Covariance Matrix Localization Using Drainage Area in an Ensemble Kalman Filter

The Ensemble Kalman filter has been widely researched because of its availability of real-time updating of reservoir models and uncertainty quantification. There have been many studies to solve the two typical problems: overshooting and filter divergence, and to increase its accuracy. One of the methods is covariance localization, which excludes data having relatively low correlation between reservoir parameters and observations. This article proposes covariance matrix localization using a drainage area, which can be easily obtained by checking the direction of oil flow. In applications to synthetic reservoirs, the proposed method gives a better prediction of the permeability distribution by history matching and, therefore, future performances. It also provides reliable results in cases of small ensemble sizes.