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By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By G. M. BUTLER

TWENTY-ONE of the states in the Union, the Territory of Hawaii, and seven provinces of Canada now have in operation laws requiring that professional engineers be registered or licensed. In addition, two states require that civil engineers be registered, and one other state demands registration of structural engineers. Moreover, nearly every year sees additions made to the list. The registration movement, fostered by the American Association of Engineers, now has the powerful, energetic backing of the An1,erican Society of Civil Engineers, which is itself now fostering registration legislation, and there is a strong sentiment in favor of registration in the American Institute of Electrical Engineers and the American Society of Mechanical Engineers. Only in the American Institute of Mining and Metallurgical Engineers is anti-registration sentiment, strongly dominant, but many members of this organization are enthusiastic advocates of registration.

Jan 1, 1930

By Thomas V. Falkie, Robert Stefanko

Recently The Wall Street Journal featured a series of articles titled "The Dirty Work-Brutal, Mindless Labor Remains a Daily Reality for Millions in The US.-Mining Coal, Shoveling Slag, Gutting Hogs Pays Bills But Can Drain Spirit, Hope." The article was devoted to describing how tough and dangerous is mining (and some other jobs) and how rough life is for miners and their families. Similarly during the past few years some psychiatrists and sociologists have devoted increased attention to the attitudes and life styles of miners. Unfortunately most of their approaches have been neither scientific nor objective, and very little good clinical research has been done on the subject.

Jan 1, 1971

By Paul Averitt

The U. S. Geological Survey has been actively engaged in work on coal for more than 50 years. During this long period we have released more than 300 publications containing information about coal and coal reserves, including details on the thickness, distribution, and quality of coal, and the structure and stratigraphy of the coal-bearing rocks. We have also cooperated with state surveys on many similar publications. For many areas these reports are the only reliable published data on our resources of coal. During the last several years we have substantially increased our activities above the wartime low. We now have field work in progress, or reports in preparation, on 13 detailed mapping projects distributed as follows: 1. Pennsylvania anthracite field 2. Casselrnan Basin, Md. 3. Leslie County, Ky. 4. Deep River field, N. C. 5. Coosa field, Ala. 6. Powder River field, Mont. 7. Spotted Horse field, Wyo. 8. Yampa field, Colo. 9. Paonia field, Colo. 10. Trinidad field, Colo. 11. Durango field, Colo.

Jan 1, 1949

By Sherwin F. Kelly

FRONTIERS of geological knowledge retreated further this past year before an ever-widening geophysical attack, as governments and endowed institutions continued to take an increasing practical interest in the geophysical line of approach to the study of earth phenomena. A year ago I opened this annual review with a brief account of the efforts to discover what formations lie concealed beneath the deep sediments which form the superficial portions of the Continental Shelf off the eastern United States. That work was but the beginning, and 1938 saw its continuation and expansion. With the assistance of a Guggenheim Fellowship, Maurice Ewing pushed his researches in the development of instruments and techniques for deep-sea seismic refraction studies. Ewing&apos;s early refraction profile from the Virginia Capes to the edge of the Continental Shelf has been followed by a similar traverse in Great Britain from the coast of Cornwall to the edge of the Continental Shelf southwest of England. This showed that the thickness of the sedimentary mantle and the rates of slope of the basement surfaces there are comparable to those in the Virginia Cape district.

Jan 1, 1939

By R. T. ROLFE

IN this critical age, people are not content .with the judgments passed on men and things long ago, but must needs revise them. It is an excellent spirit, so long as we do not start out with the idea that old opinions must necessarily be wrong, and that all ancient malefactors must therefore be whitewashed. That interesting ogre, Gilles de Retz, to whom the process has recently been applied, is no longer with us, so no one will be the worse for it, but the old bugbear8 of the steelmaker, sulfur and phosphorus, still are, and now Mr. McIntosh, in a recent article in these pages, asks us to regard one of them in a new light.&apos; This article is a most interesting one, with much of which one must agree. One of his -statements, how- ever, although correct, is somewhat&apos; misleading, and he rather discounts the fundamental objection of the steelmaker to phosphorus, its dangerous propensity to segregate and the secondary effect on the carbon distribution and therefore on the homogeneity of the steel that is produced thereby. Further, the evidence on which he bases his claim that phosphorus does not lower the impact strength of steel is rather slight. The writer views with the utmost misgiving any proposal to increase the amount of phosphorus in steel, and cannot regard it in any other light than as a prejudicial impurity, to be kept down to as low a proportion as possible. It thus becomes necessary to examine the evidence upon which Mr. McIntosh&apos;s claims are based

Jan 1, 1926

By Harold Vagtborg

Equilibrium vaporization ratios were obtained for light hydrocarbons, nitrogen, carbon dioxide, and hydrogen sulfide in a reservoir fluid containing 35 mole per cent hydrogen sulfide. The data cover the range from 700 to 2500 psia at 154°F. The results of this study are compared with results obtained by other investigators on systems containing less hydrogen sulfide. When large amounts of hydrogen sulfide are present, the equilibrium vaporization ratios for ethane and heavier hydrocarbons are greater than the ratios for systems containing little or no hydrogen sulfide. Large amounts of hydrogen sulfide have the reverse effect on the ratios for methane. Routine PVT studies were performed on the reservoir fluid including flash and differential liberations of the dissolved gas. The pressure-volume relationships of the saturated fluid were also determined. It is shown that the use of published correlations on physical properties of reservoir .fluids can lead to gross errors when applied to systems containing large amounts of hydrogen sulfide. INTRODUCTION Equilibrium vaporization ratios for various components in naturally occurring crude oil and condensate systems have been reported in the literature.1,2,3,4 Recently, several papers have been published with emphasis on non-hydrocarbon components such as nitro- gen, carbon dioxide and hydrogen sulfide.5,6,7,8,9 The increased discovery of reservoir fluids having high concentrations of these non-hydrocarbon components, particularly hydrogen sulfide, has created a need for a further study of their phase behavior. Equilibrium vaporization ratios are known to vary with pressure, temperature, and overall composition of the system.&apos;" It was anticipated that ratios for systems containing large amounts of hydrogen sulfide would differ from the ratios for systems containing small amounts of hydrogen sulfide. Therefore, the present work was undertaken in order to obtain reliable equilibrium vaporization ratios for the reservoir-fluid in question. PROCEDURE The procedure followed was evolved after considerable experimentation on methods of handling the very sour crude. It was found that drying agents (e.g. CaCl2 and CaSO4) absorbed an appreciable amount of hydrogen sulfide from the gas used to prepare the recombined samples. The concentration of hydrogen sulfide dropped as much as 10 mole per cent in a single pass through a 3-ft drying tube. It was also found that when undried gas was agitated with mercury in the PVT cell, a black scum, believed to be mercuric sulfide, was formed and the hydrogen sulfide content of the gas dropped several mole per cent. Because composition changes during a run could not be tolerated, separation of the mercury and sour fluid was necessary. In order to effect this separation, a stainless steel piston, equipped with Teflon O-rings, was placed in the PVT cell between the mercury and the sour fluid. This piston had to be constructed in three parts because

Jan 1, 1955

By Edwin S. Smith

Current research in the phenomenon of liquefaction has indicated some of the in situ material properties which should be considered in the planning of waste deposits. Practical experience in tailings disposal, however, must be combined with the results of theoretical and laboratory studies to develop the most economical and safe techniques against liquefaction failure. One of the many responsibilities of mining engineers and mill superintendents is providing for the safe and economic disposal of wastes (or tailings) that remain after a mineral has been extracted from an ore. The cost of disposal of these tailings exerts a considerable influence on the minimum grade of ore extracted from the mine. It varies to a great extent with each project and is dependent on many diverse factors, such as the local topographical, meteorological and seismological conditions together with the applicable water pollution laws of the area. The process used to extract a mineral from an ore determines the physical characteristics of the tailings and, thus, is one of the more important factors to be considered in the planning of disposal facilities. Today&apos;s trends in ore-processing operations complicate the problems of waste disposal: recently developed extraction methods result in the production of finer tailings, the use of lower grade ores produces greater volumes of wastes, and the enhanced land values in the vicinity of industrial plants preclude the former practice of spreading wastes laterally and force the expansion of waste deposits upwards to greater heights. The frequent occurrence of stability problems in waste deposits indicates that many mining organizations may not be employing current soil mechanics concepts and practices. One of the most spectacular, and often most disastrous, types of tailings dike failure is that resulting from liquefaction of the fine particles combined with a breach of the main retaining dike. TAILINGS DISPOSAL Since the many variations in site conditions, ore bodies and extraction processes dictate the general disposal procedures and mill superintendents incorporate special facilities to provide the most economical disposal method consistent with accepted safety standards, it is only natural that there are almost as many different disposal techniques as there are disposal areas. Methods used in the construction of retaining dikes include: (1) transporting granular material from an adjacent borrow pit and (2) mechanically segregating the total effluent and allowing the coarse fraction to form a retaining dike by hydraulic deposition. The location of a plant and the surrounding topography exert the greatest influence on the layout of tailings disposal facilities. Most of the above-ground waste deposits can be classified as side-hill, (Fig. 1,) cross-valley, (Fig. 2,) or stockpile deposits. Side-hill disposal areas are probably the most common type of layout because of the natural advantage of gravity flow, without the disadvantage of river diversion usually needed for tailings ponds formed behind cross-valley dikes. Stockpiles, which are placed on relatively level ground, require four retaining dikes and the effluent generally has to be pumped up into the disposal area. Changing production techniques or developments adjacent to disposal areas have produced variations or partial combinations of these three categories. In a series of articles, Lenhart describes many of the problems encountered in the disposal of tailings and certain innovations used to overcome them. He discusses weaknesses in design and layout and shows that disposal techniques are often learned the

Jan 1, 1970

R. F. McELVENNY.- The next item is: "Center and other methods, vs. side charging." That was all discussed in the Carson case, and I do not know but what many of the plants are still using center charging. Some are using side charging. Did I understand that where you use the wet charge it is all side charging on the wet ore? B.-G. C. HONEYMAN.- We were on center charging for about a year with wet ore. R. F. McELVENNY.- Then you went to side charging. Has anyone any remarks to make on side versus center charging? E. A. BARNARD.- We have one side and one center, both on deep bath. It is an experimental proposition so far, but the side charge looks very favorable.. R. F. McELVENNY.- This is with calcine? E. A. BARNARD.- This is with calcine on a floating charge proposition.. They are both water jacket. The charge acts very similar on both center and side charging. The calcine spreads much the same as it does on the center charge. It will run down 75 ft. on the furnace side as well as the center. The advantage is in taking care of secondaries and things of that nature. C. BARDWELL.- Do you get any side wall protection from it? E. A. BARNARD.- No. R. F. McKENZIE.- Do you not project the side wall up to protect the skewback? E. A. BARNARD.- There is a slot projection down around the top of the bath; but the repairs on the side wall have been practically the same; that is, they, have been practically the same as they have on the center charge. A. H. RICHARDS.- A point I would like to make is that if you have any doubt about the center charging, we feel that we get better tonnages and lower fuel ratios and better slags with center charging than we ever got with side. Different kinds of charges would, of course, vary, and I could readily see that if you had the same advantage with deep bath smelting that you mention you would probably get just as good a slag and as good fuel ratios. E. A. BARNARD.- In fact, I think the calcine charge spreads more on the side than on the center charge. A. H. RICHARDS.- If you maintain a deep bath. E. A. BARNARD.- That is one thing we have to be careful about, to hold the charge back.

Jan 1, 1930

By A. F. Melcher

THE present paper is a progress report. on an investigation of the physical factors of oil and gas and especially of their sands, I such as-pore space, size of pores or permeability, retentivity, viscosity of the oil, temperature, pressure, thickness and area of the pay sand, water relations, and capillarity. The purpose is to determine as many of these physical factors as possible, and to ascertain the relations existing, directly or indirectly, between these physical factors and the production of oil and gas. As yet only pore space2 and size of grains of pay sands have, been investigated, although an apparatus has been designed to determine the permeability of a sand to oil, water, or gas under definite drops of pressure between the entrance face and exit face of the sample. Messrs. E. W. Shaw, R. Van A. Mills, D. Dale Condit, G. B. Richardson, G. C. Matson, and C. H. Wegemann collected the samples upon which the physical determinations were made. Acknowledgment is made to my colleagues of the United States Geological Survey for many suggestions and criticisms; to Mr. Mills for the production data given of the oil wells from which some of the samples were collected; to Mr. A. W. McCoy of the Empire Gas and Fuel Co., Bartlesville, Okla., for many ideas.

Jan 4, 1920

By H. H. Stout

IN the early fall of 1925, the writer was conducting, in the Ledoux and Co. labora-tory, New York, experiments directed to-ward ascertaining the effect on its impurity content when cathode copper was subjected to a current of various gases at an elevated temperature below the melting point, The apparatus consisted of a vertical 1-in. dia. silica tube about 12 in. long, heated on the outside, The cathodes were broken to pass a8-in. mesh, and a current of various differ-ent gases was passed up through a 4-in, long column of these loose cathode particles in the vertical tube furnace. Temperature was maintained to i500° to 1600°F. and the gas treatments lasted from 3 to 6 hr, The writer observed that whenever reducing gas (H2 or CO) was used, these cathode par-ticles stuck together at points of contact with each other. The cohesion was so marked and tenacious that an examination was made of the fractured surfaces, when cathode particles were broken from the cluster. Crystal growth was always found to have taken place across the surfaces where separate particles were in contact, but only after all oxides, sulphates, etc, had been completely removed. The idea of a possible new process was then conceived and was disclosed to A. M. Smoot (V. P. Ledoux and Co.) with intent to obtain his views. The first conception as given Smoot was "to gas-clean broken cathodes, put them in an extrusion press, solidify and extrude them at around 1500°F," Smoot&apos;s reaction, after a few moments considera-tion, was, "It looks perfectly all right to me."

Jan 1, 1940

By Robert H. Weber

INCREASING acceptance of perlite products, chiefly in the fields of lightweight structural aggregates and thermal and acoustic insulation, has led to expanding market demands that have encouraged many new producers to enter the field. In some instances, however, the failure of these producers to anticipate the variable response of perlite to conventional processing methods has led to difficulty in establishing an economical flowsheet by which a predictable specification product could be obtained. It is not the writer&apos;s intent to provide a solution to these problems, but rather to summarize their nature. It is to be hoped that members of the industry who have hurdled some of these obstacles will document solutions arising from their experience. In this treatment the term perlite will not be restricted to the petrographic definition but will apply to all volcanic glasses. Expansible obsidians and pitchstones are accordingly included in this broader industrial classification. Chemical Properties: Although perlite has been reported to range in composition from that of rhyolite to that of andesite, it is probable that most of the glasses have the composition of rhyolite. When recalculated to an anhydrous basis, the five analyzed glasses from New Mexico, representing five distinct physical types from widely separated deposits, show an amazingly uniform oxide composition. Water content is the only major compositional variable; total water ranges from a low of 0.37 pct (non-expansible obsidian) to a high of 8.95 pct (expansible pitchstone). The wide range in expansion characteristics exhibited by these samples cannot be related to significant variations in the composition of the nonvolatile fraction and has been only partially correlated with variations in water content.

Jan 1, 1956

By Charles R. Keyes

I. INTRODUCTION. FOR a period of several years, and in a large number of cases, the Metallurgical Laboratories of the New Mexico School of Mines were employed in umpire work. During this time many important local problems were solved. Against the results of careful chemical analyses of ores, assay-returns were often checked. In many cases the assay-methods of mine and custom-smelter were compared, and both often found faulty for the ore concerned. A wide range of ores was covered. Many of the chemical analyses and assays were made by Dr. F. C. Lincoln, Professor of Metallurgy, now of the Montana State School of Mines. A varied series of instructive assays was prepared by Prof. R. B. Brinsmade, now of the West Virginia State University. Single assays and given series of tests were undertaken by H. T. Goodjohn, now chief chemist to the Cia. Metalurgica de Torreon, Coahuila, Mexico; by H. J. Hubbard, now superintendent of the Butters Divisadero Mines, Jocoro,. San Salvador, C. A.; by E. D. Morton, now superintendent of the Arizona & Nevada Copper Mining Co., at Lunning, Nev. ; and by A. W. Edelen, now superintendent of the Angangueo Unit of the American Smelting & Refining Co., in Michoacan, Mexico. A critical comparison of assay-methods that were found to be followed in the case of certain gouge-ores mined in the Mimbres range in New Mexico, and about which there had been much controversy, was made by D. F. Riddell, then Acting Professor of Assaying, and now superintendent of the Providentia Mines Co. of Parral, in Chihuahua, Mexico. To him is due the credit of much that is contained in the following notes, which be has generously permitted -to be used in advance of the publication of the complete results.

Jul 1, 1911

By John Hays, Hammond

IT is both a pleasure and an honor to be a guest of the Institute and I thank you, Mr. President and fellow-members, for giving. me the opportunity of meeting you this evening. My esteemed friend, President Smith, has requested me to do a bit of "reminiscing" as to the earlier years of my career as a mining engineer, which has now covered a period of fifty years. Let me reassure you by promising that my narrative will not include all the experiences I have had over that long period. You will, I trust, pardon what might seem egotistical but I do not see how a personal narrative could well be otherwise.

Jan 1, 1928

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

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

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

Jan 1, 1962

By D. C. Sisti

A technical evaluation of actual performance of the preparation facilities at Beaver Consolidated Coal Co.&apos;s Stinson plant is presented, with special emphasis on sulfur reduction in 1-1/2 x 3/8 in., 3/8 in. x 28 mesh, and 28 mesh x 0 size fractions. Evaluation of the heavy medium section of the plant and the treatment of the 28 mesh x 0 coal is included. Design criteria considered for sizing and selection of equipment required to process 1-3/4 million tpy of raw coal on coals of divergent washability characteristics are summarized.

Jan 1, 1976

By L. Ianniello

AMONG the more interesting peculiarities of plutonium is the brittleness of its room-temperature monoclinic phase, a, since the adjacent higher-temperature phase (transformation temperature, 112C), ß, is also monoclinic but very ductile. Other elements, e.g., tin and manganese, have phases which exhibit similar contrast in plasticity. However, it was considered unusual when the a phase which has less than 0.1 pet tensile elongation&apos; was rolled to 90 pct reduction in thickness at room temperature.&apos; Since brittle behavior often is a structure-sensitive property, but could also be the result of covalent-type bonding, further experiments reported here have been conducted in an attempt to illuminate the problem. Electrorefined plutonium was rolled under various conditions and examined to determine the strain-hardening characteristics and also to determine under what conditions rolling could be performed. The rolling mill had 6.0-in.-diam heatable rolls with a variable roll speed (6.25 to 445 in. per min). Microhardness measurements were taken using a square-base diamond indenter with loads from 50 to 1000 g. The method used for rolling plutonium at room temperature consisted of prior

Jan 1, 1964

By R. I. Jaffee, H. R. Ogden, D. J. Maykuth

IN THE past year, Jaffee and Campbell&apos; and Finlay and Snyder2 reported on the mechanical properties of titanium-base alloys, some of which were in the same ranges of composition as are covered in this paper. In this paper, evidence confirming that given by Finlay and Snyder on the effects of carbon, oxygen, and nitrogen on titanium will be presented; and, in addition, new data will be given on the effects of these elements on the flow properties and phase transformation of titanium. Materials and Preparation of Alloys The preparation and general properties of iodide titanium have been adequately described elsewhere.&apos; , As-deposited iodide titanium rod, prepared at Battelle, of Vickers hardness less than 90 was employed as the base metal in the present work. This was the same material as that used by Finlay and Snyder.2 The probable analysis reported by them for standard quality metal holds here also: N 0.005 pct, 0 0.01 pct, C 0.03 pct, Fe <0.04 pct, A1 <0.05 pct, Si <0.03 pct, and Ti 99.85 pct. Carbon was added in the form of flake graphite supplied by the Joseph Dixon Crucible Co. Oxygen was added in the form of c.p. grade TiO, powder, produced by J. T. Baker Chemical Co. Nitrogen was added in Ti3N4 powder, supplied by the Remington Arms Co. Individual ingots weighed 7 or 8 g. Carbon, oxygen, or nitrogen was added by placing the corresponding powder in a capsule made from as-deposited iodide titanium rods and melting the capsule with the balance of the charge. The charge was are-melted with a tungsten electrode on a water-cooled copper hearth under a partial vacuum of very pure argon (99.92 pct minimum). Melting was practically contamination free. Vick-ers hardness increases of less than 10 points were normal for unalloyed iodide titanium control melts. Nitrogen analyses of are-melted iodide titanium showed a nitrogen content of 0.005 pct, about the same as is present in the as-deposited rod. No tungsten pickup was found in a melt of iodide titanium analyzed for tungsten. Weight losses in melting nitrogen-free alloys were very small and varied consistently from nil to 0.015 g (0 to 0.2 pct). This permitted the use of nominal composition for these alloys. Chemical analyses made for carbon, which can be analyzed conveniently by combustion methods, justified this procedure. Where nitrogen was added, considerable splattering took place. Here it was necessary to analyze for nitrogen by the Kjeldahl method. The ingots were hot rolled at 850°C to about 0.045 in. thick. After hot rolling, the strips were descaled by mechanical grinding, and then given a cold reduction of 5 to 10 pct to insure a uniform thickness throughout the length of the specimen. The edge strips and the tensile strips were annealed in a vacuum of 1x10-4 mm Hg pressure for 3 1/2 hr at 850°C and furnace cooled. Methods of Investigation Hardness Measurements: At least five Vickers hardness measurements were taken using a 10-kg load on each sample in the following conditions: (1) top and bottom of each ingot, (2) top and bottom surface of as-rolled and annealed sheet, and (3) on cross-section of annealed sheet and all quenched specimens. Tensile Tests: Tensile tests were conducted on Baldwin-Southwark testing machines having load ranges of 600 or 2000 lb. Tests were made on 1-in. gauge-length specimens, 3 1/4-in. overall length, 1/2 in. wide, 0.040 in. thick, with a reduced section 1 1/4 in. long and 0.250 in. wide. Two SR-4, A-7 strain gauges, one mounted on each side of the specimen, were used to measure the strain over a limited range to determine the modulus of elasticity. After the modulus of elasticity readings had been taken, load vs. strain readings were taken, using only one strain gauge, at increments of 0.0001 in. until the yield points were passed and then at 0.001-in. increments to the limit of the strain-gauge indicator (0.02 in.). Strain readings above 0.02 in. per in. were taken every 0.01 in., using dividers to measure the strain between the 1-in. gauge marks until the maximum load had been reached. Crosshead speed, when using the SR-4 gauges, was 0.005 in. per min, and, when using dividers, 0.01 in. per min. Flow Curves: Flow curves were determined using the true stress-true strain data obtained during the tension test. The usefulness of this type of information has been dealt with very adequately elsewhere by L. R. Jackson,&apos; J. H. Hollomon,6 and many others. Flow curves of true stress vs. true strain could be converted to the more conventional cold-work curve of 0.2 pct offset yield strength vs. percentage of cold reduction by means of the transformation, 1/1 = 1/1-R, where R is the fraction reduction in cold working. Thus, the true strains corresponding to percentage reduction can be calculated, and the 0.2 pct offset yield strengths scaled off the — 6 curve by taking the true stresses corresponding to the values of 6 + 0.002 strain. Heat Treatment: For the transformation studies, the alloys were heat treated in a horizontal-tube furnace using a dried 99.92 pct argon atmosphere, and quenched into water. Essentially no contamination was found after several hours of heat treatment at temperatures up to 1050°C. Metallography: Specimens were prepared in the

Jan 1, 1951