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By J. W. van der Merwe, C Strydom, D. C. Odendaal, M. I. Sampson

Keywords: Sphalerite, Bio leaching, Chemical leaching Sphalerite concentrates were prepared from tailings dam samples obtained from Rosh Pinah Mine in Namibia. The samples were subjected to froth flotation and concentrates containing between 7% and 14% Zn were prepared. Leaching of these froth flotation concentrates were studied in ferric chloride solutions at different Fe3+ concentrations for different times at different temperatures with the influence of other species on the kinetics in mind. Complementary to this research, GeoBiotics, LLC and Exxaro Resources have developed proprietary bioleaching technology for the oxidation of base metals concentrates using GEOCOAT bio heap leaching technology in a sulphate medium. The ferric chloride laboratory work was performed in a fluidising leach reactor. The studied material was obtained from flotation concentrate produced during an investigation into the recoverability of a tailings pile at Rosh Pinah mine in Namibia. The optimum conditions for the laboratory investigation were found to be a Fe3+ concentration of 0.3 mol/dm3 at 80°C. A control was performed by using synthetic zinc sulphide. GEOCOAT evaluation tests are performed for the purpose of evaluating the bioleaching of ore and flotation concentrates by means of mesophilic bacteria, Column tests were carried out on the flotation scavenger concentrate from Rosh Pinah to assess the application of the GEOCOAT® process for the oxidation of a low grade zinc concentrate. In this study an attempt was made to demonstrate the relationship between the Kinetic models and the experimental data by plotting the fraction of Zinc leached against time and applying the different equations to the data. The kinetic models were applied to the data obtained from both the test regimes. Habashi (1999) proposed that if a process is controlled by a chemical reaction at the interface (phase boundary controlled reaction), the following equation applies. kCt =1 ? (1-R) 1/3 Alternatively a process is controlled by diffusion through the product layer the following equation applies: [kt = 1 23- X (1 ? X) 2/3] As the anodic dissolution reaction progresses, reaction product forms either a more or less dense reaction product layer on surface As this product layer forms, a diffusion problem develops governed by the nature of the product layer. The conclusion from the study was that the kinetics is very dependent on the type of ore processed relating to the mineral composition of the ore body.

Jan 1, 2007

By J. Zwartendyk, A. Azis

"Every nation must decide how it should exploit its mineral resources so as to contribute most to its national objectives. It is argued that the present value of the future corporate income tax flow derived from mineral exploitation may serve as a useful indicator in moving toward a taxation policy that would contribute optimally toward the greatest public benefit.The future stream of corporate income taxes depends largely on the mineral endowment, consisting of deposits now being mined, known unmined deposits, and unknown deposits.Unknown deposits may be estimated by geological inference. Both known and unknown deposits can be categorized according to grade and size, and divided into economic and uneconomic deposits on the basis of certain prices, costs, rate of return and taxation levels.Computer simulations can be run of discounted cash flow models at various taxation levels to show the impact of taxation changes on future tax revenues."

Jan 1, 2014

The statistical methods described in the previous chapter permit the estimation of the average value p of a deposit, and the calculation of confidence limits for this value. They are based on the assumption of independence of sample values. As soon as a reasonable number of samples has been obtained from a deposit, local valuation, or estimation of blocks of ore within the mineral deposit, becomes necessary. The assumption of independence of values must then be rejected. Local valuation is possible only if there is a relationship between the value of a sample and the value of the surrounding ore, provided this relationship is a function of the position of the sample with respect to the blocks of ore to be valued. Whichever method is used for the valuation of a block of ore, the following assumptions are always made: ? The values of samples located near or inside the block are related to the value of the block. ? The values of the samples located closest to the block are most closely related to the value of the block. These assumptions will hold true only if the following assumption can also be made: ? There exists a relationship between sample values which is a function of the distance between samples. We are saying that the value x (z) of a sample centred at a point z has properties which are functions of this point. A certain spatial structure exists in the sample distribution. We are therefore dealing with a regionalized phenomenon, and we must treat x (z) as a regionalized variable. This can be done statistically by means of a model chosen to represent the spatial structure of the phenomenon. We shall see that the relationship between block values and sample values can be deduced from the relationship between sample values, and all local valuation problems can be solved using the statistical model obtained from the analysis of the sample values. It is important to realize that this statistical model is obtained by analysing the properties of known sample values, and will be used for the estimation of unknown block values. Such a statistical inference is valid only if the model developed represents the properties of both the sampled section of the ore body and the section to be valued: some stationarity conditions must be satisfied, and the model with the least restrictive conditions is preferred. In the following chapters, the most important models used in spatial geostatistics are presented. The models which can be used when there is no significant drift (trends) in values are described in Chapters 3-1 1. These models can also be used to solve some specific valuation problems when a linear drift is present. A general study of the more difficult problem of analysis of an ore body whose values present a drift is described in Chapter 12. Note that the area considered for local valuation of a block of ore is often small enough for any drift which might be present to be ignored.

Jan 1, 1978

By A. M. Engelbrecht

Paper written on project work carried out in partial fulfilment of B Eng. (Chemical) Membrane processes are vital to a diverse range of technical and biological systems, which also feature in mineral processing applications such as the treatment of mine effluent and extraction of metals. In this study, the use of cellular automata to model a semi-permeable membrane that separates two compartments is considered. Cellular automata are simple models that enable the analyst to represent well-understood local effects, such as the chemical or steric interaction between molecules themselves and between molecules or particles and their environment, which can lead to very complex behaviour on a macroscopic scale. Various physical phenomena, including reverse osmosis, were simulated. Initial results for the effect of temperature, membrane structure and chemical properties of the solutes on the performance of the membrane appear promising. Keywords: cellular automata, dynamic modelling, filtration, membrane fouling, osmosis.

Jan 1, 2007

By G. van Aswegen, J. D. Bosman

Gold bearing deposits in the Witwatersrand consist predominantly of narrow tabular conglomerates with quartzite host rock. Extensive mining of these deposits at depth results in significant stresses being induced in the periphery of the tabular excavations. Where remnant pillars are created excessive stresses have resulted in the dynamic failure of the abutments. At the Hartebeestfontein Mine four brittle shear zones have recently been exposed and investigated. For most part, they represent abutment failure into the weaker hangingwall strata, striking parallel to the abutment, dipping towards the stope, with a sense of displacement consistent with closure of the stope from above. These shear zones are similar to those described in various publications by Ortlepp2: they are essentially brittle shear zones characterised by the presence of very finely comminuted ‘rock flour’ on an obviously freshly sheared surface. The angle between the shear zone wall and extension fractures indicate the sense of shear and the intersection of the extension fractures with the shear zone walls define a strong lineation normal to the direction of slip. It is suggested that these structures are referred to as ‘mining induced dynamic brittle shears’. Les gisements d’or du Witwatersrand consistent principalement de conglomérats tabulaires peu épais contenus dans une quartzite mère. Une exploitation poussée de ces gisements en profondeur a pour résultat l’apparition d’importantes contraintes induites à la périphérie des excavations tabulaires. Là où des piliers restants sont créés, des contraintes excessives ont eu pour résultat une rupture dynamique des appuis. Dans la Mine d’Hartebeestfontein, quatre zones fragiles de cisaillement ont été récemment exposées et étudiées. Dans la plupart des cas, elles représentent une rupture des appuis dans les strates moins solides de la paroi suspendue, orientée parallèlement à l’appui, inclinée en direction du chantier d’abattage avec une direction de mouvement consistante avec l’affaissement du toit de la galerie d’abattage. Ces zones de cisaillement sont similaires à celles décrites par Ortlepp2 dans diverses publications: Ce sont essentiellement des zones cisaillement fragiles caractérisées par la présence de « farine de roche » très finement réduite sur une surface évidemment fraîchement cisaillée. L’angle entre la paroi de la zone de cisaillement et les fractures de tension indiquent le sens du cisaillement et l’intersection des fractures de tension avec les parois de la zone de cisaillement définit une forte délinéation perpendiculaire à la direction du glissement. Il est suggéré que l’on se réfère à de telles structures comme des « cisaillements dynamiques fragiles induits par l‘exploitation ». Goldablagerungen im Witwatersrand bestehen überwiegend aus schmalen tabularen Konglomeraten mit Quarzitwirtgestein. Der umfangreiche Abbau dieser Ablagerungen in der Tiefe resultiert in signifikanten Drücken, die auf die Peripherie der tabularen Aushöhlungen wirken. Wo Restpfeiler hergestellt wurden, resultierten exzessive Drücke im dynamischen Versagen der Auflager. In der Hartebeestfontein Grube wurden kürzlich vier spröde Scherzonen freigelegt und untersucht. Zum größten Teil representieren sie Auflagerversagen im Stratum der schwächeren Stollenfirste, parallel zum Auflager verlaufend, in Richtung Abbaustelle abfallend, mit einem gewissen Grad an Verschiebung konsistent mit der Schliessung der Strosse von oben. Diese Scherzonen sind jenen ähnlich, die in den verschiedenen Publikationen von Ortlepp2 beschrieben werden: sie sind im Wesentlichen spröde Scherzonen, charakterisiert durch das Vorhandensein des sehr fein pulverisierten „Gesteinsmehls“ auf einer offensichtlich frisch abgescherten Oberfläche. Der Winkel zwischen der Scherzonenwand und den Bruchverlängerungen deutet die Richtung der Scherung an und die Kreuzung der Bruchverlängerungen mit der Abscherzone grenzt sich gegen eine starke Lineation normal zur Richtung der Lehne ab. Es wird vorgeschlagen, daß diese Strukturen als `vom Abbau verursachte dynamisch spröde Scherungen’ bezeichnet werden.

Jan 1, 2003

By Phil Morriss

During the last 12 months, Sandvik?s Technical Service Group has carried out nine Scoping and Pre-feasibility studies for the application of In-pit crushing and conveying (IPCC) for large mining companies; the majority in conjunction with the Snowden Consulting Group. During these studies several key and recurring drivers have been identified: 1. Mining schedule issues ? there are several issues which crop up repeatedly, including: ?the unnecessary curvature of pit walls, ?very high rates of vertical advance which are (created by schedule optimisers to minimise stripping at all times) which are at the limit of what can be realistically achieved (and which of course make it harder for IPCC to achieve any impact), and ?The allocation of material to semi-mobile systems to maximise the ability for IPCC to be an effective alternative. 2. IPCC productivity issues ? the key issues are the IPCC system operating hours achievable, and the system throughput (both instantaneous and the average). 3. IPCC Risk issues ? there are perceptions about the risks associated with the use of IPCC which are a mix of reality and fiction, but which nonetheless create negativity towards the use of IPCC. In this paper, the authors wish to address specifically the factors affecting the IPCC productivity.

Jan 1, 2008

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

By H. Vuthaluru, O. Kavianipour, C. -Z. Li, N. Suresh, D. Sahu

The paper describes a CFD model developed for 76mm Dense Medium Cyclone (DMC) using Ansys Fluent Software to gain insights into the separation of particles according to their size and density. The simulation used in this paper includes the Reynolds stress model to predict the turbulence inside the cyclone body. An Eulerian-Eulerian multiphase CFD model was applied to model a number of physical aspects such as the separation of coal particles and the segregation of magnetite media solids. The experimental results generated in a laboratory scale DMC were used for the validation purpose and the predicted results of CFD have been validated for the flow splits of water, magnetite and coal. The simulation results obtained from the Eulerian-Eulerian multiphase model revealed that the prediction agreed with experimental results, and matched reasonably well in terms of the mass flow rates of water, magnetite and coal. Furthermore, the partition curve of the DMC when mapped for the separation of - 3.0+0.50 mm size also showed to be in agreement with the experimentally obtained curves. The gravity of cut (SG50), also predicted by the Eulerian-Eulerain multiphase CFD model, was found to be in the vicinity of observed experimental value of SG50. Keywords: Dense medium cyclone, Eulerian-Eulerain multi-phase modelling, computational fluid dynamics, cut gravity (SG50)

Jan 1, 2020

By G. Iabichino, M. Cravero, F. Nacci, L. Rinaldi, L. Vigliero

ABSTRACT: The proposed paper is aimed at analysing the failure of a steep cliff slope that, in the past, was exploited for open pit mining operations. A volume of over 400,000m3 of gneissic aplitic rock was involved in the slope failure. An evaluation of possible failure mechanisms is given, based on a structural description of the rock mass, a mechanical characterisation and on computation methods. The block theory and limit equilibrium techniques for sliding and block toppling were applied and a comparison is given with the result obtained by using DEM models. RESUME: Le document proposé vise l’analyse des mécanismes de rupture d’une falaise qui a été intéressée dans le passé par une mine à ciel ouvert. Un volume supérieur à 400.000 m3 de aplite-gneiss a été concerné par la rupture de la falaise. Le document fournit une évaluation des possibles mécanismes de rupture, basée sur une description structurale de l’amas rocheu, une caractérisation mécanique et des méthodes de calcul numérique. L’analyse a été développée à l’aide de la théorie des blocs et de la technique de l’équilibre limite, soit pour le glissement que pour le basculement des blocs, et une comparaison avec le résultat obtenu par application des modèles DEM a été effectuée. ZUSAMMENFASSUNG: Die vorgeschlagene Arbeit zielt darauf ab, den Einsturz einer steilen Felswand zu analysieren, an der in der Vergangenheit eine Mine im Übertageabbau betrieben wurde. Der Einsturz betraf ein Volumen von über 400000 m3 an Gneis und Aplit. In der Arbeit ist eine Einschätzung des möglichen Mechanismus angegeben, der zum Bruch geführt hat, und sie basiert auf einer strukturellen Beschreibung der Felsmasse, einer mechanischen Charakterisierung sowie auf der Anwendung von Berechnungsmethoden. Angewandt wurden die Blocktheorie und die Methode der Gleichgewichtsgrenze für das Abrutschen und Kippen von Blöcken. Darüber hinaus wird ein Vergleich mit den Ergebnissen angestellt, die unter Verwendung von DEM-Modellen erzielt wurden.

Jan 1, 2003

By C. J. Van Niekerk

When gold plant residues are cycloned for producing a coarse product for backfilling the gold and uranium values are upgraded in the backfill product. Gravity concentration, wet high intensity magnetic separation and froth flotation were investigated as first-stage recovery processes to recover these economic values from backfill prior to placement underground. This paper addresses the recovery of values from flotation concentrates and also details the economic feasibility of a treatment route including flotation, followed by roasting of flotation concentrate to liberate gold entrapped in pyrite and reverse gold leaching of the calcine so produced.

Jan 1, 1988

Determination of mineral composition is of significant importance for the mineral sands industry as this information is required for orebody evaluation, the control of mineral processing plants and the determination of product quality. Mineral processing is made more difficult by the presence of pseudorutile, leucoxene, altered-ilmenite and particle inclusions. The paper investigates the properties of such elements from a single product stream using an MLA approach.

Jan 1, 2007

By M. Steyn

Until 2000, pricing involved profit taking and cost covering combined with limited global published information. Market information was mostly subjective in nature and large resource companies benefited exclusively from aggregated company information and data. The market constituted producers and consumers only. The nineties saw massive cost cutting drives and re-engineering initiatives and this underwrote the structural changes evident in the late 1990s? economy. This supported South African producers on the international FOB cash cost curve, and ensured profitable coal mining operations. As the debate on relative scarcity of fossil fuels ensued, producers and buyers looked to the developing terminal coal market for direction. The much needed direction was provided when the API coal indices were developed and derivative trading was embraced to include financial institutions, trading houses and hedge funds. The liquidity of coal trades increased rapidly and vastly and market information became obtainable on a daily basis. Interpretation of current and future coal prices became available to all market players and contributed to the sophistication of the market that is now able to participate in risk management of prices, capital expenditure and brownfield developments.

Jan 1, 2010

By Z. Szczepanik, D. Milne, K. Kostakis

Abstract This paper presents the results of a series of creep tests performed on a total of nine samples of Lac du Bonnet granite from the Underground Research Laboratory near Pinawa, Canada. Each of the nine samples were subjected to stresses in excess of 80% of the average uniaxial compressive strength of the granite and were maintained at that level of constant loading for periods of time ranging between a few minutes and several months. Acoustic emission was recorded in order to monitor the development and accumulation of brittle microfracture damage in the samples throughout the long-term loading. According to previously published theoretical predictions and field results, as well as similar experimental results of creep tests in granite, samples should fail when loaded to 70% of their UCS for an extended period of time. Six of the samples did not fail when subjected to stresses in excess of 80% of their UCS over periods of several months and were subsequently subjected to uniaxial compression to failure. The average strength of the samples that had previously been subjected to long-term loading were comparable to the average published strength of this rock. Three of the nine samples had increased end confinement and these three samples failed under long term loading. Résumé Cet article présente les résultats d'une série d'essais de fluage de roche exécutés sur neuf échantillons de granite de Lac du Bonnet, du laboratoire souterrain de recherches près de Pinawa, Canada. Chacun des neuf échantillons a été alors soumis aux charges au-dessus de 80% de la résistance à la UCS moyenne du granit et a été maintenu à ce niveau du chargement constant pendant des périodes s'étendant entre quelques minutes et plusieurs mois. L'émission acoustique a été enregistrée pendant les essais afin d'obtenir des indications des dommages pendant le chargement à long terme. Selon des résultats théoriques précédemment édités et les résultats expérimentaux semblables des essais à long terme en granite, échantillons devrait échouer si chargé à 70% de leur UCS pendant une période prolongée. Six des échantillons n'ont pas cassé quant ils ont été soumis aux charges au-dessus de 80% de leur UCS et ont été plus tard soumis à la compression uniaxiale à la rupture. La force moyenne des échantillons qui avaient été précédemment soumis au chargement à long terme étaient comparable à la force éditée moyenne de cette roche. Trois des neuf échantillons avaient augmenté le confinement de fin et ces trois échantillons ont cassé sous le chargement à long terme. Zusammenfassung Dieser Artikel beschreibt die Resultate von Kriechversuchen, die an neun Proben aus dem Lac du Bonnet Granit des "Underground Research Laboratory" bei Pinawa in Kanada durchgeführt wurden. Jede der neun Proben wurde Drücken unterworfen, die mehr als 80% der einaxialen Druckfestigkeit des Granites entsprechen. Diese Drücke wurden für verschiedene Zeitspannen von wenigen Minuten bis zu einigen Monaten auf einem konstanten Niveau gehalten. Während der gesamten Langzeitbelastung wurden akustische Emissionen aufgezeichnet, um die Entwicklung und gesamthafte Beschädigung der Proben durch Sprödbruch aufzuzeichnen. Entsprechend bisher veröffentlichter theoretischer Vorhersagen, Feldversuchen und auch experimentellen Resultaten von Kriechversuchen an Granitproben wäre ein Versagen der Proben zu erwarten gewesen, wenn sie über längere Zeit einer Last von 70% ihrer einaxialen Druckfestigkeit unterworfen werden. Wider Erwarten trat bei sechs der Proben kein Versagen ein, als sie mit über 80% ihrer einaxialen Druckfestigkeit über mehrere Monate belastet wurden; daher wurden sie im Anschluss bei einaxialer Kompression zum Versagen gebracht. Die mittleren Festigkeiten der im Langzeittest verwendeten Proben sind vergleichbar mit den normalerweise für diesen Gesteinstyp angegebenen Festigkeiten. Drei der neun Proben versagten unter der Langzeitbelastung; diese drei Proben hatten eine erhöhte Endflächenreibung.

Jan 1, 2003

By Willem J. Marais

The management of unpaved mine road networks on large surface mines rarely results in optimal road maintenance strategies and minimised total road-user costs. This is ascribed mostly to the complex and dynamic combination of variable road networks and loading and discharge points. In a dynamic mining environment - typically those mines in which production is managed by a centralised truck dispatch system ? there is no guarantee that a particular road maintenance intervention will contribute significantly to reducing total road-user costs or increasing productivity. Most large surface mines operating ultra-heavy mine trucks rely on an integrated on-board diagnostic data collation, communication and GPS-asset location system as a real-time fleet management tool. By extending this system to incorporate a multi-sensor analytical procedure in which specific truck vital signs are monitored and filtered, a road defect can be recognised and a trigger level set to relay the location of defects on the mine haul road to the centralised truck data management system. Previous work established the feasibility of the multi-sensor approach to road defect recognition on large mine haul trucks, and outlined the defect recognition, analytical and modelling issues and system limitations. This paper presents the development of the analytical procedure used as a basis for evaluating the truck on-board data to establish maintenance priorities amongst a network of mine roads. Following an introduction to the system architecture, the results of system field trials are analysed and the results discussed in the light of defect density and traffic volume as the primary variables in an approach to prioritising road maintenance. The paper concludes that by supplementing the existing mine communication and asset management systems, road maintenance can be managed on a near real-time basis and maintenance equipment dispatched to where most immediate benefit will realised from a maintenance intervention on the network, thereby generating the maximum improvement in service and reduction in cost per ton hauled.

Jan 1, 2008

By G. Lyman

The cross-belt sampler is a device that is very widely used even though it has not been ratified by the Standards associations. This paper is concerned with the bias testing of two cross-belt sampler designs against stopped belt samples and a cross-stream cutter at the belt end. The bias analysis is carried out using size distribution as the analyte and conventional t-testing and the Hotelling T squared test, which are compared for their effectiveness. The paper considers the issue of detectable bias and the statistical planning of bias tests.

Jan 1, 2009

By W. K. Osae

A value assessment model which uses deal objectives, financial and non-financial indicators as a guide to assess value creation in mergers and acquisitions. The extent to which post- merger deal objectives are achieved and the potential benefits derived from mining deals that may not necessarily be financial of nature, but which are necessary to sustain and enhance future performance, were considered. The pre-merger and post-merger performances based on some financial indicators that reflect profitability for shareholders were also used. This value assessment model was used to assess four major deals that have occurred in the South African mining industry since 2003 as part of a postgraduate dissertation. In this paper, the Harmony and ARMgold merger is used as an example of how the model can be applied. The model?s relevance and applicability can also serve as a guideline in developing a framework or holistic guideline in assessing whether mining BEE deals in South Africa create value.

Jan 1, 2011

By E. J. Magri

This paper describes a geostatistical study of the relative merits of diamond-saw sampling and conventional chip sampling, using results from experimental work carried out on Randfontein Estates Gold Mine and Western Areas Gold Mine. The diamond-saw sampling procedure is described, and it is concluded that this is a very efficient operation and leads to good-quality sampling that is clearly an improvement over conventional chip sampling. The study principally involved the computation of the errors of estimation of the mea gold value of mining panels for the two sampling methods, revealing that, in the normal production environment, the diamond-saw sampling method is a significant improvement over conventional chip sampling, as evidenced by the reduced estimation errors achieved. The question of optimum sample spacing is discussed, and it is concluded that the required spacing for chip sampling needs to be smaller than for the diamond-saw method.

Jan 1, 1986

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

[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 R. L. Robinson

An analytical framework is formulated to assist mining companies in assessing the relative merits of mineral exploration and acquisition strategies. The anticipated costs, risks, and returns of each strategy are conceptualised using decision trees. Economic criteria - expected net present value, expected return per unit of investment, and the probability of success - for each strategy are derived(from the appropriate decision tree network. Application of the analytical framework is illustrated using the example of a medium-size company in the Canadian base metal sector.

Jan 1, 1987