Open Access Prediction of the Permeability of Fibrous Porous Media Using the Lattice Boltzmann Method in Conjuction with Coarse Numerical Lattices

Abstract: In this study the lattice Boltzmann method (LBM) is used to simulate Stokes flow through unimodal fibrous porous media. A systematic analysis is carried out to determine the suitability of the LBM to predict the permeability of such porous media using relatively coarse numerical lattices. The discretization of fibres using the LBM is discussed in detail with respect to the introduced errors. Subsequently the LBM is calibrated with the aim of compensating for the dominant error terms. For this purpose, simulations of the flow through simple square arrays of parallel cylinders are carried out for fibre-discretizations up to a radius of six lattice units and for solid volume fractions (SVFs) ranging from 0.1 to 0.4. The results obtained are compared to literature data to obtain an estimate for the dominant error terms. Employing the idea of an effective hydrodynamic radius, the error estimates can be taken into account when modeling fibrous porous media. To assess the suitability of this approach, computations for the flow through random arrays of parallel fibres and for random disordered fibrous media are carried out and the predicted permeabilities are compared with literature data. For small SVF, 0.2, the LBM predictions are found to agree well with literature data even for very coarse lattices. At higher SVF the accuracy of the method quickly deteriorates