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By Dermot M. Ross-Brown

Introduction Slope angles are one of the major factors affecting the shape of the final pit and the location of the walls Due to differences in geology, the optimum slope angles vary from pit to pit and within different parts of the same pit. Indeed, it is not unusual to have different slope angles for the top and bottom portions of the same cross section. The optimization of these slope angles is a major study in itself and this chapter is intended as a general introduction to the subject. It is not intended to be a comprehensive text for the absolute beginner The objective is to put the various aspects of slope stability analysis into relative perspective by describing the vari¬ous analytical techniques available and indicating when each may be most appropriately used References are made to the many excellent texts and papers on slope stability for the reader who does not have a formal training in soil or rock mechanics. In writing this chapter, an assumption has been made that a tentative mining plan has been drawn up, includ¬ing a preliminary estimate of the slope angles. It has also been assumed that all the necessary field and laboratory data has been collected and reduced to a form suitable for input into the stability analyses.

Jan 1, 1979

ALTHOUGH iron ores occur in many parts of Sweden the two principal deposits are those at Grängesberg (see accompanying map) and at Kiirunavaara-Gellivare. Both of these deposits are con-trolled by a holding company, Trajikaktiebolaget Grängesberg-Oxelösund, which sells annually about one-half of, the iron in ore traded in world markets and has a fleet of 24 seagoing ore boats, with a total dead weight capacity of 172,500 tons. Because of its pre-eminence in international iron ore trade a brief outline of its operations will be of interest. ORE DEPOSITS OF GRÄNGESBERG The Grängesberg deposits have been known since the Middle Ages, but up to the middle of the nineteenth century the ore was transported from the mines to the furnaces in winter in. sleighs. Railway building began in 1853, and in 1873 the complicated structure of capital investment was tottering, but the basic bessemer process created a demand for ore high in phosphorus, as this is, and refinancing on the initiative of Sir Ernest Cassel put the principal operation on a firm footing. There are numerous property owners in the district, but they are all controlled by a joint administration board, and 90 per cent of the ore is produced by a subsidiary of the Grängesberg company from proper-ties which it either owns or leases. The ore, a mixture of magnetite and specular hematite, is in lenticular bodies, dipping about 70 E. in. fine-grained gneiss, and contains about 61 per cent Fe and 1 per. cent. P. There are two principal veins; the total ore reserves to a depth of 500 meters are estimated at 150,000,000 tons. As seen in the accompanying illustration, the ores were first worked in open cuts, but eventually underground shrinkage stoping was adopted. Difficulties were encountered in the support of the workings and from the freezing of the ore in the stopes, so slicing was adopted, although block-caving is used in one place. Most of the mining is now done at a depth "of 150 to 190 meters. The present annual output is about 1,400,-000 tons of crude ore, which yields about 1,000,000 tons of concentrate after being subjected to magnetic con-centration and jigging.

Jan 1, 1927

By Edward Sampson, Allan B. Griggs

Surveying of many holes drilled by the U. S. Bureau of Mines in the Metaline district has shown surprising deviations. The holes start in the Ledbetter slate (Ordovician) and pass into the underlying gently dipping Metaline limestone (Cambrian) at varying depths, locally in excess of 1000 it. All holes start vertical, but one had deflected as much as 35° at a depth of only 300 it. One hole was found to be deflected 70' at a depth of 1000 ft. These deviations were not indicated to the drillers by any action of the rods or machines. Analysis of the survey data in the light of the observed geology indicates that the holes deviate most in the Ledbetter slate and scarcely at all in the Metaline limestone. The upper part of the "limestone'" in most holes is a massive rock strongly altered by hydrothermal action and essentially homogeneous. The slate is only obscurely bedded but has a cleavage, varying from slight to strong, which is unrelated to bedding. Drill holes have deflected to become nearly perpendicular to the cleavage. Several plans and cross sections are submitted showing the behavior of various holes. Introduction The Metaline district of northeastern Washington has received much attention recently and has promise of becoming even more important as a source of zinc than at present. Exploration has been conducted largely by deep diamond drilling, and in the course of this work it was found that holes became seriously deflected. This paper deals with the nature and causes of these deflections. The district lies along the Pend Oreille River in the northeastern corner of Washington, about loo miles north of Spokane, 9 miles from British Columbia, and 15 miles from Idaho. Three mines are now in operation and for a number of years have furnished a considerable production of zinc and lead. The ore contains zinc and lead in a ratio of about 31/2 to I, and occurs in the upper part of the Metaline limestone of Cambrian age, the upper member of which, where unaltered, is a rather pure limestone. This is overlain by Ledbetter slate of Ordovician age. Ore has formed by replacement of limestone, commonly 100 to 200 ft. below the slate, in areas of gentle dip, resulting in extensive tabular ore bodies. In and near ore, limestone has been intensely altered to granular dolomite and fine-grained quartz, which, where it predominates, forms "jasperoid." As part of their war program, the Geological survey and Bureau of Mines of the U. S. Department of Interior have been cooperating in an investigation of the district. The exploration by the Bureau of Mines in 1943 and 1944 was conducted largely by deep diamond drilling in which as much as 1000 ft. or more of Ledbetter slate was penetrated before the ore-bearing Metalin-2 limestone was reached. During the course of this drilling it was found that holes were seriously deflected while traversing the Ledbetter slate.

Jan 1, 1949

By Jerome Strauss, Carl L. Shapiro

THIS is a critical examination of the theory that the amount of carbon necessary to form the iron-carbon (carbide) eutectoid is lowered by the addition of any carbide-forming element. Although this theory has been built up over a long period of years,, it appears, in the light of recent published investigations upon the ternary constitutional diagrams of iron with carbon and other alloying elements, to be no longer tenable. A survey of these new results, summarized below, shows that (as is known) some metals lower the carbon content of the iron-carbon (carbide) eutectoid, whereas others raise it, but (as not heretofore clearly set forth) some first move the eutectoid in one direction and then, at higher concentrations, shift it in the opposite direction. Moreover, these differences in behavior exist even among the common alloying metals classed as carbide formers. PART I INFLUENCE OF BODY-CENTERED CUBIC ELEMENTS The effects of the various body-centered cubic metals (chromium, tungsten, molybdenum, vanadium, columbium and tantalum) are reviewed individually. Iron-carbon-chromium System.-In the monograph on Alloys of Iron and Chromium, Kinzel and Crafts' concluded that the carbon content of the eutectoid is lowered by increasing the chromium content. The quantitative influence of chromium on the eutectoid point of iron-carbon alloys was shown by Monypenny2 (Fig. I) and no data have been forthcoming to refute his findings. Iron-carbon-tungsten System.-Gregg,3 in the monograph on Alloys of Iron and Tungsten, accepted the data showing that tungsten decreases the amount of carbon required to form the eutectoid. The influence of tungsten on the eutectoid percentage of carbon as determined by Oberhoffer and Daeves4 is shown in Fig. a; these results have received general approval. Iron-carbon-molybdenum System.-In the monograph on Alloys of Iron and Molybdenum, Gregg5 reviewed the work of Guillet,6 Swinden,7 and Reed,8 all showing that molybdenum lowered the carbon content of the eutectoid, whereas Takei9 contradicted this conclusion. Svetchnikoff and Alferova,10 a little later, showed that large additions of molybdenum shift the eutectoid to the right. These last-named investigators found that molybdenum, up to 1.2 per cent, shifts the pearlite point and the point of maximum solubility of cementite in the gamma phase only slightly in the direction of lower carbon content; on the other hand, increasing amounts of molyb-

Jan 1, 1943

By William A. Johnson

IT was pointed out in an earlier paper1 that our understanding of the atomic mechanism by which diffusion occurs in metallic alloys is scarcely in an advanced state. This unsatisfactory condition is the result not of any lack of interest, but of the difficulty of designing experiments that will yield suitable data. The diffusion coefficient of an alloy, measured in the usual way, is simply a number specifying the rate of homogenization of a nonhomogeneous metal; this number, of itself, can furnish neither the rate at which the individual atoms move nor information as to the mechanism by which they move. It does not necessarily follow, however, that such information cannot he obtained, even if the path to be followed is still not clear. Much success has been attained in the study of diffusion in ionic crystals. A number of experiments, for which there are few counterparts in connection with metals, yields information often indicating a detailed mechanism by which diffusion probably occurs. From such work, quite acceptable theories of lattice imperfections have been developed by Wagner, Schottky, Frenkel, Jost and others.2 It is postulated that real crystals of stoichiometric composition contain, in equilibrium, certain imperfections of which the most important types are: (I) vacant cation sites, with an equal number of interstitial ions; (2) vacant anion sites, with an equal number of interstitial ions; (3) equal numbers of anions and cations in interstitial positions; (4) equal numbers of vacant anion and cation sites. The classification of a particular crystal according to this scheme then follows from studies of the variation of electrical conductivity with pressure of the electronegative component surrounding the crystal, with ion size, and with temperature; other physical phenomena, such as the Hall effect, have aided in establishing the classification. The relative mobility of the anion and cation may be determined by chemical analysis of the salt at the electrodes following electrolysis. With such information, and knowing that one ion never occupies the lattice site normally belonging to an ion of opposite sign, it is usually possible to ascertain the diffusion mechanism. It is clear that the same experiments are not applicable to metal crystals, and substitute experiments that yield as much information have not yet been devised. Much can be learned, however, about the mobilities of the two* kinds of atoms in alloys by the use of radioactive metals as indicators. Only one such experiment has been performed in the past. In 1933, Seith and Keil,3 in an effort to explain the great difference between the rate of diffusion of gold in lead and of lead in lead, measured the rate of diffusion of radioactive lead in a gold-lead

Jan 1, 1942

By G. D. Arsdale

This paper describes a series of experiments leading to the development. of a method for leaching the mixed ores of the Inspiration Consolidated Copper Co., containing chalcocite and silicates of copper, by the use of solutions acidified with sulfuric acid and carrying ferric sulfate. Iron is added to the solutions and ferric iron is regenerated electrolytically to a percentage high enough to act as an efficient solvent. The decreased yield is partly compensated for by a higher current density. AN IMPORTANT problem in modern copper metallurgy, particularly in the Southwest, has been to obtain good recoveries from what are commonly known as mixed ores; that is ores in which the copper occurs partly as oxide and partly as sulfide compounds. The dividing line between mixed ores and ores commonly accepted as concentrating is not definite. In other words, much ore now being concentrated carries considerable copper in non-sulfide form, on which recoveries are hot so good as on ores carrying less of these constituents. While treatment by concentration may be commercially profitable, on ores carrying oxide copper within certain limits, there are large deposits for which the application of con-centration could not be considered, and yet which have not been considered amenable to leaching because they carried too much sulfide. The Inspiration Consolidated Copper Co. has large amounts of such mixed ores, and this paper is an account of the experimental work by which a method was developed for their treatment, and for which a large plant is now being erected by the Inspiration Co. It is not claimed that the method is a general solution of the problem of mixed-ore treatment but it is apparently well adapted for leaching the ores of the Inspiration Co., for which it was designed. The work done has covered preliminary laboratory and test-plant investigation, and .a pilot-plant run, extending from March to the middle of December, 1923. Thoroughly consistent and satisfactory results, were obtained continuously for more, than six months in the pilot plant; and it is believed that the results; and probable costs that can be had on a large scale have been definitely, proved. The method, however, was designed for local conditions; and while the basic principles are general, there are ores on which it will not work and other ores for which considerable modification may be required.

Jan 10, 1925

By E. G. Woodruff

The earlier struggles in petroleum geology were directed to solving the Qrigin and method of accumulation of petroleum. We are now fairly well agreed on those subjects. Most of us think that the great mass of petroleum commercially produced comes from plants or animals, or possibly from both. We are confident that the oil was not produced where it is now found but has accumulated in reservoirs of various kinds. The types of reservoirs are certainly variable but they just .as certainly follow definite geologic laws. Some of these types of reservoirs can be determined from surface study; others cannot. We know, too, that these types of reservoirs (largely structures such as anticlines, domes, and terraces) are much more widespread than the oil pools. In other words, there are many places where good sands and good structures exist but where oil is not found. It is the purpose of this paper, therefore, to attempt to analyze, from a regional standpoint, some of the conditions that control the presence or absence of oil pools and to group them in a regional way, hence the term "Petroliferous Provinces." The paper lays no claim to presenting new facts but attempts to group and classify the information that so many have expressed again and again. The essential factors for an oil field are petroleum, a reservoir material, and conditions under which the petroleum can enter the reservoir but cannot escape except through the drill holes. The paper will first discuss the source of petroleum as it occurs in definite regions, then the regional arrangement of reservoir strata, and finally the areal arrangement of structures. To have petroleum, there must be a source. Since living matter is considered the source of the petroleum, geological conditions must have been such that living organisms were abundant. Arid regions on the earth's surface have not given rise to living things in sufficient abundance to produce oil; similarly, too cold regions and saline inland lakes. The converse of this is that warm moist conditions must prevail to produce an abundance of vegetable matter. Before an area can be

Jan 1, 1921

By J. K. Gustafson

MEASURED in terms of ore tonnage, the New Quebec and Labrador iron ore fields promise to rank with the greatest iron ore districts of the world. -- Over 400 million tons of high-grade ore for direct shipping have been discovered to date. Much greater amounts of lower-grade beneficiating ores are indicated by outcrops. Many hundreds of square miles of iron formation await testing.

Jan 6, 1953

By D. H. Fleming

DURING 1950 the jet-piercing process was used commercially in the piercing of primary blast- holes in magnetic taconite at the preliminary taconite plant of the Erie Mining Co., Aurora, Minn. The Erie Mining Co. purchased a jet-piercing ma- chine and associated equipment in 1949, and the machine has been in operation since its installation in the summer of that year. An overall view of the pit with the JPM-1 jet-piercing machine in operation is shown in Fig. 1.

Jan 7, 1951

By N. A. D. Parlee, E. M. Sacris

OXYGEN solubility in liquid silver has been well studied.1-6 It has been established that the solubility follows Sieverts' law reasonably well5'6 up to po2

Jan 1, 1968

By Henry E. Colton

Very little information has been published concerning the Tennessee coal-field. The State never appropriated over $600 per annum for a geological survey, and that was discontinued about 1870. Yet even with that small sum Dr. J. M. Safford made a

Jan 1, 1886

By Milton Ohring, Stephen M. Edelglass

THE recently determined coefficients for diffusion of very dilute impurities in aluminum are shown in Table I. Of these data the activation energies for Ag110, cu54, Mn54 and zn85 are clustered about the value of self-diffusion in aluminum; for the remaining

Jan 1, 1970

By Ian Campbell

THE year 1952 was marked by several new alltime highs in industrial mineral production; by an easing of the critical situation with respect such minerals as fluorspar and sulphur; by important production of asbestos, lithium, and rare earths; by the perfecting of new products which will place new demands upon industrial mineral supplies, such as "Fiberfrax", and the finding of new uses for old minerals, such as wollastonite; by continuation of basic and applied research; and publication of a notable study of the national mineral economy, viz., the "Paley Report".

Jan 2, 1953

Papers published by the Institute are issued in a variety of forms MINING TECHNOLOGY, issued every other month, contains the TECHNICAL PUBLICATIONS on Metal Mining, Minerals Beneficiation (milling and concentration), Industrial Minerals (nonmetallic) and Mining Geology, Mining Administration, and Geophysics papers relating to Metal Mining (A, B, H, I, K, L ) METALS TECHNOLOGY, issued eight times a year, contains the TECHNICAL PUBLICATIONS of the Iron and Steel Division and the Institute of Metals Division, and once or twice during the year those on Non-ferrous Metallurgy (reduction and refining of nonferrous metals) (C, E, and D ) PETROLEUM TECHNOLOGY, issued every other month, contains the TECHNICAL PUBLICATIONS of the Petroleum Division, together with Geophysics papers relating to -the finding of Petroleum (G, L ) COAL TECHNOLOGY, issued four times a year, contains the TECHNICAL PUBLICATIONS of the Coal Division (F ) MINERAL INDUSTRY EDUCATION DIVISION papers appear in a TECHNOLOGY according to classification of subject matter DISCUSSIONS appear in the respective TECHNOLOGY as available MINING AND METALLURGY is the monthly magazine, which contains papers of general interest and news of the membership

Jan 1, 1952

By Robert A. Cummings, Francis S. Kendorski

The behavior of the rock mass during block caving affects the production of the mine and dictates the loads and deformations placed on required drifts. Traditionally, the drifts used are massively reinforced and buttressed against very high and erratic mining- induced abutment loads or swell muck loads, resulting from undercut- ting. Extensive field investigations in numerous block caving mines in the porphyry intrusive environment, coupled with models developed for tunneling and longwall coal mining, have allowed the development of a unified hypothesis for ore bodies of various degrees of competence. In general, the hypothesis incorporates several sequential steps in the driftlrock mass deformation history, each with characteristic magnitudes, duration, and areal extents depending on ore body competence. 1. Prior to initiating caving, but subsequent to drift development, the rock mass and drift are in a state of near-equilibrium. Zones of stress concentration have stabilized, as for a tunnel. 2. For a newly undercut panel, the rock mass and drifts directly beneath the undercut respond by dilating towards the void created, and undergo a release of compressive strain that manifests itself as tensile failures. 3. For adjacent areas, the rock mass is compressed as the load is shed from the undercut level.

Jan 1, 1983

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By R. D. Young, E. A. Harre

Nitrogen exists in two broad categories commonly designated as elemental nitrogen and fixed nitrogen. Elemental nitrogen is found in nature as a diatomic molecule and constitutes about 78%, by volume, of the earth's atmosphere. Fixed nitrogen is a common term used for nitrogen that is chemically bound to other elements. Although elemental nitrogen is very abundant, nonleguminous plants cannot utilize nitrogen unless it is in the chemically combined form. The content of this chapter is confined to fixed nitrogen since the uses and properties of elemental nitrogen and the fixed nitrogen compounds are different. Certain bacteria associated with legumes are able to fix atmospheric nitrogen, but not to the extent required by succeeding nonleguminous crops. The need to use fertilizers containing fixed nitrogen compounds to grow food crops has been recognized for hundreds of years, and from antiquity farmers have used organic wastes such as animal manures, vegetable wastes, sewage sludge, fish scraps, etc., containing these compounds for fertilizers. These organic materials have a low nitrogen content, however, and cannot support large-scale food production. Known commercial-size deposits of natural nitrates containing much higher nitrogen content exist only in Chile, and the possibility of the discovery of other significant deposits is remote. The Chilean deposits were the major source of nitrogenous fertilizers until the Haber-Bosch process for the production of synthetic ammonia was developed. In the Haber-Bosch process, nitrogen reacts with hydrogen at high temperatures and pressures and in the presence of a catalyst to form ammonia. Modern plants use air, water, and natural gas or other hydrogen sources to produce the ammonia that is now the key building block of the fixed nitrogen industry. Several major problems that developed in the 1970s continue with the nitrogen industry into the 1980s. These are (1) the continuing sharp escalation in the cost of feedstocks for ammonia production as well as all energy sources, and (2) the very steep increase in the investment cost of production facilities. More than 75% of the fixed nitrogen produced domestically is consumed as fertilizers. The types of materials used as fertilizers have changed significantly during the past years. There has been a trend from the use of low-analysis fertilizers to types which contain high percentages of plant nutrients. The average plant nutrient content (N + P2O5 + K2O) of fertilizers used in the United States has increased from 18% in 1930 to 32% in 1960 and today approaches an average of 44%. In the case of nitrogen fertilizers, the low analysis natural nitrates (16% N) gave way to ammonium sulfate (20% N) after about 1920. After World War II, ammonium nitrate (33.5% N) previously used in munitions, became established as the leading nitrogen fertilizer. Urea use as a fertilizer (46% N) began in the 1960s, and in the past 10 years has become the world's leading solid nitrogen fertilizer. Nitrogen Materials Anhydrous Ammonia-Anhydrous ammonia is a colorless gas at ambient temperatures and pressures and has a sharp pungent odor. Anhydrous ammonia is stored and transported as a liquid in high-pressure cylinders and tanks at ambient temperature, and in low-pressure tanks, barges, and ships at -28°F. Anhydrous ammonia is applied directly at 4 to 7-in. depths in the soil as a high-pressure liquid by special applicators, after which it expands to a gas that dissolves in the soil moisture or is absorbed on soil colloids. In other systems ammonia is metered into irrigation water and is thereby introduced into the soil.

Jan 1, 1983

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By J. F. Myers, S. D. Michaelson, F. C. Bond

This work was undertaken with the object of collecting plant data on rod milling, making laboratory tests on representative samples of the various ores, and arriving at a basis for comparing the relative efficiencies of different mills operating on widely different materials and under varying conditions. These efficiencies consider only power consumption and do not include the other elements of operating costs. The over-all economic efficiency may be quite different from the consumption efficiencies with which this paper is concerned. It is hoped that these collected data will be of value in indicating the most favorable conditions of rod-mill operation. Operating-plant data on 14 different installations from II plants throughout the United States and Canada were collected, and laboratory tests were made on samples of these ores. The plant rod mills were all operated wet, and either in open circuit or with circulating loads so small as to be negligible. Data were obtained on one roll-crushing operation at the Utah Copper Co., for comparison. The rolls were operated wet in closed circuit with 10-mesh vibrating screens, and with a high circulating load averaging about 600 pct. This particular roll operation can be considered as a model of efficiency. The collected plant data are necessarily incomplete in some instances. Each ore was assigned a code number, and the name and location corresponding to the code number are listed in Table I when permitted. The power data in every instance refer to motor input. Net power was reported by the operator for samples 1-30 and 1-45, and this was increased by 20 pct to compensate for motor losses and power factor. The plant rod-mill data are listed in Tables 2 and 3. In Table 2 the speeds are calculated on the basis of partly worn rod-mill liners 2 in. thick. Where D

Jan 1, 1949

By E. T. Turkdogan, M. L. Pearce

The rates of sulfurization and desulfurization of calcium aluminate, silicate, and ferrite melts by CO + CO2 + SO2 mixtures at 1550°C are reported. It is shown that for melts 10 to 15 mm deep transport of sulfide ions within the melt controls the rate of sulfur transfer. The rate data from shallow melts, i.e., 1 to 4 mm deep, have been analyzed on the basis of a diffusion or a reaction controlled process and indications are that the both processes may play a part in controlling the rate of sulfur reaction. The rates of desulfurization of silicate XVEACTION equilibria between metals, metal oxides, and gases have received considerable attention in recent years. However, the understanding of and aluminate melts increase with increasing PCO2/PCO ratio in the gas stream, the effect being most marked for aluminate melts. The sulfide equilibrium data obtained from the present work are shown to be in accord with the results of previous studies. It is shown that carbon dioxide has a measurable solubility in silicate, aluminate, and ferrite melts. Consideration is given to the partial equilibria which control the directions and the rates of reactions occurring simultaneously in complex heterogeneous systems. the kinetics of heterogeneous reactions, particularly those occurring at elevated temperatures has not been improved appreciably. Almost all the metallurgical reactions occur in heterogeneous systems involving two or more phases. Although in many authoritative text books and original Papers the basic principles concerning the kinetics of heterogeneous reactions are clearly underlined, they are seldom used to the best advantage in kinetic studies, particularly those involving the metallurgical reac-

Jan 1, 1963