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Correction published on 4 August 2020, see Water 2020, 12(8), 2194.
Open AccessArticle

Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
Division of Hydrologic Sciences, Desert Research Institute, Reno, NV 89512, USA
Dipartimento Ingegneria Civile ed Ambientale Politecnico di Milano, Piazza L. Da Vinci, 32, 20133 Milano, Italy
Author to whom correspondence should be addressed.
Water 2019, 11(1), 53;
Received: 1 December 2018 / Revised: 19 December 2018 / Accepted: 24 December 2018 / Published: 29 December 2018
(This article belongs to the Special Issue Heterogeneous Aquifer Modeling: Closing the Gap)
In this work, we develop a novel Lagrangian model able to predict solute mixing in heterogeneous porous media. The Spatial Markov model has previously been used to predict effective mean conservative transport in flows through heterogeneous porous media. In predicting effective measures of mixing on larger scales, knowledge of only the mean transport is insufficient. Mixing is a small scale process driven by diffusion and the deformation of a plume by a non-uniform flow. In order to capture these small scale processes that are associated with mixing, the upscaled Spatial Markov model must be extended in such a way that it can adequately represent fluctuations in concentration. To address this problem, we develop downscaling procedures within the upscaled model to predict measures of mixing and dilution of a solute moving through an idealized heterogeneous porous medium. The upscaled model results are compared to measurements from a fully resolved simulation and found to be in good agreement. View Full-Text
Keywords: heterogeneous porous media; upscaling; mixing; dilution heterogeneous porous media; upscaling; mixing; dilution
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MDPI and ACS Style

Wright, E.E.; Sund, N.L.; Richter, D.H.; Porta, G.M.; Bolster, D. Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model. Water 2019, 11, 53.

AMA Style

Wright EE, Sund NL, Richter DH, Porta GM, Bolster D. Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model. Water. 2019; 11(1):53.

Chicago/Turabian Style

Wright, Elise E.; Sund, Nicole L.; Richter, David H.; Porta, Giovanni M.; Bolster, Diogo. 2019. "Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model" Water 11, no. 1: 53.

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