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

Life of mine (LOM) production scheduling is a critically important part of open pit mining ventures and deals with the efficient management of cash flows in the order of hundreds of millions of dollars. A LOM production schedule determines the quantity and quality of ore and waste materials to be mined over time, so as to maximise the net present value (NPV) of the mine. Life of mine production scheduling is an intricate and complex problem to address and it is adversely affected by geological risk, which can, however, be accounted for and managed while constructing production schedules. In the present study, the LOM scheduling process of a disseminated copper deposit demonstrates the intricacies of a new scheduling approach based on the technique of simulated annealing and stochastically simulated representations of the copper orebody. The study documents the benefits of incorporating geological uncertainty in the mine scheduling process through the proposed approach. The stochastic approach is f...

Stochastic optimisation model for open pit mine planning: application and risk analysis at copper deposit

Conventional approaches to optimising open pit mine design and production scheduling are based on a single estimated orebody model, which does not account for geological variability. Conditional simulation can be employed to quantitatively address the resulting grade uncertainty. Multiple simulated orebody models provide a suitable input for stochastic integer programming (SIP), a type of mathematical programming that generates the optimal result for a defined set of objectives under uncertainty. In the case of production scheduling, the objectives are to maximise the total net present value (NPV) and to minimise unsatisfied demand for processed ore. Using a set of multiple simulated orebody models as input into an SIP model allows for the integration of in situ deposit variability and uncertainty directly into the production scheduling optimisation process.

Stochastic Optimisation of Long-Term Production Scheduling for Open Pit Mines with a New Integer Programming Formulation

The production scheduling of open pit mines is an intricate, complex and difficult problem to address due to its large scale and the unavailability of a truly optimal net present value (NPV) solution, as well as the uncertainty in key parameters involved. These key factors are geological and mining, financial and environmental. Geological uncertainty is a major contributor in failing to meet production targets and the financial expectations of a project especially in the early stages of a project. Stochastic integer programming (SIP) models provide a framework for optimising mine production scheduling considering uncertainty. A specific SIP formulation is shown herein that generates the optimal production schedule using equally probable simulated orebody models as input, without averaging the related grades. The optimal production schedule is then the schedule that can produce the maximum achievable discounted total value from the project, given the available orebody uncertainty described through ...

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Stochastic integer programming for optimising long term production schedules of open pit mines: methods, application and value of stochastic solutions

https://www.ige.unicamp.br/sdm/ArcSDM3/documentation/data_drive-fuzzylogic.pdf

Data-driven fuzzy analysis in quantitative mineral resource assessment

Over recent years, new methods have been developed to integrate uncertainty into the optimisation of life-of-mine production planning. One of these methods is based on scheduling with a simulated annealing (SA) algorithm and equally probable realisations of a given mineral deposit. The latter realisations are used to generate production schedules that minimise the possibility of deviating from production targets, and result in schedules with a substantial improvement in the net present value (NPV), shown to be in the order of 25% when compared to conventional scheduling within the conventionally optimal pit limits. To facilitate the utilisation of this method, a sensitivity analysis is presented in this study. The study documents the case of a copper deposit where 10 simulated realisations are sufficient to provide stable life-of-mine optimisation results. In addition, the study shows that the selected true optimal pit limits are larger than those derived through conventional optimisation. Stochas...

Stochastic mine design optimisation based on simulated annealing: pit limits, production schedules, multiple orebody scenarios and sensitivity analysis

Roussos Dimitrakopoulos

Papers

Stochastic optimisation model for open pit mine planning: application and risk analysis at copper deposit

Stochastic Optimisation of Long-Term Production Scheduling for Open Pit Mines with a New Integer Programming Formulation

Stochastic integer programming for optimising long term production schedules of open pit mines: methods, application and value of stochastic solutions

Data-driven fuzzy analysis in quantitative mineral resource assessment

Stochastic mine design optimisation based on simulated annealing: pit limits, production schedules, multiple orebody scenarios and sensitivity analysis