Use of fractal models to define the scaling behavior of the aquifers\u2019 parameters at the mesoscale

C Fallico,G F A Brunetti,S De Bartolo,G Severino

doi:10.1007/s00477-020-01881-2

Abstract

We present an experimental study aiming at the identification of the hydraulic conductivity in an aquifer which was packed according to four different configurations. The conductivity was estimated by means of slug tests, whereas the other parameters were determined by the grain size analysis. Prior to the fractal we considered the dependence of the conductivity upon the porosity through a power (scaling) law which was found in a very good agreement within the range from the laboratory to the meso-scale. The dependence of the conductivity through the porosity was investigated by identifying the proper fractal model. Results obtained provide valuable indications about the behavior, among the others, of the tortuosity, a parameter playing a crucial role in the dispersion phenomena taking place in the aquifers.

Highlights

The study of flow and transport in groundwater is affected by uncertainty, mainly addressed to the impossibility to get a direct and timely access to the porous medium
We present an experimental study aiming at the identification of the hydraulic conductivity in an aquifer which was packed according to four different configurations
The hydraulic conductivity (K) values were determined for each injection volume and for each configuration taken into consideration

Summary

Introduction

The study of flow and transport in groundwater is affected by uncertainty, mainly addressed to the impossibility to get a direct and timely access to the porous medium. The aquifers’ characterization is commonly faced by considering average values of the various parameters, determined by laboratory and/or field measurements Such an uncertainty is propagated in the models of flow and transport processes (Severino et al 2009; Fallico et al 2010). 1995; Rovey and Cherkauer 1994; SchulzeMakuch and Cherkauer 1997, 1998; Schulze-Makuch et al 1999; Fallico et al 2010, 2012, 2016; Fallico 2014) Most of these studies show that hydraulic conductivity tends to increase when the scale increases and the causes of this behavior are commonly attributed to the medium heterogeneity. Traditionally defined of laboratory, with the characteristic dimensions of the soil

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