Summary
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, model-based reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date observations of production data so that the performance predictions and the associated uncertainty are up-to-date for optimization of future development/operations. The ensemble Kalman filter (EnKF) method has been shown to be quite efficient for this purpose in large-scale nonlinear systems.
Previous studies show that a relatively large ensemble size is required for EnKF to reliably assess the uncertainty, and a confirming step is recommended to ensure the consistency of the updated static and dynamic variables with the flow equations. In this paper, we further explore the capability of EnKF, focusing on some practical issues including the correction of the linear and Gaussian assumptions during filter updating with iteration, the reduction of ensemble size with a resampling scheme, and the impact of data assimilation time interval.
Results from the example in this paper demonstrate that the proposed iterative EnKF performs better with more accurate predictions and less uncertainty than the traditional noniterative EnKF. The use of iteration reduces the impact of nonlinearity and non-Gaussianity. Results also show that iteration may only be required when predictions are considerably deviated from the observations. The proposed resampling scheme can significantly reduce the ensemble size necessary for reliable assessment of uncertainty with improved accuracy. Finally, we show that the noniterative EnKF is sensitive to the size of time interval between the assimilation steps. Using the proposed iterative EnKF, results are more stable, more accurate reservoir models and predictions can be obtained even when a large time interval is used. This also indicates that iteration within the EnKF updating serves as a process that corrects the stronger nonlinear and non-Gaussian behaviors when larger time interval is used.
Introduction
Reservoir models have become an important part of day-to-day decision analysis related to management of oil/gas fields. The closed-loop reservoir management concept (Jansen et al. 2005) allows real-time decisions to be made that maximize the production potential of a reservoir. These decisions are based on the most current information available about the reservoir model and the associated uncertainty of the information. One critical requirement in this real-time, model-based reservoir management process is the ability to rapidly estimate the reservoir models and the associated uncertainty reflecting the most current production data in a real-time fashion. Based on a number of studies, the EnKF method was shown to be well-suited for such applications compared to the traditional history-matching (HM) methods (Evensen 1999; Gu and Oliver 2006; Wen and Chen 2006).