Improvement of ensemble smoother with clustered covariance for channelized reservoirs

Abstract

Ensemble Kalman filter (EnKF) has been researched for reservoir characterization in petroleum engineering. However, the repeated assimilation causes lots of simulation cost. Ensemble smoother (ES) assimilates all available data once. It has advantages over EnKF: efficiency and simplicity. The two ensemble methods are based on the same assumptions: Gaussian distribution and trust in the mean of all ensembles. Many researchers have pointed out that EnKF gives overshooting and filter divergence problems when the two key assumptions are not satisfied. This paper presents characterization of channel fields using ES with the concept of clustered covariance, especially improper ensemble design. The standard EnKF, ES, and the proposed method are applied to a 2D synthetic channel field with 200 ensembles. From distance-based clustering method, we separate initial ensembles into 10 groups based its on similarity. The proposed method uses 10 Kalman gains, since each cluster has own Kalman gain. They can represent ensembles properly by using similar ensembles instead of 200 different ensembles. For the channel fields, the standard EnKF and ES show overshooting and filter divergence problems. Updated permeability fields have extreme values and lose the continuity of channel stream. However, the proposed method manages those two problems and provides reasonable results. We can get future prediction with reliable uncertainty. The proposed method only requires about 5% of simulation time compared to EnKF, since it is based on ES. It can be applied to the characterization of channel fields, even though we have improper ensembles due to limited information.