The major spreading and trapping mechanisms of carbon dioxide in geological media are subject to spatial variability due to heterogeneity of the physical and chemical properties of the medium. For modelling to make a useful contribution to the understanding of carbon dioxide sequestration and its associated risk assessment, the impact of heterogeneity on flow, transport and reaction processes and their uncertainties must be identified, characterised, and its consequences quantified. Complex computer simulation models based on systems of partial differential equations with random inputs are often used to describe the flow of groundwater through this heterogeneous media. The Monte Carlo method is a widely used and effective approach to quantify uncertainty in such systems of partial differential equations with random inputs. This thesis investigates two alternatives to Monte Carlo for solving the equations with random inputs; the first of these are techniques developed for improving the computational performance of Monte Carlo, namely methods such as, multilevel Monte Carlo, quasi Monte Carlo, multilevel quasi Monte Carlo. The second alternative, Gaussian process emulation, is an approach based on Bayesian non parametric modelling, in which we build statistical approximations of the simulator, called emulators. Numerical calculations carried out in this thesis have demonstrated the effectiveness of the proposed alternatives to the Monte Carlo method for solving two dimensional model problems arising in groundwater flow and Carbon capture and storage processes. Multilevel quasi Monte Carlo has been proven to be the more efficient method, in terms of computational resources used, among Monte Carlo, multilevel Monte Carlo and quasi Monte Carlo. Gaussian process emulation has been proven to be a reliable surrogate for these simulators and it has been concluded that the use of Gaussian process emulation is a powerful tool which can be satisfactorily used when the physical processes are modelled through computationally expensive simulators.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682671 |
| Date | January 2016 |
| Creators | Crevillen Garcia, David |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/31084/ |
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