A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media

Journal of Contaminant Hydrology
Felipe P J de BarrosAlberto Bellin

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 theore...Continue Reading

References

Dec 18, 2007·Journal of Contaminant Hydrology·Robert D BauerChristian Griebler
May 2, 2008·Journal of Contaminant Hydrology·Olaf A CirpkaMarco Dentz
Nov 10, 2009·Journal of Contaminant Hydrology·Massimo RollePeter Grathwohl
Jun 22, 2010·Journal of Contaminant Hydrology·Marco DentzBranko Bijeljic

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Citations

Jul 6, 2019·Journal of Contaminant Hydrology·Arianna LiberaHaruko Wainwright

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