A new method to improve estimation of uncertain parameters in the Ensemble Kalman filter by re-parameterization employing prior statistics correction

• A new method for data assimilation of non-Gaussian parameters is proposed.
• The proposed method improves the estimation by correcting the prior statistics.
• It has solutions for deficiencies of NS-EnKF in estimation of uncertain parameters.
• Uncertain permeability and facies map are characterized using this method well.
• Unknown relative permeability functions with no prior information are estimated.

The Ensemble Kalman Filter (EnKF) is a Monte Carlo based method to assimilate the measurement data sequentially in time. Although, EnKF has some advantages over the other Kalman based methods to deal with non-linear and/or high dimensional reservoir models, it also suffers from deficiency in estimation of non-Gaussian parameters. In this work, we propose a re-parameterization method to handle non-Gaussian parameters via Ensemble Kalman Filter framework. For this purpose, concept of cumulative distribution function transformation has been used. In addition, the statistics of prior information have been aggregated in the state vector in order to capture the prior uncertainties of non-Gaussian parameters. To evaluate the performance of the new method, three estimation examples have been implemented. These examples are designed to evaluate the performance of the proposed method to estimate both local and global parameters. The performance of method in handling non-Gaussian prior as well as capturing the prior uncertainty has been assessed. The results revealed that, the proposed method handled both non-Gaussian prior and capturing of the prior uncertainties of the local and global parameters quite efficiently. Compared to previously conducted researches, new algorithm would considerably reduce the number of required ensemble members to converge to the appropriate solution. Standard ensemble Kalman filter and normal score transformation have been also implemented for each setup; the obtained results show that the new proposed method outperforms the other alternate methods.