Analytical prediction of the formation factor for anisotropic mono-sized unconsolidated porous media

Abstract

The rectangular Representative Unit Cell (RUC) models for mono-sized isotropic unconsolidated porous media have been extended to anisotropic media. Volume averaging was applied to Ohm's law in order to propose analytical expressions for the formation factor for electrical conduction in terms of the pore-scale linear dimensions. The formation factor, crucial for understanding electrical conduction in porous media, has significant applications in subsurface geophysics, petroleum reservoir characterization, and the durability assessment of construction materials. These analytical models provide valuable insights for optimizing the electrical properties of porous structures in various engineering fields, for example in mapping groundwater resources, differentiating oil-bearing zones in reservoirs, and predicting ion migration in concrete. Aspect ratios of the cell and solid dimensions have been introduced, and the formation factor expressed in terms thereof for five different arrays, i.e. a regular, a non-overlapping streamwisely fully staggered, an overlapping streamwisely fully staggered, a non-overlapping transversally fully staggered, and an overlapping transversally fully staggered array. The Laplace equation has furthermore been solved numerically for two-dimensional versions of the different arrays and the formation factor computed for several values of the aspect ratios. The proposed analytical models have been validated against the generated numerical data and compared to experimental and numerical data obtained from the literature. The proposed models have also been adapted to include a percolation threshold porosity in order to improve the model predictions for very low porosity media.