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arXiv · 1808.09997

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

Zhijie Xu·Paul Meakin
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Abstract

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 {\epsilon} 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, {\epsilon}), dependent on the P\'eclet number Pe, and on a dimensionless parameter {\alpha} that represents the effects of microscopic heterogeneity. The parameter {\alpha}, 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 {\epsilon}. 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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Zhijie Xu, Paul Meakin. 2018-08-29. Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields. https://doi.org/10.1016/j.apm.2013.03.070

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