Physics-based hybrid method for multiscale transport in porous media

Despite advancements in the development of multiscale models for flow and reactive transport in porous media, the accurate, efficient and physics-based coupling of multiple scales in hybrid models remains a major theoretical and computational challenge. Improving the predictivity of macroscale predictions by means of multiscale algorithms relative to classical at-scale models is the primary motivation for the development of multiscale simulators. Yet, very few are the quantitative studies that explicitly address the predictive capability of multiscale coupling algorithms as it is still generally not possible to have a priori estimates of the errors that are present when complex flow processes are modeled. We develop a nonintrusive pore-/continuum-scale hybrid model whose coupling error is bounded by the upscaling error, i.e. we build a predictive tightly coupled multiscale scheme. This is accomplished by slightly enlarging the subdomain where continuum-scale equations are locally invalid and analytically defining physics-based coupling conditions at the interfaces separating the two computational sub-domains, while enforcing state variable and flux continuity. The proposed multiscale coupling approach retains the advantages of domain decomposition approaches, including the use of existing solvers for each subdomain, while it gains flexibility in the choice of the numerical discretization method and maintains the coupling errors bounded by the upscaling error. We implement the coupling in finite volumes and test the proposed method by modeling flow and transport through a reactive channel and past an array of heterogeneously reactive cylinders.