Improvement of ensemble smoother with SVD-assisted sampling scheme

Abstract

Abstract Ensemble-based methods have been researched for reservoir characterization in petroleum engineering. Using observed data, ensemble members are assimilated to production data and then we can get reasonable uncertainty ranges for future performances from multiple models. However, these methods require hundreds of ensemble members for reliable future predictions. If a reservoir becomes heterogeneous, more ensemble members are needed for stable results. This paper proposes an improved sampling scheme for efficient simulation of Ensemble Smoother (ES). For principal components analysis using singular value decomposition (SVD), we select singular values preserving the original spectrum of the values. To verify the sampling scheme, we apply 2D fields. The qualities of ES results are compared for 3 cases with 400 ensembles, randomly chosen 100 ensembles, and 100 ensembles selected by the proposed method. The results are also checked with conventional sampling scheme of picking the largest singular values. By using randomly chosen 100 ensembles, it shows overshooting problem and provides poor future performances. For the conventional sampling scheme of adopting the largest singular values, it has a potential of biased results as the reference field is complex and heterogeneous. However, our proposed method using 100 ensembles represents as large spectrum as using all 400 ensembles. It also reduces overshooting problem and improves the quality of future reservoir performances. Through ES with the improved sampling scheme, it ensures efficient and reliable reservoir characterization for history matching.