Search Documents

By R. T. DeHoff

A general method for determining the geometric properties of structures composed of particles which are all the same shape and size is presented. The application of the method requires a knowledge of' the qualitative shape of the particles in the structure, ad a maximum of three simple counting measurenzents, which are made on a representative plane section taken through the structure. It is also shown that the number of different kinds of measurements necessary JOY the complete description of the structure can be decreased if some independent information about individual particles is available. The geometric properties that can be determined quantitatiz~ely from counting measurements for susch structures are size, shape, number, surface area, vlolume, ad such extensive properties as volume Mction and surface area per unit volume. THE simplest kinds of measurements that may be made on a metallographic section are counting measurements. There are three such simple counting measurements, which are determined by sampling the microstructure with a point, a line, and an area. The first of these, the point count, is probably the most familiar among metallographers. The second count, the number of intersections a test line makes with particle outline, is somewhat more recent in its origin and application. The third counting measurement, the number of particle sections observed in unit area of the plane of polish, has long been used in the estimation of grain sizes. The real utility of these three counting measurements lies in the fact that they are rigorously and unambiguously related to certain extensive geometric properties of the three-dimensional structure of which the metallographic section is a sample. These relationships will be reviewed briefly below. Of somewhat secondary importance to the fundamental relationships is the observation that, if some simplifying assumptions about the geometry of the three-dimensional structure are introduced, manipulation of the counting measurements gives a more complete description of the structure. Specifically, in addition to the extensive properties which these measurements rigorously estimate, the number of particles, their size, and their shape may be determined. The purpose of the present paper is to explore the consequences of introducing the assumption of constant size and shape. A later paper will deal with the estimation of geometric properties of structures which may be characterized by a two-parameter size distribution. It should be mentioned that the introduction of this simplest of assumptions, while clearly not generally justified in metallurgical structures, is not without precedent. For example, many estimates of the number of particles per unit volume of structure, based upon a single counting measurement, are scattered throughout the literature.13 Virtually all of these developments assume a constant particle shape, e.g., spherical or polyhydral, and constant size. That such an assumption is necessary is evident from the fact that, for more general structures, more than a single parameter is required to describe the three-dimensional structure, so that the determination of a single parameter on a section would be insufficient to specify the structure. Similar developments for the estimation of particle size from a single counting measurement, e.g., routine grain-size determinations, make the same very limiting assumption,435 but have nonetheless proven of practical value. The present paper embodies a generalized approach to the development of relationships among the two-dimensional counting measurements and the three-dimensional geometry of the structure, subject to the assumption of constant particle size and shape. It is the hope of the author that by presenting the relationships and the assumptions involved in dealing with this approximation, in a single, unified treatment, the reader may be impressed with the usefulness of the counting measurements, may be guided in their application to the estimation of details of the geometry in specific structures in which he may be interested, and may be moved to apply the results, with understanding, to new structural problems. Several authors6, 7 have demonstrated independently that it is possible to obtain unbiased estimates

Jan 1, 1964

By G. E. Pralle

INTRODUCTION The decade from 1969 to 1979 saw the crest of a wave of investments by companies and investors, primarily from the major industrial nations, in the metals and minerals industries of the so-called lesser developed countries. This was brought about by two major considerations: 1). The higher ore grades and therefore the higher profit potential of the mineral deposits in the third world countries, and 2). The desire, particularly by the European countries and by Japan, to ensure a safe supply of raw materials not available in their own countries. The decade began with the start of the Toquepala mine in Peru and the major investments in the Bougainville mine in Papua New Guinea and the Ertsberg mine in Indonesia. It ended with the start-up of Southern Peru Copper Company (SPCC) Cuajone mine in Peru and Inco's Soroako mine in Indonesia and the investments in several major alumina or aluminum projects in Australia and Brazil. Concurrent with this huge flow of funds into the mineral resources industry of the developing world was the build-up of a psychological fear in the host countries of exploitation/domination by the foreign investors. This resulted in an increasing trend towards: 1). Nationalization of existing mineral ventures, and 2). Tougher legal/fiscal frameworks for new ones. NATIONALIZATION Nationalization appeared in its earliest form as "Mexicanization" of the petroleum industry in Mexico in the 1930's, followed later by Mexicanization of the mining industry in general. This was enacted with the Mexican Mining Law of 1961 which required that 51% of the equity be owned by Mexican nationals. Later in the decade the equity share for foreign investors was reduced to 33 1/3% for the developers of the Frasch sulphur operations in the Isthumus of Tehuantepec. However, the law was not fully implemented in the copper industry until late 1970 with the purchase of 51% of the ownership in the Cananea Mining Company. The trend toward nationalization of the copper industry progressed to Chile where in 1967 under the Government of Eduardo Frei the major North American copper companies were induced to sell a one-half interest in their Chilean mines to the State. Likewise, in 1970, "Zambianization" took place, when the two major operating companies Roan Selection Trust (Amax) and Zamanglo (Anglo American) were restructured into Roan Consolidated Mines (RCM) and Nchanga Consolidated Mines (NCCM) providing the government with 51% of the equity ownership. Whilst the earlier forms of nationalization in general constituted a fairly priced buy-out (El Teniente, Chile for US$80 million, RCM for US$117.8 million, NCCM for US$178.7 million), the total nationalization of the Chilean mining companies in 1970 under Salvador Allende did not. Later, "Western" countries joined this trend and on October 29, 1973, Mr. Gough Whitlam proclaimed that "overseas capital must continue... in partnership with Australian capital" and "in some special energy cases we have an objective of 100% Australian ownership". In 1974 Mr. Pierre Trudeau stated: "The Liberal Party of Canada sets as an objective that new resources projects in the natural resource field should have at least 50% and preferably 60% Canadian equity ownership". FOREIGN INVESTMENT The situation for the foreign investor in the worldwide resource industry rapidly deteriorated from then on. New features appeared in mineral exploitation and operating agreements, centering not only on local government/local companies ownership but also on increased taxation. The new tax rate (mineral tax, royalty, and income tax) for the semi-government companies NCCM and RCM in Zambia became an effective 73%. Likewise the much publicized and discussed renegotiated Bougainville agreement brought dramatic increases in the total "take" by the PNG Government. More innovative forms of indirect taxation made their appearance and were added to the normal tax burdens of the mineral industry which already

Jan 1, 1985

By W. W. Mein

IN March 1949 the Calaveras Cement Co. was sued by five landowners whose properties are located in the vicinity of the plant. These landowners—all of them cattle ranchers—sued for dust damages of $120,338 and for an injunction preventing the company from casting dust upon their properties in injurious quantities. The issue was split, the jury deciding the amount of damages and the court handling the injunction features. The action came to trial before a jury in April of that year and resulted in damages being awarded in the amount of $7,508. A month later the court issued its injunction requiring recovery of stack dust to an 87 pct minimum. The Calaveras plant, shown in Fig. 1, is located three miles from San Andreas in the heart of the Mother Lode country, about 45 miles east of Stockton, Calif. Since it is in a small town, the company's responsibilities to its employees and to the community are different from those of plants located in large centers of population. Construction of the plant was begun in 1925, and production was started the following year. Standard gray Portland cement as well as several specialty cements are produced. Production facilities have been continually enlarged so that the present capacity is more than double what it was 25 years, ago. The most important item in the company's expansion program was the purchase in 1945 of an 11 ft 3 in. x 360 ft Allis-Chalmers kiln which had been declared surplus by the Defense Plant Corp. The company is now able to produce about 2,500,000 bbl of cement a year, and employment at the plant is approximately 300. The production of cement has always involved a dust problem, solution of which has been attempted in a number of different ways. By far the most efficient method of catching dust discharge is electric precipitation. Soon after the company went into production in the 1920's, the landowners near the plant began complaining about dust discharge. The company settled the matter by paying them a total of $27,000 for dust damages incurred during the period from 1929 to 1938. In the latter year the two-unit Cot-trell Electric Precipitator shown in Fig. 2 was installed and collected over 85 pct of the dust resulting from operation of the two 11 ft 3 in. x 10 ft x 240 in. kilns. From 1938 until 1946 the landowners registered no objection and were apparently satisfied with that dust recovery. In 1946, however, the substantially higher production resulting from operation of the new kiln immediately overtaxed the facilities of the existing two-unit precipitator. In a short time claims for dust damages were again received from the landowners. The company informed them that because of postwar shortages it would take several years to install a new precipitator. The company stated that it intended to purchase an additional precipitator and offered in the meanwhile to pay the landowners a fair amount to cover their damages. This offer was rejected and the landowners filed suit in the Superior Court of Calaveras County asking for total damages of $120,-338 and for the injunction outlined above. Case for the Ranchers The attorneys for the plaintiffs produced three different types of witnesses: first, the landowners themselves and members of their families; second, other cattle raisers who were sympathetic to the plaintiffs; and third, several types of technical experts: veterinarians, soil chemists, and an aerial photographer. The testimony of these witnesses was designed to establish that the flue dust from the plant had not only damaged the land and the forage, but had also caused fluorine poisoning to their animals. By a combination of these causes, the plaintiffs attempted to prove substantial loss of profits.

Jan 1, 1952

By O. B. Buchlen, J. W. Smith

The Coal Research Bureau of the School of Mines at West Virginia University, using an experimental flotation cell designated an airlift-cyclone was able to obtain a clean coal product containing 7.64% ash with 94% yield and 97% coal recovery. This favorable performance was obtained with the experimental flotation cell operating as a simulated three-stage unit on slurry taken from the fine coal circuit of a coal preparation plant. This experimental device, consisting of a sheet metal cyclone-like unit mounted on a U-shaped uplift pipe, uses a combined flotation and cyclone action to beneficiate the minus 14 mesh partially cleaned feed product. In addition to providing comparable analytical results, the airlift-cyclone possesses other attractive features among them being a low capital expenditure, utilization of moderate plant floor space, efficient operation on high density feed slurry, and absence of moving parts. The primary shortcoming of the experimental cell is its limited capacity. The Coal Research Bureau presently has under construction a larger unit which, it is hoped, will provide the capacity and quality to establish the airlift-cyclone as a commercially feasible unit. Froth flotation of fine coal is a practice which has only recently gained wide acceptance in this country. Various explanations can be put forth for this delayed acceptance of a very selective and efficient system of coal preparation. Among these reasons would be the advent of continuous mining machines resulting in the increased production of coal fines, the change in market patterns from domestic and rail consumers who did not want fines to a predominantly utility market which normally consumes fines, and also the imposition of legal restrictions in regard to stream pollution. However, the major detriment is probably the high cost involved both in installation and operation of the flo- tation unit and auxiliary systems. These facts assume greater emphasis when considering that froth flotation installations normally process a low quality feed product. A recent estimate' of installation costs including dryers, filters, and other auxiliary equipment for a flotation system was $5000 to $7000 per ton of capacity while the operating costs, exclusive of auxiliary equipment, were estimated at 10 to 306 per ton of feed. The Coal Research Bureau of the School of Mines at West Virginia University is currently developing a simplified froth flotation cell, designated an airlift-cyclone, which may provide considerable savings in capital and operating costs without sacrificing product quality or recovery. This experimental cell consists of three primary components: 1) a vertically mounted U-shaped pipe; 2) an air injector device; and 3) an integrally mounted cyclone-like unit (Fig. 1). A feed slurry is introduced at the top of one leg of the U-pipe while compressed air is injected near the base of the other leg. The air serves both to aerate the pulp and to cause it to flow upward into the base of the cyclone unit where the floated clean coal is separated from the reject material and unfloated coal which remains in slurry. The Coal Research Bureau's experimental airlift-cyclone is somewhat similar in principle to a flotation device developed by Russian engineers in the late 1950's. In tests upon a two-stage pilot-size device, the Russians obtained very favorable cleaning efficiencies.' However, later experience with production models demonstrated that rated capacities and acceptable product quality could not always be maintained.3 Because of these limitations, Russian engineers subsequently recommended that conventional, mechanical cells be used when cleaning difficult to float slurries. Engineers at the Coal Research Bureau felt that such a device utilizing the combined actions of a cyclone and a froth flotation machine offered numerous attractive features and merited investigation. Accordingly, a small capacity experimental airlift-cyclone was designed and, with the permission of the Christopher Coal Company Div. of Consolidation Coal Co., installed in Christopher's Humphrey preparation plant near Morgantown, West Virginia.

Jan 1, 1964

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy's law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy's law,

By C. C. Harris

The characteristics of some common size distribution equations are critically discussed. A generalized form of several well-known size distribution equations is obtained from a differential equation describing statistical distributions. The equation contains three parameters and can describe the major features of size distributions in the fine and the coarse size regions. A graphical method for its implementation is provided. The application of this and other equations to sets of data are compared both for the quality of fit and from a comminution kinetics viewpoint. If a narrow size range of a brittle material is broken sufficiently to obliterate the feed sizes, but not so severely that excessive secondary breakage occurs, a plot of cumulative fraction by weight undersize (Y) vs. sieve size (X) on a log log grid (sometimes called the Gates-Gaudin-Schuhmann plot)1-3 gives a straight line of slope ~ 1 over much of its range. On closer inspection, deviations in the extreme coarse range covering perhaps 10 to 30% of the total sample may be apparent (frequently, a change in slope from ~ 1 to a value different from unity) together with over-all slight irregular departures from a smooth line. One model of breakage postulates that the same fracture pattern persists throughout all size ranges.4 The fracture pattern is characterized by the slope of the line on a log log grid. Accordingly, a distribution of sizes broken in the manner specified earlier is expected to produce a size distribution having the same slope as that of a broken narrow size range. Additionally, the slight irregularities mentioned above should even out in the summation process, giving a smooth straight line of slope ~1 on a log log plot. This idealized state of affairs does not, however, describe the distribution of a multi-event process such as that for a tumbling mill product. On the average, these curves (plotted again log log) tend to have a slope in the fine region different from and usually less than unity,5 while the coarse size region curves with increasing slope for cases of mild reduction, and with decreasing slope when moderate or severe size reduction has occurred. In addition, there are usually slight irregular deviations from a smooth curve. Most curves display two distinct regions — fine and coarse — and a few curves show one or more intermediate regions. Feed size studies6,7 show an effect which theory is required to explain. For the same material, mill loading and other operating conditions, and the same time of grinding, plotting the dimensionless ratios Y vs. X/(feed size) does not reduce the size distribution data to the same curve. Y vs. X does not correlate the coarse region, but it can provide a crude correlation of the fine region which improves as size diminishes and as grinding time increases. The size distribution in the coarse region is somewhat more dependent on the feed size than is the distribution in the fine region wherein the degree of dependence diminishes as time proceeds; the distribution of sizes in the fine region are determined largely by the nature of the material and the comminution conditions. A comprehensive model of comminution must recognize that several different patterns or modes of breakage can occur in a mill; 5,8,9 that there can be some selection in that some size ranges are broken more than others; and that, while some particles may be the product of a single fracture event, or may even remain unbroken, others result from multiple rebreak-age. Thus, breakage in a tumbling mill is more complex than the Schuhmann4 model admits in that several different types of comminution micro-events* occur rather than just one type, and these events, though different in size scale, are of the same overall pattern as that which is visualized by the model. The concept of an average comminution micro-event has, therefore, a mathematical rather than a physical connotation, at least for tumbling milling. Equations with which to describe particle size distributions have been sought for over half a century.10-13 No equation presently in general use was first derived from an analysis of the statistical mechanics of breakage; whatever theoretical basis the existing

Jan 1, 1969

By John W. Weeton, Donald W. Petrasek

Relatively few metal-metal systems exist that would permit the creation of fiber-metal composites consisting of mutually insoluble constituents. It is anticipated that most high strength-to-weight ratio and high -temperature fiber composites ultimately to be produced will utilize high-strength fibers embedded in a highly alloyed matrix. An investigation was conducted to determine the effect of alloying on the tensile Properties and micro-structure of tungsten-fibey-reinforced composites. Composites were made of tungsten fibers infiltrated with copper binary alloys that contain elements of varying solubility in tungsten. Room-temperature tensile tests were made on the composites, and a metallographic study of the microstructure of the fiber-metal-matrix interfaces was conducted. It was shown that, as the depth of penetration of some alloying elements into the fiber increased, a decrease in both tensile strength and ductility of the composite results. A notch effect, due to the formation of a brittle alloy zone with the tungsten fiber, was observed and gave rise to greater reductions in tensile properties and ductility behavior than would be Predicted by a law-of-mixture relation alone. In recent years, investigators have considered combining fibrous materials with relatively weak binder materials. The interest in fiber-reinforced composites results from the fact that fibers or wires may be exceedingly strong and exhibit mechanical properties superior to those of the bulk materials from which they are derived. For example, tungsten wires drawn to less than 1 mil in diameter may have strengths of over 600,000 psi,' while steel wires ranging from 10 to 3 mils in diameter may have strengths of the order of 300,000 to over 600,000 psi.2 Both metallic and ceramic whiskers are known to have very high strengths. For example, iron whiskers have been shown to have strengths of 1.9 million psi3 and sapphire whiskers have been reported to have strengths of the order of 1.7 million psi.4 If all or part of the strengths of such fibers could be retained, subsequent to the incorporation of the fibers in an engineering material, a superior material could result. In previous work done at the Lewis Research Center, McDanels, Jech, and weeton5 demonstrated the feasibility of fabricating metal-fiber—metal-matrix composites that utilized the full strengths of the fiber and matrix materials. Tungsten fibers were combined with a copper matrix by a liquid-infiltration method such that the tungsten fibers were uniaxially oriented parallel to the tensile axis of the composite. A linear relation was established that related the tensile strength of the composite with the volume percent of the fibers. Mutually insoluble constituents were selected for the study so that the strength of the composite could be quantitatively related to the strength of the individual constituents. The fact that there are only a few metals that are mutually insoluble with tungsten, e.g., copper, silver, gold, and zinc, and that these either have low melting points, high vapor pressures, or poor oxidation resistance, makes it necessary to utilize other metals that are soluble in tungsten, where high-temperature applications are ultimately contemplated. It was anticipated that, for most practical fiber-reinforced composite materials, it would be necessary to use a fiber and metallic matrix that would have varying degrees of solubility for each other. A logical extension of the earlier work was thus felt to be a study that would determine the effects of elements that had mutual solubility with the tungsten. Numerous investigators have found that tungsten fibers may be damaged by thermal treatments or contamination of the surface of the fiber by alloying elements.6-10 On the other hand, surface treatments may improve the strength of such fibers."-" Relatively little work with composites containing tungsten fibers have been reported. The work of parikh14 has shown that kinked, short-length tungsten, steel, and molybdenum fibers could str'engthen such matrices as silver, gold, and copper. Some of the combinations of fibers and matrices studied by

Jan 1, 1964

By A. L. Barnes

Residual oil in watered-out reservoirs is a tremendous reserve which has been unrecoverable by established production methods. A study of the new recovery methods indicated that the forward combustion urocess might- recover oil from such reservoirs; however, no thermal recovery operating experience in a watered-out system was available. The Delaware-Childers pilot thermal test was undertaken to test the feasibility of thermal recovery in this watered-out reservoir. The pilot test consisted of a 2.22-acre, inverted five-spot in the 600-ft deep Bartlesville sand. The reservoir in the pilot area had a porosity of 20.6 per cent, a permeability of 118 md and an average sand thickness of 45 ft. The reservoir contains a 33' API, 6-cp oil. Combustion was started Nov. 22, 1960. The initial air injection capacity was 750 Mscf/D, but it was eventually increased to 2,000 Mscf/D. The test was surrounded by an active water flood; therefore, water production was initially high, but decreased as the heat wave moved toward the producing wells. Oil-bank arrival at an individual well was indicated by a drop in GOR and WOR, and an increase in oil production. Combustion-front arrival was evident at three of the pilot producers, and they were plugged. Cumulative oil production from pilot area wells war over 12,000 bbl. Operational difficulties were negligible and only conventional equipment was necessary. The combustion efficiency of this test averaged over 80 per cent. Results from coring showed that the leading edge of the combustion front tended to be wedge-shaped but a nearly complete sweep of the reservoir was eventually obtained. An isopach map based on evidence from 10 core holes and the existing wells showed that 126 acre-ft had been swept by the heat wave. Using this swept volume, an air requirement of 15.7 MMscf/acre-ft was calculated. It was calculated that 275 ,STB/acre-ft was consumed bv the heat wave. INTRODUCTION There is a large amount of oil remaining in reservoirs that have been water flooded. A study of ways to recover this oil showed that the forward combustion process might be applicable. Results from a number of forward combustion tests have been reported in the literature, but none of these tests were conducted in a watered-out system. The Delaware-Childers pilot thermal test was initiated in 1960 to define the operating characteristics of underground combustion in this watered-out Bartlesville sand reservoir, The purpose of this paper is to present the pilot test results in detail. FORWARD COMBUSTION PROCESS The forward combustion process consists of initiating combustion in the formation surrounding an injection well and driving this heat wave through the formation toward offset producing wells. As the combustion front progresses through the reservoir, oil and formation water are vaporized, driven forward in the gaseous phase, and recon-densed in the cooler part of the formation. These distilled liquids, water of combustion and gaseous combustion products, form a bank or three-phase region ahead of the burning front. This bank pushes mobile reservoir fluids toward the production wells. The rate of movement of the combustion front is controlled by the rate at which the nondistill able residue which serves as process fuel can be completely burned off the sand. The production performance from a heat wave conducted in a watered-out oil reservoir will differ from one conducted in a dissolved gas-depleted reservoir because of the difference in fluid saturations. The primary depleted reservoir contains connate water saturation, relatively high oil saturation and some gas saturation. The watered-out reservoir contains a highly mobile water saturation, residual oil saturation and little gas saturation. As the combustion front moves forward in either type of depleted reservoir, it drives the distillable oil, the water in place and the water of combustion ahead, and burns the nondistillable portion of the oil. The heat-wave process in a watered-out reservoir differs from the process in a

Jan 1, 1966

By N. J. Themelis, P. Spira

The efficiency of the reverberatory furnace operation in producing. slags of 1020 copper content depends on the mixing and flow conditions in the bath. Radioactize-tmcer tests have indicated the jkaction of bath volume engaged inflow and the mixing conditions in the bath. The factors controlling the flow pattern of slag have been classified as laminar transfer flow, natrsral convection, and flou, due to the rapid addition or removal of slag.. Similarity criteria for model studies have been developed. The pyrometallurgical processing of copper begins with the smelting of either flotation concentrates, or direct-smelting ores which have been partially roasted to calcines. These materials are generally smelted in a reverberatory furnace, Fig. 1, and separate into two liquid phases, a sulfide matte and an iron silicate slag. he matte is tapped and subsequently reduced to metallic copper in a converter, while the reverberatory slag is usually discarded without any further treatment. Molten slag from the converting operation is returned intermittently to the reverberatory in order to recover its high copper content (1 to 3 pct Cu). The reverberatory furnace is about 115 ft long by 30 ft wide. In general, the solid charge is fed at intervals through openings along the sides of the roof and forms sloping banks from which the molten materials trickle down into the bath; the charge banks extend over a length of about 70 ft from the firing wall. The depth of the slag and matte layers varies from smelter to smelter; in the Noranda furnaces, the slag depth is 24 to 30 in., while the depth of matte at the taphole is about 20 in. Apart from smelting, the functions of the reverberatory are to recover most of the copper content in the converter slag by physical and chemical interaction with the furnace bath, and to provide adequate time for optimum separation between matte and slag. The efficiency of these operations depends on the mixing and flow conditions in the bath and is reflected on the copper losses in the slag. In the present study, the reverberatory furnace is considered as an open-channel chemical reactor and the driving forces for material transport through the bath are examined by means of flow and mathematical models. FLOW CONDITIONS IN THE REVERBERATORY FURNACE To facilitate the study of mixing conditions in continuous-flow reactors, two idealized patterns of flow have been accepted by workers in this field.' The term "backmix" flow is used to describe complete and instantaneous mixing in the reactor (perfect mixing); all particles have the same chance of leaving the system, independently of their time of entrance, and the fluid is uniform in composition throughout the vessel. On the other hand, "plug" flow, or "piston" flow, assumes that a fluid element moves through the reactor without overtaking or mixing with fluid entering at an earlier or later time. In addition to the two idealized patterns of flow, "deadwater" flow accounts for that portion of the fluid which is moving so slowly that it may be assumed to be stagnant. According to the definition by evensppiel,' the cut-off point between active and stagnant fluid may be taken as material which stays in the vessel for a period twice the mean residence time. The flow patterns in real vessels may be approximated by a combination of the above flows. Thus, the vessel is assumed to consist of interconnected flow regions with various modes of flow existing between them. The flow pattern may be determined directly from the flow paths of fluid through the essel. -However, the difficulty of obtaining and interpreting such information has led to the alternate approach of determining the residence time distribution of fluid elements by means of stimulus-response studies. The stimulus is provided by introducing a tracer in the inlet stream and the response by the record of the change in tracer concentration in the exit stream from the reactor. Such tests have been conducted in glass tank furnaces using either chemical7"9 or radioactive tracers1'-'' and, in one case, experiments have been reported for a metallurgical furnace.'"

Jan 1, 1967

By M. C. Flemings, G. E. Nereo

General expressions are given to describe macro-segregation in castings and ingots which results from mass flow of solute-rich liquid to feed solidification and thermal contractions. Analytical solutions are given for solidification with planar isotherms (unidirectional and bidirectional heat flow). These solutions describe inverse segregation and centerline segregation. Numerical examples are given for A1-4.5 pct Cu alloy. In 1540, Vannoccio Biringuccio published one of the first references to macrosegregation, describing the problem of exudation and inverse segregation in the manufacture of bronze gun barrels.' Since then, a great many studies of macrosegregation have been reported. Recent work of particular engineering interest includes that of Marburg 2 and others:" on centerline segregation and other types of segregation in large steel ingots, and work of Adams,5 Scheil, 6 and Kirkaldy and youdelis7 on inverse segregation in nonferrous ingots. In most studies on this subject, the various types of macrosegregation have been treated as separate phenomena. For example, quite different mechanisms have been proposed for formation of centerline segregation, negative cone of segregation, inverse segregation, banding, and so forth. In this, and in several papers to follow, it is proposed that these as well as other types of macrosegregation result from the same basic mechanism and can be quantitatively described by the same basic equation. It has often been suggested that some types of segregation (such as centerline segregation and banding) occur as a result of buildup of solute at the tips of growing dendrites.2-4 ,8-10 As example, banding can be induced in centrifugal castings by mechanical vibration, and Northcott 10 suggests this might be due to the influence of the vibration on the boundary layer at the dendrite tips of the growing dendrites. However, in view of the extremely small boundary layer known to exist at the tips of the dendrites,11,12 any interpretation of macrosegregation based on this boundary layer is clearly incorrect. Note that experiment has shown that significant buildup of solute does not occur at dendrite tips in ingot solidification, but even if such buildup occurred the thickness of the enriched zone would only be the order of D/U where D is liquid diffusion coefficient and U is dendrite tip velocity. For usual casting or ingot solidification this solute-enriched layer is 10"3 cm, far too small to account, for example, for centerline segregation.11'12 It has also been suggested that convection in the bulk liquid (ahead of the advancing dendrites) might cause segregation by sweeping away the solute-rich boundary layer in front of the dendrites.3 However, since there is no significant boundary layer, this explanation must be incorrect. The convection might directly cause segregation by penetrating between the dendrite arms, and presumably in a rimming steel ingot it is sufficiently vigorous to cause some segregation in this way. Centerline segregation, however, cannot be interpreted as resulting from this convection since a sharply segregated zone is usually found near the centerline, with the bulk of the ingot being nearly of nominal composition. If convection in the bulk liquid were the direct cause, a gradual change in ingot composition over the entire cross section would be expected. It is known that sudden changes in convection of the bulk liquid during solidification can result in banding,14 but it is not clear that the banding results directly from the effect of convection on solute distribution. Changes in convection also affect thermal conditions in the liquid-solid region of a solidifying ingot. It will be seen later in this paper, and in a paper to follow, that macrosegregation is strongly influenced by these thermal changes. Recognizing that in some cases of ingot solidification (as in solidification of rimming steels) convection in the bulk liquid may have a direct effect on solute distribution, we neglect it in this paper and in the several to follow. We then derive general expressions describing macrosegregation which results from the mechanism of interdendritic flow of solute-rich liquid

Jan 1, 1968

By Milton E. Wadsworth, R. Ted Wimber

Cobalt sulfate solutions containing ammonium acetate and chloroplatinic acid were reduced by hydrogen in a pyrex-glass lined autoclave in the temperature range of 170o to 232°C and hydrogen partial pressure range of 115 to 830 psia. The reduction rate was directly proportional to the hydrogen partial pressure and surface area of the pyrex glass and was independent of the quantity of chloroplatinic acid added initially. Experiments involving the variation of the relative concentration of ammonium acetate indicated that the reducible cobalt complex was probably the diacetate complex of cobalt, Co(AC)4H20, or a new mononcetate complex Co Ac, which was in solubility equilibrium with a pink precipitate of CO(AC)-4HzO. THE reaction in which a metal is dissolved by an acid to produce gaseous hydrogen and a salt solution was discovered early in the history of chemistry. In 1859 Beketoff found experimentally that this reaction could be reversed; i.e., a salt solution could be reduced by gaseous hydrogen to produce a metal and an acid. A review of work done on this phenomenon since that time may be found elsewhere., The hydrogen reduction of a cobalt salt solution is facilitated by complexing the cobalt ion. An ammonia complex of cobalt has been reduced commercially in the recovery of cobalt metal. A new reducible complex of cobalt was discovered5 when it was found that a co-baltous sulfate solution containing ammonium acetate could be reduced by hydrogen at temperatures in the region of 200°C. When a cobalt sulfate-ammonium acetate solution was heated to a temperature below its normal boiling point, a violet color became apparent, indicating complex formation. The nature of this complex was investigated5 by the addition of NH4Ac to a CoSO4 solution maintained at 85o. During the first additions of NH, Ac, the pH of the solution remained fairly constant at about 5.85. However, as the ratio of NH,Ac to CoSO, approached two, the pH rose and then leveled off at about 6.05. The absorption spectra of a Co(Ac), solution and a CoSO,, NH Ac solution were obtained at 85°C and were compared and found to be the same. These findings suggested that the diacetate complex of cobalt, Co(Ac),.4H20, was formed at 85°C. When a cobalt sulfate-ammonium acetate solution was heated to a temperature above about 165o, a finely divided pink precipitate appeared. The X-ray diffraction pattern of this precipitate indicated that it was Co(Ac), - 4H,O. In addition, it was discovered that when chloroplatinic acid, H,PtCl;, was added initially to the cobalt sulfate-ammonium acetate solution, a faster reduction was obtained. The roles of the solution complex, pink precipitate and chloroplatinic acid in the reduction process were then investigated. APPARATUS The experimental work was carried out in a two-liter stainless-steel autoclave. Adetailed description of the autoclave and the auxiliary equipment used in maintaining constant temperature and pressure may be found elsewhere.= Because the stainless steel was corroded, and also because it acted as a hydrogena-tion catalyst, an all-glass liner was fabricated such that the solution came only into contact with flame-polished pyrex glass. EXPERIMENTAL PROCEDURE The solutions used in the experimental work were prepared by dissolving reagent grade chemicals in distilled water. Although variation of the brand of ammonium acetate appeared to have no effect on the experimental results, CoSO, 7H O from the J. T. Baker Chemical Co. of Phillipsburg, N. J.,was found to give faster reductions than that prepared by Allied Chemical and Dye Corp., N. Y. The former was used throughout the course of the experimental work and was weighed up at the outset of each experiment. The ammonium acetate was dissolved to form a 6M stock solution, which was stored under refrigeration. A 10 pct solution of chloroplatinic acid (J. T. Baker Chemical Co.) was diluted to a 1.15 x 1Q2 M stock solution, which was standardized by precipitation of K,PtCl, as outlined by Scott. The appropriate volume of the chloroplatinic acid, H,PtCl,, solution was pipetted into the clean, dry glass liner. The cobalt sulfate-ammonium acetate solution, which had previously been saturated with

Jan 1, 1962

By Carl F. Lutz, Robert F. Mehl

A layer of brass was formed on 0 brass using a vapor-solid reaction technique. The variation in composition with distance within the phase layer and across the a -ß interface was determined by an electron probe. The diffusivities were calculated as a function of concentration; the diffusion coefficient in brass was found to change by a factor of twenty-five over a compositional range of 8 at. pct. An explanation is proposed to account for the large change in the diffusivity, based on possible stresses in the diffusion zone; it is suggested that the concentration dependence of the thermodynamic factor might decrease the activation energy with increasing zinc content. ALTHOUGH the body of data on diffusion coefficients (D- values) in terminal solid solutions and in isomorphous systems is quite large, there is but little quantitative information for intermediate alloy phases. This paper recounts measurements of D-values for the ? phase in the Cu-Zn system. The experimental method employed consists in the forming of alloy layers and determining and analyzing the concentration-distance (c-x) curve. The experimental method employed could have been applied to several systems; the Cu-Zn system was chosen because the D-values in the a and ß phases are well known, and can thus be used for purposes of comparison. The rates of growth, of intermediate alloy layers are known for a number of systems. In nearly all cases the thickness varies parabolically with time, as to be expected if the rate of growth is controlled by the D-values. In a few cases, nonparabolic behavior has been noted.1 Nonparabolic growth may be the result of a) a variation of the composition at the phase interface with time, b) interface-controlled kinetics, c) short diffusion times coupled with long vacancy lifetimes (in vacancy diffusion),2 and d) crystal reorientation during diffusion in anisotropic systems.3 In the Al-Ni system4 and in the Al-u5 system parabolic growth kinetics are slowly approached after an initial transient period. In general those phases stable at a given temperature in a system A-B appear as separate phase layers when A and B are put in contact and given a diffusion he at-treatment. In most cases the compositions at the interface of adjacent phase layers are those read from the phase diagrams for the termini of the respective phases. This discontinuity in concentration is taken as independent of time, and the growth of one phase at the expense of another is assumed to be independent of interface kinetics, i.e., the rate of interface movement is controlled by volume diffusion in the phases concerned. wagner6 has given many solutions for multi-phase diffusion processes, assuming that the chemical diffusion coefficient, D, is independent of concentration, as have others. Jost7 has pointed out that the familiar Boltzmann-Matano solution is as valid for a (c-x) curve exhibiting concentration discontinuities at phase boundaries as for the usual single-phase case. Heumann and associates8,9 have applied this solution to the multi-phase case, but lacking concentration data within the several layers were forced to assume linear concentration gradients, thus calculating only average D-values. The purposes of the present study were: 1) to determine the dependence of D on concentration, 2) to calculate the intrinsic diffusion coefficients D?Cu and D?Zn, 3) to establish the time-law for the movement of the interface, 4) to determine the concentration limits at the ß-? interface, and, 5) to attempt to clarify the mechanism of diffusion. EXPERIMENTAL PROCEDURE The ? phase is exceedingly brittle; conventional solid couples and conventional sectioning methods were thus inapplicable. Vapor-solid couples were accordingly employed. Unfortunately the equilibrium vapor pressures of Zn for the ? phase are unknown; to escape this awkwardness, samples were enclosed in a capsule containing powder of an alloy of known composition, sufficiently large in quantity as to be effectively an infinite source, maintaining the concentration of Zn at the sample surface constant with time. The sources of Zn-vapor which can be employed in reaction with Cu, or a brass, or ß brass, to form a layer of ? brass satisfactorily wide in concentration range, are alloys of the phases ?, or ? + E or ? + d (depending on the temperature).

Jan 1, 1962

By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By Mayumi Someno, Kazuhiro Goto, Masahiro Kawakami

The apparent rates of decarburization of liquid alloys of Fe-C, Fe-C-S, Ni-C, and Co-C systems and the rate of oxidation of solid graphite with pure carbon dioxide gas and with gas mixtures of carbon monoxide and carbon dioxide have been measured in the temperature range of 1000° to 1600°C. The cotnposition of carbon dioxide and carbon monoxide gas at the reaction surface has been measured by oxygen concentration cells with the ZrO,-CaO solid electrolyte. 1) The apparent rates of the carbon removal are essentially the same for all the cases of solid graphite, Fe-C, Fe-C-S, Ni-C, and Co-C systems under the same experimental conditions. 2) The apparent rates are independent of the carbon content in the high carbon concentration range but very much affected by the flow rate and the gas composition of the CO-CO2 reactant gas mixture. The ratio of the gas consumed by the reaction to the total quantity of the supplied gas is very large under the present experi~nental conditions. 3) There is a concentration gradient of' carbon dioxide in the vicinity of the reaction surface and the content of CO, becomes extremely small at the reaction surface. 4) A large time fluc-tuation of the gas composition was observed. This jluctuation implies the presence of unstable flow in the gas phase in the vicinity of the reaction surface. THE decarburization of molten steel by an oxidizing gas or by slag may be one of the most important chemical reactions in steelmaking processes. Nevertheless, the kinetics of this heterogeneous chemical reaction do not seem to be well-solved even with the previous studies. Although the conditions for the reaction in steelmaking processes are quite different from those in the laboratory scale, some critical experiments may give information on the mechanism of the decarburization. From the previous work,'-' it is known that the rate of the decarburization is independent of the carbon content in liquid iron with more than about 0.2 wt pct C when the oxidizing gases are supplied to the surface of liquid Fe-C alloys on a laboratory scale. Two rate-controlling steps have been proposed for the decarburization of liquid iron with the high carbon content: one is the surface reaction control proposed by Swisher and Turkdogan;' the other is that the rate is controlled by the gaseous diffusion through the gaseous stagnant layer. proposed by Baker. Warner, and Jenkins.7 and also by .Ito and Sano.2 In the present study, some experiments have been carried out for the evaluation of these rate-controlling steps in the decarburization of liquid iron with high carbon content. The apparent rate of decarburization of liquid iron has been compared with the rates of carbon removal of liquid Ni-C, Co-C, and solid graphite under the same experimental conditions. The composition of carbon dioxide and carbon monoxide gas at the reaction surface has been measured by oxygen concentration cells. I) EXPERIMENTAL PROCEDURE Fig. 1 shows the schematic diagram of the reaction chamber. Solid graphite and liquid metals were contained in an alumina or magnesia crucible of 32 mm ID and 35 mm in height. The samples were heated by high-frequency induction and the temperature was measured by the calibrated optical pyrometer. The temperature was held constant to within 10°C. The re-actant gases were supplied to the surface of the samples through the quartz tube of 8.0 mm ID. The distance from the end of the quartz tube to the surface was 20 mm. The block of high-purity graphite was cut and shaped to the inner profile of the crucible. The height of the shaped graphite was 18 mm, which corresponded to the depth of the liquid iron of 100 g. About 100 g of Fe-C alloy (4.20 to 4.40 pct C), Ni-C alloy (1.84 pct C), Co-C alloy (1.85 pct C), and Fe-C-s alloy (4.35 pct c, 0.5 or 1.0 pct S) were melted in the crucible. The reactant gases were pure CO, and gas mixtures of CO-CO,: the flow rates were controlled by capillary flowmeters with bleeders.

Jan 1, 1970

By P. G. Shewmon

Radioactive MgZA has been used to study the rate of self-diffusion in oriented single crystals of magnesium in the temperature range 468O to 635OC. The diffusion coefficients parallel and perpendicular to the c-axis are: Dl, = 1.0 exp (—32,200IRT) cm2 per sec and Dl = 1.5 exp (—32,500IR T) cm Qer sec. The ratio Dl/Dll was found to vary from 1.13 at 468 to 1.24 at 575 C. Assuming a vacancy mechanism, an explanation of this aniso-tropy of diffusion follows from a consideration of the difference in the saddle points for diffusion in and out of the basal plane. RECENT discovery of radioactive Mg2"'-' has made possible the study of self-diffusion in magnesium. The experimental procedure and the results of a study of diffusion in polycrystalline magnesium have been described in an earlier paper.V he present work is an application of the same techniques to the study of self-diffusion in oriented single crystals of magnesium. In the general diffusion problem the diffusion coefficient is a second order tensor relating the two vectors, the diffusion flux, and the concentration gradient. In a hexagonal lattice, such as magnesium, the complete determination of the diffusion coefficient D as a function of direction in the lattice requires a knowledge of D,, and D,, i.e., the diffusion coefficients parallel and perpendicular to the c-axis, respectively. It can be proven quite generally that in a hexagonal lattice D is independent of direction in the basal plane, and that out of the basal plane it varies with 0, the angle between the c-axis and the direction of diffusion, according to the equation D(B) = D,,cos2B + D,sin2B. [I] The proof of Eq. 1 depends only upon the symmetry elements of the hexagonal lattice and upon the transformation properties of a second order tensor." Therefore, Eq. 1 holds for any mechanism of diffusion and any c/a ratio. Experimental Procedure The experimental procedure used with polycrystalline specimens can be briefly outlined as follows. Radioactive Mg" was produced by bombarding a NaCl crystal with 350 mev protons and was chemically separated from the target as MgO. The Mg" was then vapor deposited on a specially cleaned magnesium specimen by heating the MgO on a tantalum ribbon in a vacuum. During the diffusion treatment, oxidation and vapor loss of the radioactive material were minimized by annealing the samples in pairs with the active faces in contact, each pair being inside a magnesium container, which was in turn surrounded by an argon atmosphere in a sealed Pyrex tube. The distance-activity profiles were obtained by measuring the activity of thin sections cut parallel to the original interface with a lathe. The only technique which was peculiar to this work was the preparation and orientation of the single crystal specimens. The single crystals used in this work were grown by E. C. Burke of the Dow Chemical Co., using a modified Bridgman method, in which the furnace and specimen were stationary while the temperature gradient moved.' In growing these crystals the starting material was distilled magnesium, the crucibles were machined from Acheson electrode graphite, and the furnace atmosphere was tank argon. The crystals were grown from sublimed magnesium with the following analysis: 0.0002 pct Al, 0.0017 pct Fe, 0.0009 pct Mn, 0.0001 pct Ni, 0.0006 pct Pb, and less than 0.01 pct Ca, 0.0001 pct Cu, 0.001 pct Si, 0.001 pct Sn, and 0.02 pct Zn. The two crystals used were roughly lh in. diam and eight in. long. The c-axis made angles of about 7" and 78", respectively, with the specimen axes. If the values of D obtained by the use of these two crystals are taken equal to D,, and D,, respectively, the error introduced by this assumption is less than 1 pct. This can be shown by combining Eq. 1, the identity sin% + cos'8 = 1, and the experimental fact that DJDn in magnesium was always less than 1.25.

Jan 1, 1957

By M. A. Jones

Performance of a pilot flood in eastern Kansas indicates improved recovery and accelerated production resulting from mobility ratio control obtained by adding a high moleculur weight polymer to injected water. Ultimate pilot flood recovery of the 75-cp reservoir oil is anticipated to he 350 bbllacre-ft during the six-year flood life. Cumulative recovery to date totals 242 bbl/acre-ft after 30 months of injection. Reservoir parameters and flood performance are disc~rssed in detail to provide a case history relating to the feasibility of polymer flooding. INTRODUCTION The Vernon Polymer flood of the Brazos Oil & Gas Co., located in Sec. 2, 24 S., 16 E., Woodson County, Kans., was begun in late Oct., 1963. Injection of a 500 ppm solution of Pusher* polymer was initiated in a 15-acre pilot to determine feasibility of improving oil recovery by mobility ratio control. Performance to date and the anticipated recovery of 115,000 bbl from the 329 acre-ft pilot indicate efficient displacement of the viscous reservoir oil. Dependence of flood recovery on the displacing fluid-displaced oil mobility ratio has long been recognized. Displacement efficiency of the reservoir oil decreases with increasing mobility ratio. Therefore, economic reduction of this parameter is an attractive approach to improving oil recovery. particularly from viscous oil reservoirs where mobility ratios are often quite high. Waterflood mobility ratios can be controlled by dilute solutions of certain polymers'; which provide a displacing fluid with considerably reduced mobility. Reservoir parameters and flood performance are emphasized in this paper to provide data relating to polymer flood applicability. THEORY The polymer used in the Vernon pilot exhibits the property of unusually high resistance to flow through porous media.'.' A small concentration in injected water effects a mobility reduction considerably beyond that predicted from increases in bulk viscosity as measured in a capillary or rotating cup viscosimeter. Water mobility in the subject flood is reduced by a factor of 7.55 with the addition of 500 ppm Pusher chemical to injected water while the bulk viscosity is increased from 1.03 to only 1.40 cp at 75F. The exact flow mechanism causing resistance to flow has not been established; however, it is observed only in tortuous flow systems and appears to be influenced by brine properties, rock properties and oil saturation. Consequently, mobility reduction is estimated from flow studies for a given sample of reservoir rock and is expressed in terms of a "resistance factor".' This parameter is defined as the ratio of brine mobility to polymer solution mobility measured at residual oil saturation: RF= ?m/?p= (km/µm)/(kp/µp)M.......(1) where RF = resistance factor (dimensionless) k*. and A, = mobility of water and polymer solution, respectively k,,, and k,, = water and polymer permeability, respectively (darcies) µie and µp = viscosity of water and polymer, respectively (poise). Eq. 1 is similar to the expression commonly used to relate the relative mobility of the water bank at residual oil saturation to oil-bank mobility at irreducible water saturation: where M =mobility ratio of water to oil (dimension-less) A, = mobility of oil k, = permeability to oil (darcies) )i* = oil viscosity (poise). From Eqs. 1 and 2 it is apparent that the polymer-solution-to-oil-mobility ratio can be approximated by dividing the brine-to-oil ratio by the resistance factor RF: Mpn=M10/RF...........(3) where M,-, = mobility ratio of polymer solution to oil (dimensionless). This simplified presentation assumes no dilution of the polymer solution by connate water. Also, the presence of a connate water bank separating the polymer solution from the displaced oil is not considered. Displacement of oil by waterflooding is increasingly dominated by viscous forces as the viscosity of the oil displaced increases. When the oil mobility is less than that of the injected water, the oil-water interface is not a piston-like front.3,' Instead, instabilities occur at the flood front in the form of viscous fingers which tend to penetrate the less mobile oil bank. The magnitude of these protrusions, or the degree of channeling, increases

Jan 1, 1967

By M. W. Burkart, B. Lustman

Uranium-base alloys exposed to high temperature water fail either by uniform oxidation or by sudden cracking and disintegration of the metal. The disintegration results from the oxidation of a second phase which is precipitated during the corrosion process. The precipitate has been identified as a metastable hydride of uranium. URANIUM-BASE alloys consisting of the body-centered-cubic ? phase are susceptible to two different modes of corrosion failure when exposed to high temperature water. In the first process, a smooth oxide film is formed on the metal surface which continually flakes off during exposure and results in a uniform weight loss of the specimen. The oxide is present as a thin, adherent layer whose thickness remains approximately constant. As the metal oxidizes during corrosion, a nonadherent layer is built up on this film and continually sloughs off. Coincident with the uniform corrosion just mentioned, another process occurs which eventually leads to failure of the metal by cracking and general disintegration. The failure takes place during a relatively short time compared to the total exposure. To distinguish this type of failure from the uniform corrosion, the cracking or disintegration of the metal will be referred to as discontinuous failure. For the ? phase uranium alloys it is discontinuous failure rather than uniform corrosion that limits the useful corrosion life of the alloy. This paper will be concerned primarily with the mechanism of discontinuous failure. Physical Changes During Corrosion—The alloys used in this investigation were ? phase uranium alloys containing 7 to 12 wt pet Mo or Cb. The preparation of the alloys, the method of corrosion testing, and the actual corrosion results are presented in another paper.' The ? quenching treatment consists of annealing the alloy for 24 hr at 900°C in a sealed Vycor glass tube filled with helium and then water quenching to room temperature without breaking the tube. The corrosion behavior typical of a ? phase uranium alloy is shown in Fig. 1. This specimen was a U-12 wt pet Mo alloy tested in pressurized, degassed water at 650°F. The corrosion rate was practically constant at 0.28 mg per sq cm per hr or increased slightly until about 15 to 20 days of exposure, when the onset of discontinuous failure occurred in this particular sample, and the specimen soon began to crack and disintegrate. The simultaneous increase in the observed corrosion rate is a result of the increased area of exposure due to cracking of the specimen. The microstructure of a specimen that failed by cracking is shown in Fig. 2. The presence of a plate-like precipitate can readily be seen. Metallographic examination of corrosion specimens reveals that the onset of discontinuous failure is always preceded by the formation of a plate-like second phase in the ? uranium matrix. Hydrogen analyses of specimens periodically withdrawn from corrosion test reveal that the hydrogen content of the alloy increases on exposure to the high temperature water, as shown in Fig. 3. The hydrogen is available as a corrosion product resulting from the formation of UO2 by the reaction of the alloy with water. Specimens analyzed just prior to discontinuous failure contained as much as 1200 ppm H, whereas the plate-like phase appears to precipitate out at a hydrogen concentration of between 10 and 25 ppm. The observed increase in hydrogen content prior to and during the formation of the plate-like precipitate suggests that this constituent may be a hydride of uranium. Additional evidence linking the identity of this phase to a hydride is that it can be removed by vacuum annealing at temperatures of 100°C and above. Decomposition products of the ? phase would certainly not dissolve at such temperatures, nor could other likely products of corrosion, such as oxides, be dissipated at any of the test temperatures. The precipitation and growth of the second phase during corrosion is accompanied by an increase in hardness of the specimen. The hardness increase results from the dispersion of the harder precipitated

Jan 1, 1959

By S. R. Titley

The recent emphasis placed upon the use of molybdenum as a geochemical indicator has stimulated considerable inquiry into the behavior of molybdenum in the zone of oxidation. This paper represents a summary of recent and continuing experimental work and calculations in an investigation of a portion of the system Mo-Fe-S-H20 and treats the stability of various iron and molybdenum compounds with respect to oxidation potential and pH. Using experimentally determined free energy values for ferrimolybdite, diagrams of the stability fields of this mineral have been calculated with respect to ilsemannite (?), molybdenite, pyrite and limonite. This theoretical approach is the one utilized by Garrels3'4 in studies of the relationships of various minerals in the zone of oxidation. Use of this approach is particularly suited to the study of geochemistry in the zone of supergene processes because of the low temperatures, low pressures and other relatively easily determined and duplicated factors that exist in the near surface environment. Such a study of molybdenum, however, is complicated by several factors. One of these is the fact that the strong amphoteric behavior of molybdenum makes possible a wide variety of substances and complexes whose exact chemical natures are unknown. The second factor is the dearth of thermodynamic data for many of the simplest of the possible compounds and ions important to the study. For the purpose of this study, the problem of complexes has been approached through considering only the simpler possibilities realizing that the complexes and systems so treated may be gross oversimplifications. All the complexes considered, however, have been suggested in the chemical 2,7,9,12 or geologi-cal literature. EXPERIMENTAL WORK Studies of the behavior of molybdenum ions and ferrimolybdite have been carried out in aqueous sys- tems, and reactions have been followed by simultaneous measurement and recording of pH and oxidation potential. A major problem involved in this study was the long periods of time necessary for equilibrium to be established in some of the systems considered; in a few instances, these periods exceeded four weeks, that is, four weeks during which measured conditions changed continuously. Another problem, in some instances, was the indeterminate nature of the reactions that have taken place. Because of the tendency of molybdenum to complex, reactions which take place under some of the more extreme imposed conditions of oxidation and acidity or alkalinity are unknown. However, useful data for the present work were obtained from studies of the molybdate ion and ferrimolybdite between pH 2 and 8 and under only moderately oxidizing to nonoxidizing conditions. Instruments used in the experiments were a Hewlitt-Packard Model 412A VTVM, a modified Beckman Zeromatic pH Meter and two Varian model 11 recorders. pH was measured between glass and calomel electrodes and Eh was measured between calomel and platinum electrodes. Conditions of pH were varied with 1N H2SO4 and 1N NH4OH and 1N NaOH. Eh was varied with gaseous nitrogen, oxygen or aqueous H202. Ambient temperature was essentially uniform at 24ºC and was increased in the reaction vessel by the positioning of a magnetic stirrer whose temperature was sufficient to bring the temperature to 2S°C in the reaction. The temperatures of reaction did not vary more than 1/2ºfrom 25°C. Two reactions were investigated, the ferrimolybdite-limonite-water reaction and the reduction of molybdate ion. Studies of both reactions yielded useful data that were used in preparation of the Eh-pH diagrams. The traces of the reactions are shown on Fig. 1. Ferrimolybdite-Limonite- Water: Studies of this reaction involved analysis of the solution of ferrimolybdite and simultaneous formation of ferric hydroxide. The data are summarized on Fig. 1. In this reaction, equilibrium was attained at various pH's when coexistence of the two solid phases (ferrimolybdite and ferric hydroxide) was attained. At the proper pH, controlled by the amount of ferrimolybdite and thus the dissolved content of molybdate species, both phases were observed and reaction times to complete the transition were on the order of weeks. The reac-

Jan 1, 1963