With the ensemble Kalman filter (EnKF) or smoother (EnKS), it is easy to adjust a wide variety of model parameters by assimilation of dynamic data. We focus on the case where reallizations and estimates of the depths of the initial fluid contacts as well as gridblock rock property fields are generated by matching production data with the EnKS. The objective is to account for uncertainty in the depths of the contacts and provide improved estimates of the depths by conditioning reservoir models to production data. The efficiency of EnKF and EnKS arises because data are assimilated sequentially in time and so "history matching data" requires only one forward run of the reservoir simulator for each ensemble member. For EnKS and EnKF to yield reliable characterizations of the uncertainty in model parameters and future performance predictions, the updated reservoir simulation variables, e.g., saturations and pressures, must be statistically consistent with the realizations of these variables that would be obtained by rerunning the simulator from time zero using the updated model parameters. This statistical consistency can only be established under assumptions of Gaussianity and linearity that do not normally hold. Here, we explore the use of iterative EnKS methods that are statistically consistent to improve the performance of EnKS.

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