Variable Compact Multi-Point Upscaling Schemes for Anisotropic Diffusion Problems in Three-Dimensions

Simulation is a useful tool to mitigate risk and uncertainty in subsurface flow models that contain geometrically complex features and in which the permeability field is highly heterogeneous. However, due to the level of detail in the underlying geocellular description, an upscaling procedure is needed to generate a coarsened model that is computationally feasible to perform simulations. These procedures require additional attention when coefficients in the system exhibit full-tensor anisotropy due to heterogeneity or not aligned with the computational grid. In this thesis, we generalize a multi-point finite volume scheme in several ways and benchmark it against the industry-standard routines. Specifically, we extend a local transmissibility upscaling method to three-dimensional domains and incorporate adaptive mesh refinement. Our method uses spatially varying and compact multi-point flux approximations (MPFA), based on the Variable Compact Multi-Point (VCMP) method previously introduced for two-dimensional Cartesian grids in Lambers et al. \cite{lambers2008accurate}. Moreover, the optimization algorithm that selects the transmissibility weights is generalized. Numerical results show that VCMP improves upscaling accuracy compared to local TPFA upscaling methods and the local-global TPFA upscaling method