| Summary: | A successful development of oil and gas reservoirs requires a deep understanding of key subsurface complexities, possible development outcomes, and execution of optimal development actions. This is achieved through the utilization of detailed reservoir models that integrate all available data and modern reservoir simulation, which incorporates the whole spectrum of physical and chemical processes associated with development activities. To further improve reservoir models, we condition them to the collected production data through the history matching process. This process employs sequences of reservoir simulation runs to searches for changes in reservoir description that can improve reservoir model prediction accuracy. Over the past decades, multiple assisted history matching algorithms were proposed in order to speed up the process and extend it to handling multiple alternative realizations. However, the history matching process is still highly computationally expensive and associated with compromises in the robustness of the algorithms that have to be made to keep it practical. In this work, we investigate the application of fast Radial Basis Function (RBF) proxy models as a substitute for reservoir simulation in history matching. First, we review the general background in proxy modeling and state-of-the-art developments in the RBF application in engineering optimization problems. We also review the background and recent progress in the development of some popular ensemble-based and multi-objective algorithms and discuss outstanding challenges in their practical implementation. Then we introduce a modified ensemble Kalman filter method (RBF-EnKF) that utilizes RBF proxy models as a partial substitute to numerical simulation. This method improves the accuracy of the cross-covariance estimation between the model parameters and model dynamic responses for small ensemble size. To achieve higher accuracy of RBF proxy models, an improved heterogeneous and anisotropic formulation for basis functions scaling was implemented. The proposed method was tested using a synthetic case and showed significant improvement in cross-covariance estimation and good history matching results. Next, we extended the proposed RBF-EnKF algorithm for application to practical size history matching problems. This was achieved by introducing Grid Connectivity Transforms (GCT) parametrization to convert spatial variables to a set of discrete inputs for proxy models and iterative sensitivity-based GCT coefficients selection to further reduce the number of proxy model input parameters. An extended version of the algorithm outperformed EnKF with localization and showed a close match to conventional EnKF with significantly larger ensemble size in history matching of Brugge and Norne field models. Finally, we proposed a modified of Multi-objective Evolutionary Algorithm based on decomposition and dominance (MOEA/DD) that utilizes RBF proxy models to reduce computational requirements. The proposed RBF-MOEA/DD algorithm adopted the GCT parametrization and Gradual Deformation approach to enable history matching of model spatial variables such as absolute permeability. Optimization workflow was modified to incorporate RBF proxy modeling with adaptive and sparsity-based iterative improvement. The proposed method was applied to the Brugge case history matching and showed the quality of the match and computational improvement similar to the RBF-EnKF method.
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