Non-Fickian Transport Under Heterogeneous Advection and Mobile-Immobile Mass Transfer

Comolli, Alessandro; Hidalgo, Juan J.; Moussey, Charlie; Dentz, Marco

doi:10.1007/s11242-016-0727-6

Cited by 26 publications

(36 citation statements)

References 58 publications

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“…Since the TDRW defined by Eq. (5) is Markovian in the transition n (no memory of previous transitions) and only allows transitions to adjacent nodes, this fully characterizes the system. In order to find the first arrival time PDFs, we solve a Green function problem, for Eq.…”

Section: First Arrival Times In the Unit Cellmentioning

confidence: 99%

“…Physical and chemical heterogeneity, which often spans multiple scales, has important consequences for solute transport in natural and engineered media. It is well known that heterogeneity may lead to anomalous (non-Fickian) characteristics, even if the transport mechanism is advective or diffusive at smaller scales [1,2,3,4,5]. Upscaling transport dynamics is essential for understanding, and providing efficient methods for predicting, large-scale solute transport.…”

Section: Introductionmentioning

confidence: 99%

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A coupled time domain random walk approach for transport in media characterized by broadly-distributed heterogeneity length scales

Aquino

Dentz

2018

Advances in Water Resources

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Section: First Arrival Times In the Unit Cellmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A coupled time domain random walk approach for transport in media characterized by broadly-distributed heterogeneity length scales

Aquino

Dentz

2018

Advances in Water Resources

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“…In order to examine different degradation rates in the mobile and immobile zones, we separate the total transition time for a solute particle into the time the particle is mobile and the time it is immobile, and model the sum of immobile times as a compound Poisson process (Margolin et al 2003;Benson and Meerschaert 2009;Dentz et al 2015;Comolli et al 2016). The total concentration, C, is defined as:…”

Section: Appendixmentioning

confidence: 99%

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Burnell¹,

Hansen

et al. 2018

Groundwater

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Many studies indicate that small-scale heterogeneity and/or mobile-immobile mass exchange produce transient non-Fickian plume behavior that is not well captured by the use of the standard, deterministic advection-dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non-Fickian transport coupled with simultaneous sequential first-order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed-form, steady-state, multi-species analytical solutions are also derived for non-Fickian transport in highly heterogeneous aquifers with linear sorption-desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi-species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over-estimate cleanup rates and under-predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.

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“…It manifests itself in heavy tails in solute arrival time distributions, or breakthrough and the non-linear evolution of the second centered moments of solute distributions. Anomalous dispersion can be caused by different physical processes, chemical heterogeneity [6,7], the interplay of physical heterogeneity and diffusion [8,9], and physical heterogeneity alone. Here, we concentrate on the impact of physical heterogeneity in the distribution of hydraulic conductivity [4,5,10,11].…”

Section: Introductionmentioning

confidence: 99%

“…Berkowitz and Scher [2,21], have realized that the CTRW provides the dynamics needed to characterize non-Fickian hydrodynamic transport in heterogeneous porous and fractured media. The CTRW describes particle movements as a random walk in space and time as [9,22] x n+1 = x n + n , t n+1 = t n + n v n , (1) * marco.dentz@csic.es with n the transition length and v n the particle velocity. The spatial jumps and waiting times may be independent or correlated random variables [23].…”

Section: Introductionmentioning

confidence: 99%

Mechanisms of anomalous dispersion in flow through heterogeneous porous media

et al. 2016

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We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large scale transport.

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Non-Fickian Transport Under Heterogeneous Advection and Mobile-Immobile Mass Transfer

Cited by 26 publications

References 58 publications

A coupled time domain random walk approach for transport in media characterized by broadly-distributed heterogeneity length scales

A coupled time domain random walk approach for transport in media characterized by broadly-distributed heterogeneity length scales

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Mechanisms of anomalous dispersion in flow through heterogeneous porous media

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