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

Elise Wright,David Richter,Diogo Bolster,Nicole Sund,Giovanni Porta

doi:10.3390/w11010053

Abstract

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.

Highlights

Mixing is the process that brings dissolved chemical species together
Incomplete mixing typically results in an overestimation of the amount of reaction that will occur, presenting the need to artificially, and often non-physically, alter the effective reaction rate used in the model to better match observations [19]
We have extended the Spatial Markov model to predict effective mixing in flows through idealized two-dimensional heterogeneous porous media

Summary

Introduction

Mixing is the process that brings dissolved chemical species together. accurately accounting for mixing is important in the context of correctly predicting mixing-driven chemical reactions [1,2,3,4]. The correct prediction of reaction rates has many practical implications in the context of porous media and aquifers, e.g., the prediction of contaminant migration [23,24], the remediation of contaminated groundwater [25,26], and the fundamental prediction of naturally occurring geochemical reactions that shape the subsurface below us. For these reasons, the development of models that accurately describe mixing behaviors are necessary

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Conclusion