Evaluation of hydraulic conductivity of reconstructed granular media generated using low-order probability functions

The hydraulic conductivity of three-dimensional artificial two-phase (fluid phase and solid phase) models with varying solid clustering sizes are evaluated to explore the effect of phase clustering, using low-order probability functions. The original random and heterogeneous microstructure models are made by placing randomly dispersed voxels with varying clustering sizes and the same porosity. The two-point correlation and lineal-path functions are applied to extract characteristics of phase clustering. The reconstructed models whose low-order probability functions are analogous to the original models are then made by a stochastic optimization process. This process allows one to generate equivalent reconstructed models to the original microstructure. The hydraulic conductivity values of both original and reconstructed models along three perpendicular directions are evaluated by solving Navier-Stoke's equation and averaging local velocity values of fluids with the aid of finite element scheme. Results are analyzed to evaluate the applicability of reconstruction approach depending on the phase clustering. The fluid flow through porous media is further examined with the observation of flow resistance and percolation path. The effects of anisotropy of the fluid phase are also discussed to explore the applicability of stochastic optimization process. It is concluded that the low-order probabilistic functions provide an efficient tool to reconstruct three dimensional microstructures up to certain degree of clustering sizes and to simulate the flow behavior in porous media.