Speaker
Description
Fluid flow through heterogeneous porous media is ubiquitous in a variety of subsurface engineering applications, including hydrology, geothermal energy production, hydrogen storage, and carbon dioxide sequestration. To efficiently study macroscopic fluid flow---as well as other macroscopic phenomena---in these systems, rigorous upscaling techniques can be employed to derive coarse-grained models with a priori error estimates and applicability conditions (i.e., physical conditions under which a model will meet its a priori error estimates). No fitting parameters are required in the formulation of such models, as the coarse-grained descriptions are derived using fine-scale information (e.g., the microstructure geometry and equations describing the fine-scale physics) to accurately account for multiscale behaviors. Despite their benefits in accuracy and efficiency, a majority of upscaling techniques depend on a strict set of methodological assumptions (e.g., diffusion- or viscous-dominated physics, periodic geometries at finer scales, scale separation, and negligible effects from the boundaries of a system) that hinder their ability to be rigorously applied in practice. To overcome these limitations, we previously developed a novel upscaling methodology, the Method of Finite Averages (MoFA), that avoids the aforementioned assumptions and provides a unique combination of rigor and generality while modeling physical phenomena in heterogeneous porous media. In this work, we apply MoFA to rigorously upscale the Navier-Stokes equations and develop a model for fluid flow in heterogeneous porous media. The resulting upscaled model rigorously accommodates temporally-varying, system-scale boundary conditions and low-Reynolds-number flows (i.e., $\text{Re} \sim 1$). We demonstrate these capabilities and discuss the computational efficiency achieved with the MoFA model through numerical validation experiments.
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