Upscaling transport of a sorbing solute in disordered non periodic porous domains

Sherman, Thomas; Janetti, Emanuela Bianchi; Guédon, Gaël Raymond; Porta, Giovanni; Bolster, Diogo

doi:10.1016/j.advwatres.2020.103574

Cited by 7 publications

(16 citation statements)

References 51 publications

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“…Our model is able to predict different transport dynamics, particularly regarding the influence of Pe on transverse plume spreading. Our results are in line with previous laboratory and numerical studies (Chiogna et al, 2010;Rolle et al, 2012). In particular, the change in Pe, due to a change in the diffusion coefficient of the compound, had marked effects on transverse spreading of the solute and this is well captured by our upscaling approach.…”

Section: Discussionsupporting

confidence: 91%

“…Results obtained through the tSMM are in close agreement with those yielded by the DNS. We observe that the change in Pe has marked effects on transverse spreading of the solute, as has been previously observed in laboratory and numerical studies (Chiogna et al, 2010;Rolle et al, 2012). In particular, the standard deviation y continuously increases as a function of the longitudinal distance traveled for Pe = 100.…”

Section: Water Resources Researchsupporting

confidence: 82%

“…The information collected in the parameterization step is then used to build the following tSMM:

\begin{matrix} aligned \\ left x_{i}^{k + 1} & right = (k + 1) L_{x} \\ left y_{i}^{k + 1} & right = y_{i}^{k} + Δ y [s_{i}^{k} | {\hat{y}}_{o u t} (s_{i}^{k - 1})] \\ left t_{i}^{k + 1} & right = t_{i}^{k} + τ [s_{i}^{k} | {\hat{y}}_{o u t} (s_{i}^{k - 1})] \end{matrix}

where both

y_{i}^{k + 1}

and

t_{i}^{k + 1}

are determined through a Markov chain, which is related to the transverse location assigned to the particle in the periodic cell during successive steps k , leveraging the information given by the trajectories in s i . The innovative feature of the model in Equation with respect to previous implementations (Sherman, Bianchi Janetti, et al, 2020; Sund et al, 2017) is that it allows for predictions of transverse spreading over successive Markov steps. This is achieved by considering y as a continuous variable; that is, the Markov chain has a longitudinal fixed spatial step L x , while transport along y is considered through the Δ y ( s i ) obtained from the trajectories s i recorded during the parameterization stage.…”

Section: Methodsmentioning

confidence: 99%

“…This formulation was successfully employed, for example, to interpret transport and mixing in microfluidic systems characterized by relatively simple geometries (Willingham et al, 2008). However, studies performed in the last decade have demonstrated the impact of molecular diffusion on transverse dispersion through experiments and numerical simulations (Chiogna et al, 2010;Muniruzzaman & Rolle, 2015;Rolle et al, 2012;Ye et al, 2016). Such results can be qualitatively linked with analytical and numerical studies showing that the dispersion tensor becomes asymmetric in advection-dominated scenarios (Auriault et al, 2010;Pride et al, 2017).…”

Section: 1029/2020wr028408mentioning

confidence: 99%

“…Notably, such an approach is effective in the presence of advection‐dominated scenarios that become challenging to upscale with classical Eulerian approaches. The advantages of employing a spatial Markov approach to obtain the solute breakthrough curve (or first passage time) at a given longitudinal distance has been demonstrated in a number of previous works, relying on both numerical and laboratory‐scale experimental data sets (e.g., Bolster et al, 2014; Le Borgne et al, 2011; Sherman, Bianchi Janetti, et al, 2020; Sherman et al, 2018). Several recent works have discussed methodologies that employ Lagrangian SMM‐like approaches to predict solute particles' space‐time locations at various scales of observations (Russian et al, 2016; Wright et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

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Upscaling of Solute Plumes in Periodic Porous Media Through a Trajectory‐Based Spatial Markov Model

Janetti

Sherman

Guédon

et al. 2020

Water Resources Research

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We propose an approach to upscale solute transport in spatially periodic porous media. Our methodology relies on pore-scale information to predict large-scale transport features, including explicit reconstruction of the solute plume, breakthrough curves at fixed distances, and spatial spreading transverse to the main flow direction. The proposed approach is grounded on the recently proposed trajectory-based spatial Markov model (tSMM), which upscales transport based on information collected from advective-diffusive particle trajectories across one periodic element. In previous works, this model has been applied solely to one-dimensional transport in a single periodic pore geometry. In this work we extend the tSMM to the prediction of multidimensional solute plumes. This is obtained by analyzing the joint space-time probability distribution associated with discrete particles, as yielded by the tSMM. By comparing numerical results from fully resolved simulations and predictions obtained with the tSMM over a wide range of Péclet numbers, we demonstrate that the proposed approach is suitable for modeling transport of conservative and linearly decaying solute species in a realistic pore space and showcase the applicability of the model to predict steady-state solute plumes. Additionally, we evaluate the model performance as a function of numerical parameters employed in the tSMM parameterization.

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Section: Discussionsupporting

confidence: 91%

Section: Water Resources Researchsupporting

confidence: 82%

“…The information collected in the parameterization step is then used to build the following tSMM: