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A robust iterative ensemble smoother method for efficient history matching and uncertainty quantification Disclosure Number: IPCOM000244777D
Publication Date: 2016-Jan-14
Document File: 4 page(s) / 229K

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A robust iterative ensemble smoother method for efficient history matching and uncertainty quantification

History matching is a type of inverse problem in which observed reservoir behavior is used to estimate the parameters of a reservoir model that caused the observed behavior. The history matched model is then used for predicting reservoir performance to guide reservoir development decisions. The problem of history matching is almost always ill-posed in the sense that many combinations of the reservoir model parameters will result in equally good matches to the historical data. Consequently, the ability to quantify uncertainty in the predicting future reservoir performance from multiple history matched models is an important aspect of history matching. Much of the recent developments in generating history matched models that approximately characterize uncertainty are associated with the iterative ensemble smoother (ES) methods based on either multiple data assimilation (ESMDA) or Levenberg-Marquardt (ESLM) scheme.

The performance of these methods highly depends on the appropriate choice of the regularization parameter. However, both methods either use a fixed sequence (ESMDA) or a heuristic way (ESLM) to change the parameter which may result in slow convergence or even fail to converge sometimes. Therefore, a new method utilizing adaptive choice of the regularization parameters will be of paramount importance as it can improve the performance and reliability of the method. In addition, all existing methods assume the noise level of the data is known a priori and follows a Gaussian distribution. However, in reality, the noise level is often not known and the data sometimes even contains outliers which will significantly affect the history matching results. Thus, a robust regression method which can automatically estimate the noise level and reduce the effect of the outliers in the data is also essential for realistic field application.

The method involves using the gain ratio to derive an iterative updating formula for the regularization parameter in ensemble smoother method. The gain ratio ๐œŒ is chosen as the ratio between the actual decreases in the objective function value to the predicted decrease from first order Taylor approximation to the objective function at each iteration. A large value of ๐œŒ indicates the first-order Taylor expansion is a good approximation to the objective function at the current parameter value. So we can choose a smaller regularization parameter. Therefore, the goal is to ensure the first-order Taylor approximation to linearize the objective function is accurate enough for each iteration. The equation of gain ratio at ๐‘˜๐‘กโ„Ž iteration is:

๐œŒ = ๐‘‚(๐‘š๐‘˜) โˆ’ ๐‘‚(๐‘š๐‘˜ + ฮ”๐‘š) ๐ฟ(0) โˆ’ ๐ฟ(ฮ”๐‘š)

where ๐‘š๐‘˜ is the model variable value from ๐‘˜๐‘กโ„Ž iteration. ๐‘‚(๐‘š๐‘˜) is the objective function value. ๐ฟ(ฮ”๐‘š)...