Effective approaches and solution techniques for conditioning, robust design and control in the subsurface

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When predicting processes in the subsurface, the need for uncertainty quantification and risk assessment is evident. Yet, this is merely the first within a full spectrum of tasks in stochastic modelling, which includes calibration, robust design, optimal monitoring and predictive control. Monte-Carlo simulation is the most simple and universally applicable option for stochastic modelling, but its computational costs become strictly prohibitive when joining it with the above follow-up tasks. Polynomial chaos expansions (PCE) are computationally much more efficient, and receive a quickly increasing attention. However, only little work has been done to make PCE available to the full spectrum of tasks. The proposed work will make PCE accessible for the full spectrum of tasks named above. We will develop a new, integrative and efficient framework, where all involved quantities will be treated via an overall functional approximation that represents the system’s behaviour within the entire range of un-certain parameters, design or control variables. Thus, the strongly increased computational costs of follow-up tasks will be drastically mitigated. We will further reduce storage requirements and improve computational efficiency via data-sparse and low-rank tensor representations throughout all tasks. The drastic gain in computational efficiency will finally allow tackling advanced follow-up tasks for full-scale, complex and real-world problems, even under uncertainty. We will demonstrate this by application to CO2 injection into the deep subsurface. Site characterization and selection, design and control of injection strategies under uncertainty, as well as optimal monitoring of CO2 leakage to the surface will be performed within the new framework, leading to better assessment, management and reduction of the involved risks.