Roussos G Dimitrakopoulos

• Research Contributions
• Ongoing Research Programs
• Achievements of Selected Completed Projects

Research Contributions

High-order and Multi-scale, Non-linear and Non-Gaussian Stochastic Models of Spatial Uncertainty
Spatially distributed natural phenomena, such as attributes of mineral deposits, petroleum reservoirs, environmental phenomena, represent complex non-linear and non Gaussian systems. Their spatial distributions are typically studied using second-order spatial statistical models, or ad-hoc multipoint models, which are limiting considering the spatial complexity of natural phenomena. High-order geostatistics is a new area of research based on higher-order spatial connectivity measures. This research aims to develop a new framework for enhanced simulation of complex geological structures using high-order spatial cumulants in the high-dimensional space of Legendre polynomials, among other mathematical constructs. Complementary to this is the development of methods that facilitate the integration, analysis and spatial modeling multi-scale processes based on wavelet decomposition approaches.

Mine Design and Production Scheduling Optimization under Uncertainty – Stochastic Mine Planning
Quantification of uncertainty and risk has major implications in mine planning, design and production scheduling, as it relates to the management of cash flows in the order of millions of dollars. Geological uncertainty is a recognized contributor to mining risk. The past years, my research efforts have focused on ongoing research to address key issues in mine design and production scheduling with uncertainty. In addition, it has looked at strategic risk management with particular emphasis on technical (geological and mining) risk. A key goal of this research is to shift current mine design and planning formulations towards a stochastic paradigm that includes both supply (orebody) and demand (commodity price and exchange rates). The above goal requires new risk-based models and technologies and leads to: (a) developing new optimization formulations in mine planning to deal technically with risk in a “holistic” sense; and (b) modeling uncertainty at its source(s), including geological, mining and market. The two modeling “engines” considered are stochastic mathematical programming for mine optimization and stochastic modeling of orebodies.

Subsurface CO2 Sequestration
With the current interest in CO2 injection for improved oil recovery, recycling in gas condensate reservoirs and CO2 sequestration in saline aquifers, a high priority is given to CO2 based production schemes as well as recycling. A large portion of current CO2 injection projects worldwide is in naturally fractured reservoirs. The matrix part of these reservoirs constitutes the major oil storage unit and this oil is targeted during CO2 injection. My work intends to contribute to the understanding that this media could also be used as a permanent CO2 storage unit, while recovering oil from it. This relates to both my past work in reservoir engineering. Part of my current work focuses on the accurate and robust mesh generation that remains a significant challenge when considering fractured reservoirs and the need to account for complex connected and discrete fracture configurations near and away the wellbore, and efficiently discretize and/or mesh these configurations for CO2/oil flow simulations. The other part of my research relates to characterization of geologic storage using high order stochastic models.

Environmental Risk Analysis
Quantitative methods and their use in the sustainable development of mineral resources is an increasingly recognized, relatively new and challenging area of interest. My research under this heading includes developing methods and applications for (a) spatial or spatiotemporal waste characterization and mine rehabilitation, (b) pollutant contaminated site assessment, (c) quantitative mineral resource development as linked to environmental conservation, biodiversity and the broader area of mineral resource management.

Orebody Risk and Reserve/Resource Modelling
The ability to deal with uncertainty and manage geological risk is critically dependent on our ability to model the uncertainty in our understanding of the orebody being mined. Similarly, a link to mine planning requires the quantification of in situ orebody variability. The framework of spatial stochastic simulation offers the concepts needed to develop methods suitable to simulate a multitude of geological characteristics of orebodies. My research efforts on this topic address key issues in this area of work, with particular emphasis on: (a) new and very efficient algorithms that can facilitate the routine use of the methods in the industry environment; and (b) new methods that directly and quantitatively model geology, including high-order spatial statistics.

Sustainable Mineral Resource Development
Quantitative methods and their use in the sustainable development of mineral resources is an increasingly recognized, relatively new and challenging area of interest. My research under this heading includes methods for waste characterization and mine rehabilitation, quantitative mineral resource development with links to environmental conservation, and the broader area of mineral resource management.

Ongoing Research Programs

1. Sustainable Development and Utilization of Mineral Resources: A Stochastic Mine Planning Optimization Framework with Uncertain Metal Supply and Market Demand (April 2011 – on going)

The sustainable development and utilization of mineral resources and reserves ensures the continued supply of raw materials, metals and energy we rely upon. Sustainable development is a critical global problem, particularly given the fast growth and demand of emerging economies and increasing environmental concerns. Several sources of uncertainty impact sustainable mineral resource development: technical, financial, and environmental. Technical and economic uncertainties include the ability of orebodies to supply raw materials, operational mining uncertainties, fluctuating market demand for raw materials and related commodity prices. Based upon our research and learning to date, a new five year research program has commenced to explore and further develop our new stochastic mine and production scheduling paradigm, through: new computationally efficient stochastic optimization methods, new high-order stochastic models, and risk-based financial models. This will include expanding the field of research, addressing new problems encountered in our past research, full-field testing of new methods, and increasing our understanding of the new stochastic framework and related technologies.

2. Developing New Global Stochastic Optimization and High-Order Stochastic Models for Optimizing Mining Complexes with Uncertainty (June 2011– ongoing)

Modelling and optimization techniques have become a standard core aspect of mine design and production scheduling (MDPS) because they maximize the economic value contributed by ore production from a mine and define a technical plan to be followed from a mine's development to its closure. MDPS optimization is a complex problem to address due to its large scale, the unavailability of a truly optimal net present value (NPV) solution, uncertainty in the key parameters involved (geological/mining, financial) and the absence of a method for global or simultaneous optimization of the individual elements of a mining complex. To take our past research developments to the next level, research efforts focus on developing optimization that integrates uncertainty in a global sense and simultaneously considers all elements of a mining complex.

Founded upon our research outcomes to date, global optimization of mining complexes id based on two complementary elements: (I) A new stochastic combinatorial optimization framework for MDPS that integrates multiple mines, material types, ore/waste processing streams including stockpiles, and generates different product specifications suitable for a diverse group of commodities and mining complexes. (II) New 'high-order' spatial mathematical models of uncertainty for multiple material types generating inputs for Point (I), suitable for modeling complex nonlinear, non-Gaussian geologic formations and spatial architectures. Research aims to contribute new methods to the Canadian and global mining industry that aim to change the way problem-solving in the field is approached and impact on: (a) risk management and maximization of return on investment; (b) economic performance and sustainability; (c) enhancement of production and product supply; (d) objective and technically defendable decision-making; and (e) training highly qualified personnel.

Achievements of Selected Completed Projects

1. Demand-Driven Mine Design and Production Scheduling
2. Risk Management and Waste Deferment in Life-of-Mine Production Scheduling
3. Moving Forward from Traditional Optimization: Grade Uncertainty and Risk Effects in Open-Pit Design
4. Using Quantified Geological Risk for Maximum Upside Potential and Minimum Downside Risk Open Pit Mine Design
5. Integration of Fault Uncertainty in Longwall Coal Mining
6. Measurement and Modeling of Ore Processability Characteristics
7. Risk Analysis and Optimization in Stope Design
8. Probabilistic Production Scheduling in Open Pit Mining
9. Uncertainty and Risk Quantifying Optimization for Open Pit Mine Design and Production Scheduling
10. Generalized Sequential Gaussian Simulation for Large Field Simulations
11. The Direct Block-Support Sequential Simulation Method
12. Quantification of Geological Uncertainty and Risk Assessment in Coal Resource Classification
13. Efficient Joint Direct Block Simulation of Multiple Variables
14. Successive conditional simulation of random fields by residuals
15. Successive non-parametric estimation of conditional distributions
16. Conditional Simulation of Fault Systems and Fault Uncertainty
17. Valuing Regional Geoscientific Data Acquisition Programs: Addressing Issues of Quantification, Uncertainty and Risk
18. Sustainable Mineral Development and Environmental Conservation: A Framework for Decision-Making
19. Environmental Reclamation Decisions for Polluted Soils Under Spatial Uncertainty
20. Quantifying Risk to Reduce and Manage Uncertainty in Rehabilitation Sign-Off for Mine Closure
21. Stochastic Models and Optimization for Mine Planning with Uncertain Mineral Supply and Demand - Towards Sustainable Mineral Resource Development
22. Developing a New Probabilistic Network Flow Framework and High-Order Stochastic Models for Open Pit Mine Design and Production Scheduling

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1. Demand-Driven Mine Design and Production Scheduling

An open pit mine can be seen as an industrial operation with ore and waste as products. Accordingly, mine production must meet demands for both ore and waste whilst there are limits in the rate of production and feasible combinations of the ore and waste products that can be generated from the mine. The optimal mine production schedule lies within these feasible ore and waste combinations, or the so-called "feasible domain". The search for an optimal solution involves the evaluation of all the alternate schedules that are characterized by different spatially evolved working zones within this given feasible domain. In reinventing optimization formulations, this project considers that: the mine is an industrial operation with ore and waste as products; production must meet demand while there are limits in the rate of ore production; and there are limited feasible combinations of the production of ore and waste products.

Within the above context, a new framework was developed to establish the solution domain for the optimization of long-term production scheduling based on: (a) an economic model including interest rates, commodity prices, equipment costs and life span, operating and idle costs, capital availability; (b) maximization of the quantity of metal to be mined on a competitive basis mining waste deferment; (c) a technological mine-production scheme; and (d) given production demand. The proposed optimization model delivered a life-of-mine schedule for ore production and waste removal and provided the mining capacity to maximize the project’s NPV for a given set of economic and technological parameters.

The project outcomes included the development of methods and applications at the Fimiston open pit gold and Mt Keith nickel mines in Western Australia. The optimization approach has the ability to improve forecasted life-of-mine performance, as well as opening possibilities to deal effectively with risk issues.

2. Risk Management and Waste Deferment in Life-of-Mine Production Scheduling

This project developed a new framework for the integration of grade uncertainty into a generalized optimization of long-term production scheduling (see the preceding project). This integration was developed through the concept of a "stable solution domain" (SSD) and a new scheduling algorithm based on simulated annealing. The approach generates the mining sequence representing the "100%" confidence production schedule and cash flows for the contained ore reserve, given the understanding of the orebody.

It is important to note that mine design and production scheduling approaches based on single estimate assessments may provide misleading estimates of the key project indicators. The SSD integrates grade uncertainty, metal optimization and waste deferment, and accounts for the technological setup of the mine site. The formulation leads to the stabilization of mining rates over the mine life, and balances purchase and ownership costs of production capacity to facilitate the effective use of the available mining equipment.

In the application of this new risk-based optimization formulation, the SSD and a simulated annealing scheduling algorithm were developed and used to produce a minimum risk life-of-mine schedule for a mining project using data from the Fimiston Pit in Western Australia. The results from the minimum risk life-of-mine schedule show a potential increase of 28% in the NPV of the mine and provide a schedule that minimizes the chance of deviating from mill feed requirements. The project outcomes included the development of methods and applications at Fimiston open pit gold mine, Western Australia. The approach provides risk resilient LOM schedules and increases asset value by managing risk.

3. Moving Forward from Traditional Optimization: Grade Uncertainty and Risk Effects in Open-Pit Design

The quantification of uncertainty and risk has major implications for open-pit design and production scheduling. Optimization in mine planning has been accepted as a set of techniques that introduce analytical mathematical methods into planning. The most common approach in open-pit design and planning is based on the Lerchs–Grossmann three-dimensional graph theory, implemented in industry applications as the nested Lerchs–Grossmann algorithm.

Modern project valuation frameworks can elucidate the paramount positive economic effects of the quantification of uncertainty and risk. In particular, this is the case with geological uncertainty, a major source of risk in mining projects that has detrimental effects on assessing key performance parameters of open-pit mining projects. Quantification of geological uncertainty and risk can enhance optimization in mine design. Geological uncertainty in this project is quantified using conditional simulation in combination with open-pit optimization. An accurate assessment of uncertainty arising from grade variability in the ore reserve allows risk in a mining project to be quantified and considered in decision-making processes. This knowledge adds value to a project before the ore reserve is depleted and before development capital is committed to the project. Conditional simulation technologies provide some answers as to how well the project, and in particular, the orebody being mined, is known. The project demonstrated the effects of geological uncertainty on open pit mine design and key project performance indicators and developed an approach quantifying risk in project performance indicators for any open pit mine design.

4. Using Quantified Geological Risk for Maximum Upside Potential and Minimum Downside Risk Open Pit Mine Design

Orebody uncertainty is a critical factor in strategic mine planning, the optimization of mine designs and long-term production schedules. Several approaches for mine design and long-term production scheduling are available. However, none of them is explicitly developed to effectively deal with, nor incorporate, manage and take advantage of geological risk; in particular, conventional approaches do not generate designs that capture the upside potential of a deposit being considered while minimizing downside risk.

This project developed a new approach to mine design based on risk quantification and alternative strategic decision-making criteria. The approach was founded on the definition of two components. The first component includes the key project indicators to be considered, such as the minimum annual ore production, the amount of metal produced in given mining periods, or discounted cash flows over the life of a mine. The second component includes decision-making criteria, such as a minimum acceptable return on investment, minimum acceptable risk in meeting production targets, and minimization of cash flow risk in the short-term, while maximizing the potential (measurable probability) for profits in the future. The project has detailed an approach to geological risk-based mine design based on conventional optimization technologies and conditional simulation of orebodies.

5. Integration of Fault Uncertainty in Longwall Coal Mining

Fault uncertainty and risk have widely recognized adverse impacts on the mining of underground coal deposits, especially longwall mining. Geological uncertainties may cause significant delays in production schedules, impose substantial changes on mine plans, reduce expected recoverable coal quantities, adversely affect safety and heavily influence the financial viability of a mine. There is a need to implement a more effective, quantitative and practical approach to geological risk modeling and management so that mining companies can better plan longwall operations.

This project, developed to assist in meeting the above need, demonstrated the practical use of state-of-the-art technologies in quantifying fault uncertainty and linked the quantification of uncertainty to decision making in longwall mine planning and production management. The project introduces quantitative risk modeling, an important aspect of which is that it adds flexibility. This flexibility may be regarded as increasing an asset’s value from the mere fact that uncertainty is explicitly quantified and integrated into financial analysis and decision-making for longwall mining.

Case studies from Goonyella-Riverside, Moranbah North, Newlands coal mine, and North Goonyella mine, Queensland, Australia, demonstrated the application of the methods developed. Implementation of the technologies from this project showed measurable benefits, including: use of fault probability maps to optimize longwall designs based on maximizing mineable coal reserves; categorization of coal reserves based on geological risk; and combination of quantified geological risk with longwall layouts to assess and minimize fault impact on mine economics.

6. Measurement and Modeling of Ore Processability Characteristics

Sustainability and profitability of minesite and downstream operations can be improved by optimizing ore processing through more effective modeling and planning. For many mines, this means that ore "processability" attributes need to be spatially modeled and integrated into planning and design aspects of mining and milling. The outcome would be a more efficient use of the mineral resource as well as the delivery of economic and environmental benefits. This pilot project aimed to investigate two aspects related to ore processability: (a) modeling ore textures; and (b) spatial forecasting of ore "grindability" indicators.

Texture may be taken to mean the juxtaposition of mineral phases in the rock, including relative grain sizes, colour and other attributes. Texture is considered to influence, or be a measure of, liberation characteristics. The quantification and spatial modeling of ore textures at various support scales is a critical starting point if textures are to be linked to processability. The challenge is to develop new measurement methods, modeling and interpretive tools and to assess the stochastic properties of ore texture for enhancing production forecasting and planning.

Comminution is usually the largest single consumer of power on a mine site. Reducing the power demand will substantially reduce costs and thus the greenhouse footprint. The task therefore is to allow the comminution circuit performance to be integrated into mine planning through the spatial modeling of grindability indicators, a challenging task as the related characteristics are "process" properties rather than rock properties. This, as well as issues of support-scale, make current modeling frameworks unsuitable for grindability indicators. The project has demonstrated new methods for ore texture simulation and integration of grindability into grade control.

7. Risk Analysis and Optimization in Stope Design

Underground mines represent complex operations that extend over several years and involve large capital expenditures and risk. Risk is the "possibility of loss or injury" and can manifest itself in a variety of ways. Geological uncertainty is technical risk and refers to the inability to accurately assess ore grades, tonnes and reserves. Risk can lead to inadequate revenues, mine life, or returns on investment for a project. The integration of new orebody modeling methods for evaluating geological risk and uncertainty with underground mine design and planning techniques provides a means of managing uncertainty and can thus shelter strategic investments.

To date, uncertainty and associated risk in mine optimization and scheduling has focused on open cut operations. This project focuses on assessing and quantifying risk associated with underground sub-level stoping. Sub-level stoping is highly selective and capital intensive, making it susceptible to geological uncertainty and subsequent risk. Founded on methodologies similar to those used in open pit mining and BRC projects, a comparison between traditional stope design and risk-based designs is made by quantifying the geological risk associated with each.

In a case study at Kidd Creek mine, Canada, an estimated deposit was used to generate a traditional stope design. The traditional design was assessed using conditional simulation and results showed the traditional design to have a 54% potential of producing more tonnes of ore than anticipated, but also a 31% chance of financial loss. Probabilistic (risk-based) designs were then developed using a mathematical programming formulation that optimized stope design for a set of given parameters. Resulting designs have profiles that allow the consideration of the upside/downside characteristics of designs.

The project achievements to date include documentation of grade risk in conventional stope design and the development of a new a probabilistic optimization approach to stope design.

8. Probabilistic Production Scheduling in Open Pit Mining

Optimization of long-term production scheduling is important for managing the substantial cash flows inherent in open pit mining ventures. Discrepancies between actual production and planning expectations arise through uncertainty about the orebody, in terms of ore grade, tons and quality. These aspects of uncertainty are integrated in a new probabilistic optimization formulation for multi-element production scheduling, which also takes into account risk quantification, equipment access and mobility, and other operational requirements. Furthermore, the approach introduces the concept of orebody risk discounting and its integration into production scheduling. In a case study of an Australasian nickel-cobalt laterite orebody, this new risk-based approach produced superior results to traditional approaches.

It is worth noting that the probabilistic approach in this project introduced the new concept of geological risk discounting that technically links geological uncertainty and production scheduling and, inevitably, project valuation. The project developed a new probabilistic scheduling approach and introduced production scheduling based on geological risk discounting.

9. Uncertainty and Risk Quantifying Optimization for Open Pit Mine Design and Production Scheduling

Open pit mine design and production scheduling (OPDPS) deals with the management of cash flows in the order of hundreds of millions of dollars, and is a critical aspect of mining ventures. To enhance decision-making under conditions of uncertainty, this project aims to develop a new methodology for OPDPS based on mathematical and statistical techniques which model uncertainty in key parameters (geological, mining and market/cost) and their effects on economic forecasts. The new formulation is founded on stochastic integer programming, and its integration with spatial stochastic simulations of geological attributes.

Accurately modeling uncertainty, and integrating quantified risk into mine optimization and long term planning allows an enhanced and informed approach to valuing assets, assessing future mine performance, or designing and managing a mining project. This is distinctly different from the traditional single estimate assessments of pertinent parameters, including project NPV, expected cash flows, metal quantities, and expected production costs. Traditional optimization in mine design and planning has two major flaws: (i) it ignores uncertainty from geological, mining and market sources; and (ii) current mathematical models cannot handle input uncertainty models, vis-à-vis stochastically described inputs.

In addressing the above issues, this project: develops a stochastic open pit mine planning framework that directly and efficiently incorporates pertinent uncertainties in open pit design and long-term production scheduling (stochastic OPDPS); formulates multi-time period production scheduling mathematical models; and benchmarks new against traditional methods.

10. Generalized Sequential Gaussian Simulation for Large Field Simulations

The modeling of spatial uncertainty in attributes of geological phenomena is frequently based on the stochastic simulation of Gaussian random fields. This NSERC funded project started at McGill in the late 1990’s and developed a generalization of the sequential Gaussian simulation method founded upon the group decomposition of the posterior probability density function of a stationary and ergodic Gaussian random field, into posterior probability densities of a set of groups of nodes of size ν. The method, which is termed generalized sequential Gaussian simulation on group size ν, relies computationally on sharing the neighborhood of adjacent nodes and simulates groups of ν nodes at a time, instead of the traditional node-by-node simulation.

The new method is computationally efficient and was found to be suitable for simulation on large grids of nodes. Results show that, in terms of computing cost (time), an optimal size ν of a group is about 80% of the optimal neighborhood used for sequential Gaussian simulation and that computation can be up to 50 times faster than the regular sequential Gaussian method, with very little loss in accuracy. The effectiveness of the method has been assessed using a general measure of accuracy, the "screen-effect approximation loss".

11. The Direct Block-Support Sequential Simulation Method

A key bottleneck for the widespread application of conditional simulation technologies in mining operations is the computational efficiency of current simulation methods. This is particularly exacerbated in the case of large orebodies that may be represented by hundreds of thousands of nodes that need to be simulated a number of times. Typically, mining problems require the simulation of orebody attributes at the block-support scale representing mining units used in all processes, from mine design to planning production scheduling. The traditional simulation approach generates simulations at point-support and then approximates mining block values by averaging contained simulated point values. Computational performance of existing simulation algorithms including processing, storage, and data management becomes a limiting factor.

This project developed a new conditional simulation method that overcomes efficiency limits by generating simulations directly at block-support. The efficient and fast simulation of block values is based on a generalized sequential Gaussian algorithm, which is further developed to integrate multi-support conditioning information. Memory requirements are reduced by as many times as the number of nodes necessary to discrete the blocks. The reductions in processing time and memory allocation allow the simulation of very large orebodies in relatively short periods of time, a major requirement in the industrial environment. An application of the new simulation method at the Golden Mile gold deposit (Superpit), Western Australia, was used to test the method. The simulated models were then used for assessment of the uncertainty in the available in situ resources, evaluation of resource classification schemes, and pit optimization.

12. Quantification of Geological Uncertainty and Risk Assessment in Coal Resource Classification

This research project developed and demonstrated a practical, state-of-the-art quantitative approach for reliable, repeatable and standardized resource delineation, assessment and classification, based on the quantification of geological risk. Main expected outcomes include: a procedure for assigning quantified levels of confidence for resource classification purposes; technologies that significantly reduce coal mining investment risks; and new practical tools for the Australian coal mining industry.

To date, a general framework based on stochastic simulations has been developed for the modeling of geological uncertainty and quantification of risk, as linked to the classification of coal resources and the optimization of drilling programs. A key element of this framework is the ability to spatially simulate coal quantity and quality characteristics of interest to assess classification risk, or to sample and assess expected errors. The project involves extensive testing in field studies, including back-analysis, at the mine sites of Peak Downs and Oaky Creek (Queensland) and West Pit (Coal & Allied Hunter Valley, NSW). The development of new methods for: (i) assisting Competent Persons to meet JORC requirements while undertaking coal resource classification; and (ii) drillhole spacing optimization.

13. Efficient Joint Direct Block Simulation of Multiple Variables

The modeling of multiple attributes of a mineral deposit with stochastic simulation is a challenging task. Known methods are impractical, particularly when more than two variables, and/or medium to large size deposits, are considered. The efficient conditional simulation of multiple attributes was developed in this project in the context of the so-termed simulation of vector random fields. The method developed is based on minimum/maximum autocorrelation factors. The approach was developed in the context of direct block simulation and generates realizations of correlated non-Gaussian variables directly at the block support scale. The combination of the decorrelation of the initial variables and the simulation directly at the block support scale generates an algorithm that is very efficient in terms of both computing speed and data management, and allows for the practical joint simulation of several elements in large deposits. The project outcomes included the development of the mathematics and initial testing of the related algorithm in a controlled environment. Testing showed excellent performance, which was superior to conventional methods. Field testing at Yandi Central 1, iron ore deposit, WA, verified expectations.

14. Successive conditional simulation of random fields by residuals

This project developed the mathematics of a new approach to the Lower/Upper decomposition method (LU) for the simulation of stationary random fields. The approach overcomes the size limitations of LU and is suitable for simulations of any size. In addition, the proposed approach can uniquely facilitate fast updating of generated realizations with new data when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the Lower matrix expressed in terms of successive conditional covariance matrices, the approach shows that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. As a result, it can be used for the LU decomposition of matrices of any size. The method is a "successive conditional simulation by residuals" as successively at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

15. Successive non-parametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current non-parametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This project avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates was performed, as additional data were successively included into the estimation process. In addition, the approach led to an efficient non-parametric simulation algorithm for non-Gaussian random functions for dealing with categorical variables.

The project developed a new mathematical formulation of efficient simulation methods that include data updating. The non-parametric spatial estimation of conditional distributions for modeling categorical variables is an important development.

16. Conditional Simulation of Fault Systems and Fault Uncertainty

The modeling of geological fault uncertainty is critical for the development and mining of underground deposits. In this project, a new method for the conditional simulation of fault systems was developed and tested in field studies, to assist quantification of fault uncertainty and related risk assessment. The method is based on the statistical description of fault attributes and the simulation of the locations of the centres of the fault traces. Fault locations are generated from the thinning of a Poisson-like process using a spatially correlated field. The method integrates soft data, such as geological interpretations and geomechanical information. Characteristics of fault simulations include: equally probable fault realisations reproducing all the fault data and their statistical characteristics (fractal "power-law" relationships of fault size distributions, length versus maximum throw, spatial fault patterns). Achievements of the project include the testing of the fault simulation method through a back-analysis study at a mined out part of an underground longwall coal mine found the method to be very effective and able to accurately quantify fault risk. Traditional assessments based only on only fault data were shown to underestimate fault risk.

17. Valuing Regional Geoscientific Data Acquisition Programs: Addressing Issues of Quantification, Uncertainty and Risk

Geological surveys worldwide are involved with research in support of sustainable mineral resource development. The socio-economic benefits to be derived from these activities, however, continue to raise organizational and government sector questions. Fundamental questions include whether or not the resources committed are appropriate and in economic balance with the total benefits to be derived. Another question concerns the degree to which the community at large should fund such services. These questions in turn raise important issues regarding the role and cost of geological surveys, the impact of their services, and how they should maximize community benefit from their activities and expertise. To assess the value of geoscientific information, standard valuation processes need to be modified. This project developed a methodology designed to quantify the "worth" of programs upgrading regional geoscientific infrastructure. An interdisciplinary approach was used to measure the impact of geoscientific information using quantitative resource assessment, computer-based mineral potential modeling, statistical analysis and risk quantification to model decision-processes and assess the impact of additional data. These modeling stages were used to address problems of complexity, uncertainty and credibility in the valuation of geoscientific data. The project produced a new exploration data valuation framework and a case study demonstrated the application of the methodology to generate a dollar value for current regional data upgrade programs in the Geological Survey of Queensland, Australia.

18. Sustainable Mineral Development and Environmental Conservation: A Framework for Decision-Making

Implementing sustainable mining strategies is a sought after goal by the mining industry. As both developed and developing countries strive towards sustainable development, a framework to assist the mining industry to examine the trade-offs of location, size and impact of a mine in light of certain environmental issues is required. Such a framework is proposed based on a valuation of the landscape in a given area that would include both mining operations and, for example, natural areas to be put aside for conservation. Prime mining sites, potential mineral deposits, exploration leases and environmental variables are assessed using advanced heuristic algorithms, which assign values of "irreplaceability" across a region of interest. This framework is implemented using a transparent, GIS-based methodology that generates alternative maps displaying and quantifying various options based on the valuation of irreplaceability. An example from Guyana, South America, demonstrated that the framework allows the mining industry to participate in sustainable practices, while maximizing both mining options and addressing conservation needs. Hence, the proposed framework maximizes economic profitability and long-term sustainability. The project demonstrated a transparent and objective decision-making framework for land valuation and allocation based on "irreplaceability" that contributes to sustainable mining practices.

19. Environmental Reclamation Decisions for Polluted Soils Under Spatial Uncertainty

Risk assessment where people do the sampling requires the sources, distribution and environmental behaviour of contaminants to be investigated on a site-specific basis. It often deals with complex and large variance data sets, which are relatively small and affected by sampling gaps. Conditional simulation generates contaminant concentration values at unobserved zones using observed values, honouring all the observed and relevant information and thus providing tools for decision-making. In the case of a gold reprocessing plant in Canada which was contaminated by mercury, a sequential Gaussian simulation algorithm was used: (a) to detect contaminated zones within the site (which is under environmental investigation) and (b) to address the problem of accounting for uncertainty about pollutant concentrations in environmental decision-making such as delineation of mercury contaminated zones where remedial measures should be taken. The uncertainty was assessed on a block-support level using a local transfer function with two block-support concentration thresholds as imposed by regulatory agency. The resulting monetary impact was evaluated using a loss function approach, which accounts for both false-positive and false-negative errors involved in a decision, and accommodates the needs of regulatory agency. The project produced a novel approach to soil remediation based on spatial modeling methods.

20. Quantifying Risk to Reduce and Manage Uncertainty in Rehabilitation Sign-Off for Mine Closure

Government regulators can be reluctant to provide sign-off and take on the risk of future liabilities following mine closure. One of the areas of uncertainty creating this risk is that the quality of rehabilitation can be spatially highly variable due to the heterogeneity of growth media resulting from the mining and/or mineral processing operations. This pilot project tested the applicability of stochastic modeling concepts and risk quantification in the context of rehabilitation and mine closure, using existing and demonstration datasets from open cut mines. The project developed a basic methodology for quantifying risk related to the quality of rehabilitation, and successfully completed a case study.

Stochastic Models and Optimization for Mine Planning with Uncertain Mineral Supply and Demand - Towards Sustainable Mineral Resource Development

This research program focuses on exploring a key element of sustainable mineral resource development, namely a new risk-based framework for holistic mine planning, design and production scheduling founded upon stochastic optimization and modelling. This framework aims to drastically changes the way we currently approach problem-solving in the field and impacts on the: (i) economic performance and sustainability; (ii) risk management; (iii) maximization of return on investment; (iv) enhancement of production and product supply; (v) management of mine waste and remediation; (vi) minimization of environmental effects from mining; and (vii) objective and technically defendable decision-making. The program will explore new areas of research that, in our view, will generate new concepts and research avenues, future research projects, as well as train qualified students.

Developing a New Probabilistic Network Flow Framework and High-Order Stochastic Models for Open Pit Mine Design and Production Scheduling

Open pit mine design and long-term production scheduling is a critically important part of mining ventures as it deals with the efficient management of cash flows in the order of hundreds of millions of dollars. Mine design and production scheduling determines both the economic outcome of a project and the technical plan to be followed from mine development to mine closure. It is an intricate and complex problem to address due to its large scale, unavailability of a truly optimal net present value solution, and uncertainty in the key parameters involved (geological and mining, financial, and environmental). Geological uncertainty is a major contributor in failing to meet project expectations in projects, as recognized in several studies worldwide, while mining costs and equipment availability are additional contributors.

This research program focuses on two key interrelated elements of open pit mine design: (i) A new risk-based mathematical framework for designing the so-called pushbacks within an open pit under geological uncertainty, and (ii) new 'high-order' spatial mathematical models of geological uncertainty generating inputs for (i), suitable for modelling complex non-linear, non-Gaussian geological processes and orebodies. The above research aims to contribute new methods to the Canadian mining industry that will change the way we currently approach problem-solving in the field and will impact on (a) risk management and maximization of return on investment; (b) economic performance and sustainability; (c) enhancement of production and product supply; (d) objective and technically defendable decision-making; and (e) training highly qualified personnel. In addition, this work will put Canadian R&D in the forefront of developments in this field worldwide.