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By Paul D. Dupree

Introduction Trapper mine is a dip-line strip coal mine, located about 10 km (6 miles) southwest of Craig, CO. The mine provides the Craig Generating Station, operated by Colorado-Ute, with about 2 Mt (2.3 million st) of coal annually. The Trapper mine is situated on a hillside that climbs in elevation from 2 to 2.5 km (6500 to 7400 ft) at average grade of 15%. The coal seams dip at about 16% down-grade and they outcrop near the top of the hillside. They exceed maximum stripping depth in 1 to 1.7 km (3500 to 5500 ft) of pit length. Stripping in the three existing pits is performed with three Page 752 23 m3 (30 cu yd) walking draglines. Two of the pits are currently being cast blasted. Until the active cut, the Derringer pit was cast blasted only where the lower mined seam exceeded stripping capabilities and the pit was a single seam operation. Now, a 9-m (30-ft) interburden bench has been incorporated into the stripping plan. This bench protects the first seam of coal from shear when the overburden is cast blasted. The cast blasted section of the 1.6 km (53,000 ft) long pit has been increased from the 457 m (1500 ft) casted previ¬ously to 1 km (3500 ft). High speed films show the coal losses due to shear of the blast are minimal. The pit width in Derringer pit is 61 m (200 ft). This is necessary for efficient spoil side stripping of a relatively thin interburden in the two-seam section of the pit. The Enfield pit is entirely cast blasted. The single seam pit is 46 m (150 ft) wide, 1.1 km (3600 ft) long, and varies from 15 and 46 m (50 and 150 ft) in overburden depth. The overburden strata at the mine consists of medium-hard layers of sandstone, shale, and

Jan 1, 1987

By Deepak Malhotra

The first step in the development of a gold deposit is the detailed mineralogical examination of the ore types, major and minor mineral constituents and their association. It is extremely difficult and expensive mineralogically to characterize the occurrence and association of gold with other minerals for low-grade refractory ores (less than 0.1 troy oz/t Au). Even if a mineralogist can identify a gold-associated particle or two, one wonders how representative they are of the deposit. What alterative does a metallurgist have for characterization of gold-bearing ores? Diagnostic leach procedures, consisting of a series of sequential leaches, can provide the metallurgist/mineralogist with reasonably good Indication of the deportation of gold in the various mineral matrices. This information con help the metallurgist concentrate on the most promising process options In the Initial stages of the project development process.

Jan 1, 1993

By D. Newman

Ground control is critical to the success of a safe and productive underground stone mining operation. The primary focus of the ground control engineer is the stability of the roof or back; development and benched pillar stability; stability of the sill pillar between vertically adjacent mining levels; and floor stability. Roof stability begins with the selection of a stable back horizon based on the presence of a thin shale parting, stylolite or other discontinuity from which the production shot can easily peel away, leaving a stable back stratum. Bed thickness, fracture spacing, jointing and the material properties of the roof strata control the room width; the decision whether to bolt the roof; the bolt length, type and diameter; and the spacing of the roof support. Horizontal stress controls the header and crosscut azimuth. The mine operator should avoid driving perpendicular to the maximum horizontal stress direction. Where this is unavoidable, narrowing the opening width, narrowing pillar centers, increasing the support density and using three-way intersections are alternatives to remediate shearing along the roof-rib interface. Stable pillar dimensions depend upon the interaction of the vertical stress resulting from overburden thickness and multiple-level interaction of overlying level or levels; the mining height during development and the final mining height after floor shots are taken during benching; the presence of faults, folds or joints passing through the pillar; and limestone lithology, recognizing that the presence of oolitic bands, shale partings, joints and bentonite beds creates zones of weakness that can destabilize an otherwise competent pillar. Floor stability is typically not a significant issue for underground stone mines because the bearing capacity of the stone typically exceeds the vertical pressure transferred through the pillar. However, floor heave can be a ground control issue where shale partings, moisture-sensitive strata, weak stone bands or horizontal stress is present. Roof stability and pillar stability problems can be initiated as the floor heave enables the pillar and roof to settle. To illustrate these ground control issues, this paper presents four case histories that are a mix of ground failures and successful mining. The focus is on the geotechnical data required for roof, pillar and floor design and stability analysis.

Jan 8, 2017

By D. Malhotra

Metallurgists are continuously striving to improve recovery. But optimization of profits and/or revenue dictates that recovery can be sacrificed at the expense of throughput. However, recently there has been significant interest in the concept of retreatment of tailings to enhance recovery and hence revenue while maintaining high throughput. The authors discuss the technical and economic factors that need to be considered in evaluation of the feasibility of retreatment of tailings including the potential feed streams (i.e., rougher tailings, cleaner tailings, etc.) and processing options (i.e., physical beneficiation, chemical processing, etc.). A case study for base metals is discussed.

Jan 1, 1994

By MAURICE SUNKPAL, Taghi Sherizadeh, Kutay E. Karadeniz, Dogukan Guner, Samuel Nowak

In this study, various rib bolting scenarios were investigated to better understand the effectiveness of the support systems. A coal mass constitutive model is implemented to a distinct element method (DEM) code, and rib factor-of-safety (RibFOS) analyses were performed by applying strength reduction for the coal matrix and explicitly modeled face cleats. Ribs with various overburden depths and mining heights composed of solid banded bright coal were considered. Different scenarios such as rib bolt length and number of bolts were studied to quantify the effect of primary rib support density on rib stability. As a result of the unsupported coal rib analyses, a decaying exponential relationship is proposed between the mining height-overburden depth and the RibFOS. The developed coal rib models clearly show the coal-rib bolt interaction and illustrate how the addition of rib bolts restricts the movement of the coal rib. The results reveal that the strength-reduction method in DEM code with the coal-mass model can aid in the development of practical primary sup- port charts, which can help in the rib support design process.

Feb 1, 2024

By J. D. McAteer

It is widely agreed throughout the mining community that federal mine safety and health legislation administered by the Mine Safety and Health Administration (MSHA) deserves significant credit for the past quarter-century's remarkable improvements in miner safety and health. Recently, however, it has been suggested that the mining industry in the United States has now evolved to a point that current mine safety and health law may be obsolete. This proposition deserves attention. Today, I propose to give it the close logical scrutiny that is its due. I conclude that the obsolescence of current mine safety and health law is not supported by the evidence. The existing mine safety and health law continues to serve as a critically important supplement to mine operators' safety programs at a modest cost to the taxpayer. At the same time, trends in a changing industry do call for responsive adaptations in the Federal mine safety and health program. I will argue that timely and appropriate responses to changing needs can be accomplished within the framework of existing legislation, provided federal officials avail themselves of the flexibility provided by existing law.

Jan 1, 1996

By Neal Cochran

I consider it a distinct privilege to be afforded the opportunity of discussing the program of the Office of Coal Research. The principal activities I will be discussing are concerned with projects that fall in the utilization area. I will, to be sure, touch on other activities of the Office of Coal Research but am not equipped to discuss these activities in great detail. Research activities of the Office of Coal Research are conducted on a contract basis with commercial, academic, and non-profit institutions. We do not operate any laboratories of our own but we do maintain a very small staff for technical and administrative supervision of our contractors. We have consistently attempted to interest outstanding, creative, and practical research organizations in our program. We are constantly seeking the imaginative new idea that will materially reduce the cost of mining coal, transporting it, or will process it into a more convenient and useable form. In assessing proposals and in developing our program, we search for the improvements that will develop large-scale new uses for coal or coal products or those that support these new uses.

Jan 1, 1963

By Justin Cardwell, Alyson Cartwright

"Grade estimation is the cornerstone of longrange mine planning. Pit designs, metal recovery, mining costs, reserves calculations and reporting are all dependent upon a reliable grade model. If the geology is poorly understood or the interpolation methods and parameters have been haphazardly constructed, then massive financial losses will be the inevitable outcome. Therefore, a properly trained geologist must use all of the appropriate tools available including deposit knowledge and advances in modeling technology to construct the most geostatistically and practically sound long-range block model.Certain deposits, such as the sedimenthosted deposits at Tenke-Fungurume, require an interpolation method that best suits the style of mineralization. In 2014, Hexagon Mining developed a tool in MineSight called dynamic unfolding (MSDU) that has the potential to improve upon previous Euclidean-based interpolation methods. MSDU utilizes the nonstationarity of a folded grade trend to more accurately construct variograms and improve interpolation results based upon a modeled three-dimensional surface.Geology overview. The sediment-hosted Tenke-Fungurume mining district is located in the southeastern part of the Democratic Republic of the Congo (Fig. 1). The rocks within the district are primarily dolomites and shales from the lower half of the Roan Supergroup that were mineralized by ascending pregnant copper and cobalt rich brines within a massive sedimentary basin (Cailteux et al., 2005) (Fig. 2). These oxidized brines likely found a fluid channel in the porous RSC unit. The surrounding rock units provided a redox boundary for copper and cobalt precipitation along organic rich beds, forming a massive stratabound deposit that was later broken up by several subsequent tectonic events (Dewaele et al., 2006)."

Jan 1, 2015

By J. D. Noll

An effective technique to minimize miners? respirable dust and diesel exposure on mobile mining equipment is to place mine operators in enclosed cabs with designed filtration and pressurization systems. Many factors affect the performance of these enclosed cab systems, and one of the most significant factors is the effectiveness of the filtration system. High-efficiency particulate air (HEPA)-type filters are typically used because they are highly efficient at capturing all types and sizes of particles, including those in the submicron range such as diesel particulate matter (DPM). However, in laboratory tests, minimum efficiency reporting value (MERV) 16 filters have proven to be highly efficient for capturing DPM and respirable dust. Also, MERV 16 filters can be less restrictive to cab airflow and less expensive than HEPA filters. To verify their effectiveness in the field, MERV 16 filters were used in the enclosed cab filtration system on a face drill and roof bolting mining machine and tested at an underground limestone mine. Test results showed that DPM and respirable dust concentrations were reduced by more than 90% when the cabs were properly sealed. However, when the cab door was opened periodically throughout the shift, the reduction efficiency of the MERV 16 filters was reduced to 80% on average.

Feb 1, 2014

By D. Arku

The increased use of sensors to facilitate automation has led to an explosion of data. As data sets grow in size, their use becomes more complex. Therefore, there is an incentive for reducing the size of the datasets, as long as this does not compromise information gleaning. With this in mind, this project explored basic aggregation as a viable alternative to amassing large amounts of data. The goal of the project was to determine if one would arrive at different conclusions had they analyzed aggregated data instead of raw data. In a mine, operational data is typically used for tracking process statistics, correlation between factors, autocorrelation and multivariate models (for a factor of choice). Therefore, this project compared results from such analyses when it was conducted with aggregated data (AD) with the results of analyses conducted with raw data (RD). The data consisted of one-minute-apart readings from a semiautogenous grinding (SAG) mill on the horsepower, feed rate (tons per hour), rotations per minute (rpm), noise, recycle (tons per hour), density (% solids) and bearing pressure (psig). This data was aggregated by averaging five and 10 continuous (one-minute) observations. Changes in statistical measures between the two approaches were typically within 5% of each other. Differences in correlation coefficients between RD and AD(s) were also within this range. Autocorrelations present within RD were preserved in AD, as long as the time lags were scaled for the amount of aggregation. Regression and neural network models were also developed for power consumption. The prediction performance of developed models was similar whether one used raw data or aggregated data. Overall, it appeared that aggregating the data based on 5- or 10-minute time spans would not have resulted in conclusions (from simple or complex analyses) being different from using raw data. In other words, whether one had used raw data or aggregated data, the conclusions would have been the same, suggesting that time domain aggregation, a common industry practice, is a good alternative to storing high-density data in this case.

By S. Yap, F. J. Sotillo, L. P. Irwin, F. M. Utsey

Slimes, especially clays, are detrimental to several processes in the Mining Industry. The efficiency of classification, clarification, gravity separation, and flotation decreases significantly in the presence of slimes and clays. This problem is particularly critical in the Phosphate and Sulfide Industries. To reduce the effect of slimes in mineral processing, several desliming techniques and chemical additives are used, such as sodium silicate, sodium carbonate, sulfuric acid, tripolyphosphate, hexameta phosphate, etc. Lately, the Mining Chemical industry has shift to more “Specifically Developed” reagents that offer the most efficient and cost effective performance, mainly using organic polymers. For this purpose, the Mining Chemical Industry needs to understand the crystal chemistry of minerals, the chemistry of the aqueous media, the interactions in solids-aqueous-gas interfaces, the rheology of the system, and the plant operation conditions and parameters. This paper describes the use of surface chemistry fundamentals on the design of an organic polymer capable of modifying the rheology of clayish slurries of a phosphate ore. The change in the rheological characteristics of the clayish phosphate slurries allow fine ore particles to settle faster by reducing the slurry viscosity. Thus, abetter separation of the ore from the slimes is possible using gravitational or centrifugal forces. As examples of the application of this reagent, industrial and pilot plant tests on desliming using tanks and hydrocyclones are presented. These tests showed the reduction of 32%-36% in ore losses for different phosphate ores during desliming operations, and the increase of cyclones desliming efficiency to 80%. Tests were also carried out to improve the rejection of unwanted iron bearing slimes in phosphate feed. These tests demonstrated that it is possible to reduce by 0.25%-1.23% Fe2O3content in the flotation feed product. As a result, significant economical benefits are observed with the use of this new technology without any adverse effect on down stream operations, such as clay settling or phosphate flotation.

Jan 1, 2003

By L. Yuan, J. H. Rowland

"In 1995 and 2003, the U.S. Mine Safety and Health Administration (MSHA) conducted surveys to determine the number of atmospheric monitoring systems (AMS) that were being used in underground coal mines in the United States. The survey reports gave data for the different AMS manufacturers, the different types of equipment monitored, and the different types of gas sensors and their locations. Since the last survey in 2003, MSHA has changed the regulation requirements for early fire detection along belt haulage entries. As of Dec. 31, 2009, point-type heat sensors are prohibited for use for an early fire detection system. Instead, carbon monoxide (CO) sensors are now required. This report presents results from a new survey and examines how the regulation changes have had an impact on the use of CO sensors in underground coal mines in the United States. The locations and parameters monitored by AMS and CO systems are also discussed.IntroductionThe last survey conducted by the U.S. Mine Safety and Health Administration (MSHA) on atmospheric monitoring systems used in underground coal mines in the United States was in 2003 (Francart, 2005). A total of 146 active mines were surveyed. The survey report states that since 1995 there had been a steady increase in the use of atmospheric monitoring systems in underground coal mines as the technology of carbon monoxide (CO) sensors was improved by manufacturers. Atmospheric monitoring systems had become more reliable, and some CO sensors could be purchased with the capability to discriminate between the CO produced by a fire versus CO produced by diesel equipment. This increase in reliability had reduced the number of false alarms and the response time. The faster response time to a developing fire allowed miners to take the necessary action to put out the fire or exit the mine.At the time of the last MSHA survey, some mines still used point-type heat sensors to detect the presence of a fire on conveyor belts. This detection method works by measuring the temperature of the air around the sensor. As a fire starts to develop, smoke and hot gases are produced from the combustion process, and the air is heated up. Once the air and gases reach a designated temperature detected by the point-type heat sensor, a fire alarm signal is generated. Studies have shown that the response times for detecting the presence of a fire using CO sensors are much shorter than when using point-type heat sensors (Conti and Litton, 1995)."

Jan 2, 2018

By Carl R. Christiansen

Excellent underground industrial sites and warehouse facilities have been constructed in Europe and at several locations in the United States. Many quarry and mine operators are considering, or should consider, the possibilities of the development of their mineral properties in such a manner as to make underground space that is suitable for a secondary industrial use. Before proceeding with mine or quarry development, the operator should answer the following questions: 1) Is there a need for underground industrial space in your geographical area? 2) Is your deposit suitable for development of space for industrial usage? 3) If the deposit is suitable, what methods of development can be used? 4) What are the comparative economics of the different methods of space development? An honest analysis of the first two questions may eliminate the need for proceeding to the third. Affirmative answers to questions 1 and 2 should be followed by the engineering and economic studies required in response to questions 3 and 4.

Jan 1, 1975

By S. M. Moore

Each year more than 400 coal miners are injured (fatally and nonfatally) by rock falling from between or around roof supports. Many of these injuries can be prevented by the installation of roof screen. However, many coal mines are reluctant to use roof screen because of the added cost. The goal of this study was to determine the potential savings in workers' compensation (W C) premiums that can be achieved due to a reduction in rock fall injuries after roof screening. The WC rate-setting methods utilized by Illinois and Kentucky were investigated in this study. Using data obtained from the Mine Safety and Health Administration, national and state WC bodies and individual insurance companies (e.g., average cost per injury, loss cost rate, number of injuries per year, number of injuries preventable each year with roof screening), baseline mines (representing two mine sizes: 67 and 150 employees) were constructed with realistic ranges for estimates of injuries and WC premium costs. Using each state's actual WC rate-setting formulas, a sensitivity analysis was conducted to determine the total savings in WC costs after a three-year period. Annual savings in WC premiums ranged from $41,000 to $326,000 for the 67-person mine, and $96,000 to $843,000 for the 150-person mine. An economic analysis of the cost of a roof screening program at a 67-person mine was also conducted. The annual cost of a roof screening program here was estimated at $240,000. At this mine, the reduction in WC premiums alone could pay for the entire screening program.

Jan 1, 2010

By Takashi Sakaguchi, Takehiko Tsuruta, Akira Nakajima

Some attempts were made to recover gold from aqueous systems using immobilized persimmon tannin. This adsorbent adsorbed gold from solutions containing hydrogen tetrachloroaurate (III) with high efficiency, whereas there was minimal adsorption from solutions containing gold (I) sodium thiomalate and sodium dicyanoaurate (I). The adsorption of gold was rapid, and was affected by the pH of the solution, temperature, external gold concentration and amount of adsorbent. Adsorbed gold was easily desorbed with 1 M thiourea solution, indicating that immobilized persimmon tannin can be repeatedly re-used for the recovery of gold using adsorption-desorption cycles.

Jan 1, 1995

By A. E. Michon

My comments today are directed toward western coal and its impact on Burlington Northern. I will be discussing three major topics. These are: location and extent of mining activities, the flows of this coal traffic into the various market territories, and finally the interaction of this western coal with coals found in the balance of the United States. When we at BN speak of western coal, we refer to those substantial deposits lying in southeastern Montana and north-eastern Wyoming. This territory covers many different coal formations. For the sake of simplicity, I will be referring to this general area as the Powder River Basin (or the "western" coal fields). This slide highlights the area overlayed by a map of the BN rail system. The U.S. Bureau of Mines estimates the demonstrated reserve base of Montana and Wyoming to be approximately 176 billion tons. Of this figure, about 73 billion tons is minable by surface methods. This is roughly 72% of the total strippable reserves in the western united states, BN does not have sole access to this coal for there are deposits in southern Wyoming near the union pacific railroad. I will say more about this later.

Jan 1, 1978

By Steve Kral

In recent years, junior mining companies, mostly listed in Canada, have taken a beating in the finance markets. Simply put, potential investors have been leery of sinking millions into exploration and mining projects due to volatile commodities prices and an uncertain regulatory climate in developed and developing countries. The 2014 edition of the Prospectors and Developers Association of Canada (PDAC), however, seemed to be a bit different for some juniors. Equity valuations have improved and metals prices appear to be stabilizing. So, for some of the stronger junior companies, there is some hope. Merger and acquisition (M&A) activity is picking up and, believe it or not, companies are raising some capital. Billed as the largest annual mining meeting in North America, the PDAC conference attracted more than 25,000 mining and exploration professionals from around the world. Organizers were anticipating attendance to break the 30,000 mark. But, given the state of the exploration end of the mining business, 25,000 is still a respectable number. Junior companies that are in the project feasibility stage, or have made promising discoveries that stand a good chance of proceeding to production, are being looked at by potential investors. Those are the survivors of the last three years of dismal M&A activity. On the other side are the juniors that are still around ? and there are plenty of juniors that were at the PDAC last year but have since disappeared ? but have little or no working capital. One analyst calculated that there are about 850 companies with less than $200,000 in working capital and about 600 with negative working capital. This will likely result in fewer junior mining and exploration companies as the year progresses but the ones that remain should be stronger.

By Raja V. Ramani

Worldwide, promulgation and enforcement of health and safety laws and regulations have been the primary means of ensuring minimum and uniform standards of health and safety in the mining industry. In U.S. coal mines, a new era was ushered-in in 1969 for the control of health hazards from respirable coal mine dust. Since then significant progress has been made on all aspects of the respirable dust problem-its definition, monitoring, reduction, and control. In the intervening years, our ability to monitor, analyze, and characterize the mine atmospheric environment and the health of miners has increased many fold. Also, advancements in production technology have far outdistanced enhancements in environmental control technology. Therefore, questions are continuing to be raised on the adequacy of the characterization and control measures with regard to both the airborne respirable dust in mines and the health effects of respirable dust. Late in 1995, the Secretary of Labor appointed an Advisory Committee on the Elimination of Pneumoconiosis Amona Coal " Mine Workers (Dust Advisory Committee) to review the progress towards elimination of coal worker's pneumoconiosis (CWP) and silicosis, and in the program to control respirable coal mine dust in underground and surface mines, and make recommendations including improved standards and other appropriate measures for the control of exposure to airborne coal mine dust. The Committee's report was released in October, 1996. In this paper, a summary of the recommendations of the Committee is presented. A brief discussion of the background, and the issues and findings leading to the recommendations is also presented. The Committee concluded that the progress made towards making mines safer from the health hazards of respirable coal mine dust is substantial but that it is not sufficient to achieve the intent of the 1969 Coal Act. The Committee's recommendations encompass a wide range of issues addressing permissible exposure limits (PELS), sampling, dust control plans, hazard and medical surveillances, role of miners, training, and research and development.

Jan 1, 1997

By M. R. Shahan, C. E. Seaman, S. E. Mischler, T. W. Beck

"Float coal dust is produced by various mining methods, carried by ventilating air and deposited on the floor, roof, and ribs of mine airways. If deposited float dust is re-entrained during a methane explosion, without sufficient inert rock dust quantities, this float coal dust can propagate an explosion throughout mining entries. Consequently, controlling float coal dust is of critical interest to mining operations. Rock dusting—adding inert material to airway surfaces—is the main control technique currently utilized by the coal mining industry to reduce the float coal dust explosion hazard. To assist the industry in reducing this hazard, NIOSH’s Pittsburgh Mining Research Division (PMRD) initiated a project to investigate methods and technologies to reduce float coal dust in underground coal mines through prevention, capture, and suppression prior to deposition. Field characterization studies were performed to determine quantitatively the sources, types, and amounts of dust produced during various coal mining processes. The operations chosen for study were a continuous miner section, a longwall section, and a coal handling facility. For each of these operations, the primary dust sources were confirmed to be the continuous mining machine, longwall shearer, and conveyor belt transfer points, respectively. Respirable and total airborne float dust samples were collected and analyzed for each operation and the ratio of total airborne float coal dust to respirable dust was calculated. During the continuous mining process, the ratio of total airborne float coal dust to respirable dust ranged from 10.3 to 13.8. The ratios measured on the longwall face were between 18.5 and 21.5. The total airborne float coal dust to respirable dust ratio observed during belt transport ranged between 7.5 and 21.8. INTRODUCTION During the extraction of coal, various dusts are produced that can be classified into two categories of interest: respirable and float coal dust. Respirable dust (diameter 10.0 = µm) has the capability to penetrate beyond the terminal bronchioles and become deeply embedded into the human lungs, leading towards respiratory disease complications (Potts et al., 1990). Float coal dust is defined as coal dust having a diameter less than 74 µm (Harris et al., 2009). During the mining process, float coal dust can be deposited on the floor, roof, and ribs of mine airways. With the proper mixture of methane gas (between 5% and 15%) and an ignition source, a methane gas explosion can occur (Barker and Humphreys, 1996). The resulting explosion can develop a pressure wave which lifts the deposited float coal dust material into the air, propagating a disastrous coal mine explosion (Harris et al., 2010). The current technique to safeguard against the propagation of a coal mine explosion is to treat the mine airways with incombustible rock dust (typically limestone), maintaining an 80% total incombustible content of the deposited material. NIOSH initiated a project to investigate control technologies that could be aimed at reducing the amount of float coal dust allowed to deposit in the mine airways using three approaches: prevention, capture, and suppression prior to deposition. Reducing the float coal dust being generated during the mining processes and capturing or suppressing airborne float coal dust prior to deposition would in turn increase the efficiency of the applied rock dust used to prevent mine explosions."

Jan 1, 2017

By M. C. Williams

As the flaws in the population balance model (PBM) comminution model are examined more deeply, further errors and problems were discovered. The Levenberg-Marquardt algorithm for systems of constrained non-linear equations was used to solve the dynamic PBM grinding equations to obtain the grinding selection and breakage rate functions. The fact that the PBM model equation Inverse Problem is degenerate or underspecified is demonstrated. Multiple solutions to the same PBM equations are provided. It is shown that there is no unique solution to the Inverse Problem unless additional constraints are provided or assumptions are made such as the Arbiter-Bhrany normalization assumption. The severity of the non-uniqueness problem for dynamic grinding is demonstrated. Each solution to a dynamic PBM, while giving the same prediction for a given grinding time interval, gives different solutions or predictions for mill composition for other grinding times. Actual experimental grinding data was assessed to determine the functionality of mill selection and breakage functions.

Jan 1, 1993