An iterative ensemble Kalman filter for multiphase fluid flow data assimilation

The dynamical equations for multiphase flow in porous media are highly non-linear and the number of variables required to characterize the medium is usually large, often two or more variables per simulator gridblock. Neither the extended Kalman filter nor the ensemble Kalman filter is suitable for assimilating data or for characterizing uncertainty for this type of problem. Although the ensemble Kalman filter handles the nonlinear dynamics correctly during the forecast step, it sometimes fails badly in the analysis (or updating) of saturations. This paper focuses on the use of an iterative ensemble Kalman filter for data assimilation in nonlinear problems, especially of the type related to multiphase flow in porous media. Two issues are key: (1) iteration to enforce constraints and (2) ensuring that the resulting ensemble is representative of the conditional pdf (i.e. that the uncertainty quantification is correct). The new algorithm is compared to the ensemble Kalman filter on several highly nonlinear example problems, and shown to be superior in the prediction of uncertainty.