Transport in capillary network models of porous media: theory and simulation

Abstract

The recent correlated ramdom walk theory, for transport in random networks, is developed here also for cubic networks. A comparison of correlated ramdom walk theory and effective medium theory predictions for cubic networks with simulation results shows the latter to be more accurate in general. For random networks a hybrid alternative, combining the effective medium and correlated random walk theories, is formulated and found to compare better with simulation results. However, under normal conditions, in which percolation effects are not dominant, the correlated ramdom walk theory is found to be adequate. Under conditions involving positional variations in pore structure, or non-linear field-variable-dependent flux laws, the correlated random walk theory appears as the only analytical alternative. Based on this theory, an accurate semi-emperical expression for the conduction threshold is also developed, suggesting directions for its further development incorporating the considerations of disorder.