Observability-Aware Ensemble Kalman Filter for Reservoir Model Updating

Reservoir model update is an ill-posed inverse problem that has been considered challenging due to the high dimensionality (similar to 10(5) to 10(6)) and the high-nonlinearity of the reservoir dynamics. Recently, the ensemble Kalman lilter (EnKF) has been efficiently employed as a feasible alternative to the extended Kalman filter in reservoir history matching and large-scale problems in general. The EnKF is a Monte Carlo implementation of the standard Kalman filter algorithm that reduces the required computational power by searching the solution in an ensemble subspace that is much smaller than the original state-space. Consequently, the performance of the algorithm depends fundamentally on the members of the ensemble. In this paper, a systemic observability-based strategy to sample the EnKF is introduced as an efficient alternative to random sampling. The proposed method is described and assessed on the basis of a twin experiment of a 2D two-phase reservoir, and the results are compared with the original random sampling strategy. In addition, an algorithmic-differentiation-based approach is derived to obtain the linearized model of the extended (augmented state/parameter) nonlinear model directly from the numerical simulator. Numerical experiments show promising results for the proposed observability-based sampling strategy over the random sampling strategy in terms of estimating the permeability fields of the subsurface porous media from noisy sparse production data.