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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
EstimatesTruth
Desired scenario Reality: ensemble collapse
Ensemble collapse: a phenomenon in which estimated reservoirmodels 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
AbsoluteCorr ≤threshold
AbsoluteCorr >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 caseSlide 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 caseSlide 15
Box plots of data mismatch at different iteration steps
Distance-based Correlation-based
Application to the Norne field caseSlide 16
Production forecasts
Distance-based Correlation-based
Application to the Norne field caseData 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 localizationEasy 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 inThe 13th EnKF workshop, May 2018ECMOR, 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).