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Thesis (M.Sc.(Engineering))--University of the Witwatersrand, Faculty of Engineering, 1951.

Thesis (D.Sc.)--University of the Witwatersrand, 1963

We consider several problems motivated by issues faced in the mining industry. In recent years, it has become clear that mines have substantial tail risk in the form of environmental disasters, and this tail risk is not incorporated into common pricing and risk models. However, data sets of the extremal climate behavior that drive this risk are very small, and generally inadequate for properly estimating the tail behavior. We propose a data-driven methodology that comes up with reasonable worst-case scenarios, given the data size constraints, and we incorporate this into a real options based model for the valuation of mines. We propose several different iterations of the model, to allow the end-user to choose the degree to which they wish to specify the financial consequences of the disaster scenario. Next, in order to perform a risk analysis on a portfolio of mines, we propose a method of estimating the correlation structure of high-dimensional max-stable processes. Using the techniques of (Liu Et al, 2017) to map the relationship between normal correlations and max-stable correlations, we can then use techniques inspired by (Bickel et al, 2008, Liu et al, 2014, Rothman et al, 2009) to estimate the underlying correlation matrix, while preserving a sparse, positive-definite structure. The correlation matrices are then used in the calculation of model-robust risk metrics (VaR, CVAR) using the the Sample-Out-of-Sample methodology (Blanchet and Kang, 2017). We conclude with several new techniques that were developed in the field of robust performance analysis, that while not directly applied to mining, were motivated by our studies into distributionally robust optimization in order to address these problems.

Sampling is an error generating process and these errors should be reduced to a minimum if an accurate ore reserve estimation is to be made from the sample values. Error in sampling can arise from the sampling procedure as well as where and how each sample is taken from the deposit . Sampling procedure involves sample collection, sample reduction and analysis, and the error from each of these three stages has an equal influence on the total error of the process. Error due to sampling procedure should be identified and eliminated at an early stage in the evaluation programme. An ore deposit should be subdivided into sampling strata along geological boundaries, and once these boundaries have been established they should be adhered to for the evaluation programme. The sampling of each stratum depends on the small-scale structures in which the grade is distributed, and this distribution in relation to sample size controls sample variance, sample bias and the volume of influence of each sample. Cluster sampling can be used where an impractically large sample is necessary to reduce sample variance or increase the volume of influence of samples. Sample bias can be reduced by composing a large number of small samples . Sampling patterns should be designed with reference to the volumes of influence of samples, and in favourable geology, geostatistical or statistical techniques can be used to predict the precision of an ore reserve estimation 1n terms of the number of samples taken. Different are deposits have different sampling characteristics and problems which can be directly related to the geology of the mineralization. If geology is disregarded when sampling an are deposit, an evaluation programme cannot claim to give an accurate estimate of the ore reserves .

A research report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science, / In 2004, the Department of Minerals and Energy (DME, predecessor to the current Department of Mineral Resources - DMR) published a guideline to calculate the amount that a mining right holder would require for financial provision at mine closure. This research report reviews the guideline, specifically focussing on the “rules-based approach” for determining the quantum of financial provision. Some authors have recorded the misapplication of this guideline in practice and their research supports a conclusion that the guideline does not provide adequately for the real costs of mine closure. This research report makes a comparison between the DME guideline master rates for mine closure costs and actual tendered prices for those same elements of mine closure in the period from 2009 – 2016. The analysis of the actual tender prices for the various master- and component rates in comparison with the DME guideline rates delivered mixed results. While the actual tender values exceeded the guideline master rates in most cases, there were notable exceptions where the actual tender results lagged the master rates. The data obtained from the actual tender prices for mine rehabilitation projects by a third party suggests that the use of CPI to escalate mine rehabilitation costs was very quickly overtaken in reality by higher annual costs and rate increases for most of the DME guideline master rates that relate to surface mining. It means that the DME guideline master rates were not reflective of actual rehabilitation costs by the time that the use of the DME guideline was superseded by the publication of new regulations by the Department of Environmental Affairs in November 2017. Whilst no perfectly linear and distinct relationship could be deduced, the results broadly support the findings of several authors that the actual costs to rehabilitate a mine are much more than the DME guideline document would lead a mine to provide for. The application of a rules-based approach remains an exercise mired in controversy and with many potential inaccuracies. The new NEMA regulations for financial provision completely negate the need for a guideline and relevant State Departments and mining companies alike are consequently dependant on third parties to prepare closure cost estimates. / E.R. 2019

A project report submitted to the Faculty of Engineering, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 1997. / Due to the extreme costs of establishing new shaft systems in Witwatersrand gold mines it is essential that the resource estimation is optimised, The result of poor Of sub-optimal estimation could be catastrophic even.to the largest of mining companies. This project examines the application of Compound Lognormal Distribution theory and shows the advantages of this distribution model over more traditional models, for the Carbon Leader Reef. The incorporation of information from mined out areas of a deposit in resource estimation is demonstrated. The critical role played by accurate geological modelling is highlighted. The process of Macro Co-Kriging in conjunction with Compound Lognormal Theory is discussed in detail and is shown to be a more accurate estimation technique than traditional techniques using Lognormal theory. Finally the use of the Macro Co-kriged limits are shown to be useful in the classification of Mineral Resources. / AC2017

A research report in partial fulfilment of the requirements for the degree of Masters of Science in Engineering submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, 2019 / Mining operations are by nature capital intensive. Historically mining companies have in general been poor at capital allocation decision making, which translated in poor returns on capital invested and impairments. Better capital allocation strategies are required for mining companies to unlock more value from invested capital. This research focussed on identifying factors to consider during the capital allocation decision-making process that can potentially unlock value in mineral projects. The research included a review of capital allocation decisions and performance of five mining companies from 2001 to 2017. This period covers one full commodity price cycle to determine the impact of the prevailing commodity price on capital allocation decisions. Through analysis of the historical capital allocation of the five mining companies the research aimed to test if it is possible to unlock value by allocating capital in a counter cyclical approach compared to the prevailing commodity prices. From the analysis of the historical capital allocation decisions made by five mining companies a number of common trends were identified. The research found that during a period of higher commodity prices, mining companies focussed primarily on volume growth. This is confirmed by a strong correlation between the value of capital approvals and the average commodity prices of the basket of minerals produced. The higher allocation of capital towards growth initiatives, such as expansionary capital and acquisitions, have in a number of instances resulted in significant capital over-expenditures in projects. The over-expenditures have directly contributed to a number of impairment charges made by the diversified mining companies during a declining commodity price cycle. Conversely, during periods of declining commodity prices mining companies focused on rationalisation of mining projects and operations and disposal of assets that do not meet minimum investment criteria. During these periods capital allocation towards growth projects were reduced, with most capital allocated to reduction of net debt on the balance sheet. The research found a common trend of higher capital allocation towards growth projects during historical high commodity prices, and during subsequent lower commodity prices capital allocation was directed towards reduction of net debt and disposal of loss making assets. Results from the research conducted on the five mining companies indicated that there may be correlation between return on investment and the timing of the capital investment in relation to the position on the commodity price cycle at the time of the investment. However, the results obtained for the five mining companies were influenced by operational returns from existing operations, which makes it difficult to determine returns realised on incremental capital expenditures. From the results obtained from the analysis the following recommendations are made for a capital allocation strategy to increase the probability of unlocking value over the long term. Firstly, a company should have a clear capital allocation framework that is guided by the mining company’s strategic objectives. The framework should clearly indicate the hierarchy of importance when allocating capital to different areas. Secondly the company should clearly identify the minimum investment criteria to be met before capital is allocated to an investment. Lastly the mining company should aim to consistently invest capital throughout the commodity price cycle, and be cautious of over allocating capital towards growth projects during periods of high commodity prices. / TL (2020)

A research report submitted to the Faculty of Engineering and Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering specialising in Mineral Economics, Johannesburg 2018 / South Africa‘s economic growth has been declining since 2009. Mining contributes to economic growth in various ways, including foreign earnings and taxes. It contributes to the economy through direct, indirect and quasi taxes. Quasi taxes are near taxes that are imposed on mining projects in the national interests of protecting the environment and the social, cultural and economic needs of local communities. They have implications on tax design, they are often significant and are regulated by various Acts. They include contribution to local communities, foreign exchange control, environmental taxes, performance bonds and government equity in mining projects. Because of their implication on tax design and related aspects, the research was conducted to assess the extent which they contribute to the economic growth of South Africa, to assess how the country can enhance the effectiveness of quasi taxes on economic growth, to assess whether the country has a good mining tax regime, to assess their impact on mining investments decisions and planning. The research involved a literature survey for qualitative and quantitative data from various sources. These were various books, journals and others publications. It used an internet-based method of data collection and hard copies from various institutions, including libraries. Annual reports of three mining companies that are mining in South Africa and are listed on the Johannesburg Stock Exchange, were randomly sampled and assessed, to gain an understanding of the manner in which these taxes contribute to economic growth. The work also used a Discounted Cash Flow model to assess the impacts of quasi taxes on mine planning and mine investments. It further assessed the extent to which quasi taxes can be applied to the determinants of economic growth. The findings are that quasi taxes contributed 0,77 percent (%) in terms of mining exports earnings per unit of GDP created, between the years 2007 to 2016 and R2 billion to community development in the year 2015. It was found that transparency and lack of clarity are some of the impediments to the contribution of quasi taxes to economic growth. A good mining tax regime is required in order to reap maximum benefit from these taxes. The country must also use Community Engagement Plans to manage expectations, to explain the level of benefit from mining, for clarity and transparency between interested and affected parties. Quasi taxes affect mine planning and investment decisions. Quasi taxes must also be used for clustered and sustainable projects in the form of the Public Private Partnership approach, in line with the determinants of economic growth. / XL2019

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science in Mining Engineering. February, 2016 / Mineral Resource estimation provides an assessment of the quantity, quality, shape and grade distribution of a mineralised deposit. The resource estimation process involves; the assessment of data available, creation of geological and/or grade models for the deposit, statistical and geostatistical analyses of the data, as well as determination of the appropriate grade interpolation methods. In the grade estimation process, grades are interpolated/extrapolated into a two or three – dimensional resource block model of a deposit. The process uses a search volume ellipsoid, centred on each block, to select samples used for estimation. Traditionally, a global orientated search ellipsoid is used during the estimation process. An improvement in the estimation process can be achieved if the direction and continuity of mineralisation is acknowledged by aligning the search ellipsoid accordingly. The misalignment of the search ellipsoid by just a few degrees can impact the estimation results. Representing grade continuity in undulating and folded structures can be a challenge to correct grade estimation. One solution to this problem is to apply the method of Dynamic Anisotropy in the estimation process. This method allows for the anisotropy rotation angles defining the search ellipsoid and variogram model, to directly follow the trend of the mineralisation for each cell within a block model. This research report will describe the application of Dynamic Anisotropy to a slightly undulating area which lies on a gently folded limb of a syncline at Driefontein gold mine and where Ordinary Kriging is used as the method of estimation. In addition, the optimal Dynamic Anisotropy resolution that will provide an improvement in grade estimates will be determined. This will be achieved by executing the estimation process on various block model grid sizes. The geostatistical literature research carried out for this research report highlights the importance of Dynamic Anisotropy in resource estimation. Through the application and analysis on a real-life dataset, this research report will put theories and opinions about Dynamic Anisotropy to the test.