Estimating Channelized-Reservoir Permeabilities With the Ensemble Kalman Filter: The Importance of Ensemble Design

摘要

Efficient management of smart oil fields requires a reservoir model that can provide reliable forecasts of future production and realistic measures of prediction uncertainty. Reliable forecasts depend on an accurate representation of reservoir geology, which is conveyed largely by the permeabilities used in the reservoir simulator. Because these permeabilities cannot be measured directly, they must be inferred from measurements of related variables, using procedures such as history matching or Bayesian estimation. The ensemble Kalman filter (EnKF) is an attractive option for permeability estimation in real-time reservoir-control applications. It is easy to implement, provides considerable flexibility for describing geological heterogeneity, and supplies valuable information about prediction uncertainty. However, it is more suited for geological heterogeneities that are amenable to second-order (covariance-based) descriptions. In this paper, we investigate the performance of the EnKF for estimation of channel permeabilities that usually follow a bimodal distribution. We consider two synthetic water-flooding problems based on true permeability distributions characterized by conductive channels. The permeability ensembles are obtained from a multipoint geostatistical simulation method. If the ensemble replicates are derived from training images that do not describe the channel geometry properly, the Kalman filter has difficulty identifying the correct permeability field. In fact, the permeability estimates tend to diverge from the true values as more measurements are included. However, if the filter-ensemble replicates are generated by a training image that contains features that are consistent with those in the true permeability field, the filter's estimates are much better. These results emphasize the importance of generating realistic permeability replicates when using ensemble methods to estimate reservoir properties. In fact, a realistic permeability ensemble appears to be essential for successful estimation performance. With a proper ensemble design, despite the bimodality in the initial permeability distribution, the filter exhibits good performance in identifying the patterns in the true permeability field. In practical applications where the true permeability distribution is highly uncertain, the prior information used for ensemble generation should properly reflect the full range of possible geological conditions.