History matching of facies distribution with the EnKF and level set parameterization

In this work, we develop a methodology to combine the Ensemble Kalman filter (EnKF) and the level set parameterization for history matching of facies distribution. With given prior knowledge about the facies of the reservoir geology, initial realizations are generated by commonly used software as the prior guesses of the unknown field. Furthermore, level set functions are used to reparameterize these initial realizations. In the reparameterization process, a representing node system is set up, on which the values of level set functions are assigned using Gaussian random numbers. The mean and the standard deviation of the Gaussian random numbers are designed according to the facies proportion, and the sign of the random numbers depends on the facies type at the representing nodes. The values of the level set functions at the other grid nodes are obtained by linear interpolation. The level set functions on the representing nodes are the model parameters of the EnKF state vector and are updated in the data assimilation process. On the basis of our numerical examples for two-dimensional reservoirs with two or three facies, the proposed method is demonstrated to be able to capture the main features of the reference facies distributions.