SPE Journal
Volume 17, Number 1, March 2012, pp. 152-162

SPE-145192-PA

Improved Uncertainty Quantification in the Ensemble Kalman Filter Using Statistical Model-Selection Techniques

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DOI  More information 10.2118/145192-PA http://dx.doi.org/10.2118/145192-PA

Citation

  • Sætrom, J. Hove, J., Skjervheim, J.-A., and Vabø, J.G. 2012. Improved Uncertainty Quantification in the Ensemble Kalman Filter Using Statistical Model-Selection Techniques. SPE J.  17 (1): 152-162. SPE-145192-PA. http://dx.doi.org/10.2118/145192-PA.

Discipline Categories

  • 6.5.8 History Matching
  • 6.5.6 Dynamic Model Update Algorithms
  • 6.5.5 Evaluation of Uncertainties
  • 3.2.1 Risk, Uncertainty, and Risk Assessment

Keywords

  • Regression Model Overfitting, Dimension Reduction, Cross-Validation, Reservoir Characterisation

Summary

The ensemble Kalman filter (EnKF) is a sequential Monte Carlo method for solving nonlinear spatiotemporal inverse problems, such as petroleum-reservoir evaluation, in high dimensions. Although the EnKF has seen successful applications in numerous areas, the classical EnKF algorithm can severely underestimate the prediction uncertainty. This can lead to biased production forecasts and an ensemble collapsing into a single realization.

In this paper, we combine a previously suggested EnKF scheme based on dimension reduction in the data space, with an automatic cross-validation (CV) scheme to select the subspace dimension. The properties of both the dimension reduction and the CV scheme are well known in the statistical literature. In an EnKF setting, the former can reduce the effects caused by collinear ensemble members, while the latter can guard against model overfitting by evaluating the predictive capabilities of the EnKF scheme. The model-selection criterion traditionally used for determining the subspace dimension, on the other hand, does not take the predictive power of the EnKF scheme into account, and can potentially lead to severe problems of model overfitting. A reservoir case study is used to demonstrate that the CV scheme can substantially improve the reservoir predictions with associated uncertainty estimates.

© 2012. Society of Petroleum Engineers

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History

  • Original manuscript received: 28 June 2010
  • Revised manuscript received: 16 December 2010
  • Manuscript approved: 22 December 2010
  • Published online: 31 January 2012
  • Version of record: 13 March 2012