IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i20p6562-d654646.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/20/6562/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/14/20/6562/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Noel Cressie & Andrew Zammit-Mangion, 2016. "Multivariate spatial covariance models: a conditional approach," Biometrika, Biometrika Trust, vol. 103(4), pages 915-935.
    2. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Isabelle Grenier & Bruno Sansó & Jessica L. Matthews, 2024. "Multivariate nearest‐neighbors Gaussian processes with random covariance matrices," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    5. D'Angelo, Nicoletta & Adelfio, Giada & Mateu, Jorge, 2023. "Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    6. Aaron Osgood‐Zimmerman & Jon Wakefield, 2023. "A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling," International Statistical Review, International Statistical Institute, vol. 91(2), pages 318-342, August.
    7. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    8. Thurner, Stephanie D & Converse, Sarah J & Branch, Trevor A, 2021. "Modeling opportunistic exploitation: increased extinction risk when targeting more than one species," Ecological Modelling, Elsevier, vol. 454(C).
    9. de Iaco, Sandra, 2017. "The cgeostat Software for Analyzing Complex-Valued Random Fields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i05).
    10. Pebesma, Edzer & Bivand, Roger & Ribeiro, Paulo Justiniano, 2015. "Software for Spatial Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i01).
    11. Azaïs, Jean-Marc & Chassan, Malika, 2020. "Discretization error for the maximum of a Gaussian field," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 545-559.
    12. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2015. "Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i07).
    13. Xavier Barber & David Conesa & Antonio López-Quílez & Joaquín Martínez-Minaya & Iosu Paradinas & Maria Grazia Pennino, 2021. "Incorporating Biotic Information in Species Distribution Models: A Coregionalized Approach," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    14. Ghorbani, Mohammad & Vafaei, Nafiseh & Dvořák, Jiří & Myllymäki, Mari, 2021. "Testing the first-order separability hypothesis for spatio-temporal point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    15. Moreva, Olga & Schlather, Martin, 2023. "Bivariate covariance functions of Pólya type," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    16. Brown, Patrick E., 2015. "Model-Based Geostatistics the Easy Way," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i12).
    17. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    18. Cécile Hardouin & Noel Cressie, 2018. "Two-scale spatial models for binary data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 1-24, March.
    19. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    20. Dolder, Paul J. & Minto, Cóilín & Guarini, Jean-Marc & Poos, Jan Jaap, 2020. "Highly resolved spatiotemporal simulations for exploring mixed fishery dynamics," Ecological Modelling, Elsevier, vol. 424(C).

    More about this item

    Keywords

    MAWMA; mixing; heterogeneity;
    All these keywords.

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:14:y:2021:i:20:p:6562-:d:654646. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.