Next Generation Multiscale Methods for Reservoir Simulation

In this thesis, we discuss multiscale simulation techniques for flow and transport in porous media, discretized on unstructured grids. The model equations considered are taken from the field of reservoir simulation, where several orders of magnitude variation in parameters and complex fluid physics result in highly challenging simulation problems. We consider several novel multiscale solvers and the subsequent extension to compressible multiphase black-oil and compositional flow. The examples include both conceptual models and full field-scale models with industrial complexity in properties, fluid physics, geology and grid types. The thesis also describes the application of numerical experiments termed flow diagnostics for optimization and ranking problems, with and without multiscale solvers. In order to facilitate the research on linear and nonlinear solvers, an open source general purpose simulator framework based on object orientation is developed. This framework aims to enable researchers to rapidly extend or improve existing models and solvers, which is exemplified in this thesis by the development of a simulator for polymer flooding with non-Newtonian fluid physics. Finally, we also consider transport solvers based on a novel parametrization of Newton updates for the three-phase saturation equations with nonconvex, non-monotone flux functions that can converge for much larger timesteps than the current state of the art solvers