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By R. G. O’Meara, M. M. Fine

ONE of the principal activities of the Bureau of Mines connected with the recent war was to help to increase the supply of strategic and critical minerals. Fluorite was one of the most critical of the nonmetallic minerals because of the increased demand for it as a flux in basic open-hearth and electric steel furnaces and as a raw material for the production of artificial cryolite used in the aluminum industry. Wartime developments in the technology of hydrofluoric acid, such as the use of the anhydrous acid as a catalyst in production of high-octane gasoline and the use of organic fluorides as carriers for insecticides, also increased the demand for acid-grade fluorite.[t] In 1943 the consumption of acid-grade fluorite was advancing at a more rapid rate than production, and was only slightly less than production during the latter half of the year.1 The outlook for the postwar market for fluorite is encouraging. Steel production is expected to remain high until the domestic demand for commodities not manufactured during the war is satisfied. The uses for hydrofluoric acid are expected to increase under the impetus of war-initiated research. In consideration of these and other factors some authorities predict a postwar demand for fluorite equal to about 60 to 75 per cent of the wartime production.1,2 Others believe that the postwar fluorite industry will be permanently expanded over its prewar status.3 ACKNOWLEDGMENT This paper is one of many reporting on various aspects of the Bureau of Mines program directed toward the more effective utilization of our mineral resources. The program has been under the general supervision of R. S. Dean, Assistant Director, since July 1942. The scope of the paper falls in the province of the Metallurgical Branch, whose activities embrace the separation of difficultly beneficiated ores, the production of pure metals from domestic deposits, the exploitation of marginal ore reserves, the recovery of secondary metals, and the improvement of present industrial metallurgical practice. The investigation was initiated at the request of Mr. J. H. Steinmesch, vice-president and general manager, Minerva Oil Co., Eldorado, Ill. His hearty cooperation and helpful suggestions, and those of Mr. O. E. Anderson, mill superintendent,

Jan 1, 1946

By O&apos, R. G. Meara, M. M. Fine

One of the principal activities of the Bureau of Mines connected with the recent war was to help to increase the supply of strategic and critical minerals. Fluorite was one of the most critical of the nonmetallic minerals because of the increased demand for it as a flux in basic open-hearth and electric steel furnaces and as a raw material for the production of artificial cryolite used in the aluminum industry. Wartime developments in the technology of hydrofluoric acid, such as the use of the anhydrous acid as a catalyst in production of high-octane gasoline and the use of organic fluorides as carriers for insecticides, also increased the demand for acid-grade fluorite. † In 1943 the consumption of acid-grade fluorite was advancing at a more rapid rate than production, and was only slightly less than production during the latter half of the year.' The outlook for the postwar market for fluorite is encouraging Steel production is expected to remain high until the domestic demand for commodities not manufactured during the war is satisfied. The uses for hydrofluoric acid are expected to increase under the impetus of war-initiated research. In consideration of these and other factors some authorities predict a postwar demand for fluorite equal to about 60 to 75 per cent of the wartime production.1,2 Others believe that the postwar fluorite industry will be permanently expanded over its prewar status3 Acknowledgment This paper is one of many reporting on various aspects of the Bureau of Mines program directed toward the more effective utilization of our mineral resources. The program has been under the general supervision of R. S. Dean, Assistant Director, since July 1942. The scope of the paper falls in the province of the Metallurgical Branch, whose activities embrace the separation of difficultly beneficiated ores, the production of pure metals from domestic deposits, the exploitation of marginal ore reserves, the recovery of secondary metals, and the improvement of present industrial metallurgical practice. The investigation was initiated at the request of Mr. J. H. Steinmesch, vice-president and general manager, Minerva Oil Co., Eldorado, Ill. His hearty cooperation and helpful suggestions, and those of Mr. 0. E. Anderson, mill superintendent,

Jan 1, 1947

By M. M. Fine, R. G. Meara, O&apos

One of the principal activities of the Bureau of Mines connected with the recent war was to help to increase the supply of strategic and critical minerals. Fluorite was one of the most critical of the nonmetallic minerals because of the increased demand for it as a flux in basic open-hearth and electric steel furnaces and as a raw material for the production of artificial cryolite used in the aluminum industry. Wartime developments in the technology of hydrofluoric acid, such as the use of the anhydrous acid as a catalyst in production of high-octane gasoline and the use of organic fluorides as carriers for insecticides, also increased the demand for acid-grade fluorite. † In 1943 the consumption of acid-grade fluorite was advancing at a more rapid rate than production, and was only slightly less than production during the latter half of the year.' The outlook for the postwar market for fluorite is encouraging Steel production is expected to remain high until the domestic demand for commodities not manufactured during the war is satisfied. The uses for hydrofluoric acid are expected to increase under the impetus of war-initiated research. In consideration of these and other factors some authorities predict a postwar demand for fluorite equal to about 60 to 75 per cent of the wartime production.1,2 Others believe that the postwar fluorite industry will be permanently expanded over its prewar status3 Acknowledgment This paper is one of many reporting on various aspects of the Bureau of Mines program directed toward the more effective utilization of our mineral resources. The program has been under the general supervision of R. S. Dean, Assistant Director, since July 1942. The scope of the paper falls in the province of the Metallurgical Branch, whose activities embrace the separation of difficultly beneficiated ores, the production of pure metals from domestic deposits, the exploitation of marginal ore reserves, the recovery of secondary metals, and the improvement of present industrial metallurgical practice. The investigation was initiated at the request of Mr. J. H. Steinmesch, vice-president and general manager, Minerva Oil Co., Eldorado, Ill. His hearty cooperation and helpful suggestions, and those of Mr. 0. E. Anderson, mill superintendent,

Jan 1, 1947

By B. H. Bergstrom, D. D. Crabtree, C. L. Sollenberger

Experimental data is given for several natural minerals on the load required for the fracture of single specimens over a very wide size range. The experimental results are compared with published data, such as for coal specimens from 30 to 64 in. in size. Correlations of the specific energy (per unit mass) required for fracture with specimen size are given as functions of specimen shape and the experimentally observed load-size relationships. These correlations are discussed with reference to comminution theory. Comminution, through compression or impact, can result only if sufficient force, or energy, is applied to a specimen of a given size. The relation of specimen size to force requirements has not been adequately considered previously. For single particle fracture, it was previously shown 1 that the specific energy (energy, e, per unit mass, M) at fracture of single glass spheres was inversely proportional to the product size modulus, k, as indicated in the equation: e/M = C/k [1] This was found true not only for numerous glass specimens of the same nominal size but was true for all nominal sizes tested from 1/8 to 1 in. Also, it was observed that the smaller spheres required a greater specific energy at fracture than the larger spheres and consequently had a smaller product size modulus. However, the relationship giving the required fracture energy as a function of specimen size was not further elaborated upon. This paper will extend the development of the feed size effect on specific fracture energy for brittle materials. SPECIFIC ENERGY-FEED SlZE RELATIONSHIPS FROM PREVIOUS DATA For the particular glass spheres tested in the previously described experiments,' it can be shown, as on Fig. 1, that the specific energy varied inversely as the 4/3 power approximately of the feed size, F, in the span of nominal sizes ranging from 1/8 to 1 in. The load at which a 3-in. diam glass sphere (a crystal gazer's ball) was broken was within the range predicted by an extrapolation of this energy-feed size relationship. The product size distribution from this

Jan 1, 1963

By R. C. Earlougher, F. G. Miller, T. D. Mueller, H. J. Ramey

There are many studies of flow in radial systems that can be used to interpret unsteady rerervoir flow problems. Although solutions for systems of infinite extent can be used to generate solutions fur finite ow systems by superposition, application is tedious. In this paper a step is made toward simplifying calcu1ations of such solutions for finite flow systems. Superposition is used to produce a tabulu-lion of the dimension1e.s.s pressure drop function at several locations within a bounded square that has a well at its center. The square system provides a useful building block that may be used to generate flow behavior for any rectangular shape whose sides are in integral ratios. Values of the tabulated dimensionless pressure drop function are simply added to obtain the dimensionless pressure drop function for the desired rectangulm system. The rectangular system may contain any number of wells producing at any rates. Furthermore, the outer boundaries of the rectangular system may be closed (no-flow) or they may he at constant pressure. Mixed conditions also may be conyidered. Tables of the dimensionless pressure drop function for the square system are presented and various applications of the technique are illustrated. Introduction In 1945, van Everdingen and Hurst' published solutions for the problem of water influx into a cylindrical reservoir. Since this problem is mathematically identical with the depletion of a cylindrical reservoir with a well at the origin, the van Everdingen-Hurst solution may be used to study the depletion problem. In their analysis, they assumed that the fluid had a small, constant compressibility such that flow was governed by the diffusivity equation For a constant production rate q starting at time zero, van Everdingen and Hurst showed that the unsteady pressurc distribution for both finite and infinite systems could be expressed in terms of a dimensionless pressure 'Sabulations of the dimensionless pressure drop for a unit value of r, were provided by van Everdingen and Hurst,' and later by Chatas.' Others also presented values in graphical or tabular form." If the radius of the well becomes vanishingly small, r,+ O, the line source solution may be used for Eq. 2 when infinite systems are considered. Eqs. 5 and 6 are excellent approximations for Eq. 2 under certain conditions: In 1954, Matthews, Brons and HazebroekV emonstrated that solutions such as Eq. 5 can be superposed to generate the behavior of bounded geometric shapes; i.e., the behavior of a bounded single-well system can be calculated by adding together the pressure disturbances caused by the appropriate array of an infinite number of wells producing from an infinite system. These wells are referred to as image wells. Matthews, Brons and Hazebroek considered systems containing a single well producing at a constant rate. This superposition can be represented analytically as

Jan 1, 1969

By Donald L. Katz, Leslie J. Noaker

Experimental data are presented for hydrate formation conditions for mixtures of hydrogen sulfide and methane. Vapor-solid equilibrium constants for hydrogen sulfide are also presented. Equilibrium constants, defined here as the ratio of the mole fraction of hydrogen sulfide in the vapor phase (dry basis) to the mole fraction of hydrogen sulfide in the solid phase (dry basis), were calculated using the vapor-solid equilibrium constants for methane presented in an earlier paper. The conditions at which a natural gas will form gas hydrates with water may be computed from its composition, when hydrogen sulfide is present in addition to carbon dioxide and the paraffin hydrocarbons. INTRODUCTION Many gases are known to form solid hydrates in the presence of liquid water at temperatures above 32°F. This hydrate formation is of importance to the natural gas industry inasmuch as most of the constituents found in natural gases will form hydrates. The attention of the industry was called to hydrates by Hammer-schmidtl0 in 1934. A number of papers have been written giving the temperatures and pressures at which these hydrates will form3,4,5,6,7,8,9,10,13,14,15,18,19 and a bibliography on the subject has been compiled13. Deaton and Frost4,5,6,7,8 report work for various pure gases and for some natural gases. Katz and co-workers3,4,13,14,18,19 have reported data for various gases at high pressure. They developed a method of predicting conditions for hydrate formation from equilibrium constants3,19 and from gab gravity." The effects of anti-freeze agents on the formation of hydrogen sulfide hydrate were reported by Bond and Nelson.' The hydrogen sulfide-water system, including hydrate, has been the subject of recent investigation by Sage and co-workers." Mixtures of hydrates behave as solid solutions and an equilibrium exists between the vapor phase and the solid phase that appears to be comparable to the equilibrium between vapor and liquid phases.3,10 By means of the vapor-solid equilibrium constants which have been published for methane, ethane, propane, iso-butane, and carbon dioxidel6 it is possible to determine the temperature and pressure at which hydrates will form for a specific gas mixture when water is present. Hydrogen sulfide which is frequently found in natural gases has a very strong tendency to form hydrate and must enter the solid solution when present in a natural gas forming a hydrate. To determine the effect of hydrogen sulfide when computing the conditions for gas hydrate formation, it is necessary to have the equilibrium constant giving the ratio of the concentration of hydrogen sulfide in the gas phase to the concentration in the solid phase. This paper presents data on hydrate formation for mixtures of hydrogen sulfide and methane and presents the equilibrium constants which were calculated from these data. EXPERIMENTAL PROCEDURE The apparatus used to determine the conditions of hydrate formation for the methane-hydrogen sulfide system was similar to that employed by previous investigators.3,18,19 A charge gas cylinder was used to supply the hydrogen sulfide-methane mixtures, called the charge gas, and to supply the pressure up to 1.000 psia. This

Jan 1, 1955

By N. A. Gokcen, M. N. Dastur

In metallurgical process industries a knowledge of true melting and casting temperatures is very essential for increasing the operating efficiency as well as improving the quality of the finished product. Optical pyrometers are widely used for the purpose because of their cheapness and ease of operation. It is an unfortunate fact, however, that this mode of measuring temperature entails a source of severe error inasmuch as with all non-black bodies, the temperature observed is always below the true temperature owing to deficient emissive power. Hence, the need for emissivity correction arises. In 1913 Bidwell1 obtained emissivity values of 0.36-0.48 for a temperature range of 1520-1800°C. He measured the true temperature of molten iron by sighting into a carbon cavity immersed in the iron under an atmosphere of hydrogen. In 1914 Burgess2 determined the emissivity of a smooth surface of liquid iron free from oxide to be 0.37 under an atmosphere of hydrogen. He claimed to have attained an accuracy of within 5°C at 1500°C with an optical pyrometer using monochromatic light. He reported that no difference appeared to exist between the emissivities of pure iron and of steels containing considerable percentages of carbon, nickel or manganese; nor was there any appreciable variation of emissivity with temperature from 1530 to 1571°C. Wensel and Roeser3 found an elnissivity value of 0.4 for temperatures above 1375°C for cast iron. The average emissivity value for carbon steels reported by Leiber,4 odd,5 Hase6 and Umino7 range from 0.4 to 0.45. Knowles and Sarjant8 made an extensive study of emissivity of molten iron and steel over a wide range of workshop and laboratory conditions. Observations of true temperature were made with immersion thermocouples, and correlated with apparent temperatures indicated by optical pyrorneter readings taken on the pouring stream as it passed over the lip of the crucible. The emissivity of Armco iron was shown to be of the order of 0.4, rising slightly with increasing temperature. But for plain carbon steels containing up to 1.0 pct carbon the emissivity was shown to fall slightly with increasing temperatures. The results of their investigation are in agreement with those of Guthmann.9 Naeser,10 Spencer," Todd5 and Hase6 in regard to the relation between emissivity and temperature for plain carbon steels. However, Goller12 has found a rise of emissivity with increasing temperature for the same steels. Results of several investigations are given in Fig 1. Measurement of True and Apparent Temperatures The necessity for an accurate optical temperature scale for liquid iron in studies of gas-metal equilibria led to this investigation. Experimental measurements were carried out in the induction furnace used by Dastur and Chipman13 in their studies of the reaction of hydrogen with oxygen in liquid iron. The furnace as modified for this work is shown in Fig 2. The atmosphere of the furnace was a mixture of purified argon with hydrogen containing a small controlled amount of water vapor. Gases were preheated by means of a platinum-10 pct rhodium resistance coil. The stream of hydrogen sweeping across the surface of niolten iron vir-

Jan 1, 1950

By H. H. Rachford, D. S. Howard

In the withdrawal of fluids from tilted aquifers it is of value to be able to predict pressure patterns during the course of the pressure decline. As an example of this, in the displacement of fluids from oil reservoirs being produced by water-drive, prediction of the reservoir pressure is an important factor in fixing production rate. The prediction of pressure patterns in the depletion of an inclined aquifer has conventionally been made by solving the well known flow equations for the pressure Patterns in a horizontal aquifer, and correcting these patterm for the pressure difference due to the hydrostatic head associated with the vertical distance between a point in the horizontal aquifer and the corresponding point in the tilted aquifer. Inasmuch as the equation describing flow in tilted strata is different from that for horizontal flow. there was question as to the validity of the simple corrective procedure current1y in use. To examine the magnitude of error made using this procedure, an inclined aquifer was chosen for which the error was expected to he large, and the equation for flow in this tilted stratum was solved numerically. The results of the conventional procedure of correcting the solution of the equation for horizontal flow was compared with the solution of the correct equation by studying the difference between predicted pressures by the two methods. Three forms of the hydrostatic head correction were studied. The results for all three forms of the head correction are similar. The error in the approximate solution is quite dependent on the position of the horizontal aquifer with respect to the inclined one. The error is greatest at the producing end ad increases with amount of fluid withdrawn. The magnitude of the errors is not large if a good choice is made for the position of the horizontal datum. The most satisfactory position for the datum in all cases is near or slightly about the mid-point of the inclined stratum. Use of the best approximate method studied with the best datum tested yielded predicted pressures in error no greater than 7 psi. INTRODUCTION The movement of water by expansion from an aquifer to displace fluids from a contiguous oil reservoir was first recognized over 20 years ago.9 Since that time much work has been done to relate this mechanism to reservoir behavior mathematically. The result of this effort on the part of many workers has led to an understanding of underground fluid movement which has enabled us to follow and predict the behavior of the water-drive reservoir. One reason that good progress has been made in the application of mathematics to the study of pressure patterns and water movements in aquifers has been that the differential equation which describes this process is of a relatively simple form. The equation for the isothermal, horizontal, viscous flow of water through homogeneous sandstone is identical with that for the diffusion of heat through homogeneous solids, and this equation and means of obtaining solutions for it with many types of boundary conditions have been studied extensively. That this work has been highly successful is clearly emphasized by the large number of solutions developed for problems of interest both by methods of formal mathemat-

Jan 1, 1957

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By Paul A. Beck, John Towers, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350' to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.' Fig I shows a log D vs. log t plot of French's data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French's data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.' Walker's specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker's data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

By John Towers, Paul A. Beck, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350' to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.' Fig I shows a log D vs. log t plot of French's data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French's data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.' Walker's specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker's data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

By Charles Law McCabe, Lyndon H. Everett, Edna A. Dancy

It has been found that the carbide phase present at equilibrium in the system M-H2-CH4, at about 600°C, is MC for the rare-earth metals Ce and Pr. X-ray diffraction analysis showed that the monocarbides have fcc structures with lattice constants of 5.036 + 0.009Å and 5.131 + 0.001Å for CeC and PrC respectively. Gaseous equilibrium measurements were used to calculate the standard free energy of formation of the monocarbides from the elements. for the formation of (+ 1300) for the formation of PrC. THE rare-earthdicarbides, and their crystal structures, have been known for some years,l but only more recently were the carbides CeC,2,3 Ce2C3 2 and CeCS3 reported. In 1958 to 1959, Spedding et al. published work on the lanthanum-carbon system4 and other rare-earth metal-carbon systems,5 proving the existence of M2C3 and MC2, and measuring the lattice constants. They also demonstrated that tri-rare earth carbides, M3C, exist for the rare-earth metals samarium through ytterbium. However, they concluded that the cerium monocarbide reported by Brewer and Krikorian2 and by Warf,3 and given a fcc structure with a lattice constant of 5.130Å bythe former workers, was, in fact, cerium metal with carbon dissolved in it. They were also unable to find any evidence for the existence of Warf's CeC3, for which no structural details had been given. Even more recently, Palenik22 reported the existence of only M2C3 and MC2, having been unable to find any evidence for the existence of any other rare-earth carbides. There are no published experimentally derived thermodynamic data for the formation of any of these carbides, although Brewer and Krikorian6 have estimated values of for CeC, Ce2C3 and CeC2. The objective of the present investigation was; to determine experimentally the free energy of formation of any of the reported carbides of cerium and praseodymium, through a study of the rare-earth metal-hydrogen equilibrium. EXPERIMENTAL A methane-hydrogen mixture was circulated, in a closed system over previously prepared cerium or praseodymium hydride, and when equilibrium had been attained, the gas mixture was analyzed by selectively oxidizing the hydrogen and condensing out the water formed. The metal hydrides were used as starting material for convenience because, otherwise, the hydrogen in the gas mixture would immediately dissolve in the metals; in addition, the metals would not react with methane alone at the experimental temperature (around 600°C). The circulating system was based on that used by Browning, DeWitt, and Emmett7 for similar studies on iron carbides. It consisted of a quartz reaction vessel, all-glass circulating pump, analysis tube containing copper oxide that could be heated to 300" C by means of a small furnace, a solid CO2-methanol trap, and a double limb absolute manometer, Fig. 1. A cathetometer, capable of reading to 0.005 cm, was used to measure the difference in height between the two columns of mercury. In its final form, the reaction vessel was enclosed in an outer jacket, containing approximately the same pressure of hydrogen as that within, to reduce errors due to diffusion of hydrogen out through the fused silica of the reaction vessel., The circulating system was supplied with

Jan 1, 1962

By H. R. Brannon, R. J. Robinson, G. W. Kattawar

Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and .98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gulf water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. INTRODUCTION Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydro-dynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. l-3 One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice5.6 in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker 7 have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire,8 among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii,10 establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other areas as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents (1) a practical approach to computing wave profiles hat depict shapes of waves for use in force calculations, (2) a summary of relations for predicting probabilities of wave crest elevations, (3) correlations of parameters needed to apply these methods in the Gulf of Mexico and (4) examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities. These relations also identify quantities that must be related to storm

By L. S. Darken

A quadratic formalism is developed lor the representation of the excess free energy, and of the activity coefficients of each component of a ternary system in the vicinity of a single component selected as solvent. This formalism, in contrast to the e formalism, is thermodynamically consistent at .finite concentrations. Numerous specific systems are used as illustrations, with cross checks where possible; these systems are Fe-C-X systems in the vicinity of 1600°C and include practically all those for which reliable data are available. It is shown that this formalism is usually quite adequate to rebresent available data up to a solute concentration of 20 to 30 at. pet. It is hoped that the formalism here presented may prove useful for the treatment and tabulation of data on ternary and multi-component solutions. SINCE, as discussed in a prior paper,' we do not as yet have an adequate basic understanding of the nature of binary metallic solutions, we cannot hope to be in better position for ternary and multicomponent systems. However, the accumulation of thermodynamic data on ternary and multicomponent metallic solutions has led to an urgent need for a rational formalism for the presentation and use of such data. Notable attempts to represent the isothermal isobaric thermodynamics of ternary solutions were made by Benedict et 01.' and by Wohl.3 These attempts were directed toward developing an analytic expression adequate to encompass the entire ternary triangle, primarily for organic systems; they generally involve the power-series approach, which has been shown' to be inappropriate, in general, even for binary metallic systems. On the other hand, interest in the thermodynamics of ternary and multicomponent metallic solutions has tended to focus either on general thermodynamic relations4-10 over wide compositional ranges, or on cases where one or more components have been at rather low concentration. This latter approach has been followed by Wagner,= by chipman,11 and by Alcock and Richardson,12 and more recently in many publications by the same and other authors. It has already been shown' that the thermodynamic behavior of binary metallic systems is, in general, relatively simple only in the terminal regions. Hence, it would appear that any approach, at this time, to a simple formalism for ternary and multicomponent systems must, a fortiori, be limited to the vicinity of the major component or solvent. The present treatment is aimed to be useful for a given solvent with moderate solute concentrations ranging up to 20 or 25 at. pet and in exceptional cases to considerably higher concentrations. In order to achieve even this modest objective, it is necessary that any appropriate formalism have built into it 1) a thermodynamic consistency (at least within the desired degree of approximation), and 2) an approach at infinite dilution to Raoult's law for the solvent and to Henry's law for each solute. Let us first formulate the condition of thermodynamic consistency for a ternary system. Under isothermal isobaric conditions, we may write for the molal value G of any extensive function dG - C1 dN1 + G2 dN2 + G3 dN3 [l] where the G's are the corresponding partial molal quantities and the N's are the atom fractions. Taking component 1 as the solvent, this relation may be rewritten in terms of the independent variables N2 and N3

Jan 1, 1968

By H. N. Hall

Reservoir and producing characteristics can govern the decision to use either a one-, two- or three-dimensional model for making predictions for gravity-drainage reservoirs. Examples of conditions requiring one-, two- and three-dimensional calculations are given. In 1961 the author presented a method for predicting one-dimensional gravity-drainage performance. This work has been exrendcd to obtain a three-dimensional model, which is described and for which a sample problem is presented. Introduction Many papers on gravity drainage or gas-cap drive'-3 have been presented for conditions where the reservoir is treated as a single areal segment so that, in effect, only one-dimen-sional flow is considered. Other authors'-Q ave given evidence showing that the one-dimensional concept would be unsatisfactory to predict reservoir performance for certain types of reservoirs. Experience has indicated that specific reservoir and producing conditions govern whether one-, two- or three-dimensional concepts must be used as a basis for reliable reservoir performance predictioils. Previously the author presented a paper outlining a method for predicting the performance of gravity-drainage reservoirs.' That paper treated the reservoir as a single areal segment so that it was applicable for only one-dimensional flow. The work has been extended to obtain a three-dimensional model that can be used to predict performance of gravity-drainage reservoirs. Although capable of being three-dimensional, it can be used equally well for one- and two-dimensional predictions. This paper discusses those reservoir and producing conditions governing the choice of model, and also describes a three-dimensional model suitable for predicting reservoir performance in the more complex situations. Discussion The Choice of Model To predict reservoir performance, it is necessary to represent the reservoir by a physical model. A mathematical model, based on the assumed physical model, then is used to predict the movement of oil and gas within the reservoir. The word "model" is used here to connote the combination of both a physical model and a mathematical model based on the physical model. Certain types of reservoir situations may be predicted suitably with a one-dimensional model, whereas two- and three-dimensional models may be required for other situations. This section illustrates reservoir conditions associated with the use of a specific type of model. Many types of reservoir structures are such that gravity drainage possibly could be an important factor in oil production. Production practices, as well as the nature of the structure. can influence the type of model that should be used. obviously, it is impossible to discuss all combinations of reservoir structure and production practices that might be encountered in gravity-drainage reservoirs. The following are typical examples of conditions where a choice must be made among a one-, two- or three-dimensional model to predict reservoir performance satisfactorily. Conditions Requiring a One-Dimensional Model Fig. la shows contours for an asymmetrical anticline in which gravity drainage might be expected to be important. Fig. Ib depicts a cross-section along Line A-A in Fig. la. Existence of a gas cap is a good clue that gravity drainage will be an important factor in producing oil from this type of reservoir. However, it is not essential since a gas cap will form as oil is produced from the reservoir. If the proper combination of reservoir permeability and withdrawal rates is present, the reservoir will behave like a

Jan 1, 1969

By T. H. Janes

NATURAL abrasives of some type are found in all countries of the world. In order of their hardness the principal natural abrasives are diamond, corundum, emery, and garnet, which are termed high grade, and the various forms of silica, including pumice, pumicite, ground feldspar, china clay and, most important, sandstone. The properties qualifying materials for use as abrasives are hardness, toughness, grain shape and size, character of fracture, and purity or uniformity. For manufacture of bonded grain abrasives such as grinding wheels, the stability of the abrasive and its bonding characteristics are also important. No single property is paramount for all uses. Extreme hardness and toughness are needed for some applications, as in diamonds for drill bits, while for other purposes the capacity of the abrasive to break down slowly under use and to develop fresh cutting edges is of greatest importance, as with garnet for sandpaper. In dentifrices, soaps, and metal polishes, of course, hardness and toughness are objectionable. First among the natural abrasives, industrial diamonds are essentially of three types: l—bort, which includes off-color, flawed, or broken fragments unsuitable for gems; 2—carbonado, or black diamond, a very hard and extremely tough aggregate of very small diamond crystals; and 3—ballas, a very hard, tough globular mass of diamond crystals radiating from a common center. Bort comes from all diamond-producing centers, carbonados only from Brazil, and ballas chiefly from Brazil, although a few of this last group come from South Africa. By far the largest producer of industrial diamonds is the Belgian Congo; the Gold Coast, Angola, the Union of South Africa, and Sierra Leone supply most of the remainder. There is no production in Canada, which imports $6 to $9 million worth of industrial diamonds annually. Industrial diamonds find innumerable uses in modern industry. They are used for diamond drill bits for the mining industry; in diamond dies for wire drawing; in diamond-tipped tools for truing abrasive wheels and for turning and boring hard rubber, fibers, and plastics; and in diamond-toothed saws for sawing stone, glass, and metals. High-speed tool steels, cemented carbides, and other hard, dense alloys can be cut, sharpened, or shaped efficiently only with diamond-tipped tools and diamond grinding wheels. .. Second only to the diamond in hardness is corundum, an impure form of the ruby and sapphire gems consisting of alumina and oxygen (Al²O³) with impurities such as silica and ferric oxide. Corundum generally crystallizes from magmas rich in alumina and deficient in silica, as in the nepheline syenites of eastern Ontario. Grain corundum is used in the manufacture of grinding wheels; very coarse grain is used in snagging wheels. Both types of wheels are employed in the metal trades, where the hardness of corundum, coupled with its characteristic fracturing into sharp cutting edges, makes it an ideal cutting tool. The finest corundum (flour grades) is used for fine grinding of glass and high-precision lenses. From 1900 to 1921 Canada was the world's leading producer of corundum. Following this period the deposits located in northern Transvaal of the Union of South Africa supplied more and more of the world's requirements, and since 1940 South Africa has provided almost the entire output, which has ranged between 2500 to 7000 tons a year during the last decade. Minor amounts have also been produced in Mozambique, India, and Nyassaland. Opportunities for Mining Corundum Corundum deposits in southeastern Ontario are of three types, which may be described as follows: 1—Scattered, irregularly-shaped deposits of coarse-grained corundum which could be mined by means of small pits. About 10 groups of such deposits are known. Although the tonnage of individual deposits of this type is not great, it has been estimated that several years' ore supply is available for a small tonnage operation. Deposits average about 9 pct corundum. 2—Large irregular deposits of coarse-grained corundum which would require mining by adit with possibly a scavenger operation on the remains of former surface deposits. The Craigmont deposit of this type produced about 20,000 tons of corundum concentrate during operations between 1900 and 1913. Most of the readily available surface ore was removed by operators during that time. Reserves of ore above road level have been estimated to average 7 pct corundum, but none of the so-called reserves have been blocked out, or even indicated, by diamond drilling. From 1944 to 1946, 2025 tons of

Jan 1, 1955

By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.' The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

Vermont State Geological Survey, Burlington, Vt. G H. Perkins, State Geologist Most of the file reports of the State Geologist of Vermont were destroyed in a flood at Montpelier two or three years ago Full sets of 17 volumes may be seen only in libraries. The Annual Report for 1928 and the Annual Report for 1930 may still be had, as well as a few copies for the following years: 1901-2, 1907-8, 1909-10, 1915-16, 1921-22, 1923-24. These are distributed without charge. Flood-damaged copies of the two vols, Geology of Vermont, by Hager and Hitchcock, cost $3 plus postage For any of these volumes address State Librarian, Montpelier, Vermont.

Jan 1, 1933

Senator Smoot recently introduced his bill providing for the leasing of oil and coal lands. This bill provides only for the leasing of these lands from the Government and advocates government ownership of all government coal and oil lands. Under the provision of the bill as now proposed, 50 per cent. of all money received under the measure is to be paid to the state in which the land is located. The money must be used, however, for the construction and maintenance of roads and for schools. The last leasing bill was defeated when it was about to become law largely because of the fact that it allowed the sale of coal lands.

Jan 9, 1919

By O. P. Arora, I. L. Caplan, H. von E. Doering

ThE interpretation of X-ray and electron diffraction data obtained in plastic deformation studies of hcp a titanium requires knowledge of angular relationships between crystallographic planes and directions. Rarey el 01.' have calculated both interplanar angles and angles between directions for a number of c/a ratios. This information, although useful for approximate applications, does not provide exact data for specific hcp metals. Recently, Hu2 has tabulated interplanar angles specifically for hcp titanium. The present study augments the existing data on titanium by providing the angles between plane normals and rational crystallographic directions in addition to interplanar and interdirectional angles. These angular relationships were calculated on an IBM 360 Computer using a Fortran IV program.* Cal-

Jan 1, 1969