Data Assimilation by Ensemble Kalman Filter with ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Data Assimilation by Ensemble Kalman Filter with Reparameterization for Nonlinear Problems
Author:Yan Chen <> (The University of Oklahoma)
Dean S. Oliver <> (The University of Oklahoma)
Dongxiao Zhang <> (The University of Oklahoma)
Presenter:Yan Chen <> (The University of Oklahoma)
Date: 2006-06-18     Track: Special Sessions     Session: Data assimilation in water resources modelling

Owing to its simplicity and efficiency the Ensemble Kalman filter (EnKF) has recently been applied for assimilating static and dynamic measurements to continuously update the estimate of the state vector, such as reservoir properties and responses. Many EnKF implementations showed promising results. However, the Gaussian assumption is an implicit requirement for obtaining a satisfactory estimate through EnKF or its variants. EnKF may not work properly when the state vector is strongly nonlinear and thus non-Gaussian. For instance, a direct application of EnKF to estimating the saturation of two-phase flow may lead to a non-physical behavior at the interface of the two immiscible phases. There exist methods which reduce this non-Gaussian effect, such as the iterative EnKF and the Gaussian kernel filter. In this work, we propose a new approach which reduces the non-Gaussian effect through reparameterization. Instead of directly updating the saturation, which is bimodally distributed, the time of saturation arrival (at a particular location) is included in the state vector. The time of arrival is correlated with the reservoir properties and other reservoir responses and can be approximated by a Gaussian distribution without losing much information. After updating the time of arrival through the EnKF, the local saturation history is used to estimate the saturation of the reservoir at a particular time. The EnKF with reparameterization provides reasonable and more accurate saturation estimation which is the basis of assimilating further observations. The new approach is illustrated on a heterogeneous reservoir of two-phase flow with dynamic measurements, and the results are compared with other methods, in terms of accuracy and efficiency.