In the last decade mineable oil sands production in Canada has grown rapidly. Constraints on the planning and design processes employed by surface mining oil sands operations vary in distinct ways from other commodities mined by both hard and soft rock open pit methods. The unique waste handling needs, including tailings disposal, of contemporary oil sands mining requires specific planning considerations. It is the purpose of this research to analyze and document a conventional hard rock, metal mine planning system, and contrast this with the unconventional mine planning system used by oil sands mines. Systems activity models of both the conventional and unconventional systems are developed in support of documenting and contrasting the two systems. Constraints unique to oil sands mine planning are identified and their impact on the oil sands mine planning system are documented. The impacts of challenging waste handling and storage requirements and a uniquely prescriptive regulatory environment defining mineable ore are identified as key constraints. The research concludes with a proposal for a new planning system to better support the planning of oil sands mines. The proposed system respects the unique waste management considerations in oil sands planning and revisits the current regulatory approach to ensuring resource recovery. The proposed system is compatible with traditional approaches to economic analysis in open pit planning, and with emerging best practices to manage technical and economic uncertainty, improve project optimization, and develop robust mine plans. / Thesis (Ph.D, Mining Engineering) -- Queen's University, 2012-10-02 17:52:18.223

A fundamental problem in open pit mine planning is that of determining the optimum ultimate pit limits of the mine. These limits are that pit contour which is the result of extracting a volume of material which maximizes the difference between the value of extracted ore and the total extraction cost of ore and waste whilst satisfying certain practical operational requirements, such as. safe wall slopes. The determination of the optimum pit contour provides information which is essential in the evaluation of the economic potential of the mineral deposit.A number of optimization techniques have been proposed for determining the optimum pit contour. Of these techniques, those based on graph theory, linear programming and dynamic programming are mathematically rigorous, but only those based on graph theory are more suited to solving the three-dimensional problem. Unfortunately, direct application of these techniques to large ore- bodies may cause considerable difficulties because of the exceptionally high demand on computer storage and time requirements. Indeed, 25 years of research effort has not satisfactorily resolved these computational problems.A major contribution of the work presented in this thesis is the successful implementation of a system of techniques to solve the graph theoretic model, particularly when applied to large ore- bodies. A measure of this success is the fact that pits, as much as seven times larger may be designed with a given amount of computer storage, at a fraction of the time required by current software packages. The solution strategy presented involves the application of a modified Dinics Maximum Flow algorithm, together with an efficient data reducing technique. Computational results of these techniques applied on data from gold producing mines in Western Australia are used to demonstrate the success of this strategy.The relationships ++ / between the rigorous pit optimization techniques are also considered in this work. In particular, the Lerchs-Grossman graph-theoret ic method is shown to be stepwise equivalent to a modified version of the Dual-Simplex Linear Programming technique and not as efficient as the Network Flow method.

Commodity markets are fundamentally cyclical, exposing mining companies to large swings in profitability during periods of economic boom and bust. Although this is well documented, companies continue to produce mine plans based on present market conditions that fail to acknowledge long-term metal price variability. The purpose of this thesis is to adapt McIsaac’s (2008) mathematical model for determining the most robust underground mining plan under conditions of metal price uncertainty for application in an open pit environment. An overview of conventional open pit algorithms is given to demonstrate that a circular analysis precludes the determination of an optimal solution when metal prices are uncertain. Under the proposed methodology, the optimal solution is achieved by selecting the cutoff grade and production rate under stochastic metal prices such that the net present value and probability of a positive net present value are maximized. The mathematical model was formulated with costs represented as a function of the level of production, rate of production or both. Revenues are achieved from either a mill, heap leach or stockpile process dependent on the level of production and metal price in the year of consideration. Metal prices are generated annually according to a stochastic model that balances short-term volatility with long-term trends. The compiled cash flow model determines the optimal net present value for a given production profile under input metal prices. The feasible area of production is established based on mine life, resource and financing constraints. Net present values are generated for a broad search grid, which converges towards a unimodal solution according to a golden search algorithm. The process is then repeated many times in order to identify the production profile at which the optimal solution is repeatedly reached. As a visual representation, the solutions are plotted on a bubble graph where the size of the bubble corresponds to the frequency of the solution; the largest bubble is associated with the optimal solution. The methodology is tested on two massive copper porphyry deposits, contained within a single claim, for which a Preliminary Economic Assessment has been completed. / Thesis (Master, Mining Engineering) -- Queen's University, 2010-02-08 22:07:52.331

Modern large-scale open pit mines move hundreds of thousands of tonnes of material daily, from the loading sources to the destination zones, whether these are massive mine dumps or, to a lesser extent, to the grinding mills. Mine dumps can be classified as leach or waste dumps, depending upon their economic viability to be processed in-place, a condition that has experienced great progress in the last decades and has reconfigured the open pit haulage network with an increase in the number of dumps. Therefore, new methods for dump design optimization are of the highest priority in mine planning management. This paper presents a methodology to model and optimize the design of a dump by minimizing the total haulage costs. The location and design of these dumps will be given mainly by the geological characteristics of the mineral, tonnage delivered, topographical conditions, infrastructure capital and transportation costs. Spatial and physical design possibilities, in addition, provide a set of parameters of mathematical and economic relationship that creates opportunities for modelling and thus facilitates the measurement and optimization of ultimate dump designs. The proposed methodology consists of: (1) Formulation of a dump model based on a system of equations relying on multiple relevant parameters; (2) Solves by minimizing the total cost using linear programming and determines a "preliminary" dump design; (3) Through a series of iterations, changes the "preliminary" footprint by projecting it to the topography and creates the ultimate dump design. Finally, an application for a waste rock dump illustrates this methodology.

In this dissertation, we apply stochastic approximation (SA) to two different problems addressed respectively in Part I and Part II. / The contribution of Part I is mostly theoretical. We consider the problem of online tracking of moving targets such as a signals, through noisy measurements. In particular, we study a non-stationary environment that is subject to sudden discontinuous changes in the underlying parameters of the system. We assume no a priori knowledge about the parameters nor the change-times. Our approach is based on constant stepsize SA. However, because of the unpredictable discontinuous changes, the choice of stepsize is difficult. Small stepsizes improve precision while large stepsizes allow the SA iterates to react faster to sudden changes. / We first investigate target estimation. Our work appears in [Levy 09]. We propose to combine a small constant stepsize with change-point monitoring, and to reset the process at a value closer to the new target when a change is detected. Because the environment is not stationary, we cannot directly apply the usual limit theorems. We thus give a theoretical characterization and discuss the tradeoff between precision and fast adaptation. We also introduce a new monitoring scheme, the regression-based hypothesis test. / Secondly, we consider an online version of the well-known Q-learning algorithm, which operates directly in its target environment, to optimize a Markov decision process. Online algorithms are challenging because the errors, necessarily made when learning, affect performance. Again, under a switching environment the usual limit theorems are not applicable. We introduce an adaptive stepsize selection algorithm based on weak convergence results for SA. Our algorithm automatically achieves a desirable balance between speed and accuracy. These findings are published in [Levy 06, Costa 09]. / In Part II, we study an applied problem related to the mining industry. Strategic management requires managing large portfolios of investments. Because financial resources are limited, only the projects with the highest net present value (NPV), their measure of economic value, will be funded. To value a mine project we need to consider future uncertainties. The approach commonly taken to value a project is to assume that if funded, the mine will be operated optimally throughout its life. Our final aim is not to provide an exact strategy, but to propose an optimization tool to improve decision-making in complex scenarios. Of all the variables involved, the typically large investments in infrastructure, as well as the uncertainty in commodity price, have the most significant impact on the mine value. We thus adopt a simplified model of the infrastructure and extraction optimization problem, subject to price uncertainty. / Common optimization methods are impractical for realistic size models. Our main contribution is the threshold optimization methodology based on measured valued differentiation (MVD) and SA. We also present another simulation-based method, the particles method [Dallagi 07], for comparison purposes. Both methods are well-adapted for high dimensional problems. We provide numerical results and discuss their characteristics and applicability.

O mapeamento da incerteza dos teores através de métodos de simulação geoestatística é uma metodologia que está começando a ser amplamente utilizada na indústria mineira. No entanto, o uso correto desse intervalo de incerteza para os processos subsequentes à avaliação de recursos ainda carece de entendimento e aplicação no setor industrial, onde o modelo de krigagem é empregado para o planejamento de mina. O sequenciamento da produção de longo prazo, com o objetivo de maximizar o Valor Presente Líquido (VPL), é uma das etapas mais importantes no planejamento de lavra e, portanto, o acesso à informação da variabilidade dos teores torna-se de grande importância permitindo a maximização dos lucros e da extração dos recursos. O objetivo deste estudo é avaliar o impacto da incerteza geológica no planejamento de lavra de modo a definir um sequenciamento a partir das simulações. Para isso ser alcançado, propõe-se uma análise probabilística incorporando as incertezas dos teores no sequenciamento de lavra, e quantificando, através de um índice de classificação proposto no estudo, os potenciais ganhos e riscos de perda associado a cada cenário sequenciado. O método de co-simulação por bandas rotativas é utilizado para gerar cenários equiprováveis. Em seguida, o sequenciamento de lavra é definido para cada cenário de teor simulado utilizando um software de otimização. Então, cada sequência de extração dos blocos obtida foi reavaliada para cada simulação de teor. Além disso, um índice de classificação é utilizado para definir o sequenciamento de lavra que gera o maior VPL. Por fim, é realizada uma comparação entre a opção de planejamento selecionada pela metodologia proposta e o modelo utilizado tradicionalmente na indústria obtido a partir de interpolações lineares (krigagem) dos teores. / Mapping grade uncertainty through geostatistical simulation is becoming widely used in the mining industry. However, the proper use of this uncertainty interval for subsequent decision making processes still lacks of understanding and use, where a grade kriging model is mostly employed for mine planning. The long-term scheduling aiming at maximizing Net Present Value (NPV) is one of the most important stages in mine planning, and therefore the assessment of grade variability is of great importance and allowing maximizing profit and resources extraction. The aim of this study is to evaluate the impact of geological uncertainty in mine planning in order to define the best scheduling given grade uncertainty derived from the simulations. For this to be achieved, it is proposed a probabilistic analysis incorporating grade uncertainties in the mining sequencing and quantifying, through a proposed classification index, the potential gains and risks of loss associated with each sequenced scenario. Turning bands algorithm is used to generate equally probable scenarios. Next, it is defined the mining sequence for each grade simulated scenario using an optimization software. Then, each block extraction sequence obtained is reevaluated for each grade simulation. Furthermore, a classification index is used to select the schedule which leads to the highest NPV. Finally, a comparison is performed with the selected schedule and the one obtained using the model traditionally used based on kriged grades.

O mapeamento da incerteza dos teores através de métodos de simulação geoestatística é uma metodologia que está começando a ser amplamente utilizada na indústria mineira. No entanto, o uso correto desse intervalo de incerteza para os processos subsequentes à avaliação de recursos ainda carece de entendimento e aplicação no setor industrial, onde o modelo de krigagem é empregado para o planejamento de mina. O sequenciamento da produção de longo prazo, com o objetivo de maximizar o Valor Presente Líquido (VPL), é uma das etapas mais importantes no planejamento de lavra e, portanto, o acesso à informação da variabilidade dos teores torna-se de grande importância permitindo a maximização dos lucros e da extração dos recursos. O objetivo deste estudo é avaliar o impacto da incerteza geológica no planejamento de lavra de modo a definir um sequenciamento a partir das simulações. Para isso ser alcançado, propõe-se uma análise probabilística incorporando as incertezas dos teores no sequenciamento de lavra, e quantificando, através de um índice de classificação proposto no estudo, os potenciais ganhos e riscos de perda associado a cada cenário sequenciado. O método de co-simulação por bandas rotativas é utilizado para gerar cenários equiprováveis. Em seguida, o sequenciamento de lavra é definido para cada cenário de teor simulado utilizando um software de otimização. Então, cada sequência de extração dos blocos obtida foi reavaliada para cada simulação de teor. Além disso, um índice de classificação é utilizado para definir o sequenciamento de lavra que gera o maior VPL. Por fim, é realizada uma comparação entre a opção de planejamento selecionada pela metodologia proposta e o modelo utilizado tradicionalmente na indústria obtido a partir de interpolações lineares (krigagem) dos teores. / Mapping grade uncertainty through geostatistical simulation is becoming widely used in the mining industry. However, the proper use of this uncertainty interval for subsequent decision making processes still lacks of understanding and use, where a grade kriging model is mostly employed for mine planning. The long-term scheduling aiming at maximizing Net Present Value (NPV) is one of the most important stages in mine planning, and therefore the assessment of grade variability is of great importance and allowing maximizing profit and resources extraction. The aim of this study is to evaluate the impact of geological uncertainty in mine planning in order to define the best scheduling given grade uncertainty derived from the simulations. For this to be achieved, it is proposed a probabilistic analysis incorporating grade uncertainties in the mining sequencing and quantifying, through a proposed classification index, the potential gains and risks of loss associated with each sequenced scenario. Turning bands algorithm is used to generate equally probable scenarios. Next, it is defined the mining sequence for each grade simulated scenario using an optimization software. Then, each block extraction sequence obtained is reevaluated for each grade simulation. Furthermore, a classification index is used to select the schedule which leads to the highest NPV. Finally, a comparison is performed with the selected schedule and the one obtained using the model traditionally used based on kriged grades.

Em lavra a céu aberto, a diluição nem sempre é um fator analisado e calculado sistematicamente, muitas vezes é apenas um número ajustado para atender necessidades de auditorias, por exemplo. A diluição, assim como a perda, são fatores que devem ser sempre considerados nas estimativas de teores e massas para quantificação de reservas. Estes fatores andam sempre conjugados e são determinados considerando diversas particularidades do depósito (complexidade geológica, geometria do corpo de minério, dureza da rocha, etc.) e características da operação (equipamentos, geometria de cava, habilidade dos operadores, entre outros). O principal objetivo deste estudo é a determinação de um fator de diluição que possa ser utilizado no planejamento de lavra (modelo de estimativas), levando em consideração diversas particularidades do depósito e da operação, além de considerar fatores objetivos relacionados à geometria. A reconciliação pode ser definida como uma comparação entre teores e massas estimados no modelo de blocos com as medidas reais dos teores e massas produzidos, dentro de um mesmo volume. O processo de reconciliação de teor e massa entre o planejamento e o executado atua como uma maneira para verificar se o planejamento está adequado, e se não estiver, identificar onde se encontram os problemas de falta de aderência. Além de verificar a confiabilidade dos procedimentos de construção do modelo utilizado, a reconciliação permite definir medidas corretivas e priorizá-las para aproximar os resultados entre produção e o planejamento. Para saber se o fator de diluição utilizado está correto e adequado às necessidades do depósito é necessário primeiramente, saber se existe uma boa aderência na reconciliação entre planejado e executado. Com o resultado, é possível saber quais fatores estão sendo causadores de diluição e/ou perdas de minério e onde estes estão ocorrendo. O fator de diluição pode ser uma ferramenta muito positiva se aplicado de maneira correta, já que este varia a partir de diferentes etapas ao longo do planejamento de mina, influenciando áreas a serem mineradas, orçamentos, eficiência da produção e também melhora do resultado financeiro do projeto. / In open pit mining, not always the dilution is a factor analyzed and systematically calculated, often is only a number adjusted for attending the needs of audits, for example. The dilution, as well as loss, are factors that should be always considered for tonnage and grade estimates during mine planning. These factors are always associated and can be determined considering several particularities of the deposit (like geology complexity, orebody geometry, rock hardness, etc.) and the operation itself (e.g. mining equipment, pit design, experience, among others). The main objective of this study is to determine a dilution factor that can be used in mine planning (estimation model), taking into consideration those particularities of the deposit and operation, besides considering objective factors related to the geometry. Reconciliation could be defined as a comparison of predicted grade and tonnage from the block model estimates against the effective measures of mined mass and produced ore, within a block. The reconciliation process of grade and mass of planning against executed is a way to check if planning is appropriate, and if not, identify where the problems of lack of adherence are. In addition to checking the reliability of the procedures used in the block model creation, reconciliation allows one to define corrective measures and prioritize them to optimize production and planning. To understand if the dilution factor used is correct and appropriate to the needs of the deposit it is first required knowing if there is a good adherence in reconciliation between planned and executed. With the results, is possible to know which factors are causing dilution and/or losses of ore and where they are occurring. The dilution factor can become a very positive tool if better assessed, because it varies from different locations along the mine planning, influencing areas to be mined; budgets; production efficiency and also profit increase.

This thesis looks at the medium term mine planning process and tools in the Leveäniemi open pit mine operated by LKAB Svappavaara. The current planning process uses software, Chronos, which was previously used successfully to perform medium term planning for the Gruvberget mine, which is also operated by LKAB Svappavaara. Because of scale and geological differences this method is much less successful when applied in Leveäniemi, which has created the need to investigate other possible methods. Since the Maptek scheduling solution Evolution is already available for use, this is the first candidate to be investigated. This report uses a case study approach, where both methods are evaluated in their intended operating environment. Results obtained indicate that Evolution could be a viable replacement to conduct medium term planning. Testing indicates that Evolution is able to produce a schedule satisfying the planning criteria to the desired standard. The fact that Evolution is able to produce schedules with longer time horizons without having to sacrifice detail means that it could also improve the integration between long and medium term planning. Besides replacing Chronos it was demonstrated that there are also some things that can be done using Evolution that are not possible using the Chronos module. From what has been demonstrated it can be concluded that there is a possibility to achieve significant benefit using these extra functions.

Em lavra a céu aberto, a diluição nem sempre é um fator analisado e calculado sistematicamente, muitas vezes é apenas um número ajustado para atender necessidades de auditorias, por exemplo. A diluição, assim como a perda, são fatores que devem ser sempre considerados nas estimativas de teores e massas para quantificação de reservas. Estes fatores andam sempre conjugados e são determinados considerando diversas particularidades do depósito (complexidade geológica, geometria do corpo de minério, dureza da rocha, etc.) e características da operação (equipamentos, geometria de cava, habilidade dos operadores, entre outros). O principal objetivo deste estudo é a determinação de um fator de diluição que possa ser utilizado no planejamento de lavra (modelo de estimativas), levando em consideração diversas particularidades do depósito e da operação, além de considerar fatores objetivos relacionados à geometria. A reconciliação pode ser definida como uma comparação entre teores e massas estimados no modelo de blocos com as medidas reais dos teores e massas produzidos, dentro de um mesmo volume. O processo de reconciliação de teor e massa entre o planejamento e o executado atua como uma maneira para verificar se o planejamento está adequado, e se não estiver, identificar onde se encontram os problemas de falta de aderência. Além de verificar a confiabilidade dos procedimentos de construção do modelo utilizado, a reconciliação permite definir medidas corretivas e priorizá-las para aproximar os resultados entre produção e o planejamento. Para saber se o fator de diluição utilizado está correto e adequado às necessidades do depósito é necessário primeiramente, saber se existe uma boa aderência na reconciliação entre planejado e executado. Com o resultado, é possível saber quais fatores estão sendo causadores de diluição e/ou perdas de minério e onde estes estão ocorrendo. O fator de diluição pode ser uma ferramenta muito positiva se aplicado de maneira correta, já que este varia a partir de diferentes etapas ao longo do planejamento de mina, influenciando áreas a serem mineradas, orçamentos, eficiência da produção e também melhora do resultado financeiro do projeto. / In open pit mining, not always the dilution is a factor analyzed and systematically calculated, often is only a number adjusted for attending the needs of audits, for example. The dilution, as well as loss, are factors that should be always considered for tonnage and grade estimates during mine planning. These factors are always associated and can be determined considering several particularities of the deposit (like geology complexity, orebody geometry, rock hardness, etc.) and the operation itself (e.g. mining equipment, pit design, experience, among others). The main objective of this study is to determine a dilution factor that can be used in mine planning (estimation model), taking into consideration those particularities of the deposit and operation, besides considering objective factors related to the geometry. Reconciliation could be defined as a comparison of predicted grade and tonnage from the block model estimates against the effective measures of mined mass and produced ore, within a block. The reconciliation process of grade and mass of planning against executed is a way to check if planning is appropriate, and if not, identify where the problems of lack of adherence are. In addition to checking the reliability of the procedures used in the block model creation, reconciliation allows one to define corrective measures and prioritize them to optimize production and planning. To understand if the dilution factor used is correct and appropriate to the needs of the deposit it is first required knowing if there is a good adherence in reconciliation between planned and executed. With the results, is possible to know which factors are causing dilution and/or losses of ore and where they are occurring. The dilution factor can become a very positive tool if better assessed, because it varies from different locations along the mine planning, influencing areas to be mined; budgets; production efficiency and also profit increase.