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By J. F. Brand, J. C. van Dyk, F. B. Waanders

"Syngas from Africary’s Theunissen underground coal gasification (UCG) project will be used for power production and synthesis of liquid fuels and commodity chemicals. However, some of the coal components, especially condensable water, oils, tars, inorganic trace elements, and a small fraction of fly ash and particulate matter, make their way to the surface via the production well and can cause adverse impacts on downstream processes. Africary’s standard design incorporates a cold gas clean-up system that relies on relatively mature techniques based on highly effective wet scrubbers and acid gas removal (AGR) systems such as Rectisol®, but with the downside of low energy efficiency and waste water generation. In this paper, novel technologies for removing contaminants and species separation from the hot (T > 300°C) raw syngas are compared. Comparisons are made between supersonic gas separation (SGS), Ranque–Hilsch vortex tube (RHVT), vortex gradient separation (VGS), and inertia vacuum filtering (IVF), and a vortex-based gas separation concept is proposed for UCG applications. IntroductionImpurities in gasification feedstock (coal, biomass, waste, etc.), especially sulphur, nitrogen, chlorine, and inorganic mineral matter, often end up in the syngas and can cause adverse impacts on downstream processes. Africary’s standard design incorporates a cold gas clean-up system that relies on relatively mature techniques based on highly effective wet scrubbers and acid gas removal (AGR) systems such as RectisolR, SelexolR or aMDEAR; but with the downside of low energy efficiency and waste water generation.Hot (T > 300°C) gas clean-up technologies are attractive because they avoid cooling and reheating of the syngas stream. Some available warm gas cleaning technologies include traditional particulate removal devices such as cyclones, candle filters, membranes, and molecular sieves. The warm gas desulphurization process technology developed by RTI LLC (2018) requires hot syngas to remove sulphur and has become commercially ready. Many other hot gas cleanup systems are still under development, given the technical difficulties caused by extreme environmental and operating conditions."

Jan 1, 2018

By K. L. Morton

Groundwater and associated pore pressure represent elements that can have a negative impact on surface mining and slope stability. Groundwater flow and deformation within a slope influence each other. An increase in pore pressure will result in a decrease of effective stress; and conversely, if the pore pressure decreases, the effective stress increases. Slope analysis and slope design calculations require good information on pore pressure distribution around an open pit excavation. Until recently very little pore pressure data were available and assumptions had to be used. Location and design of measuring points depend on geological and structural setting, geotechnical domains and practicality. Good planning and the use of sensitive point piezometers to measure in situ pore pressures means that real-time data can be collected and used for the construction of flow nets, the determination of pore pressure distribution around an open pit mine, the validation of the dewatering/depressurization requirements, the calculation of the efficiency of the dewatering system and finally the use of pore pressure data in slope stability analysis. The recommended layout for a monitoring system, types and design of piezometers, data collection and use of the pore pressure data are presented.

Jan 1, 2008

By J. H. Zietsman, M. W. Erwee, P. J. A. Bezuidenhout, Q. G. Reynolds

"Pyrometallurgical furnaces are tapped through tap-holes that are opened with drills and oxygen lances. The lance is often used on its own or as the last step of opening the tap-hole. Interaction of oxygen with molten material inside the tap-hole can occur, and is a phenomenon that is not well understood. As part of a study that focuses on the effect of lancing on flow inside and around the furnace tap-hole, a cold-model validation was done. The validation study focuses on validating the MULTIPHASEINTERFOAM multiphase flow solver in OpenFOAM® for the problem involved. The sensitivity of the model to different materials properties (viscosity and density in particular) is presented with both cold models and the results from flow simulations in OpenFOAM®. IntroductionMany pyrometallurgical operations are carried out in furnaces where molten material accumulates continuously. Once enough material has accumulated and is ready to be removed from the furnace, material is tapped through one or more tap-holes in the furnace. Tap-holes differ significantly in both geometry and materials of construction, depending on the process involved – examples of different types of tap-hole configurations can be found in, for example, Nelson and Hundermark (2014). Tapholes all share one common feature: they are high, wear areas of the furnace. Molten material at high temperature flows through these areas, after which the tap-hole is sealed, usually using tap-hole clay. The purpose of the tap-hole clay is to harden inside the tap-hole and seal it until the next tap.Once ready to tap, a pneumatic drill and/or oxygen lance is used to open the tap-hole. The extent of lancing a furnace tap-hole depends strongly on the type of furnace. In, for example, many blast furnace operations lancing is limited as much as possible, and done only if drilling was not effective. In other operations, such as on small-scale pilot furnaces with short tap-holes, only lancing is used to open the tap-hole."

Jun 1, 2019

By P. J. Knottenbelt

Outcomes from a workshop organized through the SAIMM revealed that the minerals and metals industry must develop its ?Engineering Team? if it is to continue to meet the challenges of globalization. The very economy of the country is largely dependent on a competitive and stable engineering team within the minerals and metals sector. With the Chamber of Mines (COM) passing on its education and training initiatives to the industry, the professional bodies like SAIMM must (despite meagre resources) continue the good work done through the COM in the past. The workshop highlighted recruitment and selection, further/higher education, socialization and initial training, deployment and retention and continuing education as priority areas. These are further detailed in this report. Office Bearers have considered the outcomes and the areas where the Institute should or should not be involved have been stated.

Jan 1, 2002

By J. A. Luckmann

"SynopsisThe purpose of this paper is to introduce an innovative approach to risk management in surface mining operations, namely, positive risk. Traditionally, risk management focused on mitigating losses (negative). Positive risk, on the contrary, reverses the approach and focuses on exploiting a project’s inherent benefits (positive).The inability to accurately determine project objectives during the project planning phase and the failure to achieve those objectives during the execution phase is a major problem for any project management in the mining environment.The advance of computer aided design models for mine planning enables mining engineers to examine various options within a very short time. Employing positive risk management combined with drivers-based risk management when evaluating these options provides an ideal opportunity to investigate areas for improving the mining project’s profits. Furthermore, harnessing positive risk returns during the planning phase contributes immensely to the successful achievement of project objectives.Mining has inherent business risks, which can appear overwhelming when considering the risks associated with a mining project schedule, cost, and safety or resources, etc. The question is – how to manage risks in a surface mining environment, and what process methodologies, work methods, processes, and standards should be used when considering the surface mining risks. Applying the principles of positive risk management to manage surface mining risks is not only relevant, but definitely beneficial to mining projects and to the mining industry as a whole.It would be beneficial for risk managers and risk professionals to understand the roles of positive risk ‘drivers’, also known as ‘propitious attractors’. Identifying, analysing, estimating, and understanding the propitious attractors, their behaviour and their influence on project risk events helps considerably during the planning and execution phases. The theoretical and practical knowledge of both sides of the risk – the downside risk (negative risk) and upside risk (positive risk) – can add substantial value to any organization when downside risk is adequately mitigated and upside risk is beneficially exploited."

Jan 1, 2015

By A. P. Squelch

The high incidence of accidents and fatalities in the South African mining industry, in particular those associated with falls of ground, is often attributed to ineffective and/or inappropriate training methods and material. Recently introduced mine health and safety legislation in South Africa also requires that all mine workers receive appropriate and effective training to enable them to operate safely in their given mining environment. There can, therefore, be no doubt that methods to provide effective training, in particular safety related training, are urgently required in the South African mining industry. In the search for alternative and improved training approaches, attention has fallen on virtual reality (VR) technology as a possible solution. VR has found acceptance in a number of industries as an effective method of training for a variety of work place activities, including those of a safety related nature. VR has successfully been applied in a number of industries to improve the effectiveness of safety and hazard awareness training. The CSIR: Division of Mining Technology (CSIR Miningtek), in conjunction with the Safety in Mines Research Advisory Committee (SIMRAC), therefore evaluated the potential of VR to be used as a training medium in the South African gold and platinum mining industry. Aspects of the evaluation included an assessment of the technical capability of VR to represent a typical underground mining environment with sufficient realism and the relevance of the VR training concept for a largely illiterate workforce. For these purposes, a prototype PC-based VR hazard awareness training simulator has been developed by CSIR Miningtek, and a series of evaluation sessions conducted at a typical deep level gold mine. The conclusion from this evaluation work is that virtual reality technology has the potential to provide effective training systems that are relevant to the South African mining industry. Keywords: Virtual reality, mine training, safety training.

Jan 1, 2001

By A. W. Bester

Paper written on project work carried out in partial fulfilment of B. Eng. (Mining Eng.) Cullinan Diamond Mine currently handles 3.2 million tons of run of ore per annum. This is done by means of an underground train system, which is located at 763 metre level. Four trains, one in each quarter of the pipe, collect ore from passes and transport it to centrally located tips in the north and south of the pipe. The ore is then split into coarse and fine fractions. The coarse fraction proceeds to the primary crushers in the north and south. Historically, mining has been performed in such a manner that an equal amount of ore has reported to each quarter of the pipe. However, the tonnage profile of the mine will change such that the ore will no longer be split equally. For approximately five years the majority of ore will report to the east and thereafter most of the ore will report to the western portion of the mine. This will continue for the remainder of the current infrastructure level?s operational life. Coupled with this is the fact that the mine is aiming to increase its annual production to 3.8 million tons. The result is that the current ground handling system cannot accommodate the additional tons and therefore alternative ground handling options have been investigated. The continued existence of Cullinan Diamond Mine relies on finding a system that can economically handle the additional tonnage. Three options were investigated. Firstly, a train option, which would be an upgrade of the current system, was investigated. Two truck options were also investigated, the first of which was a conventional truck option. The second truck option was more interesting and involved an unfamiliar Combi truck system. The truck options were investigated primarily due to the fact that the block height of the BA West (a new production block) can be increased by 15 meters if a truck option is decided upon. This would create a significant increase in revenue for the BA West project. Each of the options was assessed in terms of its physical and financial feasibility. In terms of the physical constraints, it was found that all three systems could work. Detailed financial analysis indicated that either of the two truck options would be a suitable solution. However, due to the limited information regarding the Combi truck option, it should be further investigated. This applies particularly to the actual running and maintenance costs for the equipment.

Jan 1, 2005

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

By G. A. Harrison

The introduction of extra low profile (XLP) mechanized equipment within Anglo Platinum is aligned with the overall New Mining Technologies strategy to focus on continuing modernization of our mining operations` incorporating injury-free production and cost-effective mining technologies. The method allows for the introduction of a suite of ultra-low profile equipment in narrow reef (1.2 m) stoping operations. For the first time it is now possible to achieve total trackless mechanization at these widths and indications are that XLP mining has the potential to add more value when benchmarked with conventional mining and low profile (1.8 m) room and pillar methods. Various mine layouts were tested at different sites within Anglo Platinum and the XLP breast mining layout proved to be the most effective. This paper describes the results of the trials at Waterval Shaft and concludes with recommendations on our future strategy on implementation of XLP technology within Anglo Platinum.

Jan 1, 2006

This paper describes a simple finite element (FE) modelling approach which leads to the computation of seismic energy release rate (ERR) and strain energy storage rate (ESR) which result from mining. The concept of critical strain energy is introduced as a means to help evaluate the strainburst potential in mine structures. A new, energy-based, burst potential index (BPI) is proposed. The use of ERR, ESR and BPI is demonstrated by a cut-and-fill stope case study. The merits of using such energy parameters in the interpretation and analysis of strainburst phenomena are discussed. While the study gives promising results, site-specific back analyses would be required to first calibrate the model and fit it with the local mine conditions, before it can be adopted as a routine design tool.

Jan 1, 1999

By J. Gunaselvam

This article deals with an investigation into the specification and use of appropriate seating systems to reduce whole-body vibration (WBV) exposure in typical vehicles used in the SA mining industry. The EU Directive EU/44/2002 to be legislated in 2005 in European countries, provides legal and economic motivation for this project. The criteria for seat selection can be condensed to the requirements in the directive, which mandates an action level of 0.5 m/s2and a vibration exposure limit of 1.15 m/s2 for an equivalent 8-hour daily exposure period. As part of this study six suspension seats, which the manufacturers claim satisfy the requirements in ISO 70966, were tested to determine the most suitable seat for an articulated dump truck. Six test subjects, three ?light? and three ?heavy? as specified in ISO 70966, were used to estimate the seat transmissibility functions in the vertical direction of the six different suspension seats. Transmissibility functions were measured in the laboratory with two excitation levels of 1 m/s2 and 2 m/s2 r.m.s. in the 0.5?30 Hz frequency range, as well as one spectrum approximating the EM5 spectral class. SEAT values were calculated for road vibration data measured on a typical articulated dump truck. A set of seat selection guidelines that can be followed by vehicle manufacturers and suppliers, procurement officers and and the technical staff on a mine is proposed in this article. It is recommended that additional studies of the use and operating conditions of seating systems in the SA industry, as well as an epidemiological survey be commissioned to gather additional information on this subject. Nomenclature ADT Articulated dump truck DSTF Dynamic seat testing facility EM1 Frequency spectra associated with earth moving equipment (?articulated or rigid frame dumper?) according to ISO 7096 EU European Union ISO International Standards Organisation PSD Power spectral density r.m.s .Root mean square SEAT Seat effective amplitude transmissibility WBV Whole-body vibration

Jan 1, 2005

By V. Yahorava

Resin-in-pulp (RIP) technology has recently often been considered for the direct recovery of base metals and uranium from dense pulps. Implementation of RIP will eliminate the requirement for any solid-liquid separation downstream of leaching and has the potential to combine the recovery and purification steps, hence reducing both capital and operating costs. The recovery of the valuable metal is expected to be higher when RIP is used, especially where the leached solids are difficult to settle or filter, and to wash. The main concerns about the use of RIP for uranium recovery from dense pulps are the impact of silica on the resin?s metallurgical performance and the operating costs that would be associated with resin loss. Although a number of resin manufacturers have been developing much improved RIP-grade resins, it is critical that the most cost-effective resin be selected. Mintek currently is doing a significant amount of work on silica fouling of RIP-grade strong-base resins in acidic leach liquors and the effect it has on the performance of the resin, including its durability. This paper describes the results of the test work done on silica fouling and its impact on plant design input data. Resin durability test work was done using various laboratory techniques, but durability was also evaluated on a relatively large scale using actual pumps, screens, and mechanical agitation. Based on the results generated, a preliminary economical evaluation was done to estimate the impact of resin loss on the overall economic viability of a specific application. Keywords: resin-in-pulp, silica fouling, resin loss, equilibrium, kinetics, elution, durability, mechanical strength, resistance to attrition.

Jan 1, 2009

By D. D. Ndenguma

This investigation compares the results from an experimental and numerical study of air flow in a scaled-down underground coal mine model. This was done in order to determine if numerical analysis can be relied upon when searching for ventilation solutions to control high concentration of coal dust and methane gas in underground coal mines. Steady state analyses were used to identify flow patterns and recirculation regions within the mining section while transient state analyses were used to determine the time taken to extract the initial air from the model. The agreement between the experimental and numerical results indicates that numerical modelling is useful in this regard. The study went further to devise a method of determining the optimum position of the jet fan that is responsible for mine-gas dilution at different stages of mining.

Jan 1, 2014

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 B. Erdem

This article introduces a computer model, which emphasizes panel design for draglines deployed in direct side-casting mode. The study covers flat and inclined coal-seam conditions with the dragline operating along the strike-line. Two casting methods are embedded in the model: material is placed in the open set adjacent to the one on which the dragline is located (the DNS method) and material is placed in the open set adjacent to the one the dragline excavates (the DND method). While in the first method the unproductive walking time is reduced as the set is enlarged, in the second method the cycle time is lessened as the dragline swings along an acute angle. The side-casting model is shaped so as to provide several panel configurations instead of a single one to conform to the characteristics for an opencast mine. This is achieved by assigning the pit width an interval of values ranging from a minimum to a maximum. The model includes solutions to other critical design parameters such as: set length, swing angles at key cut and main cut positions, and required dragline reach at key cut and main cut positions. The model outcomes reveal the following: the stripping operation is largely affected when the coal-seam is inclined. The downhill spoiling mode should be applied wherever possible. The DNS pattern allows wider pit width intervals as well as longer sets and longer reaches.

Jan 1, 2004

This paper characterizes the copper cycle, that is, the flows of copper entering and leaving the African economy over a one-year period (1994). The major flows over the entire life-cycle of copper are examined; these include production (mining, milling and refining), fabrication of semi-products and manufacturing of finished products, use, and the waste management system. The results reveal that substantial amounts of copper (of order705 Gg/yr) are mined in Africa; of that amount, about 70 per cent is exported following processing, 18 per cent is utilized by African fabricators, and 12 per cent is discarded. The flows of copper products from African fabricators and product imports from other continents exceed product discards by large amounts. This difference, about 0.25 kg Cu/capita/yr on average, is added to in-use stock, largely as wire, plumbing tube, and in electronics. Some 65 per cent of the copper in discard flows is contained in electrical and electronic products, where it is relatively easy to collect and process for reuse. About a third of the copper discard flows known is recycled. The actual percentage is almost certainly higher because of informal (and unrecorded) recycling. Much of the remaining discarded copper is diluted into the municipal waste stream, where recovery and recycling are probably not economically justified. Keywords: material flow analysis, resource management, material budgets, copper, stocks and flows, systems analysis, Africa, developing country

Jan 1, 2003

Poorly designed sampling protocols generally result in high project risk by artificially increasing grade variability (ie the nugget effect). Sample collection, preparation and assay protocols that suit the ore type, together with QA/QC systems, will reduce this risk. All reporting codes (eg JORC, 2004) require the Competent Person to consider the quality and implication of sampling and assaying programs. High sampling errors beget higher project uncertainty; despite this fact, sampling does not receive the attention it deserves. The case studies presented show that many sampling issues frequently go unrecognised or unaddressed, resulting in poor project decisions during exploration through to feasibility and production. The overall conclusion is that correct sampling is critical to mining project success and that there is often a need for its optimisation.

Jan 1, 2007

By P. Wittke-Gatterman

ABSTRACT: A three dimensional constitutive law for swelling rock is presented. It can be applied to the osmotic swelling of mudstone as well as to the swelling of rocks containing anhydrite. It describes the development of time-dependent strains and stresses due to swelling considering elastic and viskoplastic behaviour. Furthermore an anisotropic swelling behaviour can be considered. This constitutive model was implemented within a numerical computation program according to the finite element method and calibrated on the basis of the results of measurements in the investigation drift of the Freudenstein tunnel which is completely located in the unleached Gypsum Keuper. A parameter combination could be found which results in a good agreement between numerical solutions and results of measurements. Therewith an analysis procedure which enables the design of tunnels in swelling rock is available. ZUSAMMENFASSUNG: Im vorliegenden Beitrag wird ein dreidimensionales Quellgesetz vorgestellt, das nach derzeitigem Kenntnisstand sowohl auf das osmotische Quellen von Tonsteinen als auch auf das Quellen anhydrithaltiger Ton- beziehungsweise Schluffsteine anwendbar ist. Das Stoffgesetz wurde in ein Finite-Elemente-Programm implementiert und anhand von Meßergebnissen des im unausgelaugten Gipskeuper liegenden Untersuchungsstollens des Freudensteintunnels kalibriert. Es ist gelungen, eine Kennwertkombination zu finden, mit der alle Meßergebnisse gut beschrieben werden können. Damit steht ein Bemessungsverfahren für Tunnel in quellfähigem Gebirge zur Verfügung. RÉSUMÉ: Dans l'article présent un loi de gonflement à trois dimensions est présenté, qui peut être appliqué aussi bien au gonflement osmotique de l'argile compactée q'au gonflement de l'argile compactée ou du limon compacté contenant de l'anhydrite. Le loi de comportement était implémenté dans un programme numérique d'éléments finis et calibré avec des résultats de mesures de la galerie de recherche du tunnel de Freudenstein, situé dans le Keuper de gypse non lessivé. On est réussi à trouver une combinaison de paramètres avec laquelle tous les résultats de mesures peuvent être bien décrits. Par ce moyen, une méthode de dimensionnement existe pour des tunnels dans de la roche capable de gonfler.

Jan 1, 2003

By N. Lock

"Despite the pre-eminence of the Jwaneng Diamond Mine as the world’s richest diamond mine, the discovery story has long been clouded in mystery. This is the 45-year old untold story of the Jwaneng discovery and contemporaneous Bechuanaland/Botswana political and socioeconomic history. Diamond exploration by De Beers in Bechuanaland began in 1955, with the first true kimberlite discovery near Letlhakane in 1967, before Clifford’s Rule was applied and before the use of indicator mineral chemistry. Surface deflation soil sampling and bioturbation by termites was the foundation for exploration into the Kalahari. The 1962 reconnaissance programme south of Jwaneng had failed to make any discoveries. Improved sampling methods were applied to the Kalaharicovered areas in 1969 and positive results were received by year-end. The Whateley’s Wish percussion drill-hole in December 1972 was confirmed as Jwaneng 2424D/K2 with drill core in early 1973. Jumper drills were required to penetrate the Kalahari sand cover. Diamond resources were demonstrated despite multiple technical problems. IntroductionThe Jwaneng Diamond Mine is, by value, the world’s richest diamond mine. Harry Oppenheimer is quoted as saying that Jwaneng is ‘the most important primary deposit found anywhere in the world since the discovery at Kimberley more than a century ago.’ (Taylor III, 1982) The mine opened in 1982 after some nine years of evaluation and construction since discovery in February 1973. Debswana (2017) states that 2015 production was 7.87 Mt of ore from which 10.408 million carats were recovered at a grade of 132 carats per 100 t (cpht). Although the value is not reported, it was noted that Jwaneng contributes 60–70% of Debswana’s total revenue from all mines, including Orapa, Damtshaa, and Letlhakane (Debswana, 2017)."

Feb 1, 2019

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