LOG-K VARIANCE, CONNECTIVITY, UNCONFORMITIES AND NON-FICKIAN TRANSPORT

The need for new theories of transport that account for non-Fickian processes arises from fundamental hydrogeologic characteristics of porous media. The typically large values of Ln-K variance (e.g., 5-25) result in juxtaposed fast and slow velocity zones wherein the latter can be dominated by diffusion processes. Moreover, empirical and theoretical studies of the last 15 years demonstrate that in the absence of spatially persistent unconformities, the percolation threshold in 3D will be small, at about 13 to 20%. In other words, without unconformities that might systematically interrupt connectivity, in 3D the upper 13 to 20% of K values will produce percolating paths that connect fully in all three dimensions. In contrast, human intuition is much more comfortable with the notion of a 50% percolation threshold, which applies to the 2D but not the 3D case. The high variance and tendency for interconnection of the high-K fraction leads to a connected-network paradigm of the subsurface that is consistent with field observations, wherein tracer first breakthroughs can occur much sooner than conventional models would predict, and late-time tailing can persist decades to centuries longer than conventional models would predict (e.g., the ubiquitous difficulty of pump-and-treat even for non-reactive contaminants). These fundamentals provide a solid foundation for new, non-Fickian theories of transport while also providing a logical explanation for the extreme scale-dependent behavior of dispersivity.