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. 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 the uncertainty especially for problems that are highly non-linear. In this paper, the distributions of reservoir model realizations from 20 independent ensembles are compared with the distributions from 20 randomized maximum likelihood (RML) realizations for a 2D water-flood 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 Markov chain Monte Carlo method (McMC) on highly nonlinear problems and relatively more efficient than the McMC.
Despite the nonlinear relationship between 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.