GENERALIZED SCALING OF PERMEABILITIES - VALIDATION AND EFFECT OF SUPPORT SCALE

The permeabilities and dispersivities of geologic media are known to v ary with the scale of observation. Particularly well documented is the consistent increase in apparent longitudinal dispersivity with the me an travel distance of a tracer. This has been previously interpreted b y the author to imply that the permeabilities of many geologic media s cale, on the average, according to the power-law semivariogram gamma ( s) = c square-root s where c is a constant and s is distance. Tracer t est data support this conclusion indirectly at least over scales from 10 cm to 3,500 m. The present paper cites evidence for such behavior o ver scales from 10 cm to 45 km based directly on permeability and tran smissivity data. The paper then investigates theoretically the implica tions of such power-law behavior on the equivalent permeability of a b lock of rock having a characteristic length (support scale) L. It pred icts that the equivalent isotropic permeability should generally decre ase with L in one-dimensional media, increase with L in three-dimensio nal media, and show no systematic variation with L in two-dimensional media. This prediction appears to be consistent with observations.