Colin Clark1, Larry Winter2
1Department of Mathematics, The University of Arizona, Tucson, Arizona
2Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, Arizona
We investigate the effect of percolation on the effective conductivity of highly heterogeneous, irregular, composite porous media. Composite media consists of different materials (e.g. sand and clay) that have been deposited by geologic processes into disjoint configurations where each material has a different hydraulic conductivity. The effective conductivity is a single parameter that represents the aggregate behavior of the conductivity field for the equation. When the values of conductivity vary by several orders of magnitude, the irregular geometry and topology of the configuration influences the flow and for volume fractions near the percolation threshold, the event of percolation marks a transition between two different regimes. We develop a phenomenological model to describe the effect of heterogeneity and volume fraction near the percolation threshold. We use probabilistic arguments to motivate the model and numerical simulation for validation.