A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method

Abstract

Fluid flow analyses for porous media are of great importance in a wide range of industrial applications including, but not limited to, resin transfer moulding, filter analysis, transport of underground water and pollutants, and hydrocarbon recovery. Permeability is perhaps the most important property that characterizes porous media; however, its determination for different types of porous media is challenging due its complex dependence on the pore-level structure of the media. In the present work, fluid flow in three-dimensional random fibrous media is simulated using the lattice Boltzmann method. We determine the permeability of the medium using the Darcy law across a wide range of void fractions (0.08 ⩽ ϕ ⩽ 0.99) and find that the values for the permeability that we obtain are consistent with available experimental data. We use our numerical data to develop a semi-empirical constitutive model for the permeability of fibrous media as a function of their porosity and of the fibre diameter. The model, which is underpinned by the theoretical analysis of flow through cylinder arrays presented by [Gebart BR. Permeability of unidirectional reinforcements for RTM. J Compos Mater 1992; 26(8): 1100–33], gives an excellent fit to these data across the range of ϕ. We perform further simulations to determine the impact of the curvature and aspect ratio of the fibres on the permeability. We find that curvature has a negligible effect, and that aspect ratio is only important for fibres with aspect ratio smaller than 6:1, in which case the permeability increases with increasing aspect ratio. Finally, we calculate the permeability tensor for the fibrous media studied and confirm numerically that, for an isotropic medium, the permeability tensor reduces to a scalar value.