Upscaling colloid transport and retention under unfavorable conditions: Linking mass transfer to pore and grain topology

Johnson, William P.; Hilpert, Markus

doi:10.1002/wrcr.20433

Cited by 50 publications

(67 citation statements)

References 62 publications

(121 reference statements)

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“…The parameter η describes the efficiency of colloid delivery to the surface (favorable conditions) or the near‐surface fluid domain (unfavorable conditions) at the pore scale. Its implementation into continuum‐scale models (upscaling) is performed under the simple assumption that the control volume considered in the continuum model is represented by a collection of identical pore‐scale collectors comprising the same volume and having the same porosity as the control volume [ Logan et al ., ; Nelson and Ginn , ; Johnson and Hilpert , ]. Under this assumption, the equation expressing

η

as a rate constant ( k ) for the Happel sphere‐in‐cell geometry is

k = - \frac{3 {(1 - θ)}^{1 / 3}}{2 d_{c}} ln (1 - η) v

where d c is the average collector diameter,

v

is velocity, and

θ

is porosity.…”

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

“…Hence, mixing of near‐surface and bulk fluid between subsequent collectors is reasonably inferred. In contrast, absence of mixing between collectors under unfavorable conditions would yield increasing excess of colloids in the near‐surface fluid (via secondary minimum attraction), increasingly so with each subsequent collector, such that k would increase with increased transport distance [ Johnson and Hilpert , ]. Whereas k does vary with transport distance under unfavorable conditions (e.g., hyperexponential and nonmonotonic profiles of retained colloids), it does not strictly increase with transport distance.…”

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

“…Nevertheless, the association of distance‐varying k and extended tailing with unfavorable conditions suggests a relationship with colloid accumulation in the near surface under unfavorable conditions. Johnson and Hilpert [] speculated that incomplete mixing of bulk and near‐surface fluid between subsequent grains may at least partially drive the observed extended tailing (and nonlog linear retained profiles) under unfavorable conditions. This, in addition to the above‐described potential influence of discrete heterogeneity on amplifying heterogeneity among the colloid population, provide potent mechanisms to potentially explain these critical phenomena observed under unfavorable conditions.…”

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

“…Since colloid transfer from the bulk to the near‐surface fluid occurs at forward flow stagnation points, and colloid transfer from the near‐surface to the bulk fluid occurs largely at rear flow stagnation zones (less so for Brownian‐dominated colloids) [ Johnson and Hilpert , ], the degree of mixing between collectors is a topological issue that depends on the alignment of the local flow field with the grain‐to‐grain contacts [ Johnson and Hilpert , ]. Whereas experimental evidence that topology (degree of alignment of flow field and grain‐to‐grain contacts) governs retention at the continuum scale has been provided [ Johnson and Hilpert , ], the opportunity exists for many additional studies to explore experimentally and theoretically the relationship of observed profiles of retained colloids to topology (as governed by packing structure). Such information can guide development of upscaling techniques for nonuniform media.…”

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

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Predicting colloid transport through saturated porous media: A critical review

et al. 2015

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Understanding and predicting colloid transport and retention in water‐saturated porous media is important for the protection of human and ecological health. Early applications of colloid transport research before the 1990s included the removal of pathogens in granular drinking water filters. Since then, interest has expanded significantly to include such areas as source zone protection of drinking water systems and injection of nanometals for contaminated site remediation. This review summarizes predictive tools for colloid transport from the pore to field scales. First, we review experimental breakthrough and retention of colloids under favorable and unfavorable colloid/collector interactions (i.e., no significant and significant colloid‐surface repulsion, respectively). Second, we review the continuum‐scale modeling strategies used to describe observed transport behavior. Third, we review the following two components of colloid filtration theory: (i) mechanistic force/torque balance models of pore‐scale colloid trajectories and (ii) approximating correlation equations used to predict colloid retention. The successes and limitations of these approaches for favorable conditions are summarized, as are recent developments to predict colloid retention under the unfavorable conditions particularly relevant to environmental applications. Fourth, we summarize the influences of physical and chemical heterogeneities on colloid transport and avenues for their prediction. Fifth, we review the upscaling of mechanistic model results to rate constants for use in continuum models of colloid behavior at the column and field scales. Overall, this paper clarifies the foundation for existing knowledge of colloid transport and retention, features recent advances in the field, critically assesses where existing approaches are successful and the limits of their application, and highlights outstanding challenges and future research opportunities. These challenges and opportunities include improving mechanistic descriptions, and subsequent correlation equations, for nanoparticle (i.e., Brownian particle) transport through soil, developing mechanistic descriptions of colloid retention in so‐called “unfavorable” conditions via methods such as the “discrete heterogeneity” approach, and employing imaging techniques such as X‐ray tomography to develop realistic expressions for grain topology and mineral distribution that can aid the development of these mechanistic approaches.

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η

as a rate constant ( k ) for the Happel sphere‐in‐cell geometry is

k = - \frac{3 {(1 - θ)}^{1 / 3}}{2 d_{c}} ln (1 - η) v

where d c is the average collector diameter,

v

is velocity, and

θ

is porosity.…”

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

Section: Upscaling From Pore To Continuum Scalementioning

confidence: 99%

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Predicting colloid transport through saturated porous media: A critical review

et al. 2015

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“…These two states are sufficient to track mobile colloids as they move through the dual networks of pores and grains. However, a colloid can also be immobilized onto a grain via primary energy minimum interactions, when it reaches State a in which it attaches to a grain surface [ Johnson and Hilpert , ]. …”

Section: The Modelmentioning

confidence: 99%

A binomial modeling approach for upscaling colloid transport under unfavorable conditions: Emergent prediction of extended tailing

Hilpert

Rasmuson

2017

Water Resources Research

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Colloid transport in saturated porous media is significantly influenced by colloidal interactions with grain surfaces. Near‐surface fluid domain colloids experience relatively low fluid drag and relatively strong colloidal forces that slow their downgradient translation relative to colloids in bulk fluid. Near‐surface fluid domain colloids may reenter into the bulk fluid via diffusion (nanoparticles) or expulsion at rear flow stagnation zones, they may immobilize (attach) via primary minimum interactions, or they may move along a grain‐to‐grain contact to the near‐surface fluid domain of an adjacent grain. We introduce a simple model that accounts for all possible permutations of mass transfer within a dual pore and grain network. The primary phenomena thereby represented in the model are mass transfer of colloids between the bulk and near‐surface fluid domains and immobilization. Colloid movement is described by a Markov chain, i.e., a sequence of trials in a 1‐D network of unit cells, which contain a pore and a grain. Using combinatorial analysis, which utilizes the binomial coefficient, we derive the residence time distribution, i.e., an inventory of the discrete colloid travel times through the network and of their probabilities to occur. To parameterize the network model, we performed mechanistic pore‐scale simulations in a single unit cell that determined the likelihoods and timescales associated with the above colloid mass transfer processes. We found that intergrain transport of colloids in the near‐surface fluid domain can cause extended tailing, which has traditionally been attributed to hydrodynamic dispersion emanating from flow tortuosity of solute trajectories.

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The impact of immobile zones on the transport and retention of nanoparticles in porous media

Molnar

Gerhard

Willson

et al. 2015

Water Resources Research

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Nanoparticle transport and retention within porous media is treated by conceptualizing the porous media as a series of independent collectors (e.g., Colloid Filtration Theory). This conceptualization assumes that flow phenomena near grain-grain contacts, such as immobile zones (areas of low flow), exert a negligible influence on nanoparticle transport and assumes that retention and release of particles depends only on surface chemistry. This study investigated the impact of immobile zones on nanoparticle transport and retention by employing synchrotron X-ray computed microtomography (SXCMT) to examine pore-scale silver nanoparticle distributions during transport through three sand columns: uniform iron oxide, uniform quartz, and well-graded quartz. Extended tailing was observed during the elution phase of all experiments suggesting that hydraulic retention in immobile zones, not detachment from grains, was the source of tailing. A numerical simulation of fluid flow through an SXCMT data set predicted the presence of immobile zones near grain-grain contacts. SXCMT-determined silver nanoparticle concentrations observed that significantly lower nanoparticle concentrations existed near grain-grain contacts throughout the duration of all experiments. In addition, the SXCMT-determined pore-scale concentration gradients were found to be independent of surface chemistry and grain size distribution, suggesting that immobile zones limit the diffusive transport of nanoparticles toward the collectors. These results suggest that the well-known overprediction of nanoparticle retention by traditional CFT may be due to ignoring the influences of grain-grain contacts and immobile zones. As such, accurate prediction of nanoparticle transport requires consideration of immobile zones and their influence on both hydraulic and surface retention.

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Upscaling colloid transport and retention under unfavorable conditions: Linking mass transfer to pore and grain topology

Cited by 50 publications

References 62 publications

Predicting colloid transport through saturated porous media: A critical review

Predicting colloid transport through saturated porous media: A critical review

A binomial modeling approach for upscaling colloid transport under unfavorable conditions: Emergent prediction of extended tailing

The impact of immobile zones on the transport and retention of nanoparticles in porous media

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