JOINT SIMULATION OF CONTINUOUS AND CATEGORICAL VARIABLES FOR MINERAL RESOURCE MODELING AND RECOVERABLE RESERVES CALCULATION

Spatial variability and uncertainty of continuous variables (grade) and categorical variables (rock-types) in mineral evaluation significantly impact the economics of mining projects. The conventional approach of simulating grades using deterministic rock- types is problematic since spatial variability, and uncertainty of grades at rock-type contacts are not well captured in deposits where the grade changes gradually between rock-types. Therefore, jointly simulating these variables can improve confidence (reduce uncertainty) in a resource model. Also, resource classification and recoverable reserve calculation can significantly improve the understanding of the deposit and its economic viability. This research utilized the Plural-Gaussian geostatistical simulation to jointly simulate rock-types and grade. A joint coregionalized model of random fields via fitting theoretical variograms is achieved. Equiprobable realizations of rock-types and grades are generated through a co-simulation of these variables. Resource classification of simulations and ultimate pit limit calculations are produced and validated using a real gold deposit in Alaska

Uncertainty modeling of ore body and grades using single normal equation simulation and sequential gaussian simulation: an application to an iron ore mine

A conventional, deterministic orebody model would lead to over estimation or under-estimation of the grade, volume and other parameters related to a deposit. This will lead to improper mine planning and thus incur huge financial risk. A proper orebody and grade modeling provide better confidence to mine owners regarding financial decision. However, only using few number of borehole data it is always difficult to come up with such type of accurate decision. Always there are certain amount of risk are associated with the estimation as well as decision. This thesis aims at providing a better risk assessment at minimizing the grade and volumetric uncertainty of the ore body. The multipoint simulation algorithms eliminate the demerits of variogram based geostatistics modeling and preserve multi-point information borrowed from training image. In this thesis, a case study of iron ore deposit from India is performed to analyses the volumetric and grade uncertainty the volumetric and grade uncertainty. Single normal equation simulation (SNESIM), a multi-point categorical simulation algorithm, was performed to measure the volumetric uncertainty of orebody. Ore volume uncertainty was performed by generating. 10 equiprobable orebody simulated models are developed. The grade uncertainty modeling was performed by applying sequential Gaussian simulation (SGM) with orebody model generated by SNESIM algorithm. The result shows that if the training image –based multi-point simulation is applied for ore body modeling, there would have been 7 % increase in volume as compared to traditional method. The grade-tonnage uncertainty reveals that uncertainty-based generates more high grade ores when compared with ordinary kriging method

An adaptive neighborhood search algorithm for optimizing stochastic mining complexes

Les métaheuristiques sont très utilisées dans le domaine de l'optimisation discrète. Elles permettent d’obtenir une solution de bonne qualité en un temps raisonnable, pour des problèmes qui sont de grande taille, complexes, et difficiles à résoudre. Souvent, les métaheuristiques ont beaucoup de paramètres que l’utilisateur doit ajuster manuellement pour un problème donné. L'objectif d'une métaheuristique adaptative est de permettre l'ajustement automatique de certains paramètres par la méthode, en se basant sur l’instance à résoudre. La métaheuristique adaptative, en utilisant les connaissances préalables dans la compréhension du problème, des notions de l'apprentissage machine et des domaines associés, crée une méthode plus générale et automatique pour résoudre des problèmes. L’optimisation globale des complexes miniers vise à établir les mouvements des matériaux dans les mines et les flux de traitement afin de maximiser la valeur économique du système. Souvent, en raison du grand nombre de variables entières dans le modèle, de la présence de contraintes complexes et de contraintes non-linéaires, il devient prohibitif de résoudre ces modèles en utilisant les optimiseurs disponibles dans l’industrie. Par conséquent, les métaheuristiques sont souvent utilisées pour l’optimisation de complexes miniers. Ce mémoire améliore un procédé de recuit simulé développé par Goodfellow & Dimitrakopoulos (2016) pour l’optimisation stochastique des complexes miniers stochastiques. La méthode développée par les auteurs nécessite beaucoup de paramètres pour fonctionner. Un de ceux-ci est de savoir comment la méthode de recuit simulé cherche dans le voisinage local de solutions. Ce mémoire implémente une méthode adaptative de recherche dans le voisinage pour améliorer la qualité d'une solution. Les résultats numériques montrent une augmentation jusqu'à 10% de la valeur de la fonction économique.Metaheuristics are a useful tool within the field of discrete optimization that allow for large, complex, and difficult optimization problems to achieve a solution with a good quality in a reasonable amount of time. Often metaheuristics have many parameters that require a user to manually define and tune for a given problem. An adaptive metaheuristic aims to remove some parameters from being tuned or defined by the end user by allowing the method to specify and/or adapt a parameter or set of parameters based on the problem. The adaptive metaheuristic, using advancements in understanding of the problem being solved, machine learning, and related fields, aims to provide this more generalized and automatic toolkit for solving problems. Global optimization of mining complexes aims to schedule material movement in mines and processing streams to maximize the economic value of the system. Often due to the large number of integer variables within the model, complicated constraints, and non-linear constraints, it becomes prohibitive to solve these models using commercially available optimizers. Therefore, metaheuristics are often employed in solving mining complexes. This thesis builds upon a simulated annealing method developed by Goodfellow & Dimitrakopoulos (2016) to optimize the stochastic global mining complex. The method outlined by the authors requires many parameters to be defined to operate. One of these is how the simulated annealing algorithm searches the local neighborhood of solutions. This thesis illustrates and implements an adaptive way of searching the neighborhood for increasing the quality of a solution. Numerical results show up to a 10% increase in objective function value

Development of a Grade Control Technique Optimizing Dilution and Ore Loss Trade-off in Lateritic Bauxite Deposits

This thesis focusses on the development of new techniques to improve the resource estimation of laterite-type bauxite deposits. Contributions of the thesis include (1) a methodology to variogram-free modelling of the ore boundaries using multiple-point statistics, (2) an approach to automate the parameter tuning process for multiple-point statistical algorithms and (3) a grade control technique to minimise the economic losses due to dilution and ore loss

Risk Adjusted Evaluation of Mineral Assets Using Transaction Based Statistical Models

This thesis addresses “how the characteristics of gold deposit transactions affect their price” through investigation of four hypotheses related to risks that often affect price: ownership, commodity price, certainty and country-risk. An empirical approach based on geostatistical methods is used to determine the behaviour of gold deposit prices in response to the risks. The results identify differences between security and asset price behaviour, as well as challenge the validity of accepted pricing methods and assumptions