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[†ADAIR, ARTHUR C., Corp 4th Co., 1st. Training Bat., 154th Depot Brigade. ADAMS, HENRY, Major Chemical Warfare Service. ARLUCK, A. A Headquarters, 1St Corps of Artillery. ASKIN, THOMAS B. H Ensign.] [ ]

Jan 1, 1925

The airplane, while not a product of the war, owes its present very prominent place to the war; if it had not been for the war its development would have been retarded many years. War planes were made for various purposes, but their most important use was for photographing the enemies' lines. The same methods; with some modifications, are now

Jan 6, 1919

EVERY mould, of whatever kind it may be, must have an entrance appropriate to the material if it is wished to fill its inner space with bronze or other metal. It is likewise necessary that it have vents, that is, air holes, for there is nothing that is not full of air even though it be called empty. Now, molten bronze is a material that has an immediate effect because of its heaviness, and because it is as hot as fire or even hotter,

Jan 1, 1942

By Ernest L. Bohnet

Jan 1, 1985

By N. M. Macmillan, R. S. Kalyoncu, A. R. C. Westwood

The environment-sensitive hardness and laboratory-scale rotary drilling behavior of granite, quartz, and feldspar have been studied. By controlling the chemistry of the drilling environment, it is possible to triple the rate of drilling granite. Pre-existing flaws or other microstructural features play a minor role.

Jan 1, 1975

By J. C. Donnell, O&apos

Sinking an inclined ventilation shaft at the Never Sweat mine of The Anaconda Co. has required a unique underground hoisting arrangement because the shaft changes direction from vertical to 71.5º. Access to the project is made through the High Ore shaft to the 2800-ft level, then by crosscut to the bottom of the vertical Never Sweat shaft. The 71.5º incline shaft starts at this point, which makes an unusual operation as the 60-cu ft sinking skip coming up the incline changes into a vertical position above the 2800-ft level before going into the dump scrolls. This requires both rollers and guide shoes on the skip. Coming up the incline to the collar of the shaft the loaded skip enters into a guard before reaching the vertical section. The tendency of the surface- mounted Never Sweat hoist is to lift the front wheels of the skip off the track, so the guard keeps the skip on the rails during the transition.

Jan 11, 1965

By J. A. Bownocker

The existence of petroleum in the rocks of Ohio and Indiana seems to have been first shown by wells dug for salt. The fuel, however, was objectionable owing to its odor and inflammability. Not until the Drake well was drilled in 1859 did the people appreciate the value of rock oil, and then they at once began plans to secure the coveted fuel. The first successful well in these two states was near Macksburg, in southeast Ohio, where at a depth of 59 ft. (17 m.) oil was found in commercial quantity (1860). A year later this fuel was secured on Cow Run, in the same county, and at about the same time in Noble, Morgan and perhaps other counties in that part of Ohio. The second great step in the production of oil in Ohio and Indiana was taken in 1884 when the reservoir of natural gas in the Trenton limestone of northwest Ohio was tapped, and where a year later oil was secured in the same formation. Petroleum in this limestone was obtained in Indiana in 1889.' The third step in the production of oil in Ohio and Indiana is associated with the Clinton sand of Ohio. Natural gas in large volume was discovered in that rock at Lancaster, in 1887, and the area has been extended until it has become the largest individual producer in the world. The presence of natural gas in such great volume all but demonstrated to the driller that oil lay hidden near by. Soon the search for it was started but not until 1899 was petroleum in commercial quantity found in the Clinton sand, and a large pool was not located in it until 1907. The fourth step in the developrllrnt of the industry was taken in 1913, when the pool in Sullivan County, in western Indiana, was opened. The producing rock is the Huron sandstone, which is the topmost member of the Mississippian system.²

Jan 1, 1921

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By Clarence Linville

IN an article published in the Iron. Trade Review 1 I gave a convenient arrangement for the installation of wet and dry bulb thermometers for use in making moisture determinations in the air being blown into a blast furnace, and also gave a chart for use in obtaining moisture values from the thermometer readings. The data from which this chart was prepared were obtained from the tables in use by the U. S. Weather Bureau.2 The work of Carrier 3 has shown that these tables are somewhat in error. He has recalculated the values for moisture as referred to, wet and dry bulb thermometer readings, and he has prepared a psychrometric chart from the values thus obtained. This work has priced the subject of psychrometry upon a correct scientific basis. I think it is proper that we should recognize the importance of his work and give him credit for one of the most interesting and valuable researches that have been published in recent years. Blast-furnace men are not ready to use, as he suggests 4 a value expressed in grains of water accompanying a pound of dry air. However convenient this may be for heating and ventilating work and other engineering problems, there are several reasons for preferring the use of a value expressed in grains of water in a. cubic foot of mixed air and water vapor, in connection with combustion phenomena and the effects of moisture on blast-furnace operation. Previous papers presented to the Institute have used such values and we have

Jan 10, 1913

By D. N. Stevens, D. N. Bloom, M. A. Klugman

This paper represents a portion of a larger study concerning dispersion of major, minor and trace elements in wall-rock about orebodies in part of the Colorado Mineral Belt. This phase of the work pertains to the Mg/Ca ratio variations in wall-rock adjacent to orebodies in two mines, one in the Horseshoe Mining District (Hilltop mine), and the other in the Alma Mining District (Phillips mine). The two districts lie adjacent to one another, the Horseshoe District on the south and the Alma District on the north, and are commonly referred to as one, the Alma-Horseshoe Mining District. The Alma-Horseshoe Mining District is located 80 miles southwest of Denver, Colo., (Fig. 1) in Park County, on the eastern slope of the Mosquito range. The area is typified by rugged relief with altitudes of from 10,500 to 14,000 ft. The Horseshoe District is separated from the Lead-ville Mining District by the crest of the Mosquito range, with the Leadville District to the west. The Alma-Horseshoe District has been considered as peripherial to the Leadville District, and has not received the detailed attention that the Leadville District has. These two mines were selected for this study because of their ease of access; the attitude of the workings and the drill holes to the known mineralization; the similarity of the mineralization; and because the mineralization occurs in carbonates in both mines but are of different ages. In the Hilltop mine mineralization is confined to the Leadville dolomite (Mis-issippian) and is principally lead with subordinate zinc and silver. In the Phillips mine the mineralization occurs in the Peerless dolomite and shale (Cambrian) and in the Manitou dolomite (Ordovician) and is principally zinc with subordinate lead, silver,

Jan 1, 1964

By F. A. Hames, D. S. Eppelsheimer

The ferromagnetic copper-manganese-aluminum and copper-manganese-tin alloys (Heusler alloys) owe their ferromagnetism to the beta phases (body-centered cubic structure) in their respective systems.l,2,3 The ternary beta phase regions in these systems are extensions of the beta fields of the binary copper-aluminum and copper-tin systems into the ternary models of the copper-manganese-aluminum and copper-manganese-tin systems respectively. X ray analysis has indicated the presence of long-range order in the more strongly magnetic alloys.3,4,5 The ideal ordered structure is obtained in alloys of compositions Cu2MnAl and Cu2MnSn; the copper atoms occupy positions at cube centers while the aluminum (tin) and manganese atoms alternate at cube corners. This atomic arrangement is illustrated in Fig 1. The compositions Cu2MnAl and Cu2MnSn are also those that show maximum magnetic saturation moment. 3,4,6,7 Departures from these compositions result in a decrease in the degree of order attainable and a decrease in magnetic saturation moment. In view of the chemical similarities of aluminum, tin, indium, and gallium, and the existence of beta phases in the binary systems copper-indium and copper-gallium, it may be suspected that ternary beta phases exist in the systems copper-manganese-indium and copper-manganese-gallium, and that these are ferromagnetic. The purpose of this investigation was to determine whether ferromagnetic beta phases exist in the systems copper-manganese-indium and copper-manganese-gallium analogous to the ferromagnetic beta phases in the systems copper-manganese-aluminum and copper-manganese-tin. Previous Work At the time this investigation was started no information could be found regarding the constitution of copper-manganese-indium and copper-manganese-gallium alloys, nor of the binary manganese-indium and man-

Jan 1, 1950

By M. W. Hayward

THE object of this paper is to record and tabulate the data and field observations obtained by the writers and their associates during 10 years of intensive study of lead-zinc deposits in the Cretaceous limestone areas in Northern Mexico, particularly in mines owned by the Cia Minera de Peñoles, S. A. At the El Paso meeting of the Institute in October, 1930, J. G. Barry made the suggestion that a committee be appointed to correlate the ideas and theories which have been put forth by the numerous engineers and geologists who, during recent years, have made a study of the ore deposits in the area under consideration. The first step in a work of this nature would be to record all of the observed facts, and these facts would have to be accepted by those who attempted to formulate a theory of ore deposition. It is with this idea in mind that the writers have described as accurately as possible the actual, observed facts pertaining to the occurrence of the lead-zinc ores in dolomites or dolomitic horizons. By most writers the term "dolomite" is loosely used to designate magnesium-bearing limestones, regardless of the percentage of MgO present. Since no true dolomites exist in the areas to be described, we shall also loosely use the terms dolomite or dolomitic limestone to desig-nate those beds having a magnesia content of 5 per cent MgO or more. For a number of years the writers have been impressed with the fact that in areas where dolomite beds occur a large percentage of the lead ore is found in these beds, in spite of the fact that such beds may be overlain or underlain by pure limestone, which one would assume to be just as favorable for replacement as the dolomite, if not more so on account of its being more soluble in acid solutions than the dolomite. It is true that in some limestone areas, such as the Erupcion-Ahumada districts, Chihuahua, and Providencia, Zacatecas, where no dolomite beds have been found, large tonnages of lead ores have been mined. We venture to predict, however, that had there been dolomitic beds in these areas, the

Jan 1, 1932

By A. L. Field

Bureau of Mines Technical Paper 189 consists of a record of the scientific data obtained in the iron blast-furnace slag investigation which is reported in Technical Paper 187, "Slag Viscosity Tables for Blast-Furnace Work." It includes a description of the method of preparing the synthetic melts, construction of an improved electric furnace, and refinements in laboratory methods of measurement. Only the general features of the work and the conclusions drawn from the experimental data can be given attention here. Silicates in the Liquid State In the manufacture of refractories, Portland cement, glass, and porcelain, and in pyrometallurgical operations, importance attaches to the behavior of silicate compounds at temperatures beyond the range of common experience. This field of research has not been investigated as carefully as its scientific and industrial importance would seem to warrant. Probably the most important of the unsolved problems in the, chemistry of silicates is the question of their stability in the liquid state. That little progress toward the solution of this problem has been made is not strange if there be borne in mind the difficulties attending experiments made at temperatures at which silicates become fluid, and the comparatively short time since it became possible to measure these temperatures. On the other hand, considerable progress has been made in the study of the compounds in the solid state because of the directness and simplicity of methods of optical examination.

Jan 12, 1917

By Philip H. Nelson, Richard Lingle

Vibrating wire stressmeters (VWS's) and borehole deformation gages (BDG) were deployed in two in-situ heater experiments at Stripa, Sweden to determine the thermally induced stress changes in the rock mass. The heater experiments ran for 18 months, including a six- month cool-down period after the heaters were turned off. Gages were installed in both horizontal and vertical boreholes and were subjected to temperatures ranging from 10°C to 120°C, depending upon the distance of a gage from the central heater. Most gages operated in a moist environment because groundwater flowed into many of the instrument boreholes during the experiments Of the 36 VWS's installed, six failed. Failures were attributed to corrosion of the vibrating wire due to moisture entering the gage body. Of the 30 BDG's installed at the beginning of the experiments, 22 failed, also as the result of water entering the gage body. Modification and reinstallation of the gages eliminated the problem of water infiltration, but much data from early stages of the experiments was lost due to gage failures. Calibration of the VWS in blocks of Stripa granite showed a lack of repeatability. Variability in calibration results are attributed to seating effects, to variations in the elastic modulus of the rock, and to changes in temperature. These three effects combined to produce an error judged to be approximately ±33% of the stress changes measured at Stripa. In contrast, the major source of error in determining stress with the BDG appears to be the uncertainty in rock modulus and thermal expansion coefficient. Sample calculations based on data acquired near the end of the experiments (during cool-down)

Jan 1, 1982

By Cyril Wells, Robert F. Mehl

THE practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out 1,13 This importance ties chiefly, though by no means only, in the study of carburizing and in the study of reactions involved in the eutectoid inversion in steel The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in y-Fe and their mutual effects are measured with precision The present paper reports the results of meas¬urements of diffusion coefficients D of manganese in -y-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients [$] Data on the rate of diffusion of manganese in y-Fe have been reported by Fry2 and by Paschke and Hauttmann 3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq cm per sec at 960°, which will be shown to be incorrect by many orders of magnitude Paschke and Hauttmann gave a rough value of 9 6 X 10-8 sq cm per sec at 1400° Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon METHOD AND MATERIALS Method -The method employed is identical with that used earlier 5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded The diffusion anneals were performed in argon, except one (test 18) in which hydrogen was employed for purposes noted below The temperatures reported are accurate to about 3° and constant within I°C , the diffusion times are reported to the nearest half hour The specimens were furnace-cooled after the diffusion anneal at about 2° per min Layers, usually 0 004 in thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0 01 per cent Mn, the distances of these layers from the interface was measured to ±0 0002 in The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions e The D values calculated by these two methods do not differ appreciably 5 The Grube solution was used except in tests in which the effect of concentration upon D was greater than 50 per cent, in such cases the Matano method, which explicitly provides for the variation of D with concentration,1 is the more reliable In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer In 3 of the 30 tests, however, this is not justified, and the D values

Jan 1, 1941

By Thomas Egleston

DURING the year 1873, my attention was called to the frequent accidents, resulting from the breaking of rails, on the different railroads in this' country, and I was requested to investigate the subject. The plan of investigation I proposed was to ascertain, in as many cases as possible, the exact hist* of broken rails, both in this country and in Europe; to collect information in Europe relating to the tests which rails used there were required to undergo, and to experiment upon the pieces of rails broken on the road, with a view to ascertain whether their fracture was due to their chemical constitution, bad manufacture, to a reduction in strength owing to temperature, or to physical changes in the constitution of the rail. The investigation was commenced by the collection of statistics, and for this purpose I spent several months in Europe, collecting information on the subject of broken rails, as well as the life of iron and steel rails generally, and inquiring into the systems of purchasing and of testing them employed by the railroads there, intending, on my return, to make a series of analyses of rails broken, both in this country and in Europe; to ascertain, if possible, how far great cold had an influence on the fracture; to examine whether the rail broken, either on the road or afterwards, underwent, at or about the fracture, any physical change, and to make a series of experiments on the strength of rails manufactured in the United States or sold in the American market. Unfortunately, the panic of 1873 came on, just before my return from Europe, and prevented the carrying out of the larger part of the plan proposed; as, however, I had collected in the meantime, a large number of statistics of different kinds from all parts of Europe, and had made a number of interesting experiments and investigations, I have thought it would be worth while to communicate some

By P. Duwez, C. B. Jordan

A. J. SHALER*—I should like to congratulate the authors for having carried out such a precise set of experiments. It has been found useful, in sintering experimental compacts in vacuo, to make certain that the residual gas is not one which reacts with the metal. Since traces of oxygen can be kept away only with great difficulty, the technique is often adopted of using a "getter " of powder in the vicinity of the compacts, and, in addition, of permitting a small hydrogen leak to flow into the vacuum chamber. Did the authors use similar devices? This paper brings up a question concerning the definition of the word ' sintering.' The authors restrict its use to the adhesion between particles. Kuczynski, in a paper presented at this meeting, applies the word to the growth of areas of contact between particles. I have used it to mean both these phenomena and also the dimensional changes which continue to take place after the first two have run their course. May I suggest that we should come to an agreement on the use of these words ? Fig 1 and 2 show an interesting feature: extrapolation of the curves to zero time does not give a densification parameter of zero. The higher the temperature, the higher is the intercept on that axis. These observations agree with the concept of a practically instantaneous densification taking place while the compact is being brought to heat. Such a change may be brought about by plastic deformation and primary creep. The stress pattern causing this first rapid flow is, to my mind, due to the force of attraction between the surfaces of opposite particles in the regions immediately flanking their common areas of contact. The stress is not temperature-sensitive, but at room temperature plastic deformation only proceeds until the metal in the area of contact can support it elastically. As the metal is heated, the elastic limit falls, and further plastic flow occurs. At the higher temperatures, this is followed by primary creep, and finally by the steady-state rate-reaction which the authors are seeking. If they were to recalculate their densification-parameter values, using, not the initial density of the cold compact, but the density after the compacts have been brought to temperature, the systematic deviations from linearity in Fig 3 and 4 might be eliminated. Such initial densities might be obtained by extrapolating the curves of Fig 1 and 2 to zero time. I am naturally pleased to see that such a very well done series of experiments leads to a heat of activation (for the densification process in hydrogen) that is much higher than that for self-diffusion, in confirmation of the less elaborate results reported by Wulff and myself (Ind. and Eng. Chem., (1948) 40, 838). J. T. KEMP*—I would like to comment on Dr. Shaler's remarks. There are apparently different interpretations of the word "sintering." It seems to me that an accurate definition of our word is essential in all metallurgy. May I point out, in this connection, that in practical metallurgy the word "sintering" has been applied to a bonding process in the preparation of ores and flue dust for fur-nacing. It would be unfortunate if in the area of powdered metallurgy we should establish a definition that is essentially different in meaning. F. N. RHINES*—I think that I can answer the question by saying that I see no essential difference between the use of the term "sintering" in extractive metallurgy and in powder metallurgy; physically the same things are going on. I admit sintering is used for different end purposes in the two cases. When we resort to the sintering of lead ore mixture we are doing so to obtain a chemically reactive, loose texture of some rigidity. This is only a difference in use. After all, in powder metallurgy we sometimes deliberately produce a very porous material which has just a little strength, just as in the case of sinter cake. P. DUWEZ (authors' reply)—We agree that it would be helpful to have well-established definitions of such terms as "sintering." Since the question has now been raised, the time might be appropriate for its consideration by some suitable committee of one or more of the metallurgical societies. In answer to Dr. Shaler's first question, no getter nor hydrogen leak was used in our vacuum experiments, except insofar as the guard disks (used to reduce friction between specimens and trays) may have acted as getters. Dr. Shaler's statement that extrapolation of the curves of Fig 1 and 2 does not lead to zero densification at zero time apparently overlooks the logarithmic

Jan 1, 1950

By Albert Sauveur

Iron, like other metals, solidifies through the formation of dendritic crystals; iron alloys forming solid solutions, like other solid solutions, solidify likewise through the formation of dendritic crystals. The alloying elements or impurities as well as the inclusions segregate generally in the interstices, or "fillings," between the axes and branches of the dendrites; that is, in the portions last to solidify. This results in dendritic segregation or heterogeneity, which is generally persistent and makes possible the revelation of the dendritic crystallization of the metal through the selective action of a suitable etching reagent.' For this purpose, a cuprie solution, such as Le Chatelier's, is generally used, copper being deposited on the pure, or relatively pure, ferrite present in the axes while the fillings remain free, or relatively free, from copper deposition. The dendritic structure, formed on solidification in a steel containing 0.50 per cent. carbon, 0.37 per cent. manganese, 0.12 per cent. silicon, 0.07 per cent. sulfur, and 0.035 per cent. phosphorus is shown, after treatment with Le Chatelier reagent, in Fig. 1 under a magnification of 8 diameters. Commercial steel always contains inclusions of manganese sulfide, which are located in the fillings of the dendrites. Comstock has shown that boiling sodium picrate imparts a dark coloration to these inclusions. We find that this reagent likewise reveals dendritic segregations in commercial steel, as shown in Fig. 2, under a magnification of 8 diameters. which represents the same spot as that shown in Fig. 1. The fillings have been darkened while the axes remain white, the action being, therefore, the reverse of that of cupric reagents. On closer examination, under higher magnification (Fig. 3) it is found that the picrate blackens the small particles of manganese sulfide, that these are frequently surrounded by a rim of white, or relatively white, ferrite, and that both the ferrite

Jan 1, 1924

By Cyril Wells, Robert F. Mehl

THE two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these [] data are needed chiefly in order to treat data on carburization, on the rate of formation of pearlite, and on the rate of austenizing in a quantitative way. 1,2,9,10 In the present investigation rates of diffusion of nickel in -?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of impurities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel [ ] in -?-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200T., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. METHOD AND MATERIALS Method.-Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors' laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris's review,' the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert's analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969