Adaptive Regularization in the Ensemble Kalman Filter for Reservoir History Matching

Abstract

Abstract Using a small ensemble size with the ensemble Kalman filter (EnKF) to update numerical reservoir models has proved to be an efficient method of reservoir history matching but, unless some type of localization is used, the standard EnKF update with a small size ensemble can lead to poor parameter estimates due to spurious correlations between observations and model variables. To reduce the impact of spurious correlations on model variable updates, distance-dependent localization has been widely used and is frequently effective at eliminating spurious correlations beyond a predefined distance. However, distance-dependent localization is not always appropriate for assimilating non-local observations, or when the prior covariance is complex due to previous data assimilation. Since the updates of parameters and state variables in the EnKF algorithm are largely determined by the Kalman gain, an improvement in Kalman gain estimation will in turn result in improved estimates of state and model variables. Several adaptive Kalman gain estimation methods, including the bootstrap sampling method, have been proposed recently with promising results but with residual small-amplitude high-frequency noise in the estimate of the Kalman gain. In this paper, we propose a thresholding method for improving the Kalman gain estimation to completely eliminate correlations that are unreliable. We show that by screening the Kalman gain using an adaptive, element-wise threshold level, much of the noise in the estimate of the Kalman gain is removed at a low computational cost. We apply the new thresholding method and the previously developed bootstrap screening EnKF to a deepwater field with approximately 200,000 unknown model parameters. Results from both adaptive EnKF methods are better than results from manual history matching and are comparable to results from a standard EnKF method with distance-based localization.