared with a high barium content were found to consist mainly of BaAl4. The structure of BaAl4 has previously been reported by Alberti and Andress.8 They found that BaAl4 was body-centered-tetragonal with an a0 = b0 = 4.530Å and c0 = 11.14Å. An alloy whose composition was found by chemical analysis to be almost 100 pct BaA1, was used to determine the relative intensities. The d-spacings were obtained from the same alloy to which a small amount of tungsten had been added as a calibrating material. Accurate values for a, and c, were calculated according to the method proposed by Taylor and Floyd.' The calculated values are: a, = b, = 4.566Å and c0 = 11.250Å. The measured d-values for BaAl4 are shown in Table I along with relative peak intensities above background and hkl indices. Acknowledgment The authors are grateful to L. J. Cronin, the head of the Techniques Dept., for suggesting the problem and for his constant interest. References 1Froges and Camargue: German Patent No. 809107, 1951. French Patent No. 935324, 1949. 2E. Bonnier: Annales de physique, 1953, vol. 8, pp. 259-312. 3M. Orman and E. Zemhela: Prac Institute of Metals; 1952, vol. 4, pp. 437-445. 4E. Fujita and H. Yokomizo: Reports Gov. Chemical Industrial Research Institute, Tokyo, 1952, vol. 47, pp. 291-297. 5E. Alberti: Ztsch. fur Metallkunde, 1934, vol. 26, p. 6. 6E Alberti and K. R. Andress: Ztsch. fur Metallkunde, 1935, vol. 27, p. 126. 7 A. Tnslor and R. W. Floyd: Acta Crystallographica, 1950, vol. 3, p. 285.

Jan 1, 1958