Shape and Distributed Parameter Estimation for History Matching using a Modified Ensemble Kalman Filter and Level Sets

In this paper, we introduce a novel method for the automatic history matching of 3D reservoirs with two lithofacies. The method simultaneously estimates distributed geological reservoir properties and facies boundaries by combining the general Ensemble Kalman Filter (EnKF) strategy with the level set method for shape propagation in 3D. Each iteration of this novel Ensemble Kalman Filter-Level Set (EnKF-LS) scheme combines the update of the boundaries of two lithofacies, represented by associated level set functions, with an update of the corresponding parameter fields, namely porosity and permeability. A narrow band technique is employed for restricting the shape motion to a neighbourhood of the current interfaces. The proposed algorithm is tested on a synthetic 3D reservoir model which is a modification of the popular SPE10 model. We use an initial ensemble of porosity and permeability fields created by a multiple-point statistics-based algorithm for a channelized test case. We compared the proposed method with an implementation of the standard EnKF algorithm and showed that the proposed EnKF-LS scheme not only provides more adequate results for such a channelized structure, but also produces a better data fit than the standard EnKF approach.