Precise numerical modelling of physical transport in strongly heterogeneous porous media

Abstract

A library comprised of precise numerical simulation results for two-dimensional flow and advective transport through statistically-equivalent, structured, porous media is being created to investigate upscaling procedures for contaminant dispersal and physical transport at large space and long time-scales. Several technical challenges were overcome to achieve high precision in the velocity fields and particle paths. A Cholesky Decomposition method for efficient media generation has been extended to generate 'artefact'-free, areally-extensive random fields of hydraulic conductivity variation. An efficient mixed finite-element method, capable of handling periodic boundary conditions was used to compute the flow distributions through the generated media. The method permits exact solution of particle trajectories. Comparison of particle migration patterns with available analytical solutions confirms persistent non-Fickian behaviour of particle migration at large space and times-scales, as well as confirming the accuracy of the simulations. Boundary effects on particle trajectories are found to be significant and cannot be removed totally from the steady-state flow fields. Periodicity, both parallel and perpendicular to the flow direction, results in particle trajectories that are almost periodic and so are inappropriate for transport studies of realistic media. A compromise solution has been adopted whereby only the domain boundaries parallel to the flow are periodic.