Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications |
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Authors: | Alexandre Emerick Albert Reynolds |
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Institution: | (1) State Key Laboratory of Pollution Control and Resources Reuse, Nanjing University, 210093 Nanjing, People’s Republic of China;(2) Department of Hydrosciences, Nanjing University, 210093 Nanjing, People’s Republic of China; |
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Abstract: | Sampling errors can severely degrade the reliability of estimates of conditional means and uncertainty quantification obtained
by the application of the ensemble Kalman filter (EnKF) for data assimilation. A standard recommendation for reducing the
spurious correlations and loss of variance due to sampling errors is to use covariance localization. In distance-based localization,
the prior (forecast) covariance matrix at each data assimilation step is replaced with the Schur product of a correlation
matrix with compact support and the forecast covariance matrix. The most important decision to be made in this localization
procedure is the choice of the critical length(s) used to generate this correlation matrix. Here, we give a simple argument
that the appropriate choice of critical length(s) should be based both on the underlying principal correlation length(s) of
the geological model and the range of the sensitivity matrices. Based on this result, we implement a procedure for covariance
localization and demonstrate with a set of distinctive reservoir history-matching examples that this procedure yields improved
results over the standard EnKF implementation and over covariance localization with other choices of critical length. |
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