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By Manuel Pérez-Tello, María M. Salazar-Campoy, Óscar Rodríguez-Hoyos

A common problem during the operation of the Kaldo furnace is the formation of accretions and blockage of the injection lance due to splashing. This typically occurs during the processing of anodic slimes for the production of doré. In this work, a 1:7 scale model of the Kaldo furnace currently in operation at Metalúrgica de Cobre, Mexico, was built in transparent acrylic plastic. Water and colored oil were used to represent the doré and slag, respectively. The model was used to determine the maximum penetration distance of the injection lance under a variety of experimental conditions at room temperature. Input variables included two types of oil, rotation speed, inclination angle, and the fraction of the vessel volume occupied by the liquids (φ). A mathematical correlation for the dimensionless maximum penetration distance of the injection lance d ∗ as a function of φ, the Froude number of the liquids in the vessel (Fr), the Reynolds number of the gas jet (Re), and the oil-to-water kinematic viscosity ratio (η)was developed. Reasonable agreement between the calculated and experimental values was obtained. Digital images showed that splashing was caused by the turbulent gas jet impinging upon the free surface of the liquids, whereas the cascade effect was negligible. The results of this work have been useful to improve the operation of an industrial Kaldo reactor.

By H. Gurgenli

Mining companies require accurate short-term mining forecasts to meet budget targets and customer needs. Challenging mining conditions along with employee turnover and lack of standard geologic modeling and mine planning processes can result in time-consuming and inconsistent mine plans. Documentation and automation of the processes involved in mine planning, as well as proper software utilization, are critical in overcoming these challenges. This paper discusses the steps involved in achieving an optimized mine planning system to accomplish productive and cost effective operations. In addition, a case study is included to describe the process of implementing a semi-automated system whereby the geologic model and mine scheduling database are updated monthly to incorporate changes in geology in a relatively complex open-pit coal mine. This case study proves that the ability to update geologic models based on the latest information gathered from production drilling and mining activities can greatly enhance the ability to accurately predict short-term mining production.

Jan 1, 2011

By Mervin D. Marshall

A quick-reaction, mine permissible rescue vehicle (MERV) was developed for use by rescue teams. The MERV is a 6-wheeled, battery-powered unit with life support equipment and instrumentation; designed for a two-man team, with provisions for handling two victims or tools in a trailer. The vehicle is 100 inches long, 56 inches wide, and maximum height of 34 inches. It can be lowered down most mine shafts and has clearance to travel mine railways. The vehicle has power to all six wheels with power transmitted separately to either or both sets of wheels. Low-pressure, high-traction tires give the vehicle the ability to handle soft, muddy mine floors, flooded areas and significant obstacles, and can negotiate a 45% grade. Power and life support are sufficient for a 4-hour mission. The life support system is a commercially-available, approved unit currently used by MESA rescue personnel. A payout wire system provides communication between the vehicle and home base over a distance of 10,000 feet. On-board monitoring of carbon monoxide, methane and oxygen is provided, with master and individual alarms to warn of gas concentrations outside pre-set limits. A lightweight, water-tight trailer was developed for carrying victims or hauling tools and equipment.

Jan 1, 1979

By Charles L. Allie

Since Reserve Mining Co. began commercial operations at Silver Bay, MN, some 25 years ago, major improvements in taconite processing technology have become available. In addition, significant new government standards have been imposed on industrial operations. By implementing a $370-million modernization program, Reserve was able to accomplish two major company objectives: the quality of concentrates produced from the Peter Mitchell mine has improved, and the operation meets both present and foreseeable environmental standards. Process modifications at Reserve were designed to: •Reduce the pellet silica content from 9% to 5%; •Increase the pellet iron content from 62.5% to 65.8%; •Implement a tailings disposal system utilizing "best available technology" water quality controls; and •Reduce air emissions by installing "best available technology" air emission controls. By adding dry cobbing, fine screening, and flotation to the concentrating process, pellet silica content has been reduced; the process reclaims and reuses all process waters; all tailings are stored in a zero discharge tailings basin; and all air emission standards are being met. Initial Beneficiation at Silver Bay Reserve's Peter Mitchell mine at Babbitt, MN, is on the eastern end of the Biwabik iron formation. The open-pit mine is approximately 16 km long, 0.8 km wide, and presently has a maximum depth of about 50 m. Principal constituents of the ore body are magnetite, quartz, and iron-magnesium silicates. The company's large commercial plant began operating at Silver Bay, 75 rail km from the mine, in 1955. Facilities have historically had the capacity to process 31.5 Mt/a of taconite, containing an average 24% magnetic iron, into 11 Mt/a of iron ore pellets. Reserve's initial beneficiation process-which existed up to early 1979-consisted of two crushing stages at the Babbitt mine site, two additional crushing and screening stages at Silver Bay, grinding in a conventional rod-ball¬regrind mill circuit, size classification with cyclones, and concentration with magnetic and hydraulic separators. Concentrate produced by that circuit assayed 65% iron and 8.5% silica, with a screen analysis of 94% -44 µm, and a surface area of 9300 cm2/cm3. Pellets produced from this concentrate assayed 62.5% iron and 9% silica (dry basis). Construction began in 1977 to modify Reserve's operation. Process modifications were designed from pilot scale operations that had been operated and researched by Reserve for more than 10 years. There were two design restraints imposed on the process: economic constraints that Reserve continue to use much of the existing processes and structures in the new operation; and a substantial number of government-imposed permit constraints. In effect, the tailings process was designed first and then a concentrating process was developed that would "fit" the tailings disposal system. Operation of the modified process began in June 1980. Crushing Remains Unchanged No changes in process flow were made at either the Babbitt mine and crushing plant or at the Silver Bay fine crusher. Gyratory crushers reduce run-of-mine taconite to -90 mm-diam at the mine. Taconite is then transported to Silver Bay by intra-plant railroad. There are 10 fine crushing lines. Each consists of a double deck screen, followed by a heavy duty short head crusher, a second double deck screen, and second short head crusher. All screen undersize material bypasses the crushing lines, resulting in an open circuit crushing process. Fine crusher product is approximately 98% - 20 mm, 80% -12 mm, and 50% -10 mm in diameter. Each fine crusher line processes about 400 t/h of crude taconite. Cobbing Provides Aggregate for Tailings Dams The first major process change was the addition of dry cobbing, a dry magnetic separation step between the fine crusher and concentrator. Dry cobbing serves two major purposes in the new process. Its principal function is to provide large volumes of dry coarse aggregate for use in construction of tailings dams. This process rejects about 20% of the fine crusher product as tailings with a size analysis of 98% -20 mm and 50% - 10 mm. These tailings are free draining and have high frictional shear strengths-two key requirements for dam building aggregates. Fine crusher product is conveyed to a new dry cobbing building. Here crushed ore is discharged into one of two 30-minute capacity surge bins. Crushed ore is withdrawn by 12 constant speed conveyor belts; each discharges 500 t of crushed taconite into a dry cobbing machine. Each machine consists of a 3-m-long riffle splitter and two vari-

Jan 12, 1980

By J. J. Gusek

Several final pits in the Seneca No. 1 Surface Coal Mine were abandoned in the 1960's without king reclaimed. In addition, a progressive landslide aggravated by the abandoned mine land conditions was threatening a county mad and private property. An AML-funded project to stabilize the landslide and reclaim the final pits was completed in 1986 for the Colorado Division of Mines and Geology (formerly Colorado Mine Land Reclamation Division). The site was visited after ten growing seasons. The land is stable and the vegetation re-establishment is strong. Volunteer native plant species are now invading the reclaimed sites.

Feb 24, 1997

Even though the economy of the United States remains in recession ? or not, depending on which economist you listen to ? muicipalities still need improved transportation, water and wastewater transit systems. And they are willing to spend the necessary funds on those systems, provided they are affordable, environ-mentally friendly and sustainable. From June 20-23, professionals in the tunneling and underground construction industry from around the world gathered in Portland, OR to learn new ways of providing those systems using the latest technology available. The North American Tunneling (NAT) conference attracted 803 attendees and 108 exhibiting suppliers of equipment and services.

Jan 1, 2010

By A. G. Doll

"Many power-based grinding models exist, and most operators are familiar with Fred Bond's ""third theory"". Bond's model is most commonly used to describe primary and secondary grinding to product sizes above, for example, 100 µm. Operators sometimes use Bond's equation to describe grinding in situations where it is not appropriate, such as fine grinding below 50 µm. Using an alternative model would be a better choice in this situation.Bond's equation is one in a large family of models. Related equations better suited to fine grinding include the “signature plot”, Von Rittinger's model and Charles' equation. These models have a similar form to Bond's and can be fit to industrial regrind mills and laboratory tests using the simple regression tools in the charts of computer spreadsheets. Operators will find that fine grinding calculations are both easier and more accurate when using the alternative equations to fit their regrind milling surveys or when performing laboratory regrind mill scale-up for plant design.None of these models are new: Charles' equation was published in 1957 and Von Rittinger's model was proposed in 1867. A quick refresh how to apply these equations can turn these oddities from the undergraduate curriculum into useful tools for plant optimization. They can be fit to any type of mill including stirred and tumbling ball mills.IntroductionBuilding a case for fine grind modelling requires reviewing some theory before building a framework for doing fine grinding calculations. The actual calculation procedure recommended is easy and can be applied by plant metallurgists. Don’t be frightened by the theory; the end result is reasonably simple.The observation that mineral breakage is related to the absorption of energy is usually attributed to Von Rittinger (1867). Lynch and Rowland (2005) describe that the ability to empirical test and calibrate energy models of breakage didn’t exist until the widespread adoption of electric motors in the mining industry during the 1930’s and 1949’s. A series of technical papers published by the Allis Chalmers company during the 1940’s demonstrate that they were attempting to do such a calibration using Von Rittinger’s model which is usually stated as: “the energy consumed in the size reduction is proportional to the area of new surface produced.”"

Jan 1, 2017

By R. Marleau, R. Assad, J. Dugas

"A study of the geological features of known occurrences of mineralization in Gaspe is the basis for a classification. Nickel, chromite, asbestos and some copper are pre-or syn-Taconic, whereas the most important deposits are tied to granitic post-Taconic stocks. Most occurrences are clearly related to igneous rocks: nickel, chromium and asbestos to Ordovician serpentinite; copper to volcanic rocks of different ages; and copper, zinc and lead to acidic intrusions with apparent zoning. Some lead-zinc deposits lying between the Grande Greve and York Lake formations are stratigraphically controlled. Some occurrences are tied to faults; e.g., the nickel-copper mineralization along the North Grand Pabos fault. Northerly-trending transverse structures appear to coincide with the Gaspe Copper, Mount McGerrigle (Tabletop) granite and Lemieux dome areas of mineralization. JEAN DUGAS, after graduating"

Jan 1, 1969

Mineral ownership determination is not always straight forward as in many cases the relevant details are not recorded on the latest Land Transfer title held in the local Land Registry Office. To determine mineral ownership can be difficult, time consuming and expensive especially in a confused sector. Non statute minerals can be owned by the Crown, Land Owner or other persons. Statute minerals (Gold, Silver, Petroleum, Uranium) are always owned by the Crown and thus present no problems. In simple terms the only accurate and reliable method of determining the mineral ownership under subject land is to historically search back to the first registration when the land and minerals were definitely intact. Then carefully ascertain from the evidence gathered along the way to the present day whether any legislation or private agreement altered or affected the status quo.

Jan 1, 1998

By William P. Blake

The ancient city of Guanajuato, the capital of the State of that name, has been built up and sustained chiefly by the milling industry based upon the veins of the Veta Madre and La Luz. It is distant about twelve hours, by rail, from the City of Mexico. Its elevation above the sea is about 6300 ft., and it has a salubrious climate. The population, at the date of my visit in 1891, was estimated at from 80,000 to 100,000 persons. The place is justly celebrated for the antiquity, depth and extent of the mines, the magnitude of the deep shafts, and the enormous total yield of the district in silver and gold, which is comparable with that of the Comstock Lode in the United States. Several important public institutions are located at this center. The State office for the records of claims and of the statistics of mining and production is known as the Deputacion de Mineria. The Mining College, with its fine collection of ores and minerals from the mines of the region, is highly interesting to mineralogists. A mint for the coinage of silver, but not of gold, coins from four to twelve millions of' silver dollars annually. The silver received at the mint is melted in an open-hearth furnace, and is ladled out and cast into long and thin bars, which are rolled down to the proper thickness for the blanks. The bars contain some gold which is not parted. There is an export of dore bars to Germany, amounting in value to from $1,000,000 to $1,500,000 annually. There were, in 1891, upwards of forty reduction-works in and about the city where the silver ores were treated, chiefly by the ancient patio method. In these works were 65 Chilean mills, 301 arrastres of large size, and 936 of smaller dimensions. There were 36 steam engines, but mule-power was generally used at the ar-

Jan 1, 1902

The research described in this report was conducted under a cooperative research agreement between the U.S Bureau of Mines Twin Cities Research Center (TCRC), Cleveland-Cliffs Inc. (CCI), and three operations in Northern Michigan managed by CCI: the Empire and Tilden surface taconite mining operations, and the Central Shops maintenance facility. All of these operations are in or near Ishpeming, MI. The Human Factors Research Group at TCRC is responsible for designing, planning, and conducting the research, and reporting on the findings. This project was carried out in order to investigate the high prevalence of back injuries being experienced by workers employed at the three CCI Northern Michigan sites, In an analysis of Company accident records for workers employed at these sites, it was determined that back injury problems confronting the CCI sites mirror those confronting the entire mining industry.

Jan 1, 1994

By M. H. Attia

The concept of sustainable development has been evolved into a working framework for sustainable manufacturing, in which the environmental requirements are introduced into product development at the design stage. This keynote paper is discussing a number of issues pertaining to the impact of manufacturing on the environment. The conflicting requirements of sustainable development, sustainable manufacturing (SM) and economical growth are presented in the light of successful case studies that were able to convert conflicts into opportunities. Integration of SM into the product life cycle is also presented. A number of concepts that are related to Ecoefficiency, e.g., inverse manufacturing, demanufacturing and re-manufacturing are also discussed. The paper underlines the fact that the positive impact of this new philosophy is equally applicable and beneficial to both; developed and developing countries. The paper concludes with an overview of Global trends in environmentally benign manufacturing (EBM); e.g., product-take back and emerging material and processing technologies. The state-of-the-art approach to Life Cycle Impact Assessment and integration of design for the environment DfE principles are demonstrated through some case study.

Jan 1, 2006

By Brad Hewitt, Jeff Belke

"Murrin Murrin Operations has not had a successful beginning. Numerous reliability and operability issues many of which are the result of design decisions have been addressed through mechanical and operational changes and the CCD circuit is no exception. Four design aspects of the CCD circuit that have caused and continue to cause operational problems are:1. the inclusion of solution neutralisation gypsum in the CCD circuit feed which was designed solely for HPAL residue without proper investigation of its impact on the achievable underflow density and resulting wash efficiency;2. the decision to construct the thickener base from thickened solids;3. the lack of redundancy in the overflow, underflow and tailings pipe work; and4. the lack of thickener operational flexibility in the central rake-lift and feedwell dilution system.In November 2002, the lack of operational flexibility in the rake-lift and the feedwell dilution system through mechanical modification as follows:•, CCD1 has a modified rake mechanism that now allows central vertical lift of 600 mm;•, CCD1 has forced dilution using the Outokumpu Turbodil® technology and replacing the E-Duc® technology of Eimco;The decision to install, the installation and the results of the CCD1 rake-lift mechanism and feedwell dilution system are discussed in this paper. The installation was justified on improved operational robustness and an increase in the in the underflow density of 1 per cent (per cent w/w). At approximately the same time process modifications in the solution neutralisation circuit were implemented and these changes altered the rheology of the slurry reporting to CCD1. Since the modifications to CCD1 and the solution neutralisation circuit, the CCD circuit has averaged a 2 per cent improvement in the circuit underflow density.The CCD1 modification was completed on time and mechanically has performed well. From a risk point of view, the central rake-lift and Turbodil®dilution system add a degree of freedom and robustness to CCD1 operation that has extended the range of operational confidence. In this respect, the modification has been a success and is complementary solution neutralisation improvements."

Jan 1, 2005

By NA UMC

Abstract Booklet

Dec 2, 2023

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959

By FREDERICK MCAKCCOY

THE production of tin from Mexico has never reached the point of being considered a national industry, but the distribution of tin ores is so widespread that there are possibilities that one day it may become of importance. Of the twenty-seven states of the Republic, tin claims have been taken up in sixteen. In all there had been taken up to the end of 1926, two hundred and twenty-five claims, of a total area of about 7400 acres. The first historical mention of tin in the Americas is found in a letter of Cortez to the Emperor, Charles the Fifth, of Spain, which is as follows: Speaking of his manufacture of some small cannon, he says: "For these reasons I took considerable pains to get copper from some provinces of this country, and bought it at a high price in order to get it quicker.

Jan 1, 1929

By Manuel Sanchez, Marcial Medina, Matt Hurley, Hugo Granados, Pramod Kumar, Raj Rajamani, Jose A. Delgadillo

"Large-diameter ball mills have traditionally used steel liners—steel being a highly durable material that can be shaped into any desired geometry, among which the double-wave has been the preferred design. Such a design produces a purely cascading charge motion, which is ideal for the shearing action needed to produce a finer product. Today, however, rubber liners, which have been in existence for over forty years, are now preferred over traditional steel, largely because they weigh less and are easier to maintain. In this paper, we show the operating data from the Hudbay Minerals’ Constancia Mine, wherein the liners on a 26-by-40-foot mill were changed from conventional steel liners to PolyStl™ liners. It is then shown that this change reduced the amount of energy consumed whilst being able to maintain previous grind and throughput levels. The design is verified via discrete element simulations.IntroductionThe Constancia Mine (“Our Business: Peru,” 2016) is located in the southeastern Andes of Peru, at an elevation of approximately 4,200 m. It can be accessed via the CU-126 road, about 95 km from the town of Espinar in Espinar Province. The mine also contains both the Constancia and Pampacancha deposits in the Province of Chumbivilcas. Hudbay Minerals, Inc. acquired the mine in 2011, through the purchase of Norsemont Mining, Inc. and currently retains sole ownership of the property. Production of the Constancia Mine began in 2014, with commercial production levels being achieved in April 2015.The Constancia and Pampacancha deposits primarily include hypogene, supergene, and skarn ores. The Mine’s main products, however, are copper concentrate, with silver contents, and molybdenum concentrate. These mineral reserves are expected to last approximately 22 years. Constancia’s open-pit mine supplies a processing plant that is designed for 81,900 metric tons per day of throughput. Average annual copper production is estimated to be 82,000 mT (contained metal in concentrate). Actual plant production can be found in Table 1."

Jan 1, 2017

By S. G. Hardcastle, C. K. Kocsis

Ventilation is an expensive prerequisite for underground mining. Current mining trends, including increasing depth and mechanization and more stringent health regulations would generally dictate that more air volume is required in order to provide good working conditions underground. However, any increase in the mine’s intake airflow can produce a disproportionate increase in power consumption and hence operating costs due to the cubic relationship between the sup-plied air power and the airflow (Power a Flow3). Furthermore, forecasts of significant increase in energy prices and new commitments with regard to reductions of greenhouse gas(GHG) emissions, determined the mining industry to look into developing new concepts, design tools and incorporate the latest mining technologies in order to lower capital and operating costs while meeting commitments regarding GHG emissions. The advances in computing power and modelling software now make it possible to design, model and schedule a mine from opening to closure. A developing trend is to design and plan the mine by means of orebody modelling software, followed by using discrete-event simulation techniques to predict production rates and evaluate various operating scenarios throughout the life of the mine. The authors are currently evaluating how such process simulators could be adapted in order to forecast the need for materials or a specific resource, and one of these would be the mine’s “life-cycle” airflow demand as a function of scheduled production rates and mine operating characteristics. Further to this, based upon the mine’s life-cycle airflow demand schedule, the ventilation system could then be designed using a mine ventilation simulator. This new design approach would integrate in parallel the development of the ventilation system with the current mining conditions, therefore, heading towards “develop-as-you-go” as opposed to developing the system for final requirements with high upfront costs. This new ventilation system design criteria would also incorporate the use of the “ventilation-on-demand” technology, which will further lower development and production costs and implicitly, the mines’ GHG emissions.

Jan 1, 2004

By O. M. Arafat, J. A. Finch

"The Functional Performance Equation calculated from a plant grinding survey defines two distinct ball mill circuit efficiencies and how they relate to total production rate through the target grind size. The survey data are also used to calculate a complete ball mill size distribution model, represented by the energy specific grinding rates, not just through the target grind size, but through all the size classes. Cyclone separation performance is represented by individual size recoveries to underflow. When these two unit operation performances are entered into the circuit modelling program (Streamline™), along with the circuit feed rate and size distribution, all the circuit survey size distributions and mass flows are perfectly regenerated by the program. The many issues associated with the historical Epstein (breakage-selection) models are eliminated. Once the circuit program is populated, pump and cyclone performance changes can be evaluated using a step-by-step procedure in order to maximize Classification System Efficiency. Mill water use and media sizing opportunities are also diagnosed in order to maximize Mill Grinding Efficiency at the size of interest. An example is provided. This circuit analysis and modelling system, and related training, is provided through a web-based application.IntroductionSince its development (McIvor, 1988), the Functional Performance Equation for ball milling has facilitated new understanding of industrial circuit cause and effect relationships, leading to significant strides in operational performance. Success stories of this refreshing approach to plant circuit performance improvement are now too numerous to list. Finch and McIvor (circa 1986) also discovered that the Functional Performance “Mill Grinding Rate” at the size of interest was the same cumulative grinding rate that is calculated from mill feed and discharge size distributions using a first-order rate equation. By calculating these cumulative grinding rates for all screen sizes, a complete ball mill model is generated (as used by Finch and Ramirez, 1981). Others in industry, Hinde and Kalala (2009), for example, have noted the same. Lacking the complexity needed to maintain their interest, most researchers have ignored this model, broadly opting instead for Epstein’s (1948) characterization of grinding as a chemical reaction, combining “selection rate” and “breakage size distribution” functions. The much simpler ball mill model presented here has previously been incorporated into a proprietary circuit modeling program (McIvor, 2005) and used for plant improvement work (for example, see McIvor and Finch, 2007, and McIvor, 2014). Now, by combining this extremely business-friendly ball mill model with optimization criteria from Functional Performance Analysis, a circuit modeling system (including the needed supplementary steps to assure successful plant implementation of circuit design changes) is at the disposal of every plant metallurgist, grinding equipment/material provider, and circuit designer."

Jan 1, 2017

By Julián M. Ortiz

Uncertainty quantification of a spatially distributed variable at any scale can be handled through geostatistical simulation. Large computation time, storage, and post-processing of the realizations are required to obtain a final assessment of block uncertainty. Multi-Gaussian kriging is a flexible alternative to simulation. The idea is to compute the conditional distribution of uncertainty after normal score transformation of the original samples. Under the multi-Gaussian assumption, all marginal and conditional distributions are Gaussian, hence fully defined by their mean and variance. The parameters of the conditional distributions are obtained by simple kriging and can be back-transformed to the original units of the variable of interest. An estimate and any summary of uncertainty can be easily retrieved. The main disadvantage of performing multi-Gaussian kriging is that change of support is not straightforward, that is, calculating uncertainty of block grades. We propose a methodology to overcome this limitation by considering a matrix simulation to generate multiple probability fields. Each probability field is used to draw spatially correlated point values from the point-support conditional distributions, and multiple realizations of the average can be obtained. This permits the calculation of the average over the block and its uncertainty. These blocks may correspond to selective mining units or to volumes from longer production periods relevant for engineering decisions. They can even be disjoint blocks, such as when several faces are mined at the same time. POSTMG, a Fortran program to perform these calculations, is described and a case study is provided.

May 1, 2004