In this paper, we study the application of the probabilistic collocation based Kalman filter (PCKF) approach to history matching. Kalman filter is a classical approach for data assimilation and model calibration that has been widely used with success. It updates state variables (i.e., model input and output parameters) based on their correlations, which is challenging to compute efficiently for non-linear models. A popular alternative to estimating the correlations is to use an ensemble of models, which is the basis of the Ensemble Kalman filter (EnKF). The PCKF is an alternative to the EnKF in the sense that it estimates the correlations between the state variables from the Polynomial Chaos Expansion (PCE). The coefficients in the PCE are determined by the Probabilistic Collocation Method (PCM). In this paper, the PCKF method is applied to a synthetic reservoir model that mimics a deep water deposit of amalgamated channel complexes. This model exhibits complex flow patterns under different production scenarios making it useful for testing the PCKF algorithm. Acceptable history matches were obtained with a relatively small number of simulations. Our study suggests that PCKF may be a useful way to reduce the size of the ensemble required in Kalman filter methods, thus improving the efficiency of the history matching process.

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