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By S. M. M. Safvi, A. Jowett

Small-scale continuous flotation tests are described in which the influence of 1) pulp density and 2) feed rate on the rate of flotation are investigated. The results provide further evidence of first-order kinetics for flotation and indicate that tests at different feed rates provide a particularly simple method of determining rate constants. Flotation kinetics are discussed in general terms. Over a period of many years numerous research workers have studied the rate of recovery of valuable materials from flotation pulps with a view to deter-mining the mechanism of the froth flotation process. Froth flo ation is fundamentally a collision process involviug at some stage collision and then mutual attachment between air bubbles and mineral particles. It is possible to draw analogies therefore between the flotation process involving mainly macroscopic particles and the ordinary processes of chemical reaction kinetics involving collisions between atoms, molecules and ions. By adopting this analogy we may postulate a general equation representing the kinetics of the flotation process: -dC/dt =K.CC ,Aa (1) The rate constant, K, will be a complex function involving reagent concentrations, particle and bubble sizes, induction times and no doubt flotation cell design. However, these are factors which can be kept constant in any series of experiments, permitting investigation of the exponents a and c, which determine the order of the reaction occurring in flotation. The various research investigations carried out so far have all aimed at evaluating a and c and in the majority of cases only since the concentration of air has usually been kept constant in a series of tests, so that a relationship of the following type has been investigated: -dC/dt = K1 Cc (2) The techniques of both batch testing and continuous testing have been used to investigate this relationship. The technique of continuous testing, in which steady-state conditions are established, permits direct investigation of the above equation. In the case of batch testing, C is decreasing continuously

Jan 1, 1961

By R. A. Wattenbarger, H. J. Ramey

The trend in gas well testing has been to rely more on the early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modern gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks. It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore. Russell and Truittl published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark2 applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis. The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz3 presented the drawdown equations for *Now with Scientific Software Corp., Denver. ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice. Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore. The Mathematical Model The geometry of our mathematical model is similar to that used by Prats.4 The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through the wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model. The equation for the flow of real gas in a porous medium with uniform porosity, permeability and thickness is5-7

Jan 1, 1970

By W. C. Maurer

A study of the mechanics of shear failure of rock under pressure has been made. The transition from brittle to ductile failure occurs when the friction along the fracture surfaces exceeds the shear strength of the rock. A machine has been developed for measuring both the shear strength of rock and the friction along rock fracture surfaces. In this shear machine, the fractures are forced along definite planes; as a result, the rock is stronger than in compression tests where the fractures choose the weakest paths through the specimens. Friction is composed of several forces: (1) the forces to slide irregulurities on surfaces over each other; (2) forces to shear some of these irregularities; (3) molecular attractions across the fractures; and (4) forces required to break bonds resulting from melting and welding at the tips of irregularities on the surfaces. Friction along rock fracture surfaces is not proportional to contact pressure as usually assumed; instead, it increases as the contact pressure raised to the 0.4 to 0.8 power. INTRODUCTION It is difficult to produce tensile stresses under the high compressive stresses present in the earth; therefore, in deep drilling and geological faulting, shear failure predominates. This shear failure mechanism is complicated because rock is a heterogeneous material containing pore spaces, microfractures, elastic discontinuities and other imperfections. A study of shear failure of rock under pressure has been made to obtain a better understanding of this complex mechanism. A machine has been developed and used to measure the shear strength of rock and friction along sheared surfaces. This machine has certain advantages over the compression test — shear properties can be measured under low normal stresses and shear stress and normal stress can be varied independently. The first part of this paper is a description of shear failure of rock under pressure. The role of shear strength and friction along fracture surfaces in the shear failure mechanism will be discussed. The second part consists of a description of the shear machine and a discussion of the shear strength and friction data obtained using this machine. It will be shown that shear strength depends upon the size of the stressed zone, and that friction does not increase linearly with contact pressure as usually assumed. Attempts are made to relate some of the new concepts to tectonic failure and to dril ling. SHEAR FAILURE IN ROCK TRIAXIAL TESTS The shear failure mechanism is illustrated by the triaxial test shown in Fig. 1. In this test, a cylindrical rock specimen is subjected to a confining pressure, PC, and an axial pressure, pa. These external pressures produce normal a and shear T stresses on inclined planes within the specimen equal to1 where 0 is the angle between the specimen axis and a normal to the inclined plane. Fig. 2 shows how triaxial specimens deform as the axial pressure is increased. The pressure is

Jan 1, 1966

By A. M. Gaudin

Jan 1, 1962

By J. C. Bayles

Jan 1, 1885

This discussion was prepared by members of the Phelps Dodge Corpn. staff who were designated to review the minutes. It is confidential but permission has been granted to distribute copies among those who attended the Conference. The minutes of the above conference contain numerous references to the plants and practices of Phelps Dodge Corporation. As many of these references are inaccurate, the following notes are made covering such points: Construction Magnesite Brick in Reverb. Arch (1) An.18" arch, 20 feet long, was built on one furnace with 5 feet on each side of magnesite brick, the center portion .being of silica brick. The furnace was put in operation February 13, 1930 and on April 23rd after 68.8 days' operation it was replaced due to failure of the silica brick forming the center of the arch. At this time, while the silica brick had completely gone, there was 14" of magnesite left. Bridgewall Tapping (2) Tapping matte through the burner wall was first tried at the Copper Queen Smelter in April, 1925. At that time, a copper casting with 1 ½ extra heavy pipes for water cooling cast in it, and having one taphole block was used. Later, on the other (old) furnaces, similar castings, but equipped with two tapholes, were used. We found with these furnaces that we could tap through the burner wall at the beginning of a campaign, but would subsequently have to go back to side wall tapping. This was the case until sometime in 1926. The new furnaces, that went in operation at the beginning of 1927, each had water. cooled castings with two tapholes. These have been used entirely and have been quite successful. Sometime after the furnaces were put into operation sidewall tapholes were put in, simply for the removal of any accumulation of matte that might be temporarily retained at the front end by bridges or dams in the furnace formed by overcharging locally.

Jan 1, 1930

By R. P. Fischer

The Colorado Plateau region has been the principal domestic source of uranium, vanadium, and radium. The value of these commodities produced from the region through 1964 slightly exceeds $2 billion. Most of the deposits occur in streamlaid lenses of sandstone in the Chinle and Morrison Formations. The ore minerals below the zone of oxidation are low-valent oxides and silicates of uranium and vanadium; all of these, except the quite stable vanadium silicates, oxidize readily to a variety of high-valent uranium and vanadium minerals. The ore minerals partly replace fossil wood but mainly impregnate sandstone, typically forming tabular ore bodies that are nearly concordant to the bedding of the host rock. The deposits range in size from those containing only a few tons of ore to those containing more than 1 million tons. Stratigraphic, lithologic, and sedimentary structural factors obviously influenced the localization of these deposits, but igneous activity, hydrothermal mineralization, and tectonic structures show no similarly consistent influence on localization. The deposits are epigenetic, but the source of the ore metals, the nature of the ore-bearing solutions, and the time of ore emplacement are uncertain. A few uranium deposits in the region are dominantly discordant to bedding and occur in collapsed breccia pipes or along linear fractures. Their origins are also uncertain.

Jan 1, 1968

By Arthur Notman

THE raw material men in all industries, and copper is no exception, are accustomed to think of them- selves as the whole show, and not without justice, for if there were no copper mines the world would have no copper. Nevertheless, many different things costing money and resulting in profits must be done to their product before it is ready for the world's use. In other words, they are making the frequent mistake of Chinking in terms of partial costs. Nobody really uses electrolytic copper. Possibly that is why nobody seems willing to pay anything for it. The manufacturers, being canny, do not buy any more electrolytic than they feel that they can work up and sell profitably, although they like to make the raw material men Chink that they will take all that can be produced. This is a state of affairs that has aroused my sympathy and curiosity, and has induced me to study the financial history of the copper wire and brass industry of the country or such portion of it as publishes any records readily available to the curious minded. About 60 per cent of the electrolytic copper used in this country is drawn into wire and consumed by the electrical industries. The remaining 40 per cent is

Jan 1, 1926

By J. F. Kemp

The use of nickel-steel has directed increasing interest of late towards the deposits of nickel, and at the same time the parallel advance in our knowledge of the basic igneous rocks has rendered these deposits a subject of important geological inquiry. Investigations have led to some views, more or less new, on the igneous origin of certain ores, which, though not universally accepted, have a growing number of adherents. In Europe, the mines in Norway have been especially suggestive subjects of study, and others somewhat less generally known have also added their testimony; while in this country the great economic importance and scientific interest of the developments in the Sudbury district of Canada, have furnished the principal texts for the discourses that have appeared among us. The purpose of the present paper is to set forth these views through the medium of one interesting ore-body, of which but little has been written ; and, by the description of another, to place in contrast two different geological associations in which nickeliferous pyrrhotite occurs, and to indicate a generalization, based upon these different geological characters, and justified by the experience so far gained. To Prof. J. H. L. Vogt, of Christiania, Norway, is due the chief credit for the revival of interest in the geology of nickel. His important contributions* of recent date have made generally available

Jan 1, 1895

CONTENTS PAGE Simons, Theodore.-Basic Principles of Gravity Concentration-A Mathematical Study : :.. 1 Taggart, Arthur F. and Gaudin, A. M.-Surface Tension and Adsorption Phenomena in Flotation 11 Hersam, Ernest A.-Factors Controlling the Capacity of Rock Crushers 12 Shaw, S. F.-The Ore Deposits of Sierra Mojada, Coahuila, Mexico 12 Wilson, Philip D.-The British Columbia Batholith and Related Ore Deposits 26 Greensfelder, N. S.-Shot-firing by Electricity 27 Mitke, Chas. A.-Metal Mine Ventilation in the Southwest 28 Foley, F. B. and Howell, S. P.-Neumann Bands as Evidence of Action of Explosives upon Metals 30 Schwartz, H. A., Payne, H. R., Gorton, A. F., and Austin, M. M.-Conditions of Stable Equilibrium in Iron-carbon Alloys 30

Jan 12, 1922

By F. C. Canney

Geochemical prospecting seeks hidden mineral deposits by sampling for variations in the chemical composition of naturally occurring materials. Usually the samples are of soils and other products of weathering and erosion-surface materials extremely susceptible to contamination by human activities. Except when a survey is conducted well away from populated areas, contamination is an ever-present hazard. The program's success is particularly endangered when the contaminants are the elements sought; if these occur erratically throughout an area, spurious anomalies completely unrelated to mineralized areas can be formed. Evenly distributed contamination can be dangerous too, if it raises the background to such a level that true anomalies can no longer be easily detected. Suppose, for ex- ample, that in an area where the lead background is 20 parts per million the soil over a lead vein contains 1000 ppm of lead. Here the contrast would be 50 to 1, which is very satisfactory for geochemical surveying. Now if 1000 ppm of lead from some source were added evenly to the soil in this area, the contrast would be reduced to about 2 to 1, and the anomaly would no longer be readily detectable because a threshold of significance twice the value of the background is the minimum generally used for interpreting geochemical data.

Jan 2, 1959

By V. Koump, T. F. Perzak, R. G. Olsson

Jan 1, 1965

By A. J. Terrones

THE classical papers on contact metasomatic deposits by Lindgren on the Clifton-Morenci district,' by Barrell on Marysville, Mont.,' and by Gold-schmitt on the Oslo district, Norway,' laid the foundation for understanding of the importance of separating the metamorphic process from the subsequent metasomatic stage. Knopf' made a big step forward by recognizing that sulfide ore minerals are invariably younger than silicates and by further stressing the importance of structural control" in ore finding. Some years later Harrison Schmitt" fought the idea that contact metasomatic deposits are erratic, irregular, bunchy, economically marginal, and of small size, concluding that these descriptions have little factual basis. He emphasized the importance of detail mapping and careful geological study as fundamental requirements for a better understanding of these deposits. This article presents a comparative description of the structural features at the Magistral, Antamina, Morococha, Vilca, Ferrobamba, Katanga (Quibio), Tintaya, and Huarca contact deposits (Fig. 1). Further, it will describe how these structural features controlled the emplacement of the intrusives, their shape, distribution of metamorphic and metasomatic halos, and sulfide deposition in post-skarn structural channelways. Finally, the modifications introduced by a superimposed hydrothermal stage recognized at some localities will be discussed. Primary exploration and careful sampling of recognized structural targets were instrumental in outlining the copper ore potential at the Antamina and Tintaya districts, thus proving the benefits and reward of careful geological examinations in this type of deposit. The Magistral District: This district lies in the Province of Pallasca, Department of Ancash, in northern Peru, at 8o 16' S and 77" 47' W. High to medium grade copper orebodies in garnetite, bordering a quartz monzonite stock, are exposed at the bottom of a glaciated valley in the western slope of the Andes at 4250 m (14,000 ft)* elevation.

Jan 1, 1959

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By Henry M. Howe

PART I. § 1. Introduction. After giving certain definitions, this paper gives the reasons which led to Roozeboom's form of the diagram of the freezing-point curves and general equilibrium of the iron-carbon compounds, steel and cast-iron ; and then those which led to replacing it with the present or double diagram, in which graphite is at all temperatures held to be the more stable and cementite the less stable (metastable) form of carbon. Next in § 10 the evidence supporting this greater stability of graphite is examined, then in § 17 that which seems to oppose it, and in § 22 a summary of the evidence is presented. The second part of the paper considers the topography of the graphite-iron diagram, rejecting summarily the solubility-lines based on the data of Charpy and Grenet and of Mannes-mann, on the ground that the data even on their face do not really point toward these lines, and that they are wholly incompetent to determine any solubility-lines whatsoever, because they report together with the dissolved carbon also an indeterminate quantity of cement-carbon, and because even such carbon as is actually dissolved, only in part represents the solubility of graphite, and in another and indeterminate part represents the solubility of cementite, or at least of carbon in presence of cementite as distinguished from graphite. It might be thought that graphite is but slightly soluble in iron, because of the absence of any suggestions of eutectoid graphite, corresponding to the eutectoid cementite of pearlite in very many cases in which the cast-iron seems to consist of ferrite and massive graphite only, and because of the micrographs of Goerens and Gutowsky. In these the primary austenite of cast-iron quenched but little below the eutectic freezing-

Jan 7, 1908

By J. L. Gillson

Joseph H. Birman (Chairman, Dept. of Geolcgy, Occidental College, Los Angeles, Calif.) Many thanks to J. L. Gillson for so comprehensive a survey of the titanium sand deposits of the world. Over the past two years, the writer studied rather carefully some of the Cretaceous ilmenite deposits in New Mexico and Colorado, including the Sanostee deposit shown in Gillson' s map, Fig. 6. The deposits were geologically mapped and sampled, surveyed by magnetometer, and the Sanostee deposit was drilled. Moat of the genetic interpretations made by Gillson concerning the recent sedimentary ilmenites can be clearly read in the Cre-taceous deposits in New Mexico. The deposits are in marine regressive members of the Mesaverde group. The deposits trend within a few degrees of N 55° W and persistence of this trend through both distance and time (the deposits are in different members of the Mesaverde group) implies that the deposits are offshore bar accumulations. Heavy mineral content ranges from about 10 pct to more than 50 pet. Thicknesses are from 4 ft to as much as 20 ft, widths range from 150 to 600 ft, and lengths range from a few thousand feet to a few miles. All are locally or completely overlain by carbonaceous shale and thin coal. The deposits are strongly altered, and from X-ray diffraction the principal titanium alteration product appears to be anatase. Drilling of the Sanostee deposit shows that the alteration is not related to the present erosion surface but took place at the site of deposition and before burial by the overlying sediments. Iron oxide derived from the alteration cements the grains and is the chief coloring agent in the immediately overlying shales. In the Sanostee deposit, there is virtually no feldspar, the gangue mineral being almost exclusively quartz. Sorting is excellent, but the quartz grains are subangular to angular. Petrographic examination reveals that the angularity is not due to overgrowths. Therefore, short distance transport is implied. The mineralogical composition suggests a low relief granitic terrane as the source area. Feldspar may have been decomposed by weathering at the source, but an alternative preferred by the writer is that each of the deposits represents a long-term concentration site (for example a large sand bar) which was continually being deprived of light minerals by wave action and selective transport. Feldspar may have been mechanically reduced in size more quickly than the quartz, and thus its rate of removal may have exceeded that of quartz. Concentration of heavy minerals would thus occur until the marine regression removed the zone of maximum wave energy from the site. Chemical alteration would then become the most important process until burial by encroaching swamp deposits.

Jan 1, 1961

By Sallie McCabe Johnson

LIFE IN RUSSIA for the foreign woman is hard. It is up to her whether her days are spent in tearful longing for ironic or whether she :hakes the real effort to ferret out the interesting or amusing side of such exasperating conditions as ooh a Russian can conjure. So to begin Discard all promises.. This is perhaps the most difficult thins- to learn but promises in Russia are nut what they are at home. There are many reasons for ibis, sonic good and some bad but whatever the reason. the fact remains that they are usually worthless- as each of us must slowly learn In, disappointment after disappointment. Also we must learn that we cannot expect to get or to do a certain thing just because someone else has done so. What we did yesterday perhaps cannot be dune today. What we purchased air hour ago, oxen ten minutes ago- we cannot purchase now. What our neighbor did this morning we cannot do this afternoon. Changes arc continuous. Every person's experience is different from that of another aid this in a great measure accounts for the conflicting stories brought horns. In a land of chaos we live only from hour to hour and this is one of the exceedingly exasperating conditions to face. When I wished to visit Leningrad, an overnight nip from Moscow, more than a week's lime w as required to obtain a ticket, vi en through the efficiency of lntourist: alone I might have spent a month at it. Each day

Jan 1, 1932

[Separates of all the Technical Publications published in 1.929 ,are available at Institute headquarters. All the papers are on file in public, university and technical libraries, and when so indicated in the list, maybe found in the TRANSACTIONS.] METAL MINING TECH¬ NICAL PUBLI- TITLE AUTHOR MEETING TRANS. CATION VOLUME No. AND PAGE 182-A-23 The Royal Commission on Mining Henry Louis New York Subsidence Feb., 1929 183-A-24 Cycles in Metal Production D. F. Hewett New York T29t, 65, 93 Feb., 1929 199-A-25 Ventilation ?at the United Verde Oscar A. Glacscr New York T29, 114, 141 Mine Feb., 1929 206-A-26 Air Conditioning in Deep Mines R. W. Waterfill New York T29, 99, 112, Feb., 1929 245-A-27 Bumps in No. 2 Mine, Springhill, Walter Herd New York Nova Scotia (with discussion) Feb., 1929 257-A-28 Misfires: Their Causes, Prevention ? New York and Treatment on Occurrence Feb., 1929 Misfires in Anthracite Coal T. D. Thomas Mines (With Discussion) Misfires in Bituminous Coal W H. Forbes Mines (With Discussion) Misfires in Non-metallic Mining A. W. Worthington (Limestone) (With Discussion)

Jan 1, 1929

By Robert H. Richards

(Pittsburg Meeting, March, 1910.) THIS is in part a review paper, indicating the various steps that have been taken in developing hindered-settling apparatus, some of the standard data that have been obtained, and some of the conclusions one is led to as to the effect of it in improving concentrating-methods and machinery, and in part it brings in some unpublished work. CAUSES OF LOSS IN ORE-CONCENTRATION. In making a study of the separation of valuable minerals from the waste gangue, particularly by water concentrators, it is necessary to define, first of all, what are the causes of-loss that are likely to interfere with the concentration. Having made this definition; we can then study to see in what way the machines make their losses, and plan remedies for them in an intelligent way. Losses may be stated to occur as included grains, as flat or long grains, as fine free mineral, and as absolute slime. We will take, these up one by one, as follows: Included Grains.-Fig. 1 shows by a set of diagrams how included grains may occur: first, where the heavy mineral grains attached to the quartz are of large size; secondly, where they are of small size ; and thirdly, where very fine particles of heavy mineral are included in the quartz. We have to decide in regard to included grains whether they are rich enough to go direct to, the furnace, or poor enough to throw away, or whether they lie between these two points and require recrushing as the only means of severing the values from the waste. This last case is the only one requiring special treatment at our hands. We will therefore consider that next. * By mutual consent, this paper has been presented also before the Colorado Scientific Society, and the Canadian Mining Institute, Montreal.

Feb 1, 1911

By U. N. Bhrany, N. Arbiter

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and

Jan 1, 1961