Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model
by
Elise E. Wright 1,*, Nicole L. Sund 2, David H. Richter 1, Giovanni M. Porta 3 and Diogo Bolster 1
Elise E. Wright 1,*, Nicole L. Sund 2, David H. Richter 1, Giovanni M. Porta 3 and Diogo Bolster 1
1
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
2
Division of Hydrologic Sciences, Desert Research Institute, Reno, NV 89512, USA
3
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; https://doi.org/10.3390/w11010053
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.
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Keywords:
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.
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