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Reduced Space Dynamics-Based Geo-Statistical Prior Sampling for Uncertainty Quantification of End Goal Decisions

  • Conference paper
Numerical Analysis and Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 134))

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Abstract

The inversion of large-scale ill-posed problems introduces multiple challenges. These include, identifying appropriate noise model, prescription of suitable prior information, design of an informative experiment, uncertainty quantification, incorporation of heterogeneous sources of data, and definition of an appropriate optimization scheme. In the context of flow in porous media, subsurface parameters are inferred through the inversion of oil production data (a process called history matching). In this study, the inherent uncertainty of the problem is mitigated by devising efficient and comprehensive approaches for prior sampling. Despite meticulous efforts to minimize the variability of the solution space, the distribution of the posterior may remain intractable. In particular, geo-statisticians may often propose large sets of prior samples that regardless of their apparent geological distinction are almost entirely flow equivalent. As an antidote, a reduced space hierarchical clustering of flow relevant indicators is proposed for aggregation of these samples. The effectiveness of the method is demonstrated both with synthetic and field scale data. In addition, numerical linear algebra techniques that exploit the special structure of the underlying problems are elucidated.

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Notes

  1. 1.

    Note that often appropriate integration of structure is not exercised in the course of history matching, consequently, in standard practice the emphasis is on data misfit minimization alone. Such an approach is obviously far from desirable. More generally there are various circumstances whereby the dynamical equivalence of distinct geological models may be observed.

  2. 2.

    The references to α are phase references not power indices.

  3. 3.

    Indicator of the realization could be a function of the realization such as static properties, for example, permeability or porosity, or alternatively, as we have already seen, a dynamic descriptor such as mass flux or time of flight.

  4. 4.

    Areas with particular rock characteristics.

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Acknowledgements

The authors wish to thank Ulisses Mello, Jorn van Doren, and Jan Dirk Jansen for their insightful comments and support throughout the evolution of the study.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA

    Lior Horesh & Andrew R. Conn

  2. Shell, Katy, TX, USA

    Eduardo A. Jimenez & Gijs M. van Essen

Authors
  1. Lior Horesh
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  2. Andrew R. Conn
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  3. Eduardo A. Jimenez
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  4. Gijs M. van Essen
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Corresponding author

Correspondence to Lior Horesh .

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Editors and Affiliations

  1. Department of Mathematics College of Science, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  2. Faculty of Engineering, University of Calabria, Arcavacada di Rende, Italy

    Lucio Grandinetti

  3. Department Mathematics and Statistics College of Science, Sultan Qaboos University, Muscat, Oman

    Anton Purnama

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Horesh, L., Conn, A.R., Jimenez, E.A., van Essen, G.M. (2015). Reduced Space Dynamics-Based Geo-Statistical Prior Sampling for Uncertainty Quantification of End Goal Decisions. In: Al-Baali, M., Grandinetti, L., Purnama, A. (eds) Numerical Analysis and Optimization. Springer Proceedings in Mathematics & Statistics, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-17689-5_8

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