Markov Chain Monte Carlo Algorithms and their Applications to Petroleum Reservoir Characterization
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This thesis consists of papers on stochastic reservoir characterization and Markov chain Monte Carlo algorithms. Stochastic reservoir models are very complex and naturally spatial and high dimensional. This makes them hard to study analytically. Markov chain Monte Carlo algorithms are iterative techniques for sampling probability distributions. The algorithms can be used to explore complex stochastic reservoir models. In this introduction both stochastic reservoir characterization and Markov chain Monte Carlo algorithms are discussed. The papers are then summarized in the context of these topics. Improved evaluation of petroleum reservoirs facilitates forecasts of production and the design of production strategies. Development of formalized models of reservoir variables makes it easier to break the complex evaluation problems down to specific tasks. Successful decision making can then be made by combining the results. Various sources of information are integrated in this process. Among them are seismic data, well data and production data. In this thesis only seismic and well data are considered. Measurements along well traces are at a fine scale, but do only cover a small domain. Seismic data, on the other hand, cover a large area, but are represented at a coarse scale. Neither well data nor seismic data provide reservoir quantities directly, and we rely on geophysical knowledge to tie observations to the underlying reservoir variables of interest. Geophysical interpretations of seismic and well data are associated with uncertainty, but this is rarely accounted for in traditional geophysical predictions. Stochastic reservoir models represent the reservoir variables as probability distributions. Outputs are probability statements or estimates of reservoir properties with associated uncertainty levels. These can provide valuable inputs when decisions are made.