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Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena

Author

Listed:
  • Ricardo Mendonça de Moraes

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil
    These authors contributed equally to this work.)

  • Luan Carlos de Sena Monteiro Ozelim

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil
    These authors contributed equally to this work.)

  • André Luís Brasil Cavalcante

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil
    These authors contributed equally to this work.)

Abstract

The conventional mathematical model expressed by the advection–dispersion equation has been widely used to describe contaminant transport in porous media. However, studies have shown that it fails to simulate early arrival of contaminant, long tailing breakthrough curves and presents a physical scale-dependency of the dispersion coefficient. Recently, advances in fractional calculus allowed the introduction of fractional order derivatives to model several engineering and physical phenomena, including the anomalous dispersion of solute particles. This approach gives birth to the fractional advection–dispersion equation. This work presents new solutions to the fractional transport equation that satisfies the initial condition of constant solute injection in a semi-infinite medium. The new solution is derived based on a similarity approach. Moreover, laboratory column tests were performed in a Brazilian lateritic soil to validate the new solution with experimental data and compare its accuracy with the conventional model and other fractional solutions. The new solution outperforms the existing ones and reveals an interesting fractal-like scaling rule for the diffusivity coefficients.

Suggested Citation

  • Ricardo Mendonça de Moraes & Luan Carlos de Sena Monteiro Ozelim & André Luís Brasil Cavalcante, 2022. "Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena," Sustainability, MDPI, vol. 14(7), pages 1-19, March.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:7:p:4024-:d:782105
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    References listed on IDEAS

    as
    1. van Genuchten, M. Th. & Alves, W. J., 1982. "Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation," Technical Bulletins 157268, United States Department of Agriculture, Economic Research Service.
    2. Saffarian, Marziyeh & Mohebbi, Akbar, 2022. "Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 348-370.
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