Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Data Assimilation: The Ensemble Kalman Filter
Data Assimilation: The Ensemble Kalman Filter
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In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. This paper focuses entirely on the reservoir history-matching problem. Among the ensemble-based methods, the ensemble Kalman filter (EnKF) is the most popular for history-matching applications. However, the recurrent simulation restarts required in the EnKF sequential data assimilation process may prevent the use of EnKF when the objective is to incorporate the history matching in an integrated geo-modeling workflow. In this situation, the ensemble smoother (ES) is a viable alternative. However, because ES computes a single global update, it may not result in acceptable data matches; therefore, the development of efficient iterative forms of ES is highly desirable. In this paper, we propose to assimilate the same data multiple times with an inflated measurement error covariance matrix in order to improve the results obtained by ES. This method is motivated by the equivalence between single and multiple data assimilation for the linear-Gaussian case. We test the proposed method for three synthetic reservoir history-matching problems. Our results show that the proposed method provides better data matches than those obtained with standard ES and EnKF, with a computational cost comparable with the computational cost of EnKF.