History matching and uncertainty characterization using ensemble-based methods

In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. Among these methods, the ensemble Kalman filter (EnKF) is the most popular one for history-matching applications. The main advantages of EnKF are computational efficiency and easy implementation. Moreover, because EnKF generates multiple history-matched models, EnKF can provide a measure of the uncertainty in reservoir performance predictions. However, because of the inherent assumptions of linearity and Gaussianity and the use of limited ensemble sizes, EnKF does not always provide an acceptable history-match and does not provide an accurate characterization of uncertainty. In this work, we investigate the use of ensemble-based methods, with emphasis on the EnKF, and propose modifications that allow us to obtain a better history match and a more accurate characterization of the uncertainty in reservoir description and reservoir performance predictions.;When EnKF is applied to reservoir history matching, it is necessary to keep the size of the ensemble small in order to obtain computational efficiency. However, a small ensemble size introduces sampling errors and limits the degrees of freedom to assimilate data, which deteriorate the results of the data assimilation. In this work, we introduce a distance-based covariance localization procedure to reduce these problems. The proposed method is applied to several synthetic cases and one real field case, and the results show significant improvements compared to the standard EnKF and other choices of covariance localization. In addition, we investigate other methods proposed in the literature to ameliorate the negative effects of a small ensemble. We conclude that distance-based covariance localization is, to date, the most effective method.;Another problem that often occurs when EnKF is applied to reservoir history-matching problems is that the values of the objective function obtained by the final ensemble are relatively high, especially when compared to gradient-based history matching. High values of the objective function are associated with poor data matches. More importantly, a model that results in high value of the objective function gives a small value of the posterior probability density function, which suggests that this model is a sample from a low probability region. In this work, we introduce a procedure that combines EnKF and Markov chain Monte Carlo (MCMC) for the purpose of improving the final data matches and obtaining a more accurate characterization of uncertainty. We also introduce a procedure based on multiple assimilations of the same data with an inflated covariance of the measurement errors. This procedure forms the basis of a new iterative form of ensemble smoother (ES-MDA). We applied ES-MDA to history match production and/or seismic data in synthetic reservoir problems and in a real field case. The results show that ES-MDA outperforms EnKF in terms of the quality of data matches with a computational cost comparable with EnKF.;In this work, we also investigate the use of an adjoint-based implementation of the randomized maximum likelihood (RML) method and propose a new parameterization based on an ensemble of prior realizations to reduce the computational cost of RML.;Finally, we present a comparative study among eight ensemble-based methods in terms of the quality of the data matches, characterization of uncertainty and computational cost. Among the ensemble-based methods, ES-MDA obtained the best performance and resulted in a quantification of uncertainty comparable to an adjoint-based RML.