Some Practical Issues on Real-Time Reservoir Model Updating Using Ensemble Kalman Filter

Abstract

Abstract The concept of 'closed-loop' reservoir management is currently receiving considerable attention in the petroleum industry. A 'real-time' or 'continuous' reservoir model updating technique is a critical component for the feasible application of any closed-loop reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date measured production data so that the performance predictions and the associated uncertainty are up-to-date for optimization calculations. The ensemble Kalman filter (EnKF) method has been shown to be quite efficient for this purpose in large-scale non-linear systems. Previous studies show that a relatively large ensemble size is required for EnKF to reliably assess the uncertainty and a conforming step is recommended to ensure the consistency between the updated static and dynamic variables. In this paper, we further explore the capability of EnKF focusing on practical application issues including the correction of the linear assumption during Kalman updating with iteration, the reduction of ensemble size with a simple uniform re-sampling scheme, and the impact of assimilation time interval. Results from this paper demonstrate that the predictive capability of the updated models can be considerably improved when iteration is used within the EnKF updating. The use of iteration reduces the impact of nonlinearity and non-Gaussianity. However, iteration is required only when predictions are very different from the observed data. We also show that a simple uniform re-sampling scheme can significantly reduce the ensemble size necessary for reliable assessment of uncertainty, in addition to improving accuracy compared to the traditional random sampling method. Finally, we show that the non-iterative EnKF is sensitive to the size of time interval between the assimilation steps. Using the iterative EnKF, results are more stable and more accurate reservoir models and predictions can be obtained even when a large time interval is used during the assimilation. This indicates again that iteration within the EnKF updating serves as a process that corrects the non-linear and non-Gaussian behaviors.