Spatial variability in compartmental fate modelling

A new approach is presented which is designed to address the spatial heterogeneity of the environment in compartmental mass balance models of chemical fate in the environment. It rests on the assumption of chemical equilibration within one phase despite prevailing environmental heterogeneity. Composite D- and Z-values are derived from sub-unit specific environmental parameters and are used to solve mass balance equations which can be adopted essentially unchanged from existing compartmental fugacity models. With the resulting common fugacity value for each compartment, sub-unit specific concentrations and process rates can be calculated. The approach is illustrated using the QWASI lake model to calculate the fate of hexachlorobenzene in a hypothetical lake sub-divided in four distinct sub-units. The approach allows the subdivision of each compartment in a large number of sub-units with distinct environmental characteristics without substantially increasing model complexity. This is a necessary condition for linking fugacity models to geographical information systems.     

BETR North America: a regionally segmented multimedia contaminant fate model for North America

We present the Berkeley-Trent North American contaminant fate model (BETR North America), a regionally segmented multimedia contaminant fate model based on the fugacity concept. The model is built on a framework that links contaminant fate models of individual regions, and is generally applicable to large, spatially heterogeneous areas. The North American environment is modeled as 24 ecological regions, within each region contaminant fate is described using a 7 compartment multimedia fugacity model including a vertically segmented atmosphere, freshwater, freshwater sediment, soil, coastal water and vegetation compartments. Inter-regional transport of contaminants in the atmosphere, freshwater and coastal water is described using a database of hydrological and meteorological data compiled with Geographical Information Systems (GIS) techniques. Steady-state and dynamic solutions to the 168 mass balance equations that make up the linked model for North America are discussed, and an illustrative case study of toxaphene transport from the southern United States to the Great Lakes Basin is presented. Regionally segmented models such as BETR North America can provide a critical link between evaluative models of long-range transport potential and contaminant concentrations observed in remote regions. The continent-scale mass balance calculated by the model provides a sound basis for evaluating long-range transport potential of organic pollutants, and formulation of continent-scale management and regulatory strategies for chemicals.     

The role of sediments as a source of metals in river catchments

Aquatic sediments are a known source of pollutants, but their impact on the quality of overlying waters is not easily quantified. Sediments are generally considered to behave as a sink for pollutants such as heavy metals in the aquatic environment, frequently acting as a source for their presence in waters, with implications for catchment management. This study aimed to calculate the contribution of sediments to metal levels in overlying waters, helping understand their role as a source of metals in river catchments. An aquivalence mass balance approach was modified to take into account both natural and anthropogenic influences and applied to assess sediment contribution in a reach of the River Yare in the UK. The rates of total metal transport from sediments to overlying waters were estimated to be 29.89 g d(-1) for cadmium (Cd), 1633.39 g d(-1) for lead (Pb), 8.29 g d(-1) for mercury (Hg) and 357.56 g d(-1) for nickel (Ni). The results from the case study demonstrated that sediments could be a significant source of metal emissions in river catchments. The calculations proposed in the paper could be useful in developing strategies for sediment management, not only to improve and/or maintain quality of sediments but also to inform the selection of measures of pollution control for the catchment.     

Extension of coupled multispecies metal transport and speciation (TRANSPEC) model to soil

Atmospheric deposition of metals emitted from mining operations has raised metal concentrations in the surrounding soils. This repository may be remobilized and act as a source of metals to nearby surface aquatic systems. It is important to understand metal dynamics and the impact of various chemistry and fate parameters on metal movement in the soil environment in order to evaluate risk associated with metals in terrestrial ecosystems and accurately establish critical discharge limits that are protective of aquatic biota. Here we extend our previously developed coupled multispecies metal fate-TRANsport and SPECiation/complexation (TRANSPEC) model, which was applicable to surface aquatic systems. The extended TRANSPEC, termed TRANSPEC-II, estimates the partition coefficient, K(d), between the soil-solid and -soluble phases using site-specific data and a semi-empirical regression model obtained from literature. A geochemical model calculates metal and species fractions in the dissolved and colloidal phases of the soil solution. The multispecies fugacity/aquivalence based fate-transport model then estimates inter-media transport rates such as leaching from soil, soil runoff, and water-sediment exchanges of each metal species. The model is illustratively applied to Ni in the Kelly Lake watershed (Sudbury, Ontario, Canada), where several mining operations are located. The model results suggest that the current atmospheric fallout supplies only 4% of Ni removed from soil through soil runoff and leaching. Soil runoff contributes about 20% of Ni entering into Kelly Lake with the rest coming from other sources. Leaching to groundwater, apart from runoff, is also a major loss process for Ni in the soil. A sensitivity analysis indicates that raising soil pH to above 6 may substantially reduce metal runoff and improve water quality of nearby water bodies that are impacted by runoff.     

Mercury cycling and species mass balances in four North American lakes

A mass balance model for mercury based on the fugacity concept is applied to Lake Superior, Lake Michigan, Onondaga Lake and Little Rock Lake to evaluate model performance, analyze cycling of three mercury species groups (elemental, divalent and methyl mercury), and identify important processes that determine the source-to-concentration relationship of the three mercury species groups in these lakes. This model application to four disparate ecosystems is an extension of previous applications of fugacity-based models describing mercury cycling. The model performs satisfactorily following site-specific parameterization, and provides an estimate of minimum rates of species interconversion that compare well with literature. Volatilization and sediment burial are the main processes removing mercury from the lakes, and uncertainty analyses indicate that air-water exchange of elemental mercury and water-sediment exchange of divalent mercury attached to particles are influential in governing mercury concentrations in water. Any new model application or field campaign to quantify mercury cycling in a lake should consider these processes as important.     

Mass balance modelling of contaminants in river basins: a flexible matrix approach

A novel and flexible approach is described for simulating the behaviour of chemicals in river basins. A number (n) of river reaches are defined and their connectivity is described by entries in an n x n matrix. Changes in segmentation can be readily accommodated by altering the matrix entries, without the need for model revision. Two models are described. The simpler QMX-R model only considers advection and an overall loss due to the combined processes of volatilization, net transfer to sediment and degradation. The rate constant for the overall loss is derived from fugacity calculations for a single segment system. The more rigorous QMX-F model performs fugacity calculations for each segment and explicitly includes the processes of advection, evaporation, water-sediment exchange and degradation in both water and sediment. In this way chemical exposure in all compartments (including equilibrium concentrations in biota) can be estimated. Both models are designed to serve as intermediate-complexity exposure assessment tools for river basins with relatively low data requirements. By considering the spatially explicit nature of emission sources and the changes in concentration which occur with transport in the channel system, the approach offers significant advantages over simple one-segment simulations while being more readily applicable than more sophisticated, highly segmented, GIS-based models.     

Using the multiple cell balance method to solve the problem of two-dimensional groundwater flow and contaminant transport with nonequilibrium sorption

The problem of large-scale contamination of groundwater by relatively low levels of organic contaminants is most frequently addressed by extracting and treating the impacted groundwater. This pump-and-treat strategy is often unsuccessful because of difficulties encountered in recovering the contaminants from relatively immobile zones within the porous medium. These zones can exist at the particle scale, as intraparticle or intra-aggregate porosity, and at the larger scales, as low-permeability layers or lenses interspersed in substantially more permeable layers. This work focuses on achieving an efficient numerical solution to a system of groundwater flow and contaminant transport equations that sufficiently captures the dynamics of slow desorption in a two-dimensional porous medium. The conceptual model and governing equations are presented. A numerical method for solving the governing equations, the upstream-weighted, multiple cell balance (UMCB) method, is proposed. The UMCB algorithm has been employed previously for the case of solute transport with equilibrium sorption, and is extended here to the nonequilibrium case. The approach employs a finite-element basis function and a finite-difference local mass balance, and is designed to reduce computational and storage requirements, while minimizing the mass balance error. The computational grid is formed by division of the flow domain into triangular elements. An invented node at the center of each element divides the element into three subtriangular regions. By linking the center of each triangular element and the mid-point of each elemental side, a multiangular region, referred to as an exclusive subdomain, is defined. The discretized system of governing equations is derived from the integral form that describes the mass balance in the exclusive subdomain of each node. The paper details the application of the numerical method, and demonstrates that the method is reasonably accurate and computationally efficient for a two-dimensional domain subject to nonequilibrium sorption.     

Operator-splitting procedures for reactive transport and comparison of mass balance errors

Operator-splitting (OS) techniques are very attractive for numerical modelling of reactive transport, but they induce some errors. Considering reactive mass transport with reversible and irreversible reactions governed by a first-order rate law, we develop analytical solutions of the mass balance for the following operator-splitting schemes: standard sequential non-iterative (SNI), Strang-splitting SNI, standard sequential iterative (SI), extrapolating SI, and symmetric SI approaches. From these analytical solutions, the operator-splitting methods are compared with respect to mass balance errors and convergence rates independently of the techniques used for solving each operator. Dimensionless times, NOS, are defined. They control mass balance errors and convergence rates. The following order in terms of decreasing efficiency is proposed: symmetric SI, Strang-splitting SNI, standard SNI, extrapolating SI and standard SI schemes. The symmetric SI scheme does not induce any operator-splitting errors, the Strang-splitting SNI appears to be O(N2OS) accurate, and the other schemes are first-order accurate.     

Modelling of pharmaceutical residues in Australian sewage by quantities of use and fugacity calculations

A conceptual model is presented for determining which currently prescribed pharmaceutical compounds are most likely to be found in sewage, and for estimating their concentrations, both in raw sewage and after successive stages of secondary sewage treatment. A ranking of the "top-50" pharmaceutical compounds (by total mass dispensed) in Australia over the 1998 calendar year was prepared. Information on the excretion ratios and some metabolites of the pharmaceuticals enabled prediction of the overall rates of excretion into Australian sewage. Mass-balance and fugacity modelling, applied to sewage generation and to a sewage treatment plant, allowed calculation of predicted concentrations of the compounds in raw, primary and secondary treated sewage effluents. Twenty nine of the modelled pharmaceutical residuals were predicted to be present in raw sewage influent at concentrations of 1 microgl(-1) or greater. Twenty of the compounds were predicted to remain in secondary effluent at concentrations of 1 microgl(-1) or greater.     

Multi-substrate, multi-option groundwater transport model

A user friendly, finite-difference groundwater transport model, called “Multi-substrate, Multi-option Groundwater Transport Model (MMGTM)”, has been developed to afford users several options in defining a transport sequence. In addition to advective-dispersive transport, the model incorporates a variety of adsorption and biological decay mechanisms. Adsorption can be simulated for linear, Langmuir, or Freundlich isotherms coupled with equilibrium or non-equilibrium mass transfer. Biological decay can be simulated for first-order or Monod-type approaches, and can be linked to oxygen consumption and transport. Aqueous and sorbed phase decay can be simulated.Further, the transport of two substrates and oxygen can be simulated concurrently and the interaction between them can be described as competitive, diauxic-like or simultaneous. The growth of biomass and its effect as an adsorbent can also be simulated by means of a stoichiometric yield coefficient and a biomass/adsorbent conversion factor. Continuous or pulse input of solute in conjunction with either constant-mass-flux or constant-concentration boundaries can be selected. Menu screens allow the user to configure each problem while parameters can be input individually or called from a separate data file. The input data can be viewed, modified or saved before simulation. Output is visually displayed of the screen as breakthrough and profile curves, while also being saved to an ASCII file on a disk for subsequent processing.     

Environmental impact assessment (EIA): Equilibrium fugacity calculations and worst case approach

A mathematical model UNITRISK which can be used for screening purposes and risk ranking was set up to calculate relative risk values of single chemicals and mixtures of chemicals towards single or mixtures of organisms via contamination of air, water, soil and food dose. The concentration values are calculated by applying the fugacity concept or a dose must be defined. The dose-response is assumed to be linear versus concentration and degradative processes are not considered which is the worst case. The assumption that equilibria between the environmental phases exist is simplifying the model and is also representing the worst case. A mean risk factor is calculated which is 1 if the endpoint values (LC₅₀, LD₅₀, ADI, etc.) are exceeded for the investigated organisms and man.     

A modelling assessment of the atmospheric fate of volatile methyl siloxanes and their reaction products

Volatile methyl siloxanes break down in the atmosphere by reacting with OH radicals to form OH-substituted silanols. As the silanols become increasingly OH substituted they are increasingly likely to be removed from the atmosphere by wet and dry deposition. A simple equilibrium partitioning model was constructed to explore the relative rates of removal by different mechanisms (reaction vs. deposition) for siloxanes and their resultant silanols. A mass balance is calculated for the parent siloxane molecule and for each silanol, characterised by the number of OH substitutions. The model includes the effect of incomplete equilibrium between the vapour, adsorbed and dissolved phases of silanols in the atmosphere using a non-equilibrium factor (epsilon) expressing relative departure from equilibrium. Model results show: (1) maximum vapour-phase concentrations for non-substituted siloxanes and single-OH-substituted silanols; (2) maximum dissolved-phase and adsorbed-phase concentrations for two-OH-substituted silanols; (3) >99% of the original material will be removed in wet deposition and <1% in dry deposition as silanols. For increasing OH-substitutions, the decreasing concentration of precursor molecules (as a consequence of combined removal processes) means that concentrations are negligible, in all phases, beyond three or four substitutions. Predictions were relatively insensitive to assumed departures from phase equilibrium. Predictions of silanol hydrolysis in liquid water droplets suggest that the mix of diol chain lengths in precipitation may not be in thermodynamic equilibrium and will depend on atmospheric residence time and pH.     

Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media

Nonaqueous phase liquid (NAPL) dissolution was studied in three-dimensional (3D) heterogeneous experimental aquifers (25.5 cm x 9 cm x 8.5 cm) with two different longitudinal correlation lengths (2.1 cm and 1.1 cm) and initial spill volumes (22.5 ml and 10.5 ml). Spatial and temporal distributions of NAPL during dissolution were measured using magnetic resonance imaging (MRI). At high NAPL spill volume, average effluent concentrations initially increased during dissolution, as NAPL pools transitioned to NAPL ganglia, and then decreased as the total NAPL-water interfacial area decreased over time. Experimental results were used to test six dissolution models: (i and ii) a one-dimensional (1D) model using either specific NAPL-water interfacial area values estimated from MR images at each time step (i.e., 1D quasi-steady state model), or an empirical mass transfer (Sh') correlation (i.e., 1D transient model), (iii and iv) a multiple analytical source superposition technique (MASST) using either the NAPL distribution determined from MR images at each time step (i.e., MASST steady state model), or the NAPL distribution determined from mass balance calculations (i.e., MASST transient model), (v) an equilibrium streamtube model, and (vi) a 3D grid-scale pool dissolution model (PDM) with a dispersive mass flux term. The 1D quasi-steady state model and 3D PDM captured effluent concentration values most closely, including some concentration fluctuations due to changes in the extent of flow reduction. The 1D transient, MASST steady state and transient, and streamtube models all showed a monotonic decrease in effluent concentration values over time, and the streamtube model was the most computationally efficient. Changes during dissolution of the effective NAPL-water interfacial area estimated from imaging data are similar to changes in effluent concentration values. The 1D steady state model incorporates estimates of the effective NAPL-water interfacial area directly at each time point; the 3D PDM does so indirectly through mass balance and a relative permeability function, which causes reduced water flow through high saturation NAPL regions. Hence, when model accuracy is required, the results indicate that a surrogate of this effective interfacial area is required. Approaches to include this surrogate in the MASST and streamtube models are recommended.     

Estimation of PCDD/F distribution and fluxes in the Venice Lagoon,Italy: combining measurement and modelling approaches

The available experimental information on the occurrence of PCDD/Fs in the Venice Lagoon, Italy, was compiled and used to calculate fugacities for the environmental compartments of sediment, suspended particulate matter (SPM), water and air and then used to estimate fugacity ratios and assess the likely net direction of flux between media. The bottom sediment: SPM fugacity ratios for different PCDD/Fs indicate conditions close to equilibrium, suggestive of the close coupling of SPM with re-suspended sediment. Sediment/water and the sediment/air fugacity ratios suggest that net flux directions vary depending on the congener and the location within the lagoon. Net sediment-water-air movement (i.e. re-mobilisation/volatilisation) is suggested for the lighter congeners from the industrial canals, where the highest PCDD/F concentrations in the lagoon occur. The tendency to volatilise increases with decreasing congener molecular weight. In contrast, net deposition (air-water-sediment) appears to be occurring for the heaviest (hepta- and octa-) substituted PCDD/Fs. OCDF represents a marker of the industrial district of the lagoon, decreasing in concentration and as a fraction of total PCDD/Fs with increasing distance. The fugacity-based quantitative water air sediment interaction (QWASI) mass-balance model was applied to the central part of the lagoon. The key parameters for the determination of the model output, identified by a sensitivity analysis, were: the sediment active depth, the sediment re-suspension and deposition rates, and the total input of PCDD/Fs to the system. The QWASI model also indicates the tendency for the lighter PCDD/Fs to be released from surface sediment to the water column.     

Mercury in the Mediterranean. Part 2: processes and mass balance

Mass balance of contaminants can provide useful information on the processes that influence their concentrations in various environmental compartments. The most important sources, sinks and the equilibrium or non-equilibrium state of the contaminant in individual environmental compartments can also be identified. Using the latest mercury speciation data, the results of numerical models and the results of recent studies on mercury transport and transformation processes in the marine environment, we have re-evaluated the total mercury (HgT) mass balance in the Mediterranean Sea. New calculations have been performed employing three distinct marine layers: the surface layer, the thermocline and the deep sea. New transport mechanisms, deep water formation and density-driven sinking and upwelling, were included in the mass balance calculations. The most recent data have even enabled the calculation of an approximate methylmercury (MeHg) mass balance. HgT is well balanced in the entire Mediterranean, and the discrepancies between inputs and outputs in individual layers do not exceed 20 %. The MeHg balance shows larger discrepancies between gains and losses due to measurement uncertainties and gaps in our knowledge of Hg species transformation processes. Nonetheless, the main sources and sinks of HgT (deposition and evasion) and MeHg (fluxes from sediment, outflow through the Gibraltar Strait) are in accordance with previous studies on mercury in the Mediterranean Basin. Mercury in the Mediterranean fish harvest is the second largest MeHg sink; about 300 kg of this toxic substance is consumed annually with sea food.     

Indoor Ozone Exposures

Indoor and outdoor ozone concentrations were measured from late May through October at three office buildings with very different ventilation rates. The indoor values closely tracked the outdoor values, and, depending on the ventilation rate, were 20 to 80 percent of those outdoors. The Indoor/outdoor data are adequately described with a mass balance model. The model can also be coupled with reported air exchange rates to estimate indoor/outdoor ratios for other structures. The results from this and previous studies indicate that Indoor concentrations are frequently a significant fraction of outdoor values. These observations, and the fact that most people spend greater than 90 percent of their time indoors, indicate that indoor ozone exposure (concentration × time) is greater than outdoor exposure for many people. Relatively Inexpensive strategies exist to reduce indoor ozone levels, and these could be implemented to reduce the public’s total ozone exposure.     

Influence of temporally variable groundwater flow conditions on point measurements and contaminant mass flux estimations

Monitoring of contaminant concentrations, e.g., for the estimation of mass discharge or contaminant degradation rates, often is based on point measurements at observation wells. In addition to the problem, that point measurements may not be spatially representative, a further complication may arise due to the temporal dynamics of groundwater flow, which may cause a concentration measurement to be not temporally representative. This paper presents results from a numerical modeling study focusing on temporal variations of the groundwater flow direction. “Measurements” are obtained from point information representing observation wells installed along control planes using different well frequencies and configurations. Results of the scenario simulations show that temporally variable flow conditions can lead to significant temporal fluctuations of the concentration and thus are a substantial source of uncertainty for point measurements. Temporal variation of point concentration measurements may be as high as the average concentration determined, especially near the plume fringe, even when assuming a homogeneous distribution of the hydraulic conductivity. If a heterogeneous hydraulic conductivity field is present, the concentration variability due to a fluctuating groundwater flow direction varies significantly within the control plane and between the different realizations. Determination of contaminant mass fluxes is also influenced by the temporal variability of the concentration measurement, especially for large spacings of the observation wells. Passive dosimeter sampling is found to be appropriate for evaluating the stationarity of contaminant plumes as well as for estimating average concentrations over time when the plume has fully developed. Representative sampling has to be performed over several periods of groundwater flow fluctuation. For the determination of mass fluxes at heterogeneous sites, however, local fluxes, which may vary considerably along a control plane, have to be accounted for. Here, dosimeter sampling in combination with time integrated local water flux measurements can improve mass flux estimates under dynamic flow conditions.     

Coupling geochemistry with a particle tracking transport model

Coupling geochemistry and transport appears unavoidable since it is rare that either of these two phenomena alone can account for the movement of solutes in groundwater. The chemical model is based on thermodynamic equilibrium. The method used is a Gibbs free energy minimization constrained by mass balances. The model calculates the aqueous speciation, the precipitation and the dissolution of pure minerals or solid solutions. The transport equation is solved by the random walk technique which avoids the problem of numerical dispersion for transport, but may be more time consuming than finite differences or elements if a large number of particles are necessary in order to get a sufficiently “smooth” solution. However, when the chemistry deals with a realistic number of elements (e.g., > 10), the cost of the chemistry computation largely dominates that of transport. Special techniques had to be developed in order to solve problems linked to the conditions present in some of the CEC CHEMVAL tests (boundary with fixed concentrations and very low Péclet numbers). The coupling consists of calculating the exchanges of chemical elements between two populations. The first population is sedentary, constituted by a mesh of fixed cells representing the composition of the solid phase. The other population is nomadic, represented by a set of particles which are advected by groundwater flow. A vector of real numbers is associated with each mobile particle. This vector accounts for the mass of each element dissolved in the moving liquid phase. For this reason, the transport equation is only solved once for the whole set of elements. The main assumptions that were necessary to perform the coupling in a simple way are discussed. Two applications are presented: (1) a verification compared to an analytical solution; and (2) the simulation of a percolation experiment through a sandstone core.     

Contaminant transport in groundwater in the presence of colloids and bacteria: Model development and verification

Colloids and bacteria (microorganisms) naturally exist in groundwater aquifers and can significantly impact contaminant migration rates. A conceptual model is first developed to account for the different physiochemical and biological processes, reaction kinetics, and different transport mechanisms of the combined system (contaminant–colloids–bacteria). All three constituents are assumed to be reactive with the reactions taking place between each constituent and the porous medium and also among the different constituents. A general linear kinetic reaction model is assumed for all reactive processes considered. The mathematical model is represented by fourteen coupled partial differential equations describing mass balance and reaction processes. Two of these equations describe colloid movement and reactions with the porous medium, four equations describe bacterial movement and reactions with colloids and the porous medium, and the remaining eight equations describe contaminant movement and its reactions with bacteria, colloids, and the porous medium. The mass balance equations are numerically solved for two-dimensional groundwater systems using a third-order, total variance-diminishing scheme (TVD) for the advection terms. Due to the complex coupling of the equations, they are solved iteratively each time step until a convergence criterion is met. The model is tested against experimental data and the results are favorable.