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F. WEIMER,* Washington, D. C. (written discussiont).-For electrical measuring instruments, especially those types that involve the Wheat-stone bridge or potentiometer principle and standards of electrical resist-ance, there has been, for a considerable time, a need for better resistance materials. For a satisfactory resistance material, much depends on the purposes for which it is to be used. For potentiometers and Wheatstone bridges, such as are in more or less general use, and the more common forms of resistance standards, a good quality of manganin answers fairly well. However, it should not be presumed that manganin is considered ideal for the purpose, for in measuring instruments and resistance stand-ards, there is still much to be desired. An experience of more than 10 years in the study of the resistance standards and resistance apparatus shows that manganin resistances change with time in a way that is very annoying and the maintenance of the unit of resistance to the desired accuracy requires an excessive amount of work or may be said to be prac-tically impossible. The changes in resistance are generally most rapid and erratic in resistances of very low and very high values. In resist-ances of low value, the resistance material is often in the form of thin sheets so that the surface is large and usually more or less unprotected from the atmosphere, or the oil in. the case of oil-immersed standards. In resistances of high value, the resistance material is in the form of fine wire and, therefore, the surface is large compared with the cross-section. In resistances of medium value, the surface is less, compared with the cross-section, or better protected, usually by a silk wrapping impregnated with shellac. This suggests that one of the difficulties with manganin is slow surface action or oxidation, even when an effort has been made to protect the surface from such action However, the changes observed cannot all be accounted for on this basis. There are, presumably, also some internal changes in the resistance material even when it has been annealed. Further; the changes in manganin resistances seem to be more or less independent of its electrical properties. In other respects, too, manganin is not ideal.

Jan 11, 1919

By J. A. Solomon, H. E. Shafer

As a result of the great demand for metallic aluminum and the scarcity of domestic bauxite, numerous processes have been proposed and developed to extract the oxide of this metal (Al2o3) from clays, shales, and other low-grade raw materials.1-4 An exploratory study was made to extract alumina with sulfuric acid from relatively impure coal-associated draw-slate and to establish an optimum calcination temperature for maximum recovery. Draw-slate is the term used to describe the hard, slaty material directly overlying many coal seams and may range from a few inches to a few feet in thickness. Alumina content of these draw-slates may range from as low as 15% to over 35%. Although the following results are limited in scope, some of the data should prove beneficial for further work. Coal-associated clay, shale, and gob heretofore have been considered nuisance products; any successful alumina extraction process would greatly enhance the worth of these almost limitless resources. This research demonstrated that an optimum calcination temperature for alumina extraction could be established for a coal-associated draw-slate and that this temperature was lower than those suggested in previous work with unspecified clay types. It should be noted that slightly higher acid concentrations and somewhat finer particle sizes were used in this series of tests as compared to previous work. EXPERIMENTAL WORK Essentially, alumina extraction proceeded in four steps: 1) grinding, 2) calcining, 3) acid leaching, and 4) precipitating of aluminum sulfate. An initial series of reference tests to determine the optimum temperature of solubility for alumina was run using relatively pure kaolin. Kaolin forming clays are hydrous aluminum silicates of the approximate composition 2H2O A12O3 2SiO and kaolinite is the mineral that predominates in most kaolins. 5 The kaolin was ground to -30 mesh and subsequently calcined at temperatures ranging from 100°C to 700°C. Each sample was calcined for 1 hr in a muffle furnace and in turn subjected to sulfuric-acid leaching (H2SO4, 9 molar) for a 2-hr period. The filtrates were analyzed for the amount of dissolved alumina recovered.637 Also, each sample of leached or barren residue was

Jan 1, 1968

By Richard H. Zinszer

Application Of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (I) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable corrections for sand thickness. The procedure in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory Introduction In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 it., 16 ft., and 24 ft. thick, and found the observed resistivity of the 8-ft. sand to be approximately

Jan 1, 1946

By J. P. Dunlop

THE fact is notable though probably little known that the United States is the only nation obtaining and distributing through its Government bureaus any data pertaining to waste metals and drosses. Some foreign governments do issue reports relating to mine or smelter produc-tion of primary metals, but none gives in scope and detail the information published now by the U. S. Bureau of Mines and formerly by the U. S. Geological Survey; and this is despite the fact that the funds annually allotted for those purposes are insignificant in comparison with allotments for the preparation of data relating to other industries of like importance. The earliest data on the production of metals from secondary sources in the United States were-contained in a press bulletin issued by the U. S. Geological Survey on Jan. 4, 1909. The information published was that for the year 1907 obtained and compiled by C. E. Siebenthal, who was one of the first to visualize the growing importance of the scrap-metal industry. The National Conservation Commission had emphasized its opinion that the known domestic supply of certain kinds of the more important metals was being rapidly marketed and that while there was no immediate cause for concern it was best to conserve such resources. Not only had there been a lamentable lack of any data regarding the quantity of scrap metals available or used but also gross carelessness and indifference in the segregation, collection, and effective use of scrap material. Siebenthal realized that even approximately correct statistics of recoveries from the more important base-metal scrap and drosses were nearly as essential to both producers and consumers as the statistics of the output of primary metals. There were not then nor are there now sufficient funds for complete collection of data, nor was it considered the province of the Geological Survey to do more than determine approximately the recovery of secondary metals for use in supplementing those given for the primary metals. Undoubtedly the first bulletins issued did not give the full output, for it takes time to establish contacts for an inquiry covering so

Jan 1, 1928

By Richard H. Zinszer

Application Of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (I) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable corrections for sand thickness. The procedure in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory Introduction In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 it., 16 ft., and 24 ft. thick, and found the observed resistivity of the 8-ft. sand to be approximately

Jan 1, 1946

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By Alfred R. Powell

FOR the purposes of this discussion, the direct gasification of coal means the of hydrogen and carbon monoxide by the well-known water-gas reaction. Chemicals or other synthetic products may be made from these constituents of the gas and under such circumstances the gas is called synthesis gas. Or, if the same gas is used as a fuel, it is called blue gas or water gas. This type of gas has usually been made from coke, especially in this country, and has been used both for fuel purposes and for manufacture of chemicals. Recently, natural gas has gained the ascendancy as a source of synthesis gas for manufacture of chemicals because of its relative cheapness. As natural gas becomes less readily available and more expensive, coal will take its place as a raw material for the preparation of synthesis gas. This substitution will probably take the form of direct gasification of the coal rather than the present two-step procedure of carbonization of the coal followed by gasification of the coke. The chief reason for this probability is the intensive research now being carried on by several organizations to develop successful and economical processes for the direct gasification of coal, which is a considerably cheaper fuel than coke. In the following pages an attempt has been made to predict the chemicals that will result from this future production of synthesis gas by the direct gasification of coal. CHEMICAL REACTIONS OF SYNTHESIS GAS Given the proper conditions, there are many chemical reactions leading to production of useful products that can be carried out with this mixture of hydrogen and carbon monoxide. These many reactions may be grouped into three classes: (1) interaction of hydrogen and carbon monoxide, possibly with addition of other reactants; (2) reaction of hydrogen with various substances; (3) reaction of carbon monoxide with various substances. Thus sometimes hydrogen and carbon monoxide are utilized together in the same chemical reaction while in other instances only the hydrogen or only the carbon monoxide is required as a reactant. Fortunately, practical methods are available for securing either hydrogen or carbon monoxide from synthesis gas, some of which are also applicable for changing the ratio of these two constituents in the gas when that is desirable.

Jan 1, 1953

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By J. P. Dunlop

THE fact is-notable though probably little known that the United States is the only nation obtaining and distributing through its Government bureaus any data pertaining to waste metals and drosses. Some foreign governments do issue reports relating to mine or smelter production of primary metals, but none gives in scope and detail the information published now by the U. S. Bureau of Mines and formerly by the U. S. Geological Survey; and this is despite the fact that the funds annually allotted for those purposes are insignificant in comparison with allotments for the preparation of data relating to other industries of like importance. The earliest data on the production of metals from secondary sources in the United States were contained in a press bulletin issued by the U. S. Geological Survey on Jan. 4, 1909. The information published was that for the year 1907 obtained and compiled by C. E. Siebenthal, who was one of the first to visualize the growing importance of the scrap-metal industry. The National Conservation Commission had emphasized its opinion that the known domestic supply of certain kinds of the more important metals was being rapidly marketed and that while there was no immediate cause for concern it was best to conserve such resources. Not only had there. been a lamentable lack of any data regarding the quantity of scrap metals available or used but also gross carelessness and indifference in the segregation, collection, and effective use of scrap material. Siebenthal realized that even approximately correct statistics of recoveries from the more important base-metal scrap and drosses were nearly as essential to both producers and consumers as the statistics of the output of primary metals. There were not then nor are there now sufficient funds for complete collection of data, nor was it considered the province of the Geological Survey to do more than determine approximately the recovery of secondary metals for use in supplementing those given for the primary metals. Undoubtedly the first bulletins-issued did not give the full output, for it takes time to establish contacts for an inquiry covering so

Jan 1, 1928

By S. D. Dahlgren

The plasticity of unalloyed P plutonium was studied by evaluating the strain-rate-hardening exponent, m, in the equation Values of m up to 0.33 and tensile elongations up to 680 pct were obtained for ß plutonium formed directly from the a phase. Casl bars that were cycled and tested had lower flow stresses and higher values for than uncycled bars , hut their total plastic elongations were not as great as expected because of premature failure at voids formed during cycling. Flow stresses were higher and m was lower (m = 0.15) for 9 plutonzutn formed from the y phase. ThE strain-rate-hardening exponent for plastic flow of p plutonium was determined as a function of strain rate, test temperature, and heat-treating history, and it was related to the rather large plastic elongation found previously for some plutonium tensile samples. Gardner and ~ann' obtained tensile elongations of up to 620 pct for P plutonium samples which had been completely transformed from the low-temperature a phase to the P phase before testing. Such a large percentage elongation is unusual for unalloyed metals or single-phase alloys.' The a phase is stable below approximately 112°C and (3 is stable between approximately 112" and 190"c.~ Both phases have mono-clinic structures. A temperature of 160°C is 0.58 of the effective absolute melting point, 475°C) of the p phase. The effective melting point is obtained by considering the enthalpy and entropy changes associated with the higher-temperature phase transformations and it is not the same as the experimental melting point of the highest-temperature allotrope of unalloyed plutonium. Nelson, Bowman, and Bierlein observed a striking difference between the ductility, as well as other mechanical properties, of p plutonium formed from the next higher-temperature phase (y) and the ductility of /3 plutonium formed from the a phase. The total elongation of /3 plutonium formed from the y phase was less than 5 pct. Earlier, the creep rate of 13 plutonium formed from the a phase was shown to be 200 to 500 times faster than the rate for 0 formed from y for the same test temperature and stress.

Jan 1, 1969

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

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.f 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 considerbtion 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 orc 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, 1948

By K. G. Meara, M. M. Fine, 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.f 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 considerbtion 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 orc 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, 1948

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 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 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