Parameterization of embedded discrete fracture models (EDFM) for efficient history matching of fractured reservoirs

Embedded Discrete Fracture Model (EDFM) is a promising approach to describe the reservoirs with fractures. Conventional streamline-based inversion method has been limited to the dual-porosity models where the natural fractures are modeled implicitly and flow between matrix blocks is not accounted for. To address this challenge, we propose a novel parameterization and hierarchical multi-scale history matching formulation for EDFM's. We sequentially include basis functions, from large to small scale, to calculate basis coefficient sensitivity combined with streamline-based analytical sensitivity, for updating matrix and fracture properties to match the reservoir dynamic response. In EDFM dominant fractures are explicitly represented within the matrix domain. The matrix-fracture and fracture-fracture interactions are modeled using non-neighbor connections (NNCs) with corresponding transmissibility. In this research, grid connectivity information including NNCs and the reservoir properties in the prior model are first used to construct a grid Laplacian matrix. Next, the eigenvectors of the Laplacian matrix are used as the transformation basis vectors through which matrix and fracture properties are mapped to a low-dimensional transform domain. This step significantly reduces the number of unknowns and also regularizes the inverse problem. Finally, the basis coefficient sensitivity in the transform domain is analytically calculated using streamlines and the updated basis coefficients are then used to reconstruct the reservoir property field. We first illustrate the proposed parameterization of the EDFM and its effectiveness by reconstructing low rank approximations of the spatial distribution of the matrix and fracture properties. Conventional streamline-based inversion method typically leads to large property changes along the streamlines. With the proposed parameterization approach, the basis coefficient sensitivities enable us to effectively calibrate the EDFM in a more geologically continuous manner on both matrix domain and fracture planes. We demonstrate the power and efficacy of our method through application to a field scale reservoir model with complex fault structure, channels, and dominant natural fractures. The example involves waterflood history matching with water-cut and bottom-hole pressure data. The proposed approach effectively updates the prior permeability field along the fracture planes and the matrix domain, resulting in significantly improved history match. The parameterization of EDFM has high compression power to represent important geological trend and fracture properties with significantly reduced number of parameters. The new model calibration method extends the capability of the streamline-based inversion method to explicitly model flow in natural fractures and also flow between matrix blocks.