Fractional diffusion models for radionuclide anomalous transport in geological repository systems

Wei, Qing; Yang, Shuai; Zhou, Hongwei; Zhang, S.Q.; Li, X.N.; Hou, Wentao

doi:10.1016/j.chaos.2021.110863

Cited by 8 publications

(2 citation statements)

References 37 publications

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“…Chaudhary et al [48] used conformable derivative approach to analyse the impact of time fractional derivative over classical form of convection dispersion equation and derived the solution for constant and variable dependent migration parameters, both. Wei et al [49] modelled the nuclide anomalous migration in repository formations by using fractional model of diffusion equation and validate the fraction model with corresponding theoretical and experimental data of radionuclide diffusion.…”

Section: Introductionmentioning

confidence: 98%

Anomalous transport for multispecies reactive system with first order decay: time-fractional model

Chaudhary¹,

Singh²

2022

Phys. Scr.

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The prediction of pollutant migration and its concentration variation in the subsurface hydrology is vitally requisite for the assessment and restorative treatment of polluted groundwater system. Pollutant migration for the multispecies reactive system cannot be reliably investigated by classical form of convection-dispersion equation (CDE), due to the presence of more than one reactive species. This paper establishes a time-fractional model for multispecies reactive system under the first order sequential reaction network to understand the anomalous or non-Fickian migration phenomenon for reactive pollutants. At present, most of the fractional models are presented for the classical CDE to investigate migration phenomenon for single species system, not for the multispecies reactive system due to the complexity of the modelled framework. The impact of fractional derivative model is analysed for variable dependent migration parameters and constant parameters, both for the multispecies reactive migration phenomenon. The fractional derivative is expressed in the Caputo sense and to handle the non-linearity of problem, Homotopy perturbation method (HPM) is adopted. The advantage of this method, to get the solutions, is that the HPM is independent of small parameters required for the deformation process as used in other existing perturbation techniques, which make it much more convenient to use for non-linear systems. The impact of the fractional derivative index and other migration parameters is graphically depicted for the reactive species and significant influence of fractional term is observed. The derived solutions are then validated by using the corresponding solutions obtained by other existing well-established methods to ensure the convergence of the HPM solutions. As there do not exist any solutions for such fractional models for multispecies reactive system, this study may be advantageous to convey better understanding for the anomalous or non-Fickian migration for reactive pollutants and their remediation planning in the groundwater resources.

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Section: Introductionmentioning

confidence: 98%

Anomalous transport for multispecies reactive system with first order decay: time-fractional model

Chaudhary¹,

Singh²

2022

Phys. Scr.

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“…The fractional dynamic approach is emerging as a novel description of anomalous transport processes [4][5][6]. Numerous researchers have applied the fractional derivative models to describe the turbulent flow [7], non-Darcian flow [8][9][10], transient flow [11], atmospheric pollutant dispersion [12,13], solute transport [14], and contaminant migration [15,16]. Moreover, fractional diffusion models, in terms of different definitions of a fractional derivative, also have been considered to depict the advective-dispersive transport in single porous media [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

2022

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Based on the multiple barriers concept of deep geological disposal of high-level waste, fractional advection diffusion equations for radionuclide migration in multiple layers low-permeability porous media are proposed in this work. The presented fractional advection diffusion models in terms of different definitions of fractional derivative are analytically addressed via the Laplace integral transform method. This work provides a theoretical foundation for further simulations of radionuclide migration in the multiple barriers system of the high-level waste repository.

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A robust scheme for Caputo variable-order time-fractional diffusion-type equations

Sadri¹,

Hosseini²,

Băleanu

et al. 2023

J Therm Anal Calorim

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Fractional diffusion models for radionuclide anomalous transport in geological repository systems

Cited by 8 publications

References 37 publications

Anomalous transport for multispecies reactive system with first order decay: time-fractional model

Anomalous transport for multispecies reactive system with first order decay: time-fractional model

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

A robust scheme for Caputo variable-order time-fractional diffusion-type equations

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