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

We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an approximation to the conditional PDFs is derived. Numerical results first showed the superiority of the Gamma expansion over other numerical methods. The ability of the Gamma expansion to fit mixtures of Gaussian ans super Gaussian PDFs, univariate and multivariate Lognormal PDFs, and complex geologic media is shown through different examples.

Generalized Laguerre expansions of multivariate probability densities with moments

Scheduling production in open-pit mines is characterized by uncertainty about the metal content of the orebody (the reserve) and leads to a complex large-scale mixed-integer stochastic optimization problem. In this paper, a two-phase solution approach based on Rockafellar and Wets’ progressive hedging algorithm (PH) is proposed. PH is used in phase I where the problem is first decomposed by partitioning the set of scenarios modeling metal uncertainty into groups, and then the sub-problems associated with each group are solved iteratively to drive their solutions to a common solution. In phase II, a strategy exploiting information obtained during the PH iterations and the structure of the problem under study is used to reduce the size of the original problem, and the resulting smaller problem is solved using a sliding time window heuristic based on a fix-and-optimize scheme. Numerical results show that this approach is efficient in finding near-optimal solutions and that it outperforms existing heuristics for the problem under study.

Progressive hedging applied as a metaheuristic to schedule production in open-pit mines accounting for reserve uncertainty

This paper presents a new mathematical formulation to address mine production scheduling with multiple processing streams, under mineral supply uncertainty, and where the destination is formulated ...

Long-term mine production scheduling with multiple processing destinations under mineral supply uncertainty, based on multi-neighbourhood Tabu search

A mining complex may be comprised of multiple components, including open-pit and underground operations. Traditional approaches in mine planning do not account for the various components simultaneously leading to under-value solutions. Over the last decade, some methods have been developed to incorporate multiple components of the mining value chain during optimisation. Even though these new methods incorporate more decisions and flexibility to the optimisation of a mining complex, they may either ignore uncertainties associated with the mining project or consider decisions taken before optimisation. This paper presents a method that optimises mining complexes comprised of multiple open-pits, underground operations and processing destinations. Mining, blending, processing and transportation decision variables are simultaneously optimised while accounting for geological uncertainty. The method uses a simulated annealing algorithm at different decision levels in order to generate a stochastic-based extraction sequence and processing policies. A case study shows its ability to generate a higher NPV while facing a reduced amount of risk when compared to traditional optimisation methods.

Globally optimizing open-pit and underground mining operations under geological uncertainty

A geostatistical method is presented to determine the absolute horizontal and vertical effective permeabilities at the reservoir block scale from core support-scale values required for 3D reservoir flow simulations. The key element of the geostatistical model is the definition of block support-scale permeabilities as the spatial power average of core-support values over the volume of a reservoir gridblock. Block support-scale permeabilities are then found to be a function of the permeability variogram, the averaging volume, and a power-averaging constant, which is derived separately for horizontal and vertical flow with a numerical approach. The application of the proposed method requires that core-support values be available within each reservoir block

Roussos Dimitrakopoulos

Papers

Generalized Laguerre expansions of multivariate probability densities with moments

Progressive hedging applied as a metaheuristic to schedule production in open-pit mines accounting for reserve uncertainty

Long-term mine production scheduling with multiple processing destinations under mineral supply uncertainty, based on multi-neighbourhood Tabu search

Globally optimizing open-pit and underground mining operations under geological uncertainty

Geostatistical Modeling of Gridblock Permeabilities for 3D Reservoir Simulators