Data assimilation for nonlinear problems by ensemble Kalman filter with reparameterization

In this work, we address the non-Gaussian effect through a change in parameterization. Instead of directly updating the saturation, the time of saturation arrival (at a particular saturation) is included in the state vector. The time variable is correlated with the reservoir properties and other reservoir responses and its density is better approximated by a Gaussian distribution. After updating the time of saturation arrival through the EnKF, the updated arrival time distribution is transformed back to estimate the saturation of the reservoir. The new approach has better performance in the presence of strong non-Gaussianities but requires a larger computation time than does the traditional EnKF, which works well when the Gaussian assumption is not strongly violated. In order to achieve both accuracy and efficiency, the EnKF with reparameterization can be used in conjunction with the traditional EnKF as an option to account for possible highly non-Gaussian densities. The EnKF with reparameterization is illustrated with a problem under highly non-Gaussian conditions, and the effectiveness of the combination of the new approach and the traditional EnKF is demonstrated with history matching of multiphase flow in a heterogeneous reservoir.