Study on non-Fickian behavior for solute transport through porous media

Sharma, Pramod Kumar; Agarwal, Pooja; Mehdinejadiani, Behrouz

doi:10.1080/09715010.2020.1727783

Cited by 11 publications

(6 citation statements)

References 34 publications

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“…However, as inferred from Table 1, this deviation in the heterogeneous soil is much more than that in the homogeneous soil. In general, the comparison of the fitting results of this study with those of Sharma et al's (2020) study, a relatively similar work to this paper, revealed that the α values obtained in this study are in excellent agreement with the physical properties of the homogeneous and heterogeneous soils, while those obtained in Sharma et al's (2020) study are inconsistent with the physical properties of the heterogeneous soil.…”

Section: Resultssupporting

confidence: 82%

“…Note that the distinguish between the numerical solutions presented in this study and that presented by Sharma et al (2020), a relatively similar work to this paper, is that the present study solved numerically the one‐sided s‐FADE with a positive fractional derivative by applying an implicit finite difference method and by imposing the local and non‐local boundary conditions, while Sharma et al (2020) solved numerically a two‐sided s‐FADE by applying an explicit finite difference method and by only imposing the local boundary conditions. Furthermore, the numerical solutions presented in this work are unconditionally stable, while that presented by Sharma et al (2020) are conditionally stable.…”

Section: Methodscontrasting

confidence: 68%

“…They found that the s‐FADE simulated BTCs much more adequately than ADE in 28 cases from 53 ones. An explicit finite difference method has been used to solve the s‐FADE by Sharma et al (2020). Their experimental studies revealed that, compared to the ADE, the s‐FADE better described concentration profiles through a heterogeneous soil column.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation of Solute Transport in Saturated Porous Media with Bounded Domains

Mohammadi

Mehdinejadiani

2021

Groundwater

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This work presents the first attempt to develop unconditionally stable, implicit finite difference solutions of one‐sided spatial fractional advection‐dispersion equation (s‐FADE) by imposing the nonzero Dirichlet boundary condition (ND BC) or the nonzero fractional Robin boundary condition (NFR BC) at inlet boundary and the zero fractional Neumann boundary condition (ZFN BC) at outlet boundary. The results of the numerical studies performed using artificial solute transport parameters demonstrated that the numerical solution with the NFR BC as the inlet boundary produced much more realistic concentration values. The numerical solution with the NFR BC at the inlet boundary was capable of correctly describing the Fickian and non‐Fickian behaviors of the solute transport at different α values, and it had the relatively same accuracy at different numbers of the spatial nodes. Also, the practical application of the numerical solution with the NFR BC as the inlet boundary was investigated by conducting tracer experiments in homogeneous and heterogeneous soil columns. According to the obtained results, this numerical solution described well solute transport in the homogenous and heterogeneous soils. The α values of the homogeneous and heterogeneous soils were obtained in the ranges of 1.849–1.999 and 1.248–1.570, respectively, which were in excellent agreement with the physical properties of the soils. In a nutshell, the numerical solution of the s‐FADE with the NFR BC as the inlet boundary can be successfully applied to describe the solute transport in the homogeneous and heterogeneous soils with bounded spatial domains.

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Section: Resultssupporting

confidence: 82%

Section: Methodscontrasting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation of Solute Transport in Saturated Porous Media with Bounded Domains

Mohammadi

Mehdinejadiani

2021

Groundwater

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“…Correlations are inferred between the effective mass transfer time and other parameters such as the flow rate, the capacity coefficient, the advective residence time and the experimental duration. Experiments reported in the literature involve porous media made of sand (Coats and Smith, 1964;Gaudet et al, 1977;De Smedt et al, 1986;Rambow andLennartz, 1993, Kookana et al, 1993 ;Sharma et al, 2022 ;Sutton et al, 2022), loam (van Genuchten and Wierenga, 1977; van Genuchten et al, 1977), loamy sand (Khan and Jury, 1990), clay (Jørgensen et al, 2004), stony soil (Schulin et al, 1987), glass beads (Krupp and Elrick, 1968;De Smedt and Wierenga, 1984;Berkowitz et al, 2009), field soil (Smettem, 1984, Sutton et al, 2022, loam and field soil (Selim et al, 1987), aggregate (Rao et al 1980;Seyfried and Rao, 1987;Koch and Flühler, 1993;Li et al, 1994;Nkedi-Kizza et al 1984;Brusseau et al, 1994;Bajracharya and Barry, 1997), or spherical clayey inclusions in sandy media (Tran Ngoc et al, 2020). In the aforementioned studies, porous media are either homogeneous or moderately heterogeneous.…”

Section: Introductionmentioning

confidence: 99%

Solute transport in heterogeneous model porous media under different flow rates: Experimental and modelling study

Majdalani

Guinot

2023

Journal of Hydrology

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“…Currently, to obtain a three-dimensional (3D) tracer transport averaging equation from turbulent flow, the tracer concentration in the 3D tracer transport equation is averaged over the entire fluctuating period T, also known as the classical averaging (Reynolds averaging) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], or the Global Averaging Values (GAV) [16,17]; the quantity of tracer concentration in the equation is averaged for a whole fluctuating period T:…”

Section: Introductionmentioning

confidence: 99%

Averaging equation of three-dimensional tracer transport by a dual approach

Nguyen

2023

IOP Conf. Ser.: Mater. Sci. Eng.

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The conventional method for calculating averaged tracer concentration in three-dimensional tracer transport equation relies on classical averaging, which averages tracer concentration data obtained from the tracer transport equation in turbulent flow. However, the averaging tracer concentration quantity calculated by this method is not precisely the same as the one obtained by the dual approach. To address this issue, the author proposes a more intricate dual approach for averaging the three-dimensional tracer transport equation in turbulent flow. This paper describes how the author performs two integrations: one from time t to t + r (where r < T, T being the repeated period of fluctuating concentration), and another from time t to time t + T. The fluctuating concentration quantity in turbulent flow is modeled using the trigonometric Fourier series. The resulting three-dimensional mathematical model of tracer transport obtained by this dual approach is more comprehensive than the one obtained by the classical method.

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Study on non-Fickian behavior for solute transport through porous media

Cited by 11 publications

References 34 publications

Numerical Simulation of Solute Transport in Saturated Porous Media with Bounded Domains

Numerical Simulation of Solute Transport in Saturated Porous Media with Bounded Domains

Solute transport in heterogeneous model porous media under different flow rates: Experimental and modelling study

Averaging equation of three-dimensional tracer transport by a dual approach

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