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By J. Herbst, I. Heber-Panu, Dan G. Cojocariu, E. Ene-Danalache, G. Poling

A general model which represents not only batch but also continuous flotation in multi-cell machines is presented. This model considers both the size distribution and the distribution of flotabilities in a size class for valuable mineral particles in the pulp. The general expression is shown to reduce to several previously reported models. In addition, a number of new models are found to arise for different specific assumptions concerning the flotability distribution and/or the size distribution of the particles undergoing flotation. Several of these new models are tested experimentally using laboratory-scale batch and pilot-scale continuous data. Model parameters are estimated from this data and a comparison of calculated recoveries and those experimentally determined are presented. Finally, the influence of the feed rate, aeration rate and valuable mineral content of the feed on the recovery is examined.

Jan 1, 1976

By D. N. Madge

A survey is given of production scheduling systems currently in use or contemplated for future use in Cominco operations. Emphasis in this presentation is made on the chain of decisions that are made with the help of mathematical programming models. Some attention is devoted to the structural properties of the models.

Jan 1, 1966

By R. Venkataramani

Crushed stone operations have become more difficult due to rising costs of labor and equipment, with the consequent reduction in profit margins. Competition from other operators and the encroachment of vertically integrated companies place severe restrictions on available markets. The seasonal demand for stone precludes any definite production level, and changes in productivity have to be accommodated. These influence profitability, and therefore production plans must be continuously adjusted to keep pace with rapidly changing conditions. The basic problem of stone companies seeking to maximize profits is one of balancing stone production costs, costs of inventory holding and stock-piling, marketing costs and any other charges accruing over time against the selling price of stone. Because of high peak demands, slack period production must be stored and then distributed to supplement peak period production. For a multi-plant operation, there is a need to evaluate at the same time the interaction between the plants and the various marketing sectors. In a multi-plant operation with different production capacities and production costs, stone producers are interested in the answers to the following questions: 1. How much stone should be produced at each plant in each time period? 2. What should be the optimum stone shipment from each plant to each market? 3. What are the effects on net returns and shipping plans, if production capacities are altered at the plants? These questions have many different answers that, will satisfy demands. From the point of production scheduling, the minimum production cost may be the objective. From the inventory standpoint, the best solution will be to synchronize production with sales. However, when the transportation of stone is also considered, the desired end is to achieve that delivered cost which maximizes the company f s net return. Besides, only an extremely naive analysis ,wouId attempt to

Jan 1, 1971

By Salim Akhtar

The operation of a mineral processing plant with a complex flowsheet is represented by a mathematical operator. Such a representation permits a quantitative evaluation and monitoring of the separation processes in different sections of a processing plant, and gives an overall separation efficiency of the plant.

Jan 1, 1973

By I. Koliabina

In this paper, the results of mathematical modeling of casing pipes decontamination from radio-active new mineral forms directly in boreholes using hydrochloric and hydro-silicic-fluoric acids are presented. Modeling for highly and low radioactive coatings on the walls of casing pipes of Anastasievka oil-and-gas deposit was performed using GEMS software, based on the method of Gibbs energy minimization. Calculations have shown that thorianite and goethite, that are present in low-active crusts, detected in casing pipes uplifted from comparatively low depths, are well dissolved in hydrochloric acid, but radiobarite is almost insoluble. For the same acid concentrations, almost all radiobarite of high-active coatings detected in pipes uplifted from considerable depth is dissolved. To evaluate the possibility of decontamination of pipes from radiobarite of low-active coatings, modeling of crust dissolution under the action of H2SiF6 has been performed. The results have shown that for acid concentrations of more than 13 % almost all Ra and Ba are dissolved while all iron and thorium remains in goethite-thorianite solid solution. For the same acid concentration, almost all radiobarite from high-active coatings is dissolved. Therefore, no reagent allows decontamination of pipes from coatings of both types. It seems that successive or simultaneous use of both reagents (HCl and H2SiF6) in certain ratio is required. To clarify this issue, further experimental and model investigations are necessary. The issue of decontamination of casing pipes from galena that is present in high-active crusts also needs to be clarified.

Jan 1, 2005

By J. A. Herbst

Until the past decade, the energy-size reduction relationship was the dominant form of mathematical model used in the description of tumbling mill grinding processes (1,2). Typically, in these models some single measure of product fineness (e.g. the 80% passing size, the size modules, the specific surface area) is chosen as the dependent variable and the energy input per unit mass of material being ground acts as the independent variable. In some instances these models have been useful for the correlation of experimental data, but, invariably, they have been found to be inadequate for meaningful process simulation. During the last decade considerable advances have been made in the development of phenomenological grinding models derived from population balance considerations (3-7). In these models a set of dependent variables is employed, corresponding to the set of mass fractions which constitute the product size distribution, and energy input is abandoned in favor of "time in the mill" as the independent variable. The phenomenological models have been shown to provide accurate simulations of the entire size distribution of ground products produced in batch (8-10), locked cycle(11)and steady and unsteady state, open and closed circuit continuous grinding(12,13).

Jan 1, 1973

By Boris K. Krstev

INTRODUCTION The flotation process, in the real industrial complexes, is characterized by the existence of the significant number of the close reciprocal interrelationship between the input and output Darameters. Traditional complexity is appeared with regard to absence of the suitable a priori information for the physico-chemical characteristics of the flotation process. It’s led to needful of taking of consideration about the undefinition which have got the place in the real conditions and application of the statistical methods. The identification of the flotation process through statistical methods is conception of the more-stages procedure, including the collection and previous analysis, the choice of the model structure and valuation method, the estimation of the model un- known parameters and the results interpretation. The essential concept for the subject of this paper belongs to the empirical models ("black-box") and deals with optimizing in constant industrial plant process. The offered method envisages the application of process operation data in order to improve the work process or constant accomplishment of better results for the target function in relation to the former achievement. The optimum process solution isn't afixed value under the influence of various factors, but "a moving point" along the response surface and deviates from the scheme solutions. The evolutive planning method constantly "investigates and approaches" the optimum solution for the selected target function. As a matter of fact the expert operates the plant without interrupting the normal work process. The essential concept of method is to attain changes in the standard conditions, but so limited that they will not effect either production or the product. This method is based on statistical concepts and availability of following the risk of error. The possible influental factors for the flotation process (m=l, 2, 3) is following: the metal content in the feed ore; production level (t/h); grinding fineness in the flotation pulp; pH-values; the consumption of collectors and modifiers The possible target functions are: the recovery of plant capacity, metal recovery in the concentration process and concentration quality. The application of the evolutive operativity method in the chalcopyrite flotation- Bucim concentrator, combines the statistical data and the operator's experience in the interpretation and making a decision which adds up to the precise automatic performance of the process. The advantages of this method in relation to the existing procedure for the flotation process are the following: • The method is unexpensive and losses are reduced to the time necessary to collect the data and record them in the computer. This method provides a constant process control and a quality decision which is better than those brought by an ex- pert with great experience ("hit-and-miss method"). • The method also provides incidental data about the effects. • The method should not be considered as a procedure for solving an incidental problem ("crash program"). • The obtained results must be interpreted by an appropriate expert in order to be considered instructive. MATHEMATICAL STATISTICS Taking into consideration the complexity of the enrichment processes it's necessary the application of "black-box" and mathematical modelling. The presence of the indefinite elements compel us towards the both theory of the probability and mathematical statistics. The mathematical statistics by the mineral processing investigation of the valuable raw materials in the last years has had greater signifance and widely spread application. The application of the mathematical statistics methods for the technological pro- cess analysis and the construction of the mathematical models is bound up by the task putting of the automatic control system de- sign (Fisher R. A. 1941, 1949). The statistical analysis in the enrichment processes is applied formerly, especially in the sampling estimation. Contemporary, in the last years is imposed the tendency of mathematical statistics application for the obtaining of quantity characteristics and quantity valuation from the individual influental factors. Above mentioned tendency in the significant level is based by the mathematical statistics development as a mathematical discipline close connected with the technical cybernetics general joining to the investigated object as a "black-box". Another essential factor in the mathematical statistics development is appeared the created mathematical theory of experiments as a new, to some extent, autonomous statistical domain. The theory of experiments has demonstrated exclusively importance for the investigation of the complex more-factorial processes in the chemistry, mineral processing, metallurgy etc. The investigation by the enrichment processes of the valuable raw materials and their management is possible by the statistical method application. In the same time, it's possible to use the wide-spread traditional methods of the statistical analysis, such as the methods of the dispersion, correlation, regression etc. Also, it may be mentioned above all the methods of the statistical planning of the extreme experiments. The more perspective are representatived some cybernetic methods which are based by the probability as an approach in the process analysis, for example, the identify of the ways and forms, the graph application as an additional instrument in the correlation analysis, the dynamic programming etc. The mathematical statistics application in the laboratory investigation scale is connected above all by the experimented material analysis and the compact representation of the obtained results. The mathematical statistics methods are more varrying and may be applied in the investigations of the wide circle of problems

Jan 1, 1996

By Paul L. Russell

Numbers, arithmetic, mathematics. Where did it all come from? Who needs it? We all do, but many school children would not agree. Engineers, physicists, accountants, tax collectors, and most of the general public are well aware that modern society in large part is founded on mathematics and could not exist without it. Mathematics developed over thousands of years as part of the everyday life of man. No one area, tribe, or race can claim discovery. In fact, from the records that do exist, it is evident that many facets of mathematics were discovered independently of others who made similar discoveries. While proof may be lacking, the earliest concepts of mathematics may be some 250,000 to 300,000 years old. The first use of numbers as written records is unknown. However, a bone of a young wolf deeply cut with 55 notches-arranged in two rows, one of 25 notches, the other of 30-was found in Czechoslovakia. Dated to be about 30,000 years old, it is perhaps an early record of some kind of counting system. It is assumed that mathematics was developed as an answer to man's practical needs, but anthropological studies suggest that the art of counting may have developed in connection with the needs of primitive religious ceremonial rites. Fingers probably were first used to designate sets of from one to five objects. Using both hands, up to 10 items could be indicated. As civilization developed, so did the need for more flexible systems to record items of trade, measure land, and figure taxes. Aristotle noted that the development of the decimal system comes from the fact that most people are born with 10 fingers and 10 toes. In spite of this obvious fact many early civilizations used binary, ternary, and quinary systems while vigesimal systems (with 20 as a base) and even sexagesimal systems (with 60 as a base) were used by others. A form of writing was in use in both the Mesopotamian and Nile valleys as early as 3000 to 4500 B.C. In Mesopotamia, wedge-shaped marks were impressed upon soft clay tablets that were hardened in ovens or by the sun. Many thousands of such tablets have survived. When the tablets were finally deciphered, some were found to be records of items shipped in trade, inventories, tax accounts, and mathematics exercises for teaching. Mesopotamia is also the source of an interesting board game dating back to about 2500 B.C. Its buttonlike men and triangular dice were apparently used with squares of shell, inlaid with lapis lazuli and red sandstone. Unfortunately, rules of play were not found. In Egypt, record preservation was somewhat better. Discovery of the Rosetta Stone in 1799 eventually led to deciphering the Egyptian hieroglyphics that included a numbering system at least 5,000 years old. These records show a competence in counting and numbering. A calendar of good accuracy may have been in existence as early as 4,200 years ago. Mathematics, as practiced today, developed when the Greeks added logic and proof to arithme-

Jan 12, 1982

By Robert F. Shurtz

This paper suggests that pre-occupation with the random process model notised by geostatisticians may result in neglect of more promising techniques, especially since the random process model does not appear to be essential to current geostatistical procedures. This point of view is emphasized pictorially. To emphasize the potential of new techniques a simple application of the conventional Brownian function is described. The probabilities estimated in this truly random way are different from those estimated by Kriging

Jan 1, 1980

By Douglas J. Uhren, Gary W. Gilbert

This paper describes the risk elements associated with difficult glacial geology, including boulders, heavy groundwater inflow, and potential running soils all coupled with a potentially corrosive service environment. The matrix workshop for the 168-inchfinished diameter sanitary sewer interceptor tunnel in Columbus, Ohio is assembled with the Design Team and the Owner’s design, operations, and fiscal staff. Corrosion protection alternatives are compared against cost and non-cost parameters with relative risk and weighting factors assigned. The Owner working in cooperation with the Design Team uses the matrix workshop to se

Jan 1, 2001

"INTRODUCTION Twin Metals Minnesota (TMM) (operating as a joint venture between Duluth Metals and Antofagasta PLC) assumed control of the property in 2010. Amec became involved with the project in 2011 and in 2012 incorporated additional drilling in order to update historic resource estimates. The Maturi geological model and resource estimate was updated in 2014 to incorporate additional information obtained during 2013 and 2014 drill campaigns. In 2017, Amec was purchased by the Wood Group and is now known as Wood. Geology The Twin Metals Minnesota (TMM) Maturi, Maturi Southwest, Birch Lake, and Spruce Road properties are located in northeastern Minnesota (Figure 1). This talk discussed the Maturi deposit only, although all four deposits share similarities. The following geology is summarized from Peterson and Severson (2002).Maturi lies within the Superior Province of the Canadian Shield which is exposed in central and northeastern Minnesota and extends northward into Ontario. In eastern Minnesota, the Midcontinent Rift System developed during crustal scale extension in the Mesoproterozoic Era. The rift system is traceable, as exposures of mantle-derived tholeiitic to subalkaline mafic lava flows, intrusives, and rift-filling fluvial sedimentary rocks, and in the subsurface as a gravity anomaly (high), from the eastern end of Lake Superior, arcing west across the lake basin, and extending south-southwest to northeastern Kansas. Intrusion of the Duluth Complex, circa 1,108 - 1,099 Ma, was related to rifting and is co-genetic with the North Shore Volcanic Group mafic volcanic rocks that form the hanging wall of the Duluth Complex to the east. Cu-Ni-precious metals (PM) mineralization including Pt, Pd, Au and Ag within the Duluth Complex is hosted by mafic to ultramafic intrusive rocks that are part of the overall intrusive complex. The Duluth Complex is defined as a more or less continuous mass of mafic to felsic plutonic rocks that extends northeastward for more than 170 miles (275 km) in an arcuate fashion from Duluth nearly to Grand Portage in Minnesota. It is bounded by a footwall of Paleoproterozoic sedimentary rocks and Archean granite-greenstone terranes (Peterson and Severson, 2002), and a hanging wall largely of comagmatic anorthosite, rift related flood basalts, and hypabyssal intrusions of the Beaver Bay Complex. Mineralization is hosted in the basal mineralized zone (BMZ) of the South Kawishiwi Intrusion (SKI). The SKI magmas intruded sub-horizontally between hangingwall Anorthositic Series (AN) rocks and footwall granitic rocks of the Neoarchean Giants Range batholith (GRB). The Maturi local geology and the deposit footprint (shaded orange) is shown in Figure 2."

Jan 1, 2018

By J. Paraszczak

Underground metal mining involves many challenges. Economic slowdown, tough international competition and sometimes volatile metal prices put constant pressure on mine operators to increase productivity and to reduce production cost. At the same time, countries such as Canada, the United States and Australia are experiencing skilled labor shortages that might even stall development of certain mine projects. Furthermore, some stages of underground production take place in particularly hazardous environments where the safety and health of miners is at risk. Automation of some processes in underground mining is one of the promising avenues to alleviate some of these problems. Loading and haulage are among the most critical operations and areas where implementation of autonomous vehicles has been targeted. However, although health and safety issues are a primary driver to opt for automation, the latter should ensure an acceptable level of productivity and pro?tability. With this in mind, this article focuses on the factors affecting operational effectiveness of autonomous underground loading and haulage equipment and the means to maximize it.

By J. Paraszczak

Application of teleoperated and automated (or ?autonomous?) mobile equipment in underground metal mines is a promising avenue for overcoming some of the challenges facing mine operators. These include, but are not limited to, the issues related to safety and health of underground workers, better use of the shift time leading to increased productivity, skilled manpower shortages, and remoteness of some mine sites. Autonomous load-haul-dump machines and trucks offer several benefits over man-operated ones, but their use at their full capacity is a challenging and complex task. This paper makes an overview of commercially available equipment and systems and their applications. It examines factors affecting adversely availability, utilization, and production efficiency of autonomous vehicles and compares them to conventional man-operated machines. Technical and operational aspects are discussed and their criticality is analyzed. Based on that, recommendations concerning means and measures that may help raise operational effectiveness are given. It is stressed that due to a scarcity of publicly available information on the performance and cost of autonomous loading and haulage operations, more field studies and in-depth analysis are needed.

Feb 23, 2014

By J. A. Zimmer, M. S. Hillis, D. Moredock, J. A. Organiscak, A. B. Cecala

Enclosed cabs have been used on surface mining equipment for many years to protect equipment operators from health and safety hazards. The surface mining and quarrying process is a highly mechanized process that generates large quantities of respirable dust. Due to economic factors, more older mining equipment is being used today than in years past. With this older equipment, it is common to observe deterioration of many components on the enclosed cabs, which greatly reduce their protection effectiveness. NIOSH has performed a number of different field studies, as well as a comprehensive laboratory study, evaluating various factors and parameters regarding enclosed cabs. NIOSH has recently completed a cooperative research effort to evaluate the effectiveness of a newly designed unidirectional powered precleaner, filter and pressurizer that brings clean filtered air in at the roof of the cab and extracts all recirculated air near the floor. This research effort provided another example of the enhancement in air quality that can be achieved in an enclosed cab from the implementation of an improved filtration system and by establishing positive pressurization from increased intake air volume and sealing the cab. This testing showed a significant reduction in respirable dust levels in the enclosed cab when comparing baseline versus post-testing results. Since dust levels were similar near the roof and floor of the cab during post-testing, the unidirectional flow pattern did not appear to significantly improve the performance over the conventional design in this study.

Jan 1, 2009

By A. B. Cecala

Enclosed cabs have been used on surface mining equipment for many years to protect equipment operators from health and safety hazards. The surface mining and quarrying process is a highly mechanized process that generates large quantities of respirable dust. Due to economic factors, more older mining equipment is being used today than in years past. With this older equipment, it is common to observe deterioration of many components on the enclosed cabs which greatly reduce their protection effectiveness. NIOSH has performed a number of different field studies, as well as a comprehensive laboratory study evaluating various factors and parameters regarding enclosed cabs. NIOSH has recently completed a cooperative research effort with Sy-Klone International and Vulcan Materials Company to evaluate the effectiveness of a newly designed uni-directional filtration and pressurization system that brings all the clean filtered air in at the roof of the cab and extracts all recirculated air near the floor. This design provides the highest air quality to the equipment operator. Testing on this new system showed an almost 10-fold reduction in respirable dust inside the enclosed cab. The uni-directional design is easy to incorporate and should be considered for all new and retrofit systems in surface mining equipment.

Jan 1, 2009

By Brian Carr, Craig Brewer, Jeff Grubbs

This paper examines the role of the StemTite Blast Control Plug in explosive energy confinement and explores the benefits of its successful application in gold and silver mining operations. Prior studies involving this device are consolidated.

Jan 1, 1999

By J. Evans

Including: Tailings thickeners, CCD?s, paste thickeners, HI-rate thickeners, lamella thickeners, high compression thickeners, clarifiers etc. Flocculant dosing control for mining thickeners and clarifiers is influenced by a number of process factors. 1. Flow rate into the thickener or clarifier a) As the flow rate increases into the thickener or clarifier ?retention time? decreases which causes a greater affect hydraulically on the settling solids. So as the flow rate increases it will generally mean an increase in flocculant dosing rate. b) As the flow rate decreases into the thickener or clarifier the retention time increases which reduces the hydraulic affect on settling, improving settling rates. This will generally mean that as the flow rate decreases, we will decrease the flocculant dose rate.

Jan 1, 2011

By I. Mikov

Established in the 60-ies, the Zlatna Panega quarry is a cement raw materials quarry supplying 95% of the needs of the Zlatna Panega Cement Plant with limestone, marl and other silica-aluminates. The two major types of raw materials are formed by accordingly dipping strata of Upper Jurassic limestones and lower Cretaceous marls. Between them there is a ?transition-zone? or ?contact-zone? of a high-silica content layer, about 5-m thick, defined as ?flint? by investigations including spot sampling throughout the quarry. For many years this ?contact-zone? layer was neglected due its negligible thickness. Further, with the increasing demand on the quality of the raw materials feed to the Plant and the focus on variability of the chemical and mineralogical components, it was decided not to mine any of the parts of the quarry contaminated by this material, for about three years. The latter had an impact on the availability of operating benches that could result in a substantial decrease in the total recoverable re-serves of Zlatna Panega, particularly with respect to marls. There were considerations for resorting to a partial, selective excavation of the quarry pit with a reduced lifetime for the lime-stones and re-opening of an other (currently in-active) marl quarry at a distance of 6 Km from the Plant. The Quarry Team of the Zlatna Panega quarry was assigned to study the problem. The ?contact? layer was duly confirmed with systematic geological (including mineralogy) studies, statistical analysis of available data, surface sampling and shallow exploration drills, resulted into distinguishing a third type of reserves and their credible subsurface delineation by means of geological 3-D modeling and quarry design. A new quarry design was finally elaborated with a view of providing flexibility in mining, utilization of the total volume of all available reserves and maximizing the mine life of Zlatna Panega quarry. An industrial test took place in December 2005, by using the contaminated parts of the quarry (co-mining of the ?contact-zone? materials) at a contribution of 15-20% in the raw materials mix, as dictated by their contribution in the total recoverable resources of the quarry. The purpose was to investigate the viability of this solution ? in line with improved quarry planning ? without compromising the quality of cement production and the efficiency of Plant Operations. Results were overall successful.

Jan 1, 2006

Since 1992 the Grasberg Mine, located in the remote regions of Indonesia, has utilized the Modular Mining System. Over the last several years, major steps have been taken to maximize this productivity enhancement system. These steps include; the Automated Lineup, the Linear Program upgrade, tracking of Mean Time Between Failure, a MEDS system interface, a VMIS system interface, and implementation of the new Graphical Operator Interface Console with Global Positioning, This application of new technology and innovation has lead to improved performance, understanding and reporting, as well as the quality of the Indonesian Engineers. These efforts have contributed 10 Grasberg achieving one of the lowest mining costs in the copper industry.

Jan 1, 1998

By T. Gupta, T. Ghosh

Rare earth elements (REEs) and their compounds are essential in a multitude of mundane and sophisticated applications such as renewable energy technologies, catalysts, medicine, and defense applications. The global supply deficit could be attributed to the destabilization of REE market that has, as a result, incentivized indigenous production of REEs. Cost-effective and environmentally benign opportunities are being explored for the production of REEs from non-conventional mineral sources including coal and coal by-products to stabilize the supply chain. Coal from Healy coal mine and Wishbone Hill deposits in Alaska have been quantified for REEs and were found to possess elevated total REE concentrations as compared to world average levels (60– 70 ppm). The objective of the study was to concentrate the REEs in the froth phase by froth-flotation of the fine size fraction (< 75 μm). A Box-Behnken design of experiment was employed to ascertain the main and interaction effects of operational parameters on response variable by analyzing 3D response surfaces. Experiments were carried out to maximize REE recovery and concentration by modeling and optimization of three operating variables (frother dosage, pulp density (% solids), and collector dosage). Based on the results, the optimum flotation conditions for maximum recovery at an elevated concentration of REEs in the froth fraction was obtained at 4.2% solids and 32.7 ppm of frother dosage for Healy sample and 10% solids and 37.9 ppm of frother dosage for Wishbone Hill coal sample. The quadratic relationship between the input and response variable was found to be independent of collector dosage suggesting good surface hydrophobicity and floatability of the two coal samples.