A mobile-mobile transport model for simulating reactive transport in connected heterogeneous fields

Lu, Chunhui; Wang, Zhiyuan; Zhao, Yue; Rathore, Saubhagya Singh; Huo, Jinge; Tang, Yuening; Liu, Ming; Gong, Ruoting; Cirpka, Olaf A.; Luo, Jian

doi:10.1016/j.jhydrol.2018.02.073

Cited by 16 publications

(15 citation statements)

References 49 publications

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“…This is because, as discussed in sections S1 and S3, solute transport is dominated by advection in the Monte Carlo models built in this study. It is also noteworthy that the concept of "multiple mobile zones" in model ( 7) is consistent with that in the mobile-mobile mass exchange model proposed firstly by Ginn (2018) and Lu et al (2018).…”

Section: Quantify Bimodal Super-diffusion Using a Distributed-order Fractional-derivative Modelsupporting

confidence: 81%

Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings

Yin

Zhang

et al. 2020

Journal of Hydrology

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Dissolved-phase contaminants experiencing enhanced diffusion (i.e., "super-diffusion") with a pronounced leading plume edge can pose risk for groundwater quality. The drivers for complex super-diffusion in geological media, however, are not fully understood. This study investigates the impacts of hydrofacies' mean lengths and the initial source geometry, motivated by a hydrofacies model built recently for the well-known MADE aquifer, on the spatial pattern of super-diffusion for two-dimensional alluvial aquifer systems. Monte Carlo simulations show that the bimodal velocity distribution, whose pattern is affected by the hydrofacies' mean lengths, leads to super-diffusion of solutes with a bi-peak plume snapshot in alluvial settings where advection dominates transport. A larger longitudinal mean length (i.e., width) for hydrofacies with high hydraulic conductivity (K) enhances the connectivity of preferential pathways, resulting in higher values in the bimodal velocity distribution and an enhanced leading front for the bi-peak plume snapshot, while the opposite impact is identified for the hydrofacies' vertical mean length (i.e., thickness) on the bi-peak super-diffusion. A multi-domain non-local transport model is then proposed, extending upon the concept of the distributed-order fractional derivative, to quantify the evolution of bi-peak super-diffusion due to differential advection and mobile-mobile mass exchange for solute particles moving in hydrofacies with distinct K. Results show that the bipeak super-diffusion identified for the MADE site and perhaps the other similar aquifers, which is affected by the initial source geometry at an early stage and the thickness and width of high-K hydrofacies during all stages, can be quantified by the mobile-mobile fractional-derivative model. Scale dependency, porous medium dimensionality, and stochastic model comparison are also discussed to further explore the nature of bi-peak super-diffusion in alluvial systems.

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Section: Quantify Bimodal Super-diffusion Using a Distributed-order Fractional-derivative Modelsupporting

confidence: 81%

Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings

Yin

Zhang

et al. 2020

Journal of Hydrology

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“…Fifth, one can adopt the mobile-mobile mass exchange idea proposed by Ginn (2018), Lu, Wang, et al (2018) and Yin et al (2020) to model scale-dependent and non-Fickian dispersion. The column can be conceptualized as a mixture of multiple mobile zones, where solutes can exchange mass locally, causing scale-dependency for transport.…”

Section: Modelling Scale-dependent and Non-fickian Transportmentioning

confidence: 99%

“…Hydrogeological interpretation is needed for the models before quantifying the observed transport process introduced in Section 2.1. A detailed theoretical distinction between these models can be found in our recent work (Lu, Zhang, et al, 2018). For description simplicity, only one‐dimensional models are shown below.…”

Section: Nonlocal Models In Simulating Complex Transport In Water: Review and Applicationmentioning

confidence: 99%

“…Pollutant transport in heterogeneous porous media exhibits complex dynamics, and various transport models have been developed and applied for decades; see the recent debate by Cirpka and Valocchi (2016), Fogg and Zhang (2016), Fiori et al (2016) and Sanchez and Fernandez (2016) for the theory and practice for stochastic subsurface hydrology. Boano et al (2014) reviewed various mathematical (transport) models of hyporheic exchange, and Lu, Zhang, et al (2018) applied various transport models to capture non‐Fickian transport. To the best of our knowledge, no studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these competing transport models in characterizing real‐world transport.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Zhang

Zhou

Yin

et al. 2020

Hydrological Processes

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Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scaledependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.

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“…Although the physical and chemical non-equilibrium models are based on different concepts, they can be described by the same mathematical equation in dimensionless form, see Pang and Close (1999), Toride, Leij and Van Genuchten (1995) for instance. A MIM solute transport undergoing linear sorption without degradations and source/sink reactions in the studied region is given as follows (Benson and Meerschaert (2009), Li, Wen, Zhu and Jakada (2020), Lu, Wang, Zhao and Rathore et al (2018), Schumer and Benson (2003), Van Genuchten and Wagenet (1989)):…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation for a Fractal MIM Model for Solute Transport in Porous Media

Liu¹,

Li²,

Jia³

2021

JMR

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A fractal mobile-immobile (MIM in short) model for solute transport in heterogeneous porous media is investigated from numerics. An implicit finite difference scheme is set forth for solving the coupled system, and stability and convergence of the scheme are proved based on the estimate of the spectral radius of the coefficient matrix. Numerical simulations with different parameters are presented to reveal the solute transport behaviors in the fractal case.

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A mobile-mobile transport model for simulating reactive transport in connected heterogeneous fields

Cited by 16 publications

References 49 publications

Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings

Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Numerical Simulation for a Fractal MIM Model for Solute Transport in Porous Media

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