Modeling multiphase flow in porous medium systems at multiple scales

Problems involving multiphase flow and transport in porous media arise in a number of scientific and engineering applications including oil reservoir engineering and groundwater remediation. The inherent complexity of multiphase systems and the marked heterogeneity over multiple spatial scales result in significant challenges to the fundamental understanding of the multiphase flow and transport processes. For many decades, multiphase flow has been modeled using the traditional approach based on mass conservation and the generalized Darcy's law. The traditional approach, however, is subject to model errors and numerical errors. The focus of this dissertation research is to improve models of flow and transport in porous medium systems using numerical modeling approaches for a range of scales including pore scale and continuum scale.; A major part of this research examines the deficiency of Darcy's relationship and its extension to multiphase flow using the lattice-Boltzmann (LB) approach. This study investigates the conventional relative permeability saturation relation for systems consisting of water and non-aqueous phase liquid (NAPL). In addition, it also examines the generalized formulation accounting for the interfacial momentum transfer and lends additional support to the hypothesis that interfacial area is a critical variable in multiphase porous medium systems.; Another major part of the research involves developing effcient and robust numerical techniques to improve the solution approach for existing models. In particular, a local discontinuous Galerkin (LDG) spatial discretization method is developed in combination with a robust and established variable order, variable step-size temporal integration approach to solve Richards' equation (RE). Effective spatial adaptive LDG methods are also developed to further enhance the efficiency. The resulting simulator with both spatial and temporal adaption has demonstrated good performance for a series of problems modeled by RE.