Simulation of fluid flow in granular microstructure using a non-staggered grid scheme

Abstract

A finite difference numerical scheme has been utilized to simulate fluid flow in granular microstructures. The pixels of their digital images represent the granular microstructure in the finite difference grid. The scheme utilizes a non-staggered grid arrangement, which requires only one finite difference mesh to solve the governing fluid flow equations. As such, the scheme is more efficient when it comes to dealing with non-orthogonal coordinates and complex geometry of boundary conditions such as that of granular microstructure. The numerical scheme is verified by comparing the permeability values of a medium of packed columns to a closed form solution. It is then used to evaluate the permeability coefficients of idealized and natural granular microstructures. It has been found that as the directional aspect ratio increases, the resistance of a particle to fluid flow increases, which results in a decrease in the permeability coefficient. A medium of elliptical particles has higher permeability coefficient than a medium of rectangular particles for the same porosity because of its lower surface area. The permeability anisotropy has been found to increase with an increase in the aspect ratio or a decrease in porosity. Spherical glass beads have been found to have higher permeability coefficients than Ottawa sand and Silica.