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Conditioning reservoir models on rate data using ensemble smoothers

Abstract

There are several issues to consider when we use ensemble smoothers to condition reservoir models on rate data. The values in a time series of rate data contain redundant information that may lead to poorly conditioned inversions and thereby influence the stability of the numerical computation of the update. A time series of rate data typically has correlated measurement errors in time, and negligence of the correlations leads to a too strong impact from conditioning on the rate data and possible ensemble collapse. The total number of rate data included in the smoother update will typically exceed the ensemble size, and special care needs to be taken to ensure numerically stable results. We force the reservoir model with production rate data derived from the observed production, and the further conditioning on the same rate data implies that we use the data twice. This paper discusses strategies for conditioning reservoir models on rate data using ensemble smoothers. In particular, a significant redundancy in the rate data makes it possible to subsample the rate data. The alternative to subsampling is to model the unknown measurement error correlations and specify the full measurement error covariance matrix. We demonstrate the proposed strategies using different ensemble smoothers with the Norne full-field reservoir model.

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Acknowledgements

Geir Evensen was supported by a research project funded by Statoil and for the finalization of the manuscript by the Research Council of Norway through the DIGIRES project with industry partners Statoil Petroleum AS, Eni Norge AS, VNG Norge AS, DEA Norge AS, Aker BP AS, and Petrobras.

Kjersti Solberg Eikrem acknowledges the Research Council of Norway and the industry partners; ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Maersk Oil Norway AS, DONG Energy A/S, Denmark, Statoil Petroleum AS, ENGIE E&P NORGE AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS of The National IOR Centre of Norway for support.

The study received access to Eclipse licenses from Schlumberger and benefited from the interaction and collaborations with the Nordforsk Nordic center of excellence in data assimilation, EMBLA. We are grateful to Joakim Hove and Statoil for making their Ensemble Reservoir Tool (ERT) available at Github. Finally, constructive comments from two anonymous reviewers have contributed to a clearer and more in-depth presentation and discussion.

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Evensen, G., Eikrem, K.S. Conditioning reservoir models on rate data using ensemble smoothers. Comput Geosci 22, 1251–1270 (2018). https://doi.org/10.1007/s10596-018-9750-8

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Keywords

  • History matching
  • Ensemble smoothers
  • Iterative ensemble smoothers
  • Production data