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Title: Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
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Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematical Modelling, 37(18-19):8533-8542
Research Org:
Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
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Country of Publication:
United States
solute transport; multi-scale; advection; dispersion; upscaling; heterogeneous; homogenization