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

Abstract

Analytical expressions are derived for the formation factor as a function of porosity based on the Representative Unit Cell model for unconsolidated media by applying volume averaging to Ohm’s law. Three arrays are considered, namely an over-staggered, fully staggered and regular array. Numerical simulations are performed to compute the formation factor for two-dimensional versions of the arrays by solving the Laplace equation. The absolute relative percentage difference between the numerical data and corresponding model predictions obtained for the over-staggered array is less than 20% and that for both the fully staggered and regular arrays are less than 10%. Two weighted isotropic models are introduced and a percolation threshold porosity incorporated. The models have been validated against experimental data and models from the literature. The improvement in model prediction with the percolation threshold porosity included is between 100 and 200% at the average porosity of the data set considered.