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By A. G. Weber, K. H. Coats, M. H. Terhune, R. L. Nielsen

Two computer-oriented techniques for simulating the three-dimensional flow behavior of two fluid phases in petroleum reservoirs were developed. Under the first technique the flow equations are solved to model three-dimensional flow in a reservoir. The second technique was developed for modeling flow in three-dimensional media that have sufficiently high permeability in the vertical direction so that vertical flow is not seriously restricted. Since this latter technique is a modified two-dimensional meal analysis, suitably structured three-dimensional reservoirs can be simulated at considerably lower computational expenses than is required using the three-dimensional analysis. A quantitative criterion is provided for determining when vertical communication is good enough to permit use of the modified two-dimensional areal analysis. The equations solved by both techniques treat both fluids as compressible, and, for gas-oil applications, provide for the evolution of dissolved gas. Accounted for are the effects of relative permeability, capillary pressure and gravity in addition to reservoir geomety and rock heterogeneity. Calculations are compared with laboratory waterflood data to indicate the validity of the analyses. Other results were calculated with both techniques which show the equivalence of the two solutions for reservoirs satisfying the vertical communication criterion. INTRODUCTION Obtaining the maximum profits from oil and gas reservoirs during all stages of depletion is the fundamental charge to the reservoir engineering profession. In recent years much quantitative assistance in evaluating field development programs has been provided by computerized techniques for predicting reservoir flow behavior. Because of the spatially distributed and dynamic nature of producing operations, automatic optimization procedures, such as those now in use for planning refining operations, are not now available for planning reservoir development. However, present mathematical simulation techniques do furnish powerful means for making case studies to help in planning primary recovery operations and in selecting and timing supplemental recovery operations. A number of methods have been reported which simulate the flow of one, two or three fluid phases within porous media of one or two effective spatial dimensions>-4 However, applying computer analyses to actual reservoirs have been limited mostly to two-dimensional areal or cross-sectional flow studies for two immiscible reservoir fluids. To obtain a three-dimensional picture of reservoir performance using such two-dimensional techniques, it has been necessary to interpret the calculations by combining somehow the results from essentially independent areal and cross-sectional studies. To the authors' knowledge, the only other three-dimensional computational procedure, in addition to those presented here, was developed by Peaceman and Rachford8 to simulate the behavior of a laboratory waterflood. Two computational techniques which may be used to simulate three-dimensional flow of two fluid phases are described in this paper. The first method, called the "three-dimensional analysis", employs a fully three-dimensional mathematical model that treats simultaneously both the areal and cross-sectional aspects of reservoir flow. The second method, called the vertical equilibrium (VE) analysis", is applicable

Reserves of Lake Superior Manganiferous Iron Ores Appendix-to paper by CARL ZAPFFE, presented at the Cleveland Meeting and issued, as Pamphlet No. 1664-C, with MINING AND METALLURGY, May, 1927. The author has made several test calculations on the basis of manganese units that are and may be involved. These are summarized here, as follows: On the basis of ore produced since 1902, the average annual requirement of manganese units would be 91,000 tons; on the basis of the production of the past 4 or 5 years, the requirement would be 145,000 tons; on the basis of the year 1925 only, the requirement would be 155,000 tons. Applying the percentage of increase for the next 20 years, as determined by the plat shown as Fig. 3, the total requirement for 20 years would be 3,254,000 to 3,572,000 tons, if one used either 145,000 tons or 155,000 tons as a starting point. We have the following interesting facts: (1) The Michigan ores contain only about one-half the manganese that the Cuyuna ore does; (2) the Cuyuna district now produces one-half the ore required; (3) the known tonnage of Cuyuna reserves is greater than the speculative reserve offered for Michigan; (4) at the present rate of production considered by tons, Michigan ores ought to be exhausted in 20 years or less while Cuyuna ores would last up to 44 years. We should now reduce the estimated reserves to a basis of manganese, units. Using the tonnages listed in Combinations 2, 3, 4 and 5, the reserves total 3,118,225 tons, 3,781,995 tons, 5,041,995 tons and 5,560,342 tons, respectively. Therefore, needing at the most 3,572,000 tons, as shown above, either Combination 3, 4 or 5 will not only suffice but will leave an excess-enough for 1 or 2 years for Combination 3, 9 or 10 years for Combination 4, and 12' to 13 years for Combination 5. This means that for Combination 5, without using tonnages obtained from beneficiating or from mixing poor ores, the reserves are ample for about 33 years.

Jan 5, 1927

By Newell G. Alford

Forecasts of future timber consumption in soft-coal mining are handicapped by the lack of adequate experience records for estimating properly the timber requirements of the industry. Data were obtained from plants where records are kept or from operators who collected the information and to these were added composite figures for the continental United States in 1905 and 19191 and for central and western Pennsylvania and for Illinois in 1922.2 The result, representing slightly over 928,000,000 net tons, is shown in Table 1. Some of the companies furnishing data were unable to segregate the timber into classes of use but for those who did, Table 2 shows the board feet of posts and cross ban used per ton of coal mined and the percentage of the total timber consumed that was used in roof support. The wide variation in amounts of timber per ton of coal mined is the result of

Jan 1, 1924

W. M. CURSE, Mansfield, Ohio.-Outside of the commercial valu-ation of the material, for what purpose does this alloy-90 per cent. of copper, 6 ½ per cent. tin, 2 per cent. zinc, and 1 ½ per cent. Lead-seem to be eminently fitted? C. P. KARR.-So far as our tests go, it would be eminently fitted for steam valves and pistons, and for the work for which 88-10-2 bronze is generally used, although for very large castings it would not be superior to 88-8-4 bronze. P. E. MCKINNEY, * Washington, D. C.-Some time hack, clue to a desire to avoid some of the objectionable features of 88-10-2 bronze, particu-larly on heavy castings, also to save tin where possible, we took up the question of a substitute for 88-10-2 bronze, where red bronze was ordinarily specified. After trying most of the mixtures, we found that when using as low a tin content as is given in this proposed composi-

Jan 12, 1919

By Moshe Sheinkin, Douglas E. Julin

Large tonnage operations face many problems in adequately planning ahead for future years production. In order to maintain desired levels of production, such problems as source of tonnage, man- power and equipment requirements, tailings disposal and water requirements must be anticipated. Of course, before any of these problems can be analyzed, daily tonnage requirements and its source must be determined. Looking ahead for one year or even two or three is usually not sufficient time to adequately prepare an area for production. Because of the sequence of mining and the multilevel nature of the 42,000 tpd Climax mine in Colorado long-range planning must be on a ten-year basis. By using a ten-year base, adequate time is allowed to gain access and prepare a new level for production. Usually eight years will be required for this phase of the initial mine preparation. Once production has been started on a level and access to the area is available, three years is usually sufficient to prepare a new block for production as long as it follows in the normal sequence of mining.

Jan 4, 1967

By C. W. Andrews

The various methods of by-product coke-manufacture have been quite thoroughly discussed in a number of papers recently published, and I think it would possibly be of interest and value to discuss the growth and probable future of the byproduct coke industry, rather than details of manufacture. The first by-product coke-plant in the United States, consisting of 12 ovens, was put in operation at Syracuse in January, 1893. This installation was followed by one at Johnstown, Pa., in 1895; one at Dunbar, in 1896, and one at Glassport, in 1897. The plant at Syracuse was primarily intended to supply the owners with ammonia for their alkali-works. At Glassport, for the first time, gas was sold for illuminating purposes, although it was mixed with water-gas to make it marketable. The New England Coke & Gas Co. started the plant in Boston in 1899, which was destined to change the whole trend of the establishment of by-product plants, since it manufactured for the first time illuminating-gas suitable for sale without enrichment. This was accomplished by dividing the gas on the battery into two portions. One portion, consisting of the richer part of the gas, was saved for sale, while the remaining, or leaner, portion was used in the battery. This idea was originated by Dr. Schniewind, of the United Coke & Gas Co. The coke was used for domestic, industrial, and locomotive fuel, as its sulphur-content was too high to make it suitable for use in the foundry. The successful operation of this plant led to the building of additional plants at points where the production of illuminating-gas could be sold to advantage and where there was a fair market for the coke-output. The following list of illuminating-gas plants in order of construction will give a good idea of the rapid growth of this method of combined gas- and coke-manufacture: Hamilton, Ohio; Detroit, Mich.; Camden, N. J.; Baltimore, Md.; Chester, Pa.; Milwaukee, Wis.; Duluth, Minn.; Geneva, N. Y.; Chicago, Ill.; Indianapolis, Ind. In addition to these there are now under construction plants at Muncie, Ind.; Joliet, Ill., and Waukegan, Ill., all of which will produce illuminating-gas and metallurgical coke.

Jan 1, 1913

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 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 Arthur B. Cummins

Mineral fillers are employed in United States industries to the extent of more than seven million tons annually, valued in excess of a hundred million dollars. This substantial usage involves a wide variety of mineral materials. To this may be added products manufactured from minerals, such as carbon black, portland cement, lime or chemically precipitated calcium carbonates, which would add substantially to the total. The purposes for which fillers are used differ considerably. Minerals used as fillers are mostly silicates, silicas, and carbonates as referred to hereinafter. The term "mineral filler" has various meanings in mineral technology and in the arts. Fillers are comparatively inert and their action is mainly physical. Materials that are employed primarily for chemical reactivity, or for pigment or abrasive functions ordinarily would not be considered to be fillers when used for these purposes. Nearly all filler usages are based on advantages which are gained by desired modification of composition properties or by improvements in processing. A simple definition for a filler is an inert material that is included in a composition for some useful purpose. This definition may be amplified or made more specific for each of the filler usages, the major ones of which are: paints, paper, plastics, rubber, bituminous compositions, pesticides and fertilizers. There are in addition a whole host of minor usages. Powdered minerals when employed as components in paints, varnishes and lacquers are considered as extender pigments or low refractive index pigments. In paper, the term loading material as well as filler is used; in pesticides, the terms diluents and carriers connote different functions. For bituminous compositions, rubber and plastics, the usage of the simple word "filler" is more usual, but the designation loading material is sometimes used. Minerals Used as Fillers Most of the industrial minerals, and many rock powders are employed to some extent for different filler uses. These usages vary from year to year depending on availabilities, costs, technologic trends and advancements. For the major applications, however, and for the more particular requirements at any given period, there are general trends which favor a more or less restricted group of filler products for each of the major consumer fields. This selection of materials is determined by the characteristics of the individual filler products, their effectiveness in fulfilling the primary function or functions for which they may be employed, and the cost after incorporation in the finished product. The mineral-bearing materials of major importance as fillers are: limestones, clays of several types, talc, pyrophyllite, mica, barite, diatomite, crystalline silicas, asbestos, slate and other rock dusts. Others of secondary importance include: gypsum, vermiculite, phosphate rock, perlite, and pulverized wastes, such as slag and fly ash. A considerable number of other minerals are used to lesser extent. Among these minor mineral materials are: feldspar, pumicite, wollastonite,18 tripoli, nepheline syenite,6 coal, altered volcanic rock and others.2 Indeed, most mineral materials, when reduced to fine particle size may have some potential usage as fillers, depending on their properties, availability and price. On the other hand, the more exacting filler requirements

Jan 1, 1960

Discussion of the paper of H. H. STOEK, presented at the St. Louis meeting, October, 1917, and printed in Bulletin 129, September, 1917, pp. 1385 to 1419. J. B. WARRINER, Lansford, Pa. (written discussion*).-The figures on costs given at the end of this paper. are of particular interest and it is unfortunate that they necessarily cover such limited periods, as figures giving the costs over a period of at least a year would be of much greater value; for instance, it seems hardly probable that the performances credited to the various shovels for the months for which the costs are given would represent the average of the performances of these machines over a longer period. It would seem to me that the maximum of 4000 cu. yd. (3058 cu. m.) per clay given for the 225 B shovel is much greater than could be maintained for an entire year's operation. On the other hand, the 1500-yd. figure for the 150 B shovel would seem a low average for this type of shovel. In connection with the drag-line excavators, it will be interesting to know that the Lehigh Coal, and Navigation Co. is about to install one of these machines on a clay stripping at their Nesquehoning colliery to excavate an average depth of. overburden of 65 ft. (19 m.), which, due to local conditions, will require that part of the excavated material be handled a second time and a lesser quantity a third time. The results of this operation will undoubtedly be watched with great interest.

Jan 1, 1918

By Stuart A. Bengson

It is extremely difficult to revegetate disturbed sites and mineral wastes in an arid environment because of sporadic and undependable rainfall. Thus, irrigation is often a must for starting seed germination and vegetation. Quite aside from the harsh climate, mining disturbances by themselves cause various adverse conditions for a revegetation program. The problems of revegetating a harsh soil, for instance, are often compounded by the steep slopes of mine wastes. Since these steep slopes intensify the droughty conditions by rapidly draining away soil moisture and accelerating runoff, supplemental irrigation may be the only solution for establishing vegetative cover on the slope.

Jan 8, 1976

By E. Northcott, F. N. Oberg

High-grade concentrates from Florida pebble phosphate deposits have long been recovered by wet methods. When work was begun in the field, only the coarse pebble (generally +1 mm) was recovered. In the 1920's a froth flotation process was developed to separate quartz from the finer phosphate fractions, but this method proved unsatisfactory for treating the intermediate fraction (-1 mm +35 mesh). Consequently various other processes were adapted, including agglomerate tabling and spiral separation of reagentized feed. Today the three processes are used-washing and screening for coarse pebble, tabling or spiraling for intermediate sizes, and flotation for -35 mesh material.

Jan 10, 1958

By C. A. Hartnagel, D. H. Newland

Detailed production statistics listing the operations according to producing sands, districts, etc., are not available for New York State and are scarcely obtainable without extraordinary effort and expense, hardly warranted by the current rate of developments. The oil industry is practically stabilized, so far as exploration for new sources of supply are concerned; no new pools have been tapped in the last 25 or 30 years. There is little prospect of extending the boundary of the oil fields beyond their present limits, though possibly some additional reserves may be found below the present productive sands. Natural gas, on the other hand, is not restricted to such confined areas. Drilling for gas has been fairly active, under the stimulation of some important finds in formations that previously were overlooked. The year's field operations will be covered somewhat fully. Oil production, which has been steadily advancing for a number of years, showed a further moderate gain in 1936. The output for 11 months (figures for December are not yet available) was 4,217,000 bbl., indicating a total for the year of around 4,600,000 bbl. The increase was about 10 per cent, a rate maintained for some time. Prices were more satisfactory than in the preceding five years, with an advance to $2.57 a barrel before the year's close. New York State yield is all paraffin-base, in the same class with high-grade Pennsylvania oil. Most of the output is now obtained by the water drive, which has given a new lease of life to the fields and promises to bring the total to about 200,000,000 bbl. before the known acreage has been exhausted by this method. Before its introduction the annual production was under 1,000,000 bbl. a year. The fields cover an aggrcgate area of 55,000 acres, with some 17,000 wells in operation. Development Exploring for natural gas in New York in 1936 outside of the old established pools continued actively, as in the previous year. There was an increase in total initial production. Operations were conducted in nine counties of the central and western parts of the state, and 43 wells

Jan 1, 1937

By Hugh Douglas

ANTIMONY Antimony (Sb) has been used since the early Egyptian dynasties. Prior to World War I, total demand amounted to only 6000 to 7000 tons per year (tpy). Wartime uses and rapid rise of industrialization in the Northern Hemisphere nations have pushed world antimony use to the 78,000-tpy level. An overwhelming supply of low-cost antimonial resources in the Sino-Russian bloc countries has and will continue to have a major impact on availability and price to users outside the bloc. Table 14.4.1 shows trends in world production, United States production and consumption, and prices. Demand Antimony is used principally as an alloy in lead-based metals and other alloys. Pure metallic antimony usage is small and is confined to such areas as laboratory and electronic applications. Lead-antimony alloys are used in automobile storage batteries, chemical pumps, and pipes, tank linings, roofing material, and cable sheaths. The metal increases the hardness of lead, and, for such uses as foundry printing type, reduces shrinkage for casting and lowers the melting point. Antimonial oxides are used for ceramic purposes, white paint pigments, glass forming, textile finishing, fire retardants in military clothing, matches, and solder. Wartime applications include use as hardener for bullets, an element for tracer bullets, and ingredient for producing dense white smoke for visual markers. A small but rapidly growing use for antimony is for metallic compounds in semiconductors and thermoelectric devices. In the United States demand for antimony is about evenly divided between metallic end-use markets and nonmetallic markets. In metallic end uses, antimonial lead accounts for 27% of total metallic and nonmetallic use; in nonmetallic areas major uses are flame retardants (15%) which is the fastest growing market, plastics (13 % ), and ceramics and glass (11%). While antimony has advantages in most of its applications, there are uses in which other materials can be substituted, including: mercury, titanium, lead, zinc, chromium, tin, and zirconium in paints and pigments; tin in sheathings; calcium in battery plates; and bismuth in type metal. Supply Antimony is produced from both antimony ores and as a byproduct of smelting other ores. The principal ore mineral is stibnite (Sb2S3), along with its oxidized antimonial minerals and derivatives which occur in small discontinuous replacement veins or fissure vein implacements. Stibnite occurs in quartz-gold veins and copper-lead-zinc

Jan 1, 1976

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 B. H. Bergstrom, W. Mitchell, C. L. Sollenberger

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) and D. A. Sullivan, Jr. (with the University of California) — Messrs. Bergstrom, Sollenberger and Mitchell have shown in two excellent papers that the energy per unit mass required for the breaking of spheres is inversely proportional to the size modulus of the fragments of the broken spheres. They found that the fragments of spheres broken within a steel enclosure were finer than those produced by breaking spheres encased in gelatin. This results from utilization of part of the strain energy at fracture for secondary breakage. For spheres not encased in gelatin, these authors found that after fracture the fragments of the spheres possess kinetic energy amounting to 45% of the strain energy needed for initial fracture. Breakage of a sphere in gelatin results in waste of this kinetic energy, whereas breakage inside the steel container makes use of this kinetic energy for further size

Jan 1, 1962

By William G. Pariseau

The extraction ratio approach to pillar design in flat seams is based on a mathematically exact analysis that is a reasonable physical approximation to room-and-pillar layouts in many instances. The essentials of the approach are reviewed and then mathematically approximate formulas for pillar design in inclined seams of arbitrary dip are proposed. Detailed numerical analysis of stress about a typical 5 entry, 4 pillar panel at dips of 0, 15, 30, 45, 60, 75 and 90 degrees at low and high extraction ratios show that the proposed inclined seam extraction ratio formulas for pillar normal and shear stresses, although conservative, have an accuracy quite adequate for engineering purposes. Appropriate pillar safety factors for compressive and shear failure and a safety criterion for overturning are specified.

Jan 1, 1982

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

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

Jan 1, 1965

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