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  • History Matching Using an Iterative Ensemble Smoother with Correlation-Based Adaptive

    Localization - A Real Field Case Study

    By Xiaodong Luo, IRIS / NIORC, Norway

    A research based on the collaborations with the following colleagues at IRIS:

    Tuhin Bhakta, Geir Evensen (also with NERSC), Rolf Lorentzen, Geir Nævdal, Randi Valestrand

  • Outline

    • Background and motivation

    • Correlation-based adaptive localization

    • Application to the Norne field case

    • Discussion and conclusion

  • Ensemble-based data assimilation for reservoir characterization

    Ensemble-based data assimilation methods provide a means of uncertainty quantification (UQ) for the estimated petrophysical parameters (inputs)

    Data assimilation to update reservoir models

    Reservoir models Seismic data

  • Poor assimilation performance due to ensemble collapse

    Estimates Truth

    Desired scenario Reality: ensemble collapse

    Ensemble collapse: a phenomenon in which estimated reservoir models become almost identical with very few varieties

  • Tackling ensemble collapse through localization

    ∆𝑚𝑚𝑖𝑖 = � 𝑗𝑗

    𝑘𝑘𝑖𝑖𝑗𝑗 ∆𝑑𝑑𝑗𝑗 (without localization)

    ∆𝑚𝑚𝑖𝑖: change of the 𝑖𝑖-th model variable

    ∆dj: information (innovation) from the 𝑗𝑗-th data point

    𝑘𝑘𝑖𝑖𝑗𝑗 : coefficient specifying the degree of contribution of the innovation term ∆dj to the model change ∆𝑚𝑚𝑖𝑖

    Updating model variables in ensemble-based history matching methods

  • Tackling ensemble collapse through localization

    Small ensemble size Substantial sampling errors Spurious contributions

    of ∆𝑑𝑑𝑗𝑗 to ∆𝑚𝑚𝑖𝑖

    In practice

    localization∆𝑚𝑚𝑖𝑖 = � 𝑗𝑗

    ( 𝑐𝑐𝑖𝑖𝑗𝑗 𝑘𝑘𝑖𝑖𝑗𝑗) ∆𝑑𝑑𝑗𝑗

    Tackling ensemble collapse through localization

    𝑐𝑐𝑖𝑖𝑗𝑗 ∈ [0,1]: tapering coefficients with respect to the pair (∆𝑚𝑚𝑖𝑖, ∆𝑑𝑑𝑗𝑗)

    𝑐𝑐𝑖𝑖𝑗𝑗 introduced to modify the contributions of ∆𝑑𝑑𝑗𝑗 to ∆𝑚𝑚𝑖𝑖

    𝑐𝑐𝑖𝑖𝑗𝑗 dependent on the specific localization scheme in use

    The “needed” devil

  • Production rates

    Petrophysical parameters on reservoir gridblock

    Figure from OPM simulator (https://opm-project.org/)

    Distance-based localization

  • Gaspari-Cohn tapering function*

    Slide 8

    Reservoir gridblock (Petrophysical parameters)

    Well location (Production data)

    Distance (dist)

    𝑐𝑐𝑖𝑖𝑗𝑗 = 𝑓𝑓(𝑑𝑑𝑖𝑖𝑑𝑑𝑑𝑑(∆𝑚𝑚𝑖𝑖 ,∆𝑑𝑑𝑗𝑗))

    *Gaspari, Gregory, and Stephen E. Cohn. "Construction of correlation functions in two and three dimensions." QJRMS 125 (1999): 723-757.

    Distance-based localization

  • Some long-standing issues arising in conventional localization schemes*§

    *Luo, X., Bhakta, T., & Nævdal, G. (2018). Correlation-based adaptive localization with applications to ensemble-based 4D-seismic history matching. SPE Journal, vol. 23, pp. 396-427, 2018. SPE-185936-PA.

    §Luo, X, Lorentzen, R., Valestrand, R. & Evensen, G. (2018). Correlation-based adaptive localization for ensemble-based history matching: Applied to the Norne field case study. SPE Norway One Day Seminar, SPE-191305-MS

    Dependence on the presence of physical locations

    Effect of ensemble size

    Non-local observations

    Time-lapse observations

    Different types of model-data pairs

    ISSUESUsability/re-usability

  • Outline

    • Background and motivation

    • Correlation-based adaptive localization

    • Application to the Norne field case

    • Discussion and conclusion

  • Petrophysical parameter

    Production data

    Correlation (corr)

    𝑐𝑐𝑖𝑖𝑗𝑗 = 𝑓𝑓(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(∆𝑚𝑚𝑖𝑖 ,∆𝑑𝑑𝑗𝑗))

    e.g., a hard-thresholding function*§ 𝑓𝑓 𝑥𝑥 = 𝐼𝐼( 𝑥𝑥 > λ)

    *Evensen, Geir. Data assimilation: the ensemble Kalman filter. Springer, 2009. § Luo, X., Bhakta, T., & Nævdal, G. (2018). Correlation-based adaptive localization with applications to

    ensemble-based 4D-seismic history matching. SPE Journal, vol. 23, pp. 396-427, 2018. SPE-185936-PA

    Absolute Corr ≤ threshold

    Absolute Corr > threshold

    Threshold value λ§

    Correlation-based adaptive localization

  • Overcoming some long-standing issues arising in conventional localization schemes*§

    *Luo, X., Bhakta, T., & Nævdal, G. (2018). Correlation-based adaptive localization with applications to ensemble-based 4D-seismic history matching. SPE Journal, vol. 23, pp. 396-427, 2018. SPE-185936-PA.

    §Luo, X, Lorentzen, R., Valestrand, R. & Evensen, G. (2018). Correlation-based adaptive localization for ensemble-based history matching: Applied to the Norne field case study. SPE Norway One Day Seminar, SPE-191305-MS

    Dependence on the presence of physical locations

    Effect of ensemble size

    Non-local observations

    Time-lapse observations

    Different types of model-data pairs

    ISSUESUsability/re-usability

    Tame the “needed” devil

  • Outline

    • Background and motivation

    • Correlation-based adaptive localization

    • Application to the Norne field case

    • Discussion and conclusion

  • Application to the Norne field case Slide 14

    Dataset acquired from http://www.ipt.ntnu.no/~norne

    Experimental settings (more details in SPE-191305-MS)

    Model dimension 46 x 112 x 22 (44927/113344 active)

    Parameters to estimate PORO, PERMX, NTG + other parameters; Total number 148159

    Reservoir simulator ECLIPSE 100, control mode RESV

    Production data WGPRH, WOPRH, WWPRH from 11/1997 to 12/2006; Total number 2358

    History matching algorithm

    Iterative ensemble smoother*

    Initial ensemble 100, https://github.com/rolfjl/Norne-Initial-Ensemble

    Localization Both distance- and correlation-based localization for performance comparison

    *Luo, Xiaodong, Andreas S. Stordal, Rolf J. Lorentzen, and Geir Nævdal. "Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem: Theory and applications." SPE Journal, SPE-176023-PA (2015).

  • Application to the Norne field case Slide 15

    Box plots of data mismatch at different iteration steps

    Distance-based Correlation-based

  • Application to the Norne field case Slide 16

    Production forecasts

    Distance-based Correlation-based

  • Application to the Norne field case Data mismatch for production data not used in history matching (cross-verification)

  • Outline

    • Background and motivation

    • Correlation-based adaptive localization

    • Application to the Norne field case

    • Discussion and conclusion

  • Both distance- and correlation-based localization work well to prevent ensemble collapse and improve assimilation performance

    Correlation-based localization serves as a viable alternative to distance-based one: Mitigate or avoid some long-standing issues (e.g., non-local/ time-dependent

    observations) in distance-based localization Easy to implement, and straightforward to transfer among different cases

    (2D/3D).

    Further improvements: much more efficient implementation of automatic and adaptive localization*, presented/to be presented in The 13th EnKF workshop, May 2018 ECMOR, September 2018

    *Luo, Xiaodong and Tuhin Bhakta. "Towards automatic and adaptive localization for ensemble- based history matching." To appear in ECMOR, Barcelona, Spain, September 2018.

  • Acknowledgements / Thank You / Questions

    XL acknowledges the Research Council of Norway and the industry partners – ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Maersk Oil; a company by Total, DONG Energy A/S, Denmark, Statoil Petroleum AS, Neptune Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS – of The National IOR Centre of Norway for financial supports.

    XL also acknowledges partial financial supports from the CIPR/IRIS cooperative research project “4D Seismic History Matching”, which is funded by industry partners Eni Norge AS, Petrobras, and Total EP Norge, as well as the Research Council of Norway (PETROMAKS2).

    History Matching Using an Iterative Ensemble Smoother with Correlation-Based Adaptive Localization - A Real Field Case Study�� Lysbildenummer 2 Ensemble-based data assimilation for reservoir characterization Poor assimilation performance due to ensemble collapse Tackling ensemble collapse through localization Tackling ensemble collapse through localization Distance-based localization Distance-based localization Some long-standing issues arising in conventional localization schemes*§ Lysbildenummer 10 Correlation-based adaptive localization Overcoming some long-standing issues arising �in conventi