Distance Dependent Localization Approach in Oil Reservoir History Matching: A Comparative Study

To perform any economic management of a petroleum reservoir in real time, a predictable and/or updateable model of reservoir along with uncertainty estimation ability is required. One relatively recent method is a sequential Monte Carlo implementation of the Kalman filter: the Ensemble Kalman Filter (EnKF). The EnKF not only estimate uncertain parameters but also provide a recursive estimate of system states such as pressures and saturations. Due to high computational cost, however, the EnKF is limited to small size ensemble set in practice. On the other hand small ensemble size yield spurious correlation within covariance of state. A remediation to this problem is to employ covariance localization to remove long-range spurious correlations. In this study, five distance base localization functions have been implemented and analysis on two different cases to obtain a better history matching with EnKF. The results indicate that quartic correlation function produce better results than others especially to the popular fifth-order correlation function meanwhile maintain more total variance at the end of the assimilation.