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By W. T. Cardwell, R. L. Parsons

This paper discusses the practical problem of estimating a single equivalent permeability for an oil reservoir, or a portion thereof, whose actual permeability varies in an irregular manner. Limiting averages for general types of permeability variation are developed, and illustrated by examples involving important, specific types of variation. Introduction The theory of the flow of fluids through porous media1"4 is becoming increasingly important in predictions of oil-reservoir behavior. In practical applications, however, reservoirs are seldom found to which simple theory strictly applies. Actual reservoirs have complicated shapes and nonuniform permeabilities and porosities. This paper discusses the problem of estimating a single equivalent permeability for an oil reservoir, or a segment of an oil reservoir, whose actual permeability varies in an irregular manner. The equivalent permeability of a reservoir segment is defined as the permeability of a homogeneous segment of the same dimensions that would pass the same flux under the same pressure drop- It is the permeability value that can be used in simple theoretical formulas to calculate the reservoir behavior. To the authors' knowledge, previous theoretical calculationst on systems of nonuniform permeability have been carried out only by Muskat'"; and he has not dealt with irregular variations, except in writing down the general differential equation for the pressure in variably permeable systems.lb In practical work, many calculations necessarily have been made to estimate equivalent permeabilities from the permeabiiity profiles obtained by core analyses. Regarding such calculations, Johnston and Sherborne6 say: Simple arithmetic and weighted averages have been tried on many wells and it has been found that, where frequent sampling has occurred, the arithmetic average is as satis- factory as a weighted average. It is possible that the application of statistical methods to the analysis of permeability data as recently presented by Law8 may prove fruitful. L,, has made a valuable contribution in showing how statistical analyses may aid in picturing the characteristics of a reservoir from those of a necessarily limited number of core samples. It is believed however that the particular problem of the estimation of equivalent permeabilities can be most directly approached from a fluid dynamical viewpoint as given in the present paper. An example is presented of the use of the conclusions herein in conjunction with Law's method. Theory In order to approach the problem of heterogeneity simply, it is interesting to consider a square block composed of four smaller, homogeneous, square blocks of porous medium, two of which have a

Jan 1, 1945

Bethlehem Steel Co. has just brought an all-new iron ore mine into production at Marmora, Canada, about 120 miles east of Toronto. High grade pellets produced at the mine from open-pit magnetite ore travel 64 miles by rail to the port at Picton, then go by Lake boat to help supply Bethlehem's Lackawanna, N. Y., plant. At full production about half a million tons of pellets a year will be shipped, and mining will be at a scale of more than a million tons per year of ore. Aeromagnetic surveys carried out in 1949 by the Ontario Dept. of Mines and the Canadian Geological Survey revealed an anomaly that interested Bethlehem geologists. By 1951 the company had put down some 40 diamond drillholes ranging from 460 to 1800 ft to block out the magnetite replacement deposit which lies in pre-Cambrian limestone below about 130 ft of Paleozoic limestone. The orebody, roughly 2100 ft long and up to 400 ft wide, averages about 37 pct iron, too low for direct shipment. Not only construction of concentrating and pelletizing facilities, but 20 million tons of stripping lay ahead before production could start

Jul 1, 1955

By E. T. Turkdogan, L. S. Darken

Calcium ferrite melts were equilibrated with sulfur and oxygen-bearing gases at temperatures within the range 1290°C to 1620°C. The results show that at oxygen partial pressures below 10-4 atm the sulfide-reaction occurs and at higher oxygen pressures the sulfur dissolves in the melt principally as sulfate ion. It is also observed that when the product increases, sulfate ions are converted to pyrosulfate ions and the results permit the evaluation of the pyrosulfate/sulfate ratio. It is shown that the ratio y CaSO,/rCaO increases with decreasing concentration of calcium oxide in calcium ferrite, silicate and aluminate melts. Indications are that oxy-acids, e.g. silica, alumina and ferric oxide, increase yCaS0,. A few experiments were carried out within the sul-tide range and the results are in accord with those obtained by other investigators on aluminate and silicate melts. BECAUSE of the industrial importance and theoretical interest, many investigators have studied the reactions between molten oxides, silicates or alumi-nates, and gases containing oxygen and sulfur. The early work reviewed by Schenckl and studies made by Bardenheuer and Geller2 indicates that solution of gaseous sulfur in an oxide melt resulted in the replacement of the oxide ions by the sulfide ions. Measurements made by Grant and Chipman3 on the equilibrium partition of sulfur between molten iron and complex silicate melts also demonstrated that, for a given temperature and silicate composition, the distribution of sulfur between slag and metal increased with decreasing oxygen content of the metal. Fincham and Richardson4 studied the effects of temperature and partial pressures of sulfur and oxygen on the solubility of sulfur in simple silicate and alumino-silicate melts. They observed that at oxygen partial pressures below about 10-5 atm sulfur in the gas dissolved in the melt as sulfide ions, replacing an equal number of oxide ions of the melt. At oxygen partial pressures higher than 10-3 atm, sulfur entered the melt as sulfate ions. Similar studies were made by St. Pierre and Chipman5 using calcium ferrite and calcium silico-ferrite melts. The experimental data presented in this paper were obtained in this Laboratory about 10 years ago; this is the first formal presentation although a preliminary report was given previously.6 In each of these experiments, a pure synthetic CaO-Fe2O3 melt in a platinum crucible was equilibrated with a gas mixture (SO2-O2, SO,-air, SO2-CO, or SO2-CO2-CO) at a temperature ranging from 1296°to 1620°C. The experimental technique was essentially the same as that reported by Darken and Gurry,7 the main difference being that the atmosphere in the reaction chamber contained sulfur dioxide together with oxygen, or carbon dioxide-carbon monoxide

Jan 1, 1962

By Paul A. Farrar, Harold Margolin

The Ti-Al-V system has been delineated from 50 to 100 wt pct Ti and front 600 to 1400°C by X-ray and ntetallographic techniques. Isothermal sections were delineated at 600, 700, 800, 900, 1000, 1100, 1200, 1300, and 1400°C. X-ray and metallographic evidence indicated the presence of two phases and in addition to those reported by previous investigators of the ternary system'-3. T HE titanium-rich region of the Ti-Al-V system as originally proposed by Rausch et UZ, and Jordan and Duwez3 was based on the binary Ti-Al diagram as proposed by Bumps et uZ. As additional phases have been shown to exist5-' in the region previously thought to be all a, the titanium-rich region of the Ti-Al-V system is open to serious question. Therefore, in order to determine the effect of the indicated changes in the Binary Ti-Al system on the ternary Ti-Al-V system the present investigation was initiated. EXPERIMENTAL PROCEDURE The experimental procedures in this investigation are the standard techniques used in the study of titanium-alloy systems which have been described in detail previously.1° Consequently, only details pertinent to the present work are discussed. The alloys employed for the delineation of this system were prepared from titanium obtained from the Bureau of Mines (73 BHN) 99.99 pct Al and 99.7 pct V, by the consumable arc-melting technique. The titanium was premelted into buttons of 25 g because spattering during the first melt caused uncontrollable loss of alloying constituents. Typical analyses of the material used have been reported elsewhere Attempts to hot roll the alloys prior to heat treatment were made on the first series of alloys prepared, but as the area of extensive hot workability was fairly restricted, see Table I, this practice was discontinued. The times of isothermal annealing are given in Table 11. A preliminary heat treatment of 96 hr at 1000°C was used prior to heat treatment at lower temperatures. The standard techniques used for polishing specimens involved belt-grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch. In the low-alloy region it was found that the oRo etch, developed by Ence and Margolin,o gave better contrast between phases. Where this procedure did not differentiate between phases clearly, the method of stain etching developed by Ence and was used. It has been previously reported15 that filing of titanium alloys is not desirable for producing X-ray powders, since the powder becomes contaminated by the file material. Therefore, for those samples not brittle enough to Crush, the procedure described below was used. The specimen was wrapped in molybdenum sheet and placed in a vacuum system and evacuated to 0.03 p. Palladium-pur if ied hydrogen was then admitted to the system until a partial pressure of 5o Cm of H was reached. The specimen was heated in the system to the temperature of original heat treatment and was slowly cooled over a period of 3 hr to 400°C while the partial pressure of hydrogen was maintained. The sample was removed from the system after it had completely cooled and was crushed to a powder of 230 to 270 mesh. The powder, wrapped in molybdenum sheet, was dehydrogenated at the temperature of original heat treatment until a partial pressure of 0.03 p was maintained in the system for at least 1/2 hr. The tube containing the powders was quenched in iced brine while still connected to the vacuum system. After dehydrogenation, the powder, except for the

Jan 1, 1962

By Paul L. Goddard, Alfred G. Hoyl, William R. Sirola

A good place to look for elephants is in elephant country, and old mining districts are certainly elephant country as far as minerals are concerned. In many areas probably more ore is still in the ground than has been taken out. The old timers were good miners and hard workers and when they left ore behind, it was usually for good reason; but many an old mining district has been revived by new approaches to old problems, taking advantage of new techniques and new equipment. One of these is the Front Range mineral belt of Colorado, which has produced minerals for the past 100 years through the ups and downs of mineral prices and the general economy. Gold, silver, copper, lead, and zinc have been found in abundance in the complex sulfide veins of the area. Between Idaho Springs and Central City lie several strong veins which have been mined successfully in the past. The two strongest of these veins, striking northeast-southwest, (Lake-Bald Eagle), and northwest-southeast, (Crown Point-Belman) , and dipping northeast and northwest, respectively, intersect in a flat X near the head of Virginia Canyon. From the lowest drainage of the area, Clear Creek Canyon, the old timers drove the Central, or Big Five, haulage-drainage tunnel due north. It intersects the two veins 8460 ft from the portal and 1670 ft below the surface. The two veins were mined successfully at the surface and at the tunnel level. Without an opening to the surface at the in- side end of the tunnel, ventilating became very difficult as the stopes were opened up, and mining ceased in 1929. Vertically, 1200 to 1600 ft of virgin ground remains in the veins.

Jan 6, 1959

By E. De Golyer

THE petroleum production of the world, in 1923, for the first time reached the billion-barrel mark. A preliminary estimate of production is 1,014,413,000 bbl., an increase of 159,604,000 bbl., or 18.6 per cent. over the 854,809,000 bbl. produced in 1922, the year of next highest production. This increase resulted from an increase of 178,469,000 bbl. in the production of the United States; the total for the rest of the world shows a loss of 18,865,000 bbl., a loss caused by the decrease of approximately 32,278,000 bbl. in Mexican production. The Mexican decrease more than offset increases in the production of Russia, Persia, Roumania, Venezuela, Sarawak, and various minor fields. The increase in production for the United States, and consequently for the world, was the result of flush production from development to maximum capacity during the year of eight, bonanza fields-fields reaching daily yields of 100,000 bbl. or better. It might be ascribed more exactly to the production from the three flush fields of the Los Angeles basin. Their production alone was greater than the increase in the world petroleum production, or the increase in the production of the United States, and it was cheap oil from these fields that demoralized the oil markets of the world. The Basin fields were. the features and dominating factors in the oil industry of the world during 1923. The bonanza fields of 1923, their estimated production for the year, and peak are given in Table 1.

Jan 3, 1924

By G. E. Anderson

THE Asientos-Tepezala district is in the north of the State of Aguascalientes, about 30 miles north of the city of Aguascalientes, the capital. The district is reached by a standard-gage railway on the west side through the junction, Rincon de Romos, which is on the main line of the National Railways of Mexico from El Paso to Aguascalientes. The terminal is Tepezala. On the east side a narrow gage connects Asientos with the junction, San Gil, on the main line, Asientos to San Luis Potosi. Tepezala on the west side of the Asientos hills is about 2 miles from Asientos on the east side. The area between the two mining centers is separated by a low subued divide which forms the central part of the hills. The district is in a group of isolated hills surrounded by characteristic bolson plains. The hills rise above the surrounding plains about 6500 to 10,000 ft.; the highest peak is Alta Mira. The two mining districts lie somewhat upon the flanks of the hills at about the same elevation, 7200 ft. The district is an old one and has been known since early in the 17th Century when the mines were worked by the Franciscan Monks. Their mining operations which were limited to the oxidized ore above the water level, consisted chiefly in extracting silver from the Santa Francisca vein. To judge from the old workings and the remains of surface plant, the operations were on a large scale. By modern mining operations since about 1900, the various mines of the district have been one of the principal sources of ore for the smelter located at Aguascalientes.

Jan 2, 1926

By John Chipman, A. M. Samarin

It has been long known that the gas evolved during the boil in the open-hearth furnace is mainly carbon monoxide associated with smaller quantities of other gases. A number of attempts have been made to determine the precise effects of carbon and oxygen content of the bath, and of other factors, such as temperature, upon the evolution of carbon monoxide. In his investigation of the carbon-iron oxide product in liquid steel, Hertyl showed that the value of this product at equilibrium could be approximated by plotting the value of the product observed in open-hearth reactions against rate of carbon elimination, and extrapolating to zero rate. The results of this study showed a slight but definite effect of temperature upon the carbon-iron oxide reaction. Experimental studies of the evolution of gases from rimming-steel ingots have not yet attained the degree of precision necessary for an exact understanding of the effects of pouring temperature, carbon content, and iron oxide in the metal upon the composition of these gases. Klinger2 showed that the gas consists mainly of carbon monoxide, and that considerable variation in its composition occurs during the solidification of the ingot. In order that these variations may be understood in their proper relationship to the progress of solidification of the ingot and the segregation that accompanies solidification, it is essential to have a knowledge of the condition of equilibrium in the several chemical reactions by which the gases are being formed. It is also necessary to understand the effects of temperature upon the equilibria, and further, to know the manner in which the temperature of the liquid metal within the ingot changes as the skin of the ingot is being built up. The reactions in which we will be chiefly interested are those involving in the one case the oxides of carbon, and in the other case steam and

Jan 1, 1937

By Denis Yeung, B. H. G. Brady

A hybrid finite element-boundary element code with eight noded isoparametric finite elements and three noded boundary elements is described for plane strain and linear isotropic elasticity. In the direct formulation of the Boundary Flement Method, quadratic variation of geometry and displacements, and linear variation of tractions with respect to the element intrinsic coordinates are used. The boundary element region is treated as a "super-element" in the finite element sense.

Jan 1, 1982

A week-long educational program and two-day symposium on applying the fluidizing reactor to the minerals industry drew more than 100 engineers to the University of Arizona at Tucson several weeks ago. The educational program, intended for engineers who will work closely with the reactor, attracted registrants from all sections of the U. S. and Canada. Meeting at the College of Mines on February 23 for a full week of intensive classwork, the engineers ploughed in with enthusiasm. Eight hours daily of lectures and laboratory work were followed by a generous helping of homework supplied by Professor Sigmund L. Smith, who directed the course. The study program was completed on Friday and the following Monday marked the start of a symposium of technical papers covering a wide variety of operations and new ideas.

Jan 4, 1959

By R. J. Linney

Reserve Mining Co. produces 5 million tons of iron ore pellets per year. The finished product runs about 65.50 pct Fe, with 7.75 to 8.00 pct SiO2. Less than 12 pct arrives at the blast furnaces smaller than % in. This plant was originally designed to produce 3.75 tons annually—not 5 million. To handle the increased tonnage a fifth fine crushing line was added, and some very minor changes were made. When production can be stepped up 33 1/3 pct without extensive additions or changes—within the short period of a year—basic engineering has been sound. Operators of the plant consider it the best design job they have seen or heard of, and competent authorities have said that start-up was quicker and easier than for any previous large-scale minerals beneficiation plant. One big advantage is the elbow room allowed. Generally speaking, there is an eternal conflict between operator and designer over space. The designer has his costs per cubic foot, and he is keenly aware that if he permits the number of cubic feet to rise unnecessarily, total costs will be too high. But this was a new operation, and on a large scale. There were no proven standards to go by. Realizing this, Reserve's engineers provided ample and efficient access to machinery, allowing extra space for unanticipated situations. In three years of production this planning has paid off handsomely. Gravity Flow Saves Time and Money: This plant is on a rocky hillside, the car dumper about 270 ft above Lake Superior. In locating buildings and placing machinery the designers mad= good use of gravity flow, at considerable financial savings. In the concentrator building from rod mills to filters, gravity carries the material between all stages of the operation except one—the closed circuit pumping of concentrate between cone classifiers and ball mills. Since no machine is located directly above any other, an observer can stand on the truck ramp adjacent to the offices and laboratory and see practically every phase of activity in the huge building. The first mill section started in August 1955. After a day's run several modifications were made on auxiliary chutes and launders where spillage had occurred. This procedure was followed for the first

Jan 1, 1960

By William L. Lennemann

Chemistry of uranium with respect to its hydrometallurgical recovery from carnotite ores was investigated and well defined during the radium boom period between 1900 and 1920. Since that time, methods used to extract uranium from its ores have remained basically either acid leaching or sodium carbonate leaching. Until about 1950, the only practical methods known for achieving a better than 75 pct U2O3 concentrate from the leach liquors involved fundamental chemical techniques for either purifying a solution prior to the uranium precipitation, or refining a crude uranium concentrate that was produced by neutralizing a pregnant mill liquor.

Jun 1, 1956

By J. Weertman

An explanation is advanced for the recent results of Barrett and Sherby on the high-temperature creep of fee metals. Their measurements indicate that metals with a low stacking fault energy creep at a much slower rate than metals with a high stacking fault energy. The explanation is based on the assumption that the rate of core diffusion is much smaller in partial dislocations than in perfect dislocations. An experiment is suggested to test this assumption. The explanation also requires that the jog density is small on widely split dislocations. SHERBY and Barrett1,2 recently established an important result in the field of high-temperature steady-state creep. They have shown that fee metals whose dislocations split into partial dislocations separated by a wide stacking-fault ribbon creep at a much slower rate than fee metals whose dislocations are not split appreciably. The creep rates in the two cases may differ by a factor as high as 6000. (For the purpose of comparison, the test temperature of each metal was chosen so that its rate of self-diffusion was equal to a standard value. Similarly the stress levels were such that the ratio of the stress to an appropriate elastic modulus was the same for each metal. In all cases the stresses were sufficiently low that the steady-state creep rate was proportional to the stress raised to a power.) It is the purpose of the present paper to attempt an explanation of this interesting and significant result of Sherby and Barrett. The activation energies of high-temperature creep of the metals tested by Sherby and Barrett (aluminum, nickel, copper, and silver) were equal to their self-diffusion activation energies. Hence it appears reasonable to assume that this type of creep is controlled by a dislocation-climb process, which in turn is controlled by the diffusion of vacancies to or from dislocation lines. (It will be assumed that the diffusion of interstitial atoms is unimportant in the climb process. The analysis could be repeated for the case in which interstitial atoms are important.) In prior papers374 I have treated dislocation climb by using the assumptions that core diffusion is extremely fast down a dislocation and that a dislocation always maintains an appropriate vacancy concentration in its immediate vicinity. In this

Jan 1, 1965

By Martin J. Conway

DURING the past year, the intense interest shown by the metallurgical industry in the use of relatively pure oxygen has been evidenced by the number of papers dealing with its application and production. The reason for this interest is apparent when it is realized that, weight for weight, oxygen enters into the formation of steel equally with iron. In the manufacture of steel, approximately one ton of oxygen is required to produce one ton of ingots. Until the recent development of plants capable of producing oxygen at far lower costs than had ever previously been considered possible, the oxygen required for steel manufacture was used as it occurs in air, where it is associated with approximately four times its volume of nitrogen. Because of the diluent nitrogen more than 4 tons of total gaseous material per ton of steel must be handled rather than only approximately one ton required when pure oxygen is used. In addition, provision must be made to handle the large quantity of waste, gases resulting from the process. There are cases where the reduction in gas volume alone can justify the installation of an oxygen plant.

Jan 1, 1947

NEW MEMBERS The following list comprises the names of those persons who became members during the period June 10, 1919, to July 10, 1919. ANDERSON, JOHN EDWARD, Min. Engr., Lehigh Valley Coal Co., 121 N. Laurel St., Hazleton, Pa. BENBOW, B. L., Mgr., Cleveland Wire Division, National Lamp Works, General Electric Co., 1770 E. 45th St., Cleveland, Ohio. BLAIR, CHARLES S., Geol., Tennessee Coal, Iron & R. R. Co., Birmingham, Ala. BOLAND, FRED L., Chief Draftsman, Mine Dept., Chile Exploration Co., Chuquicamata, Chile, South America. COLLIER, OTTO L., Civil & Min. Engr., Secretary, Ernest M. Merrill Engrg. Co., Mullens, Wyoming Co., W. Va. DELAMATER, GEORGE RICHMOND, Asst. Supt:, By-product. Coke Oven Dept., Steelton Plant, Bethlehem Steel Co., Steelton, Pa. DOELL, WILLIAM R Chief Engr., Mahuomen Iron .Co., Crosby, Minn. ENDO, SHINZO 365 Komagome Shimmeicho, Hongo, Tokio, Japan. EVANS, CHARLES E., Chief Draftsman, American Smelt. & Refin. Co., Murray, Utah. FISCHER, OSCAR A 62S First National Bank Bldg., Denver, Colo. FISHER, GEORGE KINGSBURY, Met. Engr 47 Baker St., Saranac Lake, N. Y. FRAZEE, VERNE, Min. Engr Moweaqua, Ill. FURNICHI, ROKUZO, Supt. of Min. Dept., Besshi Copper Mine, Baron Sumitomo Co. Ehime Japan

Jan 8, 1919

By Z. Moser, W. Ptak

The experiments were carried out by the method of measuring the electromotive force of concentration cells having zinc as a reference electrode, the second electrode being the liquid alloy Zn-Sn-Cd-Pb. The electrolyte consisted of liquid chlorides and had zinc ions. The measurements were made for seventy -five alloys of different mole fractions within the temperature range of 714° to 877°K. The experimental results enabled the calculation of the activity of zinc in tested solutions. The activities of zinc were calculated by means of Krupkowski's formulas.3 In addition, the formulas for coefficients of activity of zinc, tin, cadmium. and lead as the function of composition and temperature were given. Activity of zinc was compared with the values obtained from experimental results, and good agreement has been observed. On this basis it can be stated that the theoretical formulas are suitable for determining the thermodynamic properties of liquid quaternary metal solutions. IN the metallurgical processes being carried out at present multicomponent liquid metal solutions take part. For the thermodynamic analysis of these processes it is necessary to know the thermodynamic properties of these solutions. Therefore, many experimental and theoretical papers deal with this problem. The theoretical papers are generally based on the assumption that the structure of liquid metals is similar to their structure in the solid state. In this manner the model of liquid solution, consequently described by means of statistical thermodynamics, has been accepted. This method is being lately developed, especially for solid solutions. Statistical thermodynamics was applied among others by Guggenheim 1 for describing the thermodynamic properties. Unfortunately, the formulas of statistical thermodynamics are often not suitable for the interpretation of experimental results. Attention should be drawn to the relations obtained by means of formulas of phenomenological thermodynamics which always have constants derived with the aid of experimental methods. In the case of the multi-component solutions which contain some additions of impurities besides the basic metal, wagner2 introduced interaction parameters. Equations for the relationship between the activity coefficients and composition were also given by Krupkowski." he application of these formulas requires a good knowledge of the thermodynamic properties of the corresponding binary systems. In these formulas, as in Wagner's, there appear constants which should be determined from ex- perimental data. Nowadays, different experimental methods are applied for evaluating the thermodynamic functions of solutions, for instance: vapor pressure measurements, calorimetric methods, and the measurements of electromotive force of concentration cells. In the present paper this last method for evaluating the thermodynamic properties of four-component systems, Zn-Sn-Cd-Pb, was applied. For instance in the case of Zn-Sn solutions Alabyshev and Landratov, 4 Fiorani and Valenti, 5 and ptak6 performed the investigations. The Zn-Pb system was worked out by Kleppa 7 and Cd-Pb and Cd-Sn by Elliot and chipman.' This method was also applied for determining the activity of zinc in ternary solutions. 1) EXPERIMENTAL METHOD The experimental arrangement with detailed description is given in Fig. 1. It consists of resistance furnaces, one serving for melting samples and the other containing the flat-bottomed, measuring quartz tube with the liquid electrolyte. Liquid metals and alloys are in glass supremax tubes, which have an opening in their lower part above the metal level. This opening allows the filling of the tubes by the electrolyte. In these tubes tungsten wires are placed which by means of suitable conductors are connected with a potentiometer. It is assumed that tungsten dissolves Fig. 1—Schematic diagram of the experimental arrangement for the investigation of the thermodynamic properties of liquid metal solutions: 1, resistance furnaces; 2, autotransfor-mers; 3, galvanometers; 4, regulator of temperature; 5, gas purifier with concentrated H2SOP; 6, U-tube with P2O5; 7, thermostats; 8, steel block for thermostating; 9, supremax tubes for alloys; 10, tungsten electrodes; 11, inlet and outlet of argon; 12, measuring quartz tube; 13, tube for melting samples; 14, tube for thermocouple; 15, cover of quartz tube; 16, rubber seal; 17, bottom cover; 18, outlet of electrodes to potentiometer; 19, outlet of thermocouples to potentiometer; 20, upper view of the quartz tube cover; 21, orifices for cover screws; 22, orifice for argon inlet; 23, orifice for thermocouple; 24, orifices for tubes containing liquid metals; 25, inlet for water-cooling system.

Jan 1, 1969

By J. B. Mudd

Introduction It is difficult to think of any activity on which mankind has been more dependent than mining, and certainly there is much evidence in almost every part of the world of old workings that clearly demonstrate that man from earliest times has dug and toiled to take from the earth precious stones, metals and materials that from time to time have been essential or of value to him. In step with social development and industrial and technological advances the tempo of mining activity, regulated only by the laws of supply and demand, has quickened and in this century has accelerated rapidly in keeping with its dramatic development. Indeed, the rate of change of events has been such that if it were to continue to accelerate as fast as it has over the past decade there is reason to wonder how the insatiable demands for metals and minerals are to be met in the years that lie ahead. Shallow mines containing high-grade ore deposits either have been or are being rapidly mined out and their place can only be taken in general by ore lying at greater depth, or by ore of low grade, situated for the most part in remote and in underdeveloped areas. The cost of exploration and development is rising at an alarming rate, with the result that the expenditure now required to bring a mine to production far exceeds anything previously contemplated. It is estimated that the total capital required to maintain existing operations and develop new ones during the next 5 years will be of the order of $50,000 million and of this, new capital to bring new mines to production will be of the order of $3,000 million. Today no single mining finance company can, from its own resources, find all the money for a major mining development, and as a consequence there has been a strong trend toward joint ventures and to the formation of multinational consortiums. International lending institutions already play an important part in financing many new mining projects and their participation provides the financial umbrella under which other lenders can invest with greater security. There is little doubt that to finance the costly ventures in the future, governments and international lending agencies, banks and finance

Jan 1, 1971

By Horace Pops

Martensitic transformation has been studied during cooling and heating in ß-phase Cu-Zn alloys to which small additions have been made of Ni, Ag, Au, Cd, Ga, In, Si, Ge, Sn, and Sb. The start and finish of the martensitic reaction and the variation of transformation temperature with third-element content were determined by electrical-resistivity measurements from alloys which had either constant zinc contents or constant values of electron concentration. All of the third elements, except nickel, lowered the transformation temperature if the results were plotted along the lines of constant zinc contents in each ternary system. A significant difference in the rate of lowering of the transformation temperature per atomic percent of the third element was observed for elements which had the same nominal valence. No systematic variation of transformation temperature with the valence of the third element was observed. It is suggested that the observed increase in transformation temperature for nickel-bearing alloys is due to the transfer of electrons from the conduction band of the alloy to virtual bound states. However, electron concentration is not the most important factor controlling the instability of the 0 phase. The transformation temperatures of the ternary alloys can be predicted from the following approxilnate expression: Ms (°K) = +3280 - 80 Zn + 8 Ni - 30 Ag - 12 Au - 140 Cd -90 Ga- 145 In - 80 Ge -175 Sn - 120 Si - 150 Sb MOST binary ß -phase alloys based upon the noble metals copper, silver, and gold are unstable at low temperatures and transform spontaneously by a martensitic reaction. This transformation has been studied recently in the ordered bcc ß'-phase Cu-Zn binary al1oys1,2 where the transformation temperature is below the room temperature and decreases with an increase in zinc content. It has been reported that the transformation temperatures can be raised above room temperature by small additions of a third element such as silicon3,5 or gallium,4,5 but no quantitative study has been made. The transformation temperature of different binary alloys can be altered by third-element additions. For example, it was shown that nickel and copper may have a large effect on the Ms temperature of CU-Al6 and Au-cd7 alloys. The present investigation was made to determine systematically the influence of various third elements on the martensite-transformation temperature of Cu-Zn ß-phase alloys. Since these alloys have an electronic origin,' alloy compositions were chosen so that the transformation temperatures could be determined at constant zinc contents or at constant values of electron concentration. I) EXPERIMENTAL PROCEDURE Ten ternary alloy systems were obtained by adding nickel, the noble metals silver and gold, and some B-subgroup elements to a Cu-Zn matrix. These are arranged according to their rows and columns in the Period Table as follows: Each ternary alloy was prepared by melting and casting weighed quantities of high-purity metals (99.99+ pct) in sealed quartz tubes under a partial pressure of helium to make a 4-g ingot. The molten alloys were shaken vigorously and then quenched in water. Since the weight loss was negligible, the compositions of the ingots after casting and annealing were assumed to be the same as the nominal compositions. The ingots were homogenized after casting in helium-filled Vycor tubes for 24 hr at temperatures between 750" and 810 C and quenched into brine. Metallographic examination revealed that all alloys were homogeneous, poly crystalline ß-phase alloys, and that the grain size was in the range 1 to 5 mm. Electrical-resistivity measurements were made to determine transformation temperatures of the ternary alloys during continuous cooling or heating. Transformation temperatures of the ternary alloys can be determined by electrical-resistivity measurements since the resistance of the martensitic phase is much higher than that of the 0' phase. The technique has been described previously in connection with a study of Au-Zn alloys.9 The reproducibility of transformation temperature was approximately ±6°C. II)RESULTS A hysteresis was always observed in electrical-resistivity curves and was usually less than about 12°C.

Jan 1, 1967

By Howbert Van Dyne

THE Presidio mine of The American Metal Co. of Texas is situated 45 miles south of Marfa, Texas, a town on the Southern Pacific R. R., and lies approximately 20 miles north of the Mexican border. Communication with the railroad is maintained over a state highway. All supplies for mine and mill are hauled in by truck from Marfa and precipitates and concentrates are freighted to the railroad by the same means and shipped to Selby and El Paso, respectively. The mill is at the town of Shafter, 1 mile from the mine and at approximately 350 ft. lower elevation. The ore is conveyed to it by an aerial tramway which requires practically no power on account of the difference in elevation. The mill is a countercurrent decantation cyanide and gravity concentrating plant of 200 tons daily capacity. Coarse and fine crushing are done at the mill. Two near-by shallow wells in the bed of Cibolo Creek furnish an abundance of water. Power is generated for the mill and town by a Diesel engine plant.

Jan 1, 1930

By David Cornell, D. L. Katz

Procedures for computing turbulent flow of gas in steady state near the well bore and a graphical method for predicting unsteady state laminar flow at distances from the well have been combined to compute pressure gradients in gas reservoirs. Methods are discussed for predicting single and multiple transients at constant flow rate in an infinite reservoir, predicting constant How rate. in a finite reservoir, reproducing and interpreting back pressure test data, and prediction of the behavior of a closed-in gas well. An example of the graphical method is given for a single transient and the results are compared to a published analytical solution. A typical calculation of the pressure gradient in a reservoir and the production of gas is made .starting with data from a hack pressure test. INTRODUCTION The calculation of pressure gradients throughouse a ga-reservoir at any point in its production history is a complex problem involving turbulent flow near the well bore and unsteady state flow of the gas from the reservoir. The problem is complicated further by the variety of boundary conditions that may be imposed upon the flow. Such boundary conditions include finite or infinite reservoirs. constant or variable rates of production, constant or varying bottom hole pressures, complex initial pressure distributions throughout the reservoir, and pressure maintenance through cycling. In addition to these problems there are the practical difficulties associated with natural gas reservoir analysis These might include: (1) variation. in the permeability and porosity throughout the formation. (2) variations in the thickness of the formation, (3) communication of the producing formation with other producing zones. (4) radial variations in permeability due to influx of drilling fluid. acidizing. or the buildup of liquid in the formation around the well, (5) partial penetration of the producing zone. (6) water flood, and many others. These problems will be considered eventually. In the mean- time, it is necessary to present methods of handling the case of radial flow through a homogeneous, regular, producing stratum to a single well uncomplicated by other factors. The idealized case of steady state, radial flow from a natural gas reservoir was studied by Elenbaas and Katz5 and by Mac-Koberts.' An analysis of the unsteady flow of gases through porous media has been made by Aronofsky and Jenkins' for the one dimensional laminar case with the boundary conditions of constant downstream pressure and uniform initial pressure. Solutions for the partial differential equation for unsteady state radial flow of liquids through porous media have been given by Van Everdingen and Hurst" for the constant bottom hole pressure and constant production rate cases for laminar flow in a reservoir initially at a constant pressure. The analogous heat transfer equation has been treated by Perry and Berggren9 for the case of quenching a cylindrical hole in an infinite medium to a constant temperature. The back pressure curve, which involves the variation of the bottom hole pressure as it is determined by the behavior of the reservoir as a whole. has been studied by Rawlins and Schellhardt,10 Binck-lev,' Baumel and Breitung,' and others. No complete. adequate treatment has been given for the unsteady state, radial flow of gases into a cylindrical hole from a porous medium with or without the presence of turbulent flow and for any set of boundary conditions. If one relies only on analytical solutions of the basic equations, a new solution must be obtained for each new boundary condition. Furthermore, the complexity of the mathematical expressions for boundary conditions other than the very simple cases limits the use of analytical solutions. Graphical methods exist, however. that are general in nature, accurate, and readily employed. The analysis of steady and unsteady, laminar and turbulent, radial flow for various boundary conditions with application to specific natural gas well problems by means of graphical procedures forms the content of this paper. STEADY STATE RADIAL FLOW EQUATION FOR LAMINAR AND TURBULENT FLOW A steady state radial flow equation for laminar and turbulent flow through unconsolidated sands has been given by Muskat as discussion of the work by Elenbaas and Katz.5 This equation is based on the properties of unconsolidated

Jan 1, 1953