Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay, linear sorption, and zero-order production. The library is constructed using Green’s function method (GFM) in combination with available solutions. The library covers a wide range of solutions for various conditions. The aquifer can be vertically finite, semi-infinitive or infinitive, and laterally semi-infinitive or infinitive. The geometry of the sources can be of point, line, plane or volumetric body; and the source release can be continuous, instantaneous, or by following a given function over time. Dimensionless forms of the solutions are also proposed. A computer code FlowCAS is developed to calculate the solutions. Calculated results demonstrate the correctness of the presented solutions. The library is widely applicable to solve contaminant transport problems of one- or multiple- dimensions in uniform flow fields.     

Secondary flow within a river bed and contaminant transport

We have developed a numerical method to simulate the transport of non-sorbing contaminants within the sediment layer of a stream and the leaching of these contaminants in the steam. Typical stream bottom surfaces are uneven with triangularly shaped undulation forms. The flow of the water above such triangular surfaces causes external pressure changes that result in a “pumping effect” and a secondary flow within the sediment. The latter causes a significant contaminant advection within the sediment layer. The flow field in the porous sediment layer is obtained by solving numerically Darcy’s equations. The unsteady mass transfer equation is solved by using a finite-difference method with an up-wind scheme. The effects of parameters, such as channel slope, hydraulic head and dispersion, are studied by quantitatively comparing the numerical results of the total mass flow rate from the contaminant source, the concentration front propagation, and the contaminant mass flow rate into the water column. The “pumping effect,” increases the flow in the vertical direction and, thus, enhances the vertical advective mass transport of the contaminant. This bedform-shape induced flow is largely responsible for the mass transfer of contaminants into the water column. The numerical results also show that the mechanical dispersion inside the sediment bed will significantly increase the contaminant mass flow rate from the source.     

Contaminant transport in an unsaturated soil: laboratory tests and numerical simulation model as procedure for parameters evaluation

In this paper, lab tests coupled to a semi-pilot test section are used to derive data for the calibration of a numerical model. The paper is aimed at proposing a set of experiments, which can be used to calibrate a numerical model before using it on defined soils. The complexity of the phenomenon of transport of reactive pollutants in soil has to be faced in the most complete way. The different behaviour of soil after wet/dry cycles with respect to the fluidodynamic characteristics and the importance to consider the local biomass behaviour in case of organic contaminant has been underlined. An optimal approach has to take into account all the different components and here a simple series of experimental procedure is presented. The sensitivity analysis of the numerical model has shown that its results are not so much dependent on the classical numerical aspects (time or space increments) but mainly on a set of parameters related to soil structure which must then be derived through a good calibration.     

New parameterization scheme for effective indices for emissions from road transport

The local to regional processes of chemical transformations, washout and dry deposition cannot be directly resolved in global scale models, they rather need to be parameterized. A suitable way to account for the non-linearity, e.g., in chemical transformation processes, is the use of effective emission indices (EEIs). EEI translate the actual (small scale) emissions into input for global scale models, partially accounting for unresolved processes occurring shortly after the release of the emissions.The emissions from the road traffic have some specifics, because of which the concept of deriving EEI from the interaction of an instantaneous plume with the ambient air is perhaps not so convenient. A new parameterization scheme for the EEI from the road transport is suggested in the present paper, based on few simplifying assumptions and introducing the adjoin equations approach, which makes it possible to achieve unified, not depending on the specific emission pattern, procedure for calculating the EEI from road traffic.     

Flux-based risk management strategy of groundwater pollutions: the CMF approach

A site- and receptor-specific risk management strategy for groundwater pollution based on the measurement of contaminant mass flux is proposed. The approach is useful and compatible with the demands formulated in the European Water Framework Directive, its Groundwater Daughter Directive and the regulations applicable in the EU member states. The proposed CMF method focuses on the following: (1) capture zones, (2) the location of control planes, (3) the definition of the maximum allowed contaminant mass discharge and (4) contaminant mass flux measurements. For every control plane, such a maximum allowed contaminant mass discharge is derived and is crucial for the receptor risk management strategy. The method is demonstrated for a large area of groundwater pollution present in the industrial area of Vilvoorde–Machelen located in Flanders, Belgium.     

Interaction between sorption and biodegradation processes in the contaminant transport

The main goal of this work is to examine in detail the equilibrium and non-equilibrium sorption in a multiple species contaminant transport system undergoing multiplicative Monod biodegradation kinetics, which characterizes a scenario of subsurface contamination by organic contaminants. Mathematically, the problem is given by a nonlinear advection-diffusion-reaction partial differential system coupled by the reaction terms, associated with the biodegradation process. A new operator splitting approach is proposed for treating in a sequential fashion the convective-diffusive and reactive terms. A predictor-multicorrector algorithm with Newton–Raphson and stabilized finite element (streamline-upwind Petrov-Galerkin, SUPG) methods is used in the time and spatial discretizations, respectively. Numerical results illustrate the good applicability of the present approach, corroborating the well-known observation nonlinear physical and biological processes should be inserted in the model that to better predict the contamination scenarios.     

Numerical simulation of benzene transport in shoreline groundwater affected by tides under different conditions

● An approach for assessing the transport of benzene on the beach was proposed. ● The behavior of benzene in the subsurface of the beach was impacted by tide. ● Tidal amplitude influenced the travel speed and the benzene biodegradation. ● Hydraulic conductivity had the impact on plume residence time and biodegradation. ● Plume dispersed and concentration decreased due to high longitudinal dispersivity. The release and transport of benzene in coastal aquifers were investigated in the present study. Numerical simulations were implemented using the SEAM3D, coupled with GMS, to study the behavior of benzene in the subsurface of tidally influenced beaches. The transport and fate of the benzene plume were simulated, considering advection, dispersion, sorption, biodegradation, and dissolution on the beach. Different tide amplitudes, aquifer characteristics, and pollutant release locations were studied. It was found that the tide amplitude, hydraulic conductivity, and longitudinal dispersivity were the primary factors affecting the fate and transport of benzene. The tidal amplitude influenced the transport speed and percentage of biodegradation of benzene plume in the beach. A high tidal range reduced the spreading area and enhanced the rate of benzene biodegradation. Hydraulic conductivity had an impact on plume residence time and the percentage of contaminant biodegradation. Lower hydraulic conductivity induced longer residence time in each beach portion and a higher percentage of biodegradation on the beach. The plume dispersed and the concentration decreased due to high longitudinal dispersivity. The results can be used to support future risk assessment and management for the shorelines impacted by spill and leaking accidents. Modeling the heterogeneous beach aquifer subjected to tides can also be further explored in the future study.     

Ecological degradation and hydraulic dispersion of contaminant in wetland

For the typical case of a pulsed contaminant emission into a free surface wetland flow, a theoretical analysis is presented in this paper for the decay of the depth-averaged concentration under the combined action of ecological degradation and hydraulic dispersion. Based on a first-order reaction model extensively employed in related ecological risk assessment and environmental hydraulic design, the effect of ecological degradation is separated from the hydraulic effect via an exponential transformation for the general formulation for contaminant transport. The speed profile of a fully developed steady flow through the wetland is obtained. A hydraulic dispersion model for the depth-averaged concentration is devised as an extension of Taylor’s classical analysis on dispersion, and corresponding hydraulic dispersivity is obtained by Aris’s method of moments. Analytical solution of depth-averaged concentration is rigorously derived and characterized. For typical pollutant constituents in wastewater emission, the evolution of contaminant cloud in the wetland flow is illustrated by critical length and duration of influenced region with contaminant concentration beyond given environmental standard level, with essential implications for ecological risk assessment and environmental management.     

Long-term effects of application of sewage sludge to soil on composition of herbage with respect to potentially toxic elements

Repeated applications of metal-contaminated sewage sludge can have a drastic effect on soil levels of trace elements and lead to serious toxicity effects in plants. In some cases, land can be rendered sterile.It has been demonstrated that contamination of soils with respect to cadmium, copper, lead, mercury, nickel and zinc is largely irreversible, although there does appear to be a long-term tendency for these metals to become progressively less available to plants over a long period of time. Most national guidelines designed to regulate the disposal of sewage sludge on agricultural land are based on the assumption that relatively rapid fixation of contaminant metals does take place in the soil after sludge application. There is a dearth of information relating to the rates at which potentially toxic-elements commonly present in sewage sludge become immobilised in soils, although it is clear that contaminant boron can be leached down the profile in the short term.Evidence is presented that contamination of top soil can persist for a period of six years after a single application of sludge (150 tonnes dry matter/ha). Over this period, there was little change in available levels of boron, cadmium, copper, lead and zinc in the top soil and the degree of enhancement of these elements in perennial ryegrass grown in the sludge-treated area remained more or less unchanged.     

Solute Transport in Open-Channel Networks in Unsteady Flow Regime

In this paper we propose a robust algorithm to evaluate solute transport in open-channel networks with transient storage under an unsteady flow regime. In the proposed approach, through the integration of junction equations into the model and solving them explicitly, the analysis of solute transport problems in open-channel networks is simplified significantly. Furthermore, when coupled with a transient hydrodynamic open-channel network model for flow simulation, the proposed model can be utilized in the solution of solute transport problems under unsteady flow regimes. In the proposed model, the governing equations are written in a conservative form and are solved using a fractional-step algorithm, which is based on a relaxation and central difference scheme. The proposed algorithm is robust and accurate even for advection dominant cases. A pure advection with discontinuities, a field application and solute transport in an open-channel network in an unsteady flow regime are included, to demonstrate the performance of the proposed algorithm.     

Spatial analysis of chromium in southwestern part of Iran: probabilistic health risk and multivariate global sensitivity analysis

This study was concerned with chromium as a potential carcinogenic contaminant in 64 wells located in five aquifers, southwest of Iran. A probabilistic health risk assessment indicated a high risk to the local residents including adults and children in the study area. A sequential sensitivity analysis and a novel approach known as multivariate global sensitivity analysis using both principal component analysis and B-spline were applied to investigate the behavior of health risk model along time considering four independent input parameters in the risk equation. In this context, based on the results of sensitivity analysis, concentration of chromium in drinking water (C_w) and body weight (W) were the most influential parameters. Random forest (RF) was used as a variable selection method to choose the most influential parameters for the prediction of chromium. Five parameters, among 13 water quality variables, including phosphate, nitrate, fluoride, manganese and iron were selected by RF as the most important parameters for spatial prediction. Hybrid methods of RF and ordinary kriging (RFOK) and RF and inverse distance weighting (RFIDW) were then applied for spatial prediction of Cr using the secondary variables. The RFOK and RFIDW were more efficient than that of ordinary kriging (OK) with respect to a cross-validation algorithm. For instance, in terms of relative root mean squared error, the performance of OK was improved from 31.72 to 23.21 and 23.61 for RFOK and RFIDW, respectively.

     

Calibration and predictive ability analysis of longitudinal solute transport models in mountain streams

The first step in developing travel time and water quality models in streams is to correctly model solute transport mechanisms. In this paper a comparison between two solute transport models is performed. The parameters of the Transient Storage model (TS) and the Aggregated Dead Zone model (ADZ) are estimated using data of thirty seven tracer experiments carried out under different discharges in five mountain streams of Colombian Los Andes. Calibration is performed with the generalized uncertainty estimation method (GLUE) based on Monte-Carlo simulations. Aspects of model parameters identifiability and model parsimony are analyzed and discussed. The TS model with four parameters shows excellent results during calibration but the model parameters present high interaction and poor identifiability. The ADZ model with two independent and clearly identifiable parameters gives sufficiently precise calibration results. As a conclusion, it is stated that the ADZ model with only two parameters is a parsimonious model that is able to represent solute transport mechanisms of advection and longitudinal dispersion in the studied mountain streams. A simple model parameter estimation methodology as a function of discharge is proposed in this work to be used in prediction mode of travel time and solute transport applications along mountain streams.     

Contaminant uptake by fish and the potential for transfer to humans modelled over time

A model is developed that enables coupling of contaminant uptake with the growth dynamics of fish, exploitation, and transfer and fate. Contaminant concentration in fish is a function of the properties of the contaminant, concentrations in their food and water, of their growth dynamics, and of the level of exploitation. Exploitation has a large effect on the size and age structure of exploited populations and, therefore, it also has a large effect on contaminant concentrations and potential rates of transfer to humans. It is essential that the biological component of transfer and fate models describe these aspects of contaminant uptake but at the same time the model must be relatively simple and describe uptake as a function of time rather than age.     

Trihalomethane formation in ozonated and chlorinated surface water

The relatively recent discovery of disinfection by-products has driven the main regulatory organisms to set maximum contaminant levels for certain substances in drinking water. Trihalomethanes can be deemed as the most important group of by-products in chlorinated surface waters. The present work has focused on trihalomethane formation in a full-scale water treatment plant. We studied the effect of several factors, including ozonation, on trihalomethane levels in chlorinated treated water. The treatment scheme also includes an ozonation step. Electronic Publication     

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.     

Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence

Channel confluences at which two channels merge have an important effect on momentum exchange and contaminant diffusion in both natural rivers and artificial canals. In this study, a three-dimensional numerical model, which is based on the Reynolds Averaged Navier–Stokes equations and Reynolds Stress Turbulence model, is applied to simulate and compare flow patterns and contaminant transport processes for different bed morphologies. The results clearly show that the distribution of contaminant concentrations is mainly controlled by the shear layer and two counter-rotating helical cells, which in turn are affected by the discharge ratio and the bed morphology. As the discharge ratio increases, the shear flow moves to the outer bank and the counter-clockwise tributary helical cell caused by flow deflection is enlarged, leading the mixing happens near the outer bank and the mixing layer distorted. The bed morphology can induce shrinkage of the separation zone and increase of the clockwise main channel helical cell, which is initiated by the interaction between the tributary helical cell and the main channel flow and strengthened by the deep scour hole. The bed morphology can also affect the distortion direction of the mixing layer. Both a large discharge ratio and the bed morphology could lead to an increase in mixing intensity.     

Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments

The exchange of dissolved matter between a straight open channel and a series of shallow embayments present at one of its sides is investigated using large eddy simulation (LES). The direct link between the mechanism of mass exchange and the dynamics of coherent structures is demonstrated. It is shown that for the geometrical configuration considered in the present study, the mass exchange process is very non-uniform over the depth in the vicinity of the channel–embayment interface. Most of the contaminant is ejected from the embayments close to the free surface. The amount of contaminant re-entrained into the embayments situated downstream of the one in which contaminant was introduced is quantified. The mass exchange coefficient predicted by LES does not vary significantly with the embayment rank and is in very good agreement with the one predicted by the model proposed by Weitbrecht et al. (J Hydraul Eng 134(2):173–183, 2008) based on the value of a dimensionless morphometric groyne-field parameter. Field experiments were purposely performed in a natural stream with embayments whose length over width ratios were close to the ratio in the LES study. The concentration fields predicted by LES are compared with video-records of colored dye used to visualize the mass exchange in the field experiment. It is shown that, for both LES and the field experiment, the dominant passage frequency of the eddies inside the interfacial mixing layer is well predicted by the analytical model of Sukhodolov and Sukhodolova (in: Cowen et al (eds) Hydraulic measurements & experimental methods. Proceedings of international conference, Lake Placid, USA, pp 172–177, 2007). The model is then used to scale the time in the LES animations and field video-records showing the temporal evolution of the concentration field. The results of the comparison indicate several similarities in the mixing process, despite the differences in the bathymetry and the large difference in the Reynolds number between LES and the field experiment. This proves the usefulness of performing detailed LES and laboratory studies in well-controlled environments to understand mass-exchange processes around river groyne fields.     

Probabilistic prediction of exposures to arsenic contaminated residential soil

Probabilistic modelling using Monte Carlo simulation has been proposed as a more scientifically valid method of estimating soil contaminant exposures than conservative deterministic methods currently used by regulatory agencies. A retrospective application of probabilistic modelling to an exposure scenario involving arsenic-contaminated residential soil near the former ASARCO smelter near Tacoma, Washington is presented. The population of interest is children, aged 2–6 years, living within one-half mile (0.3 km) of the smelter site. Models that predict urinary arsenic levels based on unintentional soil ingestion and inhalation exposure pathways are used. Distributions of exposure variables are based on site-specific data and previous exposure studies. Simulated urinary arsenic levels are compared with data from two biomonitoring studies performed during the late 1980s. Arsenic distributions produced by simulation and biomonitoring are significantly different, and likely contributors to this difference are discussed. However the probabilistic model provides closer estimations of urinary arsenic levels than conservative deterministic models similar to those used by regulatory agencies, and provides useful information regarding parameter uncertainty. Soil ingestion rate was a driving variable in the probabilistic models. Further quantification of soil ingestion rates is warranted.     

Particle sedimentation in the ocean

Annual particle sedimentation is calculated for various ocean regions using an empirical equation based on studies published prior to 1980. Organic carbon sedimentation is predicted from annual phytoplankton production and water depth. Published data show that organic carbon (as weight percent) in sedimented material decreases with depth and independent of depth increases with phytoplankton production. A matrix of values of organic carbon in settled material over depth for three levels of primary production, generally consistent with published data, is derived and used to calculate dry matter sedimentation over depth for various ocean regions. Ranges of values overlap those reported since 1980 except near continental margins. Resuspension and lateral transport of particulate matter increase sedimentation in these regions above rates predicted for the open ocean.