Longitudinal dispersivity data and implications for scaling behavior

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Abstract

Longitudinal dispersivity (α) data were compiled from 109 different authors for different types of geological media. The data were subdivided into different subsets. Dispersivity values for consolidated media were subdivided as basalts, granites, sandstones, and carbonate rocks, while unconsolidated sediments were subdivided into three reliability classes. The data sets provided here may provide ground water practitioners a preliminary guide to estimate dispersivity values at various scales and to guide and verify theories on scaling behavior. Based on the data set presented here, the relationship that empirically best described the dispersivity data in regard to scale of measurement was in the form of a power law. The scaling exponent for consolidated and unconsolidated geological media varied between 0.40 and 0.92, and 0.44 and 0.94, respectively. Higher reliability subsets of data for the unconsolidated sediments and more frequently tested rock formations indicate that the scaling exponent is at the lower end of the observed range, close to 0.5. No significant difference in scaling exponent was found among different media, and no clear evidence exists for the presence of an upper bound or asymptotic behavior on the relationship for any of the analyzed media.

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