Relationship between scale effects in hydraulic conductivity and scale effects in dispersivity: A case study

Extensive aquifer testing was performed for a glacial outwash aquifer in central Iowa to investigate scaling behavior of both hydraulic conductivity (K) and dispersivity ($a$). Previous studies related to this subject generally examined only K or $a$, but not both. The few previous attempts to relate scaling behavior in K and $a$ relied on extrapolation or scattered data from multiple sites. The current study represents a significant advance beyond prior work because K and $a$ were measured systematically at various scales at a single research site.; Direct measurements of K were made using permeameter, slug, pulse, and pumping tests, each test representing a different scale within a range of approximately 0.3 to 425 ft (0.1 to 130 m). Results from well tests were used to quantify “skin” at the aquifer-borehole interface and correct values of K from the slug tests. A small-scale empirical estimate of K was made from grain size data, and regional-scale estimates of K were made from groundwater modeling and stream flow measurements at baseflow. Measurements of $a$ were made using forced-gradient and natural-gradient tracer (NaCl) tests at scales ranging from 6 to 96 ft (2 to 29 m). Additional estimates of K were made based on velocities of tracer migration and hydraulic gradient.; The results of this study indicate an increase in K with test scale until a critical scale (range) of approximately 33 ft (10 m), beyond which a constant and maximum K (sill) of approximately 280 ft/day (0.1 cm/s) is observed. In contrast, measurements of $a$, which are in the range 0.1 to 2.0 in (0.3 to $\le$5.1 cm), show no correlation with test scale. This finding is contrary to numerous previous studies in which $a$ was found to be scale-dependent.; A significant result from this study is that K values calculated from tracer velocities (30 ft/day, 0.010 cm/s) were smaller, by approximately an order of magnitude, than K's from pumping tests (280 ft/day, 0.10 cm/s), and instead were much closer to the average K from slug tests (43 ft/day, 0.015 cm/s). This surprising result may reflect similar quasi-two-dimensional flow during slug and tracer tests, as opposed to quasi-three-dimensional flow during pumping tests.