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The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media

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Listed:
  • Joaquim Soler-Sagarra

    (Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya (UPC), Jordi Girona 1-3, 08034 Barcelona, Spain
    Institute of Environmental Assessment and Water Research (IDAEA), CSIC, c/ Jordi Girona 18, 08034 Barcelona, Spain
    International Center for Numerical Methods in Engineering (CIMNE), Universitat Politècnica de Catalunya (UPC), 08034 Barcelona, Spain)

  • Vivien Hakoun

    (French Geological Survey, BRGM, F-45060 Orleans, France)

  • Marco Dentz

    (Institute of Environmental Assessment and Water Research (IDAEA), CSIC, c/ Jordi Girona 18, 08034 Barcelona, Spain)

  • Jesus Carrera

    (Institute of Environmental Assessment and Water Research (IDAEA), CSIC, c/ Jordi Girona 18, 08034 Barcelona, Spain)

Abstract

Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.

Suggested Citation

  • Joaquim Soler-Sagarra & Vivien Hakoun & Marco Dentz & Jesus Carrera, 2021. "The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media," Energies, MDPI, vol. 14(20), pages 1-18, October.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:20:p:6562-:d:654646
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    References listed on IDEAS

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    1. Alessandro Comolli & Marco Dentz, 2017. "Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(9), pages 1-18, September.
    2. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
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    Cited by:

    1. Neitzel, Leonie & Gehrig, Edeltraud, 2022. "Influence of advection in box models describing thermohaline circulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 101-112.

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    Keywords

    MAWMA; mixing; heterogeneity;
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