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By A. M. Gaudin, T. P. Meloy

This paper presents the theoretical derivation of the distribution equation for single fracture. The equation is shown to accord with experiment. Several empirical size-distribution equations have been proposed to describe the size of broken materials. Among them are the Gaudin-Schuhmann equation and the Rosin-Rammler equation.3*4 The Gaudin-Schuhmann equation relates the relative fraction of undersize to relative size —. In this relationship Mo is the total weight of crushed sample, M(x) the weight of undersize contained, x the size considered, K a quantity called the size modulus, which together with the slope parameter, m, characterizes the product. The slope parameter is usually close to unity. The Rosin-Rammler equation relates the same relative fraction of undersize to the relative size modulus by an equation of different form In this relationship, e is the base of natural logarithms. In the fine size-range when m is unity both equations give Gilvarry and Berstrom have sought a size distribution equation having a sound theoretical basis. They have come to an equation taking into account the effect of volume, surface and edge flaws in fragmentation. If the effect of the volume and surface flaws is neglected, the equation taking only edge flaws into account has the form of the Rosin-Rammler equation. In the present paper, a theoretical size-distribution

Jan 1, 1962

By H. Landsberg

Biological as well as geological research has made very successful use of the qualities that the physicists have detected in radioactive substances. Outstanding examples for the vast new fields opened in this part of the border-land between the disciplines of geology and physics are the "radio thermal geology" [July, 1909, see 1 of "References" at end of paper] and all that is connected with the use of the radioactive disintegration clock for the age-determination of rocks and minerals [2]. In structural geology, not unlike to recent bi-ological uses of radioactive material, their "tracer" properties were helpful. Changes in Radon concentra-tion in soil-air, especially accumulations, led to hidden crevices and fault-zones. High contents of Radon in spring-water gave clues as to the types of rocks they had flowed through [3, 4). One specific application of the small admixtures of radioactive material, however, has only lately found some atten-tion and that is their use in linking beds of sedi-mentary strata otherwise only poorly identified be-cause of the lack of fossils or other characteristic properties. To be useful for this purpose, two con-ditions have to be fulfilled: (1) The amount of radioactive material per unit-weight of rock in a given horizon should be uniform over a large area; (2) this same amount should change fairly rapidly in the vertical succession of layers.

Jan 1, 1940

By Oswald J. Heinrich

IN the coal review for the United States for 1875, the Engineering and Mining Journal, January 1st, 1876, remarks about the Richmond coal basin " It has contributed but little to the supply of fuel during the year past, notwithstanding the fact that it is the most favorably situated of all our coal-fields, and possesses a fuel of good quality, well adapted to many important uses. An unaccountable lethargy seems to have fallen on all who have touched this field ; and yet, in the future it can scarcely fail to become one of the great sources of coal supply." In most respects indorsing the above remarks, I take occasion to lay before the Institute the following facts in defence of the Rich¬mond basin; and not willing to criticize other mining enterprises in this field, I will make this one remark in general for all of them. While it is true that very little coal has been raised during the year in this field, it is equally true that even the little that has been raised could hardly be sold. When the output of the largest coal districts in the United States decreases, in consequence of the state of the market, it is not to be wondered at that the former small output of this basin dwindled down to almost nothing. But a far deeper¬seated evil, under which this field is suffering, may be discerned from the following remarks, which I hope will show that the latter part of the above remark in the Journal is not altogether fair. As the history of one mine in this district very nearly represents the history of the whole field, I will endeavor to give an account of the development of the Midlothian Mines, ranging amongst the old¬est in the district, partially taken from a report of Col. Wooldridge, in 1841. Coal was mined in this neighborhood as early as 1700, and used (then so-called extensively) in the vicinity in 1775. A

Jan 1, 1876

By Oswald J. Heinrich

In the coal review for the United States for 1875, the Engineering and Mining Journal, January 1st,, 1876, remarks about the Richmond coal basin: "It has contributed but little to the supply of fuel during the year past, notwithstanding the fact that it is the most favorably situated of all our coal-fields, and possesses a fuel of good quality, well adapted to many important uses. An unaccountable lethargy seems to have fallen on all who have touched this field ; and yet, in the future it can scarcely fail to become one of the great sources of coal supply." In most respects indorsing the above remarks, I take occasion to lay before the Institute the following facts in defence of the Richmond basin; and not willing to criticize other mining enterprises in this field, I will make this one remark in general for all of them. While it is true that very little coal has been raised during the year in this field, it is equally true that even the little that has been raised could hardly be sold. When the output of the largest coal districts in the United States decreases, in consequence of the state of the market, it is not to be wondered at that the former small output of this basin dwindled down to almost nothing. But a far deeperseated evil, under which this field is suffering, may be discerned from the following remarks, which I hope will show that the latter part of the above remark in the Journal is not altogether fair. As the history of one mine in this district very nearly represents the history of the whole field, I will endeavor to give an account of the development of the Midlothian Mines, ranging amongst the oldest in the district, partially taken from a report of Col. Wooldridge, in 1811. Coal was mined in this neighborhood as early as 1700, and used (then so-called extensively) in the vicinity in 1775. A

By Fred H. Poettmann, J. K. Welchon, A. F. Bertuzzi

A series of gas-lift tests was made which verified conclusions reached from previous studies and which showed that gas-lift performance could be calculated if reasonably accurate data on the producing characteristics of the well are available.' The test installation is described. Its essential features consisted of a rate-of-flow controller to regulate the input gas and an auxiliary string of small diameter tubing to conduct the input gas to the point of injection in the eductor tubing. In general, it was shown that for continuous gas-lift operation, injection should be as deep as possible consistent with available gas pressure and rate of production desired. Calculated curves are presented which completely characterize the gas-lift performance of the well tested. INTRODUCTION A correlation based on field data from a large number of flowing and gas-lift wells, covering a wide range of oper- ating conditions, was developed which permitted the logical design and prediction of the performance of continuous gaslift installations.' The procedure made it possible to calculate the depth, pressure, rate at which to inject gas, horsepower requirements, and the effect of production rate and tubing size on these quantities. As a result of these calculations certain significant facts were brought to light or re-emphasized. The presence of efficient ranges of operation and an optimum injection depth for a given rate of production were shown to exist as well as the fact that the lower the tubing pressure the less the horsepower requirements to lift the reservoir fluids. The fact that the gas lift performance can be predicted by calculation does not mean that any given installation will perform over the entire range predicted. Many of the conventional continuous gas-lift installations will not permit operation over the entire range predicted by calculation (particularly in the efficient range of operation) because of the performance characteristics of the installation. Consequently, field tests were initiated for the purpose of investigating and arriving at a simple continuous gas-lift installation which would operate under all conditions predicted by calculation. The first series of tests involved the use of mechanically operated valves. These valves were slip-joint type valves which are opened and closed by lowering or raising the tubing at the surface by means of a hydraulic jack. These valves were chosen because it was hoped that they could be opened or closed at will and did not depend on the gas pressure in the annulus or the pressure of the fluid in the tubing for their operation. Unfortunately, the valves did not operate satisfactorily and it was imossible to open or close each valve at will. Some limited data were obtained, however, which verified the predicted benefits resulting from the use of lower tubing pressures. In the next series of tests the valves were removed and the gas was injected from the annulus through a 14/64-in. orifice equipped with a reverse check valve. A packer was set below the valve to seal off the space between the 2-in. tubing and 5-in. casing. The injection point was located at 3,810 ft. This arrangement provided satisfactory mechanical operation. However, it was impossible to obtain low rates of liquid production at low tubing pressures as predicted by calculation. A minimum gas injection rate existed below which steady flow was impossible. Liquid pro-

Jan 1, 1953

By Lysle E. Shaffer

INCREASING attention has been given in the last decade to the possibilities of mine leasing in the West. The practice as described in this article does not refer to the leasing of entire properties for corporate operation. It is intended to deal rather with the advantages and problems incident to leasing portions of properties to individuals who themselves, individually or in groups, do the actual mining and transportation of the ore. These individuals are sometimes called "leasers" and sometimes called "tributors." The contracts under which they work set up an independent relationship of lessor and leaser, between themselves and the mineowner or operator. This relationship has many advantages to both sides over those created by the ordinary relationship of employer and employe. From the standpoint of the owners there is no liability on independent contractors for industrial injuries, social security taxes, unemployment taxes, or the manifold restrictions of the Federal Labor Relations and Wage Hour Acts and similar state acts where they exist. As the leaser's income depends on the quantity and quality of ore produced, there is a distinct incentive for maximum production of a good grade of ore. This in turn promotes careful mining of the areas under lease. Ordinarily in mining, labor cost is a high percentage of the total cost of operation. Under a leasing system, even if the leasers be allowed to retain half of the gross values that they produce, and the owner or operator gets half, in the case of marginal ore bodies this is ordinarily more than the lessor would realize if the property were worked by day labor. In some instances mineral deposits under a leasing system may become ore, whereas under a day-labor system they would

Jan 1, 1948

By Murray F. Hawkins

One problem of reservoir engineering is the early estimation of the size of newly discovered reservoirs. Often these reservoirs are the expansion type in which sizeable pressure drops occur incident to the production of small fractions of the oil reserve, above the bubble point, and a material balance equation may be solved to find the reserve. The early form of this equation' considered only the compressibility of the oil. Later Hall2 showed that the compressible nature of the formation rock is a significant factor in production above the bubble point, and he presented a new equation which includes a formation (rock) compressibility term. This note presents a further extension of the material balance equation as applied to volumetric, unsat-urated reservoirs above the bubble point by including a term for the presence and compressible nature of the interstitial water. DERIVATION OF EQUATION During a decline in average reservoir pressure, ?p ?p, — p1 the initial reservoir volume V,, will decrease to some value V, due to the reduction in pore volume as a result of a decline in the hydrostatic pressure within the formation, and v, = V,, [l — cr ?p]......(1) The formation compressibility c, is expressed in terms of change in pore volume per unit pore volume per psi. Simultaneously the connate water within the formation expands from an original volume V,, = S,V,, to a new volume V,, V, = s,v,, [I + c,npl.....(2) The difference [Vp — V,] is the hydrocarbon pore volume at pressure p and may be equated to the volume of the remaining oil, or [N — N,] B, = V,,, [I - C~A;] - S,.Vpi [l + cwnjl.........(3) But the initial oil in place in terms of the initial reservoir volume, connate water, and formation volume factor is Ilividing Equation 3 by Equation 4 eliminates V,, to give,

Jan 1, 1956

By Fritz Wald, Richard W. Stormont

lHE general constitution of a number of metal-lead telluride and metal-tin telluride systems has recently been studied in an effort designed to furnish background information for the study of degradation mechanisms on junctions between thermoelectric power generation materials and metals.1"4 This paper reports further results of that effort. It was found that cobalt-lead telluride constitutes a stable pseudobinary section through the ternary Co-Pb-Te system. Materials used in the study were lead and tellurium of semiconductor-grade purity (American Smelting and Refining Corp., 99.999+ pet). Cobalt (Johnson Matthey & Co., 99.999 pet purity) was used in the form of slices cut from rods of 5 mm diam. Twenty- gram charges of the alloys were melted in evacuated quartz ampoules. Thermal analysis, as described previously,2'3 and metallographic and X-ray diffraction methods (Debye-Scherrer photographs) were used as investigative tools. Substantial difficulties were encountered in polishing, as reported previously for the lead telluride-iron system.3 A number of different etches were used, including dilute aqua regia, Murakami solution, an etch containing copper nitrate,3 and HC1-HNO3-acetic acid-water mixtures. None of these etches gave consistent results over the complete range of cobalt concentrations. On the alloys containing bulk cobalt in the form of primary

Jan 1, 1969

By S. Kobayashi, A. E. Armenákas, C. Mylonas

Earlier work1-4 has shown that commercial mild steels under static loading at the lowest natural operating temperatures fracture in a brittle manner only when damaged by a suitable history of straining. Notched and then compressed plates have fractured in subsequent tension at loads as low as 10 pct of the limit load and precompressed smooth bars at a subsequent extensional strain as low as 0.01. The comparison of the average net fracture stress with the flow limit stress was shown to be an excellent criterion of brittle or ductile behavior of mild steel structures when only loads and general stress levels are known. The present investigation shows that the deformation at fracture is a far more sensitive measure of brittleness than the fracture stress. Both criteria, deformation and stress, are used to determine the amount of uniform precompression of two mild steels, ABS-B and Project E-steel, resulting in brittle fracture under the strong constraint of a subsequently machined severe circumferential groove. The fracture stress equaled or exceeded the theoretical flow limit Ól = 2.680., ('based on the elevated yield stress at each prestrain) up to prestrains of about 0.20 and then fell off to about 1 at prestrains of 0.60. Yet a prestrain of only 0.05 reduced the elongation at the shoulders by a factor of about 4. The total plastic elongation of a region surrounding a sharp notch in prestrained steel deternines whether or not fracture will be initiated in large structures, hence is a direct and realistic measure of the remaining ductility and provides an excellent test of the material's resistance to embrittlement. ALMOST all engineering structures of mild steel which failed in service in a so-called "brittle" manner exhibited appreciable local plastic deformation (more than 1 pct) and a mixture of "cleavage" and "shear" fracture surfaces. Furthermore, the peak local stress in an advancing crack is always high. Such simple criteria as pure cleavage, absence of plasticity, or fracture stress, so useful in other fields, are insufficient to characterize brittleness in engineering structures at ordnary temperatures. The "brittle)' behavior of engineering structures is caused by the limited ductility at cracks or notch regions, as shown by recent work at Brown University summarized and extended in Refs. 1 to 4. It was also shown that the local ductility of mild steel may be catastrophically reduced by a suitable strain and temperature history similar to those which may occur in real structures. Localized yielding begins at the notch roots at low loads but is contained by surrounding elastic regions. The plastic strains are hence small. They increase slowly with the load up to the flow limit or limit load for an ideally plastic material. Unrestricted plastic flow then occurs. At such strains the real material locally st rain-hardens and fractures. With work-hardening materials no flow limit exists, and the transition from low to high plastic strains is gradual but increases more rapidly at loads close to the flow limit of an equivalent perfectly plastic material. When the available ductility is sufficient for reaching the limit load, the behavior is normal or "ductile". With insufficient ductility, fracture will occur at a low load and will be defined as "brittle". Accordingly the sufficiency or not of the ductility at a notch is reflected in the magnitude of the fracture load or average net stress as compared with the limit load or flow limit. The application of this criterion gave surprising results. Service failures under semistatic loading occurred mostly below the limit load, hence were "brittle". On the contrary all static tests with undamaged commercial mild steels reached the limit load in spite of the deepest notches and temperatures below Charpy impact transition (say about -30°F or higher). Notched bars showed no brittleness even under fully dynamic axial loading up to 1.5 x107 psi per sec at -23°F and about 2.5 x l06 psi per sec at -ll0°F, but broke in a brittle manner at -200°F and l03 psi per sec.' To propagate a fracture at low load, experimenters had to trigger it by superimposing a strong dynamic impact at a notch cooled by liquid nitrogen as in the Robertson5 or Esso tests.' Once started the cracks would run through warmer regions of smaller stress. Obviously the ductility of the apparently undamaged commercial steels was "sufficient" in the laboratory tests but not in the service fracture, where it must have been reduced by some embrittling procedure of fabrication or service. These conclusions were confirmed by the achievement of low static stress (brittle) fracture initiation in unwelded steel after a local reduction of ductility by simple prestraining. Symmetrically notched plates of undamaged mild steel cooled below the Charpy V-notch transition range were tested in central static tension: Undamaged plates withstood loads of limit intensity, but when subjected to prior in-plane com-pressive prestraining perpendicular to the notch axis and to accelerated aging, the plates fractured completely or partially at very low static loads, as low as one-tenth of the flow limit.2-4 However, damage could not be easily related to the strongly variable prestrain around a sharp notch. To obtain easier strain measurements, it was decided to use axially precom-pressed bars and bent bars. Final testing was done by

Jan 1, 1970

By T. W. Healy, P. Somasundaran, D. W. Fuerstenau

The flotation behavior of quartz in the presence of alkyl ammonium acetates as a function of alkyl chain length has been interpreted in terms of hemi-micelle formation at the solid-liquid interface. The van der Waals cohesive free energy that is responsible for hemi-micelle formation has been found from these results to be 1.0 kT per CH2 group. This is in excellent agreement with literature values obtained from research on the properties of micelles in bulk systems. Collectors of the type CH3(CH2)n-2CH2-P, where P is a polar group and n is the number of carbon atoms in the straight alkyl chain, will induce flotation of an appropriate mineral at lower concentrations as n increases. This reduction in collector concentration with increasing n has been reported for such systems as xanthates on sulfides1,2 and amines on quartz.' The effect of chain length of alkyl surfactants on such solution properties as conductivity,' surface tension,' and solubility6 and such interfacial properties of solids as contact angle7 and electrokinetic potential8 have received considerable attention, but only limited quantitative descriptions of the effects have been given. The electrokinetic studies of alkyl amine salts on quartz indicated that the solution concentration of collector at which the marked change in electrokinetic potential of quartz occurs decreases systematically as the length of the alkyl chain increases. The aim of the present work was to obtain a quantitative description in terms of current theories of flotation of the effect of the hydrocarbon chain of alkyl ammonium acetates on the flotation behavior of quartz. BASIC PRINCIPLES The marked changes in electrokinetic potentials of quartz in dodecylammonium acetate (DAA) solutions were postulated to result from the association of adsorbed collector ions into two-dimensional aggregates, called hemi-micelles.9 Subsequently, the rapid increase in flotation rate of quartz was shown to coincide with hemi-micelle formation." We would like to discuss briefly the concept of hemi-micelles in terms of recent interpretations of micelles in bulk solution. Micelle hypothesis: In dilute solutions, alkyl ammonium and related salts behave as ordinary strong electrolytes, but at a certain concentration there is a marked change in physical properties of the solutions, e.g., in equivalent conductance, transport number, freezing point lowering and viscosity. To account for these phenomena, McBainl1 introduced the concept of micelles, which are aggregates of long-chain ions. It is believed that the ionic heads of the constituent ions of the micelle are in contact with water, whereas the nonpolar groups turn away from it and are in contact with each other. Work must be done to bring these charged polar groups together, but energy is gained (i.e., so called van der Waals cohesive energy) when hydrocarbon chains are expelled from the water and allowed to associate. For a given polar group, the tendency to form micelles will therefore strongly depend on the hydrocarbon chain length. Theoretical treatments of micelle formation by Shinoda12 and Phillips13 and others lead to the following expression for the concentration at which micelles form (the critical micelle concentration or cmc) in aqueous solutions of long- chain electrolytes

Jan 1, 1964

By H. J. Beach, W. C. Goins

The laboratory development and field use of oil well cement compositions* with high resistance to drilling mud contamination are described. Resistance is obtained by adding a I-lb mixture composed of three parts paraformaldehyde to two parts sodium chromate tetra-hydrate for each sack of cement. This mixture neutralizes the cement-retarding properties of quebracho and other tannins, starch, sodium carboxymethylcellu-lose, Ignite, and monovalent salts of lignosulfonic acid. The retarding properties of calcium lignosulfonate are unaffected. The decontaminating mixture may be used in common cement (designated Type I by ASTM specifica-tions,' Class A by API Std. 10A2) or in a slow set slurry prepared from common cement by addition of calcium lignosulfonate. No changes in slurry viscosities or thickening times are caused by the protecting reagents. The method has been used in 185 field jobs where an improved success ratio has been obtained in plug setting. INTRODUCTION Field experience and laboratory investigations have established contamination by drilling mud as a major factor in oil well cement failures. During 1955, 12 attempts were required to set six open-hole cement plugs in the Timbalier Bay field, La. Eighteen to 30 hours elapsed between placing and testing the plugs in preparation for sidetracking operations. Considerations of rig time expense required immediate resetting where soft cement was drilled after a reasonable waiting period. Sea water drilling mud was used in each well and daily additions of thinners, usually lignites, had been required. Sodium carboxymethylcellulose had been added regularly to control fluid loss. The 50 per cent plug failures were attributed primarily to contamination by the mud. Similar experiences can be found in other fields along the Texas and Louisiana coasts where drilling muds normally contain large quantities of organic treating materials. Cement contamination was the subject of a survey by the Mid-Continent District Study Committee on Cementing Practices and Testing of Oil-Well Cements of the API.3 Data collected from member laboratories and released in Sept., 1951, reported the effects of a number of drilling mud treating chemicals on cement. The study revealed that many of the additives, notably the organic materials in relatively small quantities, had marked effects on the properties of cements tested. Severe losses in strength and erratic thickening time resulted from small additions of mud treating chemicals such as quebracho, starch, sodium carboxymethylcellulose, and lignite. The report included no recommendations of methods for overcoming the problem. One investigation of the contamination problem reported the successful use of activated charcoal in setting cement plugs after conventional slurries had failed.4,5 The investigation indicated that an optimum concentration of 5 per cent activated charcoal was effective in combating contamination from 16.7 volume per cent of treated mud. Laboratory and field muds were included in tests and contained varied quantities of ode or more of the following: quebracho, caustic, starch, lime, and calcium lignosulfonate. The function of the charcoal appears to be physical, removing the organic materials by adsorption. The method may be employed in API Class A or Class D (unretarded slow set) cements. The chemical approach presented here is based on

Jan 1, 1958

By Alfred Weiss

Approximately 850 delegates from 24 countries met in Tokyo, Japan, May 24-27, for the second MMIJ-AIME Joint Meeting in 55 years, to exchange technical knowledge and experience in the fields of exploration, mining, metallurgy and petroleum engineering. The first such meeting was held in 1917 in Kyoto, Japan. Although the Mining and Metallurgical Institute of Japan was the sponsor, the entire meeting (machinery exposition, technical program, and tours) was a joint effort of the two institutes.

Jan 7, 1972

By W. H. Craigue

THE scope of this article covers only the mathematical principles involved in discounting to present worth future expected profits and it is believed answers definitely two questions, which were raised at a recent meeting of the Committee on Methods of Valuing Coal Properties, as follows: 1. The accumulative effect of carrying charges on the value of coal mines showing definitely the number of years beyond which the coal may not be mined at a profit and subsequent to which the possession of any unmined coal will be a liability rather than an asset. 2. The effect on the valuation of coal mines, in the presence of the carrying charges described in question 1, of an increase in plant capacity and production. In general, in considering these questions, it may be stated that the consideration of an increase in plant capacity and production follows as a matter of course after a determination has been made of the year beyond which no profits are to be realized (giving the carrying. charges accumulative effect, or in other words capitalizing the carrying charges, as shown hereinafter). For example, if it is determined that any coal that is unmined after 45 years will have no value or less than no value, the question immediately arises as to whether or not a plant should be constructed that would result in a yearly production great enough to extract the entire tonnage in a time less than 45 years, and if so the number 'of years less than 45 years that would, from a financial stand-point, be the most desirable, all under the assumption that the market for the product or the transportation facilities are such that the yearly production can be increased to the desired amount.

Jan 1, 1933

By Edward Sampson

Despite the many industrial uses, the world market for silver as a commodity is far from free, being dominated by the U.S. Government both through acts of Congress and by policy of the Treasury Department. This discussion will consider aspects of supply, demand, and price with a view to the future. Changes in Sources of Supply: The world's peak production of silver, 278 million oz, was in 1937. In the 1850's world production was about 30 million oz, having risen from a yearly average of 11 million oz for the first half of the century. From 1860 to 1940 there was a steady rise, broken only by World War I and the depression of the early 1930's.

Jan 7, 1960

By William E. Bruce

In recent investigation of drilling processes, the U.S. Bureau of Mines measured the operating characteristics of two percussive drills. Basically, this entailed measuring maximum piston velocities while drilling. The maximum piston velocity is not necessarily the same as the striking velocity. The latter is usually somewhat lower1 because most commonly used drills provide an air cushion which slows the piston just before it comes in contact with the drill rod. Penetration rates for the two drills were determined in nine rock types, and the physical properties of the same nine rocks were measured and tabulated. Then the penetration rates were plotted against the individual properties to determine the general relationships on which methods for predicting drilling rates could be based.2

Jan 1, 1970

By Wilbur T. Stuart

To assist the mining industry in attacking problems of water control, the U. S. Geological Survey has begun a program of research in mining hydrology. In certain fundamental respects water control is similar to development of water supplies from wells or to the drainage of agricultural lands, as many of the tools developed in recent years for quantitative ground-water problems are applicable, with modification, to mine-water problems. In 1952 a 30-day pumping test conducted jointly by the Eureka Corp. Ltd. and the Defense Minerals Exploration Agency provided an opportunity to gain knowledge concerning water movements around a flooded mine shaft. The methods of analyzing the data may be used as a guide for the evaluation of similar problems elsewhere.

Jan 2, 1955

By M. T. Simnad, C. E. Birchenall, M. H. Davis

The transport mechanisms previously proposed in wustite and hematite have been confirmed by movement of inert markers during the growth of these phases. By similar measurements the mechanism for magnetite has been determined. The rates of growth of multilayer scales on iron, magnetite and hematite on wustite, and hematite on magnetite have been measured. All rates are found to be diffusion controlled under the conditions of the experiments. MANY studies have been made of the rate of oxidation of iron in both the low temperature, film-forming region and the high temperature scaling range. The interpretation of the results has been greatly complicated by the formation of multi-layered scales containing the various phases of iron oxides. In most cases no attempt has been made to determine the composition of the scale and its dependence on time of oxidation in a quantitative manner. However, several recent studies'" have taken this variable into account. It is generally agreed that the growth of thick scales on iron follows a parabolic rate law for the increase of total thickness. In the thin film region agreement has been claimed with parabolic equations of various forms and with logarithmic equations. The discussion here will be concerned only with the formation of scales of considerable thickness, greater than several microns, although some of the conclusions may be applicable to thin films. A brief survey will be given of the solid phases of the iron-oxygen system, the stability of wiistite in bulk and in thin films, the relative densities of iron in the metal and oxides, and the kinetics of forma- tion of oxide scales on iron. New experimental results will be introduced at several points during the discussion, and an attempt will be made to formulate a mechanistic picture consistent with these observations. The experimental techniques are described in an appendix. Iron-Oxygen System Fig. la shows the iron-oxygen phase diagram. Wüstite ("FeO"): The lowest of the oxides has a NaCl type cubic lattice formed by close-packing of the relatively large oxide ions with the smaller iron ions arranged in the interstices. The ionic radius for 0' is about 1.3 A, while Fe++ has a radius of about 0.8A and Fe"' about 0.7A. Its range of existence on the phase diagram is very wide for an ionic material of this type and does not seem to include the stoi-chiometric composition FeO. These deviations appear to be well established as vacancies on iron lattice sites by the comparison of lattice parameters and densities for a series of compositions by Jette and Foote.4 The limits of the field are disputed, but the work which seems most reliable" indicates vacancies in from 5 pct to more than 12 pct of the iron sites. In order for the crystal to be electrically neutral, there must be electron holes which correspond to the formation of trivalent iron ions equal to twice the number of vacancies. Magnetite ("Fe³O4"): Considerable disagreement also exists in the literature about the stable range of the Fe³O4 field. Some diagrams show the Fe³O4 composition to be lower in oxygen than the formula indicates, but Schenck6 gives a diagram from the

Jan 1, 1952

By Joseph P. Brennan, Robert L. Vines

A historical comparison of the frequency of fatal coal mining accidents occurring underground in mines of various size ranges in the United States and in member countries of the Commission of the European Communities is presented. Frequencies are normalized on hours-worked and tons-produced bases. The comparisons rely on published and confirmed data and on theory for selective treatment of data in an effort to overcome reporting differences and basic differences in the mining conditions and system employed. Trends are identified ad projections made of the effect on accident records of various industry growth patterns. Conclusions are drawn regarding the reasons for differences between the records of U.S. underground coal mines and the records of those mines in European countries.

Jan 1, 1984

Jan 1, 1938

Jan 1, 1894