Statistics for Spatial Data.

Statistics and Data Analysis in Geology

Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall

Introduction to stochastic programming

At temperatures up to about 80 °C, petroleum in subsurface reservoirs is often biologically degraded, over geological timescales, by microorganisms that destroy hydrocarbons and other components to produce altered, denser 'heavy oils'. This temperature threshold for hydrocarbon biodegradation might represent the maximum temperature boundary for life in the deep nutrient-depleted Earth. Most of the world's oil was biodegraded under anaerobic conditions, with methane, a valuable commodity, often being a major by-product, which suggests alternative approaches to recovering the world's vast heavy oil resource that otherwise will remain largely unproduced.

Biological activity in the deep subsurface and the origin of heavy oil

An economic argument is presented for the incorporation of quantitative modelling of the uncertainty of grade, tonnage and geology into open-pit design and planning. Two new implementations of conditional simulation—the generalized sequential Gaussian simulation and direct block simulation—are outlined. An optimization study of a typical disseminated, low-grade, epithermal, quartz breccia-type gold deposit is used to highlight the differences between the financial projections that may be obtained from a single orebody model and the range of outcomes produced when, for example, fifty deposit simulations are run. The effects on expectations of net present value, production cost per ounce, mill feed grade and ore tonnage are presented as examples and periods with a high risk of negative discounted cash flow are identified. Further integration of uncertainty into optimization algorithms will be needed to increase their efficacy.

Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design

http://cgm.cs.mcgill.ca/~avis/courses/567/roussos/EJOR2.pdf

A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty

The annual production scheduling of open pit mines determines an optimal sequence for annually extracting the mineralized material from the ground. The objective of the optimization process is usually to maximize the total Net Present Value (NPV) of the operation. Production scheduling is typically a Mixed Integer Programming (MIP) type problem containing uncertainty in the geologic input data and economic parameters involved. Major uncertainty affecting optimization is uncertainty in the mineralized materials (resource) available in the ground which constitutes an uncertain supply for mine production scheduling. A new optimization model is developed herein based on two-stage Stochastic Integer Programming (SIP) to integrate uncertain supply to optimization; past optimization methods assume certainty in the supply from the mineral resource. As input, the SIP model utilizes a set of multiple, stochastically simulated scenarios of the mineralized materials in the ground. This set of multiple, equally probable scenarios describes the uncertainty in the mineral resource available in the ground, and allows the proposed model to generate a single optimum production schedule. The method is applied for optimizing the annual production scheduling at a gold mine in Australia and benchmarked against a traditional scheduling method using the traditional single “average type” assessment of the mineral resource in the ground. In the case study presented herein, the schedule generated using the proposed SIP model resulted in approximately 10% higher NPV than the schedule derived from the traditional approach.

/pdf/production-scheduling-with-uncertain-supply-a-new-solution-4b04w5f6i3.pdf

Production scheduling with uncertain supply: a new solution to the open pit mining problem

Graphical abstractDisplay Omitted HighlightsA stochastic global optimization framework for open pit mining complexes is proposed.The method simultaneously optimizes production schedules and downstream processes.The modeling is flexible and may be applied to numerous types of mining complexes.Three combinations of metaheuristics are tested.Results from an example show a substantial economic benefit when using this approach. 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.

/pdf/global-optimization-of-open-pit-mining-complexes-with-32vhltmq39.pdf

Roussos Dimitrakopoulos

Papers

Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design

A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty

Production scheduling with uncertain supply: a new solution to the open pit mining problem

Global optimization of open pit mining complexes with uncertainty

Geostatistics for the Next Century