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By H. S. Price, J. C. Cavendish, R. S. Varga

This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure values near wells, as well as accurate pressure pdients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subspaces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. INTRODUCTION The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield9 or Peaceman and Rachfordl0). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and weber17 and Roper, Merchant and Duvall,13 have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite often cannot even be applied. In this paper, we present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: where G is a rectangle (with sides parallel to the coordinate axis) with boundary ?G, ?/?n denotes the outward normal, and y and B are non-negative constants such that y + B > 0.

Jan 1, 1970

By Rudolph G. Wuerker

WITH the growing complexity of ore dressing processes and the diversity of equipment, efficiency control has become increasingly important in beneficiation. In the case of iron ore dressing, there have been sporadic attempts'-3 to establish the optimum separation for various ores so that grade and recovery would be readily predictable. But no rigorous statistical analysis and graphical presenta- tion of such tests could be found in the literature of this country. Tests Made with Iron Ores Expanding upon existing methods of plant supervision and efficiency control, an investigation was started in the ore dressing laboratory at the University of Illinois on the applicability of distribution analysis to iron ores. A sample of crude ore was obtained from the Ohio mine of Cleveland-Cliffs Iron Co. at Ishpeming, Mich., consisting mostly of alternating bands of hematite and siliceous gangue, both about 1/4 in. wide. The ore was heavily coated with limonite, which often filled the cracks.

Jan 1, 1959

By Robert J. McKay, F. P. Huston, WILLIAM G. HUMPTON

THE manufacture of nickel-clad steel plate and the fabrication of articles from it has progressed far enough to permit a general description of the working methods used. The manufacture of sheets made up of layers of nickel and steel is not new as a sheet of this character was patented in Germany in 1893. Present development differs mainly in the size and finish of the product. The earlier light-gage highly finished products have been limited in their application due to their similarity, in certain respects, to electro-plated and highly finished alloy sheets. The new product is a relatively heavy plate 1/4 or 3/s in. thick and heavier, with one side coated with nickel, the weight of nickel being of the order of 10 per cent of the whole. The finish is that of hot-rolled steel plate.

Jan 1, 1931

By B. H. Bergstrom, D. D. Crabtree, C. L. Sollenberger

Experimental data is given for several natural minerals on the load required for the fracture of single specimens over a very wide size range. The experimental results are compared with published data, such as for coal specimens from 30 to 64 in. in size. Correlations of the specific energy (per unit mass) required for fracture with specimen size are given as functions of specimen shape and the experimentally observed load-size relationships. These correlations are discussed with reference to comminution theory. Comminution, through compression or impact, can result only if sufficient force, or energy, is applied to a specimen of a given size. The relation of specimen size to force requirements has not been adequately considered previously. For single particle fracture, it was previously shown 1 that the specific energy (energy, e, per unit mass, M) at fracture of single glass spheres was inversely proportional to the product size modulus, k, as indicated in the equation: e/M = C/k [1] This was found true not only for numerous glass specimens of the same nominal size but was true for all nominal sizes tested from 1/8 to 1 in. Also, it was observed that the smaller spheres required a greater specific energy at fracture than the larger spheres and consequently had a smaller product size modulus. However, the relationship giving the required fracture energy as a function of specimen size was not further elaborated upon. This paper will extend the development of the feed size effect on specific fracture energy for brittle materials. SPECIFIC ENERGY-FEED SlZE RELATIONSHIPS FROM PREVIOUS DATA For the particular glass spheres tested in the previously described experiments,' it can be shown, as on Fig. 1, that the specific energy varied inversely as the 4/3 power approximately of the feed size, F, in the span of nominal sizes ranging from 1/8 to 1 in. The load at which a 3-in. diam glass sphere (a crystal gazer's ball) was broken was within the range predicted by an extrapolation of this energy-feed size relationship. The product size distribution from this

Jan 1, 1963

By P. J. Carroll, H. Colijn

Feeders must be considered an integral part of the over-all bin and feeder system. Improper design of either one of these parts will affect the performance of the whole system. Feeder load, material properties, feed rate, physical layout, and environment as well as first cost determine the selection of feeder type. This paper provides a new method of calculating feeder loads with some experimental data as verification. General design criteria for belt and apron feeder, rotary table and plow feeders are discussed and a special section is devoted to vibratory feeders. Feeders are used to provide a means of control for the withdrawal of bulk materials from storage units such as bins, bunkers, silos and hoppers. This control function can only be performed properly as long as the bulk materials flow by gravity to the feeder in a uniform and uninterrupted fashion. During the past few years various papers have been written and presented on feeders and their application.1-9 This paper will be confined to some specific bin-feeder design criteria such as feeder load and power requirements. Special attention is given to the basic design criteria for vibratory feeders. HOPPER AND BIN DESIGN Feeders must be considered an integral part of the over-all bin and feeder system. Improper design of either one of these parts will affect the performance of the whole system. A lot of effort has been devoted in the past decade to the development of functional design criteria for hoppers and bins.1,10 The integrated concept of bin and feeder design requires quantitative analysis of the bulk material characteristics before the design and the selection of components can be attempted. The design of a feeder system must begin with the proper dimensioning of the hopper outlet to prevent arching or ratholing. The hopper opening should be large enough to allow passage of the bulk solid at the required maximum discharge rate." A feeder can only throttle the flow. FEEDER LOAD DETERMINATION Over the past ten years, there have been various attempts to determine the exact load or pressure on feeders mounted directly under hopper openings. Many designers, however, still consider this pressure equal to the hydrostatic head of material above the opening, and because such pressure would be very

Jan 1, 1969

By S. J. Hruska, G. M. Pound

The critical supersaturations for appreciable nucleation rate of cadmium crystals on copper and glass substrates at 186°Kwere measured as a junction of thermal-beam energy over a range of source temperatures between 616" and 839OK. There was no effect of source temperature on critical super saturation. This implies that the adsmbate prior to nucleation is in thermal equilibrium with the substrate. THE deposition of metallic vapors on solid substrates has been found to exhibit a critical behavior in that the rate of formation of deposit increases markedly when the intensity of the vapor source is increased slightly.* Evidence of the ability of sub- where Je is the flux which would arrive if the substrate were equilibrated with bulk condensate at the adsorbate temperature. The following work was undertaken to test this hypothesis. A) Energy Exchange Between Metallic Vapor and Substrates. When a freely translating atom collides with a stationary solid body its energy and momentum undergo changes which determine whether the atom is reflected or adsorbed. An atom is considered to be reflected if it returns to a freely translating state after remaining under the influence of the body for only a time comparable to the period of oscillation of atoms on the surface. An atom which remains for a longer time is said to be in an adsorbed state. The parameter which describes the energy transfer occurring at the interface is the thermal-accommodation coefficient which may be defined in terms of energy as Ei = average energy of impingent atoms, Eeq = average energy of an emergent atom which has equilibrated with the substrate, and Eem = average energy of an emergent atom. If a temperature is assigned to each of these energies, we have at as defined by Knudsen.2 Since this allows no distinction between reflected and evaporated atoms, a more specific definition is introduced for the present purposes, namely 71 = probability that an impingent atom is transferred to an adsorbed state, aj = thermal-accommodation coefficient for reflected atoms, and aTc = thermal-accommodation coefficient for adsorbed atoms. During a time t,, the mean stay time, prior to evaporation the adsorbed atom (adatom) will interact with the substrate and this will have the net effect of transferring the adatom towards a state of

Jan 1, 1964

By J. T. Pardee

INTRODUCTION PLACER is a Spanish word, the definitions of which include "an extensive bank of sand or gravel" and "a place where currents of water deposit particles of gold."l The term, probably first used in the western hemisphere by Spanish or Mexican gold miners, is now generally applied to all detrital deposits that yield valuable minerals by washing. In the Western States placer products other than gold, including the silver alloyed with it, are chiefly sapphires, produced in Montana, and platinum alloys recovered in California and Oregon. During the war tungsten ore (scheelite) was obtained from placers in the Atolia district, California, and a number of diamonds have been found in the Sierra Nevada gold belt. Small amounts of stream tin have been produced in the Black Hills of South Dakota and a little monazite sand in the Boise Basin. Idaho. Magnetite, chromite, ilmenite, zircon, and other useful minerals are more or less abundant in the beach placers of the Pacific coast and in the heavy residues of placer mining elsewhere, but the problems of profitably separating and marketing them remain to be solved. Minerals of lead, quicksilver and other metals occur in many of the placers and although not plentiful enough as a rule to be worth recover-ng, their presence has, in several instances, led to the discovery of valuable lodes, notably at Leadville, Colorado. Historical summary.-In New Mesico, Arizona, and Southern California, placer gold was mined by Mexicans and Spanish priests in the first half of the 19th century or earlier. With these exceptions history of placer mining in the Western States begins with Marshall's discovery of gold in northern California in 1848. During the next twenty years placers were found in all of the principal mining districts that are known today. The richer deposits were soon mined out but a relatively large production was maintained from the leaner deposits chiefly by hydraulic

Jan 1, 1933

Iron Ore Resources of the World (Die Eisenersvorrate der Welt)_ By G. Einicke. Verlag Stahleisen, Dusseldorf, 1950. 418 p., with 192 tables and an atlas volume containing 100 p. of reaps. 66 German Marks.-A notable work in which the latest available information on iron ore deposits has been compiled by diligent work, continent by continent, country by country. The author reveals the effect of geological formations, iron content of ore, accessability, cost of transportation, political and economic considerations. Ore beds of importance to the German iron and steel industry are given more space than others. The bibliography contains almost 250 references. A tragic comic feature is the author's complaint that as soon as a map of iron ore resources of a country has been completed, the country's boundaries are changed. Reviewed by W. Trinks, Carnegie Institute of Technology. Industrial Research Laboratories of the United States. National Research Council, Washington, D. C. Ninth Edition. 1950. 445 p. $5.-Contains information on the research laboratories of 2845 industrial and commercial organizations, including names of research executives, location of labs, types of activity, whether any consulting services are offered. There are two appendices, one of which lists data on government labo ratories which cooperate with industry, and the :)ibex naming universities and colleges offering research services to industry.

Jan 2, 1951

By G. R. St. Pierre, L. M. Adelsberg, R. Speiser

The rate of scale fot'~I~ti0n on tantalum held in H20-Hz-Ar gns mixtures at temperatures between 840" and 1250°C is related to gas composition and ternpevature. It is found that water vapor partial pressure determines the oxidation rate at a given temperature and that the oxygen potential as fixed by the water vapor to hydrogen ratio Ins no significant effect on the oxidation rate. The Ta205 scale formed during oxidation is composed of an inner lattice-dijf~ision barrier and an outer layer of- cracked/porous oxide 1 HE oxidation of tantalum at temperatures less than 800°C is characterized by solution of oxygen into the metal,'-' the formation and growth of suboxides into the metal,')2~10-15 and the delayed nucleation of the highest oxide, Above 800°C, Ta205 is found to nucleate rapidly10, 11, 15, 16 except at low oxygen pressures:15 however, there is uncertainty regarding which does not retard the oxidation process. For each gas con~position and temperature investigated, the oxidatioz rate becomes constant after a short adjustment period. It is shozm that a constant oxidation rate nzay pre~?ail even though the tlzickness of the inner lattice-dijjitsion layer of Ta205 is clanging. TFze initial czcrz!ature of the typical 'Paralinear" oxidation curve may result froprz causes other than an increasing thickness of tlze inner protective layer. the detailed mechanisms of the high-temperature oxidation. Peterson, Fassell, and wadsworth17 observed linear oxidation behavior for tantalum in oxygen at temperatures between 600" and 1000°C. They reported that equilibrium adsorption of 0, occurs on a surface prior to the rate-deter mining step of the reaction. Cowgill and stringer1' confirmed the observations of Peterson and his coworkers. They stated that the rate-determining step of the reaction could be either the incorporation of adsorbed oxygen into the anion lattice or the dissociation of 0, at the gas-oxide interface. The relative rates of the two surface reactions were proposed to be dependent upon the reaction temperature and the oxygen pressure. stringerlo subsequently reported that the reaction surface is located somewhere

Jan 1, 1968

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

By J. C. Shyne, T. D. Gulden

The steady-state creep behavior, in compression, of indium containing a dispersion of atomized glass particles was studzed over a range of temperature, stress, and composition. The observed behavior was not consistent with a simple model of dislocation climb over dispersed particles. From room temperature to about 100°C the temperature dependence could be described by an activation energy about one and a half times that of self-dijfusion in indium while at higher temperatures a much higher ternperature dependence was observed. THE value of dispersion-hardened and precipitation-hardened alloys has long been recognized. The mechanism of hardening, however, is not completely understood, especially at elevated temperatures where dispersed particles increase creep resistance. Following the suggestion of Schoeck1 that the rate of creep in dispersion-hardened materials is controlled by dislocation climb over second-phase particles, Ansel and weertman2 derived steady-state creep equations for dispersion-hardened materials. Their derivation was based on dislocation climb over non-deformable spherical particles in a metallic matrix. For low stresses they predicted a linear relation between applied stress and steady-state creep rate. For stresses large enough to cause dislocations to pinch off around the precipitate particles, the theoretical creep rate was shown to be proportional to the fourth power of stress. For very high stresses an exponential stress dependence was predicted. In all cases the theoretical creep rate is linearly proportional to the diffusion coefficient. This provided the primary temperature-dependent factor. Subsequently, Ansel and Lenel3 reported some experimental data on SAP, a composite of aluminum and aluminum oxide, that was in good qualitative agreement with the above theories. Their experimental creep rates, however, were four orders of magnitude less than the theory predicts. This was attributed to a low density of active dislocation sources in the material; somehow the dispersed particles inactivated the dislocation sources instead of merely interferring with dislocation motion. Meyers and sherby4 have recently reported on the creep behavior of SAP. Their results were inconsistent with a simple dispersion-strengthening model and led them to conclude that a continuous network of oxide controls the high-temperature mechanical characteristics of SAP. Because of the rather complex mechanical behavior of SAP and the lack of agreement about the morphology of its oxide phase, it appeared desirable to study the creep of a dispersion-strengthened material of controlled morphology. For the present work a dispersion of spherical glass particles imbedded in a matrix of indium was chosen. The microstructure of this material was similar to the idealized uniform dispersion of hard spheres in a deforming matrix assumed by Ansel and Weertman in their theoretical treatment. SPECIMEN PREPARATION For experimental convenience, it was decided to use a low melting-point metal in this investigation. It was necessary that the metal not be oxidized readily up to its melting temperature and that it wet the second-phase particles. It was desired that the material chosen for the dispersed phase be available as a fine powder with closely controlled size and shape. The material chosen to satisfy these requirements consisted of a matrix of indium metal containing a dispersion of atomized particles of a soft soda-lime-silica glass ranging from 5 to 30 µ in diam. The glass particles had a highly regular spherical shape. The composite was made by stirring the glass powder into liquid indium maintained at a temperature just above the melting point of indium, 156°C. The creep specimens were prepared by a hot pressing operation. Five to ten g of the mixture were placed in a steel die and pressed at 125°C for 5 min under a pressure of 30,000 psi. The resulting specimens were cylinders about 3/8 in. in diam and ranged from 0.4 to 0.7 in. high. By following this procedure a uniform dispersion was obtained in the creep specimens. Typical microstructures of specimens containing twenty and forty volume percent glass powder are shown in Figs. 1 and 2. Unfortunately, grain size could not be determined by the metallo-graphic techniques used. CREEP TESTING PROCEDURE Creep tests were performed in compression under constant stress. The specimens were placed in

Jan 1, 1963

By Robert Anderson

ROUGHLY, a crack in a casting may be considered, for the moment, to be due to fracture of the alloy resulting from the stress set up by the contraction in volume on passing from the liquid to the solid state. Cracks may be external or surface, internal or deep-seated, or incipient or so-called strain cracks. Draws may appear as depressions, unevenness, and "pinching in" of the surface of a casting. Roughly, draws are due to contraction in volume and are governed largely by the same factors as cracks. A casting may be cracked, however, without being drawn. Shrinkage is a foundry term; it connotes the contraction in volume of a metal or alloy on passing from the liquid to the solid state. Pattern-makers' shrinkage is the total contraction in volume (including liquid, solidification, and solid shrinkage) that occurs when an alloy is poured into a mold. The contraction in volume of aluminum is one of the principal factors affecting the occurrence of cracks, as will be shown later, and the question of shrinkage and its control requires careful study in any treatment of cracking in castings. In the case of, sand and die castings, cracks have been attributed to a number of causes, but in the case of most light aluminum alloys, they are due to the large contraction in volume on freezing and the lack of its regulation or control. The most important factors are: (1) Contraction in volume; (2) composition of alloy; (3) quality of melting charge; (4) design of casting; (5) method of molding; (6) hardness of ramming; (7) method of gating; (8) hardness and characteristics of cores; (9) chills; (10) risers; (11) melting temperatures; (12) furnace used for melting; (13) pouring tempera-tures; (14) inclusions in alloys; (15) hot shortness of alloys; and (16) physical properties of alloys at high temperatures. Of these, the first, second, third, and eleventh to sixteenth involve ascertainable metallurgical facts; the remainder are largely matters of opinion, judgment and technical knowledge of men experienced in the production of castings.

Jan 10, 1921

By Nagel, Theodore

USE of oxygen in metallurgical operations was investigated by a committee of unusually able engineers more than ten years ago. A record of their work appeared under the title "The Use of Oxygen or Oxygenated Air in Metallurgical and Allied Processes," Serial 2502, Report of Investigations, U. S. Bureau of Mines. Shortly thereafter the A.I.M.E. published "Use of Oxygenated Air in Metallurgical Operations," based on a symposium at the New York meeting, February 1, 924. Quoting from the Bureau of Mines report In view of the many recent developments in oxygen manufacture, and considering the increasing cost and decreasing quality of our raw materials, the Bureau of Mines has taken the matter of the application of oxygen or oxygenated air to the metallurgical centers for consideration and has appointed an advisory committee to study the problem.

Jan 1, 1935

By DOOLITTLE E. M.

(Canal Zone Meeting, November, 1910.) The following notes are contributed, not with the idea of offering a complete history of the development of this very important process as applied to the Leadville district, but with the hope that the practice, as it was carried out in the Bi-Metallic Smelter, may still be of interest to others. The Bi-Metallic Smelter, at Leadville, Colo., was the first to make a commercial success of the process described in the following pages, which consisted essentially of smelting raw silver- and copper-bearing sulphide ores in blast-furnaces to form a matte, which was generally re-smelted with siliceous ores for a second high-grade matte. Robert Sticht, in his excellent monograph on the subject,1 has outlined briefly the plant belonging to this company. He says, in effect: The Boulder, Mont., enterprise set the example for others with whom the patentee (w. L. Austin) had been negotiating, and the old La Plata lead-smelter at Leadville, Colo., was fashioned into a crude, temporary experimental plant for the Bi-Metallic Company, and the feasibility of the process demonstrated by a trial run. Subsequently, the plant was considerably improved, and, being supplied with very favorable ores, continued to run without interruption from August, 1892, to June, 1893. In September, 1893, smelting was resumed in a completely remodeled establishment, some $200,000 having been expended upon the new work. Thus, aside from the Montana experiments, which, under the direction of W. L. Austin, began as early as- 1885 2 at Toston, and continued with indifferent success for six or seven years, the Bi-Metallic plant at Leadville may be said to have * Formerly Superintendent, Bi-Metallic Smelting Co. + Formerly Chief Assayer and Chemist, Bi-Metallic Smelting Co. 1 Modern Copper Smelting, E. D. Peters, 7th ed., p. 415 (1895). 2 Trans., xvi., p. 259 (1887-88).

Dec 1, 1910

By A. P. Watts

FOREWORD THE problem of concentrating the disseminated lead ore of southeast Missouri is extremely simple. The economic mineral is galena and the gangue is dolomite. The ore assays from 4 to .6 per cent. lead, 80 per cent. of which is recovered in a 70 per cent. concentrate.. The ore is crushed through 10 mm. and sized on 2 mm.; the oversize is jigged, while the undersize is tabled, and the slime treated by flotation. The district is the largest lead producer in the world, the output of metallic lead for the year 1915 being 183,906 tons. Over 20,000 tons of ore a day is being treated. The management of the different properties is progressive and always open to suggestion. The fact; however, must not be lost sight of, that the problem in the district is peculiar, as the average ore contains but 80 to 120 lb. of a metal normally selling at about 4c. per lb. The low price of the metal limits the treatment system to one of low cost. An elaborate treatment is neither logical nor advisable. An engineer first visiting the district may consider that the method of treatment could be improved

Jan 10, 1917

By J. L. Gillson

The big mass of anorthosite in the Lake Sanford district and the bodies of titaniferous magnetite that occur in a small area near the south margin of the mass have been described repeatedly, and the puzzling problems of the genesis of the rocks and ores have stimulated the deductive reasoning of geologists for a hundred years. Some of these men have taken a leading part in describing the anorthosite rock and forming hypotheses concerning its origin; some have contributed most to the study of the ore deposits; and some have made classical Studies introducing a basic approach to the problems of the anorthosite rock and genesis of the titaniferous magnetites. Much of the writing on the problems of rock and ore genesis has been based on physical-chemical reasoning rather than on field and microscope observations of the rocks and ores. Most of these geologists conclude that the anorthosite was formed by true magmatic crystallization, involving previous settling or squeezing out of ferromagnesian minerals from the parent magma. The associated gabbro is a separate segregation or later intrusion, and the lighter colored and finer grained facies of the anorthosite is either a chilled border zone of the anorthosite or the result of granulation by crushing of the coarse, dark blue rock of the main mass. This blue rock, called the Marcy type, is named after the highest peak in the range. The finer grained and lighter colored rock is called the Whiteface, after another mountain appropriately named for a cliff colored by this facies of the anorthosite.

Mar 1, 1956

By GILBERT C. DAVIS

ANY thought of Morenci naturally includes its sister town of Clifton, its gateway to the outside world. Clifton, the country seat of Greenlee County, is the terminus of a branch line of the Southern Pacific railroad from Lordsburg, N.M. Carload freight incident to the Morenci operation moves from Clifton over Phelps Dodge?s standard-gauge industrial railroad. Private freight must be hauled by truck. These two communities fell far short of supplying adequate housing for the personnel concerned with the new operations so a new townsite, Stargo, was developed adjacent to Morenci. Here 234 housing units with garages have been built and twenty similar units have been erected near the reduction works.

Jan 1, 1942

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

By F. S. McNicholas, R. L. Healy

NOTEWORTHY because of the amount of explosives used, the tonnage broken, and the wide range involved both vertically and laterally, was a large underground blast fired last November at the Hidden Creek mine, Anyox, B. C. Stoping methods and mining prac¬tices at the Hidden Creek mine have previously been described in the technical press. Earlier mining methods employed included shrinkage stoping, glory-holing, and "spiral" stoping. The latter especially has been a practice peculiar to the Granby company, having been used for years at its Phoenix mines and later at the Anyox property where conditions as to size of orebodies and strength of ground both in the ore and walls were similar. These methods all leave tremendous excavations supported at key points by pillars and braces that may only be safely mined by big blasts.

Jan 1, 1935

By AIME AIME

AT the annual .meeting of the Minnesota Section in December, Dr. Leith characterized as a question still open the exact method of origin of Lake Superior iron ores and emphasized it as an important practical problem for the future. He welcomed the step taken last year by Dr. Gruner in presenting a new hypothesis, and asked Lake Superior geologists to meet the challenge of such multiple hypotheses by unbiased, study.

Jan 1, 1932