History matching within the Bayesian framework in practice assumes perfect simulation models. However, for real field cases this assumption may lead to a spurious reduction in forecast uncertainty when a large number of data is used to constrain imperfect reservoir models. To mitigate this spurious uncertainty reduction, we propose a new approach to automatically and consistently inflate the standard deviation of measurement errors for the constraining field data. In previous work we applied the simple mitigation strategy of using a single inflation factor for all data. In this work we propose to use information from the Hessian matrix evaluated at the maximum a posteriori (MAP) points in parameter space: data are regrouped into different categories according to their sensitivities with respect to principal directions of the posterior Hessian matrix. For each group a suitable inflation factor can then be estimated from the number of data and observed mismatches in that group. The proposed procedure is applied to a synthetic as well as a field scale model. The truth of the synthetic model is selected from one unconditional realizations of a real field model with three facies. Synthetic measured production data are generated by adding Gaussian noise to those predicted from the true simulation model. During the process of history matching, a few uncertain model parameters are artificially fixed to values that are inconsistent with the truth to mimic the unknown real field case and make the model imperfect. Numerical results indicate that the proposed approach is able to give a balanced and reasonable range of forecast uncertainty for the cases considered.

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