Microscopic numerical simulations of suspension with particle accumulation in porous media

Microscopic numerical simulations of viscous flow with fine particles suspended in three-dimensional periodic porous media are conducted using the solid–liquid two-phase lattice Boltzmann method. The diameter ratios of migratory particles to that of spherical frame sand grains are 0.16, 0.20 and 0.25 and the saturation of the fine particles ranges from 0.025 to 0.125. It is confirmed that, when the fine particles are fixed in space and do not move, friction determines the permeability and, therefore, their surface area should be accounted for. On the other hand, when they are moving, the permeability depends almost solely on their volume fraction. Taking both effects into account, a unified model for the reduction in apparent permeability caused by fine particles is proposed with combining conventional models of permeability of porous media and viscosity of suspension. In the model, the ratio of the number of trapped particles to that of mobile ones is a key factor.