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Benchmarks for multicomponent diffusion and electrochemical migration

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Abstract

In multicomponent electrolyte solutions, the tendency of ions to diffuse at different rates results in a charge imbalance that is counteracted by the electrostatic coupling between charged species leading to a process called “electrochemical migration” or “electromigration.” Although not commonly considered in solute transport problems, electromigration can strongly affect mass transport processes. The number of reactive transport models that consider electromigration has been growing in recent years, but a direct model intercomparison that specifically focuses on the role of electromigration has not been published to date. This contribution provides a set of three benchmark problems that demonstrate the effect of electric coupling during multicomponent diffusion and electrochemical migration and at the same time facilitate the intercomparison of solutions from existing reactive transport codes. The first benchmark focuses on the 1D transient diffusion of HNO3 (pH = 4) in a NaCl solution into a fixed concentration reservoir, also containing NaCl—but with lower HNO3 concentrations (pH = 6). The second benchmark describes the 1D steady-state migration of the sodium isotope 22Na triggered by sodium chloride diffusion in neutral pH water. The third benchmark presents a flow-through problem in which transverse dispersion is significantly affected by electromigration. The system is described by 1D transient and 2D steady-state models. Very good agreement on all of the benchmarks was obtained with the three reactive transport codes used: CrunchFlow, MIN3P, and PHREEQC.

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Acknowledgments

Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant and a Discovery Accelerator Supplement Award held by K. Ulrich Mayer. The contribution of C. Steefel was supported by the Director, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. M. Rolle acknowledges the support of the Baden-Württemberg Stiftung under the Elite program for postdocs.

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The authors declare that they have no conflicts of interest.

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Authors and Affiliations

  1. Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, 2207 Main Mall, Vancouver, BC, V6T 1Z4, Canada

    Pejman Rasouli & K. Ulrich Mayer

  2. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Carl I. Steefel

  3. Department of Environmental Engineering, Technical University of Denmark, Miljøvej Building 115, 2800, Kgs. Lyngby, Denmark

    Massimo Rolle

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  1. Pejman Rasouli
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Correspondence to Pejman Rasouli.

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Supplementary Material

Input and database files for the three participating codes CrunchFlow, MIN3P and PHREEQC are provided. In addition, selected output files as shown in Figures 2-8 are also provided as Supplementary Material. (ZIP 1621 kb)

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Rasouli, P., Steefel, C.I., Mayer, K.U. et al. Benchmarks for multicomponent diffusion and electrochemical migration. Comput Geosci 19, 523–533 (2015). https://doi.org/10.1007/s10596-015-9481-z

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