Modelling of single phase diffusive transport in porous environments

[摘要] ENGLISH ABSTRACT: Macroscopic diffusion through porous media is considered in systems where this processdoes not occur along with or induce bulk convective flow of the diffusing species. The diffusioncoefficient present in the governing equations of suchmacroscopic diffusion is uniqueto a pair of species in a binary system. This coefficient may be determined experimentally,but such experimentation must be carried out for every different pair of species. Takingthis into consideration, a deterministic pore-scale model is proposed to predict the effectivediffusivity of homogeneous and unconsolidated porous media which ultimately dependssolely on the porosity of the media. The approach taken is to model a porous medium as eithera fibre bed or an array of granules through which the diffusive process is assumed to behomogenous and transversally isotropic. The fibre bed and granular modelsmay be viewedas two-dimensional and three-dimensional models respectively, and may also be combinedto form a weighted average model which adjusts to differing diffusive behaviour at differentporosities. The model is validated through comparison with published analytical andnumerical models as well as experimental data available in the literature. A numerical programis implemented to generate further data for various arrangements of homogeneous,anisotropic and transversely isotropic porous media. The numerical results were validatedagainst an analytical model from the literature which proved to be inapplicable to a specificcase. The weighted average analytical model is proposed for this case, instead. The resultsof this study indicate that the weighted average analytical model is in good agreement withthe numerical and experimental data and as such may be applied directly to a binary systemof which the porosity is known in order to predict the effective diffusivity.

[发布机构] Stellenbosch University