Analytical solutions of contaminant transport in homogeneous and isotropic aquifer in three-dimensional groundwater flow

Environmental Science and Pollution Research - Modeling three-dimensional contaminant transport released from arbitrary shape source geometries is useful in hydrological and environmental sciences....     

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

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

Modeling of flow and contaminant transport in coupled stream-aquifer systems

This paper describes an integrated approach for modeling flow and contaminant transport in hydraulically connected stream-aquifer systems. The code, FTSTREAM, extended the capabilities of the ground-water model, FTWORK, to incorporate chemical fate and transport in streams. Flow in the stream network is modeled as an unsteady, spatially varying flow, while transport modeling is based on a one-dimensional advection-dispersion equation. In addition to sorption and decay during transport in ground water, the model incorporates volatilization, settling and decay during transport in surface water. The interaction between surface water and ground water is accommodated by a leakage term and is implemented in the model using an iterative Picard-type procedure to ensure mass conservation across the interface between the two systems. The modeling approach is used to simulate contaminant transport in the Mad River, Ohio, which is hydraulically connected to a buried valley aquifer of sand and gravel outwash. The river is a receiving stream in the upstream part of the modeled area. Downstream, heavy pumping from a municipal well field causes the river to become a loosing stream. Induced infiltration from the river is responsible for a considerable portion of the well yield. The flow and transport model, developed for this study, simulates coupling between flow in the aquifer and the river. Hypothetical sources of contamination are introduced at selected locations in the upstream portion of the aquifer. The model is then used to simulate the expected transport in both the aquifer and the stream. A series of simulations elucidates the role of the river in facilitating the transport of the hypothetical contaminants in ground water and surface water. Effect of sorption, retardation and volatilization on contaminant transport is also examined for the case of the volatile organic compounds.     

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.     

Application of first-order reliability method to modelling the fate and transport of benzene in groundwater

Parameter uncertainty plays a significant role in decision making regarding groundwater contamination and remediation, especially for non-conservative chemicals. This paper presents a probabilistic screening model to accommodate parameter uncertainty in the aquifer media, and physical–chemical parameters, using the first-order reliability method (FORM). The application of the developed model is illustrated on transport of benzene in groundwater. The results matched those obtained using the Monte Carlo simulation method, with a smaller number of functional evaluations. Parametric studies were conducted to estimate the effect of various parameters on the results.     

Soil column experiments used as a means to assess transport, sorption, and biodegradation of pesticides in groundwater

Soil column experiments are used to investigate the fate of three pesticides of high, intermediate, and low solubility in groundwater: N- phosphonomethyl glycine (glyphosate); O,O-diethyl-S-[(ethylthio)methyl]phosphorodithioate (phorate); (2,4-dichlorophenoxy)acetic acid (2,4-D). Feed solutions are prepared by adding each pesticide (100 mg/L glyphosate, 50 micro g/L phorate, 50 mg/L 2,4-D) along with conservative tracer, KBr, in synthetic groundwater. The concentration of the pesticides in effluents is detected by ion chromatography (glyphosate, 2,4-D) and GC-FID (phorate). The Br(-) breakthrough curves are employed to estimate the dispersion coefficient and mean pore velocity in each column. Solute transport and reactive models accounting for equilibrium/non-equilibrium sorption and biodegradation are coupled with inverse modeling numerical codes to estimate the kinetic parameters for all pesticides.     

Soil column experiments used as a means to assess transport,sorption, and biodegradation of pesticides in groundwater

Soil column experiments are used to investigate the fate of three pesticides of high, intermediate, and low solubility in groundwater: N- phosphonomethyl glycine (glyphosate); O,O-diethyl-S-[(ethylthio)methyl]phosphorodithioate (phorate); (2,4-dichlorophenoxy)acetic acid (2,4-D). Feed solutions are prepared by adding each pesticide (100 mg/L glyphosate, 50 μ g/L phorate, 50 mg/L 2,4-D) along with conservative tracer, KBr, in synthetic groundwater. The concentration of the pesticides in effluents is detected by ion chromatography (glyphosate, 2,4-D) and GC-FID (phorate). The Br^? breakthrough curves are employed to estimate the dispersion coefficient and mean pore velocity in each column. Solute transport and reactive models accounting for equilibrium/non-equilibrium sorption and biodegradation are coupled with inverse modeling numerical codes to estimate the kinetic parameters for all pesticides.     

The effect of local-scale physical heterogeneity and nonlinear,rate-limited sorption/desorption on contaminant transport in porous media

Nonideal transport of contaminants in porous media has often been observed in laboratory characterization studies. It has long been recognized that multiple processes associated with both physical and chemical factors can contribute to this nonideal transport behavior. To fully understand system behavior, it is important to determine the relative contributions of these multiple factors when conducting contaminant transport and fate studies. In this study, the relative contribution of physical-heterogeneity-related processes versus those of nonlinear, rate-limited sorption/desorption to the observed nonideal transport of trichloroethene in an undisturbed aquifer core was determined through a series of miscible-displacement experiments. The results of experiments conducted using the undisturbed core, collected from a Superfund site in Tucson, AZ, were compared to those obtained from experiments conducted using the same aquifer material packed homogeneously. The results indicate that both physical and chemical factors, specifically preferential flow and associated rate-limited diffusive mass-transfer and rate-limited sorption/desorption, respectively, contributed to the nonideal behavior observed for trichloroethene transport in the undisturbed core. A successful prediction of trichloroethene transport in the undisturbed core was made employing a mathematical model incorporating multiple sources of nonideal transport, using independently determined model parameters to account for the multiple factors contributing to the nonideal transport behavior. The simulation results indicate that local-scale physical heterogeneity controlled the nonideal transport behavior of trichloroethene in the undisturbed core, and that nonlinear, rate-limited sorption/desorption were of secondary importance.     

The effect of surface-active solutes on water flow and contaminant transport in variably saturated porous media with capillary fringe effects

Organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. We used an intermediate-scale 2D flow cell (2.44 x 1.53 x 0.108 m) packed with a fine silica sand to investigate surfactant-induced flow perturbations. Surfactant solution (7% 1-butanol and dye tracer) was applied at a constant rate at a point source located on the soil surface above an unconfined synthetic aquifer with ambient groundwater flow and a capillary fringe of approximately 55 cm. A glass plate allowed for visual flow and transport observations. Thirty instrumentation stations consist of time domain reflectometry probes and tensiometers measured in-situ moisture content and pressure head, respectively. As surfactant solution was applied at the point source, a transient flow perturbation associated with the advance of the surfactant solution was observed. Above the top of the capillary fringe the advance of the surfactant solution caused a visible drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe below the point source because the air-entry pressure decreased in proportion to the decrease in surface tension caused by the surfactant. Eventually, a new capillary fringe height was established. The height of the depressed capillary fringe was proportional to height of the initial capillary fringe multiplied by the relative surface tension of the surfactant solution. The horizontal transport of surfactant in the depressed capillary fringe, driven primarily by the ambient groundwater flow, caused the propagation of a wedge-shaped drying front in the downgradient direction. Comparison of dye transport during the surfactant experiment to dye transport in an experiment without surfactant indicated that because surfactant-induced drainage decreased the storage capacity of the vadose zone, the dye breakthrough time to the water table was more than twice as fast when the contaminant solution contained surfactant. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time suggest the importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or systems, where surfactants are used for remediation of the vadose zone or unconfined aquifers.     

Effect of cell physicochemical characteristics and motility on bacterial transport in groundwater

The influence of physicochemical characteristics and motility on bacterial transport in groundwater were examined in flow-through columns. Four strains of bacteria isolated from a crystalline rock groundwater system were investigated, with carboxylate-modified and amidine-modified latex microspheres and bromide as reference tracers. The bacterial isolates included a gram-positive rod (ML1), a gram-negative motile rod (ML2), a nonmotile mutant of ML2 (ML2m), and a gram-positive coccoid (ML3). Experiments were repeated at two flow velocities, in a glass column packed with glass beads, and in another packed with iron-oxyhydroxide coated glass beads. Bacteria breakthrough curves were interpreted using a transport equation that incorporates a sorption model from microscopic observation of bacterial deposition in flow-cell experiments. The model predicts that bacterial desorption rate will decrease exponentially with the amount of time the cell is attached to the solid surface. Desorption kinetics appeared to influence transport at the lower flow rate, but were not discernable at the higher flow rate. Iron-oxyhydroxide coatings had a lower-than-expected effect on bacterial breakthrough and no effect on the microsphere recovery in the column experiments. Cell wall type and shape also had minor effects on breakthrough. Motility tended to increase the adsorption rate, and decrease the desorption rate. The transport model predicts that at field scale, desorption rate kinetics may be important to the prediction of bacteria transport rates.     

Variability of aquifer sorption properties in a field experiment on groundwater transport of organic solutes: Methods and preliminary results

Methods to characterize the organic solute sorption distribution coefficient, organic carbon content, and specific surface area of aquifer solids from the site of a field experiment on solute transport in groundwater were refined for application to small subsamples of 10-cm depth increments taken from 5-cm diameter cores. Initial results indicate that the average sorption characteristics of the Borden aquifer do not vary appreciably along the trajectory of the solute plumes. However, the sorption distribution coefficient of tetrachloroethylene varied over nearly an order of magnitude among 10-cm depth increments in one core sample. Preliminary evidence suggests that the sorption distribution coefficients for four halogenated organic solutes vary proportionally among core strata. However, the distribution coefficients for sorption of tetrachloroethylene on various depth increments are not well correlated with either organic carbon content or specific surface area, suggesting that as yet unidentified mineral phases may play a significant role in sorption of such solutes by the sandy aquifer solids.     

Simulating the fate and transport of TCE from groundwater to indoor air

This work provides an exploratory analysis on the relative importance of various factors controlling the fate and transport of volatile organic contaminants (in this case, TCE) from a DNAPL source zone located below the water table and into the indoor air. The analysis is conducted using the multi-phase compositional model CompFlow Bio, with the base scenario problem geometry reminiscent of a field experiment conducted by Rivett [Rivett, M.O., (1995), Soil–gas signatures from volatile chlorinated solvents: Borden field experiments. Groundwater, 33(1), 84–98.] at the Borden aquifer where groundwater was observed to transport a contaminant plume a substantial distance without vertical mass transport of the contaminant across the capillary fringe and into the vadose zone. Results for the base scenario model indicate that the structure of the permeability field was largely responsible for deflecting the groundwater plume upward towards the capillary fringe, permitting aqueous phase diffusion to transport the TCE into the vadose zone. Alternative permeability realizations, generated as part of a Monte Carlo simulation process, at times deflected the groundwater plume downwards causing the extended thickness of the saturated zone to insulate the vadose zone from exposure to the TCE by upward diffusive transport. Comparison of attenuation coefficients calculated using the CompFlow Bio and Johnson and Ettinger [Johnson, P.C. and Ettinger, R.A., (1991), Heuristic model for predicting the intrusion rate of contaminant vapors into buildings. Environmental Science and Technology, 25, 1445–1452.] heuristic model exhibited fortuitous agreement for the base scenario problem geometry, with this agreement diverging for the alternative permeability realizations as well as when parameters such as the foundation slab fracture aperture, the indoor air pressure drop, the capillary fringe thickness, and the infiltration rate were varied over typical ranges.     

Laboratory analog and numerical study of groundwater flow and solute transport in a karst aquifer with conduit and matrix domains

New mathematical and laboratory methods have been developed for simulating groundwater flow and solute transport in karst aquifers having conduits imbedded in a porous medium, such as limestone. The Stokes equations are used to model the flow in the conduits and the Darcy equation is used for the flow in the matrix. The Beavers–Joseph interface boundary conditions are adopted to describe the flow exchange at the interface boundary between the two domains. A laboratory analog is used to simulate the conduit and matrix domains of a karst aquifer. The conduit domain is located at the bottom of the transparent plexiglas laboratory analog and glass beads occupy the remaining space to represent the matrix domain. Water flows into and out of the two domains separately and each has its own supply and outflow reservoirs. Water and solute are exchanged through an interface between the two domains. Pressure transducers located within the matrix and conduit domains of the analog provide data that is processed and stored in digital format. Dye tracing experiments are recorded using time-lapse imaging. The data and images produced are analyzed by a spatial analysis program. The experiments provide not only hydraulic head distribution but also capture solute front images and mass exchange measurements between the conduit and matrix domains. In the experiment, we measure and record pressures, and quantify flow rates and solute transport. The results present a plausible argument that laboratory analogs can characterize groundwater water flow, solute transport, and mass exchange between the conduit and matrix domains in a karst aquifer. The analog validates the predictions of a numerical model and demonstrates the need of laboratory analogs to provide verification of proposed theories and the calibration of mathematical models.     

Groundwater flow velocities in karst aquifers; importance of spatial observation scale and hydraulic testing for contaminant transport prediction

Environmental Science and Pollution Research - We review scale dependence of hydraulic conductivities and effective porosities for prediction of contaminant transport in four UK karst aquifers....     

A PCE groundwater plume discharging to a river: influence of the streambed and near-river zone on contaminant distributions

An investigation of a tetrachloroethene (PCE) groundwater plume originating at a dry cleaning facility on a sand aquifer and discharging to a river showed that the near-river zone strongly modified the distribution, concentration, and composition of the plume prior to discharging into the surface water. The plume, streambed concentration, and hydrogeology were extensively characterized using the Waterloo profiler, mini-profiler, conventional and driveable multilevel samplers (MLS), Ground Penetrating Radar (GPR) surveys, streambed temperature mapping (to identify discharge zones), drivepoint piezometers, and soil coring and testing. The plume observed in the shallow streambed deposits was significantly different from what would have been predicted based on the characteristics of the upgradient plume. Spatial and temporal variations in the plume entering the near-river zone contributed to the complex contaminant distribution observed in the streambed where concentrations varied by factors of 100 to 5000 over lateral distances of less than 1 to 3.5 m. Low hydraulic conductivity semi-confining deposits and geological heterogeneities at depth below the streambed controlled the pattern of groundwater discharge through the streambed and influenced where the plume discharged into the river (even causing the plume to spread out over the full width of the streambed at some locations). The most important effect of the near-river zone on the plume was the extensive anaerobic biodegradation that occurred in the top 2.5 m of the streambed, even though essentially no biodegradation of the PCE plume was observed in the upgradient aquifer. Approximately 54% of the area of the plume in the streambed consisted solely of PCE transformation products, primarily cis-1,2-dichloroethene (cDCE) and vinyl chloride (VC). High concentrations in the interstitial water of the streambed did not correspond to high groundwater-discharge zones, but instead occurred in low discharge zones and are likely sorbed or retarded remnants of past high-concentration plume discharges. The high-concentration areas (up to 5529 microg/l of total volatile organics) in the streambed are of ecological concern and represent potential adverse exposure locations for benthic and hyporheic zone aquatic life, but the effect of these exposures on the overall health of the river has yet to be determined. Even if the upgradient source of PCE is remediated and additional PCE is prevented from reaching the streambed, the high-concentration deposits in the streambed will likely take decades to hundreds of years to flush completely clean under natural conditions because these areas have low vertical groundwater flow velocities and high retardation factors. Despite high concentrations of contaminants in the streambed, PCE was detected in the surface water only rarely due to rapid dilution in the river and no cDCE or VC was detected. Neither the sampling of surface water nor the sampling of the groundwater from the aquifer immediately adjacent to the river gave an accurate indication of the high concentrations of PCE biodegradation products present in the streambed. Sampling of the interstitial water of the shallow streambed deposits is necessary to accurately characterize the nature of plumes discharging to rivers.     

Matrix-immobilized organoclay for the sorption of polycyclic aromatic hydrocarbons and pentachlorophenol from groundwater

Sorbent materials consisting of organoclay immobilized onto the surface of a solid support were evaluated for use in pentachlorophenol (PCP) and polycyclic aromatic hydrocarbon (PAH) remediation of groundwater at a creosote-contaminated Superfund site. Cetylpyridinium-exchanged low pH montmorillonite clay (CP-LPHM) was bonded to either sand (CP-LPHM/sand) or granular activated carbon (GAC) (CP-LPHM/GAC) using the free acid form of carboxymethylcellulose as an adhesive. Effluent from an oil-water separator was eluted through equal bed volumes of composite (4 g 3:2 CP-LPHM/GAC or 13 g CP-LPHM/sand), affinity-extracted, and quantitatively analyzed by GC/MS. PCP, naphthalene, fluorene, phenanthrene, pyrene, and total PAHs were initially reduced by both CP-LPHM/GAC (> or =99%, 61%, 99%, > or =99%, 97%, and 94%, respectively) and CP-LPHM/sand (90%, 70%, 94%, 95%, 93%, and 86%, respectively). Complete breakthrough of naphthalene occurred after approximately 15 h of elution through 3:2 CP-LPHM/GAC and 22 h through CP-LPHM/sand. PCP showed complete breakthrough following 18 h of elution through 3:2 CP-LPHM/GAC and 26 h through CP-LPHM/sand. However, 50% breakthrough was not attained for higher molecular weight PAHs, as fluoranthene, pyrene, benzo[a]anthracene, and chrysene continued to be greatly reduced with both 3:2 CP-LPHM/GAC (98%, 95%, 94%, and 95%, respectively) and CP-LPHM/sand (75%, 73%, 76%, and 78%, respectively) after 48 h of continuous elution. Results confirm prior studies, indicating that these organoclay-containing composites have a high capacity for contaminants found in wood preserving waste. Further, results suggest that the inclusion of CP-LPHM may be useful as part of an effective strategy for groundwater remediation of high concentrations of PCP and PAHs, in particular high molecular weight and carcinogenic PAHs.     

Biodegradation during contaminant transport in porous media: 4. Impact of microbial lag and bacterial cell growth

Miscible-displacement experiments were conducted to examine the impact of microbial lag and bacterial cell growth on the transport of salicylate, a model hydrocarbon compound. The impacts of these processes were examined separately, as well as jointly, to determine their relative effects on biodegradation dynamics. For each experiment, a column was packed with porous medium that was first inoculated with bacteria that contained the NAH plasmid encoding genes for the degradation of naphthalene and salicylate, and then subjected to a step input of salicylate solution. The transport behavior of salicylate was non-steady for all cases examined, and was clearly influenced by a delay (lag) in the onset of biodegradation. This microbial lag, which was consistent with the results of batch experiments, is attributed to the induction and synthesis of the enzymes required for biodegradation of salicylate. The effect of microbial lag on salicylate transport was eliminated by exposing the column to two successive pulses of salicylate, thereby allowing the cells to acclimate to the carbon source during the first pulse. Elimination of microbial lag effects allowed the impact of bacterial growth on salicylate transport to be quantified, which was accomplished by determining a cell mass balance. Conversely, the impact of microbial lag was further investigated by performing a similar double-pulse experiment under no-growth conditions. Significant cell elution was observed and quantified for all conditions/systems. The results of these experiments allowed us to differentiate the effects associated with microbial lag and growth, two coupled processes whose impacts on the biodegradation and transport of contaminants can be difficult to distinguish.     

Porous organoclay composite for the sorption of polycyclic aromatic hydrocarbons and pentachlorophenol from groundwater

Complex mixtures of hazardous chemicals such as polycyclic aromatic hydrocarbons (PAHs) in contaminated soil and groundwater can have severe and long-lasting effects on health. The evidence that these contaminants can cause adverse health effects in animals and humans is rapidly expanding. The frequent and wide-spread occurrence of PAHs in groundwater makes appropriate intervention strategies for their remediation highly desirable. The core objective of this research was to assess the ability of a clay-based composite to sorb and remove toxic contaminants from groundwater at a wood-preserving chemical waste site. Treatment efficiencies were evaluated using either effluent from an oil-water separator (OWS) or a bioreactor (B2). The effluent water from these units was passed through fixed bed columns containing either an organoclay composite or granular activated carbon. The sorbent columns were placed in-line using existing sampling ports at the effluent of the OWS or B2. Individual one-liter samples of treated and untreated effluent were collected in Kimax bottles over the course of 78 h (total of 50 samples). Subsequently each sample was extracted by solid phase extraction methodology, and pentachlorophenol (PCP) and PAH concentrations were quantitated via GC/MS. Columns containing porous organoclay composite, i.e. sand-immobilized cetylpyridinium-exchanged low-pH montmorillonite clay (CP/LPHM), were shown to reduce the contaminant load from the OWS effluent stream by 97%. The concentrations of benzo[a]pyrene (BaP) and PCP were considerably reduced (i.e. >99%). An effluent stream from the bioreactor was also filtered through columns packed with composite or an equivalent amount of GAC. Although the composite reduced the majority of contaminants (including BaP and PCP), it was less effective in diminishing the levels of lower ring versus higher ring PAHs. Conversely, GAC was more effective in removing the lower ring PAHs, except for naphthalene and PCP. The effectiveness of sorption of PCP from the OWS effluent by the composite was confirmed using a PCP-sensitive adult hydra bioassay previously described in our laboratory. The findings of this initial study have delineated differences between CP/LPHM and GAC for groundwater remediation, and suggest that GAC (instead of sand) as the solid support for organoclay may be more effective for the treatment of contaminated groundwater under field conditions than GAC or CP/LPHM alone. Further work is ongoing to confirm this conclusion.     

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.     

Simultaneous transport of parent and daughter compounds in aquifers with linear first-order sorption kinetics

In soils, daughter compounds may be generated from a parent compound by microbial metabolism, chemical reactions, radioactive decay, or other mechanisms. These daughter compounds are also acted upon by soil physical, chemical and biological processes. A system often referred to as a cascade or chain of compounds system results. While a great deal of attention has been given to this problem with the linear equilibrium assumption applied uniformly to all transport and reacting compounds, little attention has been given to the simultaneous transport and fate of a parent-daughter chain with a first-order rate assumed for the adsorption-desorption kinetics of each compound and with the soil partitioned into three sorption classes.A general one-dimensional cascade or chain model for the simultaneous transport of parent and daughter compounds in sorbing, homogeneous, water table aquifers is presented. The model is based on an advective-dispersive mass accounting formulation for both compounds and includes: (a) first-order rate of conversion of parent to daughter; (2) first-order rates of loss of either parent or daughter or both due to metabolism, chemical reaction and/or irreversible processes; (3) partitioning of the aquifer material into three sorption classes, namely mildly sorbing, strongly sorbing and organic matter; (4) linear first-order kinetic rules for adsorption and desorption operating on each of the sorbing soil fractions for each compound; (5) constantly emitting sources of rectangular shape of parent compound; and (6) mass accounting boundary conditions; and a tailorable initial distribution on [0, ∞). Mathematical analysis yields a coupled, linear system of equations including two transport and fate equations, initial and boundary data, and six kinetic rules, namely three each for parent and daughter compound. A numerical scheme for solving the system of equations was developed using readily available procedures since analytical solutions could not be found. Solutions for scenarios based on leaking underground sources are presented.