Streamline-Assisted Ensemble Kalman Filter for Rapid and Continuous Reservoir Model Updating

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Abstract
Summary: The use of the ensemble Kalman filter (EnKF) is a promising approach for data assimilation and assessment of uncertainties during reservoir characterization and performance forecasting. It provides a relatively straightforward approach to incorporating diverse data types, including production and/or time-lapse seismic data. Unlike traditional sensitivity-based history matching methods, the EnKF relies on a cross-covariance matrix computed from an ensemble of reservoir models to relate reservoir properties to production data. For practical field applications, we need to keep the ensemble size small for computational efficiency. However, this leads to poor approximations of the cross-covariance and, often, loss of geologic realism through parameter overshoots, in particular by introducing localized patches of low and high permeabilities. Because the EnKF estimates are "optimal" only for Gaussian variables and linear dynamics, these difficulties are compounded by the strong nonlinearity of the multiphase history matching problems and for non-Gaussian prior models. Specifically, the updated parameter distribution tends to become multi-Gaussian with loss of connectivities of extreme values, such as high permeability channels and low permeability barriers, which are of special significance during reservoir characterization. We propose a novel approach to overcome some of these limitations by conditioning the cross-covariance matrix using information gleaned from streamline trajectories. Our streamline-assisted EnKF is analogous to the conventional assisted history matching, whereby the streamline trajectories are used to identify gridblocks contributing to the production response of a specific well. We then use these gridblocks only to compute the cross-covariance matrix and eliminate the influence of unrelated or distant observations and spurious correlations. We show that the streamline-assisted EnKF is an efficient and robust approach for history matching and continuous reservoir model updating. We illustrate the power and utility of our approach using both synthetic and field applications.