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.     

Multicomponent simulation of wastewater-derived nitrogen and carbon in shallow unconfined aquifers. II. Model application to a field site

A multicomponent reactive transport model as presented by MacQuarrie and Sudicky [MacQuarrie, K.T.B., Sudicky, E.A., this volume. Multicomponent simulation of wastewater-derived nitrogen and carbon in shallow unconfined aquifers: I. Model formulation and performance, J. Contam. Hydrol.] is applied to a well-studied wastewater plume in a sandy aquifer near Cambridge, Ontario. Domestic wastewater is released into the unsaturated zone via a drain field at a depth of about 0.8 m. The physical transport parameters for the model are obtained by simulating a non-reactive solute, while kinetic input data for the nitrogen and carbon reaction network are obtained from the literature. The model shows that the wastewater-loading rate has little influence on the moisture content in the unsaturated zone, thus oxygen diffusion in the air phase is an important transport mechanism. The model results are in general agreement with the field-determined moisture and oxygen profiles near the drain field. The simulation results show that oxidation of ammonium and dissolved organic carbon (DOC) goes to completion in the 1.5-m distance between the drain field and the water table, and that calcite dissolution limits the pH reduction to about 0.2 units. The model-predicted nitrate concentrations in the core of the plume are in the range of 20-25 mg N/l and are in good agreement with the field data. Overall, the results for the major reactive species from the model simulation agree well with the geochemical data obtained below the drain field and it is concluded that the major physical and biochemical processes have been correctly captured in the current model formulation.     

Numerical simulation of a fine-grained denitrification layer for removing septic system nitrate from shallow groundwater

One of the most common methods to dispose of domestic wastewater involves the release of septic effluent from drains located in the unsaturated zone. Nitrogen from such systems is currently of concern because of nitrate contamination of drinking water supplies and eutrophication of coastal waters. It has been proposed that adding labile carbon sources to septic distribution fields could enhance heterotrophic denitrification and thus reduce nitrate concentrations in shallow groundwater. In this study, a numerical model which solves for variably saturated flow and reactive transport of multiple species is employed to investigate the performance of a drain field design that incorporates a fine-grained denitrification layer. The hydrogeological scenario simulated is an unconfined sand aquifer. The model results suggest that the denitrification layer, supplemented with labile organic carbon, may be an effective means to eliminate nitrogen loading to shallow groundwater. It is also shown that in noncalcareous aquifers, the denitrification reaction may provide sufficient buffering capacity to maintain near neutral pH conditions beneath and down gradient of the drain field. Leaching of excess dissolved organic carbon (DOC) from the denitrification layer is problematic, and causes an anaerobic plume to develop in simulations where the water table is less than 5-6 m below ground surface; this anaerobic plume may lead to other down gradient changes in groundwater quality. A drain field and denitrification layer of smaller dimensions is shown to be just as effective for reducing nitrate, but has the benefit of reducing the excess DOC leached from the layer. This configuration will minimize the impact of wastewater disposal in areas where the water table is as shallow as 3.5 m.     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

One-dimensional model for biogeochemical interactions and permeability reduction in soils during leachate permeation

This paper uses the findings from a column study to develop a reactive model for exploring the interactions occurring in leachate-contaminated soils. The changes occurring in the concentrations of acetic acid, sulphate, suspended and attached biomass, Fe(II), Mn(II), calcium, carbonate ions, and pH in the column are assessed. The mathematical model considers geochemical equilibrium, kinetic biodegradation, precipitation-dissolution reactions, bacterial and substrate transport, and permeability reduction arising from bacterial growth and gas production. A two-step sequential operator splitting method is used to solve the coupled transport and biogeochemical reaction equations. The model gives satisfactory fits to experimental data and the simulations show that the transport of metals in soil is controlled by multiple competing biotic and abiotic reactions. These findings suggest that bioaccumulation and gas formation, compared to chemical precipitation, have a larger influence on hydraulic conductivity reduction.     

Development of a scalable model for predicting arsenic transport coupled with oxidation and adsorption reactions

Understanding the fundamentals of arsenic adsorption and oxidation reactions is critical for predicting its transport dynamics in groundwater systems. We completed batch experiments to study the interactions of arsenic with a common MnO2(s) mineral, pyrolusite. The reaction kinetics and adsorption isotherm developed from the batch experiments were integrated into a scalable reactive transport model to facilitate column-scale transport predictions. We then completed a set of column experiments to test the predictive capability of the reactive transport model. Our batch results indicated that the commonly used pseudo-first order kinetics for As(III) oxidation reaction neglects the scaling effects with respect to the MnO2(s) concentration. A second order kinetic equation that explicitly includes MnO2(s) concentration dependence is a more appropriate kinetic model to describe arsenic oxidation by MnO2(s) minerals. The arsenic adsorption reaction follows the Langmuir isotherm with the adsorption capacity of 0.053micromol of As(V)/g of MnO2(s) at the tested conditions. The knowledge gained from the batch experiments was used to develop a conceptual model for describing arsenic reactive transport at a column scale. The proposed conceptual model was integrated within a reactive transport code that accurately predicted the breakthrough profiles observed in multiple column experiments. The kinetic and adsorption process details obtained from the batch experiments were valuable data for scaling to predict the column-scale reactive transport of arsenic in MnO2(s)-containing sand columns.     

Evaluating the sensitivity of a subsurface multicomponent reactive transport model with respect to transport and reaction parameters.

The input variables for a numerical model of reactive solute transport in groundwater include both transport parameters, such as hydraulic conductivity and infiltration, and reaction parameters that describe the important chemical and biological processes in the system. These parameters are subject to uncertainty due to measurement error and due to the spatial variability of properties in the subsurface environment. This paper compares the relative effects of uncertainty in the transport and reaction parameters on the results of a solute transport model. This question is addressed by comparing the magnitudes of the local sensitivity coefficients for transport and reaction parameters. General sensitivity equations are presented for transport parameters, reaction parameters, and the initial (background) concentrations in the problem domain. Parameter sensitivity coefficients are then calculated for an example problem in which uranium(VI) hydrolysis species are transported through a two-dimensional domain with a spatially variable pattern of surface complexation sites. In this example, the reaction model includes equilibrium speciation reactions and mass transfer-limited non-electrostatic surface complexation reactions. The set of parameters to which the model is most sensitive includes the initial concentration of one of the surface sites, the formation constant (Kf) of one of the surface complexes and the hydraulic conductivity within the reactive zone. For this example problem, the sensitivity analysis demonstrates that transport and reaction parameters are equally important in terms of how their variability affects the model results.     

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.     

Comparison of the solution behaviour of a pyrite-calcite mixture in batch and unsaturated sand column

A successful application of reaction transport algorithms to calculate the chemical evolution of natural systems requires accurate methods to compute the rates of mineral/fluid surface reactions. Regarding the transport of radio-nuclides in mining dumps the dissolution of minerals is of special importance. Using a kinetic rate law of the mineral dissolution verified for unsaturated conditions will allow a realistic modelling of the mineral weathering in the environment. Dissolution rates of minerals in an aqueous solution are determined by several characteristics. These are surface reaction rates, morphology of the mineral's surface and, in case it is the unsaturated zone, the degree of the water saturation. For this process, the quantity of the particle surfaces which are in contact with percolating water is most decisive. In order to study the differences of mineral dissolution under saturated and unsaturated conditions batch and column experiments were carried out with a pyrite-calcite mixture. The experimental results were verified by calculations. Comparing the dissolution in batch with those in the column experiment, which was performed with a water flow velocity of 0.64 cm/day and was analyzed in the region of a water saturation of 0.11, one can conclude that only a small portion of about 5% of the grain surface is chemically reactive in this unsaturated flow.     

Modelling the geochemical fate and transport of wastewater-derived phosphorus in contrasting groundwater systems

A 1D reactive transport model (RTM) is used to obtain a mechanistic understanding of the fate of phosphorus (P) in the saturated zone of two contrasting aquifer systems. We use the field data from two oxic, electron donor-poor, wastewater-impacted, sandy Canadian aquifers, (Cambridge and Muskoka sites) as an example of a calcareous and non-calcareous groundwater system, respectively, to validate our reaction network. After approximately 10 years of wastewater infiltration, P is effectively attenuated within the first 10 m down-gradient of the source mainly through fast sorption onto calcite and Fe oxides. Slow, kinetic sorption contributes further to P removal, while precipitation of phosphate minerals (strengite, hydroxyapatite) is quantitatively unimportant in the saturated zone. Nitrogen (N) dynamics are also considered, but nitrate behaves essentially as a conservative tracer in both systems. The model-predicted advancement of the P plume upon continued wastewater discharge at the calcareous site is in line with field observations. Model results suggest that, upon removal of the wastewater source, the P plume at both sites will persist for at least 20 years, owing to desorption of P from aquifer solids and the slow rate of P mineral precipitation. Sensitivity analyses for the non-calcareous scenario (Muskoka) illustrate the importance of the sorption capacity of the aquifer solids for P in modulating groundwater N:P ratios in oxic groundwater. The model simulations predict the breakthrough of groundwater with high P concentrations and low N:P ratios after 17 years at 20 m from the source for an aquifer with low sorption capacity (<0.02% w/w Fe(OH)(3)). In this type of system, denitrification plays a minor role in lowering the N:P ratios because it is limited by the availability of labile dissolved organic matter.     

Numerical modeling of dry deposition coupled to 22 photochemical reactions

Three Eulerian models for the dry deposition of photochemically reactive species were formulated and evaluated: a K-theory model with independent transport and deposition of each species, a K-theory model coupled with 22 gas-phase reactions, and a second-order flux-budget model coupled with 22 reactions. Operator splitting was used to separately solve the reaction and dispersion terms in the models including photochemistry. In an evaluation of numerical method performance, the Adams–Moulton method with a pseudo-steady-state approximation for the free radicals was found to be consistent with, but more computationally efficient than Gear’s method for the solution of the reaction terms. The sensitivity of profiles of vertical concentration and flux to the Eulerian model formulation varied according to the species’ Damköhler number. Although a K-theory model is adequate for weakly depositing species with Damköhler numbers <10^-3, a second-order flux-budget model is required for species with Damköhler numbers that exceed unity, such as nitrogen oxides, free radicals, and those sensitive to net flux production by chemical reactions. Selection of an appropriate model formulation for the entire system depended on the most reactive species. Simple K-theory models may not accurately predict dry deposition fluxes in the urban surface layer.     

Evaluation of a reactive plume model with power plant plume data—application to the sensitivity analysis of sulfate and nitrate formation

A reactive plume model that treats secondary aerosol formation is used to investigate the major physical and chemical processes that affect the rate of sulfate and nitrate aerosol formation in power plant plumes. The reactive plume model is evaluated with experimental data collected in three power plant plumes, and model performance is shown to be quite satisfactory. One of these case studies is used to perform singleparameter and multi-parameter analyses of the sensitivity of sulfate and nitrate aerosol concentrations to various meteorological, air quality and chemical kinetic parameters. The results suggest that sulfate aerosol concentrations are most sensitive to relative humidity and temperature at high relative humidity, whereas nitrate aerosol concentrations are most sensitive to temperature, particularly at low relative humidity. The importance of the NO_x/reactive hydrocarbon chemistry to sulfate and nitrate aerosol formation is examined.     

Stochastic-convective transport with nonlinear reactions and mixing: finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion

An effective streamtube ensemble method is developed to upscale convective-dispersive transport with multicomponent nonlinear reactions in steady nonuniform flow. The transport is cast in terms of a finite ensemble of independent discrete streamtubes that approximate convective transport along macroscopically averaged pathlines and dispersive transport longitudinally as microscopic mixing within streamtubes. The representation of fate and transport via a finite ensemble of effective linear streamtubes, allows the treatment of arbitrarily complex reaction systems involving both homogeneous and heterogeneous reactions, and longitudinal dispersive/diffusive mixing within streamtubes. This allows the use of reactive-transport codes designed to solve such problems in an Eulerian framework, as opposed to reliance on closed-form (convolutional or canonical) expressions for reactive transport in exclusively convective streamtubes. The approach requires both reactive-transport solutions for a representative ensemble of one-dimensional convective-dispersive-reactive streamtubes and the distribution of flux over the streamtube ensemble variants, and it does not allow for lateral mixing between streamtubes. Here, the only ensemble variant is travel time. The discussion details the way that the conventional Eulerian fate and transport model is converted first into an ensemble of transports along three-dimensional streamtubes of unknown geometry, and then to approximate one-dimensional streamtubes that are designed to honor the important global properties of the transport. Conditions under which such an 'equivalent' ensemble of one-dimensional streamtubes are described. The breakthrough curve of a nonreactive tracer in the ensemble is expressed as a combined Volterra-Fredholm integral equation, which serves as the basis for estimation of the distribution of flux over the variant of the ensemble, travel time. Transient convective speed and the effects of errors in flux distributions are described, and the method is applied to a demonstration problem involving nonlinear multicomponent reaction kinetics and strongly nonuniform flow.     

Transport of coliphage PRD1 in a surface flow constructed wetland.

A tracer study was conducted in a 3-ha surface flow constructed wetland to analyze transport performance of PRD1, an enteric virus model. The convection-dispersion equation (CDE), including a first-order reaction model, adequately simulated transport performance of PRD1 in the wetland under an average hydraulic loading rate of 82 mm/d. Convective velocity (v) and longitudinal dispersion coefficient (D) were estimated by modeling a conservative tracer (bromide) pulse through the wetland. Both PRD1 and bromide were simultaneously added to the entering secondary treated wastewater effluent. The mass of bromide and PRD1 recovered was 76 and 16%, respectively. The PRD1 decay rate was calculated to be 0.3/day. The findings of this study suggest that the CDE model and analytical moment equations represent a suitable option to characterize virus transport performance in surface flow constructed wetlands.     

Numerical modeling of humic colloid borne americium (III) migration in column experiments using the transport/speciation code K1D and the KICAM model

The humic colloid borne Am(III) transport was investigated in column experiments for Gorleben groundwater/sand systems. It was found that the interaction of Am with humic colloids is kinetically controlled, which strongly influences the migration behavior of Am(III). These kinetic effects have to be taken into account for transport/speciation modeling. The kinetically controlled availability model (KICAM) was developed to describe actinide sorption and transport in laboratory batch and column experiments. Application of the KICAM requires a chemical transport/speciation code, which simultaneously models both kinetically controlled processes and equilibrium reactions. Therefore, the code K1D was developed as a flexible research code that allows the inclusion of kinetic data in addition to transport features and chemical equilibrium. This paper presents the verification of K1D and its application to model column experiments investigating unimpeded humic colloid borne Am migration. Parmeters for reactive transport simulations were determined for a Gorleben groundwater system of high humic colloid concentration (GoHy 2227). A single set of parameters was used to model a series of column experiments. Model results correspond well to experimental data for the unretarded humic borne Am breakthrough.     

铁屑法处理活性染料废水的实验研究

研究了反应时间、染料浓度、进水pH以及不同的废铸铁屑投加量的条件下，废铸铁屑内电解法处理模拟印染废水的脱色能力。并采用铁屑滤床强化厌氧一好氧膜生物反应器（A／OMBR）处理含活性染料的模拟废水。研究结果表明，铁屑对模拟印染废水的最佳脱色时间为12min，酸性条件下铁屑的脱色率优于碱性条件．随铁屑投加量的增加，系统对印染废水的脱色率提高，铁屑滤床强化A／OMBR处理可以提高组合工艺出水色度和COD的去除率。     

Atmospheric Chemistry of Toxic Contaminants 1. Reaction Rates and Atmospheric Persistence

Using structure-reactivity relationships between reaction rate constants and ionlzatlon potentials for structural homologues, estimates are presented for the rate constants of the reactions of ozone, the hydroxyl radical, and the nitrate radical with forty toxic air contaminants for which no or little data are available. These rate constants are in turn used to estimate the atmospheric persistence of saturated allphatics, unsaturated allphatics, and aromatic toxic organics. The corresponding atmospheric half-lives for removal by chemical reactions range from a few hours for the most reactive toxics (chloroprene, hexachlorocyclo-pentadiene, cresols, nitrosamines, maleic anhydride) to several months for the least reactive compounds (nitrobenzene, methyl bromide, phosgene).     

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

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

Implications of non-equilibrium transport in heterogeneous reactive barrier systems: evidence from laboratory denitrification experiments

Organic substrates in reactive barrier systems are often heterogeneous material mixtures with relatively large contrasts in hydraulic conductivity and porosity over short distances. These short-range variations in material properties imply that preferential flow paths and diffusion between regions of higher and lower hydraulic conductivity may be important for treatment efficiency. This paper presents the results of a laboratory column experiment where denitrification is investigated using a heterogeneous reactive substrate (sawdust mixed with sewage sludge). Displacement experiments with a non-reactive solute at three different flow rates are used to estimate transport parameters using a dual porosity non-equilibrium model. Parameter estimation from breakthrough curves produced relatively consistent values for the fraction of the porosity consisting of mobile water (β) and the mass transfer coefficient (α), with average values of 0.27 and 0.42 d(-1), respectively. The column system removes >95% of the influent nitrate at low and medium flow, but only 50-75% of the influent nitrate at high flow, suggesting that denitrification kinetics and diffusive mass transfer rates are limiting the degree of treatment at lower hydraulic residence times. Reactive barrier systems containing dual porosity media must therefore consider mass transfer times in their design; this is often most easily accommodated by adjusting flowpath length.     

Groundwater flow, multicomponent transport and biogeochemistry: development and application of a coupled process model

A research tool for modeling the reactive flow and transport of groundwater contaminants in multiple dimensions is presented. Arbitrarily complex coupled kinetic–equilibrium heterogeneous reaction networks, automatic code generation, transfer-function based solutions, parameter estimation, high-resolution methods for advection, and robust solvers for the mixed kinetic–equilibrium chemistry are some of the features of reactive flow and transport (RAFT) that make it a versatile research tool in the modeling of a wide variety of laboratory and field experiments. The treatment of reactions is quite general so that RAFT can be used to model biological, adsorption/desorption, complexation, and mineral dissolution/precipitation reactions among others. The integrated framework involving automated code generation and parameter estimation allows for the development, characterization, and evaluation of mechanistic process models. The model is described and used to solve a problem in competitive adsorption that illustrates some of these features. The model is also used to study the development of an in situ Fe(II)-zone by encouraging the growth of an iron-reducing bacterium with lactate as the electron donor. Such redox barriers are effective in sequestering groundwater contaminants such as chromate and TCE.