Search Documents

By Harry M. Callaway

IN times of a falling metal market the mine operator attempts to remain in competition by lowering his overall cost and raising the grade of ore he processes. But these adjustments can be made only within narrow limits imposed by inherent characteristics of the operation. Is there some additional method whereby the break-even point can be lowered? One approach, perhaps the only one, to lower a break-even point is careful cost analysis considering both fixed and variable costs in relation to mining rate. The following is an analysis of cost distribution and its significance in determining the most economic combination of the factors of ore grade and tonnage output applicable to a given mining operation.

Jan 4, 1958

By Howard E. Kremers

Since the discovery of the first-known rare earth elements more than a century ago, these metals have always been of academic interest. It is not so well known, however, that a rather stable, respectably large industry based on rare earths and their related materials has been in operation for more than 60 years. Rare earths, of course, are the elements having atomic numbers 57 through 71--lanthanum through lutetium in the periodic table. The most important commercial members of this group are mixtures of the lower atomic-numbered rare earths, and cerium. Although yttrium is not a rare earth, it occurs with rare earths and its properties are so similar to them that. it must be included in a discussion of these elements. In addition, thorium is important to most producers of rare earths because their ores generally contain this element. Thorium extractive metallurgy and technology is closely related to rare earth chemistry due to the frequent similarity of properties.

Jan 4, 1962

By A. J. Sinclair

Sampling methods for feasibility studies are dependent on geological characteristics of the deposit being evaluated. A preliminary geostatistical study is required, taking into account autocorrelation aspects of variables under study in order that sample plan design can be optimized to produce grade and tonnage estimates within stipulated error limits. In general, regular sample distribution is to be aimed for, and regular sample lengths (from drill core or cuttings, for example) are preferred in order to facilitate statistical analysis. Sample plans are modified and improved (either technically or economically), as a sampling program proceeds and additional information is obtained. Bulk samples for metallurgical testing can be evaluated in terms of the variance shown by all such samples in a deposit and the internal variability of grade. Attention to these sources of variability will ensure proper evaluation of pilot test results from bulk samples. In addition, a general mineralogical study of a deposit is an important, often ignored, requirement in a more general but semi-quantitative evaluation of the representativeness of a bulk sample; and, moreover, provides information useful in optimizing plant design.

Jan 1, 1978

By W. Scott Dunbar

INTRODUCTION Methods of linking boundary integral (BI) solutions with finite element (FE) solutions have been well described theoretically in other publications (e.g., Zienkiewicz, et al., 1977). The purpose of this paper is to point out some practical aspects of implementing these linkage algorithms for rock mechanics applications and to describe an alternative linkage algorithm. A not so obvious motivation for using FE-BI linkages is illustrated in Figure 1. The cost of modeling the excavation of the crusher station by the BI method can equal or exceed the cost of an equivalent FE model. This is due to the large surface area which must be modeled by the BI method. In such cases, a more economical approach might be to model the region immediately adjacent to the crusher station by finite elements and link the solution at the periphery of the FE model with a solution for the exterior region. Further economies can be realized if some flexibility in the type of exterior solution is possible. For example, it would be desirable to use a coarse discretization of the FE-BI interface for a BI solution, which would be less demanding of computer storage and time, or to use an analytical solution for the exterior region. The alternative linkage algorithm to be discussed allows such flexibility. BOUNDARY INTEGRAL METHODS There are basically two formulations of BI methods: the direct and the indirect. FE-BI linkage algorithms depend on which formulation is used. The purpose of this section is to briefly describe each method.

Jan 1, 1982

By Paul Hett

The much-heralded Deep Ruth operation of Kennecott Copper Corp., at Ruth, Nev., is scheduled to become a producer by 1957. Inaugurated as a project in 1951, production was originally scheduled to start in 1953, but excessive water hindered shaft sinking. A revised schedule called for output by 1955, but again plans had to be changed. This time the change was to permit mining of an orebody that would have otherwise been lost because of block caving methods planned for the main deposit. The new ore is within the cave limits of the larger orebody, above the first production level. Ore will start coming from this new source in 1956, a year ahead of the principal operation. (See NEWS, page 344.) There is little doubt that current economic conditions and unforeseen expenditures for early shaft development will make the Deep Ruth a high-cost producer. Yet, some of the drawbacks of the Kennecott operation may be mitigated by the possibility that additional exploration will increase the already assured 25 million tons of 0.83 pet copper ore. While Kennecott is missing out on the current high copper market and is thus left with a potentially narrowed profit, the predicted demand for copper has created an optimistic feeling. Its development is certain to enlarge known U. S. copper reserves and significantly extend the life of Kennecott's Nevada operations.

Jan 4, 1955

By John V. Beall

The mining industry of Japan is not very large, but it is very old. Some of the mines have 1000 years of history. At Nara, the capitol 1300 years ago, the great Buddha of bronze that was cast at that time was of metal mined from several localities in Japan including the Akenobe-Ikuno district, one of the present Mitsubishi properties. Methods of smelting copper and iron, it is believed, came from China via Korea. A characteristic of the Japanese mining industry today is one of buying abroad and treating at home, a variety of ores of different compositions. All in all, Japan's mineral deposits under its own flag are inadequate for its great industrial strengths.

Jan 5, 1969

For some years MINING ENGINEERING has published abstracts of the articles appearing in each issue and also of the Transactions papers published in the Quarterly. Beginning this month, a list of key words is being given with each abstract as an aid to indexing the articles for ease in retrieving them when they are needed. The value of a home or office system of indexing and retrieving technical articles is hard to over-estimate. How often is it that a technical problem comes up and someone says: "Oh yes, I've read something about that." Many hours can be expended tracing down that nebulous source. A modest indexing and retrieval system will save those tedious hours, and the person who is able to produce technical documents when they are needed will achieve an enviable status for being on the ball.

Jan 1, 1964

By D. L. Wood

This investigation was concerned with the aluminum-oxide particle dispersions, the mechanical properties, and the re-c,uystallization characteristics of some internally oxidized copper-aluminum alloys. Obserued hardness vaviations are in agreement with variations in oxide particle size revealed by electron metallographic studies. The increase in yield strength caused by internal oxidation is quite sensitive to matrix grain size and is accompanied by a loss of ductility, particularly at higher temperatures. Elevated temperature ductility is con-side,vably improved if major grain reorientation is accomplished by ve recrystallization prior to testing. The oxide particles offer a considerable restraint to softening during annealing after cold deformation. THE diffusion of oxygen under appropriate conditions into a suitable alloy causes solute oxide particles to be precipitated at an inward moving interface.1,2 Previous work has shown that the hardness

Jan 1, 1960

By C. A. Stout, S. W. Nicksic

The materials that stubilize emulsions of some Southern California crude oils were isolated from the produced crude. These substances were separated into acidic and nonionic fractions by ion exchange chromatography. Each fraction was further broken into groups of homogeneous molecular weight composition by gel permeation chromatography. Both ionic character and molecular weight of the individual fractions are reflected in the properties of the original crude oil emulsion. Specifically, the more acidic and the higher molecular weight fractions appear to be the most effective stabilizers. INTRODUCTION The treatment of oilfield emulsions is a continuing problem for the oil industry. In almost all cases, these are water-in-oil emulsions. Much more is known about the formation and stabilization of oil-in-water (O/W) emulsions than of the water-in-oil (W/O) type. To understand W/O emulsions, more information is needed on the materials responsible for their formation and stabilization. This is especially true in the case of oilfield emulsions where the stabilizing materials are complex mixtures of large asphaltene-like molecules. To study the chemical and physical properties of these emulsion stabilizers, it is necessary first to separate them from crude oil. This separation was achieved in the case of two Southern California crude oils. The materials that were isolated appear at first to be little different from an asphaltene mixture. However, if a mixture of distilled water and mineral oil containing about 1 percent of the natural emulsion stabilizers is passed through a colloid mill, the W/O emulsion formed may be stored in the laboratory for many months without any sign of breaking. This could not be done using undifferentiated asphaltenes from the same wells, indicating that there is a real difference between these materials and ordinary asphaltenes. The colloid mill used to generate the emulsion was required because tile natural emulsion stabilizers had very little effect on oil-water interfacial tension. The one characteristic — complexity of composition — that emulsion stabilizers share with asphaltenes makes virtually impossible the exact structure determination of the components of the mixture. For this reason, it was decided to investigate first the influence of molecular weight on the ability of these materials to stabilize emulsions. The emulsion stabilizers were first separated into acidic and neutral fractions according to whether or not the material was retained on a weakly basic ion exchange column. The extraction procedure was not designed to remove basic components from tile oils, and no attempt to isolate such a fraction was made. Following this separation, selected fractions were analyzed by gel permeation chromatography. Gel permeation separates according to molecular size, largely independently of chemical or polar characteristics. A heterogeneous mixture is separated into a number of fractions having much more homogeneous molecular weight distribution. A number average molecular weight of each fraction is therefore close to the true molecular weight of the principal component of that fraction. The fraction weights, expressed as weight percent of the sample, and the number average molecular weight of a representative selection of the fractions, will be referred to in this paper as the molecular weight profile of the original sample. DESCRIPTION OF GEL PERMEATION ANALYSIS The first reported gel permeation analyses were for separating partially hydrolyzed protein molecules in an aqueous system using expanded starch granules. Most of the theoretical work on gel permeation has been done by biochemists.1 This theoretical treatment is still incomplete, but the

Jan 1, 1969

By James W. Clark, William C. Dixon, Kevin L. Wiley, Thomas R. Couzens

This paper is a description of certain geologic aspects of the Inspiration mining operation. It is not a geologic description of the Inspiration deposit nor an exposition of all the geologic work. Involved in the development and exploitation of the deposit. A few specific examples of the application of geology and geostatistics to the mining process are given to illustrate the progress that has been made in making the Inspiration Mine more efficient and cost effective, and a statement of the philosophy of geologic applications is offered.

Jan 1, 1985

By M. H. Caron

D. C. Ralston—The fact that none of the organizations that have worked on these ammoniacal leaching processes have contributed discussion of Mr. Caron's papers today is a matter of some disappointment. Adaptations, modifications and improvements have been made by several organizations or individuals and to complete the record I want to document a number of them. The Nicaro Nickel Co. operated a Government owned plant at Nicaro, Oriente, Cuba, during the past war. A report on the project was written for Reconstruction Finance Corp. and is in the document file collected by the Office of Technical Services, Commerce Department and filed with the Library of Congress, where it can be consulted or bibliofilm or photostat copies obtained by asking for copies of PB 97271. Nicaro Nickel Co. has obtained a series of U.S. Patents, my list (probably incomplete) of which bears the following numbers: 2,400,098; 2,400,114; 2,400,115; 2,400,461; 2,400,612; 2,458,902 and 2,473,795. International Nickel Co. has also studied the problem and U.S. Patent 2,478,942 shows that some of the complications involving occasional low extractions have been unraveled. Forward, Samis, and Kudryk, of the University of British Columbia, have also published a study of copper-nickel sulphide concentrate.' Others are interested and it is evident that this type of hydrometallurgy is likely to find a happy application in the not-too-far distant future. Caron's two papers practically amount to a summation of his life's work on the important subject of nickeliferous iron ores and the American Institute of Mining and Metallurgical Engineers is fortunate to have been chosen the medium of publication. M. Rey—The ammonia leaching process has been the subject of certain studies in New Caledonia, but at the present time, the conditions are not very favorable to its adoption. The process is a combination of a thermal and a hydrometallurgical process. As a result, the first costs and the operative costs are rather high. To counteract this unfavorable situation, it would be necessary to make a very high extraction. But unfortunately, the process is delicate and in spite of all of Caron's valuable work, there are still many unknown factors. It is difficult to obtain regularly a high extraction, exceeding 75 to 80 pct. It would be interesting to have the opinion of Inter-national Nickel on the process and to know what the Dutch are doing in Celebes. M. H. Caron (author's reply)—I am quite familiar with the different types of nickel and cobalt ores as found on New Caledonia, and it may be pointed out that the Celebes ores are quite the same in their properties. Their behavior when treating the ores by the ammonia-leaching process is also alike and in my opinion, there is no reason why a high extraction of the New Caledonian ores could not be obtained if the process is properly applied. For the sake of completeness I may add that one of my patents has not been discussed in the papers. This patent deals particularly with the treatment of serpentine nickel ores. (Netherlands No. 62693 40a, French No. 965.786 April 21. 1948. and Cuban No. 13.625 Jan. 1950.) O F. A. Forward, C. S. Samis, and V. Kudryk: Trans. Canadian Institute of Mining and Metallurgy. (1948) 151 (Bull. 434) 350-355.

Jan 1, 1951

By Charles M. Stone, Dale S. Preece

Introduction The Strategic Petroleum Reserves (SPR) is a national program dedicated to storage of large quantities of crude oil in leached salt caverns in the Texas-Louisiana gulf coast area. The program has required storage in existing caverns at each site and includes plans to leach new ones. The structural stability of each cavern depends on the behavior of the surrounding salt. In the past cavern stability has been predicted based on experience with other caverns in the vicinity. With the development of good non-linear finite element structural computer programs, it is possible to predict stability before the cavern is created. An important step in verifying the applicability of these predictive methods is comparison of analytical and field data. The analytical data come from finite element analyses of a specific cavern where the laboratory determined material properties and an approximation to the cavern geometry are used as input. These comparisons have been made for caverns in the Bayou Choctaw Dome (Louisiana) and Eminence Dome (Mississippi) with reasonably good correlation being obtained between measured and predicted volumetric response of the caverns. This paper discusses 1) the acquisition of material properties, 2) the finite element program SANCHO, and 3) the comparison of analytical and field data for each of the caverns.

Jan 1, 1982

By P. N. Ivanov

The world experience shows that the tremendous potentialities of the computers and other technical means in improving management efficiency are not fully utilized. One of the causes is the tendency to solve the problems of management automation divorced from the management methods and schemes which demand continuous improvement in view of the steady progress of the social production. It may be safely affirmed that making decisions on management improvement divorced from management schemes or on both divorced from management automation problems cannot lead to success. The grave and sometimes unsuperable difficulties encountered in management automation arise from copying traditional management methods and schemes without solving the problems which exist both in management and automation fields. The system solution of management problems has unquestionable advantages and is not proposed for discussion. What is proposed to discuss is the difficulties emerging in developing a methodology of the system approach to management improvement and automation. Though aware of the fact that the questions proposed for discussion are not new, we think it advisable to briefly review them, first because they fall in the "chronically unsolvable" category, and, secondly, as it will enable us to illustrate the method of solving them in the framework of the proposed system approach.

Jan 1, 1977

By P. P. Gregory

Natural petroleum gas occurring in the oil-bearing reservoirs is found to exist either as free gas associated with the oil and/or in solution in the oil. In some virgin fields practically no free gas is encountered under the reservoir conditions of pressure and temperature, although in other fields a considerable section of the "pay" horizon is occupied by free gas. In other words, a given oil field may or may not have a gas cap before the exploitation takes place. However, when the reservoir pressure is reduced to a point below the critical saturation pressure by withdrawals of fluids from the producing formation, the gas dissolved in the oil inevitably begins to come out of solution and becomes free gas. Under the controlled methods of production and drilling, a portion of this gas is produced with the oil to the surface and a portion of it remains within the reservoir to accumulate at higher structural levels toward which it migrates by virtue of its low specific gravity. The rate of growth of a gas cap in a given structure depends primarily upon the rate of decline in the reservoir pressure. If the rate of pressure decline is rapid, the gas cap likewise will grow rapidly. On the other hand, shrinkage in the gas-cap area was noted in some fields in which reservoir pressures wereincreasing. Determination of Gas-oil Contact and Thickness of Gas Cap The gas-oil contact can be conveniently located in the process of drilling a well and by electrical logging. However, very little can be found in the petroleum literature concerning methods of predetermining gas-oil contacts in producing reservoirs. Therefore, the writer feels justified in describing briefly a simple, workable, and inexpensive method of determining gas-oil contacts and outlining the limits of gas-cap areas in a field where such knowledge may be essential for efficient production and development operations. The method involves the determination of the following data: (I) Structural data, such as the depth or elevation of the top' of "pay" horizon; (2) reservoir pressures; (3) tubing and casing pressures at the well head; (4) static oil-pressure gradient; (5) static gas-pressure gradient. These data can be secured with a minimum of expense, inasmuch as the

Jan 1, 1938

By Irwin Roman

IN a previous paper,1 a method was suggested for determining the depth to a bed in the simple case of a uniform overlying layer of constant thickness. The main purpose of the present paper is to show how a slight modification of that method has been used to interpret specific data obtained in the upper peninsula of Michigan by the staff of the Depart- FIG. 1.-THE TECTONIC CONFIGURATION. ment of Mathematics and Physics of the Michigan College of Mining and Technology. The method of Tagg2 has also been used on the same data, thus furnishing a comparison of the e two methods, as well as a method of using the two methods jointly. The method of measuring the apparent resistivity is that suggested by Wenner,3 and illustrated in Fig. 1. A current I enters the earth at the positive pole C and leaves it at the negative pole D. The potential V of the high electrode A, with respect to the low electrode B is measured by suitable means. The separation of the collinear points in the order shown, DBAC, is 1, the same. for each interval.

Jan 1, 1934

By R. T. Hukki, A. M. Gaudin

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;' the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By A. M. Gaudin, R. T. Hukki

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;' the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By L. Burris, C. H. Stockman, I. G. Dillion

Zone melting is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Equations are presented which 1—predict the concentration profiles after successive passes of the zone and 2—give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing in the last zone length. These equations were solved numerically using an electronic computer, and the concentration profiles are presented as a function of the solute distribution coefficient and the ratio of molten zone to total bar length. ZONE MELTING is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Separation occurs if the solid freezing from a solution at any moment has a composition different from that of the liquid from which it is freezing. Solutes which lower the freezing point will tend to remain in solution and will be moved in the direction of zone travel. Solutes which raise the freezing point will preferentially freeze out, and they will be moved in a direction opposite to that of zone travel. After repeated unidirectional passage of a molten zone through a bar of material, impurities will be concentrated in the ends of the bar. A limiting concentration gradient will be reached in the bar after a large number of passes of the molten zone. Both the magnitude of this limiting concentration gradient and the rate of movement of solute in any pass depend on the zone length and on the equilibrium concentrations of solute in the liquid and solid phases. The basic theory of zone melting was thoroughly covered by Pfann.1 The purpose of this paper is to extend the theory of zone melting by presenting 1—equations which relate the concentration profiles in successive passes of the zone and 2—equations which give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing* in the last zone length concentration of a given solute in the solid to the concentration of the same solute in the liquid. Analytical methods for determining the concentration profiles after any pass have been developed by Lord2 and Reiss. The method developed by Lord does not take into account normal freezing in the last zone and also becomes very complicated when the number of passes becomes large. The method developed by Reiss enables the direct calculation of the complete concentration profiles (including that in the last zone) after any pass for values of k close to unity (0.9 < k < 1.1). Both methods are useful and provide valuable insight into the zone melting process. The equations given in this article are based on the same assumptions used by Pfann. These are: 1—uniform composition in the liquid, 2—negligible diffusion in the solid, 3—constant distribution coefficient, 4—constant length of the liquid zone (except at the ends), and 5—solubility of the solute in the melt is not exceeded at any point. Equations for Concentrations in Successive Passes For a melted zone of length 1 at the left-hand end of a bar of uniform unit cross-section, the amount of solute in the liquid is J0Cn-1(x) dx [1] where the subscript is the number of the pass. Cn-1(x) represents the concentration (expressed as weight per unit volume) obtained in the previous

Jan 1, 1956

By R. I. Jaffee, C. T. Sims, C. M. Craighead

The fabrication of rhenium metal by powder metallurgy techniques is discussed. The following physical and mechanical properties have been measured and are reported: lattice constants, melting point, electrical resistivity, thermal expansion, spectral emissivity, modulus of elasticity, tensile properties and ductility at room and elevated temperatures, work hardening, recrystallization, grain growth, and oxidation resistance. IT is only occasionally that a metal reaches present-day technology with as little known about its properties as element No. 75, rhenium. Relatively scarce to date, it has been studied only infrequently and used less. Previous work on rhenium has been carried out primarily by European scientists. However, realization that rhenium occurs in commercial quantities in the United States recently has focused attention on this metal. Rhenium is a very dense high melting hexagonal-close-packed metal. Like tungsten and molybdenum, its highest oxide is volatile. However, when protected by reducing or inert atmospheres, its strength at high temperatures is greater than that of tungsten. Rhenium work hardens more than any other known pure metal, but, on annealing, becomes quite soft and ductile. Its vapor pressure is approximately that of tantalum, but it does not enter into the so-called "water cycle" nearly as readily as does tungsten. (The water cycle is a deleterious phenomenon causing blackening of lamp bulbs and vacuum tubes with subsequent failure of the filaments.) These and other properties, some already known and some found as a result of the current researches, have indicated that rhenium has many potential uses, primarily of an electrical or electronic nature. Rhenium or its alloys soon may be found in service as electron-tube filaments, cathodic emitters, or as electrical contact materials. In addition, rhenium or its alloys have potential use in such devices as high temperature thermocouples, and high wear-resistant parts such as precision instrument points. Rhenium, in the form of potassium perrhenate, was made available for this study by the Kennecott Copper Corp. The potassium perrhenate was reduced to rhenium metal in two stages, accompanied by leaching to remove potassium in the form of hydroxide. This impure metal was then oxidized to rhenium heptoxide and dissolved in water. The solution was neutralized with ammonium hydroxide to produce highly purified ammonium perrhenate, a typical analysis of which is shown in Table I. The ammonium perrhenate was ground to —325 mesh in a rubber-lined ball mill with Burundum balls. This operation caused a certain amount of impurity pickup, as reflected in the rhenium analysis shown in Table I. The fine ammonium perrhenate was reduced to metal with hydrogen. Particle size of the powder ranged from 1 to 25 microns, as illustrated by Fig. 1.

Jan 1, 1956

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval&apos;s heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy&apos;s Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved