Reservoir characterization using ensemble-based assimilation methods

Characterization of large reservoir models with a great number of uncertain parameters is frequently carried out by ensemble-based assimilation methods, due to their computational efficiency, ease of implementation, versatility, and non-necessity of adjoint code. In this study, multiple ensemble-based assimilation techniques are utilized to characterize the well-known PUNQ-S3 model. Accordingly, actual measurements are employed to determine porosity, horizontal and vertical permeabilities, and their associated uncertainties. In consequence, the uncertain parameters of the model will gradually be adapted toward the true values during the assimilation of actual measurements, including bottomhole pressure and production rates of the reservoir. Monotonic reduction of root-mean-squared error and capturing the key points of the maps (such as direction of anisotropy and porosity/permeability contrasts) verify successful estimation of the geostatistical properties of the PUNQ-S3 model during history matching. At the end of the assimilation process, the RMSE values for Deterministic Ensemble Kalman Filter, Ensemble Kalman Filter, Ensemble Kalman Filter with Bootstrap Regularization, Ensemble Transform Kalman Filter Symmetric Solution, Ensemble Transform Kalman Filter Random Rotation, and Singular Evolutive Interpolated Kalman filter are 1.120, 1.153, 1.132, 1.132, 1.129, and 1.113, respectively. In addition to RMSE, the quality of history match as well as prediction of future performance are looked into in order to assess the performance of the assimilation process. Obviously, the results of the ensemble-based assimilation methods closely match the true results both in the history match section and in the future prediction section. Besides, the uncertainty of future predictions is quantified using multiple history-matched realizations. This is due to the fact that Kalman-based filters use a Bayesian framework in the assimilation step. Accordingly, the updated ensemble members are samples of the posterior distribution through which the uncertainty of future performance is assessed.