A New Numerical Model for Stokes Flow and Permeability Estimation

Permeability is an important material property of porous and granular materials such as rocks, sands, and soils. The accurate measurement or estimations are very important in modeling the flow through porous media as its relevance to hydrology, soil mechanics, oil industry, and environment protections. There are two fundamental ways to obtain the estimation of permeability: experimental measurement and estimation via theoretical modeling. The experimental method measures the flow through a small sample in a laboratory, then the permeability is calculated. The permeability obtained this way is the averaged result from the representative volume and is not generally applicable in real large flow simulations. The upscaling is to try to bridge the gap between laboratory results and the field parameters. The theoretical estimation of permeability provides a good approximation by using an idealized networks of tubes/pipes through which the fluid flows, and the flow in the pipes is considered as 1-D flow with prescribed pressure or boundary conditions. The networks are generally treated as regular although recent studies begin focus on the fractal structure or statistical features. However, it is very difficult to model the detail flow patterns in random media where different sizes of particles and different porosities are presented. The common approach is to use an averaged representative volume with regular averaged particle size and uniform porosity. Clearly, this is far from the reality in the random porous media. This paper presents a new discrete element approach to the permeability modeling using spherical particles saturated in viscous fluids and treating the interactions among the particles and between fluid and particles in a discrete element manner. For a given particle size distribution, the porosity is calculated. By using the proper boundary conditions, the liquid flux is computed, and the permeability is then estimated. This will in turn give a relationship between permeability and porosity. The simulated results via discrete element method will be compared with experimental results or well-known Kozeny-Carman equations.