(246c) New Stochastic Approach to Construct Porous Media Geometry Models and Simulation of Non-Darcy Flows

Authors: 
Xiao, F., Colorado School of Mines
Newman, M., Colorado School of Mines
Yin, X., Colorado School of Mines


We present a new method to construct two- and three-dimensional porous media geometry models from Voronoi diagrams. The parameters of the algorithm can be adjusted to produce isotropic and anisotropic fully percolated geometries with both low and high effective porosities (10% to 50%). The permeability calculated using D2Q9 and D3Q19 lattice Boltzmann methods with multiple relaxation time (MRT) collision operators matched well with existing correlations. The tortuosity of the models, calculated from diffusion of tracers, ranged from 1.2 to 1.5. As an application, we studied regime transition from Darcy to non-Darcy flows. In Darcy flows, the superficial velocity through the porous media is a linear function of applied pressure gradient; in non-Darcy flows, due to the inertia of the fluid, the superficial velocity becomes a nonlinear function of the applied pressure gradient. The observed variation in the apparent permeability with the Reynolds number agreed well with existing correlations. The impact of porous media texture on flow regime transition was investigated by randomly removing grains. Porous media geometries with grains removed showed transitions to non-Darcy flows at lower Reynolds numbers and the deviations had higher slopes than those without removed grains at a similar porosity. Flow patterns within the pore space were examined in Darcy and non-Darcy regimes: bypassing streams and steady state vortices were observed when Re was increased to about 10; unsteady flows were observed when Re reached about 20.