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Upscaling bimolecular reactive transport in highly heterogeneous porous media with the LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model

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Abstract

The LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model was developed to predict upscaled bimolecular reactive transport in a flow around an array of solid cylinders. This method combines the stochastic Lagrangian Spatial Markov model (SMM) to predict transport and a volume averaged reaction rate equation to predict reactions of the form \(A+B\rightarrow \emptyset\). Here, we extend the LATERS Markov model to upscale bimolecular reactive transport in a Darcy flow through an idealized heterogeneous porous medium. In agreement with previous literature, the accuracy of the prediction is a function of the Damköhler (Da) numbers, i.e., high Da are more challenging because of incomplete mixing. It was found that a key component which must be incorporated into the upscaled model in these high Da systems is the idea that nearby A and B particles should be more likely to react than those that are farther apart. This is here achieved by appropriately reducing the resolution of the spatial grid employed to resolve the reactive process.

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Acknowledgements

This work was supported by the US Army Research Office under contract/grant number W911NF-18-1-0338. The MATLAB scripts for the Fully Resolved and LATERS models can be found at https://github.com/RichterLab/LATERS-Markov-model.git.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    Elise E. Wright, David H. Richter & Diogo Bolster

  2. Division of Hydrologic Sciences, Desert Research Institute, Reno, NV, 89512, USA

    Nicole L. Sund

  3. Dipartimento Ingegneria Civile ed Ambientale, Politecnico di Milano, Piazza L. Da Vinci, 32, Milano, I-20133, Italy

    Giovanni M. Porta

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  1. Elise E. Wright
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  2. Nicole L. Sund
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  3. David H. Richter
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  4. Giovanni M. Porta
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  5. Diogo Bolster
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Correspondence to Elise E. Wright.

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Wright, E.E., Sund, N.L., Richter, D.H. et al. Upscaling bimolecular reactive transport in highly heterogeneous porous media with the LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model. Stoch Environ Res Risk Assess 35, 1529–1547 (2021). https://doi.org/10.1007/s00477-021-02006-z

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