Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations. (English) Zbl 1382.86022

Oladyshkin, Sergey; Class, Holger; Nowak, Wolfgang

Comput. Geosci. 17, No. 4, 671-687 (2013).

Summary: Model calibration and history matching are important techniques to adapt simulation tools to real-world systems. When prediction uncertainty needs to be quantified, one has to use the respective statistical counterparts, e.g., Bayesian updating of model parameters and data assimilation. For complex and large-scale systems, however, even single forward deterministic simulations may require parallel high-performance computing. This often makes accurate brute-force and nonlinear statistical approaches infeasible. We propose an advanced framework for parameter inference or history matching based on the arbitrary polynomial chaos expansion (aPC) and strict Bayesian principles. Our framework consists of two main steps. In step 1, the original model is projected onto a mathematically optimal response surface via the aPC technique. The resulting response surface can be viewed as a reduced (surrogate) model. It captures the model’s dependence on all parameters relevant for history matching at high-order accuracy. Step 2 consists of matching the reduced model from step 1 to observation data via bootstrap filtering. Bootstrap filtering is a fully nonlinear and Bayesian statistical approach to the inverse problem in history matching. It allows to quantify post-calibration parameter and prediction uncertainty and is more accurate than ensemble Kalman filtering or linearized methods. Through this combination, we obtain a statistical method for history matching that is accurate, yet has a computational speed that is more than sufficient to be developed towards real-time application. We motivate and demonstrate our method on the problem of \(\text{CO}_2\) storage in geological formations, using a low-parametric homogeneous 3D benchmark problem. In a synthetic case study, we update the parameters of a \(\text{CO}_2\)/brine multiphase model on monitored pressure data during \(\text{CO}_2\) injection.

MSC:

86A60	Geological problems
62F15	Bayesian inference
62F40	Bootstrap, jackknife and other resampling methods
62P12	Applications of statistics to environmental and related topics

Keywords:

history matching; arbitrary polynomial; chaos; Bayesian updating; bootstrap filter; \(\text{CO}_2\) storage; uncertainty quantification

Software:

KernSmooth; EnKF

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