Streamline methods for automatic history-matching of production data

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.

Publications

1. J. E. Aarnes, V. Kippe, K.-A. Lie, and A. B. Rustad. Modelling of multiscale structures in flow simulations for petroleum reservoirs. In "Geometrical Modeling, Numerical Simulation and Optimisation: Industrial Mathematics at SINTEF", G. Hasle, K.-A. Lie, and E. Quak (Eds.), pp. 307-360, Springer Verlag, 2007. DOI: 10.1007/978-3-540-68783-2_10.
2. J. E. Aarnes, V. Kippe, and K.-A. Lie. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Advances in Water Resources, Vol. 28, Issue 3, pp. 257-271, 2005. DOI: 10.1016/j.advwatres.2004.10.007.
3. V. Kippe, J.E. Aarnes, and K.-A. Lie. Multiscale finite-element methods for elliptic problems in porous media flow. CMWR XVI - Computational Methods in Water Resources. Copenhagen, Denmark, June, 2006.
4. V. Kippe, J. E. Aarnes, and K.-A. Lie. A comparison of multiscale methods for elliptic problems in porous media flow. Computational Geosciences, Vol. 12, No. 3, pp. 377-398, 2008. DOI: 10.1007/s10596-007-9074-6.
5. V. Kippe, H. Hægland, and K.-A. Lie. A method to improve the mass-balance in streamline methods. SPE 106250. 2007 SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A. 26-28 February 2007. DOI: 10.2118/106250-MS
6. V. R. Stenerud, V. Kippe, K.-A. Lie, and A. Datta-Gupta. Adaptive multiscale streamline simulation and inversion for high-resolution geomodels.  SPE J., Vol. 13, No. 1/March, 2008. DOI: 10.2118/106228-PA.