Improving Characterization and History Matching Using Entropy Weighted Ensemble Kalman Filter for Non-Gaussian Distributions

Abstract

Abstract The Ensemble Kalman Filter (EnKF) has gained popularity over recent years as a Monte-Carlo based technique for assisted history matching and real time updating of reservoir models. The EnKF procedure utilizes an ensemble of model states (e.g. realizations of reservoir properties such as porosity and permeability) to approximate the covariance matrices used in the updating process. EnKF works efficiently with Gaussian variables and linear dynamics, but it often fails to preserve the reference probability distribution of the model parameters and to achieve an acceptable production data match where the system dynamics are strongly nonlinear, especially of the type related to multiphase flow, or if non-Gaussian prior models are used. In order to alleviate these drawbacks, we investigated various weighted averaging techniques for computing the ensemble mean by introducing a weighting factor to each ensemble; two new formulations were implemented. The first weighting factor was calculated based on the mismatch in entropy of the model parameters, a normalized measure of the spread of a given probability distribution. The second weighting factor was computed using the forecast mismatch. In addition, both weights could be applied at a single updating step for reducing the forecast mismatch and maintaining the prior distribution simultaneously. The performance of traditional EnKF and these weighted EnKF methods were evaluated by performing various simulation studies with different reservoir heterogeneity. The qualities of the final matching results were assessed by computing the experimental histogram and variograms of the final ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch. The results reveal that reasonable improvement in the efficiency of the EnKF is achieved by suggested weighted techniques. The RMSE of the predicted data is improved, and the quantity of spurious model parameters is reduced at each updating step. Taking advantage of the entropy based weighting factor assists the filter to preserve the reference distribution. The improvement indicates that the Entropy weighted EnKF (EWEnKF) has a significant potential to resolve the shortfall of traditional EnKF in reservoir characterization and history matching of challenging reservoirs with non-Gaussian distributions.