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By D. Komljenovic, V. Kecojevic

Selection of the best possible truck type (model) is of crucial importance for the mine decision-makers. In this paper, authors contribute to the body of knowledge by developing a novel methodology for the selection of mining truck. Both the Coefficient of Technical Level (CTL) and Analytic Hierarchy Process (AHP) methods were used in this study. The CTL represents a mathematical function which takes into consideration the interrelations among the main technical parameters of mining trucks. The authors developed a hierarchical structure where both attribute categories and their importance, i.e. priority or weight in the selection process were determined. For each category, a number of sub-attributes and their priorities were assigned, and a pairwise comparison among them was performed using the AHP method. In the final part of the study, the CTL was integrated into the AHP and represents a holistic approach in the selection of mining trucks. A case study on 180 tonnes truck category offered by five manufacturers was carried out. A sensitivity study of obtained results was also performed indicating a very stable solution. The methodology presented in this paper may be used by mining operators to help in the selection of a specific type when acquiring a new truck. It may also be used by equipment manufacturers to help in analysis of potential benefits of envisaged modifications concerning an existing truck type and/or development of a new type.

Jan 1, 2007

By Tim O’Neil

Caterpillar has introduced its 5090B front shovel, to work with 40 to 70 st (36 to 63 t) trucks. The new unit replaces Cat’s 5080 hydraulic excavator. The 5090B offers more engine horsepower, higher flow, greater digging forces, higher swing torque, faster swing speed and more drawbar pull than its predecessor. It can also handle larger bucket sizes than the previous model. These improvements enhance productivity and make the 5090B a high-volume material handler for hard rock and aggregates producers.

Jan 1, 2003

By Kent C. Condie

Precambrian terranes in the Rocky Mountain region decrease progressively in age from the Archean Wyoming Province (> 2.5 b.y.) to the late Proterozoic in West Texas (figs. 1,2). Within the Wyoming Province, most dates fall near 2.7 b.y. although some are recorded at 2 3.8, 2.9, and 2.6 b.y. Although Penokean (- 1.8 b.y.) deformation and plutonism are recorded in southeastern Wyoming, most Precambrian rocks south of the Wyoming shear zone, which separates the Archean and Proterozoic provinces, are < 1.76 b. years in age. Supracrustal rocks in Colorado, western Arizona, and northern New Mexico fall in the range of 1.72-1.76 b.y., those in central New Mexico about 1.65 b.y., those in southeastern Arizona and southwestern New Mexico about 1.70 b.y., and those in West Texas 1.1-1.2 b.y. The Wyoming Province is comprised chiefly of 2.7 or 2.9 b.y. tonalitic gneiss terranes intruded by 2.6 b.y. granites in the central and southern parts of the province. Supracrustal rocks are minor and include greenstone belts comprised chiefly of pillow- ed tholeiites and graywackes and remnants of quartzite-shale successions. Metamorphic grade in greenstone-gneiss terranes ranges from upper greenschist to amphibolite facies and in quartzite-gneiss terranes from upper amphibolite to granulite facies.

Jan 1, 2013

By R. L. Grayson

In 2010, MSHA began holding hearings on a new coal mine respirable dust rule, which proposes a 1.0 mg/m3 standard, a separate 0.1 mg/m3 quartz standard, and the use of single-shift samples for compliance. Small mines largely comprise the ?hot spots? where dust diseases of the lungs increased dramatically over the past decade. This paper presents findings on the feasibility of small mines? compliance with the proposed new 1.0 mg/m3 standard. It gives probabilities of noncompliance by MSHA district, seam height, and selected ?hot spot? counties. Because silicosis and respirable quartz dust appear to be the primary issues related to a recent doubling of the prevalence of dust diseases of the lungs, multiple regression models for prediction of the average total quartz content of compliance samples are given. These findings have significant implications on the need for better dust control methods.

Jan 1, 2012

By P. Zhang

A multiyear, comprehensive study of flotation reagents used in phosphate beneficiation was conducted. The study involved the evaluation of pure fatty acid compounds, comparison of various anionic collectors and testing of iso-acids. Various C12 to C22 fatty acids were tested as Florida phosphate collectors. The saturated fatty acids were found to be very poor collectors when using the standard conditioning procedure, whereas the unsaturated C16 to C22 fatty acids showed fair to good phosphate collecting ability. The C18 fatty acids oleic, impure oleic and linoleic and the C20 eicosenoic acid were shown to be the best phosphate collectors. The best flotation results were obtained using Liqro GA tall oil and oleic acid. Four isostearic/iso oleic acid type fatty acid collectors were compared with a commercial grade oleic acid and with Liqro GA tall oil as phosphate collectors using standard laboratory conditioning and flotation procedures. The most selective collector evaluated was Century 1108, a high isostearic acid-type reagent. However, it was concluded that this excellent-performing reagent was too expensive for commercial use. Overall, the most promising reagent was probably Century MO-5. This collector is essentially an iso-oleic acid/stearic acid mixture (not isostearic acid), and it costs much less. This program laid a sound foundation for developing single collector, all anionic flotation processes.

Jan 1, 2009

By Richard Wilson

In the early 1970s, it became a concern that exposure to the mineral fibers associated taconite ore processed in Silver Bay, Minnesota would cause asbestos-related disease including gastrointestinal cancer. At that time data gaps existed which have now been significantly reduced by further research. To further our understanding of the types of airborne fibers in Silver Bay we undertook a geological survey of their source the Peter Mitchell Pit, and found that there are no primary asbestos minerals at a detectable level. However we identified two non-asbestos types of fibrous minerals in very limited geological locales. Air sampling useful for risk assessment was done to determine the type, concentrations and size distribution of the population of airborne fibers around Silver Bay. Approximately 80% of the airborne fibers have elemental compositions consistent with cummingtonite-grunerite and the remaining 20% have elemental compositions in the tremolite-actinolite series. The mean airborne concentration of both fiber types is less than 0.00014 fibers per milliliter that is within the background level reported by the World Health Organization. We calculate the risk of asbestos-related mesothelioma and lung cancer using a variety of different pessimistic assumptions. (i) that all the non-asbestos fibers are as potent as asbestos fibers used in the EPA-IRIS listing for asbestos; with a calculated risk of asbestos-related cancer for environmental exposure at Silver Bay of 1 excess cancer in 28,500 lifetimes (or 35 excess cancers per 1,000,000 lifetimes) and secondly that taconite associated fibers are as potent as chrysotile the least potent form of asbestos. The calculated risk is less than 0.77 excess cancer case in 1,000,000 lifetimes. Finally, we briefly review the epidemiology studies of grunerite asbestos (amosite) focusing on the exposure conditions associated with increased risk of human mesothelioma. © 2008 Elsevier Inc. All rights reserved. Keywords: Risk; Fibers; Particles; Taconite; Asbestos; Exposures

Jan 1, 2007

By L. O’Connor, E. Tarshizi

The objective of this work is to provide a detailed review and a list of references in chronological order, comprising 80 recent technical papers, on the use of discrete-event simulation (DES) modeling in mining engineering. In this article, the review papers of published mine simulation projects through 2007 are summarized, and then a comprehensive review of individual articles published from 2008 to 2015 is presented. This survey work also includes analyses of the simulation tools used in the published projects, mining types and applications in order to assess these key features and evaluate the recent state of research in mine DES simulation. In addition, an interactive map visualization for the locations of the simulated projects is made available on a website to benefit current and prospective scholars in the field. The results of this investigation revealed that the most common application of DES in mining had been mining equipment selection and analysis, while ore processing and risk management projects were less frequently reported. The results also showed that modeling surface mines were in the majority, but the trend of publications for underground mine simulations had also increased. According to the results, ARENA was the most popular simulation software package, but several simulation tools that were only used once or twice in the mining projects are also included in this review.

Jan 1, 2018

By L. O’Connor, E. Tarshizi

The objective of this work is to provide a detailed review and a list of references in chronological order, comprising 80 recent technical papers, on the use of discrete-event simulation (DES) modeling in mining engineering. In this article, the review papers of published mine simulation projects through 2007 are summarized, and then a comprehensive review of individual articles published from 2008 to 2015 is presented. This survey work also includes analyses of the simulation tools used in the published projects, mining types and applications in order to assess these key features and evaluate the recent state of research in mine DES simulation. In addition, an interactive map visualization for the locations of the simulated projects is made available on a website to benefit current and prospective scholars in the field. The results of this investigation revealed that the most common application of DES in mining had been mining equipment selection and analysis, while ore processing and risk management projects were less frequently reported. The results also showed that modeling surface mines were in the majority, but the trend of publications for underground mine simulations had also increased. According to the results, ARENA was the most popular simulation software package, but several simulation tools that were only used once or twice in the mining projects are also included in this review.

Jan 1, 2017

By Ronald E. Heuer, Debra L. Virgens

INTRODUCTION Behavior of clay soils in response to tunneling is reasonably well understood by reference to the tunnel stability factor NT = Pz/su (Peck, 1969; Heuer, 1974). With this analysis tool, care must be taken to use a value of clay shear strength which represents the actual mass strength, considering such factors as slickensided fissures often found in stiff and hard clays. Behavior of clean sand and gravel soils is also reasonably well understood. Above the water table these soils must be assumed to act as running ground unless they are known to have significant cementation or have a very dense and angular interlocked grain structure. Below the water table they must be tunneled using some form of groundwater control such as dewatering, grouting, freezing, or internal fluid pressure in the tunnel such as compressed air or a slurry tunneling machine. The internal fluid pressure must approximately balance the external water head. Without such precautions these soils behave as flowing ground and may yield large volumes of water flow into the tunnel. A wide range of very fine sand, silty sand, cohesionless silt, and clayey sand soils exist in nature in a variety of geologic environments. The behavior of these soils in response to tunneling, and guidelines for anticipating their behavior, are not well described in the literature. Because of their content of fine particles, these materials may behave as if they initially have appreciable cohesion and moderate to low permeability. They may exhibit significant standup time, and require tunnel internal fluid pressure (compressed air or slurry pressure) less than the full external water head. It is important to be able to estimate the behavior of these soils when planning construction methods. For example, if the external water pressure is 140 kPa (20 psi), but soil stability at the tunnel face can be achieved as a compressed air pressure of 80 kPa (12 psi), a large cost savings may result.

Jan 1, 1987

By Christopher J. Bise

INTRODUCTION Perhaps no other area reflects the art as well as the science of mining-engineering design quite as obviously as strata control. This is due to the fact that the design of mining structures is difficult because rock rarely behaves as a homogeneous medium. Further, the original state of stress and the mechanical proper- ties of the in situ rock are somewhat difficult to deter- mine. However, those aspects that are hard to treat mathematically can and have been successfully approached by model studies and in situ measurements. This chapter will review the fundamentals of strata- control design and will provide examples of applications to typical problems. STRESSES AROUND MINE OPENINGS A close examination of Fig. 1 reveals that, prior to mining, stresses exerted in the overburden can be in both the horizontal and vertical directions. In the example problems of Chapter 1, it was shown that the maximum compressive stress (uv) at any depth (D) below the surface can be approximated as follows: [ ] Further, the lateral stress (oh) is related to the maxi- mum compressive stress by utilizing Poisson&apos;s ratio (µ): [ ] As soon as a heading is driven, such as the one in the coal seam shown in Fig. 2, the stresses shift to the sides, or abutments, of the opening. Clearly, these compressive stresses around the opening exceed the pre-mining conditions. The problem of designing an underground opening, therefore, is to determine the maximum stresses and to note if they exceed the ultimate strength of the rock. Table 1 lists several rocks with their corresponding strengths. Figs. 3 to 5 depict the boundary stress concentrations around circular, ovaloidal, and rectangular openings. M is the ratio of the horizontal stress to the vertical stress, or as defined above, p/(l-p). This text will concentrate on the state of stress represented by M = 0.33, which corresponds to the condition of no lateral deformation in a rock having a Poisson&apos;s ratio of 0.25. For an ovaloid with an opening width-to-height ratio of 2.0 (Fig. 4), the boundary stress concentrations are at their maximum values at the comers of the opening, with values in excess of 3.0. If the depth of overburden is 500 ft, then the maximum boundary tangential stress ([ ] ) of the ovaloid is: [ ]

Jan 1, 1986

Syncrude Canada produces a large part of Canada’s crude oil supply. The company processes about 225,000 bbl/day. The oil produced is used for jet and automobile fuel, home heating oil, plastics and other consumer synthetics. Crude oil is produced through a process of mining, extracting and upgrading bitumen. A rich supply of bitumen is contained in the Athabasca oil sands deposit in northern Alberta. Tailings from the bitumen processing are sent to a settling basin.

Jan 1, 2000

By R. S. Jurani

Sunshine Mining Co.&apos;s Kellogg operation is the primary silver producer in the US. Maintaining a comfortable working environment in this deep underground mine historically has been a complex and costly problem. To improve the ventilation and cooling systems at a time of declining and un-certain silver markets, it was proposed to optimize the performance of existing facilities at minimum cost. This paper discusses a two-year, $400,000 optimization program that resulted in increased total mine airflow, cooler ambient temperatures, reduced compressed air usage, and lower energy consumption by primary fans, air compressors, and refrigeration plants. This saved the company about $650,000 per year.

Jan 1, 1988

By Wayne E. Kilker, Michael J. McBride, William P. Levy, Thomas J. Lamb

Between 1989 and 2004 the Massachusetts Water Resources Authority (MWRA)constructed several major wastewater and water tunnels associated with three major projects in the Boston area of eastern Massachusetts. There were many similarities and differences in the bedrock conditions encountered and among the contractual approaches for these independent projects. Through a clarification of the approach similarities and analysis of the contract differences, this paper addresses and presents what are considered to be valuable lessons learned. In doing so, the paper follows the evolution of such disparate issues as contract conditions, baseline reports and dispute review boards. The authors believe that the lessons learned even represent what, in certain cases, could be referred to as “universal truths” that are intended to have application to the next generation of tunneling contracts.

Jan 1, 2005

By Mei Long, Tawum Juvert Mbah, Jianhua Zhang, Haiwang Ye

There have been many improvements and advancements in the application of neural networks in the mining industry. In this study, two advanced deep learning neural networks called recurrent neural network (RNN) and autoregressive integrated moving average (ARIMA) were implemented in the simulation and prediction of limestone price variation. The RNN uses long shortterm memory layers (LSTM), dropout regularization, activation functions, mean square error (MSE), and the Adam optimizer to simulate the predictions. The LSTM stores previous data over time and uses it in simulating future prices based on defined parameters and algorithms. The ARIMA model is a statistical method that captures different time series based on the level, trend, and seasonality of the data. The auto ARIMA function searches for the best parameters that fit the model. Different layers and parameters are added to the model to simulate the price prediction. The performance of both network models is remarkable in terms of trend variability and factors affecting limestone price. The ARIMA model has an accuracy of 95.7% while RNN has an accuracy of 91.8%. This shows that the ARIMA model outperforms the RNN model. In addition, the time required to train the ARIMA is than that of the RNN. Predicting limestone prices may help both investors and industries in making economical and technical decisions, for example, when to invest, buy, sell, increase, and decrease production.

Jan 6, 2021

By R. B. Crookston

This paper presents the status and mining method chosen by each of the active underground oil shale projects in the united States today. Potential improvements in equipment and methods on the near-term horizon are discussed. The problems and potentials that lie in the long-term future of oil shale mining are examined in light of the demands which must be met by this developing technology.

Jan 1, 1981

By P. Rosten

US mine production of iron ore in 1984 showed some improvements compared to 1983. But reduced demand from the iron and steel industry caused temporary shutdowns of many iron ore mines and pelletizing plants. US raw steel production in 1984 was slightly above 1983, but still at a depressed level. Production was 83 Mt (92 million st), compared with 77 Mt (85 million st) in 1983 and 68 Mt (75 million st) in 1982. Two major production trends continued in 1984. They were the increased production from electric furnaces and the growing use of continuous casters. Electric furnace production included 33.2% of the steel poured in 1984, compared with 31.5% in 1983. Continuous casting was used for 39% of 1984 steel production, compared with 32.1% in 1983. Statistical Process Control Statistical Process Control (SPC) has taken on new proportions in the iron ore and steelmaking industries within the last year. This mathematical technique is used to monitor, control, evaluate, and analyze a manufacturing process. The technique charts variability of important quality parameters. Training and adaptation of SPC techniaues for process control have been initiated at Inland, Steel&apos;s Minorca, Pickands-Mather&apos;s Hibtac, Cleveland-Cliff&apos;s Empire and Sherman operations, and at Reserve Mining. One of these operations has requested its bentonite supplier provide SPC charts on quality specifications. Some of the steelmaking operations (Inland Steel, Bethlehem Steel, Dofasco, LTV Steel, National Steel, Stelco, Weirton Steel, and Wheeling-Pittsburgh) have set up SPC programs within their operations. And they also have insisted that some of their suppliers use SPC. Plant Shutdowns The permanent closure of Stelco&apos;s Griffith mine at Red Lake, Ontario, has been delayed by one year. This gives employees more time to adjust. The mine is now set to close in April 1986, instead of April 1985. Sidbec (Canadian government) and its other partners (including British Steel Corp., Quebec Cartier Mining, and US Steel) closed its iron mining operations at Gagnon, Quebec. The pellet plant has been leased to Quebec Cartier. New Iron Ore Operations The massive Carajas iron ore project in Brazil is scheduled to come onstream in Jan. 1986. It is to achieve full-scale commercial shipments by July of that year. The 66% iron crude ore requires only crushing and screening before shipment. The product consists of 83% sinter feed and 17% coarse ore. Annual production capacity will be 32 Mt (35 million st) when the project is completed. Principal customer for the ore is Nippon Carajas Iron Ore Co., a consortium of Japanese steel mills. The Arab Iron & Steel Co. (AISCO) has started up a $US300 million, 3.6 Mt/a (4 million stpy) iron ore pelletizing plant built by Kobe Steel Ltd., at Al Hidd-hide in Bahrain. By 1986, this grate-kiln-cooler plant will supply high quality iron ore pellets to feed direct reduction plants in the immediate Gulf area and Far East markets. Iron ore supplied from Brazil, Peru, India, and Mauritania provides the feed to the pellet plant. Hydrated lime (2%) is used as a burden.

Jan 5, 1985

By A. Korchevisky

Environmental self-monitoring is one of the advanced approaches for industrial sustainability programs. Organization for Economy Cooperation and Development (OECD) defines self-monitoring as ?the system of organizational and technical measures put in place and financed by [the] regulated subject? in order to ensure their compliance with regulatory requirements?1. Self-monitoring is beneficial for industrial operators, communities, and governments. Industrial companies use self-monitoring as a central element of their compliance management that allows them to fulfill their duties, obligations, and to avoid citations. When industries control their emissions and ensure workers are not exposed above the regulated limits, communities are better. It is impossible for an EPA, OSHA, or MSHA inspectors to be close to every emission source or workplace full-time. It is much more effective for industries to self-monitor, under due supervision. Occupational conditions are a very important part of industry and health and safety self-monitoring should be highly prioritized. In this paper we will research the regulatory basis and best practice of occupational self-monitoring. We will show that not only is self-monitoring a vital element of an occupational health & safety management system, but that you need a management system for affective monitoring.

Jan 1, 2012

By K. P. Black, G. W. Sevick, D. E. Hockley, K. S. Sexsmith, J. T. Chapman

Mineralogical analyses of carbonates in depyritized tailings and pyrite concentrate (from depyritization of the tailings) were completed as part of the tailings characterization for the Crandon Project, a massive sulfide deposit in northeastern Wisconsin. The mineralogical study was designed to determine the proportion of calcium and magnesium carbonates, and therefore the effective buffering capacity of carbonates in the tailings. The depyritized tailings are net acid consuming and will be stored in a surface tailings management area. The pyrite concentrate is net acid generating and will be used as backfill in the underground mine workings. The majority of carbonates in the depyritized tailings were ferroan dolomite containing 10 to 15% iron (by weight) and lesser amounts of siderite and magnesian siderite. The proportion of calcium and magnesium-rich carbonates corresponds to several independent tests of carbonate neutralization potential (CO3-NP) availability. The pyrite concentrate had less CO3-NP, indicating segregation of the carbonates during pyrite flotation. These carbonates reported higher iron contents, consistent with the relatively lower availability of CO3-NP in the pyrite concentrate.

Jan 1, 2002

By J. D. Morgan

Demand for nonfuel minerals depends on the overall state of the economy, which steadily improved each quarter in 1984. New housing starts rose to 1.8 million units. Automakers turned out about 15% more cars (7.8 million) and 30% more trucks (3.1 million) than in 1983. Nevertheless, many domestic mineral operations experienced difficulties in 1984. This resulted from import competition greater use of newer engineered materials, emphasis on multi-unit housing and downsizing of motor vehicles. About 15% of our energy was imported. This in cluded $36 billion worth of crude oil and $22 billion in refined products This added significantly to the overall merchandise trade deficit of $12; billion. On the bright side for mining, coal production rose 14% to 810 Mt (890 mil lion st). Three-fourths o: the coal was burned to generate electricity and more than half of our electricity was derived from coal-burning plants. With the exception of a few large-bulk, low-value raw minerals, most minerals move relatively freely in world trade. The strong dollar encouraged imports and made exporting more difficult. Consequently, our nonfuel minerals trade deficit rose 60% to $19 billion, reflecting imports of $39 billion and exports of $20 billion. There were increased pressures from some major segments of the minerals industry for some form of import protection. But President Reagan said, "Our goal is a system of free and fair trade in goods, services, and capital. We will work toward this goal through both bilateral and multilateral trading agreements." The US minerals industry consists of domestic mines, concentrators, smelters, refineries, mineral manufacturing plants, and recyclers. It also includes many wholly- or partially-owned operations in many parts of the world, providing employment and income for US citizens and others as well. Compared with 1983, the value of US raw nonfuel mineral output rose 8%, to $23 billion. The $253 billion worth of goods processed from this crude mineral output was a 14% increase. Major Metals Raw steel production - a major indicator of both material use and mineral production-rose 10%, to 84 Mt (93 million st). This stimulated a 36% rise in domestic iron ore production, to 52 Mt (57 million st), about 98% pelletized. Iron ore imports rose 44%, to 14 Mt (15 million st). Despite the increase of steel production, output remained well below levels of just a few years ago. For example, 1984 production was still 23% less than in 1981. Raw steelmaking capacity remained steady at 122 Mt (135 million st). The industry continued to cite steel imports as a major reason for low domestic capacity. In December, pacts with seven leading steel exporting nations were announced. This is an effort to reduce import penetration to about 18.5% of the domestic market. Domestic producers of bulk ferroalloys of chromium, manganese, and silicon operated at about 50% capacity. The US mined no manganese or chromium. Only a small quantity of ferronickel was produced from domestic laterite mining in Oregon. Molybdenum production, at 45 kt (49,500 st), rose threefold. Mine shipments of tungsten, another mineral tied to steel

Jan 5, 1985

By H. Ipek

Industrial grinding machines used in the mineral processing industries are mostly of the tumbling mill type. These mills exist in various types: ball, rod, pebble, autogenous, and semi-autogenous. Balls and rods are traditionally media shapes used in the tumbling mills. In resent years, as an alternative to balls, grinding charges with various shapes are being used. Cylpebs are slightly tapered cylindrical grinding charges with length equaling diameter, and all the edges being radiused. Cylpebs of equal diameter and length have 50% greater surface area and 45% greater weight than balls of the same material. In addition, they have 9% higher bulk density than steel balls, or 12% higher bulk density than cast balls. An important advantage of cylpebs over balls is that cylpebs produce narrower granulometric distribution due to their shapes. However, some discrepancies were found in the literature regarding the milling performance of cylpebs in comparison with balls (Chi, 2004). In recent studies, Chi (2004) has provided detailed information on cylpebs and has compared these to balls in relation to media mass, size distribution, surface area, and input specific energy. Ipek (2006) has investigated the effects of cylpebs and balls with equal mass and surface area on the breakage rate of quartz, using cylpebs and balls separately. Similarly, Lameck and Moys (2006) have investigated the effects of balls and worn balls on breakage rate of material using worn balls as grinding environment. However, no study has attempted to investigate the effects of grinding environment other than balls on the brekage distribution. As indicated by Prasher (1987), the breakage distribution function is independent of the following variables in ball mills: hold-up (Mika et al., 1967; Kelsall et al. 1969), mill speed and ball load (Herbst and Fuerstenau, 1972), media load and ball density (Kelsall et al., 1973), mill diameter (Malghan and Fuerstenau, 1976), and powder charge (Shoji et al. 1980). The aim of the present paper is to compare the effects of cylpebs and balls on the breakage distribution function of quartz with respect to same mass and same surface area. BACKGROUND Comminution as a rate process is called kinetic approach. Studies on the kinetic approach are reviewed by Oner (2001). Oner states that grinding kinetics are based on studies by Kolmogorov in 1941 and that Robert (1950) is the first to suggest this approach. Later, Melzak, Loeveday, and Reid have improved the grinding kinetics equation; and, Austin and Lynch have conducted two basic studies on the analytical solutions of these equations. Considering the results of studies comparing the size reduction mechanisms, it has been accepted that breakage constitutes of two operations. These two basic operations, first defined by Epstein (1948), are those of selection of material for breakage and the distribution of breakage material to particle sizes smaller than the initial size (Lynch, 1977). Epstein defined the two operations as: ? Pn(y), the probability of breakage of a particle size in the nth step of the breakage process. ? F(x,y), the cumulative distributions by weight of particles of size x<y arising from the breakage of a unit mass of a size y. Probability of breakage is called a selection or a breakage-rate function (Si). Characteristics size distribution after breakage is called a breakage distribution or appearance function (Bi,j). Due to the difficulties in representing particle size distributions mathematically and constantly, the batch equation based on particle size fraction is suggested. Thus, as is the case in breakage distribution and specific rate of breakage, the breakage parameters were defined by batch grinding experiments conducted in laboratories (Oner, 2001). When effective breakage occurs in the mill, the breakage of material with single feed size fraction usually fits first order grinding kinetics and the specific rate of breakage values can be calculated through the slope of semi-log plot. The values of the breakage distributions are deduced from the size distributions at short grinding times where there is mainly size 1 material breaking and only small amount of smaller sizes to rebreak (Austin et. al., 1984). B values can be calculated by using BII. [ ] where j is the top size of the charge, Pi(t) is the cumulative percent undersize of i th size interval at the short grinding time which gives no more than about 30% broken out of the top size interval. Cumulative primary breakage distribution, Bi,j, is also defined in an empirical form by [ ] where xi is the top size and Bi,j is the weight fraction of primary breakage products. The parameters F, ? and ß define the size distribution of the material being ground. On plotting size versus Bi,j on log scale, the slope of the lower portion of the curve gives the value of ?, the slope of the upper portion of the curve gives the value of ß, and F is the intercept as in Fig.1. [ ]

Jan 1, 2009