Generalized scaling of permeabilities: Validation and effect of support scale

The permeabilities and dispersivities of geologic media are known to vary with the scale of observation. Particularly well documented is the consistent increase in apparent longitudinal dispersivity with the mean travel distance of a tracer. This has been previously interpreted by the author to imply that the permeabilities of many geologic media scale, on the average, according to the power‐law semivariogram γ (s)=c √ s where c is a constant and s is distance. Tracer test data support this conclusion indirectly at least over scales from 10 cm to 3,500 m. The present paper cites evidence for such behavior over scales from 10 cm to 45 km based directly on permeability and transmissivity data. The paper then investigates theoretically the implications of such power‐law behavior on the equivalent permeability of a block of rock having a characteristic length (support scale) L. It predicts that the equivalent Isotropie permeability should generally decrease with L in one‐dimensional media, increase with L in three‐dimensional media, and show no systematic variation with L in two‐dimensional media. This prediction appears to be consistent with observations.