Reservoir Multiscale Data Assimilation Using the Ensemble Kalman Filter

In this paper we propose a way to integrate data at different spatial scales using the ensemble Kalman filter (EnKF), such that the finest scale data is sequentially estimated, subject to the available data at the coarse scale (s), as an additional constraint. Relationship between various scales has been modeled via upscaling techniques. The proposed coarse-scale EnKF algorithm is recursive and easily implementable. Our numerical results with the coarse-scale data provide improved fine-scale field estimates when compared to the results with regular EnKF (which did not incorporate the coarse-scale data). We also tested our algorithm with various precisions of the coarse-scale data to account for the inexact relationship between the fine and coarse scale data. As expected, the results show that higher precision in the coarse-scale data, yielded improved estimates.