Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization |
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Authors: | Email author" target="_blank">Hans?BruiningEmail author Mohamed?Darwish Aiske?Rijnks |
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Institution: | (1) Assistant Professor, Department of Agricultural Engineering, Faculty of Agriculture, Akdeniz University, Antalya 07059, Turkey,;(2) Professor, Departments of Land, Air and Water Resources (Hydrology Program) and Biological and Agricultural Engineering, University of California, Davis CA 95616 USA,; |
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Abstract: | This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization
with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that
the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists
of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations,
which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion
tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct
dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic
media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion
coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement
for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low.
The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion
coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization
applied to Taylor dispersion discussed in the literature. |
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