Transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic interactions

Transport of reactive colloids in groundwater may enhance the transport of contaminants in groundwater. Often, the interpretation of results of transport experiments is not a simple task as both reactions of colloids with the solid matrix and reactions of contaminants with the solid matrix and mobile and immobile colloids may be time dependent and nonlinear. Further colloid transport properties may differ from solute transport properties. In this paper, a one-dimensional model for coupled and contaminant in a porous medium (COLTRAP) is presented together with simulation results. Calculated breakthrough curves (BTC's) during contamination and decontamination show systematically the effect of nonlinear and kinetic interactions on contaminant transport in the presence of reactive colloids, and the effect of colloid transport properties that differ from solute transport properties. It is shown that in case of linear kinetic reactions, the rate of exchange of mobile and immobile colloids have a large impact on the shape of BTC's even if the solid matrix is saturated with respect to colloids. BTC's during the contamination and decontamination phase have identical shapes in this case. Moreover, the slow reactions of contaminants and colloids may lead to unretarded breakthrough of contaminants. Independent of reaction rates, nonlinear reactions lead to BTC's that are steeper during contamination than in the linear case. A characteristic aspect of nonlinear sorption is that shapes of BTC's differ during the contamination and decontamination phase. It has been observed that shapes of some of the simulated adsorption and desorption curves are similar as shapes found in experiments reported in literature. This stresses the importance of incorporating both kinetics and nonlinearity in models for coupled colloid and contaminant transport and the capability of COLTRAP to interpret experimental results. Finally, to figure out whether nonlinear processes play a role, it is very important to consider both contamination and decontamination in transport experiments.     

Migration of colloids in discretely fractured porous media: effect of colloidal matrix diffusion

Numerical simulations of colloid transport in discretely fractured porous media were performed to investigate the importance of matrix diffusion of colloids as well as the filtration and remobilization of colloidal particles in both the fractures and porous matrix. To achieve this objective a finite element numerical code entitled COLDIFF was developed. The processes that COLDIFF takes into account include advective-dispersive transport of colloids, filtration and remobilization of colloidal particles in both fractures and porous matrix, and diffusive interactions of colloids between the fractures and porous matrix. Three sets of simulations were conducted to examine the importance of parameters and processes controlling colloid migration. First, a sensitivity analysis was performed using a porous block containing a single fracture to determine the relative importance of various phenomenological coefficients on colloid transport. The primary result of the analysis showed that the porosity of the matrix and the process of colloid filtration in fractures play important roles in controlling colloid migration. Second, simulations were performed to replicate and examine the results of a laboratory column study using a fractured shale saprolite. Results of this analysis showed that the filtration of colloidal particles in the porous matrix can greatly affect the tailing of colloid concentrations after the colloid source was removed. Finally, field-scale simulations were performed to examine the effect of matrix porosity, fracture filtration and fracture remobilization on long-term colloid concentration and migration distance. The field scale simulations indicated that matrix diffusion and fracture filtration can significantly reduce colloid migration distance. Results of all three analyses indicated that in environments where porosity is relatively high and colloidal particles are small enough to diffuse out of fractures, the characteristics of the porous matrix that affect colloid transport become more important than those of the fracture network. Because the properties of the fracture network tend to have greater uncertainty due to difficulties in their measurement relative to those of the porous matrix, prediction uncertainties associated with colloid transport in discretely fractured porous media may be reduced.     

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).     

Preliminary 3-D site-scale studies of radioactive colloid transport in the unsaturated zone at Yucca Mountain,Nevada

The U.S. Department of Energy (DOE) is actively investigating the technical feasibility of permanent disposal of high-level nuclear waste in a repository to be situated in the unsaturated zone (UZ) at Yucca Mountain (YM), Nevada. In this study we investigate, by means of numerical simulation, the transport of radioactive colloids under ambient conditions from the potential repository horizon to the water table. The site hydrology and the effects of the spatial distribution of hydraulic and transport properties in the Yucca Mountain subsurface are considered. The study of migration and retardation of colloids accounts for the complex processes in the unsaturated zone of Yucca Mountain, and includes advection, diffusion, hydrodynamic dispersion, kinetic colloid filtration, colloid straining, and radioactive decay. The results of the study indicate that the most important factors affecting colloid transport are the subsurface geology and site hydrology, i.e., the presence of faults (they dominate and control transport), fractures (the main migration pathways), and the relative distribution of zeolitic and vitric tuffs. The transport of colloids is strongly influenced by their size (as it affects diffusion into the matrix, straining at hydrogeologic unit interfaces, and transport velocity) and by the parameters of the kinetic-filtration model used for the simulations. Arrival times at the water table decrease with an increasing colloid size because of smaller diffusion, increased straining, and higher transport velocities. The importance of diffusion as a retardation mechanism increases with a decreasing colloid size, but appears to be minimal in large colloids.     

Strontium migration in a crystalline medium: effects of the presence of bentonite colloids

The effects of bentonite colloids on strontium migration in fractured crystalline medium were investigated. We analyzed first the transport behaviour of bentonite colloids alone at different flow rates; then we compared the transport behaviour of strontium as solute and of strontium previously adsorbed onto stable bentonite colloids at a water velocity of approximately 7.1·10(-6)m/s-224m/yr. Experiments with bentonite colloids alone showed that - at the lowest water flow rate used in our experiments (7.1·10(-6)m/s) - approximately 70% of the initially injected colloids were retained in the fracture. Nevertheless, the mobile colloidal fraction, moved through the fracture without retardation, at any flow rate. Bentonite colloids deposited over the fracture surface were identified during post-mortem analyses. The breakthrough curve of strontium as a solute, presented a retardation factor, R(f)~6, in agreement with its sorption onto the granite fracture surface. The breakthrough curve of strontium in the presence of bentonite colloids was much more complex, suggesting additional contributions of colloids to strontium transport. A very small fraction of strontium adsorbed on mobile colloids moved un-retarded (R(f)=1) and this fraction was much lower than the expected, considering the quantity of strontium initially adsorbed onto colloids (90%). This behaviour suggests the hypothesis of strontium sorption reversibility from colloids. On the other hand, bentonite colloids retained within the granite fracture played a major role, contributing to a slower strontium transport in comparison with strontium as a solute. This was shown by a clear peak in the breakthrough curve corresponding to a retardation factor of approximately 20.     

Field-scale colloid migration experiments in a granite fracture

An understanding of particle migration in fractured rock, required to assess the potential for colloid-facilitated transport of radionuclides, can best be evaluated when the results of laboratory experiments are demonstrated in the field. Field-scale migration experiments with silica colloids were carried out at AECL's Underground Research Laboratory (URL), located in southern Manitoba, to develop the methodology for large-scale migration experiments and to determine whether colloid transport is possible over distances up to 17 m. In addition, these experiments were designed to evaluate the effects of flow rate and flow path geometry, and to determine whether colloid tracers could be used to provide additional information on subsurface transport to that provided by conservative tracers alone. The colloid migration studies were carried out as part of AECL's Transport Properties in Highly Fractured Rock Experiment, the objective of which was to develop and demonstrate methods for evaluating the solute transport characteristics of zones of highly fractured rock. The experiments were carried out within fracture zone 2 as two-well recirculating, two-well non-recirculating, and convergent flow tests, using injection rates of 5 and 10 1 min⁻¹. Silica colloids with a 20 nm size were used because they are potentially mobile due to their stability, small size and negative surface charge. The shapes of elution profiles for colloids and conservative tracers were similar, demonstrating that colloids can migrate over distances of 17 m. The local region of drawdown towards the URL shaft affected colloid migration and, to a lesser extent, conservative tracer migration within the flow field established by the two-well tracer tests. These results indicate that stable colloids, with sizes as small as 20 nm, have different migration properties from dissolved conservative tracers. - 1997 Atomic Energy of Canada.     

Experimental determination of sorption in fractured flow systems

Fracture "skins" are alteration zones on fracture surfaces created by a variety of biological, chemical, and physical processes. Skins increase surface area, where sorption occurs, compared to the unaltered rock matrix. This study examines the sorption of organic solutes on altered fracture surfaces in an experimental fracture-flow apparatus. Fracture skins containing abundant metal oxides, clays, and organic material from the Breathitt Formation (Kentucky, USA) were collected in a manner such that skin surface integrity was maintained. The samples were reassembled in the lab in a flow-through apparatus that simulated approximately 2.7 m of a linear fracture "conduit." A dual-tracer injection scheme was utilized with the sorbing or reactive tracer compared to a non-reactive tracer (chloride) injected simultaneously. Sorption was assessed from the ratio of the first temporal moments of the breakthrough curves and from the loss of reactive tracer mass and evaluated as a function of flow velocity and solute type. The breakthrough curves suggest dual-flow regimes in the fracture with both sorbing and non-sorbing flow fields. Significant sorption occurs for the reactive components, and sorption increased with decreasing flow rate and decreasing compound solubility. Based on moment analysis, however, there was little retardation of the center of solute mass. These data suggest that non-equilibrium sorption processes dominate and that slow desorption and boundary layer diffusion cause extensive tailing in the breakthrough curves.     

Applied tracer tests in fractured rock: Can we predict natural gradient solute transport more accurately than fracture and matrix parameters?

Applied tracer tests provide a means to estimate aquifer parameters in fractured rock. The traditional approach to analysing these tests has been using a single fracture model to find the parameter values that generate the best fit to the measured breakthrough curve. In many cases, the ultimate aim is to predict solute transport under the natural gradient. Usually, no confidence limits are placed on parameter values and the impact of parameter errors on predictions of solute transport is not discussed. The assumption inherent in this approach is that the parameters determined under forced conditions will enable prediction of solute transport under the natural gradient. This paper considers the parameter and prediction uncertainty that might arise from analysis of breakthrough curves obtained from forced gradient applied tracer tests. By adding noise to an exact solution for transport in a single fracture in a porous matrix we create multiple realisations of an initial breakthrough curve. A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values. The suite of parameters is then used to make predictions of solute transport under lower hydraulic gradients and the uncertainty of estimated parameters and subsequent predictions of solute transport is compared. The results of this study show that predictions of breakthrough curve characteristics (first inflection point time, peak arrival time and peak concentration) for groundwater flow speeds with orders of magnitude smaller than that at which a test is conducted can sometimes be determined even more accurately than the fracture and matrix parameters.     

Dual-domain solute transfer and transport processes: evaluation in batch and transport experiments

Soil macropore networks establish a dual-domain transport scenario in which water and solutes are preferentially channeled through soil macropores while slowly diffusing into and out of the bulk soil matrix. The influence of macropore networks on intra-ped solute diffusion and preferential transport in a soil typical of subsurface-drained croplands in the Midwestern United States was studied in batch- and column-scale experiments. In the batch diffusion studies with soil aggregates, the estimated diffusion radius (length) of the soil aggregates corresponded to the half-spacing of the aggregate fissures, suggesting that the intra-ped fissures reduced the diffusion impedance and preferentially allowed solutes to diffuse into the soil matrix. In the column-scale solute transport experiments, the average diffusion radius (estimated from HYDRUS-2D simulations and a first-order diffusive transfer term) was nearly double that of the batch-scale study. This increase may be attributed to a loss of pore continuity and a compounding of the small diffusion impedance through macropores at the larger scale. The column-scale solute transport experiments also suggest that two preferential networks exist in the soil. At and near soil saturation, a primary network of large macropores (possibly root channels and earthworm burrows) dominate advective transport, causing a high degree of physical and sorption nonequilibrium and simultaneous breakthrough of a nonreactive (bromide) and a reactive (alachlor) solute. As the saturation level decreases, the primary network drains, while transport through smaller macropores (possibly intra-ped features) continues, resulting in a reduced degree of nonequilibrium and separation in the breakthrough curves of bromide and alachlor.     

Analysis of colloid and tracer breakthrough curves

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.     

Flow and transport in unsaturated fractured rock: effects of multiscale heterogeneity of hydrogeologic properties

The heterogeneity of hydrogeologic properties at different scales may have different effects on flow and transport processes in a subsurface system. A model for the unsaturated zone of Yucca Mountain, Nevada, is developed to represent complex heterogeneity at two different scales: (1) layer scale corresponding to geologic layering and (2) local scale. The layer-scale hydrogeologic properties are obtained using inverse modeling, based on the available measurements collected from the Yucca Mountain site. Calibration results show a significant lateral and vertical variability in matrix and fracture properties. Hydrogeologic property distributions in a two-dimensional, vertical cross-section of the site are generated by combining the average layer-scale matrix and fracture properties with local-scale perturbations generated using a stochastic simulation method. The unsaturated water flow and conservative (nonsorbing) tracer transport through the cross-section are simulated for different sets of matrix and fracture property fields. Comparison of simulation results indicates that the local-scale heterogeneity of matrix and fracture properties has a considerable effect on unsaturated flow processes, leading to fast flow paths in fractures and the matrix. These paths shorten the travel time of a conservative tracer from the source (repository) horizon in the unsaturated zone to the water table for small fractions of total released tracer mass. As a result, the local-scale heterogeneity also has a noticeable effect on global tracer transport processes, characterized by an average breakthrough curve at the water table, especially at the early arrival time of tracer mass. However, the effect is not significant at the later time after 20% tracer mass reaches the water table. The simulation results also verify that matrix diffusion plays an important role in overall solute transport processes in the unsaturated zone at Yucca Mountain.     

Colloid transport in unsaturated porous media: the role of water content and ionic strength on particle straining

Packed column and mathematical modeling studies were conducted to explore the influence of water saturation, pore-water ionic strength, and grain size on the transport of latex microspheres (1.1 microm) in porous media. Experiments were carried out under chemically unfavorable conditions for colloid attachment to both solid-water interfaces (SWI) and air-water interfaces (AWI) using negatively charged and hydrophilic colloids and modifying the solution chemistry with a bicarbonate buffer to pH 10. Interaction energy calculations and complementary batch experiments were conducted and demonstrated that partitioning of colloids to the SWI and AWI was insignificant across the range of the ionic strengths considered. The breakthrough curve and final deposition profile were measured in each experiment indicating colloid retention was highly dependent on the suspension ionic strength, water content, and sand grain size. In contrast to conventional filtration theory, most colloids were found deposited close to the column inlet, and hyper-exponential deposition profiles were observed. A mathematical model, accounting for time- and depth-dependent straining, produced a reasonably good fit for both the breakthrough curves and final deposition profiles. Experimental and modeling results suggest that straining--the retention of colloids in low velocity regions of porous media such as grain junctions--was the primary mechanism of colloid retention under both saturated and unsaturated conditions. The extent of stagnant regions of flow within the pore structure is enhanced with decreasing water content, leading to a greater amount of retention. Ionic strength also contributes to straining, because the number of colloids that are held in the secondary energy minimum increases with ionic strength. These weakly associated colloids are prone to be translated to stagnation regions formed at grain-grain junctions, the solid-water-air triple point, and dead-end pores and then becoming trapped.     

A multi-directional tracer test in the fractured Chalk aquifer of E. Yorkshire, UK

A multi-borehole radial tracer test has been conducted in the confined Chalk aquifer of E. Yorkshire, UK. Three different tracer dyes were injected into three injection boreholes and a central borehole, 25 m from the injection boreholes, was pumped at 330 m(3)/d for 8 days. The breakthrough curves show that initial breakthrough and peak times were fairly similar for all dyes but that recoveries varied markedly from 9 to 57%. The breakthrough curves show a steep rise to a peak and long tail, typical of dual porosity aquifers. The breakthrough curves were simulated using a 1D dual porosity model. Model input parameters were constrained to acceptable ranges determined from estimations of matrix porosity and diffusion coefficient, fracture spacing, initial breakthrough times and bulk transmissivity of the aquifer. The model gave equivalent hydraulic apertures for fractures in the range 363-384 microm, dispersivities of 1 to 5 m and matrix block sizes of 6 to 9 cm. Modelling suggests that matrix block size is the primary controlling parameter for solute transport in the aquifer, particularly for recovery. The observed breakthrough curves suggest results from single injection-borehole tracer tests in the Chalk may give initial breakthrough and peak times reasonably representative of the aquifer but that recovery is highly variable and sensitive to injection and abstraction borehole location. Consideration of aquifer heterogeneity suggests that high recoveries may be indicative of a high flow pathway adjacent, but not necessarily connected, to the injection and abstraction boreholes whereas low recoveries may indicate more distributed flow through many fractures of similar aperture.     

Colloid transport in a geochemically heterogeneous porous medium: aquifer tank experiment and modeling

To examine colloid transport in geochemically heterogeneous porous media at a scale comparable to field experiments, we monitored the migration of silica-coated zirconia colloids in a two-dimensional layered porous media containing sand coated to three different extents by ferric oxyhydroxides. Transport of the colloids was measured over 1.65 m and 95 days. Colloid transport was modeled by an advection-dispersion-deposition equation incorporating geochemical heterogeneity and colloid deposition dynamics (blocking). Geochemical heterogeneity was represented as favorable (ferric oxyhydroxide-coated) and unfavorable (uncoated sand) deposition surface areas. Blocking was modeled as random sequential adsorption (RSA). Release of deposited colloids was negligible. The time to colloid breakthrough after the onset of blocking increased with increasing ferric oxyhydroxide-coated surface area. As the ferric oxyhydroxide surface area increased, the concentration of colloids in the breakthrough decreased. Model-fits to the experimental data were made by inverse solutions to determine the fraction of surface area favorable for deposition and the deposition rate coefficients for the favorable (ferric oxyhydroxide-coated) and unfavorable sites. The favorable deposition rate coefficient was also calculated by colloid filtration theory. The model described the time to colloid breakthrough and the blocking effect reasonably well and estimated the favorable surface area fraction very well for the two layers with more than 1% ferric oxyhydroxide coating. If mica edges in the uncoated sand were considered as favorable surface area in addition to the ferric oxyhydroxide coatings, the model predicted the favorable surface area fraction accurately for the layer with less than 1% ferric oxyhydroxide coating.     

Description of sorbing tracers transport in fractured media using the lattice model approach

The transport of contaminants in fractured media is a complex phenomenon with a great environmental impact. It has been described with several models, most of them based on complex partial differential equations, that are difficult to apply when equilibrium and nonequilibrium dynamics are considered in complex boundaries. With the aim of overcoming this limitation, a combination of two lattice Bathnagar, Gross and Krook (BGK) models, derived from the lattice Boltzmann model, is proposed in this paper. The fractured medium is assumed to be a single fissure in a porous rock matrix. The proposed approach permits us to deal with two processes with different length scales: advection-dispersion in the fissure and diffusion within the rock matrix. In addition to the mentioned phenomena, sorption reactions are also considered. The combined model has been tested using the experimental breakthrough curves obtained by Garnier et al. (Garnier, J.M., Crampon, N., Préaux, C., Porel, G., Vreulx, M., 1985. Tra?age par 13C, 2H, I- et uranine dans la nappe de la craie sénonienne en écoulement radial convergent (Béthune, France). J. Hidrol. 78, 379-392.) giving acceptable results. A study on the influence of the lattice BGK models parameters controlling sorption and matrix diffusion on the breakthrough curves shape is included.     

Application of the method of temporal moments to interpret solute transport with sorption and degradation

In this note, we applied the temporal moment solutions of [Das and Kluitenberg, 1996. Soil Sci. Am. J. 60, 1724] for one-dimensional advective-dispersive solute transport with linear equilibrium sorption and first-order degradation for time pulse sources to analyse soil column experimental data. Unlike most other moment solutions, these solutions consider the interplay of degradation and sorption. This permits estimation of a first-order degradation rate constant using the zeroth moment of column breakthrough data, as well as estimation of the retardation factor or sorption distribution coefficient of a degrading solute using the first moment. The method of temporal moment (MOM) formulae was applied to analyse breakthrough data from a laboratory column study of atrazine, hexazinone and rhodamine WT transport in volcanic pumice sand, as well as experimental data from the literature. Transport and degradation parameters obtained using the MOM were compared to parameters obtained by fitting breakthrough data from an advective-dispersive transport model with equilibrium sorption and first-order degradation, using the nonlinear least-square curve-fitting program CXTFIT. The results derived from using the literature data were also compared with estimates reported in the literature using different equilibrium models. The good agreement suggests that the MOM could provide an additional useful means of parameter estimation for transport involving equilibrium sorption and first-order degradation. We found that the MOM fitted breakthrough curves with tailing better than curve fitting. However, the MOM analysis requires complete breakthrough curves and relatively frequent data collection to ensure the accuracy of the moments obtained from the breakthrough data.     

Measurement and analysis of non-Fickian dispersion in heterogeneous porous media

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection-dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a "homogeneous" packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the "homogeneous" one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.     

Analysis of the long-term behavior of solute transport with nonlinear equilibrium sorption using breakthrough curves and temporal moments

We analyzed the long-term behavior of breakthrough curves (BTCs) and temporal moments of a solute subjected to Freundlich equilibrium sorption (s = kc(n)). For one-dimensional transport in a homogeneous porous medium, we derived a power-law relation between travel time, tau, and solute displacement, chi, with the exponent being equal to the Freundlich n exponent. The mean solute velocity, derived from the first time moment, was found to change as tau(n-1). For n values larger than 0.66, the second time moment could be related to c chi(2/n), where c is a constant. An approach based on the use of a critical concentration was developed to estimate the presence of the asymptotic regime in the tail of the BTC. This approach was tested successfully using numerical case studies. One-dimensional numerical simulations with varying values of k, n and initial mass were run to verify the closed form analytical expressions for the large time behavior of temporal moments and the tailing part of breakthrough curves. Good agreement between the slope of the tailing part of log-log transformed BTCs and the predicted slope using asymptotic theory was found. Asymptotic theory in general underestimated the magnitude of the concentration in the tail. The quality of the estimated concentrations in the tail improved for small values of the dispersivity. Experimental BTCs of uranin and benazolin were analyzed in combination with sorption/desorption batch experiments using asymptotic theory. A good agreement between the value of n parameter derived from desorption experiment with benazolin and the value of the n parameter derived from the tail of the BTC was found.     

Contaminant transport in dual-porosity media with dissolved organic matter and bacteria present as mobile colloids

In riverbank filtration, contaminant transport is affected by colloidal particles such as dissolved organic matter (DOM) and bacterial particles. In addition, the subsurface heterogeneity influences the behavior of contaminant transport in riverbank filtration. A mathematical model is developed to describe the contaminant transport in dual-porosity media in the presence of DOM and bacteria as mobile colloids. In the model development, a porous medium is divided into the mobile and immobile regions to consider the presence of ineffective micropores in physically heterogeneous riverbanks. We assume that the contaminant transport in the mobile region is controlled by the advection and dispersion while the contaminant transport in the immobile region occurs due to the molecular diffusion. The contaminant transfer between the mobile and immobile regions takes place by diffusive mass transfer. The mobile region is conceptualized as a four-phase system: two mobile colloidal phases, an aqueous phase, and a solid matrix. The complete set of governing equations is solved numerically with a fully implicit finite difference method. The model results show that in riverbank filtration, the contaminant can migrate further than expected due to the presence of DOM and bacteria. In addition, the contaminant mobility increases further in the presence of the immobile region in aquifers. A sensitivity analysis shows that in dual-porosity media, earlier breakthrough of the contaminant takes place as the volumetric fraction of the mobile region decreases. It is also demonstrated that as the contaminant mass transfer rate coefficient between the mobile and immobile regions increases, the contaminant concentration gradient between the two regions reverses at earlier pore volumes. The contaminant mass transfer coefficient between the mobile and immobile regions mainly controls the tailing effect of the contaminant breakthrough. The contaminant breakthrough curves are sensitive to changes in contaminant adsorption and desorption rate coefficients on DOM and bacteria. In situations where the contaminant is released in the presence of DOM and bacteria in dual-porosity media, the early breakthrough and tailing occur due to the colloidal facilitation and presence of immobile regions.