Scale‐dependent dispersion in a stratified granular aquifer

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Abstract
The magnitude of longitudinal dispersivity in a sandy stratified aquifer was investigated using laboratory column and field tracer tests. The field investigations included two‐single‐well injection‐withdrawal tracer tests using 131I and a two‐well recirculating withdrawal‐injection tracer test using 51Cr‐EDTA. The tracer movement within the aquifer was monitored in great detail with multilevel point‐sampling instrumentation. A constant value for dispersivity of 0.7 cm was found to be representative (and independent of travel distance) at the scale of an individual level within the aquifer. A dispersivity of 0.035 cm was determined from laboratory column tracer tests as a representative laboratory‐scale value for sand from the field site. The scale effect observed between the laboratory dispersivity and the dispersivity from individual levels in the aquifer is caused by the greater inhomogeneity of the aquifer (e.g., laminations within individual layers) and the averaging caused by the groundwater sampling system. Full‐aquifer dispersivities of 3 and 9 cm obtained from the single‐well tests indicate a scale effect with the value obtained being dependent mainly on the effect of transverse migration of tracer between the layers and the total injection volume. The full‐aquifer dispersivity of 50 cm from the two‐well test is scale‐dependent, controlled by the distance between the injection and withdrawal wells (8 m) and hydraulic conductivity distribution in the aquifer. Scale‐dependent full‐aquifer dispersivity expressions were derived relating dispersivity to the statistical properties of a stratified geologic system where the hydraulic conductivity distribution is normal, log normal or arbitrary. In the developed expressions, dispersivity is a linear function of the mean travel distance. Proportionality constants ranged from 0.041 to 0.256 for the hydraulic conductivity distributions obtained from the field tracer tests.