Abstract
Calculations of effective diffusivities in three-dimensional, spatially periodic porous media are performed. For isotropic systems, it is found that, for a given porosity, the predicted value of the effective diffusivity matches experimental results for randomly-packed beds of spheres. Furthermore, the three-dimensional geometry yields approximately the same results as previous calculations employing two-dimensional representations, indicating a relative insensitivity of the effective diffusivity to local geometry. Regarding anisotropic systems, for which two-dimensional modes fail, it is found that there is a significant improvement in the prediction of the effective diffusivity perpendicular to the bedding plane when the three-dimensional model is employed using one adjustable parameter. However, the three-dimensional model overestimates the effective diffusivity parallel to the bedding plane.
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Abbreviations
- a, b :
-
Geometric parameters (Figure 3)
- c :
-
Solute concentration
- D :
-
Diffusion coefficient
- D eff :
-
Effective diffusivity tensor
- E :
-
Dimensionless effective diffusivity, defined by Equation (3.1)
- f :
-
Vector function, defined in Equation (2.8)
- l :
-
Characteristic length of the pore scale
- L :
-
Characteristic length of the macroscopic scale
- L a , L b :
-
Geometric parameters (Figure 3)
- n γκ :
-
Unit vector perpendicular to the fluid-solid interface
- r 0 :
-
Size of the averaging volume
- t :
-
Time
- t * :
-
Characteristic time
- U :
-
Unit tensor
- V :
-
Averaging volume
- ɛ :
-
Porosity
- ζ :
-
Parameter defined by Equation (3.4)
- γ :
-
Fluid phase
- κ :
-
Solid phase
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Sáez, A.E., Perfetti, J.C. & Rusinek, I. Prediction of effective diffusivities in porous media using spatially periodic models. Transp Porous Med 6, 143–157 (1991). https://doi.org/10.1007/BF00179277
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DOI: https://doi.org/10.1007/BF00179277