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Mathematical modelling of electrical conduction in unconsolidated porous media
Thesis (PhD)--Stellenbosch University, 2024.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613919752749056 |
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| access_status_str | Open Access |
| author | Awountsa, Yannick Harisson Nkocko |
| author2 | Fidder-Woudberg, S. |
| author_browse | Awountsa, Yannick Harisson Nkocko Fidder-Woudberg, S. |
| author_facet | Fidder-Woudberg, S. Awountsa, Yannick Harisson Nkocko |
| author_sort | Awountsa, Yannick Harisson Nkocko |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description |
Thesis (PhD)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/131558 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:48.089Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/131558 Mathematical modelling of electrical conduction in unconsolidated porous media Awountsa, Yannick Harisson Nkocko Fidder-Woudberg, S. Diedericks, G. P. J. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division. Electric conductivity -- Measurement Porous materials -- Electric properties Mathematical models UCTD Thesis (PhD)--Stellenbosch University, 2024. ENGLISH ABSTRACT: Electrical conduction in granular porous media is important since it has numerous applications in the chemical, soil, and petroleum engineering industries. In this study, analytical equations for the formation factor for unconsolidated granular media and fibre porous media, are derived. In the modelling approach, volume averaging theory is applied to the microscopic equation describing Ohm’s law, leading to a macroscopic equation containing an integral term over the fluid-solid interfaces. The closure of this macroscopic equation is performed using the rectangular Representative Unit Cell (RUC) model. The RUC model is presented for both isotropic and anisotropic mono-sized unconsolidated porous media and different arrays are considered. For the isotropic RUC models, equations are obtained for the formation factor as functions of porosity, which are applicable over the entire porosity range. Two isotropic models are developed by applying a weighted average to the arrays. A percolation threshold porosity is incorporated into the isotropic models to account for the effect of blocked pores. Numerical simulations are performed to compute the formation factor for two-dimensional versions of all arrays by solving the Laplace equation. The proposed models compare favourably to the generated numerical data and experimental data obtained from the literature. Furthermore, the anisotropic RUC models yield equations for the formation factor in terms of the physical characteristics of the porous medium. Aspect ratios are introduced and novel equations are obtained for the formation factor. Numerical simulations are again performed and the formation factor of the two-dimensional versions computed for several values of the aspect ratios. The developed models are validated against the generated numerical data, numerical data obtained from the literature and experimental data. Finally, an analytical prediction of the relationship between the permeability and formation factor is derived for isotropic granular porous media. It is shown that, the proposed permeability models are indirectly proportional to the formation factor and directly proportional to the square of a characteristic length. The permeability-formation factor relationship has furthermore been extended, by incorporating a percolation threshold porosity. The predictions provide satisfactory agreement with the experimental results. AFRIKAANSE OPSOMMING: Elektriese geleiding in korrelagtige poreuse media is belangrik aangesien dit talle toepassings in die chemiese, grond- en petroleumingenieursbedryf het. In hierdie studie word analitiese vergelykings vir die formasiefaktor vir ongekonsolideerde korrelagtige media en veselagtige poreuse media afgelei. In die modelleringsbenadering word die volumetriese homogeniseringsteorie toegepas op die mikroskopiese vergelyking wat Ohm se wet beskryf, wat lei tot ’n makroskopiese vergelyking wat ’n integraalterm oor die vloeistof-vastestof oppervlaktes bevat. Die sluiting van hierdie makroskopiese vergelyking word uitgevoer deur gebruik te maak van die reghoekige eenheidsel model (in Engels, Representative Unit Cell (RUC) model). Die RUC-model word ontwikkel vir beide isotrope en anisotrope ongekonsolideerde poreuse media met uniforme korrelgroottes en verskillende konfigurasies word oorweeg. Vir die isotrope RUC-modelle word vergelykings vir die formasiefaktor as funksies van porositeit verkry wat van toepassing is vir alle porositeite. Twee isotrope modelle word ontwikkel deur ’n geweegde gemiddelde op die konfiguraies toe te pas. ’n Perkolasie drempel-porositeit word in die isotrope modelle geïnkorporeer om rekening te hou met die effek van geblokkeerde porieë. Numeriese simulasies word uitgevoer om die formasiefaktor vir die tweedimensionele konfigurasies te bereken deur die Laplace-vergelyking op te los. Die voorgestelde modelle vergelyk gunstig met die genereerde numeriese data asook met eksperimentele data verkry uit die literatuur. Verder lewer die anisotropiese RUC-modelle vergelykings vir die formasiefaktor in terme van die fisiese eienskappe van die poreuse medium. Die verhoudings tussen die dimensies van die korrels word gebruik om nuwe vergelykings vir die formasiefaktor te verkry. Numeriese simulasies word ook uitgevoer en die formasiefaktor van die tweedimensionele konfigurasies word vir verskeie waardes van die aspekverhoudings bereken. Die ontwikkelde modelle word gevalideer teen die gegenereerde numeriese data asook teen numeriese data verkry uit die literatuur en gepubliseerde eksperimentele data. Laastens word ’n analitiese voorspelling van die verband tussen die permeabiliteit en die formasiefaktor vir isotrope korrelagtige poreuse media afgelei. Daar word aangetoon dat die voorgestelde permeabiliteit indirek eweredig is aan die formasiefaktor en direk eweredig is aan die kwadraat van ’n karakteristieke lengte. Die permeabiliteit-formasiefaktor verhouding is verder uitgebrei deur ’n perkolasie drempel-porositeit in te sluit. Die voorspellings verskaf bevredigende ooreenstemming met die eksperimentele resultate. Doctoral 2025-01-27T07:44:30Z 2025-01-27T07:44:30Z 2024-12 Thesis https://scholar.sun.ac.za/handle/10019.1/131558 en Stellenbosch University xxx, 239 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Electric conductivity -- Measurement Porous materials -- Electric properties Mathematical models UCTD Awountsa, Yannick Harisson Nkocko Mathematical modelling of electrical conduction in unconsolidated porous media |
| title | Mathematical modelling of electrical conduction in unconsolidated porous media |
| title_full | Mathematical modelling of electrical conduction in unconsolidated porous media |
| title_fullStr | Mathematical modelling of electrical conduction in unconsolidated porous media |
| title_full_unstemmed | Mathematical modelling of electrical conduction in unconsolidated porous media |
| title_short | Mathematical modelling of electrical conduction in unconsolidated porous media |
| title_sort | mathematical modelling of electrical conduction in unconsolidated porous media |
| topic | Electric conductivity -- Measurement Porous materials -- Electric properties Mathematical models UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/131558 |
| work_keys_str_mv | AT awountsayannickharissonnkocko mathematicalmodellingofelectricalconductioninunconsolidatedporousmedia |