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).