Modelling of single phase diffusive transport in porous environments

• Main Author: Du Plessis, Elsa
• Other Authors: Woudberg, Sonia
• Format: Others
• Language: en
• Published: Stellenbosch : University of Stellenbosch 2010
• Subjects: Diffusion; Porous media; Effective diffusivity; Microstructure; Dissertations > Applied mathematics; Theses > Applied mathematics
• Online Access: http://hdl.handle.net/10019.1/4323

Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010. === ENGLISH ABSTRACT: Macroscopic diffusion through porous media is considered in systems where this process does not occur along with or induce bulk convective flow of the diffusing species. The diffusion coefficient present in the governing equations of suchmacroscopic diffusion is unique to 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. Taking this into consideration, a deterministic pore-scale model is proposed to predict the effective diffusivity of homogeneous and unconsolidated porous media which ultimately depends solely on the porosity of the media. The approach taken is to model a porous medium as either a fibre bed or an array of granules through which the diffusive process is assumed to be homogenous and transversally isotropic. The fibre bed and granular modelsmay be viewed as two-dimensional and three-dimensional models respectively, and may also be combined to form a weighted average model which adjusts to differing diffusive behaviour at different porosities. The model is validated through comparison with published analytical and numerical models as well as experimental data available in the literature. A numerical program is implemented to generate further data for various arrangements of homogeneous, anisotropic and transversely isotropic porous media. The numerical results were validated against an analytical model from the literature which proved to be inapplicable to a specific case. The weighted average analytical model is proposed for this case, instead. The results of this study indicate that the weighted average analytical model is in good agreement with the numerical and experimental data and as such may be applied directly to a binary system of which the porosity is known in order to predict the effective diffusivity. === AFRIKAANSE OPSOMMING: Makroskopiese diffusieprosesse deur poreuse media word oorweeg in sisteme waar geen konveksie van die diffunderende stof plaasvind of geïnduseer word nie. Die wiskundige beskrywing van hierdie prossese bevat die sogenaamde diffusiekoëffisïent, ’n konstante wat uniek is tot ’n tweeledige sisteem. Dié konstante kan eksperimenteel bepaal word, maar as gevolg van die uniekhied daarvan tot verskillende sisteme moet dit vir elke tweeledige sisteem bepaal word. Op grond hiervan word ’n deterministiese model voorgestel om die effektiewe diffusiwiteit vir diffusie deur homogene en losstaande poreuse media te voorspel. Die model hang slegs af van die porositeit van die poreuse medium wat benader word as ’n veselbed of korrelstruktuur. Die diffusieproses deur dergelike strukture word beskou as homogeen en isotroop in die dwarsstroomrigting. Die veselbed- en korrelmodelle word beskou as twee- en driedimensionele modelle onderskeidelik en word gekombineer om ’n geweegde gemiddelde model te vorm wat dus by enige porositeit die verlangde porositeit gee. Die model is geverifieer deur vergelyking met analitiese- en numeriese modelle asook eksperimentele data vanuit die literatuur. ’n Numeriese program is gebruik om verdere resultate te verkry vir verskeie skikkings van homogene, anisotrope en dwarsverskuifde poreuse media. Die numeriese resultate is gekontroleer deur vergelyking met ’n analitiese model vanuit die literatuur. ’n Spesifieke geval is uitgewys waarvoor hierdie model nie toepasbaar is nie, maar waarvoor die voorgestelde geweegde gemiddelde model goeie resultate lewer. Die uitkomste dui aan dat die analitiese model goed ooreenstem met die numeriese en eksperimentele data en kan dus direk toegepas word om die effektiewe diffusiwiteit te verkry van ’n tweeledige sisteem waarvan die porositeit bekend is.