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By David Cornell, Yusuf K. Sukkar

The fundamental differential equation for fluid flow has been rearranged, integrated numerically for natural gases, and the results presented in tabular and graphical form suitable for the direct calculation of vertical gas flow problems. The integration is rigorous except for the use of a constant average temperature. Both static and flowing bottom-hole pressures may be calculated by (his method without resort to trial and error procedures. INTRODUCTION Bottom-hole pressures can be determined either by direct measurement with a bottom-hole pressure gauge or by calculation. Since measurement with a bottom-hole pressure gauge is costly, calculation of bottom-hole pressures is to be preferred when possible. Calculation involves knowledge of the wellhead pressure, the properties of the gas, the depth of the well, the flow rate, the temperature of the gas, and the size of the flow line. These quantities must be combined in a suitable equation for vertical flow. Several equations have been developed for the purpose of calculating gas flow through both horizontal and vertical pipes1,2,4,5,6,7,8,9 These equations all have the basic differential equation for flow as their starting point. They differ only in the assumptions which are made in order to simplify the integration step. The bottom-hole pressures calculated using any of the better known equations are in good agreement with bottom-hole pressures calculated by a more rigorous but considerably more tedious stepwise integration method. All of these methods, however. require a trial and error solution for the calculation of flowing bottom-hole pressures. The purpose of this paper is to present a method which provides a direct solution of static and flowing bottom-hole pressures without use of a trial and error solution. At the same time the method involves fewer simplifying assumptions than any of the previous methods used, except lor the lengthy stepwise method. The derivation of any practical flow equation begins with the basic differential equation which is rigorous for almost all flow problems. The five terms in Equation 1 represent the potential energy, the potential energy of position, the kinetic energy, the shaft work done, and the energy losses due to motion of the fluid respectively. Equation 1 reduces to Bernoulli's theorem for the case of horizontal flow of an incompressible fluid, no work done, and no energy losses due to friction. In the present case, the term (v) (dv)/(g,.) can be shown to be quite negligible compared to the other terms, and is therefore neglected in the derivation. The term — dws includes work done by a pump or turbine in the system and is zero in this case. The frictional losses in the pipe are included in the term — d(lw) which is expressed in terms of the Moody friction factor as in Equation 2. (f) (v2) (dL) d(lW) = (f)(V2) (dl)/(2) (g) (d) The specific volume of a gas can be expressed in terms of the temperature, pressure, molecular weight, and compressibility factor. The velocity of the gas can be expressed in terms of the weight rate of flow, the specific volume, and the dimensions of the pipe.The reduced pressure Pr is to be used because z can be expressed as a function of Pr and Tr alone for most natural gases:

Jan 1, 1956

By G. W. P. Rengstorff, R. B. Fischer

A study was made of the effect of impurities on the bend ductility of cast molybdenum. High purity molybdenum was repared by re-melting under high vacuum. The ductility of "transverse-grain" specimens indicated that intergranular brittleness decreased with an increase in purity of the metal. THE production of as-cast molybdenum with high ductility at room temperature would make working of the metal easier and increase the usefulness of the as-cast metal. Furthermore, a .knowledge of the factors that influence the ductility of as-cast molybdenum might be applied to the problem of making fusion weldments having satisfactory room-temperature ductility. Individual grains of commercial as-cast molybdenum are slightly ductile at room temperature. However, the presence of carbides at the grain boundaries may cause the metal to fracture in a brittle manner. This behavior has been discussed.' The amount and distribution of the impurities in as-cast molybdenum would be expected, from previous research on the metal, to have considerable influence on its ductility. Some effects of oxygen and carbon on the mechanical behavior of the metal were discussed by Parke and Ham,2 Woodside,3 and Zappfe. Landgraf, and Worden.4 Parke and Ham2 found that, if a sufficient number of molybdenum oxide particles were present at the grain boundaries, the intergranular cohesion was reduced to the extent that arc-melted molybdenum would rupture intergranularly during hot forging. They also found that if the oxygen content was less than 0.003 pct, the cast molybdenum was hot forgeable. It is suspected, however, that forgeable molybdenum may contain a small amount of oxide that could reduce the ductility of the as-cast metal at room temperature. Also, there is the possibility of the unfavorable distribution of other impurities having a detrimental effect on the ductility of cast molybdenum. The results of a study of the influence of purity on the room-temperature ductility of cast molybdenum are presented here. Vacuum Arc-Melting to Produce High Purity Mo One way of determining the effect of impurities on the ductility of molybdenum is to prepare and test metal as free of all impurities as possible. Accordingly, the present investigation was undertaken with this in view. Arc melting in high vacuum (less than 0.1 micron of mercury) was chosen as the method for reducing the impurities below the concentrations occurring in commercial molybdenum. Commercial arc melting of molybdenum is carried out at about 50 microns pressure. During the arc melting, carbon and oxygen in the metal react to form carbon monoxide. By virtue of the vacuum process, the partial pressure of carbon monoxide is maintained at such a low value that the reaction greatly lowers oxygen and carbon contents. An excess of at least 0.03 pct C is used in commercial arc melting to insure that the oxygen content will be below 0.003 pct. The excess carbon remaining after the deoxidation step forms carbides on freezing. Some of the carbides precipitate at the grain boundaries and, as will be shown, have an unfavorable effect on the room-temperature ductility. In the present work, only the small amount of carbon (0.003 pct) contained in the commercial powder-metallurgy molybdenum used for melting stock was present. Partial removal of oxygen from the melt probably occurred as the result of the volatilization of molybdenum oxides, or by distillation of oxygen at the high melting tem-

Jan 1, 1953

By Frederick V. Lawrence

Broadly speaking, fluxes are substances which promote wetting and spreading or enhance the fluidity and manipulative properties of materials in joining, fusion, and smelting operations. The term most strictly applies to substances used to facilitate soldering and brazing; but in the discussion which follows, the definition will be broadened to include materials used to promote fusion in arc welding and which aid in the smelting of metals. In each of the mentioned applications, the role of flux and its composition differs considerably; consequently in the discussion which follows, fluxes for soldering, brazing, arc welding, and smelting applications will be considered separately. Soldering and Brazing Fluxes Soldering and brazing are metallurgical joining processes in which a joint is formed using a filler metal of composition dissimilar to that of the joined pieces (base metal). The filler metal, solder or braze, is always of lower melting point than the base metal. Consequently with these processes there is no melting of the base metal. The successful creation of the joint depends upon the wetting and spreading of the solder or braze around or throughout the joint. The obstacles to successful soldering and brazing are contaminants and tenacious oxide films on the metal surfaces. In soldering and brazing applications, fluxes act to remove and exclude oxides and other impurities from the joint. There is no fundamental difference between soldering and brazing. The distinction between them is made on the basis of temperature. Join¬ing operations carried out at temperatures above 500° C are termed brazing. The higher temperatures used in brazing enable higher melting point filler metals to be used which generally provide stronger joints. The higher temperatures of brazing processes also require fluxes which are substantially different from those used in soldering and which will remain effective at high temperatures. Consequently the distinction between soldering and brazing can also be made on the basis of the fluxes used. Soldering Fluxes Even thoroughly cleaned and degreased, metal surfaces still possess tenacious oxide films which inhibit the soldering of the joint. The reactions which form these films increase with increasing temperature. The rate of oxide formation and the tenacity of the film varies with each base metal. Aluminum, magnesium, stainless and high alloy steels, aluminum and silicon bronzes when exposed to air form hard, adherent oxide films. These metals require highly active and corrosive fluxes to remove and prevent the reformation of oxide films during soldering. Metals such as copper and silver, on the contrary, form less tenacious films at a lower rate, so that mild fluxes are sufficient. Soldering fluxes must dissolve or remove oxides and promote rapid wetting and spreading of the solder. The flux removes the oxide film by loosening and floating it off into the main body of the flux. The oxide removal is often aided by the alloying of the solder with the base metal, undermining small areas of the oxide and detaching them (Anon., 1959). The flux coagulates and suspends the oxide particles which have been loosened. The flux forms a protective cover preventing the reformation of the oxides, permitting the spreading of the solder and the formation of a metallic bond between the solder and the base metal. Constituents of Soldering Fluxes: Soldering fluxes are commonly grouped into three categories: highly corrosive, intermediate, and noncorrosive. One normally would choose to use the least corrosive flux which will give satisfactory performance.

Jan 1, 1983

By V. Koump, T. F. Perzak, R. G. Olsson

The vate of dissolutioz of carbon in molten Fe-C alloys urns studied by votating- cylindrical g-vaphite sairlples in a stationary crucible containing the melt. The rate of dissolltion was determdined from the change in the bnth co)npositiorz. Alccss-tvansfev coeffi'cients, calcilated with the assurlption that the inte)yacial liquid ulas saturated with carbon, were found to be in agreement with an existing Correlation fov mass transfer jroni votating cylinders. It is corzcllrded tlat, itz the wnge of- Reynolds' numbers itzvestigated (790 to 18,000), the vate of dissolutio of carborz in Fe-C alloys is controlled by tile rate of carbon difirsion from the interface. The dissolution of carbon in molten Fe-C alloys has been the subject of a number of investigations. Most of these investigations have been inconclusive because of poorly defined experimental variables. Two of the more sophisticated studies are summarized below. Dahlke and Knacke' studied the phenomenon by, in part, immersing graphite rods into 0.5 pct carbon-steel for different lengths of time. Since the experiments were conducted in air or in CO atmospheres, the melt was strongly agitated by gas evolution. It was concluded that the change in bath composition as a function of immersion time was in agreement with the assumption that the dissolution process was transport-controlled. The hydrodynamic conditions in these experiments, however, were not well-defined and gave no indication of the nature of the dissolution process at higher fluid velocities. In a recent study Shurygin and ruk investigated the dissolution of carbon in molten Fe-C, Fe-Si, Fe-P, and Fe-Ni alloys. Small graphite disks were rotated in a crucible containing molten alloys under such conditions that only the lower face of the disk was exposed to the melt. The results of this investigation indicate that, over the range of velocities (100 to 1000 rpm) and bulk liquid concentrations (0.7 to 4.5 wt pct C) considered, the dissolution of carbon in the iron alloys is limited by the diffusion of carbon from the interface to the bulk liquid (a transport mechanism). For the particular geometry used by these authors, exact analytical solutions of hydrodynamic and diffusion problems are aailable. Hence the experimental results obtained by Shurygin and Kryuk permit the evaluation of diffusion coefficients of carbon in the four systems investigated. In the present investigation a series of experiments were conducted in which the rate of dissolution of carbon in Fe-C alloys was measured under conditions which permitted wide variation of the fluid velocity and the carbon concentration of the bulk liquid. Graphite cylinders were rotated at different speeds in a stationary concentric crucible containing various molten Fe-C alloys. THEORETICAL DEVELOPMENT In general, the resistance to mass transfer from a solid interface to a turbulent liquid is assumed to reside in a laminar boundary layer adjacent to the interface. If it is also assumed that the diffusion coefficient is independent of concentration, the steady-state rate of dissolution for the case of arbitrary liquid and solid densities can be obtained from the integration of the equations of continuity. The derivation is similar to that used by Lommel and chalmers4 for the case of pl = ps. The solution, expressed in terms where N = rate of diffusion of the solute from the interface. Exact analytical solutions of the hydrodynamic equation for the boundary layer thickness are available for only a limited number of geometries. Consequently, a mass-transfer coefficient, k, is usually

Jan 1, 1967

By Edwin B. Eckel

This paper, based on brief field examination and on data supplied by the operators, records the condition of the Italian mercury industry as of March 1945, not long after Italy's collapse. Except for the once-Italian but now Yugoslavian Idria mine near Trieste, virtually all the known mercury deposits are in the Monte Amiata district in Siena and Grosseto Provinces, 75 miles north of Rome. This district contains the Abbadia San Salvatore. the Siele. the Argus, and the Cerreto Piano mines besides numerous prospects and unproductive mines. Under pressure from Germany the principal mines were highly productive during the early part of the war, but production fell off long before its end. All of the mines were damaged in some way at the German withdrawal but by September 1944 the Abbadia had resumed production and several others were only lacking power by the early spring of 1945. The Monte Amiata district is characterized geologically by a thick series of sedimentary rocks that range from Triassic to Eocene in age . and are surmounted on Monte Amiata itself by a thick cap of extrusive trachyte. Bodies of travertine and of landslide detritus, younger than the trachyte, are rather widespread. The structure is complex and little known but most of the ore deposits seem to lie along or near a major, north-trending fault or on associated cross-fractures. Cinnabar is the only important ore mineral and clay minerals are by far the most abundant products of hydrothermal alteration. A southward increase in the amount of stibnite, relative to cinnabar, suggests horizontal zoning. The grade of ore ranges from 0.60 to 3.0 Pet and the reserves, as compared with those in American mines, are enormous. Even in the face of war-time scarcities, the mines are remarkably self-sufficient and labor is plentiful, but the costs of production are estimated to be not greatly below those of the better American mines. Notes on the principal mines, on the mining and metallurgical methods, and on the manufacture of synthetic cinnabar are included in the paper. Introduction With but few brief interludes, Spain and Italy, including the Idria mine near Trieste, which has passed from Austrian to Italian to Yugoslavian hands in the Past 3 decades, have led the world in the production of mercury, or quicksilver, for many centuries. Despite their enviable position with respect to the supplies of a metal so essential in both war and peace, there is a notable lack of up-to-date information in America on the mercury industry of either country. Duschak and Schuette' and Schuettez,3 give by far the best summaries in English known to the writer, but the latest firsthand report cited by them on the Italian mines was published in 1915.' Having been deeply interested in the geology and economics of mercury for several years, the writer naturally felt most fortunate in being the to obtain enough firsthand information on the Italian industry to fill at least a few of the gaps in our knowledge. The opportunity came during the war, soon after this industry, together with the rest of Italy, had capitulated to the Allies. Many of the facts presented here are thus definitely "dated," but others are of less transitory nature, and even the dated facts should be of interest in showing the strength and

Jan 1, 1949

By Edwin B. Eckel

This paper, based on brief field examination and on data supplied by the operators, records the condition of the Italian mercury industry as of March 1945, not long after Italy's collapse. Except for the once-Italian but now Yugoslavian Idria mine near Trieste, virtually all the known mercury deposits are in the Monte Amiata district in Siena and Grosseto Provinces, 75 miles north of Rome. This district contains the Abbadia San Salvatore. the Siele. the Argus, and the Cerreto Piano mines besides numerous prospects and unproductive mines. Under pressure from Germany the principal mines were highly productive during the early part of the war, but production fell off long before its end. All of the mines were damaged in some way at the German withdrawal but by September 1944 the Abbadia had resumed production and several others were only lacking power by the early spring of 1945. The Monte Amiata district is characterized geologically by a thick series of sedimentary rocks that range from Triassic to Eocene in age . and are surmounted on Monte Amiata itself by a thick cap of extrusive trachyte. Bodies of travertine and of landslide detritus, younger than the trachyte, are rather widespread. The structure is complex and little known but most of the ore deposits seem to lie along or near a major, north-trending fault or on associated cross-fractures. Cinnabar is the only important ore mineral and clay minerals are by far the most abundant products of hydrothermal alteration. A southward increase in the amount of stibnite, relative to cinnabar, suggests horizontal zoning. The grade of ore ranges from 0.60 to 3.0 Pet and the reserves, as compared with those in American mines, are enormous. Even in the face of war-time scarcities, the mines are remarkably self-sufficient and labor is plentiful, but the costs of production are estimated to be not greatly below those of the better American mines. Notes on the principal mines, on the mining and metallurgical methods, and on the manufacture of synthetic cinnabar are included in the paper. Introduction With but few brief interludes, Spain and Italy, including the Idria mine near Trieste, which has passed from Austrian to Italian to Yugoslavian hands in the Past 3 decades, have led the world in the production of mercury, or quicksilver, for many centuries. Despite their enviable position with respect to the supplies of a metal so essential in both war and peace, there is a notable lack of up-to-date information in America on the mercury industry of either country. Duschak and Schuette' and Schuettez,3 give by far the best summaries in English known to the writer, but the latest firsthand report cited by them on the Italian mines was published in 1915.' Having been deeply interested in the geology and economics of mercury for several years, the writer naturally felt most fortunate in being the to obtain enough firsthand information on the Italian industry to fill at least a few of the gaps in our knowledge. The opportunity came during the war, soon after this industry, together with the rest of Italy, had capitulated to the Allies. Many of the facts presented here are thus definitely "dated," but others are of less transitory nature, and even the dated facts should be of interest in showing the strength and

Jan 1, 1949

By E. I. Organick, B. H. Golding

A simple correlation is presented for the prediction of saturation pressures in condensate-gas and volatile-oil mixtures. Saturation pressure is related directly to the composition of the mixture with the aid of two generalized composition characteristics, B, the molal average boiling point, and W, the modified weight average equivalent molecular weight. The need for hydrocarbon equilibrium constants is entirely eliminated. Only the values of the two conlposition parameters need be obtained, and these are calculated in a simple and reproducible manner from the stream analysis of the mixture and the ASTM distillation for the heavy ends. The correlation is given .in the form of a set of 14 working charts in which saturation pressures, either retrograde dew points or bubble points, are plotted cs temperature, forming partial phase envelopes for mixtures having discrete values of the composition parameters, B and Wul. A locus of critical states on each chart intersects the partial phase envelopes, distinguishing retrograde dew point pressures from bubble pressures. A comparison Between experimental and predicted saturation pressures reveals that: the probable error of the predicted values, when considering the data as a whole (214 experimental points), is five per cent; for high gasjoil ratio condensate fluids (approximately 40.000 or more cu ft/bbl) the probable error is about 8 per cent. In either case, however, the probable error is comparable with the overall uncertainty of the data from which the correlation is derived. INTRODUCTION There is a present need for a simplified, yet reasonably accurate method for predicting upper phase boundaries of reservoir fluids. In the case of high gas/oil ratio fluids, namely the so-called highly volatile oils and the condensate gases, no simple method, accurate within 5 to 10 per cent, is now available by which bubble point and retrograde dew point pressures may be predicted. In order to calculate the upper phase boundary of a volatile reservoir fluid, using correlations now available, it is necessary to find and employ the proper K-values (equilibrium volatility ratios of the hydrocarbons in that fluid). This process of finding the Proper K-values usually involves a double trial and error computation. Since the K-values are in themselves dependent upon the composition of the fluid, their use in the calculation of a saturation pressure actually represents an unnecessary complication. The correlation described in this paper relates saturation pressure directly to the stream composition, entirely eliminating the need for K-values. The only data required to calculate the Stream composition are obtained from the customary low temperature fractional analyses of separator gas and liquidt and from the ASTM distillation of the c,+ fraction of the separator liquid. A considerable simplification in the procedure for predicting saturation pressures is thereby effected without significant loss in accuracy. BASIS FOR A CORRELATION Empirical relationships between the saturation pressure and the composition of the fluid in question have already been partially explored by one of the authors.V n particular, a relationship between the critical pressure for a hydrocarbon mixture and its composition was developed. The critical pressure is in reality a saturation pressure, as it repregents a limiting case either of a dew point or of a buhhle point pressure for any given mixture. It was found that the critical pressure may be correlated as a function of two generalized composition characteristics or variables. One characteristic expressed a molal average prop-erty, the other a weight average property of the mixture. Specifically, the molal average boiling point (MABP, or B as it

Jan 1, 1952

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.' Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.' Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By A. Steiner, E. Miller, K. L. Komarek

Equations have been derived to calculate the chemical potentials of the components of liquid binary alloys from liquidus and enthalpy data. The equations are applicable to systems with intermetal-lic compounds of limited solid solubility. The liquidus curve of the Mg-Sn system was accurately redetermined, and the melting point of the compound Mg2Sn was found to be 770.5° * 0.3°C. The thermo-dynamic properties of the liquid alloys were calcu -lated from the liquidus data. The activity of tin shows both positive and negative deviations from Raoult&apos;s law and the relative integral entropy is positive. THE phase boundaries in an equilibrium phase diagram are functions of the thermodynamic properties of the coexisting phases. Specifically, the shape of the liquidus curve near an intermediate compound is determined by the properties of the compound and the liquid phase. Hauffe and wagnerl have derived an equation for the chemical potential differences (ui) of the liquid alloys near the congruent melting point when the heat of fusion of the compound and the liquidus curve are known. In their derivation the temperature dependence of the ui value was neglected, and liquid of stoichio-metric composition was chosen as the reference state. To obtain chemical potentials over the ntire composition range of the phase diagram with the pure components as the reference state, equations have been derived which incorporate the temperature dependence of the chemical potentials. Such a thermodynamic analysis can be carried out when the liquidus curve and the enthalpy values are known. The equations have been applied to the redetermined liquidus curve of the Mg-Sn system to obtain the thermodynamic properties of liquid Mg-Sn alloys. The Mg-Sn phase diagram has been studied by various investigators and the results have been compiled and critically assessed by Hansen.2 Preliminary thermal analyses showed that the basic features of the diagram were correct. The system has one congruent melting compound, Mg2Sn, two eutectics, and some solid solubility of tin in magnesium. However, the published liquidus temperatures show considerable scatter. In order to perform an accurate thermodynamic analysis, the liquidus curve between the magnesium-rich and tin-rich eutectic compositions was therefore redetermined by careful thermal analysis using highest-purity starting materials. EXPERIMENTAL PROCEDURE The magnesium metal (Dominion Magnesium Ltd, Toronto, Canada) had a purity of 99.99+ pct with the following impurities (in ppm): 20 Al, 30 Zn, 10 Si, <1 Ni, <1 Cu, <10 Fe; tin (Cominco Products, Spokane, Wash.) contained 99.999+ pct Sn. The graphite crucibles were machined from graphite rods (United Carbon Products Corp., Bay City, Mich.) which had an average total ash content of less than 30 ppm. All the graphite parts were baked out in vacuum at 950" to 1000°C for a minimum of 24 hr to remove volatile organic materials. The graphite crucibles (3 in. long, 1-5/8 in. OD, 1-3/8 in. ID) were tightly closed with a threaded cover (1/2 in. thick) which had a central thermocouple well (2-1/4 in. long, 5/16 in. OD, 3/16 in. ID). Cover and thermocouple well were machined from one piece of graphite. A thin sheath of quartz was inserted in the well to protect the thermocouple

Jan 1, 1964

By M. A. Torcaso, P. Raimondi

To study mass transport in systems simulating oil recovery processes, different porous media were saturated with a mobile (carrier phase) and a stationary phase. Slugs of carrier phase containing a small amount of solute were displaced with pure carrier phase. By analogy to the chromato-graphic processes, the velocity of the solute can be predicted from a knowledge of the partition coefficient and the saturation provided that equilibrium between the two phases exists. Equilibrium was found to exist for different porous media, solutes and rates. The conditions were varied over the range normally encountered in the laboratory and in the field. The longitudinal dispersion of a solute undergoing interphase mass transfer was also investigated. INTRODUCTION The production of hydrocarbons by gas cycling, enriched gas drive and C02 or alcohol displacement involves, among other factors, relative motion between two phases and compounds, hereafter called solute, which are soluble in both phases. The solute is carried forward by the faster flowing phase at a lower velocity than the average velocity of that phase. Retardation of the solute is caused by chromatographic absorption and desorption in the slower flowing phase and by the degree of departure from equilibrium. At equilibrium the concentration of solute in the two phases can be related by the equation* CSw = K Cso ,............(1) where C, and C are the concentration of solute in the aqueous and oleic phases respectively and K is the equilibrium ratio, or partition coefficient. Displacement theories must contain an explicit assumption with regard to equilibrium, i.e., whether the compositions can be related by Eq. 1. The existance of equilibrium depends, in general, on the relative velocity between the phases. Unfortunately, other factors such as gravity segregation and viscous fingering, also depend on velocity. For this reason, whenever effects of rate on displacement were observed,2-4 it was practically impossible to discern what caused them — lack of equilibrium or the factors mentioned above. Equilibrium between phases has been the subject of extensive studies in fields such as extraction or chroma to graphy. It has received only small attention in flow through the type of porous media encountered in oil production.5 For this reason a method was developed which makes it possible to study the movement of a solute as it is affected by rate, type of porous media, partition coefficient and carrier phase, but in the absence of segregation or fingering. The information obtained enables one to determine when the assumption of equilibrium can be made. Briefly, the method consists of (1) saturating the core with a mobile and an immobile phase, (2) injecting a slug made up of the same fluid as the mobile phase and a small concentration of mutually soluble solute, (3) measuring the lag and the peak height of the slug at arrival and (4) correlating these variables with fluid properties such as partition coefficient and mixing constants of the medium. PROPOSED MECHANISM The principles of chromatography are combined with the equation of longitudinal mixing to predict the velocity of a solute slug compared to the bulk velocity and the peak height of a slug.6-9 The equation so obtained is valid under equilibrium conditions only. Therefore, a comparison between experimental and predicted results will give a measure of departure from equilibrium. This work was done with either the oleic or the aqueous phase being immobile. For simplicity, the following development is based on the case where the oleic phase is immobile. However, the treatment is the same in either case.

Jan 1, 1966

By E. A. Gulbransen, K. F. Andrew

The vacuum-microbalance method was used to study the oxidation behavior of Zircaloy-2 and -3A over the temperature range of 300 to 850°C and at 0.1 atm pressure. The results fit in well with the authors&apos; earlier studies on zirconium. Tin was found to increase the rate of oxidation and also the temperature at which the metal burns. Both the cubic-rate law and the parabolic-rate law gave imperfect fits to the rate data. Since the parabolic-rate law has been derived from accepted physical principles, this rate law was used to interpret the rate data. A heat of activation of 28,600 cal per mole was calculated. The transition phenomenon previously observed in hot-water and steam-corrosion processes was studied systematically for oxygen atmospheres. Observations on the rate of oxidation, color and properties of the oxide films show that the transition phenomenon was associated with a failure in the adherence of the oxide to the alloy. ZIRCALOY-2 and -3A have found important uses in the field of reactor metals due to their low neutron adsorption, good strength and good resistance to corrosion. One feature of the corrosion reaction in steam or hot water is the sharp transition in the rate of corrosion to a higher value after a certain amount of reaction has occurred. This paper presents a study of the reaction of Zircaloy-2 and -3A with oxygen including a study of the transition phenomenon which has been found to occur also in oxygen atmospheres. A comparison will be made between the oxidation behavior of these alloys and the pure metal. It was hoped that a study of the details of the oxygen reaction would lead to a better understanding of the reactions occurring in hot-water and steam atmospheres. Literature Kinetics-—The reaction of Zircaloy-2 and -3A with hot-water and steam atmospheres has been studied by Thomas.&apos; Goldman and Thomas,&apos; Thomas and Forscher," and Thomas and Kass.&apos; Empirical equations for the kinetics of the reaction have been given by Thomas and Forscher." The change from the initial slow rate of reaction to the final rapid rate of reaction has been termed transition with the post-transition corrosion kinetics following a simple linear equation in time. The corrosion behavior in high-temperature steam was similar in many features to the corrosion in high-temperature water. Goldman and Thomas&apos; and Pray and Peoples&apos; have shown that the addition of tin, while increasing the rate of corrosion, counteracts the deleterious effect of nitrogen. The beneficial effect of iron, nickel and chromium was to improve the adhesion of the oxide to the metal as well as to counteract the deleterious effect of nitrogen. Mallet and Albrecht" have studied the oxidation of two zirconium-tin alloys. The cubic-rate law was found to fit the oxidation data for the 1.5 pct tin alloy while the parabolic-rate law was found to fit the data for the 2.5 pct alloy. Kendall&apos; in a recent paper has studied the oxidation of Zircaloy-2 containing 1.5 pct tin in air atmospheres. Transition Phenomenon—In steam atmospheres Thomas&apos; has observed fora 1.8 pct tin alloy containing small amounts of iron, nickel and chromium that transition to a more rapid rate of corrosion at 400°C

Jan 1, 1959

By AIME AIME

T HE year 1920 will be a memorable one in the history of the world&apos;s coal supply. The prices reached were the highest of modern times, and as usually happens at such a time, the quality of the output deteriorated. In the last two years of the war, the world&apos;s output had risen close to the pre-war level. After the armistice, however, the cessation of munitions manufacture and the delay in resumption of normal business curtailed the demand for coal. Industrial disputes both in Europe and America closed many mines late in 1919 and further reduced the supply. Thus when in 1920 the world set its face to work again and industrial activity was resumed where resumption was possible, consumers&apos; reserves of fuel proved insufficient and an almost universal feeling of apprehension over the coal supply swept around the world. The reasons for this alarm-lately a thing of the past-become clear when the world&apos;s production in 1920 is cast up.

Jan 1, 1921

By K. Prins

ONE of the more pressing problems faced by the coal industry today is the development of adequate means for meeting conservation laws, particularly those involving stream pollution, in various parts of the country. Discharge of dirty coal washery water into streams and rivers is almost universally frowned upon. Many states have enacted laws carrying heavy fines to curb the practice. The Prins stream-cleaner is one of the latest machines to enter the market. It is closely related to the cyclone thickener in principle. Eleven stream-cleaners are currently operating, ranging in size from 4 to 16 in. diam. In more recent installations the water enters directly in line and on a tangent with the impeller. The impeller consists of a vertical shaft up through a packing gland and bearings, and a V-belt pulley. The lower part is a tubing fastened to the shaft above, extending through the water intake compartment and provided with six vertical flat bars welded to the tubing. Portholes are situated in the upper end of the tubing, immediately below the point where shaft and tubing join together. The portholes are placed so that they are in open communication with the upper compartment of the stream-cleaner from which the processed water is discharged. The impeller is motor driven with a wide range vari-pitch drive employed between motor and impeller. The motor is mounted vertically, and the mounting provided with a vertical hinge allowing for needed adjustment of the wide range vari-pitch drive. The dirty coal washery water entering the machine under 20 lb psi pressure, flows from the compartment above the impeller, between the impeller blades, and is whirled around in the vertical section of the impeller enclosure. The speed of the impeller supplies centrifugal force and velocity required for separating suspended solids from water. The lower part of the machine consists of a cone, whose action is similar to other machines of the same type. The underflow discharge orifice is a cold rolled steel block machined to correspond with the cone angle and allows insertion of steel tubes of different diam. On 16 in. machines a 1 ¾ in. ID vertical discharge pipe is used. Provision is made for attaching a curved section of the same diam to the vertical pipe, to which, in turn, different lengths of horizontal pipe can be connected. Curved Pipe Advantageous It has been found that a curved pipe offers resistance to discharged material flow. In addition, the rotary motion of the underflow can be easily arrested in a curved pipe. Impeller speed of the 16 in. diam machine is provided from 400 to 800 rpm. A speed of about 474 rpm is suitable for maintenance of a constant underflow in coal slurry. In one installation 5x ¼ in. coal is cleaned in a Jeffrey Baum type washer at a 225 tons per hr rate. Washer installation is of the conventional type and a drag type sludge tank is used for water clarification purposes. Capacity of the water system, including the Baum washer, is about 40,000 gal. Before placing the stream-cleaner in operation, it was necessary to flush out the entire system every five days of two shift operations. The only time the system is drained now is for repair work on the sludge conveyor or the rig. The suction line of the stream-cleaner pump terminates in a number of small branch lines located at a depth of about 4 ft above the sludge conveyor. Each branch line extends the full width of the tank and is provided with four intake ports, each one with a funnel shaped inlet projecting downward. The arrangement provides an extensive pick-up area, for dirty water, and the inlets are arranged for a low rim velocity, preventing the taking in of coarse particles. The funnels are also arranged to extend up or down in the tank. They are set to pick up -60 mesh material exclusively.&apos; The material is a high ash and high sulphur product and thus has to be disposed in the refuse conveyor. The underflow of the stream-cleaner is discharged on top of the washery refuse which is carried in a drag type horizontal conveyor, discharging into another refuse conveyor inclined at 30º with a short horizontal loading section. Some Disadvantages The impeller inherits certain disadvantages because of the nature of its construction. Additional moving parts make it subject to wear and maintenance costs. The advantage of being able to maintain a constant speed, however, to produce desired water velocity in the machine outweighs the drawbacks. Better separation between water and solids can be obtained by regulating time of residence of water through adjustment of valves in the intake and discharge lines. The amount of fines encountered during plant operation will vary because of higher or lower moisture in coal passing over fine coal vibrating screens. Even the amount of fines picked up by underground loading machines will be inconstant. Consequently, the percentage of solids will vary in water to be processed. The velocity in the feedlines to the slurry thickeners will fluctuate, with the required water velocity lacking. Another advantage advanced for the machine is its ability to operate on 15 to 25 lb line pressures at the water intake, reducing pump power required and pump maintenance.

Jan 1, 1952

By H. Doi, Y. Fujiwara, K. Miyake

In order to throw light on the mechanism of plastic deformation of WC-Co alloys, compressive tests of WC-(7 to 43) vol pct Co alloys have been carried out at room temperature, and stress-micro strain relation has been investigated in detail. The analysis of the factors affecting the yield stresses reveals that the yield stresses can be predicted by modified Oro-wan&apos;s theory if one properly estimates the planar in-terfiarticle spacings. Conzpressive straining of some of the alloys by 0.066 to 0.17pct increases the decrements by a factor of as much as 3.4 to 14, whereas the corresponding increase in the electrical resistivities is less than 10 pct. The analysis of the decrement data in terms of -Gramto and Lücke theory shows that the marked increase is attributed to increased dislocation darnping itt the binder (cobalt) phase. By cornbilling the decrement data and the conzjwession duta, one obtains the relation between flow stress in shear (?t) and increase in dislocation density (p): At = const . v6 . This is interHeted to mean that the mechanism of strain hardening of CirC-Co alloys is essentially sarne as the one for dispersion strengthened alloys. The possible effect of bridge formations between the carbide particles has also been examined. OWING to the combination of hardness, strength, and other physical and chemical properties, WC-Co alloys have opened the way for unique fields of applications, the recent ones being, for instance, anvils for super-high-pressure generation apparatuses. In such applications, the alloys are frequently subjected to very high compressive stresses: these stresses may cause the alloys to deform plastically and eventually to fail. However, much remains obscure regarding the nature of the plasticity of the alloys. Evidently, the alloys owe their high strength to the hard carbide particles which frequently occupy as much as 80 to 90 pct in volume fraction, whereas the ductility required for practical applications is provided by the small amount of the binder phase between the carbide particles. When the volume fraction of the carbide phase is not very large, deformation behavior of the alloys may be described by some of the current dispersion strengthening theories. However, greatly increasing the carbide phase is thought to lead to some carbide skeleton structure or bridge formations owing to the increased chances for direct contacts between the carbide particles;1,2 this may appreciably affect the plasticity of the alloys. Regarding the effect of formation of the carbide skeleton structure, it is interesting to note the work by Ivensen et al.3 on compression tests of the alloys containing somewhat large carbide particles; they observe extensive generation of slip bands in the carbide particles after application of some preliminary compressive stresses. They interpret the results in terms of plastic deformatiot: of the carbide particles which are supposed to have formed a skeleton structure; the binder phase plays only a passive role, at least in the early stages of the deformation. That carbide crystals exhibit microplasticity at room temperature is apparent from the work of Takahashi and Freise4 and French and Thomas5 on indentation of WC single crystals. On the other hand, Dawihl and coworkers6-10 maintain that even when volume fraction of the carbide phase is very large (for instance, more than 90 pet), a very thin binder layer generally exists between the carbide particles. They interpret the results of the extensive mechanical tests in terms of the plasticity of such a layer. Gurland and Bardzil11 point out that decrease in ductility of the alloys with increase in the carbide phase is caused by the effect of plastic constraint exerted by the dispersed carbide particles. Drucker12 further develops this concept from a continuum-mechanics approach on an assumption that a continuous thin binder layer separates the carbide particles. A common feature of the studies reported so far on the plasticity of the alloys is that the information deduced is invariably qualitative in nature. Thus, very few systematic experiments for obtaining reliable and sufficiently detailed stress-strain curves of the alloys varying widely in the microstructural features have been carried out. In particular, it may be of special interest to investigate in detail the early stages of the plastic deformation of the alloys in order to shed light on the strengthening mechanism. However, such work appears to be extremely rare. Doi et al.13 recently reported a first brief account of the results of some quantitative analysis of the plasticity of the alloys in terms of dislocation theory. Their experiment was rather limited in the composition range covered (volume fraction occupied by the carbide phase: 79 to 83 pct), and thus they could not necessarily elucidate the controlling mechanism of plastic deformation of the alloys of a more general composition range. Consequently, in the present investigation, deformation behavior and some other physical properties of the alloys were investigated and discussed in more detail over a much wider composition range. SPECIMEN PREPARATION WC-Co alloys used in this experiment were prepared in cylindrical or rectangular form by sintering in vacuo compressed mixtures of tungsten carbide and cobalt

Jan 1, 1970

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,&apos; who first dealt with the coning problem; (2) Chaney, et al,&apos; who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.&apos; Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,&apos; and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy&apos;s law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

Sec. 1. This Division shall be known as the Institute of Metals Division of the American Institute of Mining and Metallurgical Engineers. Sec. 2. The object of the Division shall be to furnish a medium of cooperation between those interested in the metallurgy, fabrication and uses of the nonferrous metals and their alloys; to represent the A. I. M. E. in so far as nonferrous metallurgy is concerned, within the rights given in A. I. M. E. By-law XI., Sec. 1, and not inconsistent with the Constitution and By-laws of the A. I. M. E.; to hold meetings for social intercourse and the discussion of nonferrous metallurgy; to stimulate the writing, presentation and discussion of papers of high quality on nonferrous metallurgy; to reject or accept such papers for presentation before meetings of the Division. Article II—MembeRs Sec. 1. Any Member, Associate, or Junior Associate of the A. I. M. E. in good standing may become a Member, Associate or Junior Associate of this Division upon registering in writing a desire so to do, but without additional dues. Sec. 2. But no one who has been continuously indebted to the A. I. M. E. or to this Division for more than three months shall be entitled to vote or to receive publications to which, as a member of the Division, he would be entitled. Article III—Funds Sec. 1. The expenditure of the funds reccived by the Division shall be authorized by the Executive Committee of the Division. Article IV—Meetings Sec. 1. The Division shall meet at the same time and place as the annual meeting of the A. I. M. E., and at such other times and places as may be determined by the Executive Committee subject to the approval of the Board of Directors of the A. I. M. E. Sec. 2. The annual business meeting for election of officers shall be held within a few days before or after the annual business meeting of the A. I. M. E. Sec. 3. At any meeting of the Division for which notice has been sent to the members of the Division through the regular mail at least one month in advance, a business meeting may be convened by order of the Executive Committee, and any routine business transacted not inconsistent with these By-laws or with the Constitution or By-laws of the A. I. M. E. Sec. 4. For the transaction of business, the presence of a quorum of not less than 25 members of the Division shall be necessary. Article V—Officers and Government Sec. 1. The officers of the Division shall consist of a Chairman, two Vice-chairInen, Secretary and Treasurer. The office of Secretary and Treasurer may be combined in one person, if desired by the Executive Committee. Sec. 2. The government of the affairs of the Division shall rest in an Executive Committee, in so far as is consistent with the By-laws of the Division and the Constitution and By-laws of the A. I. M. E. Institute of Metals Divisiori

Jan 1, 1931

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,&apos; and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,&apos; and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By B. M. Larsen, T. E. Brower

IN two previous papersl,2 dealing with the carbon-oxygen reaction, and the simultaneous content of each, in liquid steel in the furnace, we have made use of the quantity 0[O], defined as the excess oxygen beyond what would be in equilibrium with carbon then present if the pressure of carbon monoxide were I atm,; that is, if [C] X [O] is taken as 0.00222, 0[O] = [O] - 0,00222/[C] where [O] is the percentage of oxygen by weight as measured by the method described earlier.&apos; This quantity 0[O] proves to be substantially independent of carbon content over the range 0.08 to 1.2 per cent, as well as of the basicity of the slag, and is nearly always within the limits 0.015 to 0.025 per cent when the bath is boiling normally and is in what we have termed a steady state. Apparently it must be at least about 0.014 per cent before boiling occurs; but this threshold value seems to depend upon the ease of bubble formation at the metal-hearth interface, hence upon the condition of the surface of the hearth. In any case, 0[O], on the average, changes considerably following any disturbance of the bath, as by addition of ore. The present paper deals with the average changes in ?[O] level following addition of Spiegel or crop ends, or after procedures to promote stirring, or by tapping of the steel from the furnace. The observations were made on a large number of commercial heats, and consequently are subject to the influence of various disturbing factors; the results have the compensating merit of showing the consistency obtainable under the limitations imposed by practical operation. VARIABILITY OF EXCESS OXYGEN IN NORMAL OPEN-HEARTH OPERATION The preceding general statements refer to the average value of ?[O] particularly in heats that are boiling actively; on individual heats, which are less active, there may be a variable time lag between the disturbance and its effect, which complicates the interpretation of what is going on. For instance, if in the normal refining process boiling is sluggish, the slag usually is gaining oxygen from the gas phase above it, or from added ore, faster than it is losing oxygen to the metal; yet when the bath starts to boil vigorously, the opposite condition may prevail for some time. The consequence of this lag is a variation of ?[O], the interpretation of which in a single heat may not be immediately obvious, This condition is illustrated in Figs. I and 2. In Fig, I, ?[O] at the beginning of the test period was near the lower limit of its usual range (dashed lines) in the steady state as a consequence of the lime boil, which had ended about as indicated. The bath is now cold, carbon drop is slow, and the first small ore feed causes only a small rise in 0[O]; as the temperature rises and as lime dissolves in the slag, and the bath becomes more active, the

Jan 1, 1946