Permeability prediction of an analytical pore-scale model for layered and isotropic fibrous porous media

In this study an existing analytical pore-scale model for flow parallel and perpendicular to 1D unidirectional fibres are used and adapted to propose permeability predictions for in-plane and through plane flow in layered 2D fibre arrangements as well as flow through 3D isotropic fibrous porous media. This is done by application of a weighted average equation in which different weights are assigned to flow parallel and perpendicular to 1D fibre arrangements, depending on the fibre orientation and average flow direction. Different arrays are considered, based on the degree of staggering of fibres with respect to the average flow direction. The effect of fibre orientation on permeability is investigated for flow through layered 2D fibre arrangements. It is illustrated how the permeability at low solid volume fractions reduces through the incorporation of the effect of developing flow. The effect of blocked pores at high solid volume fractions is also accounted for by introducing a percolation threshold solid volume fraction beyond which no more seepage takes place. A unimodal equivalent radius is furthermore introduced into the models in order to predict the permeability of bimodal fibrous media. The proposed permeability predictions are applicable over the entire range of solid volume fractions. Comparison with theoretical models from the literature as well as available experimental and numerical data proves satisfactory. The model characteristics that distinguish the proposed models from many other models in the literature are (i) being physically adaptable to extend its range of applicability, whilst at the same time (ii) balancing accuracy and simplicity (from an analytical point of view), and (iii) containing no empirical coefficients.