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By G. F. Loughlin

More than 20 years have passed since the publication of Lindgren and Ransome's report on the Cripple Creek District,1 which was made when the district was much more active and prosperous than in recent years. They concluded that the output of the district, which had reached its maximum of about $18,200,000 in 1900, would gradually decline, and their conclusion has been confirmed by records of subsequent production. Between 1905 and 1915 annual declines were partly compensated by encouraging increases, especially in 1908, 1914, and 1915; but a rapid continuous decline followed, due largely to the war and its after-effect's, until in 1922 the value of output was only slightly more than $4,000,000. It rose to nearly $5,000,000 in 1924, but declined again in 1925 and in 1926, when it was about $4,400,000, and represented ores mainly from deep levels in the Cresson and Portland mines. The profitable operations of these two mines were the principal factors leading to a study of ore at deep levels in the district by the U.S. Geological Survey in cooperation with the Colorado Metal Mining Fund. The principal reasons for Lindgren and Ransome's conclusion were three: (I) the greater cost and difficulty of deep exploration; (2) the decrease in the number of veins with increasing depth, and (3) the probability that the telluride ore, believed to have formed at comparatively low temperature, would not persist indefinitely in depth. Operations since they made these statements have verified the first two, but call for some modification of the third. Rich telluride ore is being mined at a profit in the Portland mine 3000 ft. below the present surface, 07. 5000 ft. below the original surface of the Cripple Creek volcano, as interpreted by Lindgren and Ransome. The question arises, therefore, as to the number and extent of such deep deposits, and the answer, so far as it can now be given, must be based mainly on structural data, supplemented by data on the processes of ore deposition. Presentation of these data based on a study of deep mines in the southeast quarter of the district, the only

Jan 1, 1927

By L. Eaton, A. W. Last, J. L. Stevens

COPPER ore from Kennecott Copper's Ray mine, about 60 miles southeast of Phoenix, Ariz., is concentrated at the company's mill at Hayden, some 18 miles south of the mine. The Hayden mill is currently treating 16,000 tons of ore per day by flotation, using raconite, a crude butyl xanthate, as a collector for the sulfide copper minerals and lime as a pyrite depressant.1 The ore contains significant amounts of nonsulfide copper minerals, but recovery of these values has been low. The Hayden mill is now being modified to provide for treatment of future ores by leach- precipitation-flotation (L-P-F). This modification, costing about $5 million, is expected to reduce the loss of nonsulfide copper values and improve overall copper recovery by an additional 2 lb per ton of ore.

Jan 11, 1957

By C. G. Goetzel

Until recently porous bronzes have found many applications for self-lubricating bearings in the automotive, electrical, household appliance and general machine industries. The bulk of an annual production of several million pounds of copper powder had gone into the manufacture of these articles, of which by now more than a billion are in service. However, the war has brought severe curtailment of these bearings because of the scarcity of the two main constituents, copper and tin. The development of substitute materials of equal or superior properties has led to a large-scale replacement by products made from iron powder. In spite of the diminished interest in powdered copper-tin alloys caused by this trend, it was believed worth while to investigate some mechanical properties of these materials as a reference base for substitutes. In addition, experiments using the hot-press method were incorporated to investigate possibilities of saving vital equipment or opening new fields of applications. It must be assumed that by this time the powder metallurgy process of making porous bronzes, a development that found its first industrial applications more than 10 years ago, is well known in engineering. The patent literature and bibliography is volu- minous, most publications referring to porous, self-lubricating bronzes, containing about 10 per cent tin and I to 5 per cent graphite, with porosities in the range of 25 to 35 per cent.l-7 The excellent antifriction properties of these bearings, caused by the uniform impregnation with oil, are dependent on the interconnection of the pores and the uniform distribution of the graphite inclusions. The sintering mechanism of porous bronze, with its structural changes during the transformation of the metal powder into the sintered bearing has been shown in colored photomicrographs by Hall.* Diffusion between copper and tin was found to begin within one minute, when tin-rich transitory phases were formed. After 25 min. a homogeneous matrix of alpha was reached for an alloy containing 9.5 per cent tin and 6 per cent graphite. Price, Williams and Garrand,9 studying certain metal powder combinations in which sintering is accompanied by the cementing action of a liquid phase, including a 90-10 bronze sintered at 925°C., have found that if the treatment is carried out within the liquidus and solidus temperature range of the system, a peculiar process of alternate solution and precipitation occurs. The particles of the major solid constituent are dissolved in the minor liquid phase, but thereafter are reprecipi-tated on certain nuclei, which develop into large grains, usually rounded.

Jan 1, 1945

By Harry M. Mikami

Refractories are heat-resistant, generally nonmetallic materials used as the linings of furnaces or high temperature vessels in the steel, iron, nonferrous metals, glass, cement, lime, ceramic, chemical, petroleum, paper, and power and heat generation industries. Refractories must have structural strength at high temperatures but also, in many applications, must simultaneously resist chemical-physical corrosion-erosion from stags, metals, granular solids, or gases. Among the major uses are the pyrometallurgical processes for producing iron, steel, copper, aluminum, nickel, lead, zinc, etc. Rotary cement kilns, glass tanks, refineries, utility boilers, chemical and ceramic (including refractories) plants, and a myriad of other smaller scale users employ refractories in the high temperature parts of their operations. Thermal, chemical, and structural conditions under which refractories are used differ widely so there is a great variety of refractories to fill the various needs. Two major classifications are the "basic" and "acid" types. Basic refractories include magnesia and chromite, singly and in combinations, dolomite, and forsterite (olivine). The acid category includes aluminosilicates, alumina, and silica. There are a number of other specialized types such as carbon, graphite, silicon carbide, zircon, and zirconia that have important applications but are used in much smaller amounts than the major categories. Physically, refractories can be divided into bricks and shaped products on the one hand and unshaped or monolithic products (also termed specialties) on the other. There are many further subclassifications and divisions, a discussion of which is beyond the scope of this chapter; see Refs. 2 and 9. Raw materials for the principal basic refractories are magnesia and chrome ore. Magnesia, generally termed magnesite or periclase, is obtained mainly from seawater or saline brines extraction, but substantial amounts are produced from mined magnesite (MgCO3). Dolomite (CaCO3•MgCO3), another important basic refractory, is obtained entirely from mined sources. Acid refractory raw materials are: fire clays, flint clays, kaolin, and other natural clay minerals; aluminosilicate minerals such as kyanite, andalusite, sillimanite, pyrophyllite, bauxitic clays; calcined refractory grade bauxite, alumina from the Bayer process for the alumina group; and quartzitic rocks for silica refractories. The total value of all refractories shipped in the United States in 1974 was $989 million, a record to that date. Of this amount, about 73% represents bricks and shaped products and 27% is in nonshaped or monolithic products which comprise mortars, cements, castables, plastics, and ramming and gunning mixes. Fig. 15.4E.1 shows the rising value of all U.S. refractory shipments in the period 1948-1974. Values of brick and shapes paralleled

Jan 1, 1976

By D. S. Newton

Introduction Historically the production of zinc dust has been based upon residual and secondary zinc. Using horizontal retorts filled with diecasting scrap, galvanizers drosses and sweater billets, dust has been produced by condensation into static condensers on a 24 hour cycle. Although fairly flexible as regards input materials the process is not amenable to close control of the product, is labour intensive and unless carefully run can cause fume problems. With a steadily increasing demand for zinc dust of consistent properties and higher quality there is a demand for an improved method of manufacture in which dust can be produced continuously and which is capable of close control thus ensuring a minimum amount of oversize or unsaleable material. The Process in use in the works of Imperial Smelting Corporation (Alloys) Ltd. in England, and in Canada and Holland, satisfies the criteria stated above, and has proved to be easy to control with a minimum labour demand.

Jan 1, 1970

By AIME AIME

T'HE Columbia Section of the A. 1. M. E. took charge of the Western Mining Convention on Oct. 3, and the meeting was held under their auspices. W. L. Zeigler, chairman of the Section, called the session to order. The first paper on the program, "Lead Refining Practice at Bunker Hill Smelter," was presented in per-son by the author, A. F. Beasley, superintendent of the smelter. He pointed out the differences in the refining practice at Bunker Hill from other American refineries. The Bunker Hill plant was the first to adopt the liquation process for silver skims as developed in Australia. Details were given of operating practice with results. F. F. Colcord questioned the author in regard to the kind of metal best suited for kettles, which was said to be cast iron.

Jan 1, 1929

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By H. E. Ellis, O. L. Patterson, Granville Dutton

A large-scale water-injection program for the Holt Bryant reservoir of the Delhi field has been established by means of the new automatic multi-pool analyzer. The objectives of this program were to increase reservoir pressure and eliminate a cross-dip gradient of 200 psi. Pressure increases during the first 15 months of operation have allowed for increased oil production rates of 2,600 BID or 25 per cent. To determine the required water injection it was necessary to predict natural water influx ram. Elimination of the pressure gradients required the water-injection program to account for the fluid migration and pressure interaction between segments of the reservoir. An integral part of the ana1ysis included the determination of in-place volumes of oil and gas. The operation of the automatic multi-pool analyzer in determining the water-injection program is described. New features of the analyzer inc1ude an automatic maferial balance analog and a leart-squares computer for determination of unknown reservoir properties. Operational procedures are sufficiently simple to allow direct use by reservoir engineers on a routine basis. The rapidity and accuracy with which problems may be solved permit repeated ana1yses as a check upon reservoir performance. INTRODUCTION This paper describes the use of a new analog com- puter in determining the optimum injection program for a complex reservoir. The Holt-Bryant (Fig. 1) is the major reservoir in the Delhi field of Louisiana. Production is from the Tuscaloosa at subsea depths of 2,970 to 3,286 ft. The sand dips to the south and southwest from three to five degrees. The reservoir is approximately 12 miles long and varies in width from 1/2 to 2 miles. Various calculations have placed the initial volume of oil in-place in the wide range of 275 to 355 million STB. Two small gas caps were initially present in the reservoir. The Holt-Bryant reservoir was discovered in Dec.. 1944, and was fully developed with 188 producing wells by 1948. After development was completed, an east-west pressure gradient began to establish itself. This

Jan 1, 1957

By V. Koump, T. F. Perzak, R. H. Tien

A series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts Mere measured during essentially one-dimensional freezing of Al-Cu alloys. The dimensions of the ingots were 3 by 5 by 6 in. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experitments. For each alloy the rate of heat removal was varied to give a total jreezing time in the range 3 to 30 min. The results of these measurements cowlpared favorably with the theoretical model of freezing of binary alloys with time-dependent surface temperature. IN engineering analysis of solidification of commercia1 steels and nonferrous alloys it is a common practice to assume that an alloy freezes by propagation of an isothermal solidification front, i.e., essentially as a pure metal. In two recent theoretical investigations'j2 the present authors explored the possibility of a more realistic approach to the problem of solidification of alloys. In the proposed model the freezing of an alloy is assumed to take place by propagation of two isothermal fronts, i.e., the liquidus front and the solidus (or eutectic) front. The region between the two fronts contains both liquid and solid and is referred to as the solid-liquid region. The width and the solid content of the solid-liquid region vary with alloy type, solute concentration, and cooling rate. For a given alloy system, initial concentration of solute, and the mode of heat removal, the proposed model yields the temperature distribution within the solid skin, temperature, solid fraction, and concentration distributions with the solid-liquid region, and the rates of propagation of the liquidus and the solidus fronts. This model is obviously of considerable practical importance in engineering analysis of solidification processes, since it gives a more realistic estimate of skin strength during solidification and a better estimate of the total freezing time. Before the new model can be used with confidence, however, it is necessary to test this model experimentally. The experimental testing of the proposed model is a relatively simple matter since the effects to be measured are large and a relatively simple experiment will suffice. The theoretical model predicts, for example, that during freezing of an alloy containing substitutional type solute (negligible diffusion in the solid during freezing) the solid-liquid region occupies an appreciable portion of the ingot, even at low concentration of solute.' Another prediction of the theo- V. KOUMP, formerly with U. S. Steel Corp., is now with Research and Development Center, Systems and Process Division, Westinghouse Electric Corp., Pittsburgh, Pa. R. H. TlEN is Senior Scientist, Fundamental Research Laboratory, U. S. Steel Corp., Research Center, Monroe ville, Pa. T. F. PERZAK, formerly with U.S. Steel Corp., is now with Fiber Industries, Greenville, S. C. Manuscript submitted March 6, 1968. IMD retical model, easily verifiable by experiment, is that the rate of propagation of the solidus (or eutectic) front increases as the solidus front approaches the center of the slab. This prediction is contrary to well-known behavior of the solidification front during freezing of pure metals, where the rate of propagation of the solidification front decreases with time and freezing is completed at the lowest rate. A rather severe test of the proposed model is provided by comparison of theoretical predictions and experimental measurements of the effects of cooling rate and composition on the rates of propagation of the liquidus and the eutectic fronts. In order to test the soundness of the formulation and the method of solution of the problem of solidification of alloys a series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts were measured during essentially one-dimensional solidification of A1-Cu alloys. The A1-Cu system was chosen strictly as a matter of convenience. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experiments. For each alloy the rate of heat removal was varied to give the total freezing time in the range 3 to 30 min. The results of these measurements are compared with the predictions of the theoretical model of solidification of binary alloys, with time-dependent surface temperature.' Before the experiments described in this paper were undertaken, a serious attempt was made to utilize the measurements of previous investigators to test the theoretical model. In the course of this preliminary study a careful review was made of experiments of Pellini and coworkers3 and Doherty and Melf~rd.~ The measurements in Pellini's work were carried out using a steel containing at least four major components. Evaluation of the solid fraction-temperature relation for this steel (required in the theoretical model) is difficult and uncertain. Doherty and Melford, on the other hand, measured the solid fraction-temperature relation experimentally, but did not give sufficient data to explore the effects of composition and the cooling rates on solidification. Hence it was not possible to utilize these measurements to test our theoretical model. EXPERIMENTAL METHOD The experimental technique used in this investigation differs somewhat from the more conventional techniques employed in solidification studies. This technique was developed primarily to eliminate con-vective mixing in the molten metal caused by pouring of molten metal into the mold. In our experiments A1-Cu alloys were melted directly in the mold. The mold assembly used in solidification experiments is shown in Fig. 1. The mold was fabricated from *-in. stainless-steel sheet. The dimensions of

Jan 1, 1969

By Joseph Jensen

MANY fields have been zoned by nature with shales and intermediate waters between oil zones. Limitations thus imposed have been the basis on which the field was developed. In contrast thereto, in the Ventura Avenue Field, nature proved more generous. Always expecting to find such similar limitations, operators drilled deeper and deeper into the oil zone without finding any distinctive shale bodies other that the Gosnell shale and only one intermediate water, which became the point below which the final water shut-off of each well was made. Thus, on top of the structure, about 3300 ft. of oil-bearing zone has been penetrated below this intermediate w9ter-a distance of 4000 ft. below the Gosnell shale. At first it seemed that the greater the penetration in the zone, the better the well. The error of this assumption became evident

Jan 1, 1930

By R. E. Somers

1. INTRODUCTION 1. Location, Topography, and Climate The Burro Mountains are located in the southwestern part of New Mexico, in Grant County. The group is made up of two distinct moun-tain masses, known as the Little Burros and the Big Burros, the former lying about 6 miles southwest of Silver City-, and the latter about 9 miles farther in the same direction. They are separated by the valley of the Mangas River, a tributary of the Gila, and a stream only in name, except after a heavy down-pour of rain. . The Little Burros attain an elevation of 6,625 ft. above sea level, and the Big Burros 8,054 ft., with the surrounding country averaging about 6,000 ft. To the south of these mountains stretches the desert plain, while to the north are the more frequent elevations of the mountainous country.

Jan 5, 1915

By Charles C. Russell

Pressures developed by the coal during the coking process have been responsible for serious trouble to many companies that operate or build by-product coke ovens. The insidious nature of this trouble is indicated by the fact that oven operators, unless they have ascertained the characteristics of the coals they use, cannot determine the existence of dangerous pressures until after the damage has been done. A rather popular misconception is that ease of pushing of the charge at the completion of the coking period indicates that no dangerous pressure has been developed, but this is far from the truth; pressures developed during the coking period are often completely dissipated by the shrinkage of the charge in the completion of coking, and so any criterion based on the ease of pushing is futile. However, methods of testing coals are available that will definitely distinguish the dangerous coals from those that are safe, and such methods have been brought to a high degree of certainty. The operator should take no risk that involves either a lack of knowledge of the behavior of coals during coking or the failure to believe that certain of the coals or coal mixtures can cause damage to the oven structure. This merely tends to minimize the problem and leads to claims that coking coals of all kinds may be carbonized with no danger of damage to the oven structure provided some particular kind of byproduct oven is used. This lack of appreciation of the true situation is in itself one of the main factors leading to damage of coke-oven structures. Coals that develop more than a certain safe pressure cannot be used in by-product coke ovens without causing damage to the side flue walls. The following paper presents a highly certain method for the measurement of the pressures developed during the carbonization of coal—a method that is the culmination of many years of work on the problem in which a number of methods for the purpose were investigated and used. While actual pressures found may appear to be small when expressed in pounds per square inch, the number of square inches in each oven wall is so large that the total pressure on the oven wall becomes an enormous load.

Jan 1, 1940

By Charles C. Russell

Pressures developed by the coal during the coking process have been responsible for serious trouble to many companies that operate or build by-product coke ovens. The insidious nature of this trouble is indicated by the fact that oven operators, unless they have ascertained the characteristics of the coals they use, cannot determine the existence of dangerous pressures until after the damage has been done. A rather popular misconception is that ease of pushing of the charge at the completion of the coking period indicates that no dangerous pressure has been developed, but this is far from the truth; pressures developed during the coking period are often completely dissipated by the shrinkage of the charge in the completion of coking, and so any criterion based on the ease of pushing is futile. However, methods of testing coals are available that will definitely distinguish the dangerous coals from those that are safe, and such methods have been brought to a high degree of certainty. The operator should take no risk that involves either a lack of knowledge of the behavior of coals during coking or the failure to believe that certain of the coals or coal mixtures can cause damage to the oven structure. This merely tends to minimize the problem and leads to claims that coking coals of all kinds may be carbonized with no danger of damage to the oven structure provided some particular kind of byproduct oven is used. This lack of appreciation of the true situation is in itself one of the main factors leading to damage of coke-oven structures. Coals that develop more than a certain safe pressure cannot be used in by-product coke ovens without causing damage to the side flue walls. The following paper presents a highly certain method for the measurement of the pressures developed during the carbonization of coal—a method that is the culmination of many years of work on the problem in which a number of methods for the purpose were investigated and used. While actual pressures found may appear to be small when expressed in pounds per square inch, the number of square inches in each oven wall is so large that the total pressure on the oven wall becomes an enormous load.

Jan 1, 1940

By M. R. Todd, J. Szekely

THE mechanism of carbon oxidation in steelmaking processes has attracted considerable attention in recent years. The generally accepted model postulates that the reaction between carbon and oxygen occurs at the surface of CO bubbles that originate at the suitable nucleation points and subsequently rise through the metal bath.1-4 Although this model describes adequately the behavior of open-hearth type operations, it is not a satisfactory representation of carbon oxidation in oxygen steelmaking processes since it cannot account for either: i) the very high rate of oxidation per unit bath area,or ii) the commonly reported shapes of the curves showing the dependenie of the oxidation rate on the carbon concentration. The very high decarburization rates commonly encountered in oxygen steelmaking processes need no further elaboration; some typical plots of the rate of carbon removal against carbon concentration, taken from a publication by Li, Dukelow, and smith,' are reproduced in Fig. 1. It is seen from the curves that the decarburization tends to decrease from a peak or a plateau once the carbon concentration falls below a certain value; in the experiments reported, this critical value ranged from 1.2 to 0.2 wt pct C. The apparent dependence of the decarburization rate on the carbon concentration indicates that within this region phenomena associated with the transfer of car- bon must play an important if not predominant role. Since the concentration of oxygen in molten iron at steelmaking temperatures (removed from the immediate impact zone) is only about 0.1 wt pct,6 it is clear that simple simultaneous diffusion of carbon and oxygen to the surface of CO bubbles could not account for the rate of carbon transfer being the controlling step at carbon concentrations as high as 1.0 wt pct. The purpose of this communication is to present an alternative model which may explain at least qualitatively the apparent anomalies mentioned and may stimulate further experimental work. The Physical Model. It is suggested that the principal mechanism of decarburization is the reaction between CO bubbles and an emulsion consisting of molten iron and molten iron oxide particles in the vicinity of the "slag-metal interface9'.* This mech-

Jan 1, 1968

By F. C. Bond

SIZE of grinding media is one of the principal factors affecting efficiency and capacity of tumbling-type grinding mills. It is best determined for any particular installation by lengthy plant tests with carefully kept records. However, a method of calculating the proper sizes, based on correct theoretical principles and tested by experience, can be very helpful, both for new installations and for guiding existing operations. As a general principle, the proper size of the make-up grinding balls added to an operating mill is the size that will just break the largest feed particles. If the balls are too large the number of breaking contacts will be reduced and grinding capacity will suffer. Moreover, the amount of extreme fines produced by each contact will be increased, and size distribution of the ground product may be adversely affected. If the balls added are too small, grinding efficiency is decreased by wasted contacts that are too weak to break the particles nipped; these largest particles are gradually worn down in the mill by the progressive breakage of corners and edges. Ball rationing is the regular addition of make-up balls of more than one size. The largest balls added are aimed at the largest and hardest particles. However, the contacts are governed entirely by chance, and the probability of inefficient contacts of large balls with small particles, and of small balls with large particles, is as great as the desired contact of large balls with large particles. Ball rationing should be considered an adjunct or secondary modification of the principle of selecting the make-up ball size to break the largest particle present. Empirical Equation In 19521,2 the author presented the following emerical equation for the make-up ball size: B - ball, rod, or pebble diameter in inches. F = size in microns 80 pct of new feed passes. Wi - work index at the feed size F. Cs - percentage of mill critical speed. S — specific gravity of material being ground. D == mill diameter in feet inside liners. K - 200 for balls, 300 for rods, 100 for silica pebbles. Eq. 1 was derived by selecting the factors that apparently should influence make-up ball size selection and by considering plant experience with each factor. Even though Eq. 1 is completely empirical, it has been generally successful in selecting the proper size of make-up balls for specific operations. But an equation based on theoretical considerations should be used with more confidence and have wider application. The theoretical influence of each of the governing factors listed under Eq. 1 was accordingly considered in detail, as described below, and a theoretical equation for make-up ball sizes was derived. Derivation of Theoretical Equation Ball Size and Feed Size: The basis of this analysis is that the largest ball in a mill should be just sufficient to break the largest feed particle into several pieces, excluding occasional pieces of tramp oversize. In this article the size F which 80 pct passes is considered the criterion of the effective maximum particle feed size. The smallest dimension of the largest particles present controls their breaking strength. This dimension is approximately equal to F. As a starting point for the analysis it is assumed that a 1-in. steel ball will effectively grind material with 80 pct passing 1 mm, or with F- 1000µ or about 16 mesh. The breaking force exerted by a ball varies with its weight, or as the cube of its diameter R. The force in pounds per square inch required to break a particle varies as its cross-sectional area, or as its diameter squared. It follows that when a 1-in. ball breaks a 1-mm particle, a 2-in. ball will break a 4-mm particle, and a 3-in. ball a 9-mm particle. This is in accordance with practical experience, as well as being theoretically correct. Confirmation of this reasoning is supplied by the Third Theory of Comminution," which states that the work necessary to break a particle of diameter F varies as F. Since work equals force times distance, and the distance of deformation before breaka4e varies as F it follolvs that the breaking force should vary as F½ These relationships are expressed in Table I, with a 1-in. ball representing one unit of force and breaking a 1-mm particle. This establishes theoretically the general rule used in Eq. 1 that the ball size should vary as the square root of the particle size to be broken. Ball Size and Work Index: The work input W required per ton" varies as the work index Wi, and the

Jan 1, 1959

By AIME AIME

COUNCIL PRESIDENT OF THE COUNCIL. D. W. BRUNTON DENVER, COLO. (Term expires February, 1911.) VICE-PRESIDENTS OF THE COUNCIL. W. C. RALSTON SAN FRANCISCO, CAL. W. L. SAUNDERS NEW YORK, N. Y. H. V. WINCHELL ST. PAUL, MINN. (Term expires February, 1911.) BENJAMIN B. LAWRENCE NEW YORK, N. Y. JOSEPH W. RICHARDS SOUTH BETHLEHEM, PA. ALBERT SAUVEUR CAMBRIDGE, MASS. (Term expires February, 1912.)

Mar 1, 1910

By AIME AIME

. COUNCIL.* PRESIDENT OF THE COUNCIL. D. W. BRUNTON DENVER, COLO. (Term expires February, 1911.) VICE-PRESIDENTS OF THE COUNCIL. W. C. RALSTON SAN FRANCISCO, CAL. W. L. SAUNDERS : NEW YORK, N. Y. H. V. WINCHELL ST. PAUL, MINN. (Term expires February, 1911.) BENJAMIN B. LAWRENCE NEW YORK, N. Y. JOSEPH W. RICHARDS SOUTH BETHLEHEM, PA. ALBERT SAUVEUR CAMBRIDGE, MASS. (Term expires February, 1912.)

Apr 1, 1910

By AIME AIME

COUNCIL.* PRESIDENT OF THE COUNCIL. D. W. BRUNTON DENVER, COLO. (Term expires February, 1910.) VICE-PRESIDENTS OF THE COUNCIL. J. PARKE CHANNING NEW YORK, N. Y. FREDERICK W. DENTON PAINESDALE, MICH. JOHN B. FARISH DENVER, COLO. (Term expires February, 1910.) W. C. RALSTON..: SAN FRANCISCO, CAL. W. L. SAUNDERS NEW YORK, N. Y. H. V. WINCHELL ST. PAUL, MINN. (Term expires February, 1911.)

Jun 1, 1909

By AIME AIME

COUNCIL.* PRESIDENT OF THE COUNCIL. CHARLES KIRCHHOFF NEW YORK, N. Y. (Term expires February, 1912.) VICE-PRESIDENTS OF THE COUNCIL. BENJAMIN B. LAWRENCE NEW YORK, N. Y. JOSEPH W. RICHARDS SOUTH BETHLEHEM, PA. ALBERT SAUVEUR CAMBRIDGE, MASS. (Term expires February, 1912.) S. B. CHRISTY BERKELEY, CAL. W. A. LATHROP PHILADELPHIA, PA. GARDNER F. WILLIAMS WASHINGTON, D. C. (Term expires February, 1913.)

Mar 1, 1911

By AIME AIME

COUNCIL.* PRESIDENT OF THE COUNCIL. D. W. BRUNTON DENVER, COLO. (Term expires February, 1910.) VICE-PRESIDENTS OF THE COUNCIL. J. PARKE CHANNING NEW YORK, N. Y. FREDERICK W. DENTON PAINESDALE, MICH. JOHN B. FARISH DENVER, COLO. (Term expires February, 1910.) W. C. RALSTON SAN FRANCISCO, CAL. W. L. SAUNDERS NEW YORK, N. Y. H. V. WINCHELL ST. PAUL, MINN. (Term expires February, 1911.)

Mar 1, 1909