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By Z. Nzimande

The Constitution of the Republic of South Africa advocates the importance of sustainable economic development and justifiable environmental consciousness by business. The government needs to ensure that every citizen of the Republic has access to an environment that is protected, pollution free, and sustainable by enacting certain regulations. However, there are more than 5 700 derelict and unrehabilitated mines of all types in South Africa. Former asbestos operations were among the first to be targeted for clean-up under the programme instituted by the Department of Mineral Resources (DMR), owing to the proven direct impact of asbestos pollution on health. This paper seeks to investigate the challenges faced by the coal sector as far as mine rehabilitation and closure is concerned. For the purpose of this paper rehabilitation is defined as per the Chamber of Mines Rehabilitation Guidelines publication, which defines rehabilitation as putting the land impacted by mining activities back to a sustainable and usable condition. Some of the current rehabilitation challenges are technical skills (know-how), leadership focus, poor planning, cost saving initiatives, and the government's lack of capacity to enforcement rehabilitation requirements. It is imperative that mining companies identify rehabilitation as a critical strategic pillar that directly influences license to operate. The case study evidence indicates that relevant policies, appointment of accountable people, sufficient leadership support, and the correct choice of rehabilitation equipment can assist to improve the rehabilitation and land management challenge.

Jan 1, 2012

High pressure grinding roll (HPGR) technology is used in an increasingly diverse range of applications, predominantly iron ore, gold and diamonds. KHD Humboldt Wedag HPGRs are applied world-wide, and consistently prove to be well designed and reliable operating units, with their performance meeting the pre-set standards. This publication summarizes some of the features and experiences for recent applications in treatment of copper ore, coarse iron ore, and gold ore. Summary data of roll surface wear life and operating data are given, together with operational observations. In addition, effects of feed segregation and truncated feed are discussed, as well as the implications of a product recycle flow sheet.

Jan 1, 2012

By A. Sampson-Forsythe, P. Morissette, A. R. Punkkinen, D. R. Chinnasane

"The performance of ground support systems under dynamic loading is typically assessed in a qualitative and subjective manner. As a result, it is difficult to develop an explicit knowledge on the mechanisms of action and interaction of support elements subjected to rockbursts. This paper examines rockbursts that have occurred at Creighton, Copper Cliff, and Coleman mines since 2000, 2004, and 2006, respectively. The mines are located in the Sudbury Basin, in Ontario, Canada. The majority of pertinent information was obtained through on-site field assessments, seismic system records, and numerical elastic stress modelling. Passive monitoring is used to link the evolution of the frequency and severity of rockbursts to the evolution of mining and support practice at the three mine sites. Based on the collected data, ground support elements that enhanced the capacity of support systems to withstand dynamic loads are identified. IntroductionThe selection of appropriate mining methods, extraction sequences, rock mass de-stressing techniques, and ground support systems is of great importance in mitigating the level of rockburst-related risk. In burst-prone conditions, the design of support systems should account for the anticipated dynamic load demand and the capacity of the available support options. Furthermore, an economical design should, implicitly or explicitly, take into consideration the consequences of a rockburst and its impact on worker safety and mine productivity. Stacey (2012) has argued that we have a limited understanding of the mechanisms of rock mass behaviour in seismic conditions. This is compounded by a ‘lack of understanding of the mechanisms of action and interaction of support elements under dynamic loads’ (Stacey, 2012). Consequently, the design of support systems required to manage dynamic loads is usually based on experience. The assessment of the dynamic performance of ground support systems is typically subjected to qualitative (and sometimes subjective) interpretations from ground control personnel."

Jan 1, 2017

By J. L. Louw

The utilization of centralized blasting systems is progressively becoming a feature of the South African mining industry, owing to increased pressure from the Department of Mineral Resources (DMR) to ensure safer blasting conditions. The purpose of a centralized blasting system (CBS) is to ensure reduced blasting-related incidents and to improve the underground working environment for the mine?s employees. The brief from Samancor Western Chrome Mines (WCM) pertaining to this study was to explore?at a conceptual level?all variables pertaining to the implementation of the CBS. Studies have indicated that Sasol?s SafeBlast? was preferred due to low overall risks and user-friendliness. Empirical observations, however, indicated that attention should be given to the current shaft-clearing procedure and to the installation of additional transformers. This is required to co-ordinate the power supply from 2 level to 10 level with the required supply of the network slave station. A cost analysis indicated that an electronically initiated CBS will result in a R24 cost increase per panel, which relates to a mere 1% cost increase per panel. This cost, in addition to the R1.1 million capital cost, proved to be negligible in comparison to the possible direct and indirect costs incurred by the mine in the event of a blasting-related incident. It was found that Samancor should conduct further studies incorporating the necessary requirements to ensure a successful transition, while considering all stakeholders on the mine. This study proved that the transition to a CBS would ensure safe and efficient blasting at Samancor?s Mooinooi Mine.

Jan 1, 2012

By R. H. Matjie, J. R. Bunt, C. A. Strydom

"A number of conventional and advanced analytical techniques (proximate and ultimate analysis, low-temperature oxygen-plasma ashing, X-ray diffraction, X-ray fluorescence spectrometry, coal petrography, and lightelement electron microprobe analysis) have been integrated and crosschecked to provide detailed characterization of coals from the Highveld coalfield in South Africa, as a basis for better understanding of the mineralogical and chemical properties of the individual coal sources that are blended as feedstocks for combustion and carbon conversion processes. The techniques included methods to quantify the abundance and composition of the mineral matter (minerals and non-mineral inorganic elements), and also the abundance and chemical composition of the individual macerals in the individual coals concerned.Kaolinite is the most abundant of the minerals in the coals studied, with lesser but still significant proportions of quartz, mica and/or illite, dolomite, calcite, and pyrite. Small but variable proportions of anatase, goyazite, and siderite are present in some coal samples. Electron microprobe analysis, based on a special configuration for light-element study, shows that the vitrinite contains less carbon and more oxygen, and has significantly higher concentrations of nitrogen and organic sulphur, than the inertinite macerals in the same samples. Minor proportions of organically-associated inorganic elements, including titanium, were also identified in some of the maceral components.A comprehensive knowledge of the minerals and non-mineral inorganic elements in the coals used for feedstock preparation, obtained by integration of data from these advanced analytical techniques with more conventional analyses, may be of benefit in understanding the processes that take place during coal utilization, and also in avoiding or ameliorating some of the operational and environmental problems that may occur in different sectors of the coal utilization industry."

Jan 1, 2016

By R. W. Ottermann, N. D. L. Burger, A. J. von Wielligh, P. R. de Wet, J. L. Steyn

Underwind and overwind protection system concepts for mine hoist shafts were developed in conjunction with and for the Safety in Mines Research Advisory Committee (SIMRAC). End-of-wind operation of mine hoists is the most hazardous aspect of mine hoisting, carrying the highest risk of loss of life, injuries to workers and loss of production. Systems operating mechanically and with local actuation were developed. This was done in order to remove the increased risk associated with dependency on remote or external energy and information supply associated with most existing protection systems. The proposed underwind protection system concept absorbs the energy of motion of a conveyance overrunning the design lower limit of travel by drawing a metal strip through a set of rollers. This action causes dynamic cyclic plastic bending of the strip material that converts the kinetic and potential energy of the conveyance into strain energy of the metal. In the concept design a pair of cable slings attached to the strips catch the overrunning conveyance and transfer the retardation force. The proposed overwind protection system concept absorbs the energy of motion of a conveyance overrunning the design upper limit of travel by early detaching of the conveyance from the hoist cable. This detaching is carried out via an additional humble hook activation mechanism fitted at a sufficient height below the spectacle plate to allow the conveyance to retard to standstill under gravity before it would crash into the spectacle plate. The conveyance so brought to rest is prevented from falling by means of jack catches on the conveyance interacting with a rack (toothed profile) fitted on the guide rails in the retardation zone. Scale models (1:10 scale) of both protection systems were designed for conformance with established retardation standards. The retardation standards were limited by the requirement of passenger safety in retarding cages. The models were then built and tested in a 1:10 scale shaft model. Retardation performance close to the required levels was achieved. The retardation distance required should allow such systems to be retrofitted to most existing shafts. Given the simplicity and robustness of the designs

Jan 1, 2003

By C. M. Suhr

n order to validate the borehole analysis valuation procedure commonly used in the South African gold mining industry, a simulated orebody was used to create borehole values which would serve as data for the procedure. After confirming the distribution, calculating the variance size of area relationship, estimating the block variance, and calculating a profit measurement for each set, comparisons were made to the known population parameters. Results show only one overall bias (in the estimation of the lognormal third parameter), which is carried throughout the analysis. The remainder of the analysis is unbiased, validating the procedure.

Jan 1, 1987

By M. Gericke

Over the past few decades the commercial application of heap bioleaching technology for the extraction of base metals has become increasingly important, due mainly to the depletion of high-grade ore reserves. Heap bioleaching is widely used for the extraction of copper from secondary copper sulphide ores. The design and engineering aspects of the process have received considerable attention, but issues related to the microbiology of the process have been subjected to less rigorous scrutiny. The major role of micro-organisms in bioleaching processes is to catalyse the regeneration of ferric iron and protons, from ferrous iron and by sulphur oxidation respectively. It is accepted that even the most carefully engineered heaps are heterogeneous in terms of temperature, pH, the presence of anaerobic pockets, irrigation efficiency, and dissolved solutes. Since interactions between solution chemistry, mineralogy, and microbial populations exist in heaps, a better understanding of the correlation between microbial numbers and types with changes in these chemical and physical profiles with time would be beneficial during process design and operation of heaps, and could result in faster start-up times and higher metal recoveries. This paper reviews the role of microbiology in heap bioleaching processes. Aspects such as microbial diversity, identification and monitoring of cultures, inoculation strategies, colonization behaviour, and tolerance to metals and salts are discussed, and the potential contribution of the knowledge to the improvement of the operation and design of heap bioleach processes assessed. Conclusions are drawn with respect to the role of genetic engineering, heap inoculation practises, and remaining areas for future heap bioleaching research and development.

Jan 1, 2012

By R. Ajalloian, L. Karimzadeh

This paper describes the engineering properties of Givi dam foundation. Givi dam will be built across the Givi River on the andesitic rocks (Karaj formation) in Ardabil province (northeast of Iran). Geotechnical investigations including drilling, pumping tests, sampling for laboratory testing and discontinuity survey. Physical and mechanical properties of andesitic rocks such as density, water absorption, porosity, uniaxial compressive strength, triaxial compressive strength, durability and direct shear tests are evaluated in this paper. Discontinuity data are process for the determination of dominant sets and for the rock mass characterization in terms of classification systems ( RMR, Q and RSR ). Correlations between these three classifications are discussed. Le barrage doit être construit sur la rivi_re givi qui cou_e sur les andesites (formation de Karaj)dans la province d_ Ardebile situee_ a Nord- Ouest de l_ _Iran. Les études géophsique commesondage, Pompage. Et échantillonnage afin de verifier les discontinutés out éte_ effectuées. Lesproprietés physique et méchanique des roches andesifique ont éte_ verifieés. Les informations concernaüt aux discontinuitiés afin de montrer leur principale direction ont éte_ verifieés, les proprietés des roches dans leurs ensemble ont éte_ etudieés. Les divers classifications(RMR,Q,RSR ) ont éte_ comparés et analyseés. Dieses Schreiben ist zur Erklaerung der Ingenieureigenschaften ueber Baugrund des Givi Deiches.Dieser Deich soll im Givi fluss auf Andesitgesteine (Karaj formation) gebaut werden. Der platzdes Deiches legit im Ardebil Provinz nordwestlich von Iran. Geotechnische Untersuchungen Sind:Bohrungen, pumpen Versuche, Probenentnahme fuer Laborversuche, BrechbarkeitBestimmungen, physikalische und mechanische Eigenschaften der Andesitgesteine wurde hierausgewertet, wie Z.B.: Wasserleitfahigkeit, Porositaet, Scherfestigketswiderstand, Informationenueber Brechbarkeiten der Gesteine wurde gesamelt, und die meisten Brechbarkeiten bestimdamitman die Gesteine besser klassifizieren kann. In Endefekt wrid die Resultate verschiedeneKlassifizierung wie RMR, Q, und RSR besser geachtet und zusammen vergliechen.

Jan 1, 2003

By J. Rowe

The attrition of activated carbon, and the loss of gold associated with it, is of significant economic importance to the operation of a CIP/CIL circuit The focus of this study was on activated carbon recovered from an elution circuit which was deemed too fine for reuse. Results of cyclosizer and laser particle size analysis identified that most of the carbon was contained in the larger size fraction suggesting formation by abrasion. Digestion and AAS analysis of the individual size fractions identified a disproportionate concentration of gold in the finer size fractions which was identified by scanning electron microscopy to be due to the presence of fine metallic gold formed as a result of the acid washing process. Attempts to strip the remaining gold using sodium hydroxide or sodium sulphide based solutions proved unsuccessful due to poor elution efficiencies and re adsorption of gold. Upgrading of the material by froth flotation was also investigated using various conventional flotation reagents which had some success in concentrating the free metallic gold, however, grade and/or recoveries were considered less than desirable. Greater success was ultimately found in the transfer of gold from the fine carbon material onto coarser virgin activated carbon using a caustic cyanide solution. Sodium sulphide, sodium chloride and ammonium chloride based solutions were also trialled but proved less successful owing to their inability to mobilise metallic gold or gold cyanide species. Repetition of the transfer process proved capable of stripping 97% of the gold contained on the carbon fines for abed volume ratio of 6:1.

Jan 1, 2009

By G. G. Stanley

Mechanisms in the autogenous mill and their mathematical representation by G. G. STANLEY, B.Sc. (Eng.) (Wits.), M.E. (Queensland), Ph.D., (Fellow) The special characteristics of the autogenous mill are stated, and a suitable type of model for the mill is presented. Details of the test plant and experimental techniques for obtaining the data for model development are next given. followed by a discussion of the methods developed for the computation of the model parameters, namely the appearance matrix, the abrasion and crushing breakage-rate functions, and the discharge-rate function. Examples of results obtained with the model are given, and finally there is a brief account of confirmatory work on a fullscale autogeneous mill.

Jan 11, 1974

By A. P. Cook

Gas samples were taken from a wide range of target areas on dumps arising from coal mining activities. Some of the dumps had largely burned out, some were still burning, some were in the process of rehabilitation, and on others rehabilitation was essentially complete. It was found that rehabilitation was very effective in reducing emissions to tolerable levels. Even incomplete rehabilitation reduced the CO2 emissions to less than about 1 kg/m2/a, whereas some unrehabilitated areas showed emissions of over 100 kg/m2/a. Some areas where there was active combustion taking place were also sampled, and they showed as much as 7 000 kg/m2/a, but the areas concerned were very small and their total contribution accordingly low. Analyses were also made for SOx, NOx, NH3, and CH4, but these were generally (and unexpectedly) at very low levels. The mines sampled represented 53 per cent of all surface coal mining activity. Accordingly the estimated total emissions were scaled up, to arrive at estimates of 1950 000 ± 350 000 t/a C02, 2040 ± 580 t/a SOx, 306 ± 85t/a NOx, and 31 ± 9 t/a NH3 for all surface mines. Methane was detected only from burning coal, and due to the difficulty in sampling, no reliable estimate could be made of these methane emissions.

Jan 1, 2012

By C. Musingwini

The South African platinum mining industry is using a number of different mining methods, including variations of the same method, to extract the narrow reef tabular platinum deposits of the Bushveld Complex. These mining methods fall into three broad categories, namely conventional, mechanised and hybrid mining. A question sometimes asked in the industry is whether mechanized mining methods are more efficient than conventional mining methods. An objective answer requires the methods to be evaluated against multiple criteria simultaneously, whereby each criterion has a relative degree of importance in the overall decision. The most efficient method is the one that scores highest on each criterion. However, some of the criteria can be conflicting, such as by increasing dilution the shaft head grade decreases. The analytic hierarchy process (AHP) methodology was selected for the study because it is used to solve problems of this nature. A survey was carried out to determine the relative importance of each efficiency criterion by drawing on the knowledge and experience of mine technical services and project management practitioners in the industry. Efficiency data for four different mining methods drawn from the Egerton (2004) study were used as a case study. The conventional mining method ranked as the most efficient mining method from the four methods considered. The exercise indicates potential for the AHP to be used in the South African platinum mining industry as a tool for selecting optimal layout designs, conduct regular evaluation of the performance of production shafts, or objectively evaluate line managers for promotion. The work described in this paper is part of the methodology used in a current PhD research study at the University of the Witwatersrand. Keywords: Analytic hierarchy process (AHP); multiple criteria decision analysis (MCDA); decision-making; conventional mining, hybrid mining, mechanized mining.

Jan 1, 2008

By J. Gholamnejad

Determination of the optimum cut-off grades is one of the most important aspects of mine production planning. A cut-off is a grade below which we choose not to process material. This material is treated as waste and dumped. Dumping waste is accompanied by the rehabilitation cost which will affect the overall cost of final production and also the optimum cut-off grade. Rehabilitation cost is the cost per ton of rehabilitating material of a particular type of rock after it has been dumped as waste. One of the most popular algorithms for determination of the optimum cut-off grade is Lane?s method. Lane formulated the cut-off grade optimization, but he did not consider rehabilitation cost during the optimization process. This cost item should be evaluated first, and then considered during the cut-off grade optimization process. In this paper the rehabilitation cost is inserted directly into the cut-off grade optimization process using Lane?s theory. The cut-off grades obtained using the suggested method will be more realistic than ones using the original form of Lane?s formulations.

Jan 1, 2009

The variety and sources of sampling errors have been studied since the late 1800s, but the pioneering work of Pierre Gy in the 1950s provided insights into sampling as an error generating process. Total sampling variance is a measure of the total sampling error, but disaggregating the variance into its component parts is problematical. Ten sources of error and error generating processes have been identified, some of which can be eliminated through rigorous application of the principle of correct sampling. Others can only be minimized but never eliminated. Three principal questions relating to the appropriate mass of a sample, the fragment size of the sample and the size of the associated error are addressed. These questions relate principally to the Fundamental Error (FE), the only error that can be estimated before the sampling event. Aspects of constitutional and distributional heterogeneity are examined, as are the essential components of Gy?s formula including the shape factor (?), the granulometric factor (g), the mineralogical composition factor (c), and the liberation factor, l. Applications of Gy?s equation to the problems of sampling in the minerals industry are explained using real-life examples. The approach to sampling taken by Pierre Gy provides an excellent inferential relationship between the mass of material to be sampled, the size of the fragments being sampled, and the relative variance of the sampling error. It also provides solutions for three of the main problems associated with the Theory of Sampling.

Jan 1, 2007

By P. Saari

The Talvivaara deposits are located in Eastern Finland, within the Kainuu Schist Belt. These polymetallic sulphide deposits are of relatively low grade, but bioheapleaching enables economically profitable nickel extraction from the ore. Zinc, cobalt, and copper are also produced. Talvivaara?s production process begins with large-scale open-pit mining and four crushing stages, followed by stacking of the ore in bioleaching heaps. The ore is first leached for 13?14 months on the primary leach pad, after which the leached ore is reclaimed, conveyed, and re-stacked on the secondary heap pad. After secondary leaching, the barren ore will remain on the secondary heaps permanently. In the metals recovery process, the metals are precipitated from the pregnant leaching solution. Construction of the process was begun in spring of 2007 and first metal sulphides were produced at the plant in October 2008. The development of the bioheapleaching process was begun in a 17 000t on-site pilot heap operated during 2005?2008 and has continued in the industrial heap. At industrial scale, the development measures have focused on improving the permeability and aeration of the heap. Challenges with crushing and aerations systems at the beginning of industrial-scale leaching delayed the increase in metal recovery, but after the first two operational years the leaching results have improved significantly and the process is performing as targeted.

Jan 1, 2012

By D. Rankin, H. J. Stucke, W. K. B. Loftus

SYNOPSIS Planning for the Finsch opencast mine is described with particular reference to the proposed stages of mining, the method used to determine the limits of surface waste rock stripping and the derivation of the waste rock mining rate. Actual mining practice is described and the possibility of installing a skipway into the open mine at a later date is discussed. In addition, the waste dumping policy is referred to: this includes the cutting of slots through the hill on the west side of the pipe to increase tramming speeds. The crushing, washing and recovery sections of the treatment plant are described together with the various changes being made to the circuit. The most important of these are the installation of X-ray sorters for the final recovery of + 7 mesh diamonds, and the vibrating grease belt for the recovery of - 7 mesh diamonds. INTRODUCTION The Finsch Mine, a subsidiary of De Beers Consolidated Mines, Limited, is situated approximately 90 miles west of Kimberley, and some two miles from the village of Lime Acres, in the Northern Cape. Lime Acres is a company village shared with the Northern Lime Company which operates a limestone quarry and works near the township. The mine is near the southern end of a well mineralized belt producing limestone, asbestos, diamonds, manganese and iron ore, and the whole area has developed rapidly in the last 20 years. Power for mining operations is drawn from the Electricity Supply Commission. The mine is conveniently close to the main Kimberley-Postmasburg railway line. Water is drawn from the Vaal River through a 57 mile State-owned pipeline at present temporarily operated by mine staff. DISCOVERY AND PROSPECTING OPERATIONS The diamondiferous orebody is situated on the farm Brits, which is State-owned ground that has been leased to the Company for the period of mining operations. There are indications of interest in the area by prospectors (Richter, de Bruin and others) over a period of some 30 years and the discovery would possibly have been made years earlier but for a law preventing prospecting for precious stones on State-owned land. Although the pipe formed a clear depression on the hill where it was situated, it was overlain by some 5 to 40 ft of banded ironstone rubble which was washed into the depression from the hillside above the pipe and obscured the deposit. In 1958, Mr Allister Thornton Fincham applied for, and was granted, the right to prospect for base minerals on the farm Brits. Asbestos is known to occur in the area and, initially, was Mr Fincham's primary interest. However, during the prospecting operations, garnets were discovered and it was realised that diamonds might be present. In 1960, when the Precious Stones Amendment Act was passed, a company

By M. E. C. Snyman, N. Naudé

"Coal fines produced during processing are difficult to dewater and result in a lower quality product and consequent lower value. A South African coal mine experiences severe difficulties with belt filter dewatering operations due to the presence of fines reporting from the thickener underflows. Plant 2 currently handles super-fine particles of size -34 µm and has low belt filter efficiency: excessive moisture retention lowers the product quality and strains downstream processing. It was necessary to determine an alternative method for dewatering these fines. Blending of fine material with coarser material was proposed as a solution. The effect of coal particle size and layering during ultrafines belt filter dewatering was evaluated using various blends of the fine Plant 2 material with coarser Plant 1 material. The best layering arrangement of the two materials and its optimum blend required to achieve reduced filter cake moisture content was determined in practise using a vacuum filter to simulate belt filtration. A blend of the two materials gave improved dewatering efficiency for the belt filters compared with that of the Plant 2 material alone. The best layering configuration was with Plant 2 material at the bottom and Plant 1 material on top. The optimum blend for industrial applications comprised 48% fines from Plant 2. IntroductionFines are produced during the processing of coal. It is estimated that 2 to 3% of run-ofmine coal reports to the ultrafine portion (-100 µm) (le Roux, 2005). The particle size of coal is inversely proportional to the amount of water adsorption, so smaller particles adsorb more moisture. Moisture removal requires either mechanical processes or thermal drying: mechanical processes are less expensive, but the fines still have high moisture retention. Discarding of fines leads to economic losses, so it is essential that they be dewatered so that they can then be sold as a product: fines need to be treated for both resource management and conservation reasons (Kenney, 1994). Removal of free surface moisture from ultrafine coal particles using a belt filter therefore remains a process that needs to be continuously improved. Ultrafine coal originating from a thickener underflow is known to be difficult to dewater owing to factors such as filter cloth blockage and moisture retention due to clogging. Mixing of finer and coarser materials has been proposed to deliver better dewatering efficiency and improved the quality of the recycled water (Kenney, 1994)."

Mar 1, 2019

[The following notations will be used: O an ore body. z a point in O. z' another point in O. w0 (z) a point support of infinitely small dimensions w0 centred in z. w (z) a sample (or block) of finite dimensions kv centred in z. W (z) a block of size W greater than or equal to w. W'(z) a block of size W' greater than or equal to W. W" (z) a block of size W" greater than or equal to W'. x (z) value of the regionalized variable x with support wO at point z. p (z) average value of x in w (z). pw WZ) = E[x(z')l zt in w(z) pw (z) average value of x in W (z). pwl (z) average value of x in W' (z). pwU (z) average value of x in W" (z). Note that pW (z), pw (z), pwf (z) and pw,, (z) are (regular- ized) regionalized variables with support w, W, W' and W" respectively. The relative sizes of wO, w, W', W" and O are represented schematically in Fig. 7.1. The variance of pw (z) when w (z) takes all possible positions in O is known as the dispersion variance of w in O and is denoted by a? (w in O) or a\: 0; = a2(w in a = Ew,z, inn {[p~ (z) - p121. (7.1) For convenience, the following simpler notation will be used: a> Ew in n [(p w - pl21. Consider now a large block W (z) in O with average value p~(z), and all the possible smaller blocks (or samples) w (z') of size w in W (z). We can calculate the variance of the blocks w (z') in the block W(z), which is the dispersion vaciance of w in W (z), from the relationship a2 [w in W(z)l = Ewcz,, in W(Z) {[PW (z') -pw (z)l21. (7.2) Provided the intrinsic hypothesis is satisfied (§3.4.4), this variance is a function only of the dimensions of the supports w and W, and is independent of the position z of the block W (z). We can therefore define the dispersion variance of w in W, as follows: u2 (win W) = Ew in w [(ptti - PW)~]. (7.3) In cases where the intrinsic hypothesis is not satisfied, the variance of samples w in blocks W may vary only slightly from block to block, so that the average dispersion variance of w in W (z) for all possible W (z) in O can be used: ayw in W) = Ew(,, ~n n {a2 [W in W (z)]}. (7.4) The following example will help to illustrate the importance of the variance of dispersion. Assume that we plan to develop a bedded coal deposit Q. We consider mining the ore body with only one giant dragline, which will extract each day a block of coal of size W'. The total area mined in a year will have a size W". We want to know whether this scheme is acceptable, given that the daily variation in ash content must not exceed a given percentage specified in the sales contract, which is renewable on a yearly basis. On a given day, if we mine the block W' (z), the ash content will average pwT (z). In a period of one year, the expected daily variation in ash content is measured by the expected variance of pwf (z) in W", i.e. by a2 (W'in W"). An alternative mining method might be to use two smaller draglines, each one mining W'/2 of ore per day, and Wn/2 per year. If the draglines are used to mine two distinct sections of the deposit, the expected daily variation in ash content will be u2 (W'/2 in Wj1/2)/2 Other situations, where economic decisions cannot be made without knowledge of the dispersion variance, are illustrated in § 7.4 and 7.5 below. Remark: The notation a2 (w in W) is used in this publication because of its clarity. An alternative notation, which is increasingly accepted in the literature, is s2w/W. ]

Jan 1, 1978

By D. A. Vetter

A novel mathematical model is presented which describes the behaviour of beds of particles, of uniform size and shape but different densities, during autogenous separations. The approach used in the formulation of the dispersion model is a phenomenological one based on a statistical view, which leads to a diffusion-like representation of the autogenous-separation process. Although the model currently considers only density-related phenomena, it accounts quantitatively not only for the density-segregation aspects of the process but for the interactions between the particles. Quantitative predictions of the dispersion model are compared with the results obtained in tests using a specially constructed experimental batch jig, and it is shown that the model provides an adequate quantitative description of the process for particles of uniform size and shape. It is pointed out that, for the description of more complicated autogenous separations, a more rigorous formulation of the particle drag and density-segregation terms will have to be incorporated into the dispersion model. Nonetheless it is concluded that the model as presented in this paper provides not only a novel insight into the mechanisms of autogenous separations but a means by which to analyse similar systems.

Jan 1, 1987