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By Donald R. Rathburn, Jung K. Mok

An historical review and a survey of current practice in the application of fine dry grinding in the iron ore industry are given. Both closed and open-circuit applications are reviewed, and the advantages, disadvantages, and process considerations for these two systems are discussed. The ground ore temperature rise, and the cool-ing of ground ore and mill ventilation are also discussed, along with the agglomerating characteristics of dry ground ore. Screening during the production of high-grade lump ore for blast-furnace burden, particularly from recently developed ore deposits in Australia, South America, and Africa, has resulted in large tonnages of fine iron ore. Certain owners have decided to stockpile these fines until some later date. Others have either sold these fines "as is" for agglomeration at the steel plant or have established their own pelletizing plants to produce a premium quality agglomerate. In almost all cases some grinding is required prior to pelletizing. Most of these ores occur in the weathered state which may result in difficulty in the thickening and/or filtering stages when ground in a wet system. The resulting filter cake would probably require partial drying to provide a product suitable for the subsequent balling operation; however the partial drying and subsequent material-handling steps often produce random agglomeration. Normally, these agglomerates will cause problems in the green ball formation process. Thus dry grinding has developed as a solution to this problem. Most of the dry iron ore grinding installations utilizing the standard-type rod or ball mill are grinding high-grade natural ores that do not require beneficiation. Although power consumed per ton of final product is 120% or greater in dry grinding as compared with wet grinding, the additional power required for dewatering and handling a wet ground product can easily exceed the initial power savings. Dry grinding of raw feed and clinker has been practiced in the cement industry for many decades but its major application to the iron ore industry has taken place only within the past ten years. The successful application of dry grinding to iron ore has required the solution of several unique design and operating problems. The purpose of this paper is to review recent developments in fine dry grinding of iron ore for pelletizing and to discuss the various designs and operating parameters involved.

Jan 1, 1971

By William P. Blake

In directing attention to the newly-opened zinc-ore region in Southwestern New Mexico, I adopt a suggestion made at the Engi neering Congress last summer in Chicago by Prof. Le Neve Foster, who commended the indication of the geographical position of a district under description by means of an outline-map. Such a map is the more important in this instance, inasmuch as the region to be described is remote and little known even in the United States. Until within a few years it has been infested by the savage Apaches, has not been often visited by mining engineers, and could not be

Jan 1, 1895

By R. P. Carreker, R. L. Fullman, J. C. Fisher

CREEP tests are usually constant load tests. As deformation occurs, the cross section of the specimen changes so as to maintain approximately constant volume. Until necking starts, A _ l0 A0 - 1 where A is the cross-sectional area, 1 is the specimen length, and the subscript o indicates initial values. Thus, during a tensile creep test under constant load, the stress increases in proportion to the elongation. A A, 1, where S is the stress and F the load applied to the specimen.

Jan 1, 1954

By R. J. Brison, O. F. Tangel

The development of a new method of mineral separation was sponsored by the International Salt Company, which requested Battelle Institute to investigate means for improving the quality and appearance of rock salt from the Company's Detroit mine. Although developed specifically for removing impurities from rock salt, the general method may be applicable to other separation problems. The principal impurities in rock salt from the Detroit mine are dolomite and anhydrite which represent 2 to 5 pct of the weight of the mined salt. In the size range from 114 to 112 in. (the range of primary interest in this project) the impurities are only partially liberated from the halite in normal production. Further size reduction to improve the liberation of impurities is not practicable in view of the market requirements for the coarse grades of rock salt. Laboratory separations in heavy liquids showed that, to improve the quality and appearance of the rock salt substantially, it would be necessary to remove not only free gangue particles but also a large proportion of the locked-in particles.

Jan 8, 1960

By B. E. Morgan, C. K. Dumbauld

The need for a low-strength cementing composition for use in well cementing is reviewed and results are presented of laboratory and experimental field tests of a modified cement having a controlled ultimate tensile strength of approximately 200 psi. The modified cementing composition may he prepared from either high early strength or normal portland cements by the addition of bentonite clay and a suitable agent for dispersing and controlling the set of the slurry. Substitution of the modified cement for conventional slow-set cements may give better completion results in many wells because the modified cementing composition has lower set strength, lower slurry density, and greater slurry stability than conventional cement slurrieh. The lower ultimate strength allows greater penetration with less shattering of the set cement when perforating casing and cement. The lower elurry density allows the placement of longer columns of cement slurry, and the greater slurry stability reduces the possibility of having an uncemented section caused by the settling of cement particles before the cement set.. INTRODUCTION High strength lias always been one of the accepted criteria of a good cement. During the early use of portland cement in well cementing. emphasis was placed upon securing cements with higher strengths. In 1931, Barkis' reported that, "Normal oil well cements have been improved to develop greater strengths and uniformity of product, which has aided in producing successful jobs in cementing the deeper strings." As long as most wells were completed by the open-hole method. the use of cements having high strengths seemed desirable, and there was no objection raised against high-strength cementing compositions. For a number of years. how-ever, the industry has been completing a large numher of wells by setting and cementing casing through productive horizons and then obtaining production by gun-perforating the section of casing opposite the desired interval. Although this method has been generally successful, difficulties have been experienced in some cases in completing or recompleting wells because of apparent lack of adequate penetration by the bullets through the casing and surrounding sheath of cement and into producing formation. In addition to the penetration trouble: there have been indications that fracturing and shattering of the set cement by perforating might he a contributing factor in causing the failure of some jobs to exclude water or gas from oil producing zones. The possibility that cements having high set strengths were contributing to til difficully ill obtaining satihfartory perforating results has re. ceived attention during recent years. Gun perforating tests conducted in 1944 showed that the depth of bullet penetration into set cement varied with the hardness of the cement, the greater the strength of the cement the less being the penetration. In 1946, Farris2 pointed out that high strength cements were not needed in well cementing, and in 1947, data published by Oliphant and Farris3 showed that set cement was perforated without shattering at approximately 150 psi tensile strength. whereas at approximately 300 psi tensile strength severe cracking and shattering occurred. Oliphant and Farris suggested that wells be perforated at the proper time interval after placement of the cement so that the set cement would have the desired strength. Several difficulties may he encountered in trying to perforate a cement job at the correct time to catch the tensile strength near 150 psi. The rate of strength development of different cements varies considerably. This fact is illustrated by results of tensile strength measurements presented in Fig. 1. These data show that at 175°F the tensile strengths of three conventional slow-set cements varied from 75 to 235 psi at the end of 12 hours. After 24 hours, the tensile strengths varied from 200 to 455 psi. The rate of strength development is affected. also. by the temperature of the forniation, and this adds to the uncertainty of perforating at the rorrect time, since accurate well cementing temperatures may not he known in many cases. Furthermore, in the recomple-tion of wells it is sometimes necessary to perforate cement which has set for a long period and has developed maximum or final strength. In view of the apparent need for a cementing composition having a controlled ultimate strength, an investigation was

Jan 1, 1951

By C. K. Dumbauld, B. E. Morgan

The need for a low-strength cementing composition for use in well cementing is reviewed and results are presented of laboratory and experimental field tests of a modified cement having a controlled ultimate tensile strength of approximately 200 psi. The modified cementing composition may he prepared from either high early strength or normal portland cements by the addition of bentonite clay and a suitable agent for dispersing and controlling the set of the slurry. Substitution of the modified cement for conventional slow-set cements may give better completion results in many wells because the modified cementing composition has lower set strength, lower slurry density, and greater slurry stability than conventional cement slurrieh. The lower ultimate strength allows greater penetration with less shattering of the set cement when perforating casing and cement. The lower elurry density allows the placement of longer columns of cement slurry, and the greater slurry stability reduces the possibility of having an uncemented section caused by the settling of cement particles before the cement set.. INTRODUCTION High strength lias always been one of the accepted criteria of a good cement. During the early use of portland cement in well cementing. emphasis was placed upon securing cements with higher strengths. In 1931, Barkis' reported that, "Normal oil well cements have been improved to develop greater strengths and uniformity of product, which has aided in producing successful jobs in cementing the deeper strings." As long as most wells were completed by the open-hole method. the use of cements having high strengths seemed desirable, and there was no objection raised against high-strength cementing compositions. For a number of years. how-ever, the industry has been completing a large numher of wells by setting and cementing casing through productive horizons and then obtaining production by gun-perforating the section of casing opposite the desired interval. Although this method has been generally successful, difficulties have been experienced in some cases in completing or recompleting wells because of apparent lack of adequate penetration by the bullets through the casing and surrounding sheath of cement and into producing formation. In addition to the penetration trouble: there have been indications that fracturing and shattering of the set cement by perforating might he a contributing factor in causing the failure of some jobs to exclude water or gas from oil producing zones. The possibility that cements having high set strengths were contributing to til difficully ill obtaining satihfartory perforating results has re. ceived attention during recent years. Gun perforating tests conducted in 1944 showed that the depth of bullet penetration into set cement varied with the hardness of the cement, the greater the strength of the cement the less being the penetration. In 1946, Farris2 pointed out that high strength cements were not needed in well cementing, and in 1947, data published by Oliphant and Farris3 showed that set cement was perforated without shattering at approximately 150 psi tensile strength. whereas at approximately 300 psi tensile strength severe cracking and shattering occurred. Oliphant and Farris suggested that wells be perforated at the proper time interval after placement of the cement so that the set cement would have the desired strength. Several difficulties may he encountered in trying to perforate a cement job at the correct time to catch the tensile strength near 150 psi. The rate of strength development of different cements varies considerably. This fact is illustrated by results of tensile strength measurements presented in Fig. 1. These data show that at 175°F the tensile strengths of three conventional slow-set cements varied from 75 to 235 psi at the end of 12 hours. After 24 hours, the tensile strengths varied from 200 to 455 psi. The rate of strength development is affected. also. by the temperature of the forniation, and this adds to the uncertainty of perforating at the rorrect time, since accurate well cementing temperatures may not he known in many cases. Furthermore, in the recomple-tion of wells it is sometimes necessary to perforate cement which has set for a long period and has developed maximum or final strength. In view of the apparent need for a cementing composition having a controlled ultimate strength, an investigation was

Jan 1, 1951

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969

By P. Raffinot, M. Rey, V. Formanek, G. Sitia

CONCENTRATION of oxidized copper and lead ores by flotation has been practiced for 30 years, but flotation of oxidized zinc ores has remained unsolved until a few years ago. This problem is, however, of great importance in mining districts where large tonnages of oxidized zinc ores exist in underground mines or in dumps. Some sulphide ores also possess a degree of oxidation high enough to justify recovery of oxide zinc minerals. Various attempts have been made to float the zinc carbonate, smithsonite.

Jan 4, 1954

By C. Wert, D. Keefer

The results of this study indicate that sudden increases in aging temperature lead to reversion phenmena in carbon in the a, iron system. These phenomena are thought to be associated with the dissolution of carbide precipitates. Reversion is studied with respect to three variables: 1) Specimen grain size, 2) the initial amount of carbon in solution, and 3) difference between initial and final aging temperature. It is found that of these variables the initial carbon concentration has the greatest effect on reversion. THE solid solution of carbon in n iron has been the subject of numerous investigations throughout the past few years. Despite the great amount of effort which has been put forth toward understanding this system, however, there persist a number of interesting aspects of the system which are open to further research' Studies Of the precipitate which forms as a result of aging a supersaturated solution of carbon in a, iron appear to be particularly interesting. The present work is an attempt to determine certain

Jan 1, 1960

By S. J. Noesen, J. R. Hughes

Several four-inch-diameter tungsten ingots were arc melted in vacuum or in hydrogen atmospheres. Melting pressures, melt-off rates, effect of atmospheres, and other pertinent factors were examined. Two of these ingots were extruded at 1650°C. Subsequently, forging and rolling were carried out at lower temperatures. For a 60 per cent area reduction by rolling, a one-hour recrystallization temperature of 1250°C was obtained. This temperature is considerably lower than those reported in previously published work, and can probably be attributed to the extreme purity of the as-cast ingots (N, H, 0 all less than 1 ppm). EVER since W. D. Coolidge, in 1909, described his process for producing tungsten metal of high density and good workability via the powder metallurgy tech-

Jan 1, 1961

By Richard D. Snouffer

Prime topics of conversation these days are the new concepts of rail haulage for bulk items such as iron ore, potash and coal. We have heard such ideas as the "integral train" and the "unit train" discussed frequently during the past two years at various AIME meetings, and progress reports have kept up a steady appearance in the technical press and in local newspapers. While no railroad has a complete "unit train" in service at this moment, one has 50 fast-discharge cars under construction and the Pennsylvania Railroad has experimented with radio-controlled motive power distributed at intervals throughout the train. To a great extent, however, the promise for greater efficiency and lower costs held out to industry by these new haulage methods is dependent not on greater speed or larger cars or more dedicated equipment alone but, rather, on the utilization of modern practices in the loading and unloading of rail cars. It is the purpose here to examine these two key steps and the up-to-date procedures and equipment they entail.

Jan 7, 1963

By Henry D. Hibbard

At the beginning of a Henry M. Howe lecture it seems fitting to refer to Howe's great contributions to steel metallurgy, and particularly to the literature thereof. Most of my predecessors in this role have been able, from their association with him, to give direct testimony as to his great services; but although connected with him for years in a business way, I am less familiar with what might be called his academic side, except as it is embodied in his utterances, written and oral. Howe was adept in his genial way in extracting information in any line which, at the time, was of interest to him. In a technical lecture one expects as a rule new knowledge—something about recent advances relating to the subject. On this occasion, however, I will ask you to go back with me to the primary department of steel lore, as the title of my lecture shows, to review the more fundamental features in that field for the purpose of seeking some gaps which we can fill and so give the subject renewed interest. In thus going back one must inevitably repeat many familiar facts, but that seems to be necessary in order to reach a clear understanding of the unrecorded matters. The full interpretation of a steel analysis is at present unattainable, though much progress toward that end has been made. The ultimate analysis, giving the percentages of the five commonly determined elements, does indeed usually give a fair idea of what the steel is, and is ordinarily enough, with knowledge of its history and physical condition, to enable it to be assigned to some purpose or use for which it is reasonably suitable. But discrepancies arise. Every maker and every user of steel knows, from at least occasional examples in his own experience, that the ultimate analysis is insufficient by itself to enable one to tell positively, from its interpretation, either the mechanical properties of the steel or its adaptability to the purpose for which it was made. Further, if, while having the specified composition, it is abnormal or unsatisfactory, why it is so. Good, bad and indifferent steels may have substantially the same ultimate analysis.

By T. A. Ring

The bed filtration of colloidal particles has been modeled by performing a differential particle balance. The balance considered the localized particle deposition rate to be the sum of three rate resistances: mass transfer to a region near the surface, adhesion onto a partially filled surface, and resuspension from a partially filled surface. The differential particle balance equations, one for the free particles and one for the adhered particles, were solved by a finite difference algorithm. Results of this model are compared to experimental filter breakthrough curves.

Jan 1, 1985

By William H. Hamilton

Tunnel-driving capabilities in terms of feet per hour have advanced several hundred percent in the last century. Indications are that this capacity will double each decade for the next three decades. These future improvements will be made possible by a greatly increased need for underground excavation and the awareness of industry of its own latent capabilities. The factors of most interest to any potential user of a tunneling machine are those making possible an increase in production. The first and most obvious factor, and probably the one that has created the excitement and interest of most people, is the increase in boring rate through faster rock fracture and improved support systems. Boring rate can be increased by more horsepower in the form of increased thrust, torque, and cutterhead speed, and by better cutters and cutting methods, better material-handling systems, and better ground-control systems. All of these items are extremely important and are the basis of much discussion and effort by everyone concerned with the excavation of tunnels by machine. The second factor, just as obvious and equally important as an increase in boring rates, is "increase in production through better utilization of the tunneling machine and related equipment," which means a reduction in downtime through greater reliability of equipment. Mechanical rock attack is presently capable of cutting hard rock at 5 fph and soft rock at more than 20 fph. In current practice, however, this advance rate is maintained for less than 50% of the shift time. I predict that tunnel-driving contractors and their supporting manufacturers of tunnel-boring equipment will provide machinery that will maintain these advance rates for more than 90% of the shift time. This increase in effective production will be due to the increase in reliability of the tunneling machine and tunneling system components. Such a percentage increase in utilization of the tunneling equipment is just

Jan 1, 1970

By T. M. Yegulalp

This article summarizes some of the results of the continuing research activity at the Henry Krumb Schools of Mines, Columbia University, directed towards a better understanding of the stochastic behavior of slurry flows in underground coal-slurry pipeline systems. Fundamental ideas supported by field observations are presented and a Semi-Markov model of the slurry flows is developed. As a result of this formulation, behavior of combined slurry flows from N independent coal faces can be expressed in analytical form. The contents of a slurry surge tank receiving slurry flows with certain stochastic characteristics is investigated in a function of discharge pump characteristics and time.

Jan 1, 1983

By E. K. Olson

Eagle Mountain mine of Kaiser Steel Corp. began production in 1947 when the direct shipping ore contained 51-56% Fe. The high grade, wide ore face and low stripping ratio ores were rapidly depleted and Eagle Mountain required processing plants for upgrading and more efficient mining equipment. During 1970-71 total annual pit tonnage averaged 56 million tons of material ranking the Eagle Mountain Mine as the fourth largest in the country. Ore production averaged 12.5 million tons requiring a stripping ratio of 3.5: 1. During this period mining activities were scheduled for a three-shift, seven-day operation. The present mining rate is about 30 million tpy on a two-shift, five-day schedule.

Jan 12, 1972

By N. J. Grant, E. Gregory

The creep rupture properties of wrought aluminum powder products made from five grades of sintered aluminum powder were investigated at temperatures from 400° to 900°F for rupture times up to 1000 hr. The effect of stress concentrations on materials of this type was investigated by means of notched creep rupture tests. A tentative correlation was obtained between the creep rupture properties and the structure as revealed by electron micrographs. SEVERAL papers have been published recently concerning the production and properties of wrought aluminum powder products and their possible high temperature applications. Most of the published work in this field has come from abroad, notably Switzerland, and articles by Irmann and his colleagues were summarized in English recently.'.' Most of the papers published by Dr. Irmann are principally concerned with the retention of properties (by a product which is produced from extremely fine flake powder and is subsequently hot extruded) after heating to high temperature for prolonged times. The powder may be in atomized or flake form, and during hot working the applied pressure is reported to plastically deform the aluminum powder, thus breaking the oxide skin and welding the particles together. Irmann attributes the remarkable properties to the dispersion of oxide inclusions. Specifically, the product described by Irmann is one labeled SAP (Sintered Aluminum Powder) in which the initial flake powder is so fine that at least 50 pct of the flakes have one dimension of 2 microns or less. The composition of the starting aluminum shows in percent, Fe, 0.18; Si, 0.19; Zn, 0.06; Ti, 0.03; Cu, Mn, Mg, all nil; balance Al, approximately 99.5 pct. Aluminum is not the only material that has been found to have increased resistance to deformation at elevated temperatures when produced by powder metallurgy. It has been reported by Middleton, Pf eil, and Rhodes- hat platinum has a higher recrys-tallization temperature when produced by powder metallurgy and exhibits peculiar properties, many of which are similar to those of the aluminum powder products. Difficulties were encountered in explaining the reason for the strengthening in the case of platinum since the existence of the oxide is doubtful. The authors attributed the special properties to "a small amount of suitably dispersed porosity." This theory was supported by von -~eer-leder4 in the discussion to the paper, and the similarity between this method of hardening and that suggested by Rohner in his theory of age hardening was pointed out. R. de Fleury5 attempted to explain some of the properties in terms of the modulus of elasticity and elastic limit of alumina and aluminum while von Zeerleder examined the relationship between the yield strength and the reciprocal of the powder particle size. Boenisch and WiderholtQ dealt mainly with the corrosion resistance of the powder aluminum material and compared it with other aluminum alloys. The diffusion rates of other metals in SAP and pure aluminum have been compared by Seith and Lop-mann.' They showed that the alloying metals diffuse particularly quickly in SAP possibly due to the very fine grain size. The properties of the Alcoa products were given by Lyle.' The creep rupture properties of SAP and two of the Alcoa experimental powder products were compared by Gregory and Grant hnd it was shown that these products are vastly stronger at 900°F than are the best cast and wrought alloys at 600°F. Since the publication of these data, the authors have investigated two further aluminum powder products and it is the object of this paper to show how the high temperature creep rupture properties of the five materials vary with oxide content and with the structure as revealed by electron microscopy. Materials One of the five products, SAP, a sintered aluminum product, was supplied by the Societe Anonyme pourl Industrie de l,Aluminium, Neuhausen a/RHF, Switzerland, through Dr. R. Irmann, while the others, M276, M257, M293, and M255 were supplied by the Aluminum Company of America as experimental powder metallurgical products. M255- and M293 were made from coarse and fine atomized powders, respectively. The other materials were made from flake powders with significant differences in oxide content, the details of the type of powders used in the manufacture of these materials

Jan 1, 1955

By David B. Brooks, William A. Wallace, James R. Dunn

As the conflict between the mineral industry and preservationists steadily increases, it becomes urgent to determine as precisely as possible the costs of developing vs. not developing our domestic mineral resources so that enlightened mineral policy decisions can be made. A simple discounted cash flow equation is suggested as an approach to assigning a public-interest dollar value to mineral resources. Present value of a piece of land underlain by a mineral resource is taken as equal to the discounted cash flow derived from the resource corrected for present and future surface land values. The equation is effective as a base for mineral aggregate resource planning for metropolitan areas if transportation cost differences are substituted into the cash flow component. Suitably modified, the equation can be fitted readily into an existing computer simulation program for aggregate mineral resource planning in metropolitan areas. However, because of the lack of accurate input, the equation is less effective for other mineral commodities such as base metals and coal. Nevertheless, within a somewhat philosophical context, the equation still has utility and is effective in defining the problem of public interest values for minerals other than mineral aggregates.

Jan 1, 1972

By H. J. O’Donnell, B. C. Parks

IN 1930 the late Dr. Reinhardt Thiessen set up a method of microscopic analysis and type classification of coal that has since been followed as standard practice in the coal-petrography laboratory of the Bureau of Mines. Thiessen's terminology which designated the constituent parts of coal in terms of botanical origin was introduced in 1920.l The technique, however, of preparing a completely representative series of thin sections from a column sample of coal for use in making quantitative determinations of coal components with a microscope was developed about 10 years later by Thiessen and coworkers G. C. Sprunk and H. J. O'Donnell.2 Complete thin-section analyses subsequently have been made of 126 column samples of various ranks and types of American coals. The data and information were assembled from these thin-section studies and published in a large number of reports dealing chiefly with investigations of the coking and hydrogenation properties of certain American coals. In the years following adoption of Thiessen's method, a considerable amount of work was done in collecting column samples of many coals, making routine thin-section analyses of these, interpreting the results, and finding practical application for the information in other fields of coal research. The many reports and papers covering the work in coal petrography, however, offer very little discussion that can be considered as critical appraisal of the technique. Criticism outside the Bureau most often has voiced questioning opinions concerning the accuracy of the method used of measuring coal components microscopically and classifying the coal into arbitrary types on the basis of the quantitative determinations. The principal purpose of this paper is to discuss in some detail and present data showing the results of certain investigative work done in the petrography laboratory on the accuracy of the Bureau's method of microscopic measurement of components in coal thin sections. Data from microscopic analyses on file made by G. C. Sprunk and H. J. O'Donnell were freely used in the investigation, and a table of columnar analyses from an unpublished manuscript by Sprunk is included in this paper for reference. In the course of the experimental work a method was developed for measuring instrumentally with a planimeter the components shown in micrographs of selected thin sections. Measuring coal components with a planimeter furnished useful information for studying the accuracy of microscopically measuring the same components in thin sections. PETROGRAPHIC COMPONENTS AND TYPE CLASSIFICATION OF COAL Thiessen considered coal to be composed of two visibly different major components present in various types of coal in greatly varying proportions. He named

Jan 1, 1948

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

Based on the equation for single fracture, a formula has been obtained for repeated fracture. Solution of this equation is obtainable analytically for a few examples and numerically for all others. Graphs of the size distribution equations have been obtained; they agree broadly with the experiments of others. In another paper1 we have considered a model and a comminution distribution equation for single fracture of brittle materials. Most comminuting devices, however, depend on the occurrence of repeated fracture. This is especially true of continuous cylindrical mills of the ball, tube, or rod type. But even in primary crushers there is some repetition of the breaking process, so that this paper should be of interest in connection with all comminuting devices. HALF LIFE AND PROBABILITY OF FRACTURE To facilitate the study of fracture it is useful to introduce the concept of the half life of a particle, In the ball mill, for example, we may start with 10,000 feed particles. The time, 7, by which one half of these particles have been broken is the half life of the feed under the prevailing experimental conditions. The probability of breakage bears an inverse relationship to the half life. In a ball mill, for instance, it can be shown that the

Jan 1, 1962