Localization with the EnKF for the Automatic History Matching of the SAGD Processes

Date
2015-09
Authors
Huang, Yingchao
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Graduate Studies and Research, University of Regina
Abstract

The Ensemble Kalman Filter (EnKF) has been successfully applied to data assimilation in Steam Assisted Gravity Drainage (SAGD) processes, but applications of localization for the EnKF in SAGD processes have not been studied. Distance-based localization has been reported to be very efficient for assimilation of large amounts of independent data with a small ensemble in water flooding processes, but it is not applicable to SAGD processes, since in SAGD processes oil is produced mainly from the transition zone from steam chamber to cold oil instead of the regions around the producer. As the transition zone could be identified by saturation and temperature distribution, temperaturebased and saturation-based localization were proposed for automatic history matching of SAGD processes. The regions of the localization function were determined through covariance analysis by using a large ensemble with 1000 members. The covariance analysis indicated that the regions of cross correlations between oil production and state variables are much wider than the correlations between production data and model variables. To choose localization regions that are large enough to include the true regions of non-zero cross-covariance, the localization function were defined based on the regions of non-zero covariances of production data to state variables. Also, the non-zero covariances between production data and state variables are distributed in accordance with the steam chamber, which makes it easier to define a universal localization function for different state variables. Based on the covariance analysis, the temperature and saturation range in which oil production is contributed by the regions was determined; beyond or below this range, the localization function reduces from one and at the critical or steam temperature and initial or residual saturation the localization function reduces to zero. The temperature-based and saturation-based localization functions were obtained through modifying the distance-based localization function (Gaspari and Cohn, 1999). Localization was applied to covariance of production data with permeability, saturation and temperature, as well as the covariance of production data with production data. A small ensemble (10 ensemble members) was employed in several case studies. Without localization, the variability in the ensemble collapsed very quickly and lost the ability to assimilate later data. The mean variance of model variables dropped dramatically by 95% and there was almost no variability in ensemble forests, while the prediction was far from the reference with data mismatch remaining at a high level. At least 50 ensemble members are needed to keep the qualities of matches and forests, which significantly increases the computation time. The EnKF with localization is able to avoid the collapse of ensemble variability with a small ensemble (10 members), which saves the computation time and gives better history-match and prediction results. To further investigate the effectiveness and robustness of the localization function, these were validated with a field case, and it showed positive results with the localized EnKF.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Petroleum Systems Engineering, University of Regina. xviii, 155 p.
Keywords
Citation
Collections