Critical Evaluation of the Ensemble Kalman Filter on History Matching of Geologic Facies

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Abstract
Summary: The objective of this paper is to compare the performance of the ensemble Kalman filter (EnKF) to the performance of a gradient-based minimization method for the problem of estimation of facies boundaries in history matching. The EnKF is a Monte Carlo method for data assimilation that uses an ensemble of reservoir models to represent and update the covariance of variables. In several published studies, it outperforms traditional history-matching algorithms in adaptability and efficiency. Because of the approximate nature of the EnKF, the realizations from one ensemble tend to underestimate uncertainty, especially for problems that are highly nonlinear. In this paper, the distributions of reservoir-model realizations from 20 independent ensembles are compared with the distributions from 20 random-ized-maximum-likelihood (RML) realizations for a 2D waterflood model with one injector and four producers. RML is a gradient-based sampling method that generates one reservoir realization in each minimization of the objective function. It is an approximate sampling method, but its sampling properties are similar to the Markov-chain Monte Carlo (McMC) method on highly nonlinear problems and are relatively more efficient than McMC. Despite the nonlinear relationship between the data (such as production rates and facies observations) and the model variables, the EnKF was effective at history matching the production data. We find that the computational effort to generate 20 independent realizations was similar for the two methods, although the complexity of the code is substantially less for the EnKF.