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 prior knowledge of the data is usually insufficient.
It is common to represent distinct facies with categorical indicators, which are intrinsically non-Gaussian. We implemented discrete cosine transform (DCT) to parameterize the facies indicators. This methodology was promising for simple and two facies models. For more complex models, though observed data were matched, it failed to reproduce realistic facies distribution corresponding to the prior variogram and facies proportion.
In this paper a new step is proposed to be included in the history matching of complex reservoirs using EnKF: realizations exhibiting the largest mismatch in terms of production data, experimental variogram, and histogram are discarded after the first few update steps, and a probability map for facies modeling is derived using the remaining ensemble members. Probability field (P-Field) simulation is performed subsequently using the facies probability map to generate a new set of realizations replacing the discarded members. The new realizations are updated again from the beginning using EnKF.
Several case studies with different facies distribution and well configurations were conducted. Initial ensembles were created using known facies classification at the well locations and populating binary facies data throughout reservoir using numerous variogram models and prior facies proportions. The regenerated realizations are closer to the true reservoir state since they already take into account the first few set of production data.
The qualities of the history-matched models were assessed by comparing the experimental variograms of facies distribution and facies propositions of the final ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch.
Combination of DCT-EnKF and regenerating new realizations using P-Field simulation demonstrates reasonable improvement and reduction of uncertainty in facies detection. Incorporating the new step in the procedure assists filter to preserve the reference distribution and experimental variogram for complex reservoirs.