Reservoir Characterization Using Ensemble Kalman Filter and Drainage Area Localization

Abstract

Ensemble Kalman Filter (EnKF) overcomes many short comings of previous optimization methods and has been widely researched because of its availability of real-time updating of reservoir models and uncertainty quantification. In applications of EnKF, two problems have been reported. The first one is overshooting that model values are assimilated to too high values. The second one is filter divergence that filter does not converge to true values anymore. There have been many studies to solve these problems and covariance localization is one of these methods. Covariance localization means excluding data having relatively low correlation between reservoir parameters and observations when calculating cross covariance matrix of EnKF. We propose drainage area based covariance localization. Drainage area is subsurface area of a reservoir that is effectively depleted by one well, so it can be used to determine which region is correlated to production observations. Drainage area can be easily determined by using the direction of oil flow velocity and successfully localize covariance matrix. When ensemble size is quite small such as 40, the proposed method reliably characterize synthetic reservoir given while standard EnKF doesn't. The standard EnKF fails to predict future performances but the proposed method predicts future performances successfully.