title: A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media.
abstract: Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data.
authors: Sonny Astani Dept. of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA. Electronic address: fbarros@usc.edu.
authors: F P J
authors: FP
authors: de Barros
authors: Dip. di Ingegneria, Universita di Roma Tre, Rome, Italy.
authors: A
authors: A
authors: Fiori
authors: Dept. of Mechanical and Aerospace Engineering, University of California, La Jolla, San Diego, USA.
authors: F
authors: F
authors: Boso
authors: Dept. of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy.
authors: A
authors: A
authors: Bellin
mesh_terms: D016880:Anisotropy; D060587:Groundwater; D008962:Models, Theoretical; D016062:Porosity; D012996:Solutions / Q000737:chemistry; D013997:Time Factors; D014872:Water Movements; D014874:Water Pollutants, Chemical / Q000737:chemistry*
chemical_list: D012996:Solutions; D014874:Water Pollutants, Chemical
keywords: Aquifer heterogeneity; Contaminant dilution; Mixing; Stochastic hydrogeology