Modeling Bromide Transport in Undisturbed Soil Columns with the Continuous Time Random Walk

Shahmohammadi-Kalalagh, Shahram; Beyrami, Hossein

doi:10.1007/s10706-015-9917-1

Cited by 8 publications

(7 citation statements)

References 41 publications

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“…[7][8][9][10] One of the effective ways to quantify anomalous (or non-Fickian) transport in nonhomogeneous porous media is the continuous time random walks (CTRW's) model. [11][12][13][14][15][16] Based on various CTRW's scholars obtain several generalization types of ADE, which can be used to describe the evolution of the probability density function (PDF) of the particles undergoing anomalous dispersion in flow fields. [17,18] Note that an assumption in the used CTRW models is that the energy of the non-Fickian particles does not have a direct effect on their transport behaviors.…”

Section: Introductionmentioning

confidence: 99%

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Zhang

2016

Chinese Phys. B

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Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.

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Section: Introductionmentioning

confidence: 99%

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Zhang

2016

Chinese Phys. B

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“…Stronger statements implying that individual parameters may be interpreted in isolation are also found in the literature. For example, Shahmohammadi‐Kalalagh and Beyrami (2015) write “the single parameter β quantifies all of the mechanisms that control the transport behavior.” In this spirit, some authors only report the value of β when performing CTRW fits using TPL‐distributed ψ ( t ), but not t 1 or t 2 . (e.g., Frank et al., 2020; Hu et al., 2020; Shahmohammadi‐Kalalagh & Beyrami, 2015; Xiong et al., 2006), or report all TPL parameters alongside v ψ and D ψ but do not report τ (e.g., Heidari & Li, 2014; Jiménez‐Hornero et al., 2005; Mettier et al., 2006).…”

Section: Summary Discussionmentioning

confidence: 99%

“…The key point is the interplay of parameters in the model. Stronger statements implying that individual parameters may be interpreted in isolation are also found in the Shahmohammadi-Kalalagh and Beyrami (2015) write "the single parameter β quantifies all of the mechanisms that control the transport behavior." In this spirit, some authors only report the value of β when performing CTRW fits using TPL-distributed ψ(t), but not t 1 or t 2 .…”

Section: Ctrw Parameters Cannot Generally Be Interpreted In Isolationmentioning

confidence: 93%

“…In this spirit, some authors only report the value of β when performing CTRW fits using TPL-distributed ψ(t), but not t 1 or t 2 . (e.g., Frank et al, 2020;Hu et al, 2020;Shahmohammadi-Kalalagh & Beyrami, 2015;Xiong et al, 2006), or report all TPL parameters alongside v ψ and D ψ but do not report τ (e.g., Heidari & Li, 2014;Jiménez-Hornero et al, 2005;Mettier et al, 2006).…”

Section: Ctrw Parameters Cannot Generally Be Interpreted In Isolationmentioning

confidence: 99%

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Experimental Support for a Simplified Approach to CTRW Transport Models and Exploration of Parameter Interpretation

Hansen

2022

Water Resources Research

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In a recent paper (Hansen, 2020), we proposed an interpretation of some of the terms of the continuous-time random walk (CTRW) generalized master equation (GME), which allow its 1D form to be written in the following simplified way:(1)Here, c[ML −3 ] is concentration, M(t) [T −1 ] is a temporal memory function, ̄ LT −1 is mean groundwater velocity, and α [L] is a standard Fickian dispersivity, generated by multiplication of 𝐴𝐴 𝐴 𝐴𝐴 by some fixed, medium-specific dispersivity, α [L]; x [L] is spatial coordinate, and t [T] is time. On this approach, M(t) is defined in the Laplace domain according the formula:where superscript tilde denotes the Laplace transform, s [T −1 ] is the Laplace variable, and ψ(t) [T −1 ] is the probability distribution function for a subordination mapping representing the total time taken for solute to complete a transition that would have taken unit time under purely advective-dispersive physics as described by 𝐴𝐴 𝐴 𝐴𝐴 and α.This approach, which we refer to as the simplified approach, simplifies and physically constrains the continuous-time random walk (CTRW) generalized master equation (GME) in a number of ways and also provides an interpretation to its parameters. By contrast, in typical usage: (a) 𝐴𝐴 𝐴 𝐴𝐴 and 𝐴𝐴𝐴𝐴 𝐴 𝐴𝐴 are replaced with arbitrary fitting parameters v ψ and D ψ that do not generally have any specific relation to groundwater velocity, (b) the definition of M typically contains an arbitrary "time constant" fitting parameter with no specific interpretation, τ [T], in its numerator, and (c) the transition time distribution, ψ(t) has no particular definition; it is an additional fitting "parameter." For clarity, the standard continuous-time random walk (CTRW) generalized master equation (GME) and transformed memory function corresponding to Equations 1 and 2 are (Berkowitz et al., 2006):

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“…where C is the solute concentration, D is the hydrodynamic dispersion coefficient (cm 2 min −1 ), v is the pore water velocity (cm/min), and x and t are the distance and time, respectively (Shahmohammadi-Kalalagh et al, 2022).…”

Section: Solute Transport Modelingmentioning

confidence: 99%

Preferential flow of phosphorus and nitrogen under steady‐state saturated conditions

Malhotra,

Lamba,

Way

et al. 2024

Vadose Zone Journal

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Repeated broiler litter application on agricultural lands can cause nutrient enrichment of subsurface effluent, especially with the existence of preferential flow through soil macropores. Previous studies quantifying soil macropores have not attempted to establish a connection of soil macropore characteristics with the subsurface nutrient (nitrogen [N] and phosphorus [P]) losses, across different topographical locations in the field. This study investigated the effect of broiler litter application and preferential flow on subsurface nutrient transport (N and P) at different topographical positions (upslope, midslope, and downslope) in a no‐till pasture field located in Alabama, USA. Twelve intact soil columns (150 mm id and 500 mm length) were used, and the nutrient leaching measurements from laboratory experiments were linked to soil macropore characteristics quantified using X‐ray computed tomography image analysis and solute transport modeling. Treatments included surface broadcast broiler litter (5 Mg ha−1, on dry basis) and unamended control. Leachates were analyzed for dissolved reactive P (DRP), total P (TP), and nitrate + nitrite‐N (NO3− + NO2−–N). The bromide breakthrough curves provided evidence of preferential flow in all columns. Litter application significantly increased leachate P concentrations, and average TP and DRP concentrations were significantly higher in the leachate from upslope columns compared to those at downslope location. The NO3−–N concentrations in leachate exceeded the US EPA drinking water standard of 10 mg L−1 in all the treatment columns. The highest flow‐weighted mean concentrations of TP and DRP, at 2.7 and 2.5 mg L−1, respectively, were recorded in the upslope columns. Soil physicochemical properties and nutrient leaching losses varied substantially across topographical positions, indicating a need for variable litter application rates to reduce P build‐up and subsequent leaching in vulnerable locations within the field. The relevance of the effect of topographic position on nutrient leaching found in this study should be further tested by investigating a wider range of slopes and soil types in pastures.

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Modeling Bromide Transport in Undisturbed Soil Columns with the Continuous Time Random Walk

Cited by 8 publications

References 41 publications

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Experimental Support for a Simplified Approach to CTRW Transport Models and Exploration of Parameter Interpretation

Preferential flow of phosphorus and nitrogen under steady‐state saturated conditions

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