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The ensemble Kalman filter (EnKF) and related ensemble-based smoothers are well-suited to history match reservoir models that are multivariate Gaussian. Estimating categorical variables such as facies types is much more difficult with the EnKF, especially when the variables have complex transitional dependencies. In a previous study, the EnKF was used for updating third-order Markov-chain models in one dimension with an efficient post-processing step to ensure that the posterior samples are constrained by the prior. The efficiency of the post-processing step depended on the use of an optimization algorithm (Viterbi algorithm) that is not directly applicable in higher dimensions.

In this paper, the post-processing step is carried out with a sequential noniterative optimization algorithm that readily extends to higher dimensions. An iterative ensemble-based data-assimilation method by use of Levenberg …