History matching of fracture distributions by ensemble Kalman filter combined with vector based level set parameterization

For fractured reservoirs with unknown fracture distributions, the characteristics of fracture distributions are crucial for determining their production behaviors. Traditional history matching methods are not appropriate because the pixel-based rock property fields are usually highly non-Gaussian. In this work, a method that combines a vector-based level set reparameterization technique and the ensemble Kalman filter (EnKF) for estimating fracture distributions of two-dimensional reservoir model is presented. In the parameterization process, we first set up a group of representing nodes. The value of level set function on each node is assigned using Gaussian random number, and the sign of the function value indicates whether there is a fracture starting from the node or not. If there exists a linear fracture in a two dimensional space, the fracture would be characterized by the fracture length and orientation. Thus, the fracture distribution of the reservoir domain can be represented by a representing node system with a vector of three components on each node, which are the level set function, the fracture length, and the fracture angle. In the data assimilation process, these parameters are updated via EnKF scheme as the model parameters of the state vector. Two dimensional examples of water flooding in fractured reservoirs are set up to demonstrate the proposed method. It is shown that the method is effective to capture the main features of the fracture distributions in the reference fields. The matches of production data also improve significantly after updating.