On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions

Retention and Transport of Nanoplastics with Different Surface Functionalities in a Sand Filtration System

The efficiency of sand filtration was investigated in terms of the behavior of the nanoplastics (NPLs) with different surface functionalities. The initial condition concentrations of NPLs were varied, and their effects on retention and transport were investigated under a constant flow rate in saturated porous media. The behavior of NPLs in this porous system was discussed by considering Z- average size and zeta (ζ) potential measurements of each effluent. The retention efficiencies of NPLs were ranked as functionalized with amidine [A-PS]+ > with sulfate [S-PS]- > with surfactant-coated amidine [SDS-A-PS]-. The reversibility of the adsorption process was revealed by introducing surfactant into the sand filter system containing adsorbed [A-PS]+ at three different initial state concentration conditions. The deposition behavior on sand grain showed that positively charged NPLs were attached to the quartz surface, and negatively charged NPLs were attached to the edge of the clay minerals, which can be caused by electrical heterogeneities. The homoaggregates made of positively charged NPLs were more compact than those made of negatively charged NPLs and surfactant-coated NPLs. An anti-correlation was revealed, suggesting a connection between the fractal dimension (Df) of NPL aggregates and retention efficiencies. Increased Df values are associated with decreased retention efficiencies.The findings underscore the crucial influence of NPL surface properties in terms of retention efficiency and reversible adsorption in the presence of surfactants in sand filtration systems.

Statement of the Scientific Panel on Plant Protection Products and their Residues (PPR Panel) on the design and conduct of groundwater monitoring studies supporting groundwater exposure assessments of pesticides

Groundwater monitoring is the highest tier in the leaching assessment of plant protection products in the EU. The European Commission requested EFSA for a review by the PPR Panel of the scientific paper of Gimsing et al. (2019) on the design and conduct of groundwater monitoring studies. The Panel concludes that this paper provides many recommendations; however, specific guidance on how to design, conduct and evaluate groundwater monitoring studies for regulatory purposes is missing. The Panel notes that there is no agreed specific protection goal (SPG) at EU level. Also, the SPG has not yet been operationalised in an agreed exposure assessment goal (ExAG). The ExAG describes which groundwater needs to be protected, where and when. Because the design and interpretation of monitoring studies depends on the ExAG, development of harmonised guidance is not yet possible. The development of an agreed ExAG must therefore be given priority. A central question in the design and interpretation of groundwater monitoring studies is that of groundwater vulnerability. Applicants must demonstrate that the selected monitoring sites represent realistic worst-case conditions as specified in the ExAG. Guidance and models are needed to support this step. A prerequisite for the regulatory use of monitoring data is the availability of complete data on the use history of the products containing the respective active substances. Applicants must further demonstrate that monitoring wells are hydrologically connected to the fields where the active substance has been applied. Modelling in combination with (pseudo)tracer experiments would be the preferred option. The Panel concludes that well-conducted monitoring studies provide more realistic exposure assessments and can therefore overrule results from lower tier studies. Groundwater monitoring studies involve a high workload for both regulators and applicants. Standardised procedures and monitoring networks could help to reduce this workload.

Improved Lumped-Parameter and Numerical Modeling of Unsaturated Water Flow and Stable Water Isotopes

Characterizing unsaturated water flow in the subsurface is a requirement for understanding effects of droughts on agricultural production or impacts of climate change on groundwater recharge. By employing an improved lumped-parameter model (LPM) approach that mimics variable flow we have interpreted stable water isotope data (δ¹⁸ O and δ² H), taken over 3 years at a lysimeter site located in Germany. Lysimeter soil cores were characterized by sandy gravel (Ly1) and clayey sandy silt (Ly2), and both lysimeters were vegetated with maize. Results were compared with numerical simulation of unsaturated flow and stable water isotope transport using HYDRUS-1D. In addition, both approaches were extended by the consideration of preferential flow paths. Application of the extended LPM, and thus varying flow and transport parameters, substantially improved the description of stable water isotope observations in lysimeter seepage water. In general, findings obtained from the extended LPM were in good agreement to numerical modeling results. However, observations were more difficult to describe mathematically for Ly2, where the periodicity of seasonal stable water isotope fluctuation in seepage water was not fully met by numerical modeling. Furthermore, an extra isotopic upshift improved simulations for Ly2, probably controlled by stable water isotope exchange processes between mobile soil water and quasi-immobile water within stagnant zones. Finally, although LPM requires less input data compared with numerical models, both approaches achieve comparable decision-support integrity. The extended LPM approach can thus be a powerful tool for soil and groundwater management approaches.

Quantifying microplastic residence times in lakes using mesocosm experiments and transport modelling

The microplastic residence time in lakes is a key factor controlling its uptake by lake organisms. In this work we have, for the first time, conducted a series of microplastic addition experiments in a 12 × 3 m lake mesocosm and traced its transport through the lake water column. This was combined with a 1D physically based random walk model of microplastic transport. Four experiments were conducted using three microplastic size ranges (1-5, 28-48, and 53-63 µm) over one year during thermal stratification and lake turnover. The results showed that the residence time in the water column largely depended on particle size and lake hydrodynamics, although the smallest particles were poorly represented by the model. Residence times in the mesocosm ranged between ∼1 day for the largest particles to 24 days for the small particles during summer. The modeled residence time were similar to the measured values of the 28-48 µm and 53-63 µm particles, but for the smallest particles residence times were calculated to be >200 d. The discrepancy is likely due to aggregation between the small microplastic particles and natural lake particles, which increases the microplastic settling velocity. Aggregation is favored for the small particles due their large surface area to volume ratio. In contrast, density instabilities in the water column during autumn likely led to turbulent convective mixing and rapid microplastic transport within the water column. This work shows that microplastic transport within lakes is complex and not fully understood, especially for the smallest sizes, and involves interactions between physical, physicochemical and biological processes.

A Comparison of Six Transport Models of the MADE-1 Experiment Implemented With Different Types of Hydraulic Data

Six conceptually different transport models were applied to the macrodispersion experiment (MADE)-1 field tracer experiment as a first major attempt for model comparison. The objective was to show that complex mass distributions in heterogeneous aquifers can be predicted without calibration of transport parameters, solely making use of structural and flow data. The models differ in their conceptualization of the heterogeneous aquifer structure, computational complexity, and use of conductivity data obtained from various observation methods (direct push injection logging, DPIL, grain size analysis, pumping tests and flowmeter). They share the same underlying physical transport process of advection by the velocity field solely. Predictive capability is assessed by comparing results to observed longitudinal mass distributions of the MADE-1 experiment. The decreasing mass recovery of the observed plume is attributed to sampling and no physical process like mass transfer is invoked by the models. Measures like peak location and strength are used in comparing the modeled and measured plume mass distribution. Comparison of models reveals that the predictions of the solute plume agree reasonably well with observations, if the models are underlain by a few parameters of close values: mean velocity, a parameter reflecting log-conductivity variability, and a horizontal length scale related to conductivity spatial correlation. The robustness of the results implies that conservative transport models with appropriate conductivity upscaling strategies of various observation data provide reasonable predictions of plumes longitudinal mass distribution, as long as key features are taken into account.

Field Tracer Tests to Evaluate Transport Properties of Tryptophan and Humic Acid in Karst

The monitoring of water quality, especially of karst springs, requires methods for rapidly estimating and quantifying parameters that indicate contamination. In the last few years, fluorescence-based measurements of tryptophan and humic acid have become a promising tool to assess water quality in near real-time. In this study, we conducted comparative tracer tests in a karst experimental site to investigate the transport properties and behavior of tryptophan and humic acid in a natural karst aquifer. These two tracers were compared with the conservative tracer uranine. Fluorescence measurements were conducted with an online field fluorometer and in the laboratory. The obtained breakthrough curves (BTCs) and the modeling results demonstrate that (1) the online field fluorometer is suitable for real-time fluorescence measurements of all three tracers; (2) the transport parameters obtained for uranine, tryptophan, and humic acid are comparable in the fast flow areas of the karst system; (3) the transport velocities of humic acid are slower and the resulting residence times are accordingly higher, compared to uranine and tryptophan, in the slower and longer flow paths; (4) the obtained BTCs reveal additional information about the investigated karst system. As a conclusion, the experiments show that the transport properties of tryptophan are similar to those of uranine while humic acid is partly transported slower and with retardation. These findings allow a better and quantitative interpretation of the results when these substances are used as natural fecal and contamination indicators.

The Complexity of Porous Media Flow Characterized in a Microfluidic Model Based on Confocal Laser Scanning Microscopy and Micro-PIV

Abstract

In this study, the complexity of a steady-state flow through porous media is revealed using confocal laser scanning microscopy (CLSM). Micro-particle image velocimetry (micro-PIV) is applied to construct movies of colloidal particles. The calculated velocity vector fields from images are further utilized to obtain laminar flow streamlines. Fluid flow through a single straight channel is used to confirm that quantitative CLSM measurements can be conducted. Next, the coupling between the flow in a channel and the movement within an intersecting dead-end region is studied. Quantitative CLSM measurements confirm the numerically determined coupling parameter from earlier work of the authors. The fluid flow complexity is demonstrated using a porous medium consisting of a regular grid of pores in contact with a flowing fluid channel. The porous media structure was further used as the simulation domain for numerical modeling. Both the simulation, based on solving Stokes equations, and the experimental data show presence of non-trivial streamline trajectories across the pore structures. In view of the results, we argue that the hydrodynamic mixing is a combination of non-trivial streamline routing and Brownian motion by pore-scale diffusion. The results provide insight into challenges in upscaling hydrodynamic dispersion from pore scale to representative elementary volume (REV) scale. Furthermore, the successful quantitative validation of CLSM-based data from a microfluidic model fed by an electrical syringe pump provided a valuable benchmark for qualitative validation of computer simulation results.

Graphic Abstract

Contaminant occurrence and migration between high- and low-permeability zones in groundwater systems: A review

In recent decades, water quality problems that impact human health, especially groundwater pollution, have been intensely studied, and this has contributed to new ideas and policies around the world such as Low Impact Development (LID) and Superfund legislation. The fundamental to many of these problems is pollutant occurrence and migration in saturated porous media, especially in groundwater. Such environments often contain contrasting zones of high and low permeability with significant differences in hydraulic conductivity (~10^-4 and 10^-8 m/s, respectively). High-permeability zones (HPZs) represent the primary pathways for pollutant transport in groundwater, while low-permeability zones (LPZs) are often diffusion dominated and serve as both sinks and sources (i.e., via back-diffusion) of pollutants over many decades. In this review, concepts and mechanisms of solute source depletion, contaminant accumulation, and back-diffusion in high- and low-permeability systems are presented, and new insights gained from both experimental and numerical studies are analyzed and summarized. We find that effluent monitoring and novel image analysis techniques have been adroitly used to investigate temporal and spatial evolutions of contaminant concentration; simultaneously, mathematical models are constantly upscaled to verify, optimize and extend the experimental data. However, the spatial concentration data during back-diffusion lacks diversity due to the limitations of pollutant species in studies, the microscopic mechanisms controlling pollutant transformation are poorly understood, and the impacts of these reactions on contaminant back-diffusion are rarely considered. Hence, most simulation models have not been adequately validated and are not capable of accurately predicting pollutant fate and cleanup in realistic heterogeneous aquifers. Based on these, some hypotheses and perspectives are mentioned to promote the investigation of contaminant migration in high- and low-permeability systems in groundwater.

Identification and Estimation of Solute Storage and Release in Karst Water Systems, South China

Solute storage and release in groundwater are key processes in solute transport for groundwater remediation and protection. In karst areas where concentrated recharge conditions exist, pollution incidents can easily occur in springs that are hydraulically connected to densely inhabited karst depressions. The intrinsic heterogeneity common in karst media makes modeling solute transport very difficult with great uncertainty. Meanwhile, it is noteworthy that solute storage and release within subsurface conduits and fissures exhibit strong controlling function on pollutant attenuation during underground floods. Consequently, in this paper, we identified and estimated the solute storage and release processes in karst water systems under concentrated recharge conditions. The methodology uses the advection–dispersion method and field tracer tests to characterize solute transport in different flow paths. Two solute transport pathways were established (i.e., linear pathway (direct transport through karst conduits) and dynamic pathway (flow through fissures)). Advection–dispersion equations were used to fit the breakthrough curves in conduit flow, while the volume of solute storage in fissures were calculated by segmenting the best fitting curves from the total breakthrough curves. The results show that, greater recharge flow or stronger dynamic conditions leads to lower solute storage rate, with the storage rate values less than 10% at high water level conditions. In addition, longer residence time was recorded for solute exchange between conduits and fissures at the low water level condition, thereby contributing to a higher solute storage rate of 26% in the dynamic pathway.

Characterizing Water Flow in Vegetated Lysimeters with Stable Water Isotopes and Modeling

We have used stable water isotopes (δ¹⁸ O, δ² H) in combination with lumped-parameter modeling for characterizing unsaturated flow in two lysimeters vegetated with maize. The lysimeters contained undisturbed soil cores dominated by sandy gravel (Ly1) and clayey sandy silt (Ly2). Stable water isotopes were analyzed in precipitation and lysimeter outflow water over about 3 years. The mean transit time of water T and dispersion parameter P_D , obtained from modeling, were higher for the silt soil in Ly2 than for the gravel soil in Ly1 (T of 362 vs. 129 d, P_D of 0.7 vs. 0.12). The consideration of preferential flow (PF) paths could substantially improve the model curve fits, with 13 and 11% contribution of PF for Ly1 and Ly2 as best estimates. Different assumptions were compared to estimate the input function, that is, stable water isotope content in the recharging water. Using the isotopic composition of precipitation as input (no modification) resulted in reasonable model estimations. Best model fits for the entire observation were obtained by weighting the recharging isotopes according to average precipitation within periods of 3 and 6 months, in correspondence to changing vegetation phases and seasonal influences. Input functions that consider actual evapotranspiration could significantly improve modeling at some periods, however, this led to deviations between modeled and observed δ¹⁸ O at other periods. This may indicate the influence of variable flow, so that dividing the whole observation period into hydraulically characteristic sub-periods for lumped-parameter modeling (which implements steady-state flow) is recommended for possible further improvement.

Resilience of groundwater systems in the presence of Bisphenol A under uncertainty

Assessing the health risks associated with emerging contaminants in groundwater systems is a complex issue that has been receiving increased attention in indirect potable reuse applications. Among several emerging contaminants, our study focuses on developing a numerical model that aims to compute the transport characteristics of Bisphenol A (BPA) in a 3D spatially heterogeneous aquifer under uncertainty. Traditional approaches that characterize the health risk of BPA to humans rely on the monotonic dose-response (MDR) relationship with a regulatory dose limit. Recent public health studies indicate that BPA can cause endocrine-related health effects in specific low dose ranges, which requires the consideration of the non-monotonic dose-response (NMDR) model. This work investigates the impact of different BPA DR models (i.e., monotonic vs. non-monotonic) on the resilience of the aquifer against BPA contamination in the presence of hydrogeological heterogeneity. For the resilience estimation, a systematic stochastic methodology linking risk characterization to aquifer resilience is established. Our results show the importance of the interplay between the DR models and aquifer heterogeneity on controlling the uncertainty of the resilience loss R_L (d) at a specified environmentally sensitive target. In the increased level of aquifer heterogeneity, the uncertainty bounds are higher for R_L estimated through the NMDR model as opposed to the MDR model. Moreover, R_L is controlled by η (-), the ratio of the volumetric flow rate at the source zone to the average flow rate at the background aquifer. In a risk management perspective, the consideration of the NMDR model needs to be emphasized due to its impact on the uncertainty of R_L. A critical case is when the land use of a contamination site indicates a large number of the vulnerable population to endocrine-related health effects. In this case, η as an indicator of aquifer resilience can reduce the uncertainty of R_L.

Characterizing the impact of particle behavior at fracture intersections in three-dimensional discrete fracture networks

We characterize the influence of different intersection mixing rules for particle tracking simulations on transport properties through three-dimensional discrete fracture networks. It is too computationally burdensome to explicitly resolve all fluid dynamics within a large three-dimensional fracture network. In discrete fracture network (DFN) models, mass transport at fracture intersections is modeled as a subgrid scale process based on a local Péclet number. The two most common mass transfer mixing rules are (1) complete mixing, where diffusion dominates mass transfer, and (2) streamline routing, where mass follows pathlines through an intersection. Although it is accepted that mixing rules impact local mass transfer through single intersections, the effect of the mixing rule on transport at the fracture network scale is still unresolved. Through the use of explicit particle tracking simulations, we study transport through a quasi-two-dimensional lattice network and a three-dimensional network whose fracture radii follow a truncated power-law distribution. We find that the impact of the mixing rule is a function of the initial particle injection condition, the heterogeneity of the velocity field, and the geometry of the network. Furthermore, our particle tracking simulations show that the mixing rule can particularly impact concentrations on secondary flow pathways. We relate these local differences in concentration to reactive transport and show that streamline routing increases the average mixing rate in DFN simulations.

Analytical Solutions of One-Dimensional Contaminant Transport in Soils with Source Production-Decay

An analytical solution in closed form of the advection-dispersion equation in one-dimensional contaminated soils is proposed in this paper. This is valid for non-conservative solutes with first order reaction, linear equilibrium sorption, and a time-dependent Robin boundary condition. The Robin boundary condition is expressed as a combined production-decay function representing a realistic description of the source release phenomena in time. The proposed model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines, Non Aqueous Phase Liquid pools, or radioactive decay series. The developed analytical model tends towards the known analytical solutions for particular values of the rate constants.

Fate and transport of free and conjugated estrogens during soil passage

Endocrine disrupting chemicals, such as the free estrogens 17β-estradiol (E2), estrone (E1) and the conjugated estrogen estrone-sulfate (E1-3S) are found at low concentration levels in the environment. This is somehow contradictory to the strong sorption and high degradation potentials found in laboratory experiments. In particular, the fate and transport behavior of conjugated estrogens is poorly understood, and the importance of enzymes triggering the transformation pathways has received little attention. To address these deficiencies, the present research uses packed laboratory soil columns with pulse injections of free estrogens, either E2 or E1, or E1-3S, to provide sound evidence of the transformation pathways. It is further shown that (i) transport of free estrogens is subject to strong retardation and degradation, (ii) the transport of conjugated estrogens is less retarded and only to a minor degree affected by degradation, and (iii) arylsulfotransferase is the enzyme triggering the transformation reaction.

An upscaled approach for transport in media with extended tailing due to back-diffusion using analytical and numerical solutions of the advection dispersion equation

The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of systems that exhibit early breakthrough and extended tailing shows that the upscaled mADE model is able to describe the observed behavior with reasonable accuracy given only known physical parameters for the systems without any model calibration.

Impact of non-idealities in gas-tracer tests on the estimation of reaeration, respiration, and photosynthesis rates in streams

Estimating respiration and photosynthesis rates in streams usually requires good knowledge of reaeration at the given locations. For this purpose, gas-tracer tests can be conducted, and reaeration rate coefficients are determined from the decrease in gas concentration along the river stretch. The typical procedure for analysis of such tests is based on simplifying assumptions, as it neglects dispersion altogether and does not consider possible fluctuations and trends in the input signal. We mathematically derive the influence of these non-idealities on estimated reaeration rates and how they are propagated onto the evaluation of aerobic respiration and photosynthesis rates from oxygen monitoring. We apply the approach to field data obtained from a gas-tracer test using propane in a second-order stream in Southwest Germany. We calculate the reaeration rate coefficients accounting for dispersion as well as trends and uncertainty in the input signals and compare them to the standard approach. We show that neglecting dispersion significantly underestimates reaeration, and results between sections cannot be compared if trends in the input signal of the gas tracer are disregarded. Using time series of dissolved oxygen and the various estimates of reaeration, we infer respiration and photosynthesis rates for the same stream section, demonstrating that the bias and uncertainty of reaeration using the different approaches significantly affects the calculation of metabolic rates.

On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow

Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective-dispersive transport model, considered as "virtual truth", with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the "virtual truth" and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.

Modeling solute/contaminant transport in heterogeneous aquifers

A fissured aquifer may be considered as a dense network of fissures separated by low permeability matrix blocks. A conceptual modeling of such a system consists of an infinite number of parallel fractures separated by constant width matrix slabs. While the fissures are assumed to be main flow conduits, the fluid in the porous matrix blocks are considered to be virtually immobile. The mathematical model of the transport of a solute and/or contaminant which assumes a purely convective flow in fissures and diffusion into the matrix blocks consists of two coupled differential equations. An analytical solution of this model for the case of solute entering into the system at a constant concentration has been presented by Skopp and Warrick in Soil Sci Soc Am Proc 38:545-550, 1974. Note however, Skopp and Warrick (Soil Sci Soc Am Proc 38:545-550, 1974) have not considered the additional processes of adsorption and radioactive decay. Unfortunately, their solution had computational limitations as it involved numerical integration of a quite complex expression. Therefore, one had to turn to employing numerical Laplace transform inverters to compute the solutions. This work presents simple real space analytical solutions for the contaminant transport model described above including the adsorption and radioactive decay. The real space solutions have been developed using the method of double Laplace transform and binomial series approximation. An accurate approximate solution has also been presented which converges to the exact solution only after computing three terms in the series full solution. The developed model has been used for 1) assessment of the efficiency of numerical Laplace transform algorithms and 2) investigation of the degree and scale of contamination, and 3) designing remediation schemes for the already contaminated aquifers.

Comparison of unsaturated flow and solute transport through waste rock at two experimental scales using temporal moments and numerical modeling

This study analyzed and compared unsaturated flow response and tracer breakthrough curves from a 10-m high constructed pile experiment (CPE) in the field (Antamina, Peru) and two 0.8m high laboratory-based columns. Similar materials were used at both experimental scales, with the exception of a narrower grain size distribution range for the smaller column tests. Observed results indicate that flow and solute transport regimes between experimental scales were comparable and dominated by flow and solute migration through granular matrix materials. These results are supported by analogous breakthrough curves (normalized to cross-sectional area and flow path length) that suggest observation- or smaller-scale heterogeneities within the porous media have been homogenized or smoothed at the transport-scale, long breakthrough tails, and similar recovered tracer mass fractions (i.e., 0.72-0.80) at the end of the experiment. CPE breakthrough curves do indicate a portion of the fluid flow follows rapid flow paths (open void or film flow); however, this portion accounts for a minor (i.e., ~0.1%) component of the overall flow and transport regime. Flow-corrected temporal moment analysis was used to estimate flow and transport parameter values; however large temporal variations in flow indicate that this method is better suited for conceptualizing transport regimes. In addition, a dual-porosity mobile-immobile (MIM), rate-limited mass-transfer approach was able to simulate tracer breakthrough and the dominant transport regimes from both scales. Dispersivity values used in model simulations reflect a scale-dependency, whereby column values were approximately 2× smaller than those values applied in CPE simulations. The mass-transfer coefficient, for solute transport between mobile and immobile regions, was considered as a model calibration factor. Column experiments are characterized by a larger "mobile to immobile" porosity ratio and a shorter experimental duration and flow path, which supports larger mass-transfer coefficient values (relative to the CPE). These results demonstrate that laboratory-based experiments may be able to mimic flow regimes observed in the field; however, the requirement of scale-dependent dispersivities and mass-transfer coefficients indicates that these tests may be more limited in understanding larger-scale solute transport between regions of different mobility. Nevertheless, the results of this study suggest that the reasonably simplistic modeling approaches utilized in this study may be applied at other field sites to estimate parameters and conceptualize dominant transport processes through highly heterogeneous, unsaturated material.

On the optimization of operating conditions for Taylor dispersion analysis of mixtures

In this work, we investigate the possibility of optimizing the operating conditions, namely mobilizing pressure, capillary length and capillary radius, for performing Taylor dispersion analysis on solutes having hydrodynamic diameters between 1 and 100 nm.

Fractal continuum model for tracer transport in a porous medium

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

Analytical solutions of one-dimensional multispecies reactive transport in a permeable reactive barrier-aquifer system

The permeable reactive barrier (PRB) remediation technology has proven to be more cost-effective than conventional pump-and-treat systems, and has demonstrated the ability to rapidly reduce the concentrations of specific chemicals of concern (COCs) by up to several orders of magnitude in some scenarios. This study derives new steady-state analytical solutions to multispecies reactive transport in a PRB-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway. The solutions in this study can also be applied to other types of dual domain systems with distinct flow and transport properties. The steady-state analytical solutions are shown to be accurate and the numerical program RT3D is selected for comparison. The results of this study are novel in that the solutions provide improved modeling flexibility including: 1) every species can have unique first-order reaction rates and unique retardation factors, and 2) daughter species can be modeled with their individual input concentrations or solely as byproducts of the parent species. The steady-state analytical solutions exhibit a limitation that occurs when interspecies reaction rate factors equal each other, which result in undefined solutions. Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways.

Spatially varying dispersion to model breakthrough curves

Often the water flowing in a karst conduit is a combination of contaminated water entering at a sinkhole and cleaner water released from the limestone matrix. Transport processes in the conduit are controlled by advection, mixing (dilution and dispersion), and retention-release. In this article, a karst transport model considering advection, spatially varying dispersion, and dilution (from matrix seepage) is developed. Two approximate Green's functions are obtained using transformation of variables, respectively, for the initial-value problem and for the boundary-value problem. A numerical example illustrates that mixing associated with strong spatially varying conduit dispersion can cause strong skewness and long tailing in spring breakthrough curves. Comparison of the predicted breakthrough curve against that measured from a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida, shows that the conduit dispersivity can be as large as 400 m. Such a large number is believed to imply strong solute interaction between the conduit and the matrix and/or multiple flow paths in a conduit network. It is concluded that Taylor dispersion is not dominant in transport in a karst conduit, and the complicated retention-release process between mobile- and immobile waters may be described by strong spatially varying conduit dispersion.

Macrodispersion by diverging radial flows in randomly heterogeneous porous media

Radial flow takes place in a heterogeneous porous formation where the transmissivity T is modelled as a stationary random space function (RSF). The steady flow is driven by a given rate, and the mean velocity is radial. A pulse-like of a tracer is injected in the porous formation, and the thin plume spreads due to the fluctuations of the velocity which results a RSF as well. Transport is characterized by the mean front, and by the second spatial moment of the plume. We are primarily interested in tracer macrodispersion modelling. With the neglect of pore-scale dispersion, macrodispersion coefficients are computed at the second order of approximation, without neglecting the head-gradient fluctuations. Although transport is non-ergodic at the source, it is shown that ergodicity is achieved at small distances from the source. This is due to the fact that close to the source local velocities are quite large, and therefore solute particles become uncorrelated very soon. Under ergodic conditions, we compare macrodispersion mechanism in radial flows with that occurring in mean uniform flows. At short distances the spreading effect is highly enhanced by the large variability of the flow field, whereas at large distances transport exhibits a lesser dispersion due to the reduction of velocities. This supports the explanation provided by Indelman and Dagan (1999) to justify why the macrodispersivity is found smaller than that pertaining to mean uniform flows. The model is tested against a tracer transport experiment (Fernàndez-Garcia et al., 2004) by comparing the theoretical and experimental breakthrough curves. The accordance with real data, that is achieved without any fitting to concentration values, strengthens the capability of the proposed model to grasp the main features of such an experiment, the approximations as well as experimental uncertainties notwithstanding.

Estimating reaction rate coefficients within a travel-time modeling framework

A generalized, efficient, and practical approach based on the travel-time modeling framework is developed to estimate in situ reaction rate coefficients for groundwater remediation in heterogeneous aquifers. The required information for this approach can be obtained by conducting tracer tests with injection of a mixture of conservative and reactive tracers and measurements of both breakthrough curves (BTCs). The conservative BTC is used to infer the travel-time distribution from the injection point to the observation point. For advection-dominant reactive transport with well-mixed reactive species and a constant travel-time distribution, the reactive BTC is obtained by integrating the solutions to advective-reactive transport over the entire travel-time distribution, and then is used in optimization to determine the in situ reaction rate coefficients. By directly working on the conservative and reactive BTCs, this approach avoids costly aquifer characterization and improves the estimation for transport in heterogeneous aquifers which may not be sufficiently described by traditional mechanistic transport models with constant transport parameters. Simplified schemes are proposed for reactive transport with zero-, first-, nth-order, and Michaelis-Menten reactions. The proposed approach is validated by a reactive transport case in a two-dimensional synthetic heterogeneous aquifer and a field-scale bioremediation experiment conducted at Oak Ridge, Tennessee. The field application indicates that ethanol degradation for U(VI)-bioremediation is better approximated by zero-order reaction kinetics than first-order reaction kinetics.

Effective non-local reaction kinetics for transport in physically and chemically heterogeneous media

The correct characterization of the effective reactive transport dynamics is an important issue for modeling reactive transport on the Darcy scale, specifically in situations in which reactions are localized, that is when different reactions occur in different portions of the porous medium. Under such conditions the conventional approach of homogenizing only the porous medium chemistry is not appropriate. We consider here reactive transport in a porous medium that is characterized by mass transfer between a mobile and a distribution of immobile regions. Chemical and physical heterogeneities are reflected by distributions of kinetic reaction rate constants and residence times in the immobile zones. We derive an effective reactive transport equation for the mobile solute that is characterized by non-local physical mass transfer and reaction terms. Specifically, chemical heterogeneity is upscaled in terms of a reactive memory function that integrates both chemical and physical heterogeneity. Mass transfer limitations due to physical heterogeneity yield effective kinetic rate coefficients that can be much smaller than the volumetric average of the local scale coefficients. These results help to explain and quantify the often reported discrepancy between observed field reaction rate constants and the ones obtained under well mixed laboratory conditions. Furthermore, these results indicate that transport under physical and chemical heterogeneity cannot be upscaled separately.

Validation of a numerical indicator of microbial contamination for karst springs

Rapid changes in spring water quality in karst areas due to rapid recharge of bacterially contaminated water are a major concern for drinking water suppliers and users. The main objective of this study was to use field experiments with fecal indicators to verify the vulnerability of a karst spring to pathogens, as determined by using a numerical modeling approach. The groundwater modeling was based on linear storage models that can be used to simulate karst water flow. The vulnerability of the karst groundwater is estimated using such models to calculate criteria that influence the likelihood of spring water being affected by microbial contamination. Specifically, the temporal variation in the vulnerability, depending on rainfall events and overall recharge conditions, can be assessed and quantified using the dynamic vulnerability index (DVI). DVI corresponds to the ratio of conduit to diffuse flow contributions to spring discharge. To evaluate model performance with respect to predicted vulnerability, samples from a spring were analyzed for Escherichia coli, enterococci, Clostridium perfringens, and heterotrophic plate count bacteria during and after several rainfall events. DVI was shown to be an indication of the risk of fecal contamination of spring water with sufficient accuracy to be used in drinking water management. We conclude that numerical models are a useful tool for evaluating the vulnerability of karst systems to pathogens under varying recharge conditions.

Estimation of degradation rates by satisfying mass balance at the inlet

Using a steady-state mass conservative solute transport analytical solution that is based on the third-type (or flux-type or Cauchy) source condition, a method is developed to estimate the degradation parameters of solutes in groundwater. Then, the inadequacy of the methods based on the first-type source-based analytical solute transport solution is presented both theoretically and through an example. It is shown that the third-type source analytical solution exactly satisfies the mass balance constraint at the inlet location. It is also shown that the first-type source (or constant source concentration or Dirichlet) solution fails to satisfy the mass balance constraint at the inlet location and the degree of the failure depends on the value of the degradation as well as the flow and solute transport parameters. The error in the first-type source solution is determined with dimensionless parameters by comparing its results with the third-type source solution. Methods for estimating the degradation parameter values that are based on the first-type steady-state solute transport solution may significantly overestimate the degradation parameter values depending on the values of flow and solute transport parameters. It is recommended that the third-type source solution be used in estimating degradation parameters using measured concentrations instead of the first-type source solution.

Enhancement of dilution and transverse reactive mixing in porous media: experiments and model-based interpretation

Transport and natural attenuation of contaminant plumes in groundwater are often controlled by transverse dispersion. The extent of mixing between dissolved reaction partners at the fringe of a plume determines its length and depends strongly on the groundwater flow field. Transient flow conditions as well as the focusing of the flow in high-permeability zones may enhance transverse mixing of dissolved species and, therefore, create favorable conditions for the natural attenuation of contaminant plumes. The aim of the present study is to experimentally test the influence of these processes on solute mixing and to directly compare the results with those under analogous homogeneous and steady-state conditions. We have performed conservative and reactive tracer experiments in a quasi two-dimensional tank filled with glass beads of different sizes. The experiments have been carried out in both homogeneous and heterogeneous porous media under steady-state and transient (i.e. oscillating) flow fields. We used fluorescein as conservative tracer; whereas an alkaline solution (NaOH) was injected into ambient acidic water (HCl) in the reactive experiments. A pH indicator was added to the reacting solutions in order to visualize the emerging plume. We simulated the laboratory experiments with a numerical model and compared the outcomes of the model with the measured concentrations at the outlet of the tank and with the observed tracer plumes. Spatial moments, a newly defined flux-related dilution index, the product mass fluxes and the reaction enhancement factors were calculated to quantify the differences in mixing and reaction extent under various experimental conditions. The results show that flow focusing in heterogeneous porous media significantly enhances transverse mixing and mixing-controlled reactions, whereas temporally changing flow fields appear to be of minor importance.

Modelling of the Cr(VI) transport in typical soils of the North of Portugal

Adsorption of hexavalent chromium [Cr(VI)] onto a loamy sand soil was studied using batch and steady flow tests with contaminant solutions at pH 2, 5 and 7. In all the cases the adsorption of Cr(VI) decreased with increasing pH. The hexavalent chromium speciation and its presence as different oxyanions, according to the solution pH, were the main variables affecting the adsorption process. The influence of the ratio soil/solution concentration was also studied in flow systems at pH 2. Chromium retention increased with the increasing of its concentration in the influent solution. A two-site adsorption model was fitted to the breakthrough curves of hexavalent chromium solutions in order to estimate the Freundlich (k(F)) and Langmuir (S(max)) adsorption parameters, using CXTFIT code. These values were compared to those determined by batch tests and it was concluded that batch tests tended to underestimate these parameters. Nevertheless, they followed the same trend as the parameters determined in opened system, even when the pH of the initial solution was modified.

Analytical solution of two-dimensional solute transport in an aquifer-aquitard system

This study deals with two-dimensional solute transport in an aquifer-aquitard system by maintaining rigorous mass conservation at the aquifer-aquitard interface. Advection, longitudinal dispersion, and transverse vertical dispersion are considered in the aquifer. Vertical advection and diffusion are considered in the aquitards. The first-type and the third-type boundary conditions are considered in the aquifer. This study differs from the commonly used averaged approximation (AA) method that treats the mass flux between the aquifer and aquitard as an averaged volumetric source/sink term in the governing equation of transport in the aquifer. Analytical solutions of concentrations in the aquitards and aquifer and mass transported between the aquifer and upper or lower aquitard are obtained in the Laplace domain, and are subsequently inverted numerically to yield results in the real time domain (the Zhan method). The breakthrough curves (BTCs) and distribution profiles in the aquifer obtained in this study are drastically different from those obtained using the AA method. Comparison of the numerical simulation using the model MT3DMS and the Zhan method indicates that the numerical result differs from that of the Zhan method for an asymmetric case when aquitard advections are at the same direction. The AA method overestimates the mass transported into the upper aquitard when an upward advection exists in the upper aquitard. The mass transported between the aquifer and the aquitard is sensitive to the aquitard Peclet number, but less sensitive to the aquitard diffusion coefficient.

Feedbacks between hydrological heterogeneity and bioremediation induced biogeochemical transformations

For guiding optimal design and interpretation of in situ treatments that strongly perturb subsurface systems, knowledge about the spatial and temporal patterns of mass transport and reaction intensities are important. Here, a procedure was developed and applied to time-lapse concentrations of a conservative tracer (bromide), an injected amendment (acetate) and reactive species (iron(II), uranium(VI) and sulfate) associated with two field scale biostimulation experiments, which were conducted successively at the same field location over two years. The procedure is based on a temporal moment analysis approach that relies on a streamtube approximation. The study shows that biostimulated reactions can be considerably influenced by subsurface hydrological and geochemical heterogeneities: the delivery of bromide and acetate and the intensity of the sulfate reduction is interpreted to be predominantly driven by the hydrological heterogeneity, while the intensity of the iron reduction is interpreted to be primarily controlled by the geochemical heterogeneity. The intensity of the uranium(VI) reduction appears to be impacted by both the hydrological and geochemical heterogeneity. Finally, the study documents the existence of feedbacks between hydrological heterogeneity and remediation-induced biogeochemical transformations at the field scale, particularly the development of precipitates that may cause clogging end flow rerouting.

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.

Simplified contaminant source depletion models as analogs of multiphase simulators

Four simplified dense non-aqueous phase liquid (DNAPL) source depletion models recently introduced in the literature are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. The spill and subsequent dissolution of DNAPLs was simulated in domains having different hydrologic characteristics (variance of the log conductivity field=0.2, 1 and 3) using the multiphase flow and transport simulator UTCHEM. The dissolution profiles were fitted using four analytical models: the equilibrium streamtube model (ESM), the advection dispersion model (ADM), the power law model (PLM) and the Damkohler number model (DaM). All four models, though very different in their conceptualization, include two basic parameters that describe the mean DNAPL mass and the joint variability in the velocity and DNAPL distributions. The variability parameter was observed to be strongly correlated with the variance of the log conductivity field in the ESM and ADM but weakly correlated in the PLM and DaM. The DaM also includes a third parameter that describes the effect of rate-limited dissolution, but here this parameter was held constant as the numerical simulations were found to be insensitive to local-scale mass transfer. All four models were able to emulate the characteristics of the dissolution profiles generated from the complex numerical simulator, but the one-parameter PLM fits were the poorest, especially for the low heterogeneity case.

Solute and colloid transport in karst conduits under low- and high-flow conditions

Solute and colloid transport in karst aquifers under low and high flows was investigated by tracer tests using fluorescent dyes (uranine) and microspheres of the size of pathogenic bacteria (1 microm) and Cryptosporidium cysts (5 microm), which were injected into a cave stream and sampled at a spring 2.5 km away. The two types of microspheres were analyzed using an epifluorescence microscope or a novel fluorescence particle counter, respectively. Uranine breakthrough curves (BTCs) were regular shaped and recovery approached 100%. Microsphere recoveries ranged between 27% and 75%. During low flow, the 1-microm spheres displayed an irregular BTC preceding the uranine peak. Only a very few 5-microm spheres were recovered. During high flow, the 1-microm-sphere BTC was regular and more similar to the uranine curve. BTCs were modeled analytically with CXTFIT using a conventional advection dispersion model (ADM) and a two-region nonequilibrium model (2RNE). The results show that (1) colloids travel at higher velocities than solutes during low flow; (2) colloids and solutes travel at similar velocities during high flow; (3) higher maximum concentrations occur during high flow; and (4) the 2RNE achieves a better fit, while the ADM is more robust, as it requires less parameters.

In situ soil water extraction: a review

The knowledge of the composition and fluxes of vadose zone water is essential for a wide range of scientific and practical fields, including water-use management, pesticide registration, fate of xenobiotics, monitoring of disposal from mining and industries, nutrient management of agricultural and forest ecosystems, ecology, and environmental protection. Nowadays, water and solute flow can be monitored using either in situ methods or minimally invasive geophysical measurements. In situ information, however, is necessary to interpret most geophysical data sets and to determine the chemical composition of seepage water. Therefore, we present a comprehensive review of in situ soil water extraction methods to monitor solute concentration, solute transport, and to calculate mass balances in natural soils. We distinguished six different sampling devices: porous cups, porous plates, capillary wicks, pan lysimeters, resin boxes, and lysimeters. For each of the six sampling devices we discuss the basic principles, the advantages and disadvantages, and limits of data acquisition. We also give decision guidance for the selection of the appropriate sampling system. The choice of material is addressed in terms of potential contamination, filtering, and sorption of the target substances. The information provided in this review will support scientists and professionals in optimizing their experimental set-up for meeting their specific goals.