Comment on “Universal scaling of hydraulic conductivities and dispersivities in geologic media” by S. P. Neuman

Neuman [1990] provided insight into a problem that has troubled groundwater hydrologists for at least the last ten years.He demonstrated that a fractal model appears to explain the scaling phenomenon of heterogeneity in aquifers, as measured by dispersivity values.The purpose of this comment is to put N euman's model into a geologic context.Neuman developed a universal scaling formula to relate dispersivity to the scale of observation but noted, "A major cause for local deviations from universal behavior appears to be the presence in many geologic media of discrete natural scales at which the log hydraulic conductivity field is homogeneous" (p.1756).These "discrete natural scales" are what geologists call facies.Specifically, a facies is a "threedimensional body of rock having an environment origin that can be inferred from a set of characteristics including external geometry, internal geometry, sedimentary structures, lithology, organic content, stratigraphic relations, and associated facies" [Finley and Tyler, 1986, pp.2-3].Geologists apply the concept of facies on at least two scales: the local scale of Neuman's discrete natural scales (Figure 1 a) and a regional scale used in conceptual models of facies relationships (Figure lb).