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Abstract

Summary

Ensemble data assimilation algorithms are among the state-of-the-art history matching methods. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-leastsquares problems.

In a broader picture, history matching is essentially an inverse problem, which is often nonlinear and ill-posed, and may not possess any unique solution. To mitigate these noticed issues, in the course of solving an inverse problem, domain knowledge and prior experience are often incorporated into a suitable cost function within a respective optimization problem. This helps to constrain the solution path and promote certain desired properties (e.g., sparsity, smoothness) in the solution. Whereas in the inverse problem theory there is a rich class of inversion algorithms resulting from various choices of cost functions, there are few ensemble data assimilation algorithms which in their practical uses are implemented in a form beyond nonlinear-least-squares.

This work aims to narrow this noticed gap. Specifically, we consider a class of generalized cost functions, and derive a unified formula to construct a corresponding class of novel ensemble data assimilation algorithms, which aim to promote certain desired properties that are chosen by the users, but may not be achieved by using the conventional ensemble-based algorithms.

As an example, we consider a channelized reservoir characterization problem, and formulate history matching as some minimum-average-cost problems with two new cost functions. In one of them, our objective is to restrict the changes of total variations of reservoir models during model updates. While in the other, our goal is instead to curb the modifications of histograms of reservoir models. While these two cost functions may appear unconventional in the context of ensemble data assimilation, the corresponding assimilation algorithms derived from our proposed formula are very similar to the conventional iterative ensemble smoother (IES). As such, our previous experience with the IES can be smoothly transferred into the implementations and applications of these new algorithms. In addition, the experiment results indicate that using either of these two new algorithms leads to better history matching performance, in comparison to the original IES.

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.202035044
2020-09-14
2024-04-28

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References

  1. Canchumuni, S.W., Emerick, A.A. and Pacheco, M.A.C.
    [2019] History matching geological facies models based on ensemble smoother and deep generative models. Journal of Petroleum Science and Engineering, 177, 941–958.
     [Google Scholar]
  2. Chen, X., Xu, F. and Ye, Y.
    [2010] Lower bound theory of nonzero entries in solutions of ℓ2-ℓp minimization. SIAM Journal on Scientific Computing, 32(5), 2832–2852.
     [Google Scholar]
  3. Chen, Y and Oliver, D.
    [2013] Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Computational Geosciences, 17, 689–703.
     [Google Scholar]
  4. Chen, Y and Oliver, D.S.
    [2012] Ensemble randomized maximum likelihood method as an iterative ensemble smoother. Mathematical Geosciences, 44, 1–26.
     [Google Scholar]
  5. Cover, T.M. and Thomas, J.A.
    [2012] Elements of information theory. John Wiley & Sons.
     [Google Scholar]
  6. Emerick, A.A.
    [2018] Deterministic ensemble smoother with multiple data assimilation as an alternative for history-matching seismic data. Computational Geosciences, 22(5), 1175–1186.
     [Google Scholar]
  7. Emerick, A.A. and Reynolds, A.C.
    [2012] Ensemble smoother with multiple data assimilation. Computers & Geosciences, 55, 3–15.
     [Google Scholar]
  8. Engl, H.W., Hanke, M. and Neubauer, A.
    [2000] Regularization of Inverse Problems. Springer.
     [Google Scholar]
  9. Evensen, G.
    [2009] Data Assimilation: The Ensemble Kalman Filter. Springer Science & Business Media.
     [Google Scholar]
  10. [2018] Analysis of iterative ensemble smoothers for solving inverse problems. Computational Geosciences, 22.
     [Google Scholar]
  11. Evensen, G., Raanes, P.N., Stordal, A.S. and Hove, J.
    [2019] Efficient implementation of an iterative ensemble smoother for big-data assimilation and reservoir history matching. Frontiers in Applied Mathematics and Statistics, 5, 47.
     [Google Scholar]
  12. Iglesias, M.A.
    [2015] Iterative regularization for ensemble data assimilation in reservoir models. Computational Geosciences, 19, 177–212.
     [Google Scholar]
  13. Jafarpour, B.
    [2011] Wavelet reconstruction of geologic facies from nonlinear dynamic flow measurements. IEEE Transactions on Geoscience and Remote Sensing, 49, 1520–1535.
     [Google Scholar]
  14. Kalnay, E.
    [2002] Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press.
     [Google Scholar]
  15. Kay, S.M.
    [1993] Fundamentals of statistical signal processing. Vol 1: Estimation theory. Prentice Hall PTR.
     [Google Scholar]
  16. Li, L., Jiang, S. and Huang, Q.
    [2012] Learning hierarchical semantic description via mixed-norm regularization for image understanding. IEEE Transactions on Multimedia, 14(5), 1401–1413.
     [Google Scholar]
  17. Lorentzen, R., Flornes, K.
    and Nævdal, G. [2012] History matching channelized reservoirs using the ensemble Kalman filter. SPE Journal, 17, 137–151.
     [Google Scholar]
  18. Luo, X. and Bhakta, T.
    [2020] Automatic and adaptive localization for ensemble-based history matching. Journal of Petroleum Science and Engineering, 184, 106559.
     [Google Scholar]
  19. Luo, X., Bhakta, T., Jakobsen, M.
    and Nævdal, G. [2017] An ensemble 4D-seismic history-matching framework with sparse representation based on wavelet multiresolution analysis. SPE Journal, 22, 985–1010. SPE-180025-PA.
     [Google Scholar]
  20. and Nævdal, G. [2018] Efficient big data assimilation through sparse representation: A 3D benchmark case study in petroleum engineering. PLOS ONE, 13, e0198586.
     [Google Scholar]
  21. Luo, X., Stordal, A., Lorentzen, R.
    and Nævdal, G. [2015] Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem: theory and applications. SPE Journal, 20, 962–982. SPE-176023-PA.
     [Google Scholar]
  22. Ma, X. and Bi, L.
    [2019] A robust adaptive iterative ensemble smoother scheme for practical history matching applications. Computational Geosciences, 23(3), 415–442.
     [Google Scholar]
  23. Magnus, J.R. and Neudecker, H.
    [2019] Matrix differential calculus with applications in statistics and econometrics. John Wiley & Sons.
     [Google Scholar]
  24. Nocedal, J. and Wright, S.J.
    [2006] Numerical optimization. Springer, 2nd edn.
     [Google Scholar]
  25. Oliver, D.S., Reynolds, A.C. and Liu, N.
    [2008] Inverse Theory for Petroleum Reservoir Characterization and History Matching,. Cambridge University Press.
     [Google Scholar]
  26. Rudin, L.I., Osher, S. and Fatemi, E.
    [1992] Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60(1–4), 259–268.
     [Google Scholar]
  27. Sarma, P., Chen, W.H.
    [2009] Generalization of the Ensemble Kalman Filter using kernels for nongaussian Random Fields. In: SPE reservoir simulation symposium. Society of Petroleum Engineers, The Woodlands, Texas, USA. SPE-119177-MS.
     [Google Scholar]
  28. Simon, D.
    [2006] Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches. Wiley-Interscience.
     [Google Scholar]
  29. Soares, R.V., Luo, X., Evensen, G. and Bhakta, T.
    [2020] 4D seismic history matching: Assessing the use of a dictionary learning based sparse representation method. In preparation.
     [Google Scholar]
  30. Stordal, A.S. and Elsheikh, A.H.
    [2015] Iterative ensemble smoothers in the annealed importance sampling framework. Advances in Water Resources, 86, 231–239.
     [Google Scholar]
  31. Strebelle, S.
    [2002] Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology, 34, 1–21.
     [Google Scholar]
  32. Tarantola, A.
    [2005] Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM.
     [Google Scholar]
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Novel Ensemble Data Assimilation Algorithms Derived from A Class of Generalized Cost Functions
Conference Proceedings 2020, 1 (2020); https://doi.org/10.3997/2214-4609.202035044
/content/papers/10.3997/2214-4609.202035044
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