SUN ETD - Theses and Dissertations

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Browsing SUN ETD - Theses and Dissertations by Author "Awountsa, Yannick Harisson Nkocko"

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    Mathematical modelling of electrical conduction in unconsolidated porous media
    (Stellenbosch University, 2024-12) Awountsa, Yannick Harisson Nkocko; Fidder-Woudberg, S.; Diedericks, G. P. J.; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
    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.