Characterization of Non-Gaussian Geologic Facies Distribution Using Ensemble Kalman Filter with Probability Weighted Re-Sampling

The Ensemble Kalman Filter (EnKF) is a Monte Carlo-based technique for assisted history matching and real-time updating of reservoir models. However, it often fails to detect precise locations of distinct facies boundaries and their proportions, as the facies distributions are non-Gaussian, while geologic data for reservoir modeling is usually insufficient. In this paper, a new re-sampling step is introduced to the conventional EnKF formulation; after certain number of assimilation steps, the updated ensemble is used to generate a new ensemble with a novel probability weighted re-sampling scheme. The new ensemble samples from a probability density function that is conditional to both the geological information and the early production data. After the re-sampling step, the forecast model is applied to the new ensemble from the beginning up to the last update step (without any intermediate Kalman updates). Full EnKF is again applied on the ensemble members to assimilate the remaining production history. Combination of EnKF and regenerating new members using the re-sampling method demonstrates reasonable improvement and reduction of uncertainty in history matching of reservoir models with multiple facies. The histogram and the experimental variogram of the updated ensemble members are more consistent with the static geologic information. Moreover, the technique helps maintaining ensemble variance which is essential for uncertainty estimation in the posterior probability distribution of facies proportions.