Ensemble Kalman Filter Predictor Bias Correction Method for Non-Gaussian Geological Facies Detection

Abstract

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 facies boundaries and proportions as the facies distributions are non-Gaussian, while geologic data for reservoir modeling is usually insufficient. It is convenient to represent distinct facies with non-Gaussian categorical indicators; we implemented discrete cosine transform (DCT) to parameterize the facies indicators into coefficients of the retained cosine basis functions that are Gaussian. For highly complex and heterogeneous models, though observed data were matched, it failed to reproduce realistic facies distribution corresponding to reference variogram and facies proportion.In this paper we propose a new ensemble filtering method in-between of EnKF and PF, where EnKF as predictor combines the advantages of accurate large updates with small ensembles and corrector for non-Gaussian distributions followed by EnKF again for analysis step. Correction is performed by regenerating new realizations using a new pilot point method. The ensemble members that are more consistent with the early production history and the available geological information are considered as high weight particles and used for the applications.Combination of DCT-EnKF and regenerating new realizations using the new pilot point method demonstrates reasonable improvement and reduction of uncertainty in facies detection. Incorporating the new step in the procedure assists the filter to honor the reference distribution and experimental variogram during the history matching process and presents an important potential in improved characterization of complex reservoirs.