Abstract
The EnKF has become increasingly popular for updating and history matching reservoir simulation models. Originally the filter was developed for sequential conditioning of state variables to dynamic data. It was later extended to solve the combined state and parameter estimation problem. Within petroleum, the focus has been mainly on parameter estimation, and although an unknown model error is present in all real reservoir studies, model error is commonly neglected, assuming that all error is due to uncertainty in the estimated parameters. In this paper we investigate the effect of a model error on the EnKF behaviour for a single-phase permeability estimation problem, and whether it is possible to improve the solution and predictions by including an unknown model error in the EnKF procedure. Numerical upscaling errors are chosen for the test case. However, the procedure should be applicable for any type of unknown model errors. It is demonstrated that with model error present, but not included in the analysis, it is not possible to match the data. The permeability estimate becomes unstable, and the predictions are very bad. However, by adding an unknown model error, data can be matched, and the parameter estimates may be significantly improved. Both uncorrelated and correlated errors are tested. Correlated errors are included as additional unknowns in the EnKF state vector. Predictions, and short term predictions in particular, are significantly improved.
