Dear all,

A new fully funded PhD studentship has become available at the School of Mathematical Sciences and the Department of Mechanical, Material and Manufacturing Engineering at the University of Nottingham as part of a joint piece of research work within a large European project, PANACEA. The project is about uncertainty quantification when using complex simulators (i.e. how confident can we be in model predictions), with application to models of CO2 sequestration in deep saline aquifers (see the project description below).

We are looking for a talented student with an interest in statistics and numerical methods for a 3 year PhD project at the University of Nottingham. Although the project will be carried out between the two University departments, the PhD student will be registered with the school of Mathematical Sciences due to the nature of the work. If you are interested and would like more details please contact either me  ([log in to unmask]) or Professor Andrew Cliffe ([log in to unmask]) for further information.

We hope that the successful candidate will start in June/July. Unfortunately, the funding restrictions mean that only EU students are eligible to apply.

Best wishes,
Richard

E.U. PhD Studentships in
Analysis of uncertainties in the numerical simulation of CO2 sequestration 

Geological media are in general heterogeneous on a wide range of spatial scales, ranging from the pore to the reservoir scale. As a consequence, flow, transport and reaction processes in geological media are subject to spatial variability and also temporal fluctuations due to transient driving forces (natural and engineered). These spatial and temporal fluctuations cause fluctuations about the predicted effective behaviour and thus induce uncertainty. 

The Monte-Carlo method is a widely used and effective approach to solving systems of partial differential equations with random inputs, allowing the possible analysis of uncertainties on the variables and parameters. In this method the relevant parameter values are drawn from their probability distributions and the governing equations are solved for many such samples.  The main difficulty is in deciding which variants to study and making sure that a sufficiently wide range of alternatives have been considered. For the large-scale, time-dependent simulations that must be carried out as part of an investigation of a storage site for CO2 brute force Monte-Carlo simulation will be impractical due to its computational cost. 

The work proposed here is to investigate alternative methods to brute-force Monte-Carlo for solving the equations with random inputs.  The main source of uncertainty that will be considered is the physico-chemical heterogeneity of the rock formation. Suitable stochastic models for these heterogeneities will be developed.  Such models have an infinite number of stochastic degrees of freedom and will be approximated by a finite number of degrees of freedom using, for example Karhunen-Loeve expansions.  To solve the resulting problem three techniques will be investigated;   The stochastic collocation method in which a solution is sought in terms of polynomials in a set of random variables (polynomial chaos expansions), the use of statistical approximations the simulator called emulators, and finally the third approach is based on the PDF method described above. PDF equations will be developed that governs the statistics of the state variables (pressure, concentration, reaction rates) along the lines described above.  

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Dr Richard Wilkinson
Lecturer in Statistics
School of Mathematical Sciences
University of Nottingham

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http://www.maths.nottingham.ac.uk/personal/pmzrdw
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