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TUPREP

 

 

 

Covariance Localization for Ensemble Kalman Filter

Because of its ease of implementation, computational efficiency and the fact that it generates multiple history-matched models, which conceptually allows one to characterize the uncertainty in reservoir description and future performance predictions, the ensemble Kalman filter (EnKF) provides a highly attractive technique for history matching production data. Despite these attractive features, EnKF had not been widely adopted as a standard history matching tool because of questions about its robustness and reliability. In particular, a relatively small ensemble is necessary for computational efficiency but limits the degrees of freedom to assimilate data, often results in a significant underestimation of variance, can introduce spurious long-distance correlations between elements of the state and data vectors, can result in filter divergence and a poor estimate of the conditional mean. Covariance localization represents the primary method for mitigating the negative effects of a small ensemble size. This research project focus on determining optimal covariance localization procedures for petroleum reservoir applications.


(a) Maximum a posteriori estimate (reference solution)


(b) EnKF posterior mean


(c) EnKF posterior mean with covariance localization

Example illustrating that covariance localization helps to improve the estimate of conditional mean for a linear problem.

Recent publications:

  1. Emerick, A.A. and Reynolds, A.C.: History Matching a Field Case Using the Ensemble Kalman Filter with Covariance Localization - SPE Reservoir Evaluation and Engineering, 2011.
  2. Emerick, A.A. and Reynolds, A.C.: Combining Sensitivities and Prior Information for Covariance Localization in the Ensemble Kalman Filter for Petroleum Reservoir ApplicationsComputational Geosciences, 2010.

 

 

Comments are welcome

Last updated: Mar 20, 2012