A Multiscale Mixed Finite-Element Solver for Three-Phase Black-Oil Flow
Stein Krogstad, Knut‐Andreas Lie, Halvor Møll Nilsen, Jostein R. Natvig, Bård Skaflestad, Jørg Espen Aarnes · 2009
Abstract Previous research has shown that multiscale methods are robust and capable of providing more accurate solutions than traditional upscaling methods. Multiscale methods solve the pressure equation on a coarse grid, but capture the effects from fine-scale heterogeneities through basis functions computed numerically from local single-phase problems on the underlying geocellular grid. Published results have so far been limited to simple Cartesian grids and/or incompressible flow. Here, we present a multiscale mixed finite-element method for three-phase black-oil flow on geomodels with industry-standard complexity. In particular, we discuss which effects can be incorporated in the multiscale basis functions and which effects should be modeled only on the coarsened simulation grid. Moreover, we describe how to handle degenerate hexahedral cells and non-matching interfaces that occur across faults. Finally, we present results of flow simulations on models of industry-standard complexity and demonstrate how multiscale methods can be used to simulate three-phase black-oil flow directly on high-resolution geomodels. The multiscale methods presented herein enable varying resolution and provide a systematic procedure for coarsening or refining the simulation model.