Relation of hydraulic conductivity and dispersivity to scale of measurement in a carbonate aquifer

Tests on several scales were analyzed and conducted in a dolomite aquifer of southeastern Wisconsin to examine the variation of hydraulic conductivity and longitudinal dispersivity with scale of measurement. Scale behavior of hydraulic conductivity was shown to be dependent on the hydrofacies. In vuggy fades dominated by porous flow hydraulic conductivity increased relative to scale linearly with an upper bound on a log-log plot. A similar increase of longitudinal dispersivity with scale for these faciès is probable but not certain, due to insufficient data. In fractured-flow dominated mudstone fades hydraulic conductivity also increases with scale. However, its log-log slope was steeper, and neither an upper nor a lower bound is apparent. INTRODUCTION There are various reports of hydraulic conductivity and dispersivity increases with scale of measurement in the literature (Neuman, 1990; Wheatcraft & Tyler, 1988; Kinzelbach, 1990; Clauser, 1992). Most of the papers summarize different types of rocks and aquifers or treat scale behavior statistically (Neuman, 1994; Gelhar et al., 1985). Only a few authors have compiled data from the same aquifer or geologic formation and analyzed scale behavior in a specific rock type (Rovey & Cherkauer, 1994; Herzog & Morse, 1984). This paper will go a step further and introduce a fades approach to the scale behavior of hydraulic conductivity and longitudinal dispersivity. The study area is a carbonate aquifer of SE Wisconsin; an aquifer where porous, double-porosity and fractured hydrofacies are present. Three formations of this aquifer will be introduced: the Thiensville Formation, the Racine Formation and the Mayville Formation. The Thiensville Formation consists of four different hydrofacies: a soil faciès, a solutioned fades with big vugs, a mudstone fades and a mixed fades, which is mainly made up by recrystallized dolomite, algal laminates and packstones with thin layers of the previously mentioned fades. The four different fades can be distinguished by their hydraulic conductivities on the pressure-packer test scale (Fig. 1). The Thiensville Formation as a unit shows the porous Theis curve responses in pumping tests, and has a unimodal hydraulic conductivity distribution (as indicated by specific capacity data). The Racine Formation consists of a mudstone fades and a vuggy, porous fades called the Romeo beds. The mudstone fades can be subdivided into a fracture-flow 224 Dirk Schulze-Makuch & Douglas S. Cherkauer