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By P. Toscano

The objective of this investigation was to determine how the losses of nickel, copper and cobalt in fayalite slags could be controlled for nickel mattes with iron contents below 5 wt%. Laboratory-converting and slag-cleaning experiments were carried out at 1250°C. Several variables were investigated during and after converting to help minimize the amount of nickel and cobalt that reports to the slag. The variables used were oxygen concentration in the blast, coke breeze addition and nitrogen injection stirring. In all the experiments, slag and matte co-existed. Coke additions during converting have little effect on the losses of nickel, copper and cobalt. In fact, coke additions retard the converting process by consuming some of the oxygen injected. On the other hand, coke additions and nitrogen injection applied after converting was completed resulted in decreased slag losses.

Jan 1, 2004

By P. Toscano, T. A. Utigard

"The objective of this investigation was to determine how the losses of nickel, copper and cobalt in fayalite slags could be controlled for nickel mattes with iron contents below 5 wt%. Laboratory-converting and slag-cleaning experiments were carried out at 1250°C.Several variables were investigated during and after converting to help minimize the amount of nickel and cobalt that reports to the slag. The variables used were oxygen concentration in the blast, coke breeze addition and nitrogen injection stirring. In all the experiments, slag and matte co-existed.Coke additions during converting have little effect on the losses of nickel, copper and cobalt. In fact, coke additions retard the converting process by consuming some of the oxygen injected. On the other hand, coke additions and nitrogen injection applied after converting was completed resulted in decreased slag losses."

Jan 1, 2004

By Carlos León, David Estrella, Javier Linares

"Recently, Antamina has completed an expansion program of its operations which increased the thoughput in grinding from acapacity of 109 to 130 ktpd. After commissioning, throughput could be exceeded in grinding and downstream processes but primary crushing became a major bottleneck to the overall production process.With an objective to increase the processing capacity of the primary crusher system, a multidisciplinary team was formed with members of Mine, Concentrator and Maintenance departments, who analyzed the overall context of this process restriction. The main implementations developed were: automatic discharge systems of trucks, logic to count trucks and elaboration of a daily performance report. Following implementation of developed improvements, the numbers of discharged trucks to crusher were increased from 449 to 614 units per day. As a result, the expansion target of 130 ktpd was exceeded and processing capacity was increased from 109 ktpd to 145 ktpd. This improvement adds very significant economical value for Antamina.INTRODUCTIONAntamina is a copper-zinc mine located in the Peruvian Andes. Compañía Minera Antamina is owned by BHP Billiton (33.75%), Xstrata (33.75%), Teck Cominco (22.5%), and Mitsubishi (10%). The mine was commissioned in 2001 with a capital investment of US$2.3 billion, and had a nominal 77,000 ktpd mill capacity. Mining, milling, flotation, and tailings impoundment take place at the mine site, which sits at an altitude of 4,300 m above sea level. The deposit is a polymetallic skarn ore body with intrusive phases of quartz-monzonite porphyry into Cretaceous aged limestone. Copper is present mainly as chalcopyrite with a minor bornite component. Zinc is present as sphalerite. Molybdenum is present as molybdenite. Some lead, bismuth, and silver are associated with the sulphides. The deposit is currently classified into six main ore types [Dechert, 2006], grouped into two categories: copper and copper-zinc. The mill produces four concentrate types: copper, molybdenum, zinc, and lead-bismuth. Copper and zinc, concentrates are transported by pipeline down to the port of Huarmey. Molybdenum and lead-bismuth concentrates are bagged and trucked to port."

Jan 1, 2013

By V. K. Alves, P. Lacoste-Bouchet

"In order to improve ball milling efficiency in pellet plants, Companhia Vale de Rio Doce (CVRD), experiments new technologies in Santa Luzia (M.G. – Brazil) research center facility. Pilot grinding tests have been conducted with small grinding media, size distributed from 5 to 12 mm (millpebs). Tests have been conducted on an ore from CVRD’s Usina 5 Nibrasco, in Vitória, Brazil. A sample of the regrind circuit feed was obtained and used in comparative grinding tests with two types of grinding charges: 100% balls and a blend of 70% balls and 30% millpebs by weight. According to the balls charge, the grinding media mixture has showed the following benefits: reduction of the power draw, increase of the mill capacity, reduction of the circulating load and a slight increase of the ore blaine. Following the results obtained, CVRD is going to further explore the regrinding potential of millpebs.INTRODUCTIONCompanhnia Vale de Rio Doce (CVRD) is the largest mining company in Brazil. CVRD is involved in iron, base metals, gold and bauxite industries. Moreover, CVRD operates several pelletizing plants in Brazil and in other countries.CVRD’s Center for Mineral Development (CDM) is equipped with a comminution laboratory where studies are carried out that are aimed at the optimization of existing plants at several mining sites as well as the technical and economical feasibility of new projects. The laboratory is equipped with a complete pilot plant with several mills and classifiers, enabling continuous grinding tests in grinding circuits of almost any capacity and characteristics.In January 2004, CVRD undertook to conduct pilot tests at CDM for evaluating the effect of small grinding media on ball milling efficiency. Generally speaking, it is not unusual for operators to add oversize grinding media in a conventional regrind mill. This fact originates mainly from prohibitive prices of grinding media below 25 mm due to a production capacity decrease of grinding media producers. The size of the grinding media is an important variable affecting ball milling efficiency. Use of oversize balls decreases the number of contact surface between which particles can be caught and broken."

Jan 1, 2005

By John Lindsay

"Although diamond mining is a relative newcomer to the Canadian mining industry, with the first diamond mine coming on stream in 1998, Canada is already a significant producer of high quality diamonds. This paper will review diamond production trends and highlight some of the projects currently under development, which have the potential to enhance Canada’s role as a significant diamond producer.Diamond recovery plants generally incorporate well-established mineral processing and recovery techniques, with issues such as product security, cut-off sizes, and diamond preservation becoming important considerations when developing process flowsheets. A diamond processing plant must achieve three key objectives, namely:• Liberation of the diamonds from the host rock;• Separation of the heavy minerals, which include the diamonds, from the host rock;• Recovery of the diamonds from the heavy mineral concentrates.Processing technologies and equipment commonly utilized in diamond processing plants will be reviewed and some of the significant issues associated with each option briefly discussed.Typical process flowsheets will be presented.Finally, an overview of De Beers’ Victor diamond project, located in northern Ontario, will be provided. This potentially significant diamond producer is currently at a pre-feasibility stage of development.DIAMONDS IN CANADAWorld Diamond ProductionCommercial diamond mining commenced in earnest with the discovery of the Kimberley diamondfields in South Africa in the late 1800s, and this resulted in a dramatic increase in the supply of diamonds. As can be seen from figure 1, world diamond production, mainly from South Africa, Angola, Congo, and Namibia, remained relatively constant through the early 1900s until the development of the large Russian kimberlite pipes in the 1950s. Production increased again in the 1960s and 70s with the development of the Botswana mines, but the most significant increase in global production came from the Argyle mine in Australia, which came on stream in 1983 and produced a peak of almost 43 million carats in 1994, representing approximately 40% of the world market. Production from Argyle has since fallen-off as grades have declined and the strip ratio has increased with the deepening of the open pit."

Jan 1, 2003

By Shaun Booth

Automating Delay Reporting to Deliver Effective Maintenance Corporate Background: Technology Company: Matrikon Inc. Global software and service provider of Information Technology and Control Solutions that deliver Business Results. Case Study Facility: Bulga Coal Handling and Preparation Plant <CHPP> Australian site, part of Xstrata, an international Swiss natural resources group. Technology: ProcessMORe ? Missed Opportunity Reporting (Delay Reporting). Matrikon?s technology implemented at many facilities, to deliver effective maintenance Matrikon International Inc. Global software and service provider of Industrial Decision Support, maintenance and control solutions, with universal connectivity to existing systems and work processes. ? 1999 ? 100 employees ? 2003 ? 450 employees ? Our offices: 20 offices worldwide: ? Quebec, Toronto, Edmonton, Calgary, Ft.McMurray, Vancouver ? U.S. ? Australia (formerly Hunter Controls)

May 1, 2003

By Michel R. Julien, Michel Lemieux, Jean Cayouette, Daniel Talbot

"The Louvicourt Mine located near Val d’Or, Quebec has been in operation since 1994. It produces copper and zinc concentrates. The tailings generated from the ore processing operations have a strong net acid generating potential. Louvicourt Mine, a grass root project, was designed for closure with the best available technology at the time of design. In order to inhibit short and long time acid potential generation, sub-aqueous disposal was selected at the design stage. Given the fact that disposal in a natural lake was ruled out up front for obvious reasons related to loss of natural habitat and risks of permitting delays, a man made facility built with dams was planned. This mine includes therefore the first fully man-made sub-aqueous tailings disposal facility built in Canada. The requirement of using sub-aqueous disposal had serious implications on the placement of tailings. This tailings facility located about 9 km from the mine site has been selected based on the available natural confinement, the favorable foundation and hydrogeological conditions. This paper describes the site and the design criteria that were used. A presentation is also made on the placement technique to maximize storage and its impact on the operation of the basin. The performance of the basin, the dams and the decant structures is reviewed.Résumé : La mine Louvicourt, située près de Val d’Or, Québec est opérationnelle depuis 1994. Elle produit des concentrés de cuivre et de zinc. Les résidus générés par les opérations de traitement du minerai possèdent un fort potentiel net de génération d’acide. Le parc à résidus de la mine Louvicourt, implanté dans un milieu naturel intact, fut doté dès sa conception initiale de la meilleure technologie de fermeture disponible à l’époque, soit la déposition sous couverture aqueuse et ce, dans le but de bloquer le potentiel de génération d’acide à court et à long terme des résidus. Etant donné que la déposition dans un lac naturel fut mise de côté dès le départ pour des raisons évidentes reliées à la perte d’habitats naturels et au risque d’introduire des délais dans l’émission des permis, un étang artificiel délimité par des digues a été conçu. Cette mine fut donc la première au Canada à être dotée d’une installation anthropique de disposition des résidus sous une pleine couverture aqueuse. L’exigence d’une déposition sous couverture aqueuse a eu des implications sur le mode de mise en place des résidus. L’emplacement de l’installation de gestion des résidus a été choisi en un lieu situé à environ 9 km du concentrateur sur la base du confinement naturel disponible et des conditions hydrogéologiques et géotechniques favorables. Cet article décrit le site et les critères de conception utilisés. Une présentation est faite sur la technique de mise en place utilisée pour maximiser l’entreposage et son impact sur l’opération du bassin. La performance du bassin, des digues et des structures de décantation est également revue."

Jan 1, 2004

By John Russell

"The South American mining community leads the world in recognition and adoption of the latest grinding mill relining technologies. Clearly this region has recognised the benefits of improved relining performance.Six of the seven RUSSELL TWIN 8 Mill Relining Systems, ordered to date, are either operating or being manufactured for South American mine sites.This paradigm shift, towards very short relining times, aims at displacing mill relining activities from the critical path of concentrator maintenance shutdown schedules.The first uses of the RUSSELL TWIN 8 Mill Relining System have seen some of the highest SAG mill new liner placement rates ever observed by RME, as would be expected with two, independent Machines working simultaneously in the one mill.The liner-replacement-rate, averaged over the whole reline, is good (27% improvement over single Machine System in the same mill) but short of full potential. This modest result can be attributed to reline crews unfamiliarity with RUSSELL TWIN 8 System operation.This paper compares a sample of conventional (single machine) RME Mill Relining System performance data with one ‘double head’ mill liner handler by others. Early performance of Escondida’s new RUSSELL TWIN 8 System performance is then compared with recent single Machine data from Escondida, immediately prior to RUSSELL TWIN 8 commissioning. RME and Escondida look to constantly improving RUSSELL TWIN 8 System performance as full operational familiarity is achieved.Also, the preparation of this paper revealed a need to develop a global industry standard for mill relining data collection. A web based platform, to develop and then distribute standardised data collection templates, is discussed in Annexure 1."

Jan 1, 2010

By Gunnar Nord

Introduction ??Atlas Copco has customers both amongst Miners and Contractors ??We believe that the contractor&apos;s approach to tunnelling is worthstudying ??For a tunnel contractor the incentive is speed as ?30 % of the costs are material related ?70 % of the cost are time related ?A tunnel contractor favours utilizing of the face ?A miner favours utilizing of the gear ??Statement; In mining, a long term average advance rate of more than 10 m / day can be achieved with the excavation techniques availabletoday

May 1, 2009

By D. F. Machuca-Mory

The new algorithm for high-order simulation of ore deposit grades termed HOSIM is based on the concept of spatial cumulants. The algorithm is tested using data from Apensu, a structurally controlled gold deposit in Ghana. The required high-order spatial structures are obtained from a training image or analogue of the deposit. Using the available drillhole data and training image, HOSIM realizations are able to model well the grades and geometry of the large and well sampled mineralized structures. However, under-sampled small structures remain difficult to model. HOSIM offers a promising alternative for the spatial simulation of complex non-Gaussian orebody attributes of interest.

Jan 1, 2011

By T. G. Paradis, C. A. Mohns

"This paper summarizes the Wren CAT (Clarifier and Accelerated Thickener) deep bed thickener operation at the EKATITM Diamond Mine in Canada’s Northwest Territories. EKATITMs’ thickener project is presented in terms of initial design considerations and present day operating practices. A circuit description summarizes process equipment, reagent systems, and typical process conditions, and details of Wren CAT operating principles are provided. Operating strategies are discussed, with emphasis on process instrumentation and control and operating challenges.INTRODUCTIONThe EKATITM diamond mine, operated by BHP Diamonds, Inc., is located in the Northwest Territories near Lac De Gras, approximately 300 km NNE of Yellowknife, NT. 9000 dry metric tonnes of diamond-bearing kimberlite ore are processed daily. Processing operations commenced in October, 1998.The EKATITM process plant flowsheet features typical steps in diamond recovery plant design. Figure 1 shows the general plant flowsheet. Size reduction and feed preparation are accomplished by crushing, scrubbing, and high pressure grinding rolls (HPGR) through closed-circuit classification with vibratory screens. Heavy medium separation (HMS) is used as the initial stage of heavy mineral concentration. Secondary concentration is accomplished in the recovery plant by attrition milling; wet, high-intensity magnetic separation (both wet and dry); and X-ray sorting.The present budget throughput rate is 9000 dry tonnes per day. This will be increased to 18,000 tonnes during the first ten years of operation. Unlike most kimberlite treatment facilities, which process material from a single ore body, EKATITM’s process plant was designed to accommodate ore from five different kimberlite pipes, each with its own treatment characteristics.All processing, except for primary crushing, is carried out in a temperature-controlled environment in the main process plant building."

Jan 1, 2000

By F. P. Agterberg

"IntroductionTHE KNOWLEDGE about the mineral resources in a region ranges from relatively precise ore-reserve estimates for known deposits to probabilistic estimates concerning the speculative resources which may be discovered in future at greater depths and in the less-explored parts of the region. Previously developed probabilistic methods for regional resource evaluation (1) are based on the following two assumptions.(1) The probability that a specific block of rock, or part of a region close to the topographic surface, contains undiscovered deposits can be estimate d by weighting selected geological, geophysical or geochemical parameters for that block. The weights are computed by considering similar environments which are known to contain deposits.(2) Some of the characteristics of the undiscovered deposits, such as ore tonnages and average grades of metals contained in the ore, can be evaluated by considering probability distributions f or known deposit data. These methods were initially applied to Precambrian deposits in the Abitibi Volcanic Belt of the Canadian Shield (1).Since 1972, statistical methods for quantitative resource evaluation have been applied to the occurrences of the mainly Paleozoic base metal deposits in t he Canadian Appalachian Region. The objectives of this project (Project Appalachia) have been discussed by Leech (2) in a paper that introduces 8 papers with results of the exploratory data analysis. Project Appalachia represents an effort to develop and apply methods of combining information and concepts from regional geology, metallogeny and geomathematics for computer- aided regional mineral resource evaluation."

Jan 1, 1977

By Mike Ounpuu

"Locked cycle testing has become more common practice in the last 10 years. Reasons vary from a desire to avoid pilot plant testing, demand for more variability testing within deposits, and perhaps most importantly, a request from the financial institutions who invariably finance many of the projects. Surprisingly, many people don’t understand locked cycle testing, analysis and balancing. This paper provides a brief overview of locked cycle testing, and then progresses into a more detailed discussion on the analysis and balancing of locked cycle test data. The paper endeavors to educate CMP personnel on how to determine if the test was good and if a reasonable metallurgical projection was made. The paper uses case studies to illustrate the key points.INTRODUCTIONA locked cycle test is a repetitive batch used to simulate a continuous circuit. The basic procedure has a complete batch test performed in the first cycle which is then followed by similar batch tests which have “intermediate” material from the previous cycle added to the appropriate location in the current cycle. These batch tests, or cycles, are continued in this iterative manner for an arbitrary number of cycles. The final products from each cycle, i.e. final concentrate and final tailings, are filtered and thus removed from further processing. At the end of the test, all the products, final and intermediate, are dried, weighed and subjected to chemical analysis. The test is balanced and a metallurgical projection is made.This description can be found in many of our classical textbooks for the mineral engineer 1, 2, 3,4. Unfortunately, none of these textbooks provide any discussion beyond the basic procedure. Often, they provide comments such as in Taggart’ where he states; “It is questionable whether in any case it approximates mill results any more closely than the standard batch test”. It is truly surprising that our classic textbooks promote that locked cycle tests are more art than science, and suggest that they can be of dubious value. None of the textbooks provide meaningful insight or discussion in how to assess:"

Jan 1, 2001

By D. S. Hines

The purchase of mechanical equipment for mines is not unlike the purchase of other materials or supplies in general principle, but on account of the major part such equipment plays in the operations, and of the fact that life and valuable property are at stake, the matter demands the most careful attention on the part of the purchaser. The problems and difficulties encountered are dealt with below in their sequence in the purchasing procedure. Requisiting Although it is quite a common practice to submit a tentative specification of requirements to recognized manufacturers of equipment- soliciting alternative propositions or recommendations for study in the selection of certain equipment-as a rule the first step in purchasing procedure is the requisition. Primarily, it is the form that carries to the purchasing department the record of equipment wanted. A full and complete description or specification, and accuracy of record, are the important points to be insisted on in a requisition. Too much attention cannot be given to this detail, as this is one of &apos;the most important phases of purchasing work. Incomplete information, either in specification or detail, leads to delay in handling the requisition, and, if not detected in the purchasing department, may mean receipt of material which cannot be used for the purpose intended. In addition to description of material or equipment to be ordered, the requisition should also show where or what the equipment is for, whether for operating or new work. If for capital account, the number of the authority for expenditure should be given for record and distribution purposes.

Jan 1, 1930

By Mark McComb, Geoffrey R. Lane

"Over the years many differing approaches have been developed to clearly understand the nature, mode of occurrence, associations and deportment of both free-milling and refractory gold in a wide variety of differing geologic environments and plant products. Many approaches can be taken to characterize the ore which may occur as complex fine grained gold, ultra-fine grained gold, coarse nuggetty gold, complex Asrich refractory gold and double-refractory gold. The approach taken in assessing small drill core composites from Novo Resources Beaton Creek Paleoplacer gold project located in the Pilbara region of Australia was complicated by the nature of the ore, the small amount of sample available from current exploration work, and the gold grade and the grain size distribution. In this case the scope of the study was limited by sample availability although significant amounts of valuable information was also gained. This gold characterization study included the following elements:??Size fraction assays??Ore microscopy??Preparation of heavy mineral concentrates from sized fractions (screening) of crushed or milled head using heavy liquids and Superpan table.??Systematic scans of the heavy mineral concentrate, middling, and tailing fractions using TIMA Automated Scanning Electron Microscopy integrated with an Energy Dispersive Spectrometry to provide semi-quantitative elemental analysis of the individual grains found in the sample.The unique methodology employed to detail the gold deportment was the combination of the Tescan Integrated Mineral Analyser (TIMA) and the Oxford INCA GSR software. This technique not only allowed us to document the deportment of gold but recognize other associated minerals, which included gersdorffite, chalcopyrite, uraninite, coffinite, brannerite and several Rare Earth-bearing minerals.INTRODUCTIONGold deportment studies are commonly carried out on preliminary gold exploration projects in order to determine the various limitations, which may effect processing of the potential ore. This is often because it may be expected that there may be a refractory component to the gold, which may limit physical separation techniques and suggest more costly hydrometallurgical techniques. Often when carrying out gold deportment studies the mineralogical methods may be limited to assuming that the gold will be fine and easily found using standard techniques of optical microscopy or Scanning Electron Microscopy. This may not always be the case as various geological environments may pose their own individual problems to determining the deportment of the gold grains."

Jan 1, 2015

By R. D. Brown

"An adequate level of R & 0 is crucial to achieve gains in productivity and to strengthen Canada&apos; s position in an increasingly competitive world ." So stated Finance Minister Jean Chretien in his April 10, 1978 budget speech, on announcing a new measure designed to increase the productivity of Canadian industry and to assist in the creation of new technology. The effect of the new measure, which permits an income tax deduction of 150% of certain research and development (R & D ) expenditures , can reduce the after-tax cost of a marginal dollar &apos;s worth of such expenditures to as little as 20 cents . This article discusses the income tax treatment of R& D expenditures in general, and describes in particular the income tax incentives which relate to R& D.

Jan 1, 1978

By W. Greg Maybee

Separations, which form along stratigraphic boundaries in the roofs of potash mines, pose a serious safety concern. If these separations go undetected they can lead to falls of ground. The current method of identifying the location and extent of these separations is through manual scaling (sounding) using an aluminium rod. The potash mining companies would like to have a tool, which could quickly and reliably detect these separations and distinguish between them and clay seams. This paper presents the results of field trials undertaken at various potash mines in Saskatchewan belonging to the member companies of the Saskatchewan Potash Producers Association. A ground penetrating radar instrument from RST called SUSI (stepped frequency, ultra-wideband, synthetic aperture radar instrument) was used. SUSI has the ability of working over various frequency bandwidths. Four mines were chosen for these field trials, covering the different geological characteristics encountered in the Saskatchewan potash mines: Potash Corporation of Saskatchewan?s (PCS) Allan and Lanigan Divisions, Agrium?s Vanscoy Potash Operations and IMC Potash?s K2 Mine. These field trials indicated that stepped frequency ground penetrating radar technology could be ?tuned? to identify both separations and clay stratigraphy in the softrock, potash mine environment, based on the different spectral responses of the features.

May 1, 2004

An essential tool for every step ? Early field survey ? Handheld satellite phones ? Portable satellite phones ? Exploration and Drilling ? Handheld satellite phones ? Portable satellite phones ? Production ? Handheld and portable ? Fixed Satellites systems ? Asset tracking systems Main applications via satellite ? Voice and Fax communication ? Internet access and E-mail ? Video conferencing ? Interconnection to mobile phones, 2 way radios, long range WIFI ? Equipment Tele-maintenance ? Telemedicine ? Crew and morale calling ? Vehicle and asset tracking

May 1, 2006

By Tim Hughes, A. H. (Sandy) Gray, Jennifer Abols

"The selective recovery of gold and silver from solutions containing other metals such as copper is possible using AuRIX®100 resin in conjunction with the Gekko Resin Column. Selectivity is driven by controlling the solution pH, which enables activities such as loading copper, gold and silver and then selectively stripping copper before gold and silver. Alternatively gold and silver can be loaded and the copper left in solution. The selective loading of gold while reducing the silver loading has also been demonstrated opening the possibility of producing high grade gold doré from high grade silver pregnant leach solutions. This paper reviews the AuRIX®100 resin and Gekko Resin Column Technologies, discusses the uses of AuRIX®100 in the recovery of gold and silver and the chemistry relating to several projects for which AuRIX®100 is being tested.INTRODUCTIONGekko SystemsGekko Systems specializes in the design, development and distribution of innovative mineral processing equipment and systems with a particular focus on gravity separation for the gold and diamond industries. The company, which has been around since 1996, has five main products: the InLine Pressure Jig, the InLine Spinner, the InLine Leach Reactor (ILR), Gekko Resin Column and Modular Systems.The InLine Leach Reactor is an intensive cyanidation reactor that uses high cyanide (0.5 – 2 % NaCN) and high oxidant (20 ppm dissolved oxygen as O2 or hydrogen peroxide) to dissolve gold from medium and high-grade gravity or flotation concentrates. The ILR, which typically replaces a shaking table in the gold room, is available in both batch and continuous models. There are 42 installations worldwide. Further details on this technology can be found in papers written by Gray et al (2003) and Longley, McCallum and Katsikaros (2003). By replacing a shaking table with an ILR, the overall gravity and plant recoveries can be increased significantly. Other advantages include reduced security risks, lower operating costs, reduced operator involvement due to the automatic process and increased safety for gold room operators."

Jan 1, 2006

"In mineral exploration and mining applications, it is sometimes necessary to reduce sampling error in order to improve representivity of individual sample assays. Historic efforts to reduce sampling error have relied on the belief that larger samples exhibit less sampling error. Justifications for this belief traditionally have coupled the binomial theorem with an ideal geological material consisting of ore and gangue particles of equal size and shape (an equant grain model) and empirical tests of geological materials, to illustrate an inverse relationship between sample size and sampling variance. To date, no proof exists of this sample size-sampling variance relationship in real geological materials exhibiting variations in grain size, shape, composition, and degree of liberation.Using first principles calculus and the formula for the mean, sample mass and sampling variance are proven to be inversely proportional in all geological materials. Distribution assumptions and physically ideal geological models are not used in this proof. Furthermore, algebraic manipulations of expressions describing the variances of equant grain models consistent with binomial, hypergeometric, and Poisson distributions reveal that these models also exhibit an inverse sample size-sampling variance relationship. Thus, the sampling behaviors of these models are numerically consistent with the sampling behaviors of real geological materials, and these models can be used to estimate sampling errors in real geological materials using simple sampling parameters."

Jan 1, 2007