ThesisPDF Available

Pit Optimization on the Efficient Frontier

Authors:

Abstract and Figures

The mining industry has become increasingly concerned with the effects of uncertainty and risk in resource modeling. Some companies are moving away from deterministic geologic modeling techniques to approaches that quantify uncertainty. Stochastic modeling techniques produce multiple realizations of the geologic model to quantify uncertainty, but integrating these results into pit optimization is non-trivial. Conventional pit optimization calculates optimal pit limits from a block model of economic values and precedence rules for pit slopes. There are well established algorithms for this including Lerchs-Grossmann, push-relabel and pseudo-flow; however, these conventional optimizers have limited options for handling stochastic block models. The conventional optimizers could be modified to incorporate a block-by-block penalty based on uncertainty, but not uncertainty in the resource within the entire pit. There is a need for a new pit limit optimizing algorithm that would consider multiple block model realizations. To address risk management principles in the pit shell optimization stage, a novel approach is presented for optimizing pit shells over all realizations. The inclusion of multiple realizations provides access to summary statistics across the realizations such as the risk or uncertainty in the pit value. This permits an active risk management approach. A heuristic pit optimization algorithm is proposed to target the joint uncertainty between multiple input models. A practical framework is presented for actively managing the risk by adapting Harry Markowitz’s “Efficient Frontier” approach to pit shell optimization. Choosing the acceptable level of risk along the frontier can be subjective. A risk-rating modification is proposed to minimize some of the subjectivity in choosing the acceptable level of risk. The practical application of the framework using the heuristic pit optimization algorithm is demonstrated through multiple case studies.
Content may be subject to copyright.
A preview of the PDF is not available
ResearchGate has not been able to resolve any citations for this publication.
Conference Paper
Full-text available
Uncertainty is always present in presence of sparse geological data. Conditional simulation algorithms such as Sequential Gaussian Simulation (SGS) and Sequential Indicator Simulation (SIS) are geostatistical methods used to assess geological uncertainty. The generated realizations are equally probable and represent plausible geological outcome. Traditionally the long-term mine plans are generated based on an estimated input geological block model. The most common estimation method used in industry is Kriging; however, Kriging results do not capture uncertainty and may be systematically biased. Mine plans that are generated based on one input block model fail to quantify the geological uncertainty and its impact on the future cash flows and production targets. A method is presented to transfer geological uncertainty into mine planning. First, SGS is used to generate fifty realizations of an oil sands deposit. An optimum final pit limits design is carried out for each realization while fixing all other technical and economic input parameters. Uncertainty in the final pit outline, net present value, production targets, and the head grade are assessed and presented. The results show that there is significant uncertainty in the long-term production schedules. In addition, the long-term schedule based on one particular simulated ore body model is not optimal for other simulated geological models. The mine planning procedure is not a linear process and the mine plan generated based on the Kriging estimate is not the expected result from all of the simulated realizations.
Article
Uncertainty exists in ultimate-pit limits due to geologic variation and unpredictable economic landscapes. In this work, we show how this uncertainty affects the ultimate pit and how it can be analyzed to improve the mine planning process. A stochastic framework using geostatistical simulation and parametric analysis was used to model the effects of geologic and economic variations on ultimate-pit limits and overall project economics. This analysis was made possible by a new pit optimization implementation that can be automated and set up to calculate ultimate pits for hundreds of different scenarios in a matter of hours. Quantifying ultimate-pit uncertainty early in the mine planning process allows mining engineers to make informed decisions regarding infrastructure placement and to mitigate the possibility of incurring substantial costs to relocate critical mine facilities.
Article
Several reviews of mineral project performance in the past 35 years indicate a pattern of occasional, but recurrent, mining project failures due to shortcomings in geological information and estimation, mineral processing and metallurgical testing, feasibility study objectives and requirements, and project start-up methods. A commitment to quality assurance and continuous improvement methods and to obtaining 'ENOUGH DATA, OF APPROPRIATE QUALITY' is essential. Recent international and Canadian proposals for mineral resource and ore reserve definitions have taken a non-prescriptive stance that will undermine the formulation of requirements, guidelines and industry standards for efficient deposit delineation and estimation, and for the determination of project feasibility. To help reduce problems, every feasibility study supporting a mine development and production decision should be based on objectives and methods adequate to reach completion targets similar to the bankers', as a good business target for a profitable project. In a resource/reserve system, the use of reserve should be restricted to a project that meets required technical, economic and legal feasibility requirements for successful project implementation, and the definitions of these categories should provide explicit limits. Current shortcomings will limit the ability of the Qualified Person to provide 'adequate professional practice,' fulfill his/her professional responsibilities to his employer or client and provide adequate information to the investing public. We must take advantage of present opportunities for Setting New Standards for the new Millennium.
Article
Global optimization for mining complexes aims to generate a production schedule for the various mines and processing streams that maximizes the economic value of the enterprise as a whole. Aside from the large scale of the optimization models, one of the major challenges associated with optimizing mining complexes is related to the blending and non-linear geo-metallurgical interactions in the processing streams as materials are transformed from bulk material to refined products. This work proposes a new two-stage stochastic global optimization model for the production scheduling of open pit mining complexes with uncertainty. Three combinations of metaheuristics, including simulated annealing, particle swarm optimization and differential evolution, are tested to assess the performance of the solver. Experimental results for a copper-gold mining complex demonstrate that the optimizer is capable of generating designs that reduce the risk of not meeting production targets, have 6.6% higher expected net present value than the deterministic-equivalent design and 22.6% higher net present value than an industry-standard deterministic mine planning software.
Article
Meeting production targets in terms of ore quantity and quality is critical for a successful mining operation. In-situ grade uncertainty causes both deviations from production targets and general financial deficits. A new stochastic optimization algorithm based on ant colony optimization (ACO) approach is developed herein to integrate geological uncertainty described through a series of the simulated ore bodies. Two different strategies were developed based on a single predefined probability value (Prob) and multiple probability values. (Probnt), respectively in order to improve the initial solutions that created by deterministic ACO procedure. Application at the Sungun copper mine in the northwest of Iran demonstrate the abilities of the stochastic approach to create a single schedule and control the risk of deviating from production targets over time and also increase the project value. A comparison between two strategies and traditional approach illustrates that the multiple probability strategy is able to produce better schedules, however, the single predefined probability is more practical in projects requiring of high flexibility degree.