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By H. B. Heller, T. J. LaChapelle

Phosphorus nitride has been used as a diffusant for introducing phosphorus into silicon under various conditions. It has a temperature -dependent rate of decomposition beginning in the 500°C range, increasing very rapidly above 1000 C, producing gas -eous phosphorus and nitrogen. Best control was obtained with a two-temperature arrangement, with silicon at the proper higher diffusion temperature. It is an easier compound to use than the usual P2O5 because it is nonhygroscopic and yields temperature-controlled surface concentrations together with excellent final surfaces. Surface doping nearly as high as that produced by phosphorus pentoxide has been observed for sources at 850" to 900°C. Reproducible high sheet resistances were obtained by using slow flow rates (1 linear in. per min) and staggered-baffle gas mixing with the nitride at 550°C. Both inert gas (argon, nitrogen) and oxidizing ambients have been examined. Oxygen reacts to produce anhydrous P2O5, consuming the source at a rapid rate. Nitrogen, except for short diffusion times, suppressed the dissociation reaction and sometimes produced inferior surfaces. Argon appears to be a more useful ambient. PHOSPHORUS is a common impurity atom which may be introduced into a semiconductor lattice to create a p-n junction or an nn contact region. Various investigators1-4 have described techniques which can be used with either elemental phosphorus or certain of its compounds. This paper discusses a newly available compound of phosphorus, phos- some processes silicon wafers are precoated with a phosphate glass which acts as the doping source. Although a nonoxidizing form like elemental phosphorus or a phosphine can be used, most diffusion methods usually involve the use of phosphorus pentoxide. Because of the rapid volatility of this compound, a two-step process is often used, combining a gaseous deposition to introduce a predetermined quantity of phosphorus into the silicon with a later redistribution to obtain the desired distribution and surface concentration. Such a process usually involves predepositing phosphorus at surface concentrations greater than 1020 cm-'. At such doping levels the phosphorus-diffusion coefficient appears to be strongly concentration-dependent.596 Distribution profiles5'9 for these high concentrations of phosphorus do not follow Fick's laws, having extended subsurface regions which appear electrically to be nearly uniformly doped with ionized impurity atoms. Radioactive-tracer experiments also show near-surface anomalies in the distribution profile. Additionally, it has been shown1' that the introduction of very high surface concentrations of impurity atoms into silicon (a step necessitated by the subsequent lowering of concentration during the redistribution) creates dislocations, even in material having no dislocations originally. For device fabrication the use of oxide masking introduces certain difficulties and limitations.7'8 The standard practice of using phosphorus pentoxide as an impurity source adds other problems to these because of the speed and ease with which this compound reacts with moisture present in any gas in contact with it. In fact, P2O5 is one of the fastest and most effective drying agents for gases. Because it is such an excellent desiccant, completely anhydrous phosphorus pentoxide is difficult to obtain and is even more difficult to keep dry. Adequately dry gloved boxes must be used for storage and transfer of the chemical. The presence of even traces of moisture will cause formation of phosphoric acids which, during the high-temperature diffusion, results in polyphosphoric acids of variable composition. Such reaction by-products end up as gradually accumulating viscous fluids in the cooler parts of the diffusion furnace. The calculation of the final solute distribution for

Jan 1, 1964

By Barrie T. Wells, Raghu N. Singh, Paul S. Buddery

Rockbolting and dowelling are important methods of ground control. Their effectiveness depends upon the compatibility of the support members and the geotechnical behaviour of the rock mass. Detailed geotechnical investigations are, therefore, necessary for the design of effective rockbolting systems. The study described in the paper was concerned with improving the effectiveness of ground control at Mount Isa Mine. The paper briefly reviews the design methods avail- able when choosing a rockbolting system with a view to identifying the most suitable method. Joint surveys were used for the geotechnical assessment of rock mass stability. These were interpreted with the aid of the stereographic technique of predicting the size and shape of potentially unstable blocks of rock in both the roof and side walls of excavations. The geology and ground conditions at Mount Isa are briefly described together with the current ground control techniques. The requirements for ground control have been investigated at representative sites by analysing typical modes of rock failure and using a geological predictive technique. An application of this technique to the selection of a support system in a shallow Coal Measures tunnel is also described. The paper concludes with a general discussion on the effectiveness of this method of site investigation for the appraisal of rockbolting support in mining and civil engineering excavations.

Jan 1, 1983

By Lewis Reeve

As. part of a program of investigation of the properties of electric arc welds carried out in the laboratories of the A. 0. Smith Corporation, considerable work has been done on the determination of the oxygen, nitrogen and hydrogen content of different types of weld metal, employing for this purpose the so-called "vacuum fusion method." It is the purpose of this paper to describe certain improvements that have been introduced in this method of determining the gas content of metals, with particular references to the steel specimens examined in this investigation. The method and apparatus used at the beginning of the investigation were essentially those of the Bureau of Standards as described by Vacher and Jordan.1 Later a number of changes were introduced which resulted in. more rapid evacuation of the graphite crucibles employed and which enabled larger volumes of gas to be dealt with than could be handled conveniently in the Bureau of Standards equipment. In addition, the analyzing of the gases evolved from a melt in the same apparatus as collected was abandoned in favor of analysis outside the equipment using standard methods of gas analysis. The time required for gas analysis in the apparatus itself, as described by the Bureau of Standards, was found to be considerable, and during this time the rest of the equip-ment was tied up, preventing its use for the analysis of further steel sam-ples. As a result of the modifications introduced, the time required for the analysis of a steel sample for gas content was reduced from about 8 hours to less than 3 hours. Subsequently, the whole procedure of melting the sample and collect-ing the gases evolved was modified so as to enable a distinction to be drawn between the easily reducible oxides such as iron oxide and the more stable oxides such as silica and alumina. At the same time evidence was obtained indicating the probable existence in the steels of other nitrides than those of iron alone and making possible their quantitative determination.

Jan 1, 1933

By John D. Price

COAL blending, in the preparation of coal before coke making, is so commonly practiced as to be almost universal. But the reasons underlying this practice, the benefits resulting from it, and the materials used in blending vary widely. This paper will outline the various phases of the subject and present information which may be correlated with work that has been done elsewhere. It will deal entirely with work done on the high-volatile coking coals of the western part of the United States, special emphasis being given to the coals of Colorado and Utah. A surveyL of the 86 coke plants in active operation in the United States during 1949 indicates that only 9 plants, or 10.5 pct of the total, charged one single rank of coal into their ovens, while the remaining 89.5 pcl made use of blending in some form. This report indicated that of these total plants 5 used straight high-volatile coal, 4 used straight medium-volatile coal, 47 used blends of high and low-vola-tile coals, 25 used blends of high, medium, and low-volatile coals, 2 used blends of high and medium-volatile coals, 3 used blends of medium and low-volatile coals. The fact that certain plants operated on a single kind of coal should not be interpreted to mean that no blending was practiced there, for invariably such plants secure their coal from more than one source and in the interest of uniformity do blend the coals as received. The general term coal blending covers two fields, the first of which is the mechanical mixing of a number of coals to secure uniformity. Often it is found necessary to secure coal for coke production from a number of different mines; these coals, though of the same general type or rank, may differ in their chemical composition or in the physical qualities they impart to coke made from them. Again, it is not unusual to find that coal from different sections of the same mine may show variations in quality. Under such conditions it may be necessary, in the interest of a uniform final product, to introduce a system of blending bins, a bedding yard, or other mechanical methods of securing a uniform mixture. Unfortunately this form of blending has received very little attention up to the present time; it has not received the consideration its value merits. The second type of blending, while also for the purpose of coke improvement, deals more particularly with the use of a blending agent differing in character from the base coal: it is this form of blending that will be discussed here. To consider only the western coals, for blending may be found necessary for other reasons with other coals, blending has been practiced experimentally or commercially under the following conditions: 1—When a single coal or mixture of coals of the same rank does not produce a satisfactory coke. For example, a high-volatile coal when used alone is likely to contract when coked so that a comparatively weak coke is formed. Or, if of very low rank, the coal may be deficient in the necessary bitumens required for good coke production. 2—When a product of some special quality is required, for example, when a plant ordinarily producing blast furnace coke must operate at slow coking rate to produce a high-grade foundry coke. Under this condition the reduced daily production of all products which accompanies slow coking time may be undesirable, and the use of some blending agent to increase the size of coke made at faster coking rates may be necessary. 3—When greater yield of coke or its coproducts is needed. Depending upon economic values of the products it may be found desirable to increase the yield of one or the other. 4—When supply of a particular coal must be used, either to protect reserves of high quality coking coal or to utilize a surplus or inferior product not otherwise usable. Many materials have been used for blending purposes, the exact agent to be used depending both upon the condition to be corrected and the nature of the base coal. No universal blending agent that can

Jan 1, 1954

By Paul B. Crawford, Melvin B. Burton

A procedure is given which describes how the gelatin model may be-used to study the effect of mobility ratio on areas swept before and after breakthrough in fluid injection programs. Differences in mobility ratio are achieved through the proper selection of electrolytes for the invading and displaced fluids. The progress of the front is followed visually and photographed or traced onto plates (it desirrd positions before and after breakthrough. Example applications to standard flooding pattrrrls, vertically and horizontally fractured reservoirs and the in-situ combustion recovery process ore presentrtl. INTRODUCTION In water flooding, gas cycling and other fluid injection programs, the sweep efficiencies and swept areas after breakthrough are known to depend on the mobility ratio. Previous investigators have described the application of the X-ray technique, stepwise use of the poten-tiometric model and numerical procedures for studying these problems.1,3,4,6 Others have described the application of the electrolytic and gelatin models for studying sweep efficiencies at a mobility ratio near one.2,5,7,8,9 It is a purpose of this paper to describe a procedure for using the gelatin model to study swept areas at mobility ratios other than one. PROCEDURE The technique developed for gelatin model studies is composed of four phases: the construction of the model, the selection and preparation of electrolytes, the running procedure, and the recording of the swept areas. Each phase is discussed independently in order that the over-all procedure will not be confused. Construction of the Model Since some of the advantages of the gelatin model are its economy, and speed, it is desirable to have as small a model as is possihle without creating error through the inability to follow visually the progress of the colored front. For this work, it was found that a distance of 4 to 6 cm between salt bridges is convenient to use. Since the size is relatively small, it follows that the gelatin layer must be thin. For this study, 1/8 in. was used as the gelatin thickness in each case. The model was constructed on a flat 1/2-in. plastic (Lucite) base with boundaries constructed from 1/8-in. plastic strips. The well pattern to be studied was outlined with the 1/8-in. plastic strips on the base with narrow apertures (- - 2 mm) in the boundary to represent the wells. Behind each well opening, a rectangular area of some 8 to 12 sq cm was outlined by additional plastic strips. The plastic strips were fastened to the base by any suitable non-conducting cement so that the boundary system was liquid tight. The electrodes were constructed from sheet copper in a fashion that would allow easy removal. In this work, it was found that by simply forming a large U-shaped clip from a strip of the copper that would slip over the boundary was satisfactory and easily removed. The electrodes should be as wide as one of the sides of the rectangular area behind the well opening. If a fractured pattern is studied, fractures inside the well pattern may be represented by strips of copper of the desired shape mounted in some easily removable fashion. The reason that apertures (or salt bridges) were used for wells instead of metallic electrodes is that the plating of the electroactive ion at the cathode and the introduction of an electroactive ion at the anode has a detrimental effect on the swept area outline if these operations \rere permitted to be carried on within the well pattern itself. The anode may be used within the well pattern

Jan 1, 1957

By J. R. Ross, J. B. Rosenbaum

Bureau of Mines research has resulted in the development of fluid- bed ion-exchange columns for recovering uranium from slime pulps. In pilot plant tests, slime slurries containing up to 6 percent solids were processed at flow rates of 10 gallons per square foot per minute with high uranium recoveries and efficient resin loadings. Uranium was effectively eluted in a laboratory fluid-bed elution column at eluate-to-resin ratios of less than 5:1 and eluate flow rates of 3 gallons per square foot per minute. Construction costs of mills using these improved ion exchange techniques are estimated to be 25 percent less than for mills using solvent extraction of clear solutions. For mills having a capacity of 2,000 to 2,500 tons of ore per day, the saving would be in the range of $2.5 million. In addition, a saving of about $0.80 per ton of ore in total operating costs is indicated.

Jan 1, 1973

I HAVE told you of two parts of the mould for guns. You lack the third, which is the one for making the breech. This, in addition to being a part that is always ornamented with some piece of sculpture to make the gun beautiful, is that part which forms the bottom and closes the whole mould. It is also the one that sustains the entire burden of the bronze, and it must therefore be made with great consideration and diligence, taking care to make it strong with clay and with iron bands. Various methods are used in making this. Every master does as he knows how, either preferring to do it quickly or delighting to make his work ornate and beautiful. His choice also depends on whether they are to be just artillery or occasions for artistry. There are some who, if the guns are of a round form, make the pattern for the breech on a lathe, either of wood or of clay. If they are fluted, they make the flutes by hand in wood or clay, following the pattern of the board. In a part that perchance might not come out of the mould, they put some tallow underneath or make it entirely of tallow or wax so that it will come out. Likewise, if they wish to make cornices or other projections these can be put on either in wood or in clay. In the same way they also apply leafwork of clay or wax so that it can be taken out by hand or with the fire.

Jan 1, 1942

By K. J. Brondyke, P. D. Hess

Lack of correlation between densities of aluminum alloy samples solidified under reduced pressure (vacuum gas test) and hydrogen content of the metal is explained on the basis of inclusions serving as nuclei for hydrogen bubble formation. As a result of these findings, the vacuum gas test is suggested as a practical tool to indicate metal cleanliness and the potential effects of hydrogen. Visual obseroation of the sample during solidification under vacuum provides more useful information than that obtained either from density meas -urements or sectioning of the solidified sample. A rapid, practical method of detecting and measuring gas in molten-aluminum alloys has been sought for many years. The development of the vacuum gas test appeared to solve this problem. However, the vacuum gas test is subject to certain limitations, and the results must be interpreted mindful of these limitations, as described herein. Since the only gas which is appreciably soluble in aluminum is hydrogen, the terms gas and hydrogen will be used interchangeably in this paper. In the early days of the aluminum industry, when techniques were not as refined as they are today, it was customary to pour small "pancakes" of alumi- num on a metal plate. These were allowed to solidify under atmospheric pressure. Excessive gas in the metal was evidenced by the appearance of small bubbles on the surface of the "pancake".' It is obvious that such a method would only show very high gas levels far above any which could be tolerated by today's standards of quality required for most applications. Various attempts were made to develop methods which would be more sensitive. Among these were measurements of density of aluminum alloys solidified under controlled conditions, radiography of cast slabs, and examination of fractures. The method which showed the greatest promise and appeared most practical was the solidification of a sample of the molten aluminum alloy under vacuum. The samples so solidified are evaluated either by observation for bubble emission during solidification, by sectioning the solidified sample and examining for porosity, or by determining the density of the solidified sample. This test is known internationally as the Straube-Pfeiffer test or the reduced-pressure solidification test, but in America it is commonly referred to as the vacuum gas test2-' and will be so designated in this paper. The determination of density appeared an attractive and convenient means of providing a numerical rating for the samples. Attempts were made in some instances to correlate densities to hydrogen contents. Unfortunately, the visible loss of gas during solidification of samples with high gas contents precluded a correlation of vacuum gas test densities with the observed gas evolution. This led to Alcoa's use of two different pressures; 50 mm of

Jan 1, 1964

By J. S. Aronofsky, A. S. Lee

Results and experimental procedures are presented covering a preliminary laboratory investigation of the compaction of reservoir rocks and its effect on porosity and permeability. "Egective" compressibility was measured by subjecting core material to an overburden load and reducing pore pressure. Preliminary results showed relatively high effective compressibilities which varied from 1.8 X 10-' pore volume/pore volume /lb / in.~ for limestones to 7.7 X 10-6 pore volume/pore volume/lb/in.' and even higher for sandstone reservoirs conmining large amounts of fine clay material. It appeared from the initiol results that the effective compressibility of the material could not be correlated directly with porosity and that other factors, such as the amount of clay material present might have to be taken into account. The work to date has indicated that effective compressibility factors will have to be measured for the particular reservoirs heing studied. Oil permeability of core materid was measured under various effective overburden loads from 0 to 8,000 psi. It has been found than reduction of permeability in clean sands was relatively small and the results agreed with published data. For sandstones containing large amounts of clay, preliminary tests indicated very large reductions in permeability with increasing effective overburden pressures. It is planned to continue laboratory work on this phase because of its importance in low-permeability reservoirs. INTRODUCTION During the past few years increasing interest has been shown in the differences obtained between conventional laboratory measurements on cores at atmospheric pressure and those when reservoir conditions are simulated. Since these data are used as the basis for calculations and the prediction of reservoir behavior, their evaluation under reservoir conditions is most important. The effect of the compressibility of the rock upon the reservoir behavior, as fluid pressure declines, is an important subject which has been insufficiently studied. The total pressure on any plane through a reservoir is the result of the grain-to-grain rock pressure due to the overburden and the pressure of the interstitial fluid on the plane. As reservoir fluid pressure declines, the net load on the rock phase must increase, and the result is the compaction of the rock structure which produces a decrease in pore volume. Simultaneously, the rock grains expand into the pore space as the fluid pressure declines. The result of these two effects is defined as the effective compressibility of the rock and is expressed in units of pore volume/original pore volume/psi. Work was started by Imperial in 1954 on the effects of pressure on the porosity of reservoir rock. These studies established effective compressibility factors for some limestones and dolomites. Since that time effective compressibilities have been obtained for other Canadian and some U. S. reservoir rocks. In conjunction with the study of porosity, an investigation has also been initiated to determine the effects of pressure on permeability. One outcrop and several reservoir sandstone cores have been tested to date. ROCK COMPRESSIBILITY Apparatus anD Procedure A diagram of the apparatus used in these studies is shown in Fig. 1. The equipment was constructed so that a uniform pressure, equivalent to the reservoir overburden, could be applied by the oil pump and transmitted on all sides of the core through the Lucite sheath. The sample was completely saturated by circulating brine through the mounted core. Pressure in

By F. L. Rip, B. C. Haydon

Manganese silver ores are well known to be refractory toward cyanidation. Roasting and sulfurous acid pre-leaching have been suggested for improving their amenability. This paper describes the development and implementation of the sulfurous acid pre-leach process for retreatment of manganese silver tailings at Tonopah, Nevada. The history of the material is summarized and the mineralogy is described. A brief review of an earlier application of sulfurous acid pre-leaching of a manganese silver ore is presented.

Jan 1, 1985

By John E. Conley

THE production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.1 The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnston,2 Smyth and Adams,3 Ralston et al.,4 Furnas,5 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894º to 898º C. The dissociation of dolomite and magnesite, although studied by several investigator,4, 6, 8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (1) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1939

By M. F. Werneke, J. A. Jones

The use of a unique class of sulfhydryl collectors, the monoalkyldithiocarbamate salts (RNHCS2M) as direct collectors for malchite and azurite is presented. Microflotation and laboratory scale flotation tests were performed to define the collector properties of these reagents under a variety of flotation conditions. On the basis of the results, it is proposed that some property of the amine-hydrogen atom in the reagent has a signification influence on the unusual activity of these collectors for oxide copper minerals.

Jan 1, 1979

By E. J. Wasp, T. C. Aude, F. B. Raymer

The following paper deals with technical aspects of terminal facilities for western coal pipelines. The information is taken from the Ohio and Black Mesa pipelines and the proposed one in Wyoming. This paper first discusses the feed terminal, the product that it must produce, and the reasons for coal cleaning. Then in the delivery terminal section, the various methods of dewatering the coal and some recent innovative ideas on bunkering the dewatered product and storing the dewatered coal in large outdoor piles are discussed.

Jan 1, 1979

By John J. Dran

The elaborate analytical techniques for risk analysis used by the large mining companies in conjunction with the valuation of mineral reserve sites are totally inappropriate for the small miner. The small miner does not possess the financial and technical resources which are available to the large companies for such risk analysis. Even if these resources were available to him, the relatively small size of his investment would not justify a huge expenditure for risk analysis. What is required by the small miner is an improvement over the single point estimates provided by the valuation techniques that he currently uses. Such improvement should provide an indication of the extent to which the true value (known only after the fact) might differ from his estimated value of the mineral reserve site. In addition, a rough indication of the chance of occurrence of various differences between the true and estimated values would be helpful to him. These improvements must be obtained at low cost to be useful to the small miner. Such improvements would have to be based on a simple system requiring very few additional estimates by the miner. The small miner is not accustomed to dealing with sophisticated risk analysis techniques. Hence, any complex, time-consuming approach would be doomed to disuse or possible misuse. A simple, uncomplicated approach requiring a minimum of additional estimates by the miner can be based on a system devised by Frederick S. Hillier Although Hillier's method can be applied to various mineral reserve valuation methods used by the small miner, this note is specifically oriented to the discounted cash flow model. The basic discounted cash flow (DCF) approach provides a single point estimate of value and introduces the concept of risk (i.e. the possibility that the annual cash flows may differ from their estimated values and thus lead to an incorrect investment value) through the use of a risk-adjusted discount rate. This approach simply lowers the present value estimate with increases in the discount rate (i.e. increases in the risk assessment). The single point estimate still remains. Although the lower value estimate makes it less likely that the risky investment will be deemed profitable and undertaken, it provides no indication of risk that is suitable for examination and analysis. In addition to the "best guess" estimate of annual net cash flows required in the DCF model, application of the Hillier risk analysis model requires that the miner

Jan 1, 1976

By Comfort Adams

WHEN this country went into the war, but two concerns, The Bethlehem Steel Co. and The Midvale Steel and Ordnance Co., knew how to make steel fit for great cannons and at these concerns there were relatively few men who knew the whole art. Fortunately, certain of these men put their knowledge at the service of the Government, and proceeded to instruct the metallurgists at the arsenals and at various steel works. The then chairman of the Engineering Division of the National Research Council, Doctor Howe, suggested that this work might be facilitated, and the number of effective gun-steel makers thereby increased, if a detailed description of the best practice could be written, giving the reasons for the various steps, and issued with the endorsement of a committee composed of those who were evidently the most competent authorities. It was thought that something would be gained by clarification of the subject, and something by the eminent authority' of the members of the committee. To that end, the Engineering Division appointed-a committee, consisting of the gentlemen whose names follow, to mention only those who retained their connection with it. At, this time there were serious difficulties in the manufacture for the Government, of aircraft and high-speed engine crankshafts, of certain ordnance forgings, and of shells for both the Army and Navy. This Committee was asked to study and report upon these, with a view to betterment of practice. There were indications that the source of some of the difficulties went back to the melting of the steel and the production of the ingot. Hence, the committee first studied steel melting and ingot production, in order to guide the wartime manufacturers to an even larger percentage of useful production from the steel initially melted.

Jan 1, 1922

By Herbert Haas

The following notes describe a laboratory for metallurgical chemistry and technical analysis which I built late in 1903, while engaged, as constructing engineer, in erecting a pyrite smelter at the Afterthought mine, Ingot, Shasta county, California. This design partly supplements the paper of Mr. C. H. White, which was presented at the Atlantic City Meeting of the Institute in February, 1904.' The work of a chemist at a busy smelting-plant differs radically from the work of a student, who takes all possible care to have his analysis exact within hundredths of a per cent., and has plenty of time to devote to the operation. The works-chemist, having the shortest time in which to make his determinations, should have a laboratory arranged as conveniently as possible to save time in carrying out his work. By a conveniently-arranged laboratory, I do not mean an elaborately furnished one; but rooms suitably fitted up and supplied with the necessary apparatus to do the work expected from the chemist within the requirements of technical analyses. It is not uncommon at large smelters to have the night ae-sayer prepare 30 or more samples for titration, in time for the

Jan 1, 1905

By D. J. Freeh, W. E. Horst, R. C. Kellner

This paper is concerned with the description of grinding characteristics in a batch grinding system. A mathematical model was developed and used for simulating the system on an analog computer. A general equation describing the change of selected size fractions with respect to time is presented. The empirical verification of the model is discussed. In order to understand the performance of a grinding system, it would be desirable to have a mathematical description of the system's behavior. The development of a mathematical model to describe the performance of a batch dry-grinding operation was investigated. This is the first step toward reaching the objective of a practical mathematical description of a grinding system that could be employed for process control and optimization of a simple or complex grinding circuit. Although this article is concerned only with batch grinding performance, experimental work is being conducted to extend the model to continuous grinding systems. BASIC PROCESS CONSIDERATIONS In a paper dealing with the probability theory of wet ball milling, Roberts1 correlated the rate of change of oversize material, C, with energy input, E, as follows where the energy input is expressed in power/unit mass and k is a constant for each particle size. Experimental grinding studies were made by Bowdish2 to extend the previous work of Roberts. The work of Bowdish also showed that the rate of breaking of oversize particles in a ball mill is proportional to the concentration of oversize particles present. He further demonstrated that breaking of oversize particles is proportional to the surface area of the balls used for grinding. Rate equations were presented and it was concluded that grinding could be considered as a first order phenomenon according to the rate equation [2] di which is in accordance with Eq. 1. In Eq. 2, the effect of ball area is included in the constant k,. Other rate equations were reported to show the effect of a change in ball area and removal of fines during grinding. Correlation studies made by Arbiter and BhranY indicate a first-order rate equation for quartz; however, their data showed less than first-order rates existed for some of the other materials evaluated. More recently Kelsall4 has shown that the rate of breakage of any narrow size range of quartz could be described by a first-order rate equation. Several other investigators5-7 have described grinding behavior in terms of rate equations or kinetics. In general, the rate equations have been described for each particle size; however, the interactions between sizes and the overall relationships that exist have not been considered, at least not in the form of solving a group of simultaneous differential equations. Extensive work has been conducted by various investigators using a probabilistic approach which has expanded stein's' earlier work. Selection and breakage matrices are incorporated in the probabilistic model as contrasted with the deterministic method presented here. A batch grinding operation may be considered as an unsteady-state process from the standpoint that the conditions within the mill are a function of time. Therefore, a plot of mass fraction of the i-th size versus time would give a set of curves as shown in Fig. 1. In these curves X , represents the mass fraction of large size material, X2 intermediate size, and X3 small size material. An examination of these curves shows a strong similarity to the curves that would be obtained from a chemical reaction of the type9 A?B?C, [3] where A would be comparable to the largest size material being broken to an intermediate size, 3, and

Jan 1, 1968

By B. H. Sage

AN apparatus is described for the measurement of the pressure-volume-temperature relations of pure substances, simple mixtures and complex mixtures with an over-all absolute uncertainty, which is usually not more than 0.2 per cent. The equipment is suitable for studies in the gaseous, two-phase, and liquid regions. The behavior of such systems may be investigated at pressures as high as 10,000 lb. per sq. in. for temperatures between 70° and 600° F. The methods of measurement and the construction of the apparatus are described in some detail. The measurement of the volumetric behavior of multicomponent systems requires the simultaneous measurement of the pressure, volume, temperature and weight of each component of the system. In the present apparatus a sample having constant weight is investigated at a number of independently controlled pressures and temperatures, there-fore it is necessary only to establish the weight of each component added before a given set of measurements. This method is in distinction to that in which the total volume remains constant and the pressure is varied by addition or removal of material, the system having variable weight. An objective in the design of the apparatus to be described was to develop equipment that would yield results involving no uncertainties larger than 0.25 per cent throughout the range of pressures from 150 to 10,000 lb. per sq. in. at temperatures between 70° and 600° F. Although this over-all absolute uncertainty of measurement may not appear to be small, it necessitated care in the plans for control and measurement of each of the fundamental variables. In general, any uncertainty greater than 0.05 per cent in the pressure, volume, absolute temperature or weight of each component was considered undesirable; therefore the attempt was made to obtain a precision of measurement in each case such that the absolute uncertainty would be only half this amount except in certain regions near the ends of the experimental range of the variable under consideration.

Jan 1, 1939

By B. H. Sage, W. N. Lacey

An apparatus is described for the measurement of the pressure-volume-temperature relations of pure substances, simple mixtures and complex mixtures with an over-all absolute uncertainty, which is usually not more than 0.2 per cent. The equipment is suitable for studies in the gaseous, two-phase, and liquid regions. The behavior of such systems may be investigated at pressures as high as 10,000 lb. per sq. in. for temperatures between 70 and 600 F. The methods of measurement and the construction of the apparatus are described in some detail. The measurement of the volumetric behavior of multicomponent systems requires the simultaneous measurement of the pressure, volume, temperature and weight of each component of the system. In the present apparatus a sample having constant weight is investigated at a number of independently controlled pressures and temperatures, therefore it is necessary only to establish the weight of each component added before a given set of measurements. This method is in distinction to that in which the total volume remains constant and the pressure is varied by addition or removal of material, the system having variable weight. An objective in the design of the apparatus to be described was to develop equipment that would yield results involving no uncertainties larger than 0.25 per cent throughout the range of pressures from 150 to 10,000 Ib. per sq. in. at temperatures between 70" and 600" F. Although this over-all absolute uncertainty of measurement may not appear to be small, it necessitated care in the plans for control and measurement of each of the fundamental variables. In general, any uncertainty greater than 0.05 per cent in the pressure, volume, absolute temperature or weight of each component was considered undesirable; therefore the attempt was made to obtain a precision of measurement in each case such that the absolute uncertainty would be only half this amount except in certain regions near the ends of the experimental range of the variable under consideration.

Jan 1, 1940

By W. N. Lacey, B. H. Sage

An apparatus is described for the measurement of the pressure-volume-temperature relations of pure substances, simple mixtures and complex mixtures with an over-all absolute uncertainty, which is usually not more than 0.2 per cent. The equipment is suitable for studies in the gaseous, two-phase, and liquid regions. The behavior of such systems may be investigated at pressures as high as 10,000 lb. per sq. in. for temperatures between 70 and 600 F. The methods of measurement and the construction of the apparatus are described in some detail. The measurement of the volumetric behavior of multicomponent systems requires the simultaneous measurement of the pressure, volume, temperature and weight of each component of the system. In the present apparatus a sample having constant weight is investigated at a number of independently controlled pressures and temperatures, therefore it is necessary only to establish the weight of each component added before a given set of measurements. This method is in distinction to that in which the total volume remains constant and the pressure is varied by addition or removal of material, the system having variable weight. An objective in the design of the apparatus to be described was to develop equipment that would yield results involving no uncertainties larger than 0.25 per cent throughout the range of pressures from 150 to 10,000 Ib. per sq. in. at temperatures between 70" and 600" F. Although this over-all absolute uncertainty of measurement may not appear to be small, it necessitated care in the plans for control and measurement of each of the fundamental variables. In general, any uncertainty greater than 0.05 per cent in the pressure, volume, absolute temperature or weight of each component was considered undesirable; therefore the attempt was made to obtain a precision of measurement in each case such that the absolute uncertainty would be only half this amount except in certain regions near the ends of the experimental range of the variable under consideration.

Jan 1, 1940