Time domain random walks for hydrodynamic transport in heterogeneous media

Russian, Anna; Dentz, Marco; Gouze, Philippe

doi:10.1002/2015wr018511

Cited by 39 publications

(63 citation statements)

References 36 publications

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“…This is a reasonable assumption because flow and particle velocities are only weakly correlated between pores (Saffman 1959;Le Borgne et al 2011;Bijeljic et al 2011;De Anna et al 2013;Lester et al 2013;Kang et al 2014;Holzner et al 2015). Equation (4.1) describes a time-domain random walk (TDRW) (Cvetkovic et al 1991;Delay et al 2005;Painter & Cvetkovic 2005;Russian et al 2016;Noetinger et al 2016), or equivalently a continuous time random walk (CTRW) (Montroll & Weiss 1965;Scher & Lax 1973;Berkowitz et al 2006). It is characterised by the joint PDF of transition length ξ and time τ denoted by ψ(x, t), which encodes the pore-scale transport mechanisms.…”

Section: Pore-scale Transport Mechanisms and Upscalingmentioning

confidence: 99%

Mechanisms of dispersion in a porous medium

2018

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This paper studies the mechanisms of dispersion in the laminar flow through the pore space of a 3-dimensional porous medium. We focus on pre-asymptotic transport prior to the asymptotic hydrodynamic dispersion regime, in which solute motion may be described by the average flow velocity and a hydrodynamic dispersion coefficient. High performance numerical flow and transport simulations of solute breakthrough at the outlet of a sand-like porous medium evidence marked deviations from the hydrodynamic dispersion paradigm and identify two distinct regimes. The first regime is characterized by a broad distribution of advective residence times in single pores. The second regime is characterized by diffusive mass transfer into low-velocity regions in the wake of solid grains. These mechanisms are quantified systematically in the framework of a time-domain random walk for the motion of marked elements (particles) of the transported material quantity. Particle transitions occur over the length scale imprinted in the pore structure at random times given by heterogeneous advection and diffusion. Under globally advection-dominated conditions, this means Péclet numbers larger than 1, particles sample the intrapore velocities by diffusion, and the interpore velocities through advection. Thus, for a single transition, particle velocities are approximated by the mean pore velocity. In order to quantify this advection mechanism, we develop a model for the statistics of the Eulerian velocity magnitude based on Poiseuille's law for flow through a single pore, and for the distribution of mean pore velocities, both of which are linked to the distribution of pore diameters. Diffusion across streamlines through immobile zones in the wake of solid grains gives rise to exponentially distributed residence times that decay on the diffusion time over the pore length. The trapping rate is determined by the inverse diffusion time. This trapping mechanism is represented by a compound Poisson process conditioned on the advective residence time in the proposed time-domain random walk approach. The model is parameterized with the characteristics of the porous medium under consideration and captures both pre-asymptotic regimes. Macroscale transport is described by an integro-differential equation for solute concentration, whose memory kernels are given in terms of the distribution of mean pore velocities and trapping times. This approach quantifies the physical non-equilibrium caused by a broad distribution of mass transfer time scales, both advective and diffusive, on the representative elementary volume (REV). Thus, while the REV indicates the scale at which medium properties like porosity can be uniquely defined, this does not imply that transport can be characterized by hydrodynamic dispersion.

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Section: Pore-scale Transport Mechanisms and Upscalingmentioning

confidence: 99%

Mechanisms of dispersion in a porous medium

2018

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“…where Δs is a constant spatial increment. The process (A1) is a TDRW (Noetinger et al, 2016;Russian et al, 2016). Compared to classical random walk particle tracking, this process guarantees faster computations for our scenarios, since the number of steps does not depend on the local velocity.…”

Section: A2 Particle Trackingmentioning

confidence: 99%

Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

Comolli

Hakoun

Dentz

2019

Water Resources Research

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We study the upscaling and prediction of large‐scale solute dispersion in heterogeneous porous media with focus on preasymptotic or anomalous features such as tailing in breakthrough curves and spatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modeling approach. Direct numerical Monte Carlo simulations of flow and advective particle motion combined with a Markov model for streamwise particle velocities give insight in the mechanisms of preasymptotic and asymptotic solute transport in terms of the statistical signatures of the medium and flow heterogeneity. Based on the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaled continuous time random walk approach that can be conditioned on the flow velocities and thus hydraulic conductivity in the injection region. In this modeling framework, we identify the Eulerian velocity distribution, advective tortuosity, and the correlation length of particle velocities as the key quantities for large‐scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, their first and second centered moments, and the breakthrough curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous conductivity fields. The presented approach allows to relate the medium and flow properties to large‐scale preasymptotic and asymptotic solute dispersion.

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“…We also simulate transport of a passive chemical through an advective particle tracking approach (Russian et al, 2016) following injection of N P = 10 4 particles uniformly distributed at the block inlet in each Eulerian steady-state flow field. We measure the average solute spreading in terms of centered mean squared displacement (MSD) along the main flow direction,…”

Section: Channeling Effects On Flow and Transportmentioning

confidence: 99%

Identification of Channeling in Pore‐Scale Flows

Siena

Iliev

Prill

et al. 2019

Geophysical Research Letters

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We quantify flow channeling at the microscale in three‐dimensional porous media. The study is motivated by the recognition that heterogeneity and connectivity of porous media are key drivers of channeling. While efforts in the characterization of this phenomenon mostly address processes at the continuum scale, it is recognized that pore‐scale preferential flow may affect the behavior at larger scales. We consider synthetically generated pore structures and rely on geometrical/topological features of subregions of the pore space where clusters of velocity outliers are found. We relate quantitatively the size of such fast channels, formed by pore bodies and pore throats, to key indicators of preferential flow and anomalous transport. Pore‐space spatial correlation provides information beyond just pore size distribution and drives the occurrence of these velocity structures. The latter occupy a larger fraction of the pore‐space volume in pore throats than in pore bodies and shrink with increasing flow Reynolds number.

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Time domain random walks for hydrodynamic transport in heterogeneous media

Cited by 39 publications

References 36 publications

Mechanisms of dispersion in a porous medium

Mechanisms of dispersion in a porous medium

Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

Identification of Channeling in Pore‐Scale Flows

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