Multidimensional Upwinding for Multiphase Transport in Porous Media
- Jeremy E. Kozdon (Stanford University) | Bradley Mallison (Chevron) | Margot Gerritsen (Stanford University) | Wen H. Chen (Chevron)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2011
- Document Type
- Journal Paper
- 263 - 272
- 2011. Society of Petroleum Engineers
- 5.4.1 Waterflooding, 5.5 Reservoir Simulation
- multidimensional upstream methods, multiphase flow, monotone, volume relaxed methods, grid orientation effect
- 1 in the last 30 days
- 414 since 2007
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Multidimensional transport for reservoir simulation is typically solved by applying 1D numerical methods in each spatial-coordinate direction. This approach is simple, but the disadvantage is that numerical errors become highly correlated with the underlying computational grid. In many real-field applications, this can result in strong sensitivity to grid design not only for the computed saturation/composition fields but also for critical integrated data such as breakthrough times. Therefore, to increase robustness of simulators, especially for adverse-mobility-ratio flows that arise in a variety of enhanced-oil-recovery (EOR) processes, it is of much interest to design truly multidimensional schemes for transport that remove, or at least strongly reduce, the sensitivity to grid design.
We present a new upstream-biased truly multidimensional family of schemes for multiphase transport capable of handling countercurrent flow arising from gravity. The proposed family of schemes has four attractive properties: applicability within a variety of simulation formulations with varying levels of implicitness, extensibility to general grid topologies, compatibility with any finite-volume flow discretization, and provable stability (monotonicity) for multiphase transport. The family is sufficiently expressive to include several previously developed multidimensional schemes, such as the narrow scheme, in a manner appropriate for general-purpose reservoir simulation.
A number of waterflooding problems in homogeneous and heterogeneous media demonstrate the robustness of the method as well as reduced transverse (cross-wind) diffusion and grid-orientation effects.
|File Size||640 KB||Number of Pages||10|
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