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Abstract

The ensemble Kalman filter (EnKF) method has proven to be a promising tool for reservoir model updating and history matching. However, because the EnKF requires that the prior distributions for the parameters to be estimated are Gaussian, or approximately Gaussian, the application to facies models, and channel systems in particular, has been a challenge. In this paper we suggest two different approaches for parameterization of the facies models in terms of Gaussian perturbations of an existing "best guess" model. Method 1 is inspired by level set methods, where surfaces (here facies boundaries) are implicitly modelled through a level set function, normally defined as the signed distance from the nearest surface. Model realizations are generated by adding a Gaussian random field to the initial level set function. Method 2 is based on a similar idea, but the realizations are generated by adding a Gaussian random field to a smoothed indicator function. The smoothing is performed with a Shapiro filter, which is fast and simple to use for any number of dimensions. The performance of the methods is illustrated using a 3D model inspired by a real North Sea fluvial reservoir. It is shown that realistic facies model realizations may be generated from realizations of a Gaussian random field. Based on one realization from the prior for each of the methods, two sets of synthetic production data were generated. Then the prior model ensemble generated with each of the methods were conditioned to each of the two data sets using EnKF. Reasonably good matches were obtained in all cases, including those where the true model is not a realization from the same statistical model as is used to generate the prior realizations.

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/content/papers/10.3997/2214-4609.20146403
2008-09-08
2020-06-06
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20146403
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