In his doctoral thesis, Vegard Kippe has studied multiscale and streamline methods to be used as fast forward simulators in history matching. Three multiscale approaches specialized for porous media flow equations are discussed and compared to each other, as well as to traditional and more modern single-phase upscaling methods. It is demonstrated that all of the multiscale methods perform well for models with a relatively smooth spatial variation, and that they are typically more accurate than local upscaling methods coupled with a mass-conservative downscaling approach. For problems with highly discontinuous coefficients, particular difficulties are discovered for each of the multiscale methods, and solutions or partial remedies are suggested. One multiscale approach, based on a mixed finite-element method, is utilized within a streamline method to obtain an overall simulation strategy that is both efficient and scalable. To further increase computational efficiency, the issue of mass-balance errors in streamline methods is addressed, and an approach that allows rapid estimation of production characteristics is proposed. The resulting multiscale/streamline methodology is particularly well-suited for performance critical reservoir engineering applications such as history-matching, and this is demonstrated by using the approach within a streamline-based automatic inversion framework to history-match a million-block reservoir model in less than twenty minutes on a standard desktop computer.
Published February 25, 2008
Knut-Andreas LieSINTEF ICT, Applied Math.Phone: +47 22 06 77 10.
A portfolio of strategic research projects funded by the Research Council of Norway