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Abstract

When performing ensemble based data assimilation (DA) one can, due to the high inherent computational cost of running a complex reservoir simulator, only afford to apply a moderate number of ensemble members. Without modification it is well known that the DA procedure will fail when assimilating data in high-dimensional geophysical systems. Distance-based localization mitigate the effects of few ensemble members, but, for many cases, it is difficult to define localization in a suitable manner, this is especially the case for problems with a nonlocal relationship between data and parameters. An alternative to localization is to increase the ensemble size. With fixed computational resources, an increase in the ensemble size must be compensated for by a decrease in the cost of each reservoir simulation. This can be achieved by replacing the reservoir simulator with a proxy model. In this work, we investigate the use of a proxy model that is constructed by discretizing the reservoir model equations on a coarser grid than the original reservoir simulation model. A modest reduction in the number of grid cells should be sufficient to compensate for the increase in computation from using a large ensemble size. This reduction is achieved by a flexible and adaptive upscaling procedure, capable of handling all grids, which is constructed based on a second generation wavelet transform. Since the update step of the DA algorithm is much less computationally demanding than the forecast step, we consider a DA method where the forecast is performed on the coarse model while the update is performed on the the fine grid. This is formulated without the need for error structure correction. The large ensemble proxy DA method is compared with a localization methods on several numerical examples where localization is traditionally required.

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/content/papers/10.3997/2214-4609.201601818
2016-08-29
2024-03-28
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201601818
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