A Primer on the Dynamical Systems Approach to Transport in Porous Media

Metcalfe, Guy; Lester, Daniel; Trefry, M. G.

doi:10.1007/s11242-022-01811-6

Cited by 7 publications

(3 citation statements)

References 97 publications

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“…They are associated with the occurrence of contracting and stretching surfaces, 12 whose transverse intersection is a condition for the generation of chaotic advection. 51 Our results also showed no variation in l/l 0 upon variation in q for any given S w . This is explained by the large Pe, thus confirming that the computed isosurface deformation was not affected by diffusive effects, preserving the stretching and folding events of the plume occurring in the pore space.…”

Section: Solute Plume Deformation As a Function Of The Saturationsupporting

confidence: 53%

“…The latter is essential for quantifying the effects of the connected pore branches and mergers, i.e., locations of fluid separation and fluid convergence, respectively, around solid grains and air clusters, and of their transverse orientation to each other on the stretching history of material lines. They are associated with the occurrence of contracting and stretching surfaces, whose transverse intersection is a condition for the generation of chaotic advection . Our results also showed no variation in l / l 0 upon variation in q for any given S w .…”

Section: Results and Discussionmentioning

confidence: 99%

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Chaotic Transport of Solutes in Unsaturated Porous Media

Velásquez-Parra,

Marone,

Griffa

et al. 2024

Environ. Sci. Technol.

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Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

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Section: Solute Plume Deformation As a Function Of The Saturationsupporting

confidence: 53%

Section: Results and Discussionmentioning

confidence: 99%

Chaotic Transport of Solutes in Unsaturated Porous Media

Velásquez-Parra,

Marone,

Griffa

et al. 2024

Environ. Sci. Technol.

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“…Their ability to capture the observed behavior varies depending on the flow regime (Icardi et al., 2014), and it has been shown that their robustness is highest for low Péclet numbers in heterogeneous porous media (Sadeghi et al., 2020). Inverse modeling studies have also been performed to estimate the value of macro‐dispersion coefficients from pore‐scale data in porous media subject to steady‐state single‐ and two‐phase flow in the Darcy regime (Aziz et al., 2018; Metcalfe et al., 2022 and references therein). Otherwise, analyses considering nonlinear flow regimes are still scarce.…”

Section: Introductionmentioning

confidence: 99%

Multi‐Scale Analysis of Dispersive Scalar Transport Across Porous Media Under Globally Nonlinear Flow Conditions

Moghimi,

Mousavi Nezhad,

Guadagnini

2023

Water Resources Research

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We focus on nonlinear flow regime scenarios observed at the global scale of a porous medium and explore the impact of such nonlinearities on key features of dispersive scalar transport observed across three‐dimensional porous systems characterized by various degrees of pore space complexity. Flow and transport processes are analyzed at pore‐scale and larger scales in well‐documented digital Beadpack and Bentheimer sandstone samples. Our simulations comprise linear (Darcy) and nonlinear (Forchheimer) flow regimes and consider a broad interval of values of Péclet number (ranging from 1×10‐2 to 5×104). Sample probability density functions of pore‐scale velocities and concentrations of the migrating scalar are analyzed and related to flow conditions and degree of complexity of the pore space. Estimated values of dispersion associated with section‐averaged breakthrough curves display a power‐law scaling on the Péclet number. The scaling exponent depends on the relative importance of pore‐scale diffusion and advection. We find that the Forchheimer flow regime is characterized by enhanced mixing of the scalar field. This leads to enhanced dispersion as compared against a Darcy regime.This article is protected by copyright. All rights reserved.

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