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By M. Hopf

The use of water-cooled copper components as sidewall elements of submerged arc furnaces and other pyrometallurgical applications has become increasingly common. The high cooling efficiency of copper has made it possible to increase the service life of furnace refractories when compared to conventional refractory linings. However, even the self-healing effect of ?freezing? worn areas of the lining does not necessarily protect the copper coolers against wear or corrosion completely. In order to avoid furnace explosions, various methods have been used to monitor the wear of coolers. Unfortunately, these have not been able consistently to identify localized wear. Thos Begbie (South African) and SAVEWAY (German) jointly developed technology to embed a line sensor into the copper cooler during the casting process. This system allows an exhaustive monitoring of the copper cooler. A SAVELINE sensor is placed inside the copper-cooling panel between the water-cooling passage and the hot face of the panel. The sensor follows the meandering shape of the cooling water channels. In the first instance, the sensor provides analogue information as the thickness of the copper reduces. Secondly, this wear signal will be confirmed by a signal of interruption if the sensor is washed away. Because of the structure of the sensor, a self-diagnosis is possible and indications can be confirmed (double proofed).Subsequent to the manufacture of some test pieces, coolers for a large submerged arc furnace were manufactured. The sensorized coolers have been installed at the intermittent surface (slag line) where the largest amount of corrosion has been encountered. The system has been operating since December 2005 in what is considered one of the largest submerged arc furnaces in South Africa. Keywords: Pyrometallurgy, furnace, copper coolers, freeze lining, monitoring, Saveway

Jan 1, 2006

By Wayne Burmeister, Danie Benade, Louis Meyer, Hugo Joubert

What is not measured cannot be managed. This is true of most things, including a furnace lining. This paper describes a Lining Management System used for this purpose. It provides the operations staff with a management tool to predict long term lining life and acts as a process optimisation tool. It alarms and records upset furnace conditions. Outputs from the system are described as presented through a specially developed software package and interface. It includes vertical and horizontal furnace sections showing estimated isotherms through the lining as well as the furnace bath. It also shows calculated heat flux values, estimated lining wear and the freeze layer profile. A novel three-dimensional display is described which provides the operator with a big picture view of the furnace crucible profile under real time operating conditions. The powerful trending facility for analysing both measured and calculated values is discussed. The required instrumentation hardware as well as the installation thereof is described, with special reference to an electrically insulating thermocouple socket design. Finally feedback is provided on the first year?s performance of the system installed on an open ferrochrome furnace at Assmang Chrome, Machadodorp, South Africa.

Jan 1, 2007

By A. H. Onur

Many factors govern the size and shape of an open pit, and these must be properly understood and used in the short and long-term planning of any open pit and quarrying operation. The importance of each factor will depend on the particular project, but the geology, grade, and localization of mineralization, extent of the deposit, topography, property boundaries, production rates, bench height, pit slopes, road grades, mining costs, and cut-off grades are key elements of open pits. This paper discusses the work done on the above parameters in order to provide an optimal production plan for a limestone quarry and clay deposits that provide raw material for a cement factory in Turkey. Soke cement factory has 1 400 000 tons of clinker capacity and is located on the western part of Turkey, in the province of Aydin. It is one of the largest facilities in the cement sector in terms of capacity, and it has a large advantage over facilities because the location of the factory was chosen to obtain the raw materials necessary for cement production within very short distances. However, the old reserves that supplied limestone to the factory had been reported to have run out, and therefore new limestone reserves in the same province have been investigated over the years by experienced geologists. From surface samples, high MgO content was reported in the neighbourhood of limestone formations with high dolomatization; hence, other alternatives were taken into consideration. One alternative with better chemical composition had been found 24 km away from the factory, but the haulage cost of limestone was unacceptable for the factory due to high diesel prices in Turkey. The maximum allowable MgO content in the pre-mix feed to a rotating furnace is 2.5% MgO content in pre-mix from both limestone and clay deposits. The clay deposits belonging to the cement factory have higher MgO content than the limestone deposit, and therefore this quality problem was taken into consideration first, instead of transporting material from 24 km away. This study gives the details of work done to evaluate both the clay and limestone deposits, statistical analysis performed on core samples taken from drill holes, mathematical modelling for both sites, and most importantly of all, in-pit homogenization work that reduced the pre-mix MgO content. As a result of this study, the profitable limestone quantity has been improved in order to serve the cement factory over a projected 25 additional years without using any material from the close deposit.

Jan 1, 2008

By G. Tranell, L. Kolbeinsen, S. Gaal, J. Safarian

The effect of carbon material properties on the rate of MnO reduction from ferromanganese slag by solid graphite was investigated. A sessile drop technique was used to study the reduction rate of a synthetic slag containing 45 wt% MnO at 1500 and 1600 ºC. Different types of graphite substrates were used and the con-tact angle between slag droplets and substrate were measured in-situ. Moreover, the slag droplet volume during the interaction with the graphite substrates was calculated and normalised. The mathematical relationship between the slag density during the reduction and the normalised slag droplet volumes during the reduction were derived and the MnO reduction curves were then calculated. A method for measuring the slag reactivity of solid carbon was defined and used to qualify the propensity of the different graphites to react with the liquid slag. Some supplementary studies such as manganese evaporation measurement and EPMA analysis for determining the extent of MnO reduction were also carried out. It was observed that there is nota significant difference in the wetting angle of the graphite substrates by the slag, and the wetting is not changed within the temperature range of 1500-1600ºC. However, the changes in the contact angle during the slag reduction at 1600ºC are more than at 1500ºC. The kinetics of MnO reduction is dependent on the type of graphite and it is more dependent on the graphite properties at lower temperatures. On the other hand, the dominant properties of graphite on the reduction rate vary with temperature. A multivariate analysis on the graphite properties and the parameters related to the slag reactivity indicated that the kinetics of MnO reduction is mainly dependent on the temperature, and then on the graphite properties. It was also found that at1500 ºC the surface area and the CO2 reactivity are the most important graphite properties for the slag reduction, suggesting that the reactivity of carbon is rate controlling at 1500 ºC. However, the porosity related parameters are the most important graphite properties at 1600 ºC, suggesting that CO gas desorption is rate controlling at high temperatures.

Jan 1, 2007

By C. Legote

"This paper investigates the conditions leading to the indefinite termination of production in four critical primary panels at an underground coal mining operation, the observed shortcomings in the mining approach, and the proposed strategy to mine through the affected panels. Initial assessment of the abandoned panel conditions indicated time-dependent strata failure,(i.e. bolted roof failure overrunning intersections), which occurred from mere minutes to up to four weeks post-production, with and without prior warning of failure. This prompted the constant re-supporting of back areas, which raised safety and productivity concerns. Investigation of the initial mining conditions revealed that the failures were due to a critical combination of factors, the chief of which was isolated horizontal stress. Other factors that were initially overlooked by the mine (i.e. influence of hydraulic stress, misinterpretation of borehole data), resulted in the conditions being described as abnormal. Remedial actions were determined, and in so doing, a new strategic approach was formulated to thoroughly address all failure concerns. The four panels were explicitly planned to serve as the main intake and return airways for the recently commissioned secondary ventilation shaft, as well as providing access to millions of tons in proven coal reserves. It is thus imperative to mine the panels. A feasibility study showed that the proposed strategy set for implementation would be financially viable. Paper written as project work carried out in partial fulfilment for BEng(Mining Engineering) degree"

Jan 1, 2015

By I. A. Mwamba

Titanium sponge, which is almost pure titanium, is extremely ductile and not easily processed into titanium powder. One method of producing powder is the hydride-dehydride (HDH) process, where titanium sponge is hydrided to form brittle titanium hydride (TiH2). Titanium hydride is easily milled to produce powder and is then dehydrided to form Ti powder. In this work, titanium hydride powder obtained from titanium sponge was used as a starting material for blending and mechanical alloying with elemental powders. Firstly, titanium hydride powder was blended with aluminium elemental powder to produce a homogenized powder, which was then compacted and sintered to produce powder metallurgy compacts. Secondly, titanium hydride powder was mechanically alloyed with aluminium elemental powder and then compacted. The mechanically alloyed powder was characterized in terms of particle size distribution, morphology and microstructure. In both blending and mechanical alloying, the green compacts were characterized by assessing the green density, while the sintered compacts were characterized by their sintered density, microstructure, and hardness. The two processes have resulted in the formation of TiA13 intermetallic compound. It was established that by simple mixing and homogenizing, titanium hydride can be used as a starting material to produce powder metallurgy components in which porosity is a benefit rather than a problem, much akin to metallic foams. From the products obtained in the TiHz-Al system, it appears that titanium hydride can be used as a precursor in mechanical alloying. However, the possible formation of complex hydrides may introduce detrimental properties, and needs to be further investigated. For the production of non-porous components, it would be advisable to dehydrogenate the TiH2 powder before milling i.e. producing titanium powder by the hydride-dehydride (HDH) method. Keywords Mechanical alloying, titanium hydride, titanium aluminide and blending

Jan 1, 2011

By G. O. Oniyide, H. Yilmaz

The South African platinum mines in the Bushveld Complex (BC) have unique features that distinguish them from the gold mines. They have a higher horizontal stress closer to the surface, lower occurrence of seismic activity (caused mainly by pillar failure), and are sited in an area of high geothermal gradient. One of the future challenges of platinum mining is the increasing temperatures as the mining depth increases. High temperatures invariably bring about higher ventilation costs and require different approaches to human factors and ergonomics. Excavation stability would also be another area of concern due to increasing stresses. In this investigation, the effect of temperature on the physical and chemical properties of selected Bushveld rocks (chromitite, pyroxenite, norite, leuconorite, gabbronorite, mottled anorthosite, varitextured anorthosite, granite, and granofels) was studied by means of optical microscopy and scanning electron microscopy using energy-dispersive Xray spectrometry (SEM-EDX). The rock specimens were heated in a temperature-controlled oven a rate of 2°C /min to 50°C, 100°C, and 140°C and kept at temperature for five consecutive days. Samples were allowed to cool to ambient temperature (approximately 20°C) before image capturing. Micrographs of the specimens were taken before and after heat treatment. All the SEM samples were also subjected to heating and cooling on alternate days for ten days in order to observe the effect of repeated heating and cooling on the rocks. The results of the optical microscopy analyses showed minor physical changes in the rocks. The SEM images revealed that cracks initiating at lower temperatures extend with increasing temperature. The chemical analyses showed that the temperature range considered in this research is not high enough to induce changes in the chemical composition of rock samples.

Jan 1, 2016

A reliable laboratory method to characterize the response of free gold particles to flash flotation conditions has been developed. The test has been performed on free milling gold ores as well as synthetic ores, using either a gravity concentrate or gold powder as the gold source, to assess the floatability of gold particles. Trends in free gold flotation kinetics, as well as size and milling effects, were identified for gold recovery based on the different feed types, reagent dosages, and residence times. It was shown that the ultimate recoveries and kinetic trends of gold particles from the gravity concentrate could be enhanced with increased dosage of collector, potassium amyl xanthate. Interestingly, in comparison to gravity-recoverable gold, recovery from pure Au powders was better in collectorless flotation, and cumulative recovery decreased with higher levels of collector addition. Improved coarse particle recovery appeared linked to increased collector additions for both the gravity concentrate and the pure gold powders. In general, coarse gold particles demonstrated slower kinetic rates thaen the fine or intermediate components incomparable tests.

Jan 1, 2015

By Ö. Erdem

The investment decision making process in the insurance and finance industries is affected by new advances such as simulation techniques. These advances have improved the discounted cash flow method (DCF). In DCF, a dynamic and flexible model construction is not possible because it does not consider uncertain conditions. Each project should be evaluated taking into account the related uncertainties because the related uncertainties determine the characterization of the project. Related uncertainties can be processed in dynamic DCF, which is applicable to both financial and non-financial industries with different kind of uncertainties, such as power generation and petroleum projects. The dynamic DCF method can estimate net present value (NPV) while managing related project uncertainties with a simulation method like Monte Carlo Simulation. The simulation method is preferred because its output is unbiased. Therefore, a more realistic financial evaluation of the project can be concluded. In spite of the improvement of dynamic DCF, this project evaluation method is not used frequently in mining industry. However, the mining industry is ideally suited to this concept because it is highly dependent on estimations such as orebody size and ore grade. During the project evaluation stage, these uncertainties can be included with the dynamic DCF method. This study aims to contribute to increasing the usage of this method in mining projects. A copper reserve in Turkey is selected as a case study to apply uncertainty assessment for the evaluation of NPV.

Jan 1, 2012

By L. Hekkala, J. Ollila, J. Keihäs, P. Mäkelä

The Outokumpu Steel Belt Sintering (SBS) Technology is used for manufacturing chromite pellets that are charged into a smelting furnace for ferrochromium production. One of the main elements in successful furnace operation is the control of gas flows inside the furnace, giving improved temperature distribution in the bed during the process. Computational Fluid Dynamics (CFD) gives excellent opportunities for studying these phenomena. An investigation using CFD can be performed relatively fast. For example, implications of different configurations can be studied within a day and an optimum design chosen. Therefore, Outokumpu Technology has developed a Steel Belt Sintering Model (SBSM), which takes advantage of a commercial CFD code. Each main physicochemical event occurring in a steel belt sintering furnace is incorporated independently in the SBS model as a sub-model, enabling every event to be studied separately. The commercial CFD code solves mass, momentum, species and energy equations for determination of the gas flow, composition and temperature. In addition, the Outokumpu SBSM takes into account the moving pellet bed, drying of pellets interms of water content, coke combustion, oxidation and reduction of chromite and the decomposition of carbonates and silicates. During the development of the model, numerous laboratory-scale tests were performed. The sub-models were validated against the laboratory tests. The reliability of the Outokumpu Steel Belt Sintering Model was validated against a pilot-scale batch-sintering furnace by comparing the modelling results against measurements. The aim of this paper is to give a brief presentation of the Outokumpu steel belt sintering model by showing some general modelling examples. Emphasis has been placed on demonstrating some of the main features of the model.

Jan 1, 2007

A201 aluminium alloy is a high strength casting alloy with a nominal composition of Al-4.6Cu-0.3Mg-0.6Ag. It is strengthened by the O(Al2Cu) phase and the ??(Al2Cu) phase during heat treatment. Further strengthening of this alloy system can be obtained through the addition of transition elements, but care must be taken as other elements might have adverse effects on the mechanical properties. The objective of this study is to determine the influence of Mn on the tensile properties of rheo-processed Al-Cu-Mg-Ag alloy A201. ThermoCalc software was used to predict the different phases that can be expected in the alloys, and scanning electron microscopy(SEM) with energy dispersive spectroscopy (EDS) was used to investigate the actual phases that formed. The influence of these phases on tensile properties is quantified. SEM and ThermoCalc revealed that there is an increased amount of the Al20Cu2Mn3 with increasing Mn. The tensile properties showed that high amounts of Mn do have adverse effects on the tensile properties of alloy A201, especially the ductility. Keywords Semi-solid metal (SSM) forming, alloy A201, intermetallics, Al20Cu2Mn3

Jan 1, 2011

By J. C. Carrasco, M. Sánchez, R. Jara, F. Marquez, F. Parada, R. Parra, J. Palacios

In past years, Chile has been the largest copper producer in the world and for 2002 mining represented country average of 10 % of the GDP, accounting for 47 % of the total exportation. As copper sulphides are the main mining resources in the country, the metal is produced using the classical processes of flotation and pyrometallurgical extraction. Seven copper smelter plants, which extends from the northern Atacama desert to the central part of the country produced1,522,000 metric tons of fine copper in 2002, approximately one half of total copper concentrate production, with a notorious environmental impact due to the great amount of slag produced during these extraction steps. In this work, a global characterization of copper pyrometallurgical slags produced and disposed of in Chile and worldwide is done, and the concept of total project development is considered to explain the scopes of the study, recovering different compounds and generating new activities around mining. The presentation is completed with the proposal of various methods and techniques being developed today in a joint project between smelter plants and the University of Concepción, with the support of the Chilean government and mining companies, addressed to generate new materials from copper slag. Recovery of copper, molybdenum, precious metals, silica and iron, that is the most abundant component of the slag, are the goals for this research. Metals, commercial compounds, alloys and different forms of iron oxides for steel industry are proposed products.

Jan 1, 2004

By S Rupprech, T Lund, H Fourie, PH van Rooyen, NM Vegter

Rosh Pinah Zinc Corporation (Pty) Ltd (RPZC) operates an underground mine at Rosh Pinah in southern Namibia producing zinc and lead sulphide concentrates. It currently mines around 0.7 Mtpa run-of-mine ore containing around 6-10% zinc and 1.5-3.5% lead. As part of past exploration and current intensified exploration, a massive continuous low grade ore body was identified which grades at around 3% zinc equivalent. This ore body is near current mining infrastructure and could be amenable to bulk mining methods. In the present paper a concept is presented on how it could be exploited. As a precursor to exploitation of the low grade a number of enhancements are proposed for the current mining operations including: ? shortening load-and-haul distances by extending the conveyor raise further down the mine in a phased manner and back-filling of waste into mined-out stopes; ? use of mobile crushing plant at the crusher tip, and; ? installation of a system to allow scoops to load directly from stopes into ore passes close by combined with truck loops to haul from these ore passes to the crusher tip. To exploit the low grade ore body the following concepts are proposed: ? open stope mining from two areas at a total rate of up to 2 Mtpa; ? underground pre-beneficiation of mined low-grade ore near the stopes using either dense medium separation or X-ray sorting; ? pre-beneficiated tails back-filled to mined-out stopes and; ? pre-beneficiated product transported to surface by linking into proposed run-of-mine conveying system.

Jan 1, 2007

By T. van Heerden

A range of supported gold catalysts was prepared by ion exchange, varying many of the preparation variables, including concentration in the precursor solution, washing procedure, as well as drying and calcination procedures. These catalysts have been characterized extensively. TEM images show essentially the same crystallite size distributions, between 2?5 nm, for almost all catalysts, the only exception being catalysts not washed in ammonia, which did not show any small crystallites. Additional characterization with SEM yielded an interesting discovery. Catalysts that appear identical on the TEM also contain some large crystallites in the range of 50?500 nm. Differences in dispersion due to the drying procedure not seen on the TEM can now be observed. Oxygen chemisorption is being investigated as an additional method to characterize gold based catalysts to complement the typically used electron microscope techniques.

Jan 1, 2012

By D. J. Young

Alloys used at high temperature must resist both creep and corrosion. Design for corrosion resistance is based on the formation of a slow-growing, protective oxide scale by selective oxidation of an appropriate alloy component, usually chromium or aluminium. A successful scale will exclude other corrodents, notably carbon, which can otherwise cause extremely rapid corrosion at high temperatures. Selective oxidation of an alloy component necessarily lowers the concentration of that metal in the alloy subsurface region. Under thermal cycling conditions, mechanical damage to the scale leads to renewed oxide growth and accelerated alloy depletion. Eventually, a point is reached where diffusion of a corrodent into the alloy becomes competitive with the outward diffusion of alloy metal to repair the protective scale. Two examples of alloy failure by carbon attack are considered. In the steam cracking (pyrolysis) process, centrifugally cast tubes of heat-resisting alloy are exposed to a gas stream of hydrocarbon and steam, at a carbon activity of unity. Formation and repair of the surface chromia scale causes alloy depletion, Kirkendall void formation, and subsequent internal precipitation of chromium-rich carbides. Their formation makes chromia scale formation much more difficult, and generates internal stress. Eventually, the tubes fail by creep rupture. In other processes (e.g. steam reforming, heat treatment), synthesis gases are supersaturated with carbon at intermediate temperatures. Once the alloy's protective scale is breached, carbon attacks the depleted substrate. In the case of ferritic alloys, it forms a surface scale of Fe3C. As this scale thickens, the supersaturated carbon precipitates as graphite within its outer regions. The resulting volume expansion causes disintegration of the cementite in a process known as metal dusting. In the case of austenitic alloys, no metal carbide is formed. Instead, carbon dissolves in the depleted metal to diffuse inward and precipitate as graphite within the metal matrix. Again, volume expansion causes disintegration of the alloy, and metal dusting results. Dusting occurs at an extraordinarily rapid rate, and leads to failure by section loss or even penetration.

Jan 1, 2013

By A. Kale

A chlorination pilot plant having capacity to produce 5?10 kg/hr of titanium tetrachloride is in operation at the chlorination facility in Mintek. The bubbling fluid bed chlorination plant can be operated in batch and/or continuous process to study the chlorination kinetics of various feedstocks. The chlorination of titaniferrous ores to produce titanium tetrachloride (TiCl4) was carried out during the commissioning of the pilot plant and also as part of the titanium programme carried out at Mintek. TiCl4 is a basic raw material for producing commercial titanium dioxide pigment and titanium metal. This paper discusses the challenges faced during the commissioning and operation of the chlorination pilot plant. It also discusses the effect on the auxiliary facilities and instrumentation as a result of the harsh operating conditions of +1000°C and use of corrosive gases like chlorine and titanium tetrachloride. It discusses the effect of physico-chemical properties of the titanium tetrachloride and iron chlorides. The effect on the chlorinator refractory lining due to heating and cooling of the chlorinator is also discussed. Besides the special provisions made during the design of the chlorinator, this paper also discusses the operational experience and possible solutions to be implemented in future. Keywords Fluid bed chlorination, titanium ore chlorination, titanium tetrachloride (TiCl4) production using fluid bed technology.

Jan 1, 2011

The paper provides a brief review of a multivariate uniform conditioning and a localized multivariate uniform conditioning (LMUC) technique, and presents a production reconciliation case study based on a porphyry copper-gold deposit in Peru. The reconciliation study compares the longterm LMUC mineral resources model (typical of new mining projects, which are invariably based on drilling data on a relatively large grid) to the corresponding production blast-hole grade control model, as well as the final plant production.

Jan 1, 2014

By N. D. L. Burger

An effective prototype face support system to minimize rockfalls in rockfall-prone mines was developed and patented during a project sponsored by the Mine Health and Safety Council (MHSC). An experimental development model (XDM) roof support unit was developed and evaluated. Mines with rockfall problems in the face areas can use the roof support system to reduce fatalities and injuries in the face area of stopes. The roof support system consists of two similar support units connected to each other via two crank mechanisms. Each unit consists of a headboard supported by a ?wishbone? structure (top and bottom leg). In the first design a threaded bar with struts similar to a scissors jack keeps the legs apart. (In the final version that was field trialed, the threaded bar mechanism was replaced with a hydraulic cylinder). All the components are manufactured from steel. To move the system forward the first support unit is collapsed, the second remaining in the loaded position. The first unit then hangs from the second unit to which it is connected. The first collapsed unit is then manually cranked forward and prestressed. If the required position is still not achieved, the other unit is released and moved forward. The specification for the system was determined and presented at a workshop with industry participants. Different concepts were developed and evaluated against the system specifications. A technology demonstrator was then developed and tested on surface. The technology demonstrator development process included detail design, building and testing of components and subsystems, design reviews and the building and commissioning of the technology demonstrator. The testing of the technology demonstrator was done in a 500-ton hydraulic press, in a mock-up stope and underground. A risk analysis, in which technical, logistical and economic aspects were assessed, was done to determine the critical areas of the system. During the next phase of the project working prototypes were developed for underground tests and evaluation. This process indicated that it was necessary to adjust the system specifications and a redesign was called for. In an iterative process test units were built for purposes of evaluation, specification verification and field trialing. After the successful conclusion of the trials the equipping of a complete production stope started for purposes of integrating the system into the current mining process.

Jan 1, 2008

By P. Turcotte, E. Karampinos, F. Mercier-Langevin

In some underground hard-rock mines, squeezing compressive ground conditions are influenced by the presence of rock foliation and high stress. In these cases, the orientation of the foliation with respect to the drift direction has a considerable impact on the magnitude of the resulting deformation. Irrespective of the reinforcement and support strategy, keeping drives developed sub-parallel to the rock foliation operational is difficult, and often requires excessive rehabilitation during the lifetime of the excavation. This study uses field observations and convergence measurements at the LaRonde and Lapa mines of Agnico Eagle Mines Ltd to provide guidelines of the anticipated squeezing levels at these operations.

Jan 1, 2015

By F. Agterberg

In his 1978 monograph ‘Lognormal-de Wijsian Geostatistics for Ore Evaluation’, Professor Danie Krige emphasized the scale-independence of gold and uranium determinations in the Witwatersrand goldfields. It was later established in nonlinear process theory that the original model of de Wijs used by Krige was the earliest example of a multifractal generated by a multiplicative cascade process. Its end product is an assemblage of chemical element concentration values for blocks that are both lognormally distributed and spatially correlated. Variants of de Wijsian geostatistics had already been used by Professor Georges Matheron to explain Krige’s original formula for the relationship between the block variances as well as permanence of frequency distributions for element concentration in blocks of different sizes. Further extensions of this basic approach are concerned with modelling the three-parameter lognormal distribution, the ‘sampling error’, as well as the ‘nugget effect’ and ‘range’ in variogram modelling. This paper is mainly a review of recent multifractal theory, which throws new light on the original findings by Professor Krige on self-similarity of gold and uranium patterns at different scales for blocks of ore by (a) generalizing the original model of de Wijs to account for random cuts; (b) using an accelerated dispersion model to explain the appearance of a third parameter in the lognormal distribution of Witwatersrand gold determinations; and (c) considering that Krige’s sampling error is caused by shape differences between single ore sections and reef areas.

Jan 1, 2015