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By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By W. M. Courtis

SINCE many accounts of Silver Islet Mine, in Lake Superior, have already been published, it is supposed that the members of the Institute are familiar with the location and character of the mine. To many, however, a more detailed account of the ore and manner of treatment will, perhaps, not be without interest. The extraordinary richness of Silver Islet ores, and the difficulty of obtaining correct assays, induced the company to erect smelting works of its own. Accordingly, ground was broken at Wyandotte, Mich., early in the spring of 1871, and the work was pressed on with indomitable energy by Captain E. B. Ward of Detroit, as president, and Mr. Thomas MacFarlane, the discoverer of Silver Islet, as superintendent of the works, so that by July 1st the works were so far completed that smelting could be commenced. The intention was to work Western ores with those from Lake Superior, since the latter contain but a small amount of lead. Hence the capacity of the works is much larger than is needed for the present yield of the mine. The planned process for treatment was smelt-

Jan 1, 1874

By William M. Courtis

Since many accounts of Silver Islet Mine, in Lake Superior, have already been published, it is supposed that the members of the Institute are familiar with the location and character of the mine. To many, however, a more detailed account of the ore and manner of treatment will, perhaps, not be without interest. The extraordinary richness of Silver Islet ores, and the difficulty of obtaining correct assays, induced the company to erect smelting works of its own. Accordingly, ground was broken at Wyandotte; Mich., early in the spring of 1871, and the work was pressed on with indomitable energy by Captain E. B. Ward of Detroit, as president, and Mr. Thomas MacFarlane, the discoverer of Silver Islet, as superintendent of the works, so that by July 1st the works were so far completed that smelting could be commenced. The intention was to work Western ores with those from Lake Superior, since the latter contain but a small amount of lead. Hence the capacity of the works is much larger than is needed for the present yield of the mine. The planned process for treatment was smelt-

By J. J. Gilman

IT is well established that dislocations exist in crystals and account for crystal plasticity.' However, the origins of the dislocations are not clear. Among the means by which dislocations might originate are: a) through crystal growth accidents, b) by the collapse of condensed sheets of vacancies, or c) by stress-induced nucleation. Theoretical calculations' have indicated that the last means should require very high stresses in order to operate. The purpose of this paper is to show that the stresses around the tips of cracks are large enough to nucleate large numbers of dislocation loops. Specifically, it will be shown that (100) cleavage cracks in LiF crystals nucleate dislocations in regions of the crystals where dislocations did not exist previously. It is believed that the use of LiF for this investigation does not restrict the significance of the 1 results. In fact, it is believed that this complements and extends previous papers by the same author which dealt with metal crystals.10,14 The dislocations were detected by means of the etching techniques that were described in a previous paper by Gilman and Johnston.3 In that paper it

Jan 1, 1958

By R. W. Raymond

The death of Professor Blake removes the oldest of American economic geologists and mining engineers, and deprives this Institute of one of its earliest and most illustrious members. To many of us it brings a personal loss also, the loss of a friend. William Phipps Blake was born June 21, 1826, in New York City. His father, Elihu Blake, was a surgeon-dentist of eminence, a direct descendant of William -Blake, who settled in the Massachusetts Bay Colony about 1630. He was prs pared for college at private schools in New York, and entered the Sheffield School of Yale, where he was graduated as Ph.B. in the chemical course, class of 1852, the first graduating-class of the institution. In the same year he became chemist and mineralogist of the New Jersey Zinc Co., and chemist of chemical works at Baltimore, Md. In 1853, he started the Department of Mineralogy of the World's Fair at New York City. In 1854, 1855 and 1856, he was mineralogist and geologist of the United States Pacific Railroad Surveys of Willianlson, Pope, and Whipple, and for the War Department at

Jan 1, 1911

By G. Herget, O. Garg

Trends will continue towards more automated, and sometimes larger mining and haulage equipment to reduce pit development and haulage costs. To save labour costs, larger capitalization of open pits is required and pit design and stripping ratios have to be firmed up at a very early stage of mine planning. Bench failures will assume a greater importance with larger equipment and at present we have only a limited capability of predicting stable slopes in complex structural geological settings. Deep open pits will pose particular problems in regard to high toe and floor stresses. This will require the development of more efficient systems for rock mass exploration and an improvement of our predictive capability in regard to pit slope stability and appropriate management of ground- water and materials. To meet the challenge, we have to improve: a) Analytical tools to assess slope stability in structurally complex settings as found in large open pits; b) Core orientation methods during diamond drilling operations; c) Geophysical logging methods to obtain geotechnical and structural geological information for large volumes of rock; and d) Geotechnical data handling systems to define mechanical properties

Jan 1, 1983

By L. D. Hall, S. J. Rothman

The diffusion of lead and of trace amounts of bismuth in liquid lead have been investigated by the capillary method, using ROD and ROE as tracers. The results are compared with existing theories of diffusion in liquids, the agreement with theory being fair. The heat of activation for self-diffusion in lead is found experimentally to be close to the corresponding activation energy obtained from viscosity data. The pioneer data of Groh and von Hevesi for the self-diffusion of liquid lead, using ThB as a tracer, fit in with the present results. OMPARED with the volume of effort expended on solid state diffusion, there has been little attention paid to diffusion in liquid metals. A review of experimental work in this field, covering most of the studies up to 1951, was given by Jost.' More recent papers include those by Hoffman2 on self-diffusion in mercury, Morgan and Kitchener" and Stark, Shchilishchev, and Kazachkev4 on the diffusion of various elements in liquid iron, and Grace and Derge on the diffusion of bismuth in bismuth-lead alloys. The need for more experimental data to aid in the evaluation of existing theories prompted the

Jan 1, 1957

By Samuel S. Wyer

Magnitude and Econonmic Importance THE magnitude and economic importance of the problem of correctly valuing natural-gas leaseholds become evident when we consider that: (a) Natural gas is handled in 55 per cent. of the gas distributing plants in the United States. (b) Present known natural-gas acreage forms 47 per cent. of the total known mineral-land acreage in the United States. (c) Five acres of land are now required to protect and maintain continuous service to each of the 2,000,000 domestic natural-gas consumers in the United States. (d) The cost of acquiring and maintaining this acreage of an expendible resource represents a substantial part of the cost of the natural-gas service to the consumer. (e) "The right of a citizen by means of his ownership of or his mining leases on land to draw gas from beneath its surface is property and sometimes valuable property."1 A large number of other court decisions have established the basic legal principle that the right to drill for gas within a given area constitutes an interest in the land itself, and is necessarily an exclusive property right.

Jan 4, 1916

By Donald L. Birkimer

GENERAL INTRODUCTION To paraphrase comments made by Black and Hoek(1) on the status of rock mechanics, the general methods of applied science related to rock mechanics are: a. Observe the phenomena of nature as they occur and, wherever possible, quantify the observations. b. Propound a model or theory to explain the phenomena observed. c. Test and develop the theory by further experimentation in the laboratory and in the field. d. Use the theory developed to predict behavior in similar or extended circumstances. e. Insure by measured experiment and observation that the predictions made are valid, or that deviations from the predicted behavior can be accounted for. f. Modify the theory and practice as necessary, and continue the process until more general laws can be formulated and applied, with a useful degree of confidence, to practical problems. This paper will present an infant concept. It will, in fact, propound a possibly useful theory to help explain commonly observed phenomena. It will test and develop the theory for a material similar in nature to some rocks. It will be used to predict behavior in the extended circumstances of a

Jan 1, 1971

By W. W. Smeltzer

The linear formation rates of wustite films have been determined over the temperature range 590° to 1030°C using a vacuum microbalance technique. These rates are dependent directly on the partial pressure of carbon dioxide, Activation energies for film and scale formation in carbon dioxide and oxygen atmospheres are equivalent to either the dissociation energies of carbon dioxide and oxygen, or the activation energy for the diffusion of cation vacancies in wustite. Of the metals, iron is the most widely used basic constituent of durable alloys despite its intrinsic property of converting at a relatively rapid rate to the oxides from which it is derived. This property has accounted partially for many investigations on the oxidation of iron at low and high temperatures. Interpretation of the results have been complicated by formation of multilayers containing the various oxide phases. To aid in elucidation of the oxidation kinetics, measurements have been carried out in this investigation on the growth of the wustite surface layer. There are several studies directly related to the objective of this investigation. The growth of multilayer scales has been demonstrated to be diffusion controlled in oxygen at atmospheric pressure over the temperature range 450" to 1200°C by Davies, Simnad, and Birchenall.' To gain an insight into the diffusion mechanism, Himmel, Mehl, and ~irchenall' determined the self-diffusion coefficients of iron in wustite, magnetite, and hematite. These results were used to evaluate the oxidation rates of iron and its oxides, taking as a basis the theoretical parabolic rate equation developed by Wagner., The evaluations were compared to experimental data and were shown to provide essential confirmation of this theory. Fischbeck, Neundeubel, and salzer4 have demonstrated that the oxidation of iron in carbon dioxide and other atmospheres at high temperature obeys a linear relationship. Because the Arrhenius temperature coefficients of the reaction rate constants changed at the A, point they concluded that the passage of iron into the oxide controlled the reaction. This viewpoint has been accepted by Benard and ~albot' to explain the occurrence of linear rates in oxygen before the onset of diffusion-controlled parabolic oxidation. This basic premise of a rate-controlling reaction at the iron/oxide interface has been questioned recently by Hauffe and Pfeiffer.' Since the formation of wustite may follow a linear or parabolic relationship depending on the pressure of the gaseous re-actant, they propose that linear oxidation is determined by a chemisorption reaction while parabolic oxidation is controlled by diffusion. As confirmation of this viewpoint, Hauffe and pfeiffer6 and Pfeiffer and ~aubmeyer' have established that the linear scaling constants of wustite formation at 1000°C in carbon-dioxide or low-pressure oxygen atmospheres

Jan 1, 1961

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.' It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins' solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion' is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965

By J. L. Wyatt

J. W. Tomlison—It seems probable that the author's conclusion, that the conductivity of the slags decreases with increasing content of FeO, is erroneous due to the method of plotting the data. Thus, the results of other workers2,3,13,14 show that the conductivity of molten oxide slags increase with increasing temperature, indicating that the trend of the curve shown by the authors is due to the fact that the data for the slags containing relatively small amounts of FeO are at higher temperatures than those for the slags containing relatively large amounts of this oxide. In this connection the work of Wejnarth2 may be mentioned in which in an investigation of a series of iron silicate slags, the conductivity was found to increase with increasing content of FeO; the fact that the author's slags contained TiO2 probably does not affect the issue since it has been shown15,16 that, at least as far as conductivity is concerned, this oxide behaves essentially the same as silica and that mixtures of the oxide with silica have a very low conductivity of the order of 10-4 mhos at 1750°C. In connection with the experimental technique it may be noted that bubbles of carbon monoxide would probably be produced at the surface of the graphite electrodes in contact with the melts thus rendering the accuracy of the measurements somewhat open to question. J. L. Wyatt (author's reply)—Dr. Tomlinson makes reference to works by Martin and Derge, which indicate that slag systems containing no TiO2 are charac-terized by an increase in conductivity with an increase in temperature. Further, I have cited his examples, which indicate a drastic increase with small temperature change. The results of Dr. Derge's work have no bearing whatsoever on the results of this paper, since the slags under study here contained up to 70 pct TiO2. One cannot generalize on slag systems as a whole on the basis of any one family, for there are definite compounds of ionic nature formed in each system, and the ionic mobilization of these is something that cannot be determined without actual experimentation. Dr. Tomlinson makes reference to an unpublished work which, he claims, shows that titanium dioxide behaves the same as silica in regard to conductivity. Since I have not had 'an opportunity to see the paper I cannot make any comments, but unless the same slag system was studied there can be no specific comparison of results. If the decrease in conductivity of the slag was due entirely to temperature phenomena, as Dr. Tomlinson indicates, then one is without an explanation of the values shown in the paper for slags containing from 10 to 20 pct FeO. I cannot agree that the deviation in findings was appreciably related to temperature change; further, I believe this point was completely covered in the paper. References 13 Endell and Hellbrügge: Glasstech. Ber. (1942) 20, 277. 14 Bockris, Kitchener, Ignatowicz and Tomlinson: Faraday Society. Discussion (1948) 4, 265. 15 Tomlinson: Thesis, London 1949. 10 Bockris, Kitchener, Ignatowicz, and Tomlinson: Unpublished work.

Jan 1, 1951

By Charles E. Locke

PROSPERITY of the gold miner has continued with attendant construction of numerous plants, many of them small but some of good size. Many new mills have been erected in Canada and in the Philippines, end one should mention the new mill at Cripple Creek, Colo., a custom plant allowing a choice of flotation, cyaniding, or roasting and cyaniding. Flotation is a feature of many of the new plants and some existing mills have been remodeled to use flotation in place of amalgamation and cyaniding. The Utah Copper Co. has re- opened its Arthur mill and operations are being resumed in the big Ray, Chino, and Inspiration copper mills. Examples of new construction are the Mountain City 300-ton copper flotation mill in northern Elko County, Nevada; the Star zinc mill and one or two other mills in the Coeur d'Alene district of Idaho; and the 500-ton mill for the Buena Vista mine at Stewart, B. C. The last-named is to be installed underground, following the example of the zinc mill at Gilman, Colo., and he small Doyle jigging plant in the Wisconsin zinc fields.

Jan 1, 1937

By R. W. Fenn, H. A. Lepper, W. R. Hibbard

A. J. Shaler—I should like to congratulate the authors on the presentation of this paper, which we have been awaiting a long time. The view they have taken of the sintering process, namely that voids are comparable to particles of a second phase capable of dissolving to a slight extent in the metal phase, is an interesting but dangerous one. Pines has given a first-order solution of the problem and Has predicted a decrease in the concentration of pores near the surface. The authors of the present paper have experimentally demonstrated the second-order effects, that is, the diffusion of the space phase between voids of different sizes, and also the movement of atoms from highly curved parts of a void to less curved regions of the same void. I have recently calculated the rate of vapor-phase transport within odd-shaped pores in copper at 850 °C and found that probably at that temperature volume flow is the more rapid shape-changing mechanism. The authors of the present paper have found that at 1000°C, vapor-phase transport is dominant. There is no disagreement here, I think. The dominant phenomenon can easily be different in different temperature ranges and with different pore shapes: I used a cylinder going to a sphere, not a tricuspid going to a "triple cuspidor." But there is some danger in the other art of the explanation, that is, in the study of the diffusion of vacancies from a pore to its neighbors and to the outside. A vacancy is very different in dimension from an atom. When it moves, it carries a field of elastic strain. This has to be taken into account. A concentration gradient of vacancies can cause them to diffuse. But in the absence of such a gradient, they can be made to diffuse by a field of stress. What happens in some of our experiments, and it is most noticeable in the shrinkage of synthetic cylindrical pores, like the tubes we have been working with, may be broken down into the following steps. (1) The presence of a surface establishes a vacancy concentration gradient, as Dr. Kuczynski and the present authors have shown. (2) Vacancies then diffuse in order to decrease this gradient. (3) In so doing, they cause an elastic field to be built up in such a direction as to oppose the diffusion, so that it slows down until it reaches a steady-state rate. (4) The steady-state flow is due to the fact that the surface tension acting on curved surfaces applies a stress to the system which itself mechanically causes vacancy diffusion. What I have said is that the diffusive types of flow of the authors and of Dr. Kuczynski are transient phenomena which soon stop if the pores are large. We are then left with a mechanical problem only, and our researches have not yet disclosed just what the mechanism of flow is; it may be a slip process, or it may take place by a vacancy diffusion of the type Nabarro has de-

Jan 1, 1951

By Fred P. Peters

At first glance this paper may seem unique among those comprising this symposium on designing for powder metallurgy, since it is evidently concerned with everything but Powder metallurgy. This paradox mill be at once resolved, however, when the real Purpose of the symposium meeting is understood—to present factually and objectively the things that can and cannot he done with powder-metallurgy methods, and especially to set forth with brutal frankness the limitations of Powder metallurgy, so that costly over-enthusiasm and misapplication may be prevented. Since much of powder metallurgy's future development (and many of its present disappointments) has been in competition with other and long-established methods of fabricating parts, it is easy to see that its true competitive possibilities in any given case cannot be accurately appraised without rudimentary knowledge of what the competition can do. This paper, therefore, presents a few reminders of things you all know—a background to be kept in mind as you examine the data on each of their specialties given by the authors of the papers that follow. From the standpoint of the design engineer powder metallurgy is often in Competition with one or more of the following: sand casting, die casting, permanent-mold casting, precision investment casting, ma- chined bar stock, screw-machine parts, cold-heading, drop-forging, and stamping and drawing. We will here briefly discuss each of these individually, and set forth so, rough (and therefore dangerous) generalizations about its competitive position, especially with respect to powder metallurgy. Sand Casting Sand-casting of small parts is sometimes an inexpensive method of manufacture, for its raw-material costs (i,e., for gray iron) are the lowest of the various methods and it involves the use of no tools and dies of jewelry quality. its design flexibility— that is, the ability to make complicated, cored and undercut parts in one piece—is about the highest of the competing processes and in this respect it can do many things that are impossible by powder metallurgy. For small castings its production rates may be higher, by using multi-impression molds, than can be achieved with parts of the same size by powder metallurgy. But its labor charges for melting, pouring, patternmaking and molding are comparatively high and the waste it entails in gates and risers is always considerable. Tolerances of sand castings are wide (+1/6 to 1/32 in- per in.) and where precision approaching that of powder metallurgy is required sand castings must be machined to final size, thus increasing their cost. Steel sand castings are more expensive and less precise than iron, and nonferrous the most costly of all.

Jan 1, 1945

By C. Baldwin Sawyer

J. S. Vanick,* Washington, D. C. (written discussion).—To those who have been confronted with the study of the gas-metal reactions, this paper is a most welcome contribution. My personal interest in work bearing upon this general problem, stimulated by an appreciation of the difficulties inherent to problems of this type, prompts a few words of discussion. Table 2 of the paper shows a gradual increase in the nitrogen content with an increase in pressure, and an interpretation follows in which nitrogcn is used as the compressed medium when the conditions admit that cyanogen gas could be active as a contaminating ingredient. Fusions of electrolytic iron made in the induction furnace in an atmosphere of deoxidized nitrogen and out of contact with contaminating materials have shown no microscopic evidence of -a nitrogen increase; using a refractory-lined graphite crucible in the furnace under the same conditions or admitting air often resulted in the occurrence of nitride needles in the solidified melt. These results suggested that a nitrogenous compound served as a vehicle for the introduction of nitrogen and that such compound was not available when the pure gas and carbon-free refractory were used. The fusion of pure iron in pure nitrogen is perhaps a matter of theoretical interest. The author's work serves a more practical purpose when applied to steels rather than iron. Table 2 reports the absence of nitride needles in melts made under pressure of one atmosphere, although the quantity of nitrogen present would seem to exceed microscopically detectable percentages. In some recent work29 on carburized iron, nitride needles have been observed in areas analyzing as low as 0.015 per cent. nitrogen. This low percentage of nitrogen would indicate that the solubility limit is less than 0.030 per cent. for hypoeutectoid steels. There is the possibility that the areas of pearlite which exist in a hypoeutectoid steel restrict the distribution of nitrogen and limit its presence to the ferritie fields. In view of this work and the references quoted by the author, I am led to expect that the value for the solubility of nitrogen in solidified iron may approach

Jan 1, 1924

HeRbeRT Haas,—(communication to the Secretary*).—Fig. I plainly shows that the comparison of the steam-turbine and Diesel-engine plants was made on a basis of 6,000 kw. continuous operating load. The tabulation of costs for an 8,000-kw. load is merely done to show the relation of increased output on the unit power costs. Both plants would sacrifice their reserve capacity, which is to insure continuous operation, if operated to generate 8,000 kw. continuously; unless Mr. Hawkins advocates the operation of one of the turbines at 33.33 per cent. overload, retaining the other as a standby, which, besides overtaxing the turbine, results in a great loss of efficiency. It would be well for Mr. Hawkins to qualify certain of his statements. Thus, under the caption "Diesel Engines, Selection of Units," he says that '(two of the largest Diesel-engine builders take the position that, in the present state of the art, they would not attempt to put out units over 1,000 kw.;" he should qualify it by saying that "two of the largest American Diesel-engine builders take the position that, in the present state of the art in the United States, they would not attempt to put out units over 1,000 kw." The reason that American manufacturers restrict themselves at present to units of that size is to be found not so much in a lack of experience in building large units as in a lack of a sufficient demand for them in the United States to justify the heavy capital outlay connected with the development of such engines. There are relatively few localities in the United States where fuel prices are as high as they are in the South-, west, and regions of high fuel prices are sparsely settled and have a very limited demand for power. Where low fuel prices obtain, steam turbines are active competitors of Diesel engines for large power plants, particularly when the station load factor is low. As most of the American manufacturers of Diesel engines work under license agreements with European manufacturers, which limit their market to the United States and its possessions and Canada, a further limitation is imposed upon them, leaving to European firms practically the entire world as a market. The greater number of power plants range in size from 300 to 1,000 hp.; the average size of the central station, on a basis of all central stations in the United States, not greatly exceeding 500 kw.; in these sizes it is hard for steam engines to compete with Diesel engines, unless fuol oil prices are excessively high, and coal prices very low, or the exhaust steam is used for heating purposes.

Jan 1, 1917

By D. L. Sikarskie, B. Paul

A theory is presented for the static penetration of a single rigid wedge into brittle material. The material considered is one which exhibits both crushing and chipping phases in the penetration process. If the wedge angle and three parameters are specified, the theory predicts forces and associated penetrations during both the crushing and chipping phases. For certain ranges of the parameters agreement with the limited experimental data available is promising, except for the initial phase of the penetration process where refinements on the proposed theory are required. The theory also predicts that for certain values of the wedge angle and other known parameters, the chipping process does not occur and penetration is due entirely to crushing. When viewed in detail, the drilling of rock by percussive means involves, among other things, system dynamics, actuating forces, dynamic stress levels and the actual penetration mechanism of the bit into rock. If rock drills are to be significantly improved, a thorough understanding of the entire system would be highly desirable. In this paper, one aspect of the system, namely the mechanism of penetration of the bit, will be studied in detail. It has been found1 that for the velocities encountered in percussive drilling (of the order of 20 fps) a static analysis adequately describes the penetration process, at least for some rocks. Hence, we will only be concerned with describing analytically the static penetration of a single wedge shaped tool. It will further be assumed that the wedge is long enough to permit a two-dimensional analysis. Numerous authors have studied the static penetration of a wedge into rock. The following papers give some of this work and provide additional references to other work. Cheatham2,3 has assumed the rock to behave plastically and has obtained force-penetration equations for both Coulomb-Mohr and parabolic yield criteria. Evans and Murrell4 have studied the penetration of two types of coal and have found equations relating the penetration characteristic (P/dSc) to wedge angle for the various strength coals tested. race' attempted to find a correlation between hardness as determined by indenting the material and other mechanical properties and concluded that the results of such a test are generally inconclusive. His paper however contains a very extensive bibliography on the indenting of many different materials. Gnirk6 also has a fairly complete literature review on the static penetration of rock, of which he makes use in his indexing studies. A wide range of behavior is found in the wedge penetration of different rocks under different external conditions. For example, a rock that is essentially elastic-brittle at standard pressure may become elastic-plastic at a high confining pressure.7 It has also been observed4. " that some rocks will merely be crushed and indented by a wedge, whereas others will crack and form chips, furthermore the existence or non-existence of chips depends in great measure on the geometry of the indentor, type of rock and the depth of penetration. Hence, to attempt a theory which embraces all possible behavior is not practical at present. We, therefore, confine our attention to predicting the force-penetration characteristic and volume removal behavior for a type of rock which exhibits both crushing and chipping phases in the penetration process. Such behavior is characteristic of the harder rocks such as granites and represents a more difficult problem than the behavior of softer rocks such as coal and certain sandstones. In this preliminary study an attempt will be made to describe only the essential features of this complex penetration process. A qualitative description of these essential features is obtained with the aid of Fig. 1.1, where a wedge of vertex angle 28 is shown at some intermediate stage of the penetration process. As the wedge advances, the rock is fragmented (i.e. crushed) in some local region surrounding the wedge, the shape of this region being unknown. Simultaneous with the fragmentation in this local region, essentially elastic stresses are assumed to be building up in the surrounding rock. When a certain penetration level, di+1, is reached, the stresses along some surface are sufficient to cause failure and a chip is thus formed. The process now repeats, i.e., a crushing phase followed by the formation of a chip.

Jan 1, 1965

By John D. Verhoeven

A technique has been developed for carrying out normal freezing experiments with a current density of 2000 amp per sq cut passing through the solid-liquid interface. The equation relating the effective distribution coefficient to the equilibrium distribution coefficient in electric field-aided solidification, originally developed by Huckc et al.,1 has been modified for the case of concentrated solutions. Preliminary experiments on the Sn-Bi system give qualitative agreement with the equation. The data are analyzed by a slightly novel use of the normal freeze equation which allows one to determine the effective distribution coefficient more easily. Very extensive mixing in the liquid was found at these high current densities and it is postulated that the mixing results from a vertical component of the magnetic Lorentz force generated by the electric current. In the search for techniques of obtaining ultrahigh-purity metals the inefficient but very effective technique of electrotransport has received little attention. Electrotransport is most effective in the liquid state and a natural application, therefore, is to apply an electric field across the liquid zone of a zone-melting experiment. The present investigation was undertaken to study the effect of an electric field upon solidification of metals, so that the usefulness of electrotransport in such solidification experiments as zone melting could be determined. In zone-melting and normal-freezing experiments it is difficult to achieve complete mixing in the liquid in the immediate vicinity of the solidifying interface. Consequently a solute build-up will occur at the interface in the portion of the liquid where complete mixing does not occur (an equilibrium distribution coefficient, ko, less than one, and unidirectional atom motion will be implied throughout). This local solute build-up produces a corresponding rise in the solute concentration in the solid so that the ratio of the solute concentration between the solid and the bulk liquid is larger than the equilibrium distribution coefficient. This ratio is defined as the effective distribution coefficient, k,. The differential equation describing the solidification process may be derived by applying the continuity equation to an expression for the net solute flux at the interface. The solution to this differential equation then allows one to determine the solute distribution in the liquid and the relationship between k0 and ke. One of the most useful solutions to this equation was first derived by Burton, Prim, and Slichter,' in which they assumed that a) the equilibrium distribution of solute was maintained on the plane of the interface, 11) the solute build-up ahead of the interface in the liquid disappeared at a distance 6 from the interface, and c) the solute distribution in the liquid was invariant with time. The following well-known relation between ko and ke was then obtained, where R is the rate of solidification and D the diffusion coefficient of the solute in the liquid. This equation appears to correlate the data from a number of different types of solidification experiments very well. Application of an electric field across the solid-liquid interface can produce an additional flow of solute atoms as a result of the electrotransport. When the polarity of the field is such as to direct the electrotransport flux away from the interface the solute build-up may be diminished, even to the point of producing a solute depletion and a consequent ke smaller than ko. The quantitative description of this process and the resulting form of Eq. [I] was first given by Hucke et al.1* and then inde- where E is the electric-field intensity and U is the differential mobility, i.e., the velocity of the solute atoms with respect to the solvent atoms per unit electric field. Both authors follow the method of Burton, Prim, and Slichter in their derivation, the only difference being the additional electrotransport term in the flux equation. It has been pointed out1,3 that Eq. [2] predicts the possibility of a noticeable increase in the purification of materials by solidification in an electric field. The validity of Eq. 121 has not been checked experimentally and it is possible that other factors' arising from the presence of an electric field across

Jan 1, 1965

By G. R. Lehman

The Inspiration Consolidated Copper Co. had an orebody at Miami, Ariz., of close to 100,000,000 tons of low-grade copper ore, and the method of mining this ore most profitably was of great importance. The selection of a method was practically limited to a "top-slicing," a "shrinkage-stope" or a "caving" method. The "top-slicing" method would give a high extraction of the developed ore, at a high mining cost, and the "shrinkage-stope" or "caving" methods a lower extraction of the developed ore, at a lower mining cost. Ore-Drawing Tests To decide on the method to be used it was necessary to know about what extraction of the ore could be obtained by the "shrinkage-stope" or " caving " methods. As no definite information regarding the,question was available at the time, C. E. Mills, the general manager, thought that some information could be obtained by experimenting in drawing ore, covered with capping, from an experimental box. Some work had already been done along these lines by W. C. Browning for the Inspiration Copper Co. and by myself for the Live Oak Development Co. The idea was to represent as nearly as possible, in the experimental box, the conditions within an area of caved stopes of caved ore all ready for drawing. That is, the area was supposed to represent a semibroken mass with the capping above it in the same condition and ready to follow the ore downward as it was drawn out of the chutes under the ore. To represent the above condition, in the experimental box, crushed ore from the mine was placed in it to a given height, and red barren capping from the mine was placed on top of the ore. The Experimental Box The experimental box shown in Fig. 1 was made of wood and glass. The glass was used for the sides so that the drawing action of the outside row of chutes could be seen and noted, the latter being cut in the center by the glass sides. The length of the box was 30 in., width 20 in. and the

Jan 1, 1917