Percolation theory and models of unsaturated porous media

Abstract

Concepts from percolation theory (Broadbent and Hammersley, 1957) are applied to a model of unsaturated flow through porous media. This approach in principle allows one to build into the model aspects of the topological structure of pore space. At a very general level the input of results from percolation theory gives a relationship between minimum and maximum saturation values for a medium which should be experimentally checkable, though probably not without sophisticated techniques. Also, it gives some qualitative insight into known properties of unsaturated flow. Furthermore, there emerges a way of looking at the phenomenon of hysteresis that is quite different from the standard approach. This aspect is explored in some detail, and two possible new models are presented. A subsidiary result obtained from the detailed model used is that in a simple pore model the inclusion of a pore length parameter, statistically correlated with pore radius, is equivalent, at least in a restricted sense, to incorporating into the model the concept of tortuosity.