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By Arthur F. Taggart

THIS paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. CAPACITY Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: TR = TR80KK'K" [I] in which TR, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R50 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range-2.5 to 2.7-T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppard' has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about I.5: I: 0.6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:0.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for -150 + 200-mesh pyrite to be I.4: I : 0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value I.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciable tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 8o per cent of the feed, divided by the aperture that would pass S0 per cent of the product. It is best determined from screen tests.

Jan 1, 1941

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K'K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K'K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By Roland D. Parks

Corundum, little publicized as an industrial abrasive, has, in its small way, contributed greatly to the production of many specialized items vital to our war program and to Our allies. Optical elements Of the highest quality for range finders, bombsights, and scientific instruments; precision metal parts for torpedoes and airplane engines; quartz crystal plates for military radios; armorplate and malleable castings for tanks and guns; and eyeglasses for everyone; these are some Of the products that corundum has helped to produce in the quantities needed and on time. Unlike metals and many other raw materials, corundum is not incorporated into any Of these finished products. It is simply a grinding medium used to produce the desired finish or precision; an operating supply or tool, so to speak. With a Mobs' scale index of 9, corundum ranks next to the diamond in hardness among the natural minerals and is superior to emery and garnet. The gem varieties of corundum, including the Oriental ruby and sapphire, are frequently more highly prized as jewels than the diamond. It is the intent Of this paper to deal Only with a description of the corundum industry, the administration of wartime control, and certain economic aspects as seen by the author. Several references are listed to assist anyone who wishes further information on the geological occurrence of the mineral. Ore Production and Consumption For the past two decades, south Africa has been the world's sole producer of corundum ore. A possible exception is Russia, where, it is understood, there was considerable production during the thirties for domestic consumption but for which statistics are lacking. The United States is the world's principal consumer of corundum ore; imports lor the period 1934 through 1940 averaging 3000 Short tons per year, The years 1935 and 1936 were close to the 5000-ton mark, and imports during 1941, the last prewar year for which statistics have been released, were approximately 6000 Short tons. Again lacking statistics on Russia, the United Kingdom ranks second, but far below the United States in consumption of ore. Historically, corundum has been found in some 35 countries throughout the world, but the principal deposits are in South Africa, Canada, Madagascar, Russia and the united States. Deposits are generally small and subject to rapid exhaustion. Thus, the United States was the principal world producer for the period 1870 to 1900, when operations ceased except for two years during World War I. India was a producer of ore from 1898 through 1921, with peak output in 1916 through 1918 Canada came into production in 1901 with substantial output of ore and finished grain until 1914; the production thereafter was smaller until 1921. Madagascar has produced ore since 1910 but has had important output in only a few scattered years. South African production started in 1912

Jan 1, 1948

By Roland D. Parks

Corundum, little publicized as an industrial abrasive, has, in its small way, contributed greatly to the production of many specialized items vital to our war program and to Our allies. Optical elements Of the highest quality for range finders, bombsights, and scientific instruments; precision metal parts for torpedoes and airplane engines; quartz crystal plates for military radios; armorplate and malleable castings for tanks and guns; and eyeglasses for everyone; these are some Of the products that corundum has helped to produce in the quantities needed and on time. Unlike metals and many other raw materials, corundum is not incorporated into any Of these finished products. It is simply a grinding medium used to produce the desired finish or precision; an operating supply or tool, so to speak. With a Mobs' scale index of 9, corundum ranks next to the diamond in hardness among the natural minerals and is superior to emery and garnet. The gem varieties of corundum, including the Oriental ruby and sapphire, are frequently more highly prized as jewels than the diamond. It is the intent Of this paper to deal Only with a description of the corundum industry, the administration of wartime control, and certain economic aspects as seen by the author. Several references are listed to assist anyone who wishes further information on the geological occurrence of the mineral. Ore Production and Consumption For the past two decades, south Africa has been the world's sole producer of corundum ore. A possible exception is Russia, where, it is understood, there was considerable production during the thirties for domestic consumption but for which statistics are lacking. The United States is the world's principal consumer of corundum ore; imports lor the period 1934 through 1940 averaging 3000 Short tons per year, The years 1935 and 1936 were close to the 5000-ton mark, and imports during 1941, the last prewar year for which statistics have been released, were approximately 6000 Short tons. Again lacking statistics on Russia, the United Kingdom ranks second, but far below the United States in consumption of ore. Historically, corundum has been found in some 35 countries throughout the world, but the principal deposits are in South Africa, Canada, Madagascar, Russia and the united States. Deposits are generally small and subject to rapid exhaustion. Thus, the United States was the principal world producer for the period 1870 to 1900, when operations ceased except for two years during World War I. India was a producer of ore from 1898 through 1921, with peak output in 1916 through 1918 Canada came into production in 1901 with substantial output of ore and finished grain until 1914; the production thereafter was smaller until 1921. Madagascar has produced ore since 1910 but has had important output in only a few scattered years. South African production started in 1912

Jan 1, 1948

By V. H. Wilhelm

The year 1941 in the California oil industry was marked by an increased market demand, drilling activity, and production of crude oil. Although seven new oil fields and two gas fields were discovered during the year, additions to reserves from these discoveries, as well as extensions and revaluations of previous discoveries, were approximately 100 million barrels, as against estimated withdrawals of 230,233,000 barrels. The year was remarkable for the very great increase in domestic demand for all products, which more than compensated for the loss in shipments to Japan, which averaged 60,041 bbl. Per day during 1940. Demand in terms of crude during 1941 was 648,967 bbl. per day as against 632,647 for the same period in 1940. This abnormal increase in demand is due to increased industrial activity, and especially increased railroad activity. Gasoline consumption for 1941 was 241,011 bbl. per day as against 217,744 in 1940. Demand for fuel oil increased from 259,806 bbl. per day in 1940 to 285,896 in 1941, and caused a withdrawal from stocks of more than 7,473,000 barrels. During 1941, total oil storage declined 9,153,000 bbl., but additions to storage of 1,754,000 bbl. of light oil and light oil products were offset by a withdrawal of 10,907,000 bbl. of heavier products. Production during the year is estimated at 230,233,000 bbl. as against 222,784,386 bbl. for 1940. TraNsportation For a short time, California was affected by lack of transportation due to the diversion of tankers. This shortage affected the movement of oil from the Sari Joaquin mated to the refineries, since a large percentage of this production is moved to the coast through pipe lines, and thence by tankers to Los Angeles and San Fran-,iSco, Return of the tanker fleet, which may be temporary, indicates that there is a possibility of ample supplies of petroleum products in the Pacific Northwest. Drilling Activity Contrary to general opinion, drilling activity increased in 1941 over the pre-vious Year, 942 wells being completed in 1941 as against 890 in 1940, an increase Of 6 per cent. This increase was due to the increased demands for fuel oil, and also to the decreased drilling costs, which made many former marginal locations economic. The main activity caused by increased demands for fuel oil was in the Mt. Poso, McKittrick, Midway and Santa Maria Valley oil fields. Dry-hole footage in 1941 was 655,354 ft. as against 583,537 ft. for 1940. Curtailment Voluntary curtailment succeeded in holding production considerably below demand, although it was above the state quota. During the year the top allotment

Jan 1, 1942

By V. H. Wilhelm

The year 1941 in the California oil industry was marked by an increased market demand, drilling activity, and production of crude oil. Although seven new oil fields and two gas fields were discovered during the year, additions to reserves from these discoveries, as well as extensions and revaluations of previous discoveries, were approximately 100 million barrels, as against estimated withdrawals of 230,233,000 barrels. The year was remarkable for the very great increase in domestic demand for all products, which more than compensated for the loss in shipments to Japan, which averaged 60,041 bbl. Per day during 1940. Demand in terms of crude during 1941 was 648,967 bbl. per day as against 632,647 for the same period in 1940. This abnormal increase in demand is due to increased industrial activity, and especially increased railroad activity. Gasoline consumption for 1941 was 241,011 bbl. per day as against 217,744 in 1940. Demand for fuel oil increased from 259,806 bbl. per day in 1940 to 285,896 in 1941, and caused a withdrawal from stocks of more than 7,473,000 barrels. During 1941, total oil storage declined 9,153,000 bbl., but additions to storage of 1,754,000 bbl. of light oil and light oil products were offset by a withdrawal of 10,907,000 bbl. of heavier products. Production during the year is estimated at 230,233,000 bbl. as against 222,784,386 bbl. for 1940. TraNsportation For a short time, California was affected by lack of transportation due to the diversion of tankers. This shortage affected the movement of oil from the Sari Joaquin mated to the refineries, since a large percentage of this production is moved to the coast through pipe lines, and thence by tankers to Los Angeles and San Fran-,iSco, Return of the tanker fleet, which may be temporary, indicates that there is a possibility of ample supplies of petroleum products in the Pacific Northwest. Drilling Activity Contrary to general opinion, drilling activity increased in 1941 over the pre-vious Year, 942 wells being completed in 1941 as against 890 in 1940, an increase Of 6 per cent. This increase was due to the increased demands for fuel oil, and also to the decreased drilling costs, which made many former marginal locations economic. The main activity caused by increased demands for fuel oil was in the Mt. Poso, McKittrick, Midway and Santa Maria Valley oil fields. Dry-hole footage in 1941 was 655,354 ft. as against 583,537 ft. for 1940. Curtailment Voluntary curtailment succeeded in holding production considerably below demand, although it was above the state quota. During the year the top allotment

Jan 1, 1942

By George H. Cunningham, Allen C. Jephson

The plant for production of electrolytic zinc recently erected by the American Smelting and Rcfining Co. is situated along Nueces Bay, on the Gulf Coast, some 5 miles west by rail and highway from the city and port of Corpus Christi. A ship channel from the port now approaches to within 2 miles of the site. It is expected that this will be extended at some future date and so provide direct water shipment from the plant. In addition to Gulf shipping, an intercoastal waterway connects Corpus Christi with Houston and New Orleans. Factors leading to the establishment oi this plant in the area were: ample supplies of natural gas for the generation of electric power, advantageous shipping lanes, favorable market for acid, adequate supply of labor, and moderate climate. General Description The plant was erected primarily to assist with the production of high-grade zinc much needed for war purposes. Production started during October 1942. The purity of the slab-zinc output meets the American Society for Testing Materials' special high-grade spccifications. Other products of the plant are electrolytic cadmium and sulphuric acid. Residues containing lead, copper and silvcr are sent for treatment to the Company's smelter at El Paso, Texas. The design of the plant includes the use of Trail suspension roasting equipment, contact acid equipment, also batch leaching in mechanically agitated tanks, pressure filtering and washing of leach pulp, batch purification in mechanically agitated tanks followed by clarification in filter presses and cooling of purified solution by evaporation. Electrolysis is performed in cells using Tainton alloy anodes and aluminum cathodes. Cathode current density is 60 amp. per square foot. Except for the portion returned to the leaching division, the cell solution is continuously flowing in closed circuit through the cells to cooling towers, which hold cell temperatures within desired limits. Direct current for electrolysis, is supplied by generators driven by steam turbines. The cathode zinc is melted in a gas-fired furnace and cast in the usual way into slabs for shipment. The plant divides into five major divisions: Concentrates Storage, Roasting and Acid, Leaching, Electrolysis, Melting and Casting. No attempt is made to give many tabulated data in this paper; it is mainly a general description of the divisions and methods employed for operation. A plan is shown in Fig. I and a general flowsheet in Fig. 3. Concentrates Storage The original plan for inward shipments was to receive zinc concentrates by steamer at the port of Corpus Christi, there to unload into open railroad cars and move into the plant by rail. Up to the present, however, concentrates have been received mainly in box cars from mines in Mexico.

Jan 1, 1944

By H. W. Maynor, C. J. McHargue

DURING the course of an investigation of materials suitable for use as thermocouples at elevated temperatures by one of the authors, several nlolybdenum-rhenium alloys were prepared. Micrographs of an annealed alloy containing 25 pct Re (intended concentration; analysis not obtained) showed a number of twins, Fig. 1, suggesting a face-centered cubic structure. This note reports the structure and recrystallized wire texture of an alloy containing 25 wt pct Re. Alloys were prepared from 99.9 pct Mo (Fansteel Metallurgical Corp.) and rhenium obtained from the University of Tennessee (purity unreported). Powders were combined and briquetted at 56,000 psi and sintering was carried out at 2400°C for 5 hr in vacuum. Ingots so prepared were swaged at 982.2" to 1037.8oC into wires 0.036 in. diameter, a reduction in diameter of 85.6 pct. These wires were vacuum-annealed 1 hr at 2000°C. A North American Philips 114.59 mm powder camera and nickel-filtered copper radiation were used for structure determination. For the texture determination a Laue-type camera was used with zirconium-filtered molybdenum radiation and, because of the high background, aluminum foil was mounted next to the film. Exposures were taken with the wire perpendicular to the X-ray beam and tilted by 10". It was found that the X-ray pattern could be indexed on the basis of a face-centered cubic structure. Because of difficulties associated with obtaining a good X-ray pattern for this material, accurate parameter determinations were not made. An indicated parameter value of 3.70A was obtained. The X-ray data are given in Table I. The annealed wire texture was observed to be a sharp [111] texture. The spread about this fiber axis was k8" at the surface of the 0.036 in. wire. The annealed wire textures of aluminum have been reported as retention of the [Ill] deformation texture for anneals below 500°C and a new [1121 texture for anneals above 600°C.1 In copper wires, with a [Ill] plus [loo] deformation texture, results indicate a retention of this texture for annealing at lower temperatures and new components or the disappearance of components for annealing at higher temperatures.' The presence of the strong [I111 texture in the molybdenum-rhenium alloy after a 2000 °C anneal suggests that the deformation texture was the same. Acknowledgment The wires used in this study were prepared and heat-treated at the Institute for Atomic Research, and Ames Laboratory, Iowa State College, and the authors wish to express their thanks to the Institute for allowing the use of the material and permission to publish the results.

Jan 1, 1954

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

By C. S. Smith, L. H. Beck

KNOWLEDGE of the Cu-Zn constitution diagram was critically examined in 1944 by G. V. Ray-nor,1 who suggested the diagram reproduced in Fig. 1 as the best evaluation of available data. No pertinent work on the constitution has been published since that time, although a number of authors have discussed transformation kinetics and theory. Despite the large amount of work that has been done on the constitution of these industrially important and scientifically interesting alloys, minor uncertainties still exist. For example, it is still not possible to say definitely whether a two-phase region exists between the ordered and disordered forms of the 8 phase. A careful re-examination of the phase boundaries in this part of the diagram was therefore undertaken. Two methods were selected for the new investigation—quantitative metallography for the higher temperatures and precision lattice parameter measurement for lower temperatures. Because of the relatively narrow two-phase regions flanking the ß phase in these alloys, quantitative metallography is particularly suited for their examination, since the relative amounts of the two phases are very sensitive to their compositions. The method, however, is useless below about 350°C because of the inadequate resolution of the two constituents. Below 400°, however, the X-ray diffraction method is applicable, although it is of somewhat lower sensitivity in this system. The changes of composition that occur during quenching from above about 500°C entirely vitiate X-ray measurements at room temperature though they do not affect metallographic area measurements. The two methods overlap and supplement each other admirably. Both methods depend on the attainment of equilibrium composition of the two phases in a more or less intimate mixture and thus avoid the difficult problems of nucleation and long range diffusion involved in the conventional metallographic bracketing method. The alloys were melted from a master alloy made from re-electrolyzed cathode copper and Horsehead 99.99 pct Zn. Melting was done under a cover of either borax or charcoal and the alloys cast into a 7/8 in. sq graphite mold for the a-ß alloys or a 3/8 in. diam cylindrical graphite mold for the ß-? alloys. The a-ß alloys were rolled at 750°C to 5/8 in. sq; annealed for 24 hr at 800°C and quenched; then rolled and swaged at 200°C to 3/8 in. diam rods, annealed 24 hr at 200°C, quenched and cold rolled 2 pct reduction. This treatment was intended to obtain a small grain size and to produce many nuclei of the minor phase for growth on subsequent heat treatment. The unworkable ß-? alloys were given preliminary treatment by sealing in Vycor tubes in vacuum and annealing for 4 hr at 800°C followed by cooling in air. Samples of homogenized alloys were checked spectrographically for impurities, but the principal components were determined on samples subsequent to heat treatment. The impurities analyzed averaged approximately as follows: Ag, 0.0002 pct; Fe, 0.004; Si, 0.0008; Cd, 0.005; Mg, 0.0002; and Pb, 0.002. For metallography, samples of appropriate composition were cut into rods 5/8 in. long, sealed in pyrex tubes in vacuum and annealed for eight weeks at temperatures of 470°C and below, two weeks at 480°, 500°, and 600°C, and 4 hr at 700°C, followed by quenching in cold water. Temperatures were accurate to ±2°C. The cylinders were then machined to 8.7 mm diam and a slice weighing 1.5 g cut with a thin saw transversely from the center of each. This

Jan 1, 1953

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 I. Tamura, J. O. Brittain, T. Mura

Plain carbon steel in the cold worked or marten-sitic conditions has an internal friction peak at about 250 oC at a frequency of I cps. The influence of substitutional alloying elements on this peak was examined experimentally. The alloys were vacuum melted Co-, Cr-, Mo-, Ni-, and Si-iron (about 3 pct alloying elements), and carburized Si-iron. The internal friction of the alloys in the temperature range 30o to 500 OC was determined by means of a torsion pendulum. The 250 oC peak of the cold-worked alloys was lower in height than that observed in plain C-iron and steel. Carburized Si-iron in the quenched condition had a peak which occurred at a slightly lower temperature than in quenched plain C-steel, but the height of the peak was substantially greater than that found for the same alloy in the cold-worked condition. The activation energy of this peak for martensitic Si-steel was about 35 kcal per mol. ANNEALED a iron has two internal friction peaks due to nitrogen and carbon at 20o and 40o C respectively, at a frequency of 1 cps. If a iron is cold worked, these diffusion peaks become smaller and a new peak appears at about 250o C. The activation energy for the 250o C peak is in the range of 32 to 44 kcal per mol and has an average value of 38 kcal per mo1. It has been experimentally verified that both interstitial solute atoms and dislocations are necessary for the 250o C peak. 3 Wert has also shown that an incubation period precedes the appearance of the 250 C peak.4 With regard to quenched martensitic steel, Ke et al.596 observed two peaks at around 130o and 250o C. They conjectured that the 250o C peak in martensite was due to the same mechanism as the 250°C peak in cold worked a iron, and the 130°C peak was due to the nature of tempered martensite. They did not report the activation energy for these peaks. Chernikova7 found only one peak at about 200° C in tempered martensite. In a previous paperS we reported an activation energy of approximately 40 kcal per mol for the 250° C peak in plain carbon martensitic steels. Ichiyama8 found the activation energy to be about 36 kcal per mol for the 250° C internal friction peak in steels in the martensitic condition. The present authors proposed a theory for the 250°C peak for cold worked and quenched iron and steel.= The theory for the peak is based upon the addition of a strain-energy term to the free energy for the formation of a carbide precipitate due to the presence of a disclocation. The model employed for the relaxation process consists of the growth and solution of a carbide precipitate of critical size as a consequence of an oscillating dislocation. In this report, the influence of substitutional alloy ing elements on the 250° C peak is examined and the experimental results are discussed in terms of our theory for the peak. Most of the experimental work on the alloy steels was confined to the Fe-Si-C alloys.

Jan 1, 1962

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