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Colloid particle size-dependent dispersivity
Water Resources Research
Abstract
Laboratory and field studies have demonstrated that dispersion coefficients evaluated by fitting advection-dispersion transport models to nonreactive tracer breakthrough curves do not adequately describe colloid transport under the same flow field conditions. Here an extensive laboratory study was undertaken to assess whether the dispersivity, which traditionally has been considered to be a property of the porous medium, is dependent on colloid particle size and interstitial velocity. A total of 48 colloid transport experiments were performed in columns packed with glass beads under chemically unfavorable colloid attachment conditions. Nine different colloid diameters and various flow velocities were examined. The breakthrough curves were successfully simulated with a mathematical model describing colloid transport in homogeneous, water-saturated porous media. The experimental data set collected in this study demonstrated that the dispersivity is positively correlated with colloid particle size, and increases with increasing velocity. The dispersivity values determined in this laboratory study were compared with 380 dispersivity values from earlier laboratory and field-scale solute, colloid and biocolloid transport studies published in the literature.
Supplementary resource (1)
... This approach implied that the model treated the attachment and retention as a lump in katt, and detachment and reentrainment as kdet. Attachment refers to immobilization of colloids onto the surface of the collector through primary energy minimum, whereas retention refers to the temporary retention of colloids [73]. ...
... As mentioned above, we assigned to DNAcol particles the same dispersivity value as obtained for NaCl tracer in order to prevent over-parameterization of the Hydrus model during the inverse J o u r n a l P r e -p r o o f modelling of DNAcol transport results. However, this approach could lead to the underestimation of particle dispersivity [73], since the value also depends on particle size [73]. Additionally, prior research showed that the rate of colloidal deposition can be greater when the flow direction is upward compared to downward [74]. ...
... As mentioned above, we assigned to DNAcol particles the same dispersivity value as obtained for NaCl tracer in order to prevent over-parameterization of the Hydrus model during the inverse J o u r n a l P r e -p r o o f modelling of DNAcol transport results. However, this approach could lead to the underestimation of particle dispersivity [73], since the value also depends on particle size [73]. Additionally, prior research showed that the rate of colloidal deposition can be greater when the flow direction is upward compared to downward [74]. ...
... At first, a linear relationship or a power-law exponent of 1 was proposed (Lallemand- Barres & Peaudecerf, 1978). Later, due to concerns about the reliability of dispersivity data and acknowledging that dispersivity cannot increase indefinitely (Gelhar et al., 1992), many researchers have since proposed various nonlinear scaling relationships with power-law exponents in the range between 0.83 and 2.94 (Arya, 1986;Chrysikopoulos & Katzourakis, 2015;Hunt et al., 2011;Neuman, 1990;Xu & Eckstein, 1995). These scaling relations are based on the premise that as hydraulic heterogeneity increases with length or distance in sedimentary formations, dispersivity increases concomitantly. ...
... But does dispersivity decrease when length becomes smaller at the pore scale? Recent studies using microfluidic experiments show that dispersivity is indeed small, that is, on the order of 10 −4 m at the millimeter scale (Baumann et al., 2010;Chrysikopoulos & Katzourakis, 2015;Hunt et al., 2011), which previous scaling relationships cannot accurately predict. Thus, a knowledge gap exists about how pore structure influences dispersivity, which further controls scaling behavior with length scale. ...
... Later studies based on numerical and statistical methods, for example, using the least squares method (Xu & Eckstein, 1995) and conventional statistical techniques (Arya, 1986;Chrysikopoulos & Katzourakis, 2015;Hunt et al., 2011;Neuman, 1990) suggested that the relationship is not 1:1 but exponent, r ranges between 0.83 and 2.94. Neuman (1990) updated this best fit by disregarding the low-reliability data and incorporated a slope reduction for larger-scale data, that is, for scales ≥100 m. ...
Hydraulic heterogeneity leads to non‐Fickian transport characteristics, which cannot be entirely accounted for by the continuum‐scale advection‐dispersion equation. In this pore‐scale computational study, we investigate the combined effects of flow rate (i.e., Peclet number, Pe) and first‐order hydraulic heterogeneity, that is, resulting from intrapore geometry exclusively, on the transition from non‐Fickian to Fickian dispersion. A set of intrapore geometries is designed and quantified by a dimensionless pore geometry factor (β), which accounts for a broad range of pore shapes likely found in nature. Navier‐Stokes and Advection‐Diffusion equations are solved numerically to study the transport phenomenon using velocity variance, residence time distribution, and coefficients of hydrodynamic dispersion and dispersivity. We determine the length scale (i.e., the linear distance in flow direction) for each pore shape and Pe when non‐Fickian features transition to the Fickian transport regime by incrementally extending the length, that is, the linear array of pores. We show how velocity distribution and variance (σ²) depend on β, and directly control the transition to Fickian dispersion. Pores with a larger β, that is, complex pore shapes with constricted pore‐body or with “slit‐type” attributes, result in a substantial non‐Fickian characteristics. The magnitude of non‐Fickian characteristics gets amplified with an increase in Pe requiring a significantly longer length scale, that is, up to 1 m or a linear array of 500 pores to transition to the Fickian transport regime. We find the hydrodynamic dispersion coefficient (Dh) exponentially depends on the pore shape factor β, with its exponent dependent on flow rate or Pe. We determine constitutive relations to quantify how σ², β, and Pe, contribute to the degree of non‐Fickian characteristics, the length scale needed for the transition to Fickian transport regime, asymptotic Dh, and the length‐scale dependence of longitudinal dispersivity.
... The current literature provides contrasting evidence on the migration of MPs towards deeper soil horizons, with some studies emphasizing limited downward transport due to the combined effect of sorption and blocking processes in the unsaturated zone (Fei et al., 2023;Rong et al., 2023), and others reporting detectable MPs concentrations in deep soils (Hu et al., 2021;Weber and Opp, 2020). Simultaneously, multiple studies focusing on column experiments have examined the factors influencing the MPs' mobility in porous media, specifically, plastic size (Bradford et al., 2002;Chrysikopoulos and Katzourakis, 2015;Han et al., 2022;Leij and Bradford, 2013;Li et al., 2024), shape (Ma et al., 2011;Salerno et al., 2006;Waldschläger and Schüttrumpf, 2020), polymer type (Fei et al., 2022;Ren et al., 2021), solution chemistry (Bennacer et al., 2017;Zhao et al., 2022aZhao et al., , 2022b, input concentration Zhang et al., 2023), and grain size (Bradford et al., 2005;Li et al., 2024). However, the impact of plastic density on MP mobility remains largely unexplored. ...
... As suggested by earlier findings (Bradford et al., 2002;Keller et al., 2004), the tracer and colloids might follow different flow paths. Therefore, we followed the recommendations by Chrysikopoulos and Katzourakis (2015) and fitted MP-specific dispersity. Indeed, the resulting dispersivity is different for MPs (0.06-0.20 cm) and tracer (0.45 cm) in the gravel sediment. ...
... Through the filed investigation, Brunke, (1999) found that the content of fines colloidal particles tended to increase with depth, and get higher accumulations at intermediate depths in sediments, and interstitial detrital particles > 90 μm showed vertical distribution patterns opposing those of total particles. Chrysikopoulos and Katzourakis (2015) found that there are different dispersivities for different sized colloid particles when they transport in porous media. Results from flume experiments show that the rate of particle deposition increases with increasing particle size (Ren and Packman 2007). ...
... And thus, in the simulation, the aggregation of colloids is also ignored. (2) Dispersion: The colloids with different particle size are varying in dispersivities (Chrysikopoulos and Katzourakis 2015). To study the effects of dispersion, this paper did extra simulations in supplementary. ...
Colloid particle size plays an important role in contaminant adsorption and clogging in the hyporheic zone, but it remains unclear how the particle size changes during the transport of colloids. This study investigated the variation of the particle size of colloids in the overlying water and the effects of settlement and hyporheic exchange via laboratory experiments and numerical simulations with two main factors settlement and hyporheic exchange being considered. The results show that the particle size distribution varies when colloids transport in hyporheic zone, and both settlement and hyporheic exchange are involved in the exchange of colloids between stream and streambed. Large-sized particles are mainly controlled by settlement and advection and thus their concentration in the overlying water decreases more quickly; but small-sized particles are mainly controlled by hyporheic exchange and thus their concentration decreases more slowly, and some particles can be resuspended. The increase of retention coefficient and settling velocity will accelerate the transfer of colloids into the streambed. This study may provide important insights into the variation of the particle size of colloids in the overlying water and the effects of settlement and hyporheic exchange.
... Colloids were assumed to have the same dispersivity as that of the tracer. Colloid dispersivity has been found to be size dependent (Chrysikopoulos and Katzourakis, 2015) and can be different from the dispersivity of tracer. Chrysikopoulos and Katzourakis (2015) observed a positive correlation between colloid dispersivity and its size. ...
... Colloid dispersivity has been found to be size dependent (Chrysikopoulos and Katzourakis, 2015) and can be different from the dispersivity of tracer. Chrysikopoulos and Katzourakis (2015) observed a positive correlation between colloid dispersivity and its size. However, for simplicity we have assumed the dispersivity of colloid to be the same as that of the tracer. ...
Temporal variations in the chemistry of infiltrating water into the subsurface are known to cause remobilization of colloids from the grain surfaces, thereby increasing the travel distance of the colloidal contaminants. Hence, it is essential to thoroughly understand the transport, deposition, and release mechanisms of colloids in the subsurface, through laboratory experiments and modeling. There are only a few experiments in which the chemistry of inflow water is changed rapidly during colloid transport. Also, although some models have been presented for simulating the effect of transient chemistry on the fate of colloids, there is no consensus in this regard, as the proposed models suffer from shortcomings. In this study, we systematically investigated the effect of temporal variations in ionic strength on the remobilization of deposited colloids in saturated porous media through laboratory column experiments and numerical modeling. Four sets of column experiments were performed, in which we injected carboxylate-modified latex colloids at a given ionic strength for a specified period. After breakthrough of colloids, the ionic strength of inflowing water was decreased in a stepwise manner to 0 mM (DI water). The initial ionic strength values of the four experiments were 100, 50, 25, and 10 mM. We observed partial release of deposited colloids after several steps of ionic strength decrease with significant release observed only when the ionic strength was reduced to below 10 mM. We also found that the fraction of released colloids decreased with increasing value of initial ionic strength of inflow water. We have developed a mathematical model incorporating a novel formulation for ionic strength-dependent deposition and release. The model is found to capture the colloid breakthrough curves reasonably well for all experiments with the same set of parameter values, except the one at the initial ionic strength of 25 mM.
... Several studies [49,50,55,56] were carried out investigating plume behavior and trying to elaborate a methodology for the correct definition of a dispersion coefficient to use in the dispersion equation in the case of solutes. Several theories range from the deterministic approach [57,58] to the stochastic one [59], but few of the studies [60] reported situations of flows in which not-dissolved ...
... Several studies [49,50,55,56] were carried out investigating plume behavior and trying to elaborate a methodology for the correct definition of a dispersion coefficient to use in the dispersion equation in the case of solutes. Several theories range from the deterministic approach [57,58] to the stochastic one [59], but few of the studies [60] reported situations of flows in which not-dissolved substances like nZVI were transported and dispersed in a saturated porous medium. The theories for the definition of a value to assign to the dispersion coefficient tensor generally consider the flow velocity and the dispersion coefficient dependent on the tortuosity of the media and on the concentration gradients. ...
Zero-valent iron nanoparticle (nZVI) technology has been found to be promising and effective for the remediation of soils or groundwater. However, while nanoparticles are traveling through porous media, they can rapidly aggregate, causing their settling and deposition. When nZVI are injected in the groundwater flow, the behavior (mobility, dispersion, distribution) is unknown in groundwater, causing the use of enormous quantities of them if used at the field scale. In this paper, a laboratory experiment was carried out with groundwater flow in a two-dimensional, laboratory-scale tank to assess the nanoparticle behavior by means of an image analysis procedure. A solution of zero-valent iron nanoparticles, Nanofer 25S particles, were used and glass beads were utilized as porous medium. The laboratory experiment included the use of a digital camera for the acquisition of the images. The image analysis procedure was used to assess the behavior of nZVI plume. A calibration procedure and a mass balance were applied to validate the proposed image analysis procedure, with the hypothesis that nanoparticles would be uniformly distributed in the third dimension of the tank (thickness). The results show that the nanoparticles presented small dispersive effects and the motion was strongly influenced from the higher weight of them with respect to the water. Therefore, the results indicate that nanoparticles have an own motion not strongly influenced by the fluid flow but more determined from the injection phase and gravity. The statistical elaborations show that the nZVI plume did not respond to the classical mechanisms of the dispersion.
... In this regard, many laboratory experiments have been accomplished to establish models for the deposition and release of suspended matters [34] as well as to establish the governing equations for the cotransport of multiple components [35][36][37]. Chrysikopoulos and Katzourakis [38] demonstrated that the dispersivity of colloids is not only a function of colloid size but also a function of seepage velocity by laboratory and field studies. Bedrikovetsky et al. [39] proposed a model for discussing the pore size distribution of porous media from the longterm injection of mono-sized suspension as well as a theoretical model for predicting the corresponding transport process, taking into account the restraining effect of the pore scale of the porous media on the suspended particles as well as the nonlinear characteristics caused by cumulative deposition. ...
... During the experiment, an SP suspension, a copper ion solution, or a mixture of the two was injected into the experimental sand column at three different seepage velocities. The Reynolds number of the seepage flow was calculated to be Re < 116, which was less than the maximum value of 2300 generally considered for a laminar flow, thereby satisfying the laminar flow condition [28,38]. ...
Sand column tests were conducted to investigate the seepage transport of silicon powders (SPs) with two wide particle size ranges (30-2000 nm and 2-70 μm), including the cotransport of SPs and copper ions. The results show that the graded large-scale SP has an obvious inhibiting influence on the transport of copper ions. In contrast, in the presence of the graded small-scale SP, the concentration of copper ions in the effluent tends to increase; i.e., there appears to be a promoting effect. However, after a long transport distance, the presence of SPs, regardless of particle size, has an overall retarding effect on heavy metal pollutants (e.g., copper ions). The promoting effect of the increase in seepage velocity on the concentration of copper ions in the effluent is greater with the graded large-scale SPs than with the graded small-scale SPs. In terms of the microstructural characteristics by metallographic microscopy, the average particle size of the deposited graded small-scale SPs is almost constant at different transport distances, while that of the deposited graded large-scale SPs tend to decrease significantly with increasing transport distance; i.e., notable bed filtration is exhibited in the latter case. This physical mechanism also determines the sequence and rate of the retarding effect of SPs on heavy metal ions under seepage flow.
... where, c [ML −3 ] is the aqueous phase concentration of nZnO particles, s [MM −1 ] is the mass of nZnO particles retained in porous medium (mass of nanoparticles retained per mass of porous medium), [-] is the porosity of the porous medium, and b [ML −3 ] is the bulk density of the porous medium. It is important to note that nanoparticles tend to aggregate which leads to temporal variations in particle-size distribution (Babakhani, 2019;Bouchard et al., 2012) and dispersion coefficient which is size-dependent (Chrysikopoulos & Katzourakis, 2015;Jia et al., 2023;Katzourakis & Chrysikopoulos, 2021). However, aggregation kinetics was not incorporated in the transport model in this study as aggregation is a reasonably fast process (Raychoudhury et al., 2012), and we assumed nZnO suspension to be stable during the transport Sun et al., 2015). ...
Transport behavior of zinc oxide nanoparticles (nZnO) has been investigated widely; however, not many studies have identified the transport mechanisms through mathematical modeling by simulating both breakthrough curve (BTC) and retention profile (RP) under varying environmental conditions. Thus, this study focuses on investigating the transport behavior of nZnO in the subsurface under a wide range of environmental conditions through mathematical modeling. A mathematical model is developed to simulate nZnO transport in porous media and the values of the associated parameters are estimated by fitting the model to the experimental data under a broad range of physicochemical conditions reported in the literature. The model performance is assessed by evaluating its ability to simulate both the nZnO BTC and RP, and it demonstrates promising performance. It is found that nZnO retention in the soil is mainly governed by reversible deposition on grain surfaces and straining. Moreover, nZnO transport through coarse-grained soil at high velocity and low ionic strength (IS) in the presence of a dissolved form of natural organic matter (NOM) may lead to an increased risk of groundwater contamination. The nZnO transport behavior can be simulated better by incorporating size-dependent dispersivity in the developed model.
... This size exclusion phenomena are primarily the result of the inability of colloids to enter the pores due to their size. Other possible mechanisms include the inaccessibility of a component of the pore and therefore inducing an earlier breakthrough (Chrysikopoulos & Katzourakis, 2015). The existence of an inaccessible pore space in soils to oocysts channels their transport via preferential pathways, resulting in an increase of their initial breakthrough in comparison with a nonreactive tracer. ...
A series of laboratory experiments were conducted to study the fate and transport of Toxoplasma gondii oocysts in soils as a function of soil physicochemical properties and soil water chemistry properties. Soil columns were homogeneously packed with loamy sand soils (Lewiston and Greenson series) and sandy loam soils (Sparta and Gilford series), and subject to hydrologic conditions characterized by the absence and presence of an anionic surfactant—Aerosol 22 in the artificial rainfall. Quantitative polymerase chain reaction (qPCR) was utilized for the detection and enumeration of oocysts in soil leachates to evaluate their breakthrough and in soil matrices to examine their spatial distribution. Differences in the rate and extent of transport of oocysts were observed as a function of physical and chemical parameters tested. The breakthrough of oocysts was observed for all the soils irrespective of the presence of surfactant. However, in the absence of surfactant, the predominant fate of oocysts in soils subject to simulated rainfall was their retention in the soil profile. The presence of surfactant induced a change in the fate of oocysts in these soils exposed to rainfall simulation as the predominant fate of oocysts was found to be in the soil leachates.
... Measured breakthrough curves (BTCs, concentration time series at various distances) are typically used to obtain inverse estimates of transport parameters (e.g., Ratha et al., 2009). Note that the dispersivity of suspended particles like J o u r n a l P r e -p r o o f viruses is a size dependent parameter as exposed by Chrysikopoulos and Katzourakis (2015). In this study, we used BTC to validate the transport model and evaluate the influence of distinct transport parameters and reaction mechanisms (Fig. 2). Figure 2 portrays BTCs associated with various reactive transport models published by Schijven et al. (1999) on the basis of the series of analytical solutions submitted by Toride et al. (1995). ...
The transport of viruses in groundwater is a complex process controlled by both hydrodynamic and reaction parameters. Characterizing the transport of viruses in groundwater is of crucial importance for investigating health risks associated with groundwater consumption from private individual or residential pumping wells. Setback distances between septic systems, which are the source of viruses, and pumping wells must be designed to offer sufficient groundwater travel times to allow the viral load to degrade sufficiently to be acceptable for community health needs. This study consists of developing numerical simulations for the reactive transport of viruses in the subsurface. These simulations are validated using published results of laboratory and field experiments on virus transport in the subsurface and applying previously developed analytical solutions. The numerical model is then exploited to investigate the sensitivity of the fate of viruses in saturated porous media to hydraulic parameters and the coefficients of kinetic reactions. This sensitivity analysis provides valuable insights into the prevailing factors governing health risks caused by contaminated water in private wells in rural residential contexts. The simulations of virus transport are converted into health risk predictions through dose-response relationships. Risk predictions for a wide range of input parameters are compared with the international regulatory health risk target of a maximum of 10-4 infections/person/year and a 30 m setback distance to identify critical subsurface contexts that should be the focus of regulators.
... Moreover, particle size increase may also affect the effective dispersivity of aggregating nanoparticles. Larger particles may exhibit early breakthroughs and increased dispersivity due to possible reduction in effective porosity and exclusion from lower interstitial velocity regions [61]. Finally, due to the sorption of TM onto TiO 2 nanoparticles, all of the above factors, which are expected to enhance nanoparticle transport, are expected to also enhance the TM transport, while the inverse is also true. ...
Human activities in modern life are contributing significantly to global environmental pollution. With the need for clean drinking water ever increasing, so does the need to find new water-cleaning technologies. The ability of nanoparticles (NPs) to remove persistent pollutants from aqueous solutions makes them very important for use in water treatment technology. Titanium dioxide (TiO2) is recognized as an NP with unique optical, thermal, electrical, and magnetic properties and is widely used as an adsorbent material. Due to the extensive use of pesticides, their removal from the aquatic environment has gained widespread attention from the scientific community. In the present work, the transport of pesticide thiophanate methyl (TM), as well as the cotransport of TM and TiO2 nanoparticles, in a water-saturated column packed with quartz sand under various water conditions were investigated. Several ionic strengths (1, 10, 50, and 100 mM) and pH values (3, 5, 7, and 10) were examined. The results from the transport experiments were fitted and analyzed with the use of the ColloidFit software, while the results from the cotransport experiments were fitted with a modified version of a recently developed mathematical cotransport model. The results of this study suggested that the lowest mass recovery rate was for the cotransport experiments with the addition of NaCl. Furthermore, it was shown that TM has a weak affinity for sand but a relatively strong affinity for TiO2 at high ionic strength and acidic pH, probably accounting for the reduced mass recovery of TM in cotransport experiments.
... that of tracer transport (Chrysikopoulos and Katzourakis 2015). As shown in Table 7, we calculated the hydraulic characteristic parameters under different media particle size conditions (Table 5). ...
Physicochemical properties, such as solute concentration, flow acidity and flow rate, regulate flow and reactive transport in porous media. Mineral precipitation – dissolution (PD) dynamically changes the pore structural heterogeneity and affects the physicochemical properties, yet the interplay between the PD process and structural heterogeneity remains unclear. This study took the precipitation of Ca²⁺ and CO3²⁻ (Ca2++CO32−⇌CaCO3) as an example to study the reactive transport behavior under different physicochemical conditions in saturated, heterogeneous-packed porous media. A series of column breakthrough experiments and numerical simulations of the coupled flow and PD processes were conducted. X-ray computed tomography (XCT) and pore morphology analysis were also applied to investigate the effects of calcite precipitation on pore structure. Results demonstrate that solute concentration, flow acidity, and flow rates in homogeneous columns significantly altered the time of the PD process to reach equilibrium, leading to immediate chemical environmental changes, and thus impact reactive transport behavior. Preferential flow paths in heterogeneous-packed columns could lead to early breakthroughs and thereby promoted the transport of calcium carbonate (CaCO3) in saturated porous media. XCT images revealed that surface roughness played an important role in Ca²⁺ precipitation, i.e., CaCO3 clustered more on concave surface than convex surface, reshaping a round coat outside grain particles. The CaCO3 precipitation could also narrow or even block the pore throats, and thus decrease the pore connectivity, which hinders the breakthrough behavior. Our study provided experimental evidence for a predictive understanding of Ca²⁺ reactive transport as well as new insights into the changes in soil structural heterogeneity and transport properties during the PD process.
... The D flux was simulated by adopting the best fit soil hydraulic parameters and using a mutual heavy water diffusion coefficient of D in water from the literature (Dahal and Adhikari, 2012;Meng et al., 2018) (D d =1.33 × 10 − 3 cm 2 /min) and inversely solve the longitudinal and transverse dispersivities. Under variably saturated conditions, the dispersivities depended not only on the dimensions of the lysimeter, the median diameter of the porous media particle, free-water diffusion coefficient of the solute, the pore flow velocity (Carey et al., 2018;Chrysikopoulos and Katzourakis, 2015;Cupola et al., 2015;Mahmoodlu et al., 2020), but also on the water content in the unsaturated soil (Mortensen et al., 2006;Raoof and Hassanizadeh, 2013). The trial-and-error obtained best fit values were λ L = 0.15 cm and λ T = 0.03 cm for the loamy sand and λ L = 0.01 cm and λ T = 0.002 cm for the gravel ( Table 2). ...
Although multiple experimental studies have proven the use of free synthetic DNA as tracers in hydrological systems, their quantitative fate and transport, especially through the vadose zone, is still not well understood. Here we simulate the water flow and breakthrough of deuterium (D) and one free synthetic DNA tracer from a 10-day experiment conducted in a transient variably saturated 1m³ 10-degree sloped lysimeter using the HYDRUS-2D software package. Recovery and breakthrough flux of D (97.78%) and the DNA tracer (1.05%) were captured well with the advection-dispersion equation (R² = 0.949, NSE = 0.937) and the Schijven and Šimůnek two-site kinetic sorption model recommended for virus transport modeling (R² = 0.824, NSE = 0.823), respectively. The degradation of the DNA tracer was very slow (estimated to be 10% in 10 days), because the “loamy sand” porous media in our lysimeter was freshly crushed basaltic tephra (i.e., crushed rocks) and the microbes and DNase that could potentially degrade DNA in regular soils were rare in our “loamy sand”. The timing of the concentration peaks and the HYDRUS-2D simulated temporal and spatial distribution of DNA in the lysimeter both revealed the role of the solid-water-air contact lines in mobilizing and carrying DNA tracer under the experimental variably saturated transient flow condition. The free DNA was nearly non-selectively transported through the porous media, and showed a slightly early breakthrough, possibly due to a slight effect of anion exclusion or size exclusion. Our results indicate that free DNA have the potential to trace vadose zone water flow and solute/contaminant transport, and to serve as surrogates to trace viral pathogen pollution in soil-water systems. To our knowledge, this study is the first to simulate transport mechanisms of free synthetic DNA tracers through real soil textured porous media under variably saturated transient flow condition.
... Studies have reported that the high velocity of pore water decreased the collision time between many particulate pollutants (e.g. engineered nanoparticles , colloids (Chrysikopoulos and Katzourakis, 2015), microbial pathogens (Ren et al., 2020), etc.) and porous media, leading to a lower deposition rate coefficient. Thus, scouring of pollutants by hydrodynamic forces at high flow rate heavily promotes the release and transport depth of pollutants in porous media. ...
The ecological risk of microplastics (MPs) usually depends on their environmental behavior, however, few studies focused on the impact of hydrodynamic perturbations on the fate of MPs in hyporheic zone. This study chose quartz sand (250-425 μm) as simulated porous medium to investigate the transport of 100 nm polystyrene nanoplastics (PSNPs) under hydrodynamic factors, including flow rates (0.5, 1.0, and 2.0 mL/min), flow orientations (up-flow, down-flow, and horizontal-flow), and water saturations (50%, 80%, and 100%), as well as different salinities and temperatures. The breakthrough curves (BTCs) and retained profiles (RPs) of PSNPs were compared and analyzed by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Due to the small size and moderate density of PSNPs, as well as high flow rates, the flow orientation exhibited little effect on the PSNP transport. However, high flow rate, low salinity, high water saturation, and low temperature would facilitate the mobility of PSNPs. The increase in salinity from zero to 35 PSU (practical salinity units) caused the compression of electrical double layer and weakened the electrostatic repulsion between PSNPs and sands, which dramatically decreased the penetration rate from 100% to zero. Especially, the lower energy barrier of PSNPs-PSNPs at 3.5 and 35 PSU (16.45 kBT and zero, respectively) facilitated the adsorption of PSNPs on sand via ripening mechanism. Due to the strong adsorption of PSNPs by sand at high salinity, the effect of flow rate on PSNP transport was more pronounced at low salinity. The mobility of PSNPs at 0.035 PSU was enhanced by 41.4%-75.3% as the flow rate increased from 0.5 to 2.0 mL/min, which was contributed from the reversible deposition in lower secondary energy minimum depth at low salinity and the stronger hydrodynamic drag force generated by the high flow rate. However, the sufficient molecular diffusion at low flow rate promoted the occupation of PSNPs on adsorption sites. In addition, the penetration rate of PSNPs decreased by 25.0% as the water saturation decreased from 100% to 50%, indicating that the film straining at the air-water interface would hinder the transport of PSNPs. Finally, temperature increase impeded the penetration of PSNPs by 6.26%-23.1% via blocking mechanism. Our results suggest that low-salinity, high-flow river systems may be at greater risk of MPs contamination due to enhanced vertical transport capability.
... For example, with increasing d(s)/d(p), the sediment form changes from "random deposition" to "gradient deposition" and eventually to "inlet deposition" (Liu et al., 2016). In addition, the dispersivity of the suspended particles is dependent on the size of the suspended particles and the dispersivity is positively correlated with colloid particle size, and increases with increasing interstitial velocity (Chrysikopoulos et al., 2015). The migration of micron-scale silica powder has a pronounced particle separation property due to its coupling effect on the migration of contaminants such as heavy metal ions (e.g., Pb(2 +)), which is closely related to the concentration of injected Pb(2 +), the particle size and concentration of injected suspended particles, the rate of percolation, and the variation in the absolute zeta potential of the surface charge (Bai et al. 2020a, b;2021). ...
Under the influence of large water conservancy projects and seasonal precipitation, the groundwater levels along rivers and lakes show cyclic patterns of change. Thus, the fluctuation in water level is an important factor affecting the particle migration and deposition characteristics in the sand layers considered in projects such as groundwater recharge projects. Existing theories all treat the recharge aquifer as saturated, making it difficult to elucidate the mechanism of groundwater source heat pump recharge blockage in river and lake coastal areas. An extensive laboratory study was conducted here to assess the effect of water level changes on the deposition characteristics of particle migration in porous media. A one-dimensional sand layer migration-deposition test system was used to test particle transport and deposition characteristics at different water levels. The tests were carried out for two combinations of particle sizes at four water levels (110 mm, 220 mm, 330 mm, and 440 mm) and three seepage velocities (0.024 cm/s, 0.047 cm/s, and 0.071 cm/s). The results show that when the seepage velocity is kept constant and the water level is low, the particles flow through fewer pore channels, and as the water level increases, the particle flow through pore channels increases accordingly, so the particles are more easily deposited in the pore channels. This is ultimately reflected in the decrease in the peak relative concentration C/C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C \mathord{\left/ {\vphantom {C {C_{{0}} }}} \right. \kern-\nulldelimiterspace} {C_{{0}} }}$$\end{document} and the increase in the pore volume ratio PV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{{\text{V}}}$$\end{document}. When the water level remains constant, the hydrodynamic effect gradually becomes stronger as the seepage velocity increases, and the originally deposited particles may break away from the surface of the deposit and flow out with the water, resulting in a higher suspended particle concentration of the effluent and a higher C/C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C \mathord{\left/ {\vphantom {C {C_{{0}} }}} \right. \kern-\nulldelimiterspace} {C_{{0}} }}$$\end{document}. Smaller particles are more affected by the hydrodynamic effect than larger particles.
... 18 The dispersivity for nanoparticles is not only particle-size dependent, but also a property of the porous medium. 19 Although changes in the surface properties or deposition sites on porous medium have enhanced the deposition of large-sized NPs (200 and 2000 nm) in the presence of iron oxide, they have not influenced the transport of small-sized NPs (20 nm). 13 Similarly, the retention of NPs (100 nm) in different soils is positively correlated with the Fe/ Al oxide content. ...
The transport of nanoplastics (NPs) through porous media is influenced by dissolved organic matter (DOM) released from agricultural organic inputs. Here, cotransport of NPs with three types of DOM (biocharDOM (BCDOM), wheat strawDOM (WSDOM), and swine manureDOM (SMDOM)) was investigated in saturated goethite (GT)-coated sand columns. The results showed that codeposition of 50 nm NPs (50NPs) with DOM occurred due to the formation of a GT-DOM-50NPs complex, while DOM loaded on GT-coated sand and 400 nm NPs (400NPs) aided 400NPs transport due to electrostatic repulsion. According to the quantum chemical calculation, humic acid and cellulose played a significant role in 50NPs retardation. Owing to its high concentration, moderate humification index (HIX), and cellulose content, SMDOM exhibited the highest retardation of 50NPs transport and promoting effect on 400NPs transport. Owing to a high HIX, the effect of BCDOM on the mobility of 400NPs was higher than that of WSDOM. However, high cellulose content in WSDOM caused it to exhibit a 50NPs retardation ability that was similar to that of BCDOM. Our results highlight the particle size selectivity and significant influence of DOM type on the transport of NPs and elucidate their quantum and colloidal chemical-interface mechanisms in a typical agricultural environment.
... The mass recovered (M r [-]) of the injected solute and nanoparticles at the effluent of packed columns was determined with the following equation (Chrysikopoulos & Katzourakis, 2015): ...
Laboratory‐scale experiments were conducted to investigate the simultaneous transport of titanium dioxide (TiO2) nanoparticles and formaldehyde (FA) in columns packed with quartz sand under water saturated and unsaturated flow conditions. The effects of interstitial velocity and solution ionic strength on the TiO2 and FA cotransport were examined. The experimental results indicated that substantial retention of TiO2 nanoparticles occurs in both saturated and unsaturated porous media. The solution ionic strength was found to have a noticeable effect on the retention of TiO2 nanoparticles in the packed columns. Moreover, the results from the TiO2 nanoparticle transport experiments in water‐saturated packed columns suggested that the TiO2 nanoparticle mass recoveries increased with increasing flow rate. The results from the TiO2 nanoparticles and FA cotransport experiments in both water saturated and unsaturated packed columns did not reveal a distinct relationship between mass recoveries and flow rate. The transport of FA in both saturated and unsaturated packed columns was hindered in the presence of TiO2 nanoparticles, especially at high ionic strength. This work provides useful insights into fate and transport of TiO2 nanoparticles and FA in saturated and unsaturated porous media.
... Yao et al., 1971;Ma et al., 2013;Long and Hilpert, 2009;Rajagopalan and Tien, 1976;Tufenkji and Elimelech, 2004;Nelson and Ginn, 2011), to estimate the trajectory of a colloid near a collector. More recently, the importance of colloid size dependent dispersion (Chrysikopoulos and Katzourakis, 2015), gravity effects of colloids (Chrysikopoulos and Syngouna, 2014), mechanical equilibrium and maximum retention function (Bedrikovetsky et al., 2011;Bedrikovetsky et al., 2012), fraction of the collector surface area (S f ) contributing to colloid attachment, and importance of applied hydrodynamic and adhesive torques (Bradford et al., 2009;Bradford et al., 2015), concentration dependent colloid transport (Bradford et al., 2009), and nanoscale heterogeneity (Bradford et al., 2015;Ron et al., 2019;Ron et al., 2020) were explored and highlighted. ...
In recent years, DNA-tagged silica colloids have been used as an environmental tracer. A major advantage of this technique is that the DNA-coding provides an unlimited number of unique tracers without a background concentration. However, little is known about the effects of physio-chemical subsurface properties on the transport behavior of DNA-tagged silica tracers. We are the first to explore the deposition kinetics of this new DNA-tagged silica tracer for different pore water chemistries, flow rates, and sand grain size distributions in a series of saturated sand column experiments in order to predict environmental conditions for which the DNA-tagged silica tracer can best be employed. Our results indicated that the transport of DNA-tagged silica tracer can be well described by first order kinetic attachment and detachment. Because of massive re-entrainment under transient chemistry conditions, we inferred that attachment was primarily in the secondary energy minimum. Based on calculated sticking efficiencies of the DNA-tagged silica tracer to the sand grains, we concluded that a large fraction of the DNA-tagged silica tracer colliding with the sand grain surface did also stick to that surface, when the ionic strength of the system was higher. The experimental results revealed the sensitivity of DNA-tagged silica tracer to both physical and chemical factors. This reduces its applicability as a conservative hydrological tracer for studying subsurface flow paths. Based on our experiments, the DNA-tagged silica tracer is best applicable for studying flow routes and travel times in coarse grained aquifers, with a relatively high flow rate. DNA-tagged silica tracers may also be applied for simulating the transport of engineered or biological colloidal pollution, such as microplastics and pathogens.
... Adsorption to kinetically limited sites and/or slow detachment (Schijven and Hassanizadeh, 2000) may explain longer tailings of PSA-HS2 and T4 at >3 PV ( Fig. 1 A & B). Their higher apparent dispersivity than of Br − (Fig. 1E) is consistent with previous observations that dispersivity is size-dependent (Chrysikopoulos and Katzourakis, 2015) and higher for suspended particles than for molecular size substances (Asraf-Snir and Gitis, 2011;Bales et al., 1989;Keller et al., 2004;Toran and Palumbo, 1992). The flexible tails of PSA-HS2 may have allowed the Siphovirus to enter smaller pores and to be more dispersive than the non-flexible tail Myoviruses PSA-HM1 and T4. ...
Marine phages have been applied to trace ground- and surface water flows. Yet, information on their transport in soil and related particle intactness is limited. Here we compared the breakthrough of two lytic marine tracer phages (Pseudoalteromonas phages PSA-HM1 and PSA-HS2) with the commonly used Escherichia virus T4 in soil- and sand-filled laboratory percolation columns. All three phages showed high mass recoveries in the effluents and a higher transport velocity than non-reactive tracer Br⁻. Comparison of effluent gene copy numbers (CN) to physically-determined phage particle counts or infectious phage counts showed that PSA-HM1 and PSA-HS2 retained high phage particle intactness (Ip > 81%), in contrast to T4 (Ip < 36%). Our data suggest that marine phages may be applied in soil to mimic the transport of (bio-) colloids or anthropogenic nanoparticles of similar traits. Quantitative PCR (qPCR) thereby allows for highly sensitive quantification and thus for the detection of even highly diluted marine tracer phages in environmental samples.
... Model parameters and laboratory studies. Laboratory coreflood tests usually involve the measurement of component concentrations at the effluent and pressure drop across the core [38,[40][41][42][43][44][45]. The initial kinetics rate coefficient, λ 0 , is a kinematic property, allowing it to be determined from the breakthrough concentration, C 1 [17,40,46]. ...
We discuss reactive flows in porous media that exhibit an irreversible chemical reaction between two components, resulting in large solid-product deposition. Previous works used the analytical solution for the linear problem with low deposition to determine model parameters from the reactant breakthrough concentrations and pressure drop growth across the core during laboratory coreflood. The present work derives an exact analytical solution for the non-linear problem with large solid-product deposition. We use the solution for interpretation of the laboratory data, and determination of the type curves for the measured values. Seven sets of experimental data are shown to closely match the data from the analytical model, which validates the analytical model.
... Sommerfeldt et al. (1982) concluded less solute leaching under initial saturated condition than air-dried condition. It should be noted that many factors such as colloid size and diversity, size exclusion, blocking and expanding phenomena in the soil pores and repulsion from low-flow-rate channels can change colloid dispersion, which altered the behavior of colloid transport compared to that of solute transport (Bagheri et al., 2019;Chrysikopoulos and Katzourakis, 2015;Ahfir et al., 2009). ...
This study aimed to investigate the effects of flow rate, initial soil moisture conditions and vermicompost (VC) application on total dissolved solids (TDS), nitrate (NO3), dissolved organic carbon (DOC) and colloid leaching from soil. Columns were filled with natural soil or VC-amended soil and were leached under unsaturated flow conditions using flow rates of 4.3-5.1, 2.5 and 0.4 mL/min. Two sets of experiments were conducted, one with the soils at initial air-dried conditions and the other with initial saturated conditions. Control experiments were conducted under saturated-flow conditions using flow rates of 2.7-3.8 mL/min for comparison. Results of the leaching experiments showed that EC, nitrate and DOC levels in the effluent were higher for the VC-amended soil versus the un-amended soil. Leaching under initial air-dried conditions and at the lowest flow rate (lowest water saturation) also produced higher EC, nitrate and DOC concentrations in the effluent. Conversely, effluent colloid concentrations were slightly higher for saturated-flow conditions, and elution behavior was similar between the un-amended and VC-amended soils. Statistical analysis revealed that the total leaching of TDS, nitrate, DOC and colloid under the initial air-dried conditions was not significantly different (p<0.05) in comparison with the initial saturated conditions. Although, higher flow rates showed high amount of total leaching of TDS, nitrate, DOC and colloid, unsaturated flow rate of 2.5 mL/min leached more efficiently than flow rate of 2.7-4.3 mL/min in un-amended soil. Findings of this study would help decision makers to better manage soil salinity, drainage and groundwater pollution. Particularly, applying lower flow rates for irrigation applications to maintain unsaturated conditions can significantly decrease colloid migration and soil erosion.
... The D B can be calculated by the equation D B ¼ a B U B , where a B is the bubble dispersivity [L]. The value of a B is set to 0.1e1 cm in this study according to the literature concerning particle transport in saturated porous media (Chrysikopoulos and Katzourakis, 2015;Bradford et al., 2002;Ahfir et al., 2016). Hence, the D B varies from 2 Â 10 À6 to 10 cm 2 /s. ...
Intrusion of subsurface contaminants in vapor phase from groundwater into overlying buildings through cracks or other pathways poses potential risk to human health. Previous studies indicated that water table fluctuations may have significant impacts on vapor intrusion, resulting in fluctuated concentrations of indoor volatile organic compounds (VOCs). Analytical solutions for vapor intrusion processes are flexible tools in predicting VOC concentrations and assessing health risks of VOC-contaminated sites. However, an analytical solution considering the impacts of fluctuated water table is not available. In this study, an analytical model of the vapor intrusion with fluctuated water table was developed. The VOC transport in unsaturated zones was described by diffusion equation and the varying water table was treated as a moving boundary. The residual VOCs in the unsaturated zone induced by water table fluctuations were also considered and were described by a source term of the vapor diffusion. The analytical solution was tested with its numerical solution. The results indicate that the fluctuated water table affects the dynamics of VOCs mainly in two ways, changing the length of vapor migration path and delivering the residual VOCs into the unsaturated zone. The VOC concentration at the outlet varies inversely with the water table fluctuation owing to the release processes of the residual VOCs dominate. The analytical solution matches well to the laboratory experiment data in an existing study and could be a simple tool for the risk assessment of vapor intrusion when considering the impacts of water table fluctuations.
... В роботі [16] досліджено перенесення наночастинок заліза в пористих середовищах і їх використання для очищення забрудненого ґрунту та ґрунтових вод. Результати лабораторних досліджень по кольматації та перенесенню частинок в пористому середовищі наведені в роботі [7]. ...
... The concentrations of FA, FA-colloids, and tracer collected at the end of the packed column (x = L) were analyzed by the first absolute temporal moment, M 1 (t), which describes the mean residence time or average velocity [45]. The mass recovery, M r (-), of the injected FA or FA-colloid complex was quantified by the following equation [46]: . The mass recovery, M r (-), for each of the four different concentrations (C FA , C cc , C FA-cc , and C tr ) was determined. ...
This study examines the effects of two representative colloid-sized clay particles (kaolinite, KGa-1b and montmorillonite, ST x-1b) on the transport of formaldehyde (FA) in unsaturated porous media. The transport of FA was examined with and without the presence of clay particles under various flow rates and various levels of saturation in columns packed with quartz sand, under unsaturated conditions. The experimental results clearly suggested that the presence of clay particles retarded by up to~23% the transport of FA in unsaturated packed columns. Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energy calculations demonstrated that permanent retention of clay colloids at air-water interfaces (AWI) and solid-water interfaces (SWI) was negligible, except for the pair (ST x-1b)-SWI. The experimental results of this study showed that significant clay colloid retention occurred in the unsaturated column, especially at low flow rates. This deviation from DLVO predictions may be explained by the existence of additional non-DLVO forces (hydrophobic and capillary forces) that could be much stronger than van der Waals and double layer forces. The present study shows the important role of colloids, which may act as carriers of contaminants.
The first investigation that describes the adsorption capacity of natural colloids by solid soil media, and studies their interaction mechanism in the molecular-scale.
Black phosphorus nanosheets/nanoparticles (BPNs) are widely applied in many fields. However, the transport of BPNs in the subsurface still has not yet been reported and there is increasing concern about potential adverse impacts on ecosystems. Roles of median grain size and surface roughness, BPNs concentration, and solution chemistries (pH, ionic strength, and cation types) on the retention and release of BPNs in column experiments were therefore investigated. The mobility of BPNs significantly increased with increasing grain size and decreasing surface roughness due to their influence on the mass transfer rate, number of deposition sites and retention capacity, and straining processes. Transport of BPNs was enhanced with an increase in pH and a decrease in ionic strength because of surface deprotonation and stronger repulsion that tends to reduce aggregation. The BPN transport was significantly sensitive to ionic strength, compared with other engineered nanoparticles. Additionally, charge heterogeneity and cation-bridging played a critical role in the retention of BPNs in the presence of divalent cations. Higher input concentrations increased the retention of BPNs, probably because collisions, aggregation at pore throat locations, and hydrodynamic bridging were more pronounced. Small fractions of BPNs can be released under decreasing IS and increasing pH due to the expansion of the electrical double layer and increased repulsion at convex roughness locations. A mathematical model that includes provisions for advective dispersive transport and time-dependent retention with blocking or ripening terms well described the retention and release of BPNs. These findings provide fundamental information that helps to understand the transport of BPNs in the subsurface environments.
This study explores the transport and retention of CdSe/ZnS quantum dot (QD) nanoparticles in water-saturated sand columns as a function of electrolytes (Na+ and Ca2+), ionic strength, organic ligand citrate, and Suwannee River natural organic matter (SRNOM). Numerical simulations were carried out to understand the mechanisms that govern the transport and interactions of QDs in porous media and to assess how environmental parameters impact these mechanisms. An increase in the ionic strength of NaCl and CaCl2 increased QDs retention in porous media. The reduction of the electrostatic interactions screened by dissolved electrolyte ions and the increase of divalent bridging effect are the causes for this enhanced retention behavior. Citrate or SRNOM enhanced QDs transport in NaCl and CaCl2 systems by either increasing the repulsion energy barrier or inducing the steric interactions between QDs and the quartz sand collectors. A non-exponential decay characterized the retention profiles of QDs along the distance to the inlet. The modeling results indicated the four models containing the attachment, detachment, and straining terms - Model 1: M1-attachment, Model 2: M2-attachment and detachment, Model 3: M3-straining, and Model 4: M4-attachment, detachment, and straining - closely simulated the observed breakthrough curves (BTCs) but inadequately described the retention profiles.
水环境污染是当前人类社会所面临的严峻挑战之一,阻碍了全球生态环境和社会经济的可持续发展.潜在污染源众多和水文地质条件的复杂性导致对污染源追溯、污染范围界定和污染程度量化等问题的研判十分棘手.针对这些难题,已发展了多种水环境污染物迁移示踪系统,例如离子化合物、有色染料和同位素等,这些示踪系统的应用对水环境污染治理起到了重要的推动作用.近年来,快速发展的基于脱氧核糖核酸(deoxyribonucleicacid,DNA)纳米技术的示踪方法(DNA示踪技术)逐渐崭露头角,其是应用DNA片段作为特异性标记物进行水环境污染示踪.与已有的示踪技术相比,DNA示踪技术具有示踪剂数量巨大、特异性强、检测灵敏、运移及降解特性可控和环境友好等诸多优势,是极具潜力的新一代示踪技术.DNA示踪技术的研发与应用集成了生物化学、材料科学、环境工程和水文地质等多学科知识,是典型的交叉研究领域.为促进DNA示踪技术体系的长足发展以及水环境污染防治能力的不断增强,本文重点阐述了DNA片段作为水环境污染示踪剂的原理与方法,全面梳理了DNA示踪技术体系的发展脉络,总结探讨了DNA示踪技术在水环境污染示踪研究中的典型应用,最后展望了未来重要的研究方向.
Hypotheses:
The transport behavior of colloids in subsurface porous media is altered by surface chemical and physical heterogeneities. Understanding the mechanisms involved and distribution outcomes is crucial to assess and control groundwater contamination. The multi-scale processes that broaden residence time distribution for particles in the medium are here succinctly described with an upscaling model. Experiments/model: The spatial distribution of silver particles along glass bead-packed columns obtained from X-ray micro-computed tomography and a mechanistic upscaling model were used to study colloid retention across interface-, collector-, pore-, and Darcy-scales. Simulated energy profiles considering variable colloid-grain interactions were used to determine collector efficiencies from particle trajectories via full force-torque balance. Rate coefficients were determined from collector efficiencies to parameterize the advective-dispersive-reactive model that reports breakthrough curves and depth profiles.
Findings:
Our results indicate that: (i) with surface heterogeneity, individual colloid-grain interactions are non-unique and span from repulsive to attractive extremes; (ii) experimentally observed spatial positioning of retention at grain-water interfaces and grain-to-grain contacts is governed respectively by mechanistic attachment to the grain surface and retention without contact at rear-flow stagnation zones, and (iii) experimentally observed non-monotonic retention profiles and heavy-tailed breakthrough curves can be modeled with explicit implementation of heterogeneity at smaller scales.
The mobility of nano zero-valent iron (nZVI) will greatly affect its practical application as a remediation material for contaminated groundwater. One-dimensional (1D) column tests are commonly used in previous work to study its migration behavior, but the two-dimensional (2D) test is still very limited. This study reports a novel research system to study the 2D transport and retention behavior of colloids and solutes, which includes a 2D model test setup and the corresponding image analysis method. The transport behaviors of methyl orange (MO), nZVI, and phosphate-loaded nZVI (PnZVI) are studied using this system. The results show that the research system can reasonably describe the tempo-spatial concentration distribution of colloids and solutes. After phosphate adsorption, the mobility of nZVI is enhanced due to the increase in negative surface charge, which implies a potential environmental risk of nZVI to facilitate contaminant transport. The migration of PnZVI is not significantly influenced by its density, which is faster than MO in the longitudinal direction. The range of the plume of PnZVI in the longitudinal direction is larger than that of MO, which implies that PnZVI has a stronger longitudinal dispersion than MO.
Fluctuation of the groundwater table in the coastal zone influences the migration of colloids in vadose zone, which can further carry contaminants to transport. To capture the variable-density water flow and the migration processes, this study developed a colloid-facilitated migration model by adjusting the adsorption coefficient and considering the relationship between colloid and salinity based on the experimental observations. This model was further applied to explore the effects of freshwater and seawater fluctuations on the migration and transformation of colloids and Cr in coastal vadose zones. The greater the hydraulic conductivity of the saturated aquifer was, the more Cr were discharged into the ocean by submarine groundwater discharge. Furthermore, the increase in the freshwater fluctuation amplitude expanded the pollution ranges of colloidal Cr and dissolved Cr. The rise of the seawater fluctuation amplitude had a more obvious reduction effect on the total solid retained Cr in the contaminant source, compared with that of the freshwater fluctuation. As the seawater fluctuation amplitude increased from 0.1 m to 0.8 m, the ratio of total solid retained Cr reduction in the contaminant source to the initial value increased from 1.8% to 7.8%. The results obtained from this study deepens our understanding of how colloids and contaminants migrate across a coastal area from vadose zone induced by the groundwater table fluctuation.
The plastic concentration in terrestrial systems is orders of magnitude higher than that found in marine ecosystems, which has raised global concerns about their potential risk to agricultural sustainability. Previous research on the transport of nanoplastics in soil relied heavily on the qualitative prediction of the mean-field extended Derjaguin–Landau–Verwey–Overbeek theory (XDLVO), but direct and quantitative measurements of the interfacial forces between single nanoplastics and porous media are lacking. In this study, we conducted multiscale investigations ranging from column transport experiments to single particle measurements. The maximum effluent concentration (C/C0) of amino-modified nanoplastics (PS–NH2) was 0.94, whereas that of the carboxyl-modified nanoplastics (PS–COOH) was only 0.33, indicating PS-NH2 were more mobile than PS-COOH at different ionic strengths (1–50 mM) and pH values (5–9). This phenomenon was mainly attributed to the homogeneous aggregation of PS-COOH. In addition, the transport of PS-NH2 in the quartz sand column was inhibited with the increase of ionic strength and pH, and pH was the major factor governing their mobility. The transport of PS-COOH was inhibited with increasing ionic strength and decreasing pH. Hydrophilicity/hydrophobicity-mediated interactions and particle heterogeneity strongly interfered with interfacial forces, leading to the qualitative prediction of XDLVO, contrary to experimental observations. Through the combination of XDLVO and colloidal atomic force microscopy, accurate and quantitative interfacial forces can provide compelling insight into the fate of nanoparticles in the soil environment.
Microplastics are widely detected in the soil-groundwater environment, which has attracted more and more attention. Clay mineral is an important component of the porous media contained in aquifers. The transport experiments of polystyrene nanoparticles (PSNPs) in quartz sand (QS) mixed with three kinds of clay minerals are conducted to investigate the effects of kaolinite (KL), montmorillonite (MT) and illite (IL) on the mobility of PSNPs in groundwater. Two-dimensional (2D) distributions of DLVO interaction energy are calculated to quantify the interactions between PSNPs and three kinds of clay minerals. The critical ionic strengths (CIS) of PSNPs-KL, PSNPs-MT and PSNPs-IL are 17.0 mM, 19.3 mM and 21.0 mM, respectively. Experimental results suggest KL has the strongest inhibition effect on the mobility of PSNPs, followed by MT and IL. Simultaneously, the change of ionic strength can alter the surface charge of PSNPs and clay minerals, thus affecting the interaction energy. Experimental and model results indicate both the deposition rate coefficient (k) and maximum deposition (Smax) linearly decrease with the logarithm of the DLVO energy barrier, while the mass recovery rate of PSNPs (Rm) exponentially increases with the logarithm of the DLVO energy barrier. Therefore, the mobility and associated kinetic parameters of PSNPs in complex porous media containing clay minerals can be predicted by 2D distributions of DLVO interaction energy. These findings could help to gain insight into understanding the environmental behavior and transport mechanism of microplastics in the multicomponent porous media, and provide a scientific basis for the accurate simulation and prediction of microplastic contamination in the groundwater system.
Kaolinite clays are the most widespread natural fines attached to the rock surface; they can be mobilised by the flow with further migration in porous spaces, straining in thin pore throats and causing significant decline in the rock permeability. We conducted mathematical and laboratory studies of kaolinite detachment from solid substrates in visualisation cells. The mechanical equilibrium of the attached particles in the creeping flow was described by the torque balance. For uniform particles and substrates, this model presents fines detachment using only two rates that correspond to particles in primary and secondary energy minima, i.e., the attached concentration versus velocity is a piecewise-constant function. To observe this maximum retention function, we saturated a single-channel micromodel visualisation cell with a transparent top with kaolinite particles; it was then subjected to a flow with a piecewise-constant increasing rate. Images of the remaining attached fines were filmed after each rate increase. All the tests exhibit gradual fines detachment. To explain the phenomenon, we assumed a probabilistic distribution of the properties of the particles and the substrate. For two-parametric probability distribution functions, it adds the standard deviations to the list of model parameters. The continuous fines detachment versus velocity was highly matched by the torque balance equation with probabilistically distributed coefficients. The match allowed restoring probabilistic distributions of the selected model parameters from the measured maximum retention function. The sensitivity of the detachment rate to properties follows a decreasing order: semi-major axis, aspect ratio, lever arm ratio, and zeta potential.
This work fundamentally advances lab-based mathematical modelling of colloidal detachment from solid surfaces by developing stochastic torque-balance equation, where standard deviations of the model coefficients are tuning / matching parameters along with their mean values. This approach allows determining the probabilistic distributions of the model coefficients from the image processing, and also calculating the attached concentration variation within six standard deviations of each parameter, permitting placing the model parameters in the order of their effect on particle detachment.
Although the effects of fracture aperture variability on colloid advection and dispersion are well understood, how aperture variability affects colloid deposition under unfavorable geochemical conditions remains underexplored. To address this knowledge gap, we simulated 6,200 cases of colloid transport in variable-aperture fractures with different magnitudes of fracture aperture variability and correlation lengths. Flows were laminar (Reynolds number < 1) with dispersion-dominated transport (Peclet number < 1) in the simulations. The numerically obtained breakthrough curves (BTCs) reflected non-Fickian transport behavior with power-law tailing where the power-law exponent increased with aperture variability rather than correlation length. Solutions to the advection-dispersion-reaction equation (ADRE) and a continuous time random walk (CTRW) model were fit to the BTCs. The CTRW model faithfully reproduced BTCs that decayed according to a power law, while the ADRE failed to do so. The ensemble mean of the attachment rate (equivalent to the reaction rate in the ADRE) in the CTRW model was correlated to a measurable property (i.e., aperture variability) using a power-law function. This newly established function facilitates accurate prediction of non-Fickian colloid transport using the CTRW model where dynamic attachment and detachment of colloids are considered under unfavorable deposition conditions.
Hypothesis
Transport of suspended colloids in heterogeneous porous media is a multi-scale process that exhibits anomalous behavior and cannot be described by the Fickian dispersion theory. Although many studies have documented colloids’ transport at different length scales, a theoretical basis that links pore- to core-scale observations remains lacking. It is hypothesized that a recently proposed pore-scale statistical kinetic theory is able to capture the results observed experimentally.
Experiments
We implement a multi-scale approach via conducting core-flooding experiments of colloidal particles in a sandstone sample, simulating particles flowing through a sub-volume of the rock’s digital twin, and developing a core-scale statistical theory for particles’ residence times via upscaling the pore-scale kinetic theory. Experimental and computational results for solute transport are used as benchmark.
Findings
Based on good agreement across the scales achieved in our investigation, we show that the macroscopically observed anomalous transport is particle-type dependent and stems from particles’ microscopic dispersion and deposition in heterogeneous flow fields. In particular, we reveal that residence-time distributions (i.e., breakthrough curve) obey a closed-form function that encompasses particles’ microscopic dynamics, which allows investigations of a whole transition from pre-asymptotic to asymptotic behavior. The physical insights attained could be useful for interpreting experimental data and designing colloidal tracers.
The environmental behaviors of microplastics (MPs) have garnered ever-increasing attention globally. To overcome the limitations of commonly used “black box”, a real-time pore-scale visualization system including microscope, charge coupled device (CCD) microscope camera, and flow cell (connected with pump and sample collector) was used to unravel the transport and retention mechanisms of fragmental microplastics (FMPs) in saturated and unsaturated porous media. The breakthrough curves (BTCs) of effluent concentrations from the flow cells were used to quantitatively analyze FMPs transport. The videos gathered from different transport scenarios indicated that FMPs can move along with the bulk flow in porous media, but also move around the sand surfaces via sliding, rolling, and saltating patterns. The FMPs were retained in porous media mainly via deposition and straining in saturated porous media. Interestingly, little FMPs were captured by the air-water interface in unsaturated conditions. The mobility of FMPs varied with environmental factors, which became lower at higher solution ionic strength (IS), smaller grain size, and lower water content in porous media. Flow rate barely affected the transport of FMPs under 0.1 mM IS with the mass recovery rate ranging between 65.8%-67.5%, but significantly enhanced FMPs mobility under 10 mM IS through reducing the moving rate. The IS and grain size showed a more significant effect on the transport of FMPs in unsaturated porous media. Our findings, for the first time, visually deciphered the transport and retention patterns of MPs with fragmental shapes on pore-scale, expanding our current knowledge of the fate and transport of more realistic MPs in the environment.
Permeability reduction and formation damage in porous media caused by fines (defined as unconfined solid particles present in the pore spaces) migration is one of the major reasons for productivity decline. It is well accepted that particle detachment occurs under imbalanced torques arising from hydrodynamic and adhesive forces exerted on attached particles. This paper reviewed current understanding on primary factors influencing fines migration as well as mathematical formulations for quantification. We also introduced salinity-related experimental observations that contradict theoretical predictions based on torque balance criteria, such as delayed particle release and attachment-detachment hysteresis. The delay of particle release during low-salinity water injection was successfully explained and formulated by the Nernst-Planck diffusion of ions in a narrow contact area. In addition to the widely recognized explanation by surface heterogeneity and the presence of low-velocity regions, we proposed a hypothesis that accounts for the shifting of equilibrium positions, providing new insight into the interpretation of elusive attachment-detachment hysteresis both physically and mathematically. The review was finalized by discussing the quantification of anomalous salinity effect on adhesion force at low- and high-salinity conditions.
Accurate prediction of the colloid-driven transport of radionuclides in porous media is critical for the long-term safety assessment of radioactive waste disposal repository. However, the co-transport and corelease process of radionuclides with colloids have not been well documented, the intrinsic mechanisms for colloids-driven retention/transport of radionuclides are still pending for further discussion. Thus the controlling factors and governing mechanisms of co-transport and co-release behavior of Eu(III) with bentonite colloids (BC) were discussed and quantified by combining laboratory-scale column experiments, colloid filtration theory and advection dispersion equation model. The results showed that the role of colloids in facilitating or retarding the Eu(III) transport in porous media varied with cations concentration, pH, and humic acid (HA). The transport of Eu(III) was facilitated by the dispersed colloids under the low ionic strength and high pH conditions, while was impeded by the aggregated colloids cluster. The enhancement of Eu(III) transport was not monotonically risen with the increase of colloids concentration, the most optimized colloids concentration in facilitating Eu(III) transport was approximately 150 mg L⁻¹. HA showed significant promotion on both Eu(III) and colloid transport because of not only its strong Eu(III) complexion ability but also the increased dispersion of HA-coated colloid particles. The HA and BC displayed a synergistic effect on Eu(III) transport, the co-transport occurred by forming the ternary BC-HA-Eu(III) hybrid. The transport patterns could be simulated well with a two-site model that used the advection dispersion equation by reflecting the blocking effect. The retarded Eu(III) on the stationary phase was released and remobilized by the introduction of colloids, or by a transient reduction in cation concentration. The findings are essential for predicting the geological fate and the migration risk of radionuclides in the repository environment.
Models for the co-transport of two different colloids commonly assume a one-way coupling. This is because often a large colloid and small colloid are involved. Therefore, they assume that the spread of smaller colloid is affected by the transport of larger colloids, but not the other way around. However, a number of studies have shown that this assumption is not valid, even for large and small colloids. Therefore, in this study, a two-way coupled model is developed to simulate the co-transport of two different colloids in porous media and their effect on each other. We have considered the interactions of the two colloids with the grain surface, kinetics of heteroaggregation (of the two colloids), and heteroaggregate deposition onto the grain surface. We assumed a first-order kinetic model to represent heteroaggregate formation and its deposition on the grain surface. The model is evaluated by fitting the experimental data reported in four different papers from the literature on the co-transport of clay colloids and viruses, bacteria and graphene oxide nanoparticles, and clay colloids and graphene oxide nanoparticles. The model performance is compared with the commonly-used one-way coupled model. The two-way coupled model is found to satisfactorily simulate most of the experimental conditions reported in the above papers, except for the co-transport of montmorillonite–adenovirus, and Staphylococcus aureus- graphene oxide nanoparticles.
Understanding the transport of naturally abundant clay colloids is critical in colloid associated contaminant transport in porous media. This study was focused on the impact of the median size of sand grains and the ionic strength of solution on the transport and retention behavior of clay colloids. Two clay samples of kaolinite and illite colloids were selected to represent clay samples containing 1:1 and 2:1 clay minerals, respectively. The observed retention profiles and breakthrough curves demonstrated that the impact of ionic strength on the retention behavior of clay was consistent with other colloidal colloids such as latex colloids or graphene oxide. The quantity of the retained clay increased as the median sizes of sand decreased, and the ionic strength increased from 0 to 0.1 M. However, a similar quantity of retained illite at the ionic strength of 0.01 M and 0.1 M indicates the presence of threshold ionic strength in clay colloid retention. The exponential relationship between sand-to-clay size ratio and first-order retention coefficient at given ionic strength implies the chance in long-term prediction of clay colloid transport from the observed retention profiles.
Availability of data
The data used in this study were created by authors and available from the first author ([email protected]).
Porous silicon-coated zero-valent iron (Fe⁰@p-SiO2) is a promising material for in-situ contaminated groundwater remediation. However, investigations of factors that affect the transport of Fe⁰@p-SiO2 remain incomplete. In the present study, Fe⁰@p-SiO2 composites were prepared by a SiO2-coated technology, and a series of column experiments were conducted to examine the effects of media size, ionic strength, and injection velocity and concentration on retention and transport in saturated porous media. Results showed that the obtained Fe⁰@p-SiO2 is a core-shell composite with zero-valent iron as the core and porous silicon as the shell. Media size, injection velocity, Fe⁰ concentration, and ionic strength had a significant impact on the transport of Fe⁰@p-SiO2. Fe⁰@p-SiO2 effluent concentrations decreased with a smaller media size. Increasing initial particle concentration and ionic strength led to a decrease in particle transport. High particle retention was observed near the middle of the column, especially with high injection concentration. That was also observable in the condition of lower injection velocity or finer media. The results indicated that two transport behaviors during particles transport, which were “agglomeration-straining” and “detachment-re-migration”. Moreover, the dominated mechanisms for Fe⁰@p-SiO2 transport and retention in saturated porous media are hydrodynamic dispersion and interception. Given the results, in practical engineering applications, proper injection velocity and concentration should be selected depending on the pollution status of groundwater and the geochemical environment to ensure an effective in-situ reaction zone.
Formation damage caused by fine migration and straining is a well-documented phenomenon in sandstone reservoirs. Fine migration and the associated permeability decline have been observed in various experimental studies, and this phenomenon has been broadly explained by the analysis of surface forces between fines and sand grains. The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory is a useful tool to help understand and model the fine release, migration, and control phenomena within porous media by quantifying the total interaction energy of the fine–brine–rock (FBR) system. Fine migration is mainly caused by changes in the attractive and repulsive surface forces, which are triggered by mud invasion during drilling activity, the utilization of completion fluid, acidizing treatment, and water injection into the reservoir during secondary and tertiary recovery operations. Increasing pH and decreasing water salinity collectively affect the attractive and repulsive forces and, at a specific value of pH, and critical salt concentration (CSC), the total interaction energy of the FBR system (VT) shifts from negative to positive, indicating the initiation of fine release. Maintaining the system pH, setting the salinity above the CSC, tuning the ionic composition of injected water, and using nanoparticles (NPs) are practical options to control fine migration. DLVO modeling elucidates the total interaction energy between fines and sand grains based on the calculation of surface forces of the system. In this context, zeta potential is an important indicator of an increase or decrease in repulsive forces. Using available data, two correlations have been developed to calculate the zeta potential for sandstone reservoirs in high- and low-salinity environments and validated with experimental values. Based on surface force analysis, the CSC is predicted by the DLVO model; it is in close agreement with the experimental value from the literature. The critical pH value is also estimated for alkaline flooding. Model results confirm that the application of NPs and the presence of divalent ions increase the attractive force and help to mitigate the fine migration problem. Hence, a new insight into the analysis of quantified surface forces is presented in current research work by the practical application of the DLVO theory to model fine migration initiation under the influence of injection water chemistry.
A novel mathematical model was developed to describe the transport of nanoparticles in water saturated, homogeneous porous media with uniform flow. The model accounts for the simultaneous migration and aggregation of nanoparticles. The nanoparticles are assumed to be found suspended in the aqueous phase or attached reversibly or irreversibly onto the solid matrix. The Derjaguin‐Landau‐Verwey‐Overbeek theory was used to account for possible repulsive interactions between aggregates. Nanoparticle aggregation was represented by the Smoluchowski population balance equation (PBE). Both reaction‐limited aggregation and diffusion‐limited aggregation were considered. Particle‐size dependent dispersivity was accounted for. In order to overcome the substantial difficulties introduced by the PBE, the governing coupled partial differential equations were solved by employing adaptive operator splitting methods, which decoupled the reactive transport and aggregation into distinct physical processes. The results from various model simulations showed that the transport of nanoparticles in porous media is substantially different than the transport of conventional biocolloids. In particular, aggregation was shown to either decrease or increase nanoparticle attachment onto the solid matrix, depending on particle size, and to yield early or late breakthrough, respectively. Finally, useful conclusions were drawn regarding possible erroneous results generated when aggregation, particle‐size dependent dispersivity or nanoparticle surface charges are neglected. This article is protected by copyright. All rights reserved.
Numerical experiments are conducted to examine the effect of gravity on monodisperse and polydisperse colloid transport in water-saturated fractures with uniform aperture. Dense colloids travel in water-saturated fractures by advection and diffusion while subject to the influence of gravity. Colloids are assumed to neither attach onto the fracture walls nor penetrate the rock matrix based on the assumptions that they are inert and their size is larger than the pore size of the surrounding solid matrix
In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed.
An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $$d_{50}$$d50 of these populations was 3.5, 9.5, and $$18.3~\upmu \hbox {m}$$18.3μm . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $$d_{50} = 17.4\; \upmu \hbox {m}$$d50=17.4μm ) obtained by mixing in equal proportion (volume) the populations 3.5 and $$18.3\;\upmu \hbox {m}$$18.3μm was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.
Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.
This study is focused on the transport of Pseudomonas (P.) putida bacterial cells in a 3-D model aquifer. The pilot-scale aquifer consisted of a rectangular glass tank with internal dimensions: 120 cm length, 48 cm width, and 50 cm height, carefully packed with well-characterized quartz sand. The P. putida decay was adequately represented by a first-order model. Transport experiments with a conservative tracer and P. putida were conducted to characterize the aquifer and to investigate the bacterial behavior during transport in water saturated porous media. A 3-D, finite-difference numerical model for bacterial transport in saturated, homogeneous porous media was developed and was used to successfully fit the experimental data. Furthermore, theoretical interaction energy calculations suggested that the extended-DLVO theory seems to predict bacteria attachment onto the aquifer sand better than the classical DLVO theory. List of symbols A 123 Hamaker constant (J) (M L 2)/t 2 C Dissolved or suspended aqueous phase concentration (M species)/L 3 C* Concentration attached onto the solid phase (M species)/(M solids) C eq Dissolved or suspended aqueous phase concentration at equilibrium (M species)/L 3 C * eq
The relative transport and attenuation of bacteria, bacteriophages, and bromide was determined in a 5 m long×0.3 m diameter column of saturated, heterogeneous gravel. The average pore velocity (V), longitudinal dispersivity (α x), and total removal rate (λ) were derived from the breakthrough curves at 1, 3, and 5 m, at a flow rate of 24.8 L h -1. The experiments largely confirmed the differences in transport and attenuation patterns among bacteria, phages, and bromide, and between colloid-associated and "free" microorganisms, previously observed in a study using homogeneous pea gravel. Cultured Escherichia coli J6-2 cells were transported faster than phage MS2 and bromide, consistent with velocity enhancement of the larger particles. The evidence for velocity enhancement of phage MS2 compared with bromide was less conclusive, with some evidence of retardation of the phage as a result of adsorption-desorption processes in the finer media. On average, phage in sewage and adsorbed to kaolin particles were transported faster than free phage, suggesting that most sewage phage are adsorbed to colloids. However, average velocities of cultured and sewage E. coli differed far less, suggesting that most E. coli in sewage exist as individual (non colloid-associated) cells. There was no conclusive evidence that the wider pore size range in the heterogeneous mixture compared with pea gravel increased velocity enhancement effects. Removal rates of free phage were far higher than in the pea gravel, and were attributed to adsorption in the finer materials. Equivalent increases in removal of cultured and sewage E. coli and colloid-associated phage were attributed to straining in finer materials and settling in quiescent zones. Inactivation (μ) rates (determined in the pea gravel study) indicated little contribution to removal of either free or attached microorganisms. The results showed the importance of association with colloids in determining the relative transport of bacteria and viruses in alluvial gravels.
The term 'transport phenomena' is used to describe processes in which mass, momentum, angular momentum, and energy move about in matter. Transport phenomena includes diffusional phenomena, fluid dynamics, and heat transport. It is stated that transport phenomena may be treated with from a molecular, microscopic, and macroscopic point of view. Although the theoretical bases for the transport phenomena were virtually completed by 1950s, the continuum theory of transport phenomena was not much used in chemical engineering because of the apparent intractability of the equations.
The role of gravitational force on colloid transport in water-saturated columns packed with glass beads was investigated. Transport experiments were performed with colloids (clays: kaolinite KGa-1b, montmorillonite STx-1b). The packed columns were placed in various orientations (horizontal, vertical, and diagonal) and a steady flow rate of Q = 1.5 mL/min was applied in both up-flow and down-flow modes. All experiments were conducted under electrostatically unfavorable conditions. The experimental data were fitted with a newly developed, analytical, one-dimensional, colloid transport model. The effect of gravity is incorporated in the mathematical model by combining the interstitial velocity (advection) with the settling velocity (gravity effect). The results revealed that flow direction influences colloid transport in porous media. The rate of particle deposition was shown to be greater for up-flow than for down-flow direction, suggesting that gravity was a significant driving force for colloid deposition.
A conceptual mathematical model was developed to describe the simultaneous transport (cotransport) of viruses and colloids in three-dimensional, water saturated, homogeneous porous media with uniform flow. The model accounts for the migration of individual virus and colloid particles as well as viruses attached onto colloids. Viruses can be suspended in the aqueous phase, attached onto suspended colloids and the solid matrix, and attached onto colloids previously attached on the solid matrix. Colloids can be suspended in the aqueous phase or attached on the solid matrix. Viruses in all four phases (suspended in the aqueous phase, attached onto suspended colloid particles, attached on the solid matrix, and attached onto colloids previously attached on the solid matrix) may undergo inactivation with different inactivation coefficients. The governing coupled partial differential equations were solved numerically using finite difference methods, which were implemented explicitly or implicitly so that both stability and speed factors were satisfied. Furthermore, the experimental data collected by Syngouna and Chrysikopoulos [1] were satisfactorily fitted by the newly developed cotransport model.
Dispersive transport in porous media is usually described through a Fickian model, in which the flux is the product of a dispersion tensor times the concentration gradient. This model is based on certain implicit assumptions, including slowly varying conditions. About fifty years ago, it was first suggested that the parameterization of the second-order dispersion tensor for anisotropic porous media involves a fourth-order dispersivity tensor. However, the properties of the dispersivity tensor have not been adequately studied. This work contributes to achieving a better grasp of dispersion in anisotropic porous media through a number of ways. First, with clearly stated assumptions and from first principles, we use the method of moments to derive a mathematical formula for the fourth-order dispersivity tensor, and show that it is a function of pore geometry, fluid velocity, and pore diffusion. Second, by using pore-scale flow and transport simulations through orderly and randomly packed 2-D and 3-D porous media, we evaluate the effects of the three factors on dispersivity. Different relationships with the Peclét number are observed for the longitudinal and transverse dispersivities and for orderly and randomly packed media. Third, we discuss the limitations of 2-D periodic media with simple structures in computing transverse dispersivity, which is more accurately predicted in the 3-D periodic media and 2-D randomly packed media. Fourth, we exhibit through numerical simulations that the method of moments can, computational limitations notwithstanding, be extended to stationary porous media.
The effects of particle-size distribution on the longitudinal dispersion coefficient (
$D_{\mathrm{L}})$
D
L
)
in packed beds of spherical particles are studied by simulating a tracer column experiment. The packed-bed models consist of uniform and different-sized spherical particles with a ratio of maximum to minimum particle diameter in the range of 1–4. The modified version of Euclidian Voronoi diagrams is used to discretize the system of particles into cells that each contains one sphere. The local flow distribution is derived with the use of Laurent series. The flow pattern at low particle Reynolds number is then obtained by minimization of dissipation rate of energy for the dual stream function. The value of
$D_{\mathrm{L}}$
D
L
is obtained by comparing the effluent curve from large discrete systems of spherical particles to the solution of the one-dimensional advection–dispersion equation. Main results are that at Peclet numbers above 1, increasing the width of the particle-size distribution increases the values of
$D_{\mathrm{L}}$
D
L
in the packed bed. At Peclet numbers below 1, increasing the width of the particle-size distribution slightly lowers
$D_{\mathrm{L}}$
D
L
.
In the present work, we have analysed the experimental data presented in literature to characterize dispersion in porous media, at different dispersion regimes. The vast amount of data obtained by our group, together with the extensive data available from other sources, mostly for air and water at room temperature, provide a very detailed representation of the functions PeT = f1 (Pem, Sc) and PeL = f2 (Pem, Sc). Empirical correlations are presented for the prediction of the dispersion coefficients (DT and DL) over the entire range of practical values of Schmidt number and Peclet number. The simple mathematical expressions represent the data available, in literature, with good accuracy and they are shown to be a significant improvement over previous correlations.
To assess soil-aquifer treatment of sewage effluent for removal of viruses, studies were conducted at a recharge/recovery site near Tucson, Ariz. Two 13 m2 basins were constructed in coarse sand alluvium, one for secondary- and one for tertiary-treated effluent. Bacterial viruses, MS2 and PRDI, and a chemical tracer, potassium bromide (KBr), were added to effluent applied to these basins. Infiltration rates ranged from 0.2 to 16.8 m/d. Samples of unsaturated flow from depths of 0.30–6.08 m below the basin were taken through porous stainless steel suction-samplers. Bromide and virus results indicated the presence of preferential flow conditions that produced irregular concentration profiles with depth. Virus transport was retarded (R = 1.9) at the beginning of a flooding cycle, but viruses were transported faster than the average water velocity (R = 0.47) when applied after the infiltration rate had declined following 4 days of flooding. Virus specific removal rates (b) during percolation through soil were 2.3–120 times greater than in bottles of effluent or ground water. PRDI was removed more rapidly during percolation (b = 0.65 h−1) than MS2 (b = 0.23 h−1). Effluent type did not significantly affect b for MS2, but the PRDI rate was nearly 3 times greater with secondary effluent (1.0 h−1) compared to tertiary effluent (0.35 h−1). Virus removals at the 4.3 m depth ranged from 37 to 99.7%.
ventional methods to investigate colloid transport often involve column studies. Here, colloid concentrations are A new experimental approach and complementary model analysis measured at the column effluent or at selected points are presented for studying colloid transport and fate in porous media. The experimental approach combines high precision etching to create along the column length. Unfortunately, such methods do a controlled pore network in a silicon wafer (i.e., micromodel), with not clearly distinguish how spatial and temporal changes epifluorescent microscopy. Two different sizes of latex colloids were in hydrochemical and hydrodynamic conditions affect col- used; each was stained with a fluorescent dye. During an experiment, loid transport. For example, breakthrough curves (BTCs) water with colloids was purged through a micromodel at different obtained from column effluent represent some average flow rates. Flow paths and particle velocities were determined and behavior of colloids in the column (Baumann et al., compared with flow paths calculated using a two-dimensional (2D) 2002). Since different heterogeneous realizations can lattice Boltzmann (LB) model. For 50% of the colloids evaluated, contribute to such BTCs, the processes that control col- agreement between measured and calculated flow paths and velocities loid transport in the column are obscured. were excellent. For 20%, flow paths agreed, but calculated velocities Filtration theory (Happel, 1958; Rajagopalan and were less. This is attributed to the parabolic velocity profile across the micromodel depth, which was not accounted for in the 2D flow Tien, 1976) is often used to evaluate colloid transport. model. For 12%, flow paths also agreed, but calculated velocities were It accounts for the hydrodynamic processes that lead less. These colloids were close to grain surfaces, where model errors to a contact between particles and filter surfaces. The increase. Also, particle-surface interactions were not accounted for attachment efficiency, , describes the probability that in the model; this may have contributed to the discrepancy. For the a collision between a particle and a filter grain results remaining 18% of colloids evaluated, neither flow paths nor velocities in a permanent attachment (Elimelech and O'Melia, agreed. The majority of colloids in this last case were observed after 1990). This parameter lumps the physical and chemical breakthrough, when concentrations were high. The discrepancies may interactions between colloids and surface at the pore be due to particle-particle interactions that were not accounted for scale. Often the attachment efficiency is used as a fitting in the model. Filtration efficiencies for all colloid sizes at different parameter for the inverse modeling of colloid break- flow rates were calculated from filtration theory. Attachment rates
In this paper, we examine two questions: (1) can the effects of transverse mixing of bacteria in a system constructed to have a permeability discontinuity in the direction parallel to the flow be measured; and (2) if the effects are measurable, can they be calculated using a transverse dispersion coefficient estimated from experiments using a conservative tracer? Pulses of chloride and bacteria were transported downward through heterogeneous columns constructed with a tubule of coarse, quartz sand surrounding an annulus of fine, quartz sand. Pulses of each were also transported through homogeneous columns of the two sands. Doubly peaked breakthrough curves resulted from the columns containing two distinct sand sizes. Modeling of the breakthrough curves was performed taking into account advection, dispersion, deposition, entrainment, and pore-size exclusion. The results revealed that transverse mixing does occur during transport of bacteria through heterogeneous material and that this mixing can be estimated using a conservative tracer.
Several studies have demonstrated that the success of natural and engineered in situ remediation of groundwater pollutants relies on the transverse mixing of reactive chemicals or nutrients along plume margins. Efforts to predict reactions in groundwater generally rely on dispersion coefficients obtained from nonreactive tracer experiments to determine the amount of mixing, but these coefficients may be affected by spreading, which does not contribute to reaction. Mixing is controlled only by molecular diffusion in pore spaces, and the length scale of transverse mixing zones can be small, often on the order of millimeters to centimeters. We use 2D pore-scale simulation to investigate whether classical transverse dispersion coefficients can be applied to model mixing-controlled reactive transport in three different porous media geometries: periodic, random, and macroscopically trending. The lattice-Boltzmann method is used to solve the steady flow field; a finite volume code is used to solve for reactive transport. Nonreactive dispersion coefficients are determined from the transverse spreading of a conservative tracer. Reactive dispersion coefficients are determined by fitting a continuum model which calculates the total product formation as a function of distance to the results from our pore scale simulation. Nonreactive and reactive dispersion coefficients from these simulations are compared. Results indicate that, regardless of the geometrical properties of the media, product formation can be predicted using transverse dispersion coefficients determined from a conservative tracer, provided dispersion coefficients are determined beyond some critical distance downgradient where the plume has spread over a sufficiently large transverse distance compared to the mean grain diameter. This result contrasts with other studies where reactant mixing was controlled by longitudinal hydrodynamic dispersion; in those studies longitudinal dispersion coefficients determined from nonreactive tracer experiments over-estimated the extent of reaction and product formation. Additional work is called for in order to confirm that these findings hold for a wider variety of grain sizes and geometries.
The magnitude of longitudinal dispersivity in a sandy stratified aquifer was investigated using laboratory column and field tracer tests. The field investigations included two-single-well injection-withdrawal tracer tests using 131I and a two-well recirculating withdrawal-injection tracer test using 51Cr-EDTA. The tracer movement within the aquifer was monitored in great detail with multilevel point-sampling instrumentation. A constant value for dispersivity of 0.7 cm was found to be representative (and independent of travel distance) at the scale of an individual level within the aquifer. A dispersivity of 0.035 cm was determined from laboratory column tracer tests as a representative laboratory-scale value for sand from the field site. The scale effect observed between the laboratory dispersivity and the dispersivity from individual levels in the aquifer is caused by the greater inhomogeneity of the aquifer (e.g., laminations within individual layers) and the averaging caused by the groundwater sampling system. Full-aquifer dispersivities of 3 and 9 cm obtained from the single-well tests indicate a scale effect with the value obtained being dependent mainly on the effect of transverse migration of tracer between the layers and the total injection volume. The full-aquifer dispersivity of 50 cm from the two-well test is scale-dependent, controlled by the distance between the injection and withdrawal wells (8 m) and hydraulic conductivity distribution in the aquifer. Scale-dependent full-aquifer dispersivity expressions were derived relating dispersivity to the statistical properties of a stratified geologic system where the hydraulic conductivity distribution is normal, log normal or arbitrary. In the developed expressions, dispersivity is a linear function of the mean travel distance. Proportionality constants ranged from 0.041 to 0.256 for the hydraulic conductivity distributions obtained from the field tracer tests.
A field-scale experiment was conducted at a research site using bacterial viruses (bacteriophage) MS2 and PRD1 as surrogates for human viruses, bromide as a conservative tracer, and tertiary-treated municipal wastewater (recycled water) to investigate the fate and transport of viruses during artificial recharge. Observed virus concentrations were fitted using a mathematical model that simulates virus transport in one-dimensional, homogeneous, water-saturated porous media accounting for virus sorption (or filtration), virus inactivation, and time-dependent source concentration. The fitted time-dependent clogging rate constants were used to estimate the collision efficiencies for bacteriophage MS2 and PRD1 during vertical fully saturated flow. Furthermore, the corresponding time-dependent collision efficiencies for both bacteriophage asymptotically reached similar values at the various sampling locations. These results can be used to develop an optimal management scenario to maximize the amount of recycled water that can be applied to the spreading grounds while still maintaining favorable attachment conditions for virus removal.
An interpretation is offered for the observation that dispersivities increase with scale. Apparent longitudinal dispersivity data from a variety of hydrogeologic settings are assumed to represent a continuous hierarchy of log hydraulic conductivity fields with mutually uncorrelated increments, each field having its own exponential autocovariance, associated integral scale, and variance that increases as a power of scale. Such a hierarchy is shown theoretically to form a self-similar random field with homogeneous increments. Regardless of whether or not the underlying assumption is valid, one can justify interpreting the apparent dispersivities in a manner consistent with a recent quasi-linear theory of non-Fickian and Fickian dispersion in homogeneous media which supports the notion of a self-similar hierarchy a posteriori. The hierarchy is revealed to possess a semivariogram γ(s;) ≊ cs½, where c is a constant, and a fractal dimension D ≊ E + 0.75, where E is the topological dimension of interest. This can be viewed as a universal scaling rule about which large deviations occur due to local influences including the existence of discrete natural scales at which log hydraulic conductivity is statistically homogeneous. As such homogeneity is at best a local phenomenon occurring intermittently over narrow bands of the scale spectrum, one must question the utility of associating medium properties with representative elementary volumes and relying on Fickian models of dispersion over more than relatively narrow scale intervals. Porous and fractured media appear to follow the same idealized scaling rule for both flow and transport, raising a question about the validity of many distinctions commonly drawn between such media. Finally, the data suggest that conditioning transport models through calibration against hydraulic measurements has the effect of filtering out large-scale modes from the hierarchy.
Transport of suspended colloidal particles in porous media often appears
faster relative to molecular-scale tracers under the same flow field in
both laboratory and field studies. A similar phenomenon appears in the
transport of ionic molecules in like-charged fine-grained porous media
and is known as anion exclusion. Here a simplified empirical model of
the travel time density function for excluded tracer arrivals is
developed in terms of the travel time density of an unexcluded tracer in
the same flow field by equating the excluded particle trajectories with
unexcluded particle trajectories modified with ``detours.'' The detours
are defined generally without invoking assumptions about the detoured
trajectory velocities or proximity to pore walls, although such may be
introduced. This conceptual basis provides a representation of the
effects of exclusion on the transport alone, exclusive of reactions
terms, that is consistent with respect to mass balance as well as
particle kinematics. The analysis involves a constitutive ``speedup''
function that tells how travel times of unexcluded particles map to
those of excluded particles. A simple inverse operator that identifies
the speedup function given experimentally observed cumulative arrival
distributions (e.g., breakthrough curves) of excluded and unexcluded
particles in the same flow field is derived. The inverse analysis
requires breakthrough curve data for which the reactions and transport
are separable, as in the case of irreversible kinetic reactions. The
relations developed are exercised in calculating the breakthrough curve
of excluded particles given the breakthrough curve of a neutral and
inert molecular tracer. The method is then applied to recently published
data to determine an empirical speedup function, which is found to be in
this case invariant of solute flow rate.
The purpose of this work was to investigate the effect of solute size on transport in structured porous media. Miscible displacement experiments were performed with tracers of different sizes [i.e., tritiated water (3H2O), pentafluorobenzoate (PFBA), 2,4-dichlorophenoxyacetic acid (2,4-D), and hydroxypropyl-beta-cyclodextrin (HPCD)] in aggregated, stratified, and macroporous media. The breakthrough curves exhibited both early breakthrough and tailing, indicative of nonideal transport in these structure media. Comparison of breakthrough curves revealed that the extent of nonideality (e.g., tailing) was HPCD>PFBA, 2,4-D>3H2O. This behavior is consistent with the impact of solute size on the relative degree of ``nonequilibrium'' experienced by solutes whose transport is constrained by diffusive mass transfer. The capability of the first-order, dual-porosity mobile-immobile model to represent solute transport in these structured systems was evaluated by comparing independently determined values of the input parameters to values obtained by curve fitting of the experimental measurements. The calculated and optimized values compared quite well for the aggregated and stratified media, but not for the macroporous media. Experiments performed with tracers of different size are useful for characterizing the nature of the porous medium through which transport is occurring.
The purpose of this work was to investigate the effect of solute size,
pore water velocity, and intraparticle porosity on dispersion and to
delineate conditions under which it is appropriate to use a
tracer-derived dispersivity to represent the dispersivity of other,
dissimilar-sized solutes. This was accomplished by evaluating the
physical properties of four porous media and the results of several
column experiments performed with nonreactive tracers and these media.
Intraparticle porosities of three sandy media were shown to constitute
negligible fractions of the total porosities. As a result, intraparticle
diffusion did not contribute to dispersive flux. The contribution of
intraparticle diffusion, as well as film diffusion, to solute dispersion
in fine-grained media having small intraparticle porosities will be
negligible for most conditions. In addition, the importance of axial
diffusion decreases as pore water velocity increases. Hydrodynamic
dispersion is the predominant source of dispersion under these
conditions, and, as such, dispersivity is essentially independent of
solute size. Dispersivities determined with a tracer may therefore be
used to represent the dispersivity of other, dissimilar-sized solutes.
Under these conditions, the practice of using a nonreactive tracer such
as 3H2O to characterize the dispersive properties
of a soil column is valid. Solute dispersion in an aggregated soil was
shown to be caused by a combination of hydrodynamic dispersion, film
diffusion, and intraparticle diffusion. In addition, axial diffusion was
shown to be important at low pore water velocities. Hence, the apparent
dispersivities obtained by applying the single-component dispersion
equation to transport in structured soils will generally be a function
of solute size. The use of a tracer-derived dispersivity for solutes of
different sizes would not be valid in this case.
A solute transport model incorporating well-to-well recirculation was developed to facilitate the interpretation of pilot-scale field experiments conducted for the evaluation of a test zone chosen for in situ restoration studies of contaminated aquifers, where flow was induced by recirculation of the extracted fluid. A semianalytical and an approximate analytical solution were derived to the one-dimensional advection-dispersion equation for a semi-infinite medium under local equilibrium conditions, with a flux-type inlet boundary condition accounting for solute recirculation between the extraction-injection well pair. Solutions were obtained by taking Laplace transforms to the equations with respect to time and space. The semianalytical solution is presented in Laplace domain and requires numerical inversion, while the approximate analytical solution is given in terms of a series of simple nested convolution integrals which are easily determined by numerical integration techniques. The applicability of the well-to-well recirculation model is limited to field situations where the actual flow field is one dimensional or where an induced flow field is obtained such that the streamlines in the neighborhood of the monitoring wells are nearly parallel. However, the model is fully applicable to studies of solute transport through packed columns with recirculation under controlled laboratory conditions. The model successfully simulated tracer breakthrough responses at a field solute transport study, where an induced flow field superimposed on the natural gradient within the confined aquifer was created by a well pair with extraction to injection rates of 10: 1.4.
We consider the dispersion and elution of colloids and dissolved nonsorbing tracers within saturated heterogeneous porous media. Since flow path geometry in natural systems is often ill-characterized macroscopic (mean) flow rates and dispersion tensors are utilized in order to account for the sub-model scale microscopic fluctuations in media structure (and the consequent hydrodynamic profile). Even for tracer migration and dispersal this issue is far from settled.Here we consider how colloid and tracer migration phenomena can be treated consistently. Theoretical calculations for model flow geometries yield two quantitative predictions for the transport of free (not yet captured) colloids with reference to a non-sorbing dissolved tracer within the same medium: the average migration velocity of the free colloids is higher than that of the tracer; and that the ratio of the equivalent hydrodynamic dispersion rates of colloids and tracer is dependent only upon properties of the colloids and the porous medium, it is independent of pathlengths and fluid flux, once length scales are large enough.The first of these is well known, since even in simple flow paths free colloids must stay more centre stream. The second, if validated suggests how solute and colloid dispersion may be dealt with consistently in macroscopic migration models. This is crucial since dispersion is usually ill-characterized and unaddressed by the experimental literature. In this paper we present evidence based upon an existing Drigg field injection test for the validity of these predictions.We show that starting from experimental data the fitted dispersion rates of both colloids and non-sorbing tracers increase with the measured elution rates (obeying slightly different rules for tracers and colloids); and that the ratio of colloid and nonsorbing tracer elution rates, and the ratio of colloid and nonsorbing tracer dispersion rates may be dependent upon properties of the colloids and the medium (not the flow regime).It is important to realize that even for unretarded species, an earlier peak in the breakthrough curve does not necessarily correspond to a faster mean elution rate, or vice versa. But rather that a colloid may elute faster but disperse less than an equivalent tracer. Hence its peak may be retarded compared to that of the tracer, even assuming no retardation. Hence one must consider a combination of mean elution rate and mean dispersion rate, and not rely on “peak times” to corroborate chromatographic effects. The importance of this lies in the fact that these processes are not independent and yet upscale differently. Thus realistic estimates of effective colloid dispersion rates should be upscaled in a way consistent with that adopted for tracers within the same system.
The dispersive mixing resulting from complex flow in three-dimensionally heterogeneous porous media is analyzed using stochastic continuum theory. Stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three-dimensional, statistically anisotropic input covariance describing the hydraulic conductivity.-from Authors
The purpose of this work was to investigate the effect of solute size on diffusive-dispersive transport in porous media. Miscible displacement experiments were performed with tracers of various sizes (i.e. tritiated water (3H2O), pentafluorobenzoate (PFBA), and 2,4-dichlorophenoxyacetic acid (2,4-D)) and a homogeneous, nonreactive sand for pore-water velocities varying by three orders of magnitude (70, 7, 0.66, and 0.06 cm h−1). Hydrodynamic dispersion is the predominant source of dispersion for higher pore-water velocities (exceeding 1 cm h−1), and dispersivity is, therefore, essentially independent of solute size. In this case, the practice of using a small-sized tracer, such as 3H2O, to characterize the dispersive properties of a soil is valid. The contribution of axial diffusion becomes significant at pore-water velocities lower than 0.1 cm h−1. At a given velocity below this value, the contribution of axial diffusion is larger for 3H2O, with its larger coefficient of molecular diffusion, than it is for PFBA and 2,4-D. The apparent dispersivities are, therefore, a function of solute size. The use of a tracer-derived dispersivity for solutes of different sizes would not be valid in this case. For systems where diffusion is important, compounds such as PFBA are the preferred tracers for representing advective-dispersive transport of many organic contaminants of interest.
The dispersive mixing resulting from complex flow in three-dimensionally
heterogeneous porous media is analyzed using stochastic continuum
theory. Stochastic solutions of the perturbed steady flow and solute
transport equations are used to construct the macroscopic dispersive
flux and evaluate the resulting macrodispersivity tensor in terms of a
three-dimensional, statistically anisotropic input covariance describing
the hydraulic conductivity. With a statistically isotropic input
covariance, the longitudinal macrodispersivity is convectively
controlled, but the transverse macrodispersivity is proportional to the
local dispersivity and is several orders of magnitude smaller than the
longitudinal term. With an arbitrarily oriented anisotropic conductivity
covariance, all components of the macrodispersivity tensor are
convectively controlled, and the ratio of transverse to longitudinal
dispersivity is of the order of 10-1. In this case the
off-diagonal components of the dispersivity tensor are significant,
being numerically larger than the diagonal transverse terms, and the
transverse dispersion process can be highly anisotropic. Dispersivities
predicted by the stochastic theory are shown to be consistent with
controlled field experiments and Monte Carlo simulations. The theory,
which treats the asymptotic condition of large displacement, indicates
that a classical gradient transport (Fickian) relationship is valid for
large-scale displacements.
A critical review of dispersivity observations from 59 different field
sites was developed by compiling extensive tabulations of information on
aquifer type, hydraulic properties, flow configuration, type of
monitoring network, tracer, method of data interpretation, overall scale
of observation and longitudinal, horizontal transverse and vertical
transverse dispersivities from original sources. This information was
then used to classify the dispersivity data into three reliability
classes. Overall, the data indicate a trend of systematic increase of
the longitudinal dispersivity with observation scale but the trend is
much less clear when the reliability of the data is considered. The
longitudinal dispersivities ranged from 10-2 to
104 m for scales ranging from 10-1 to
105 m, but the largest scale for high reliability data was
only 250 m. When the data are classified according to porous versus
fractured media there does not appear to be any significant difference
between these aquifer types. At a given scale, the longitudinal
dispersivity values are found to range over 2-3 orders of magnitude and
the higher reliability data tend to fall in the lower portion of this
range. It is not appropriate to represent the longitudinal dispersivity
data by a single universal line. The variations in dispersivity reflect
the influence of differing degrees of aquifer heterogeneity at different
sites. The data on transverse dispersivities are more limited but
clearly indicate that vertical transverse dispersivities are typically
an order of magnitude smaller than horizontal transverse dispersivities.
Reanalyses of data from several of the field sites show that improved
interpretations most often lead to smaller dispersivities. Overall, it
is concluded that longitudinal dispersivities in the lower part of the
indicated range are more likely to be realistic for field applications.
Expressions for the macroscopic velocity vector and dispersion tensor for sorbing solute transport in heterogeneous porous formations whose hydrogeologic properties are repeated at intervals were derived via Taylor-Aris-Brenner moment analysis. An idealized three-dimensional porous formation of infinite domain with spatially periodic retardation factor, velocity field, and microdispersion coefficients in all three directions was considered. Sorption was assumed to be governed by a linear equilibrium isotherm under local chemical equilibrium conditions. The analytical expressions presented are based on a perturbation method where all of the spatially periodic parameters employed were assumed to have ``small'' fluctuations. It was shown that the effective velocity vector is given by the volume-averaged interstitial velocity vector divided by the volume-averaged retardation factor, and the effective dispersion dyadic (second-order tensor) is given by the volume-averaged microdispersion dyadic divided by the volume-averaged dimensionless retardation factor plus a dyadic expressing the increase in solute spreading caused by the spatial variability of the parameters.
1] We conducted column-scale experiments to observe the effect of transport velocity and colloid size on early breakthrough of free moving colloids, to relate previous observations at the pore scale to a larger scale. The colloids used in these experiments were bacteriophage MS2 (0.025 mm), and 0.05-and 3-mm spherical polystyrene beads, and were compared with a conservative nonsorbing tracer (KCl). The results show that early breakthrough of colloids increases with colloid size and water velocity, compared with the tracer. These results are in line with our previous observations at the pore scale that indicated that larger colloids are restricted by the size exclusion effect from sampling all paths, and therefore they tend to disperse less and move in the faster streamlines, if they are not filtered out. The measured macroscopic dispersion coefficient decreases with colloid size due to the preferential flow paths, as observed at the pore scale. Dispersivity, typically considered only a property of the medium, is in this case also a function of colloid size, in particular at low Peclet numbers due to the size exclusion effect. Other parameters for colloid transport, such as collector efficiency and colloid filtration rates, were also estimated from the experimental breakthrough curve using a numerical fitting routine. In general, we found that the estimated filtration parameters follow the clean bed filtration model, although with a lower filtration efficiency overall. Citation: Keller, A. A., S. Sirivithayapakorn, and C. V. Chrysikopoulos (2004), Early breakthrough of colloids and bacteriophage MS2 in a water-saturated sand column, Water Resour. Res., 40, W08304, doi:10.1029/2003WR002676.
1] A three-dimensional physical aquifer model was used to study the dissolution of a dense nonaqueous phase liquid (DNAPL) pool. The model aquifer comprised a packing of homogeneous, medium-sized sand and conveyed steady, unidirectional flow. Tetrachloroethene (PCE) pools were introduced within model aquifers atop glass-and clay-lined aquifer bottoms. Transient breakthrough at an interstitial velocity of 7.2 cm/h, and three-dimensional steady state concentration distributions at velocities ranging from 0.4 to 7.2 cm/h were monitored over periods of 59 and 71 days for the glass-and clay-bottom experiments, respectively. Pool-averaged mass transfer coefficients were obtained from the observations via a single-parameter fit using an analytical model formulated with a second type boundary condition to describe pool dissolution [Chrysikopoulos, 1995]. Other model parameters (interstitial velocity, longitudinal and transverse dispersion coefficients, and pool geometry) were estimated independently. Simulated and observed dissolution behavior agreed well, except for locations relatively close to the pool or the glass-bottom plate. Estimated mass transfer coefficients ranged from 0.15 to 0.22 cm/h, increasing weakly with velocity toward a limiting value. Pool mass depletions of 31 and 43% for the glass-and clay-bottom experiments failed to produce observable changes in the plumes and suggested that changes in pool interfacial area over the period of the experiment were negligible. Dimensionless mass transfer behavior was quantified using a modified Sherwood number (Sh*). Observed Sh* values were found to be about 2–3 times greater than values predicted by an existing theoretical mass transfer correlation, and 3–4 times greater than those estimated previously for an ideally configured trichloroethene (TCE) pool (circular and smooth). It appeared that the analytical model's failure to account for pore-scale pool-water interfacial characteristics and larger scale pool shape irregularities biased the Sh* estimates toward greater values.
A unique three-dimensional bench-scale model aquifer is designed and constructed to carry out dense nonaqueous phase liquid (DNAPL) pool dissolution experiments. The model aquifer consists of a rectangular glass tank with internal dimensions 150.0 cm length, 21.6 cm width, and 40.0 cm height. The formation of a well-defined circular pool with a perfectly flat pool-water interface is obtained by a bottom plate with a precise cutout to contain the DNAPL. The aquifer is packed with a well-characterized relatively uniform sand. A conservative tracer is employed for the determination of the longitudinal and transverse aquifer dispersivities. The dissolution studies are conducted using a circular trichloroethylene (TCE) pool. The sorption characteristics of TCE onto the aquifer sand are independently determined from a flow-through column experiment. Steady state dissolved TCE concentrations at specific downstream locations within the aquifer are collected under three different interstitial velocities. An appropriate overall mass transfer coefficient is determined from each data set. The data collected in this study are useful for the validation of numerical and analytical DNAPL pool dissolution models.
Analytical solutions to two mathematical models for virus transport in
one-dimensional homogeneous, saturated porous media are presented, for
constant flux as well as constant concentration boundary conditions,
accounting for first-order inactivation of suspended and adsorbed (or
filtered) viruses with different inactivation constants. Two processes
for virus attachment onto the solid matrix are considered. The first
process is the nonequilibrium reversible adsorption, which is applicable
to viruses behaving as solutes; whereas, the second is the filtration
process, which is suitable for viruses behaving as colloids. Since the
governing transport equations corresponding to each physical process
have identical mathematical forms, only one generalized closed-form
analytical solution is developed by Laplace transform techniques. The
impact of the model parameters on virus transport is examined. An
empirical relation between inactivation rate and subsurface temperature
is employed to investigate the effect of temperature on virus transport.
It is shown that the differences between the two boundary conditions are
minimized at advection-dominated transport conditions.
A solute transport model incorporating well-to-well recirculation was developed to facilitate the interpretation of pilot-scale field experiments conducted for the evaluation of a test zone chosen for in situ restoration studies of contaminated aquifers, where flow was induced by recirculation of the extracted fluid. A semianalytical and an approximate analytical solution were derived to the one-dimensional advection-dispersion equation for a semi-infinite medium under local equilibrium conditions, with a flux-type inlet boundary condition accounting for solute recirculation between the extraction-injection well pair. Solutions were obtained by taking Laplace transforms to the equations with respect to time and space. The semianalytical solution is presented in Laplace domain and requires numerical inversion, while the approximate analytical solution is given in terms of a series of simple nested convolution integrals which are easily determined by numerical integration techniques. The applicability of the well-to-well recirculation model is limited to field situations where the actual flow field is one dimensional or where an induced flow field is obtained such that the streamlines in the neighborhood of the monitoring wells are nearly parallel. However, the model is fully applicable to studies of solute transport through packed columns with recirculation under controlled laboratory conditions. The model successfully simulated tracer breakthrough responses at a field solute transport study, where an induced flow field superimposed on the natural gradient within the confined aquifer was created by a well pair with extraction to injection rates of 10:1.4.
A model is developed to describe the transport of colloids in a saturated fracture with a spatially variable aperture, accounting for colloid deposition onto fracture surfaces under various physicochemical conditions. The fracture plane is partitioned into unit elements with different apertures generated stochastically from a log-normal distribution. The model also accounts for colloid size exclusion from fracture elements with small apertures. Both equilibrium and kinetic colloid deposition onto fracture surfaces are investigated. Colloid surface exclusion is incorporated in the dynamics of kinetic deposition. The impact of deposited colloids on further colloid deposition is described by either a linear or a non-linear blocking function. The resulting system of governing partial differential equations is solved numerically using the fully implicit finite difference method. Model simulations illustrate the presence of preferential colloid transport in the fracture plane. It is shown that size exclusion increases the dispersion of colloids and leads to earlier breakthrough, especially for large-size particles. Furthermore, it is demonstrated that surface exclusion enhances colloid transport, and the assumption of clean-bed media may underestimate liquid-phase colloid concentrations.
A particle tracking model is developed to simulate the transport of variably
sized colloids in a fracture with a spatially variable aperture. The aperture of the fracture
is treated as a lognormally distributed random variable. The spatial fluctuations of the
aperture are described by an exponential autocovariance function. It is assumed that
colloids can sorb onto the fracture walls but may not penetrate the rock matrix. Particle
advection is governed by the local fracture velocity and diffusion by the Stokes-Einstein
equation. Model simulations for various realizations of aperture fluctuations indicate that
lognormal colloid size distributions exhibit greater spreading than monodisperse
suspensions. Both sorption and spreading of the polydisperse colloids increase with
increasing variance in the particle diameter. It is shown that the largest particles are
preferentially transported through the fracture leading to early breakthrough while the
smallest particles are preferentially sorbed. Increasing the variance of the aperture
fluctuations leads to increased tailing for both monodisperse and variably sized colloid
suspensions, while increasing the correlation length of the aperture fluctuations leads to
increased spreading.
This study is focused on Pseudomonas putida bacteria transport in porous media in the
presence of suspended kaolinite clay particles. Experiments were performed with bacteria
and kaolinite particles separately to determine their individual transport characteristics in
water-saturated columns packed with glass beads. The results indicated that the mass
recovery of bacteria and clay particles decreased as the pore water velocity decreased.
Batch experiments were carried out to investigate the attachment of Pseudomonas putida
onto kaolinite particles. The attachment process was adequately described by a Langmuir
isotherm. Finally, bacteria and kaolinite particles were injected simultaneously into a
packed column in order to investigate their cotransport behavior. The experimental data
suggested that the presence of clay particles significantly inhibited the transport of bacteria
in water-saturated porous media. The observed reduction of Pseudomonas putida recovery
in the column outflow was attributed to bacteria attachment onto kaolinite particles, which
were retained onto the solid matrix of the column. A mathematical model was developed to
describe the transport of bacteria in the presence of suspended clay particles in onedimensional
water-saturated porous media. Model simulations were in good agreement with
the experimental results.
This paper presents a novel approach to the representation of pore-scale exclusion processes, based on the truncation of the distribution of local dispersive displacements in a random-walk particle model. This approach increases the mean velocity of colloidal-sized particles relative to inert solute tracers, and decreases the apparent dispersion. An equivalent continuum model, with modified velocity and dispersion parameters, is also derived. Both the particle and the equivalent continuum models are applied to the results of laboratory experiments on bacterial transport in intact cores from a research site near Oyster, Virginia. The particle-based model requires only modest truncation (8% maximum) of the particle velocity distribution function to closely reproduce the significant observed decrease in bacterial arrival times relative to a bromide tracer. The approach provides a conceptually appealing and consistent means of incorporating the exclusion process into groundwater transport models.
h i g h l i g h t s Investigation of MS2 and X174 cotransport with clay colloids in porous media. The mass recovery of viruses and clay colloids decreased with decreasing U. The mass recovery of viruses decreased in the presence of clay colloids. Clay particles can facilitate or hinder virus transport in porous media. XDLVO is important only in the case of clay colloid attachment onto glass beads. g r a p h i c a l a b s t r a c t a b s t r a c t This study examines the cotransport of clay colloids and viruses in laboratory packed columns. Bacterio-phages MS2 and X174 were used as model viruses, kaolinite (kGa-1b) and montmorillonite (STx-1b) as model clay colloids, and glass beads as model packing material. The combined and synergistic effects of clay colloids and pore water velocity on virus transport and retention in porous media were examined at three pore water velocities (0.38, 0.74, and 1.21 cm/min). The results indicated that the mass recovery of viruses and clay colloids decreased as the pore water velocity decreased; whereas, for the cotransport experiments no clear trend was observed. Temporal moments of the breakthrough concentrations sug-gested that the presence of clays significantly influenced virus transport and irreversible deposition onto glass beads. Mass recovery values for both viruses, calculated based on total virus concentration in the effluent, were reduced compared to those in the absence of clays. The transport of both suspended and attached onto suspended clay-particles viruses was retarded, compared to the tracer, only at the highest pore water velocity. Moreover both clay colloids were shown to hinder virus transport at the highest pore water velocity. At the lower velocities MS2 transport was hindered and X174 transport was facilitated with the exception of U = 0.74 cm/min in the presence of KGa-1b. Both MS2 and X174 were attached in greater amounts onto KGa-1b than STx-1b. Also, MS2 exhibited greater affinity than X174 for both clays.
A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this 'macro-transport' equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Peclet number P equals Ua/D//f, where U is the average velocity through the bed, a is the particle radius and D//f is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The results for the longitudinal and transverse effective diffusivities as functions of the Peclet number are summarized in tabular form. Theoretical predictions are compared with experiments in densely packed beds of impermeable particles. Refs.
Coefficients of longitudinal and lateral dispersion were measured for steady uniform laminar flow through an isotropic porous medium. A unique experimental method for measuring lateral dispersion is described. It is found that the ratio of the coefficient of longitudinal dispersion D1 to the coefficient of lateral dispersion D2 is given by $\frac {D_1}{D_2} = \lambda \Re ^n$ where λ and n are dimensionless coefficients dependent upon the pore-system geometry, and [Re - real] is the Reynolds number based on the seepage velocity, the average grain diameter, and the kinematic viscosity.
This study puts under scrutiny the unique relationship between molecular diffusion and electrical conductivity data for Berea, Okesa, Tallant, and Elgin sandstones ranging in permeability from 83 to 2502 md. The experimental setups used for generating the investigated data featured the use of a four-electrode circuit that canceled the effects of contact electrode polarization and a diffusion flow system that allowed on-line calibration and established a stable baseline. The effective molecular diffusion coefficients (De) for these porous media were estimated by matching simulated concentration profiles with measured ones. Tortuosity values were calculated by using molecular diffusivity models and their analogous electrical conductivity models. Tortuosity values calculated from diffusion measurements (using the Brakel and Heertjes model; Int. J. Heat Transfer 1974, 17, 1093) matched reasonably well with those values estimated using Pirson's electrical model (Geologic Well Log Analysis; Gulf Publishing: Houston, TX, 1983). These results indicate the superiority of the latter model over a large number of formation-factor-based models for estimating rock tortuosity. This study helped in the selection of adequate tortuosity models for characterizing sandstone rocks and verified the similarity between electrical conductivity and molecular diffusivity in sandstone rocks.
Es werden verschiedene physikalische Konstanten heterogener Körper aus den Konstanten ihrer homogenen Bestandteile nach einer einheitlichen Methode berechnet. In dieser ersten Arbeit wird die Berechnung der Dielektrizitätskonstanten und der Leitfähigkeiten für Elektrizität und Wärme der Mischkörper aus isotropen Bestandteilen behandelt. Die Genauigkeit der älteren Formeln wird untersucht und die bis jetzt unbekannten Konstanten dieser Formeln werden berechnet. Sodann wird die Theorie geprüft an Messungen der Leitfähigkeit bei heterogenen Metallegierungen und an den DK. von gepreßten Pulvern und Emulsionen; die verschiedenen Formeln werden bestätigt. Bei dieser Anwendung werden einige Widersprüche zwischen früheren Untersuchungen aufgehoben und es wird versucht, einige ungenau bekannte DK. genauer zu bestimmen.
Longitudinal and lateral dispersion coefficients were measured at various axial positions in a packed bed in the Peclet number range from 102 to 104. Three different types of packings were used: uniform size particles, a narrow size distribution, and a wide size distribution. For the case of uniform particles the longitudinal dispersivities were found to be strong functions of position in the bed unless the dispersion length satisfies a constraint dependent on the value of the Peclet number. Generally, the larger the Peclet number, the larger the required length for constant axial dispersivities to be achieved. For the case of the wide size distribution, longitudinal dispersivities were larger than in the uniform particle case, and they required a longer dispersion length to achieve a constant value. This suggests a characteristic length for dispersion larger than the mean hydraulic radius. The lateral dispersivities were found to be insensitive to the distribution of particle sizes or location in the bed.