Computational Geosciences

, Volume 17, Issue 4, pp 671–687 | Cite as

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

  • Sergey Oladyshkin
  • Holger Class
  • Wolfgang Nowak
Original Paper


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 CO2 storage in geological formations, using a low-parametric homogeneous 3D benchmark problem. In a synthetic case study, we update the parameters of a CO2/brine multiphase model on monitored pressure data during CO2 injection.


History matching Arbitrary polynomial chaos Bayesian updating Bootstrap filter CO2 storage Uncertainty quantification 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Sergey Oladyshkin
    • 1
  • Holger Class
    • 1
  • Wolfgang Nowak
    • 1
  1. 1.SRC Simulation Technology, Institute for Modelling Hydraulic and Environmental Systems (LH2)University of StuttgartStuttgartGermany

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