Summary
Recently, the ensemble Kalman Filter (EnKF) has gained popularity in atmospheric science for the assimilation of data and the assessment of uncertainty in forecasts for complex, large-scale problems. A handful of papers have discussed reservoir characterization applications of the EnKF, which can easily and quickly be coupled with any reservoir simulator. Neither adjoint code nor specific knowledge of simulator numerics is required for implementation of the EnKF. Moreover, data are assimilated (matched) as they become available; a suite of plausible reservoir models (the ensemble, set of ensemble members or suite or realizations) is continuously updated to honor data without rematching data assimilated previously. Because of these features, the method is far more efficient for history matching dynamic data than automatic history matching based on optimization algorithms. Moreover, the set of realizations provides a way to evaluate the uncertainty in reservoir description and performance predictions.
Here we establish a firm theoretical relation between randomized maximum likelihood and the ensemble Kalman filter. Although we have previously generated reservoir characterization examples where the method worked well, here we also provide examples where the performance of EnKF does not provide a reliable characterization of uncertainty.
Introduction
Our main interest is in characterizing the uncertainty in reservoir description and reservoir performance predictions in order to optimize reservoir management. To do so, we wish to generate a suite of plausible reservoir models (realizations) that are consistent with all information and data. If the set of models is obtained by correctly sampling the pdf, then the set of models give a characterization of the uncertainty in the reservoir model. Thus, by predicting future reservoir performance with each of the realizations, and calculating statistics on the set of outcomes, one can evaluate the uncertainty in reservoir performance predictions.
