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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Yalchin Efendiev, Department of Mathematics
Upscaling of Multi-Phase Flow and Transport Using Non-Local Multi-Continuum Approach

Abstract

We discuss a novel multi-phase upscaling technique, which uses rigorous multiscale concepts based on Constraint Energy Minimization (CEM-GMsFEM). CEM-GMsFEM concepts use local spectral problems to design multiscale basis functions, which are supported in oversampled regions. The coarse-grid solution using these basis functions provides first-order accuracy with respect to the coarse-mesh size independent of high permeability contrast. The degrees of freedom in multiscale methods represent the coordinates of the solution in the multiscale space. To design an upscaled model, we modify these basis functions such that the degrees of freedom have physical meanings, in particular, the averages of the solution in each continua. This allows rigorous upscaled models and account both local and non-local effects. The transmissibilities in our upscaled models are non-local and account for non-neighboring connections. To extend to nonlinear two-phase flow problems, we develop non-linear upscaling, where the pressures and saturations are interpolated in an oversampled region based on averages of these quantities. Multicontinua concepts are used to localize the problem to the oversampled regions. Our upscaled model shares some similarities with pseudo-relative permeability approach with the following differences: (1) upscaled relative permeabilities are non local depend on pressures; (2) local problems, in oversampled regions, involve constraints and require multi-contiuum concepts.