Flow relevant covariance localization during dynamic data assimilation using EnKF
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Multiphase dynamic data integration into high resolution subsurface models is an integral aspect of reservoir and groundwater management strategies and uncertainty assessment. Over the past two decades, advances in computing and the development and implementation of robust algorithms for automatic history matching have considerably reduced the time and effort associated with subsurface characterization and reduced the subjectivity associated with manual model calibration. However, reliable and accurate subsurface characterization continues to be challenging due to the large number of model unknowns to be estimated using a relatively smaller set of measurements. For ensemble-based methods in particular, the difficulties are compounded by the need for a large number of model replicates to estimate sample-based statistical measures, specifically the covariances and cross-covariances that directly impact the spread of information from the measurement locations to the model parameters. Statistical noise resulting from modest ensemble sizes can overwhelm and degrade the model updates leading to geologically inconsistent subsurface models. In this work we propose to address the difficulties in the implementation of the ensemble Kalman filter (EnKF) for operational data integration problems. The methods described here use streamline-derived information to identify regions within the reservoir that will have a maximum impact on the dynamic response. This is achieved through spatial localization of the sample-based cross-covariance estimates between the measurements and the model unknowns using streamline trajectories. We illustrate the approach with a synthetic example and a large field-study that demonstrate the difficulties with the traditional EnKF implementation. In both the numerical experiments, it is shown that these challenges are addressed using flow relevant conditioning of the cross-covariance matrix. By mitigating sampling error in the cross-covariance estimates, the proposed approach provides significant computational savings through the use of modest ensemble sizes, and consequently offers the opportunity for use with large field-scale groundwater and reservoir characterization studies. 2009 Elsevier Ltd. All rights reserved.
