Prediction of effective diffusivities in porous media using spatially periodic models

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.