Scaling analysis of hydraulic conductivity and porosity on a sandy medium of an unconfined aquifer reproduced in the laboratory.

Abstract Many studies have shown that the characteristic parameters of an aquifer, specifically the hydraulic conductivity, increase with an increase in the portion of the aquifer tested. The main cause of this behavior is the heterogeneity within the aquifer. Sets of measurements performed on an artificial aquifer by different methods are utilized here, because it was verified that the scale dependence of hydraulic conductivity does not depend on the specific method of measurement. The unconfined aquifer in question was created in the laboratory utilizing sandy porous medium with a well-known grain-size distribution. An experimental scaling law of the power type was obtained for the hydraulic conductivity, utilizing values measured at different scales by different methods (on undisturbed soil samples by flux cells, on the artificial aquifer by slug tests and aquifer tests). Similarly, porosity measurements of a direct and indirect type were carried out: the former performed in the laboratory and the latter utilizing a relation between k and ϕ based on the particle size analysis of the porous media considered. Successively, a new empirical relationship is proposed here, to derive ϕ , since the k values and vice versa, are well-known, the validity of which is limited to the sands with effective grain size between 0.059 mm and 0.82 mm and for volumes of aquifer not higher than those investigated here.