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.     

Direct coupling of a genome-scale microbial in silico model and a groundwater reactive transport model

The activity of microorganisms often plays an important role in dynamic natural attenuation or engineered bioremediation of subsurface contaminants, such as chlorinated solvents, metals, and radionuclides. To evaluate and/or design bioremediated systems, quantitative reactive transport models are needed. State-of-the-art reactive transport models often ignore the microbial effects or simulate the microbial effects with static growth yield and constant reaction rate parameters over simulated conditions, while in reality microorganisms can dynamically modify their functionality (such as utilization of alternative respiratory pathways) in response to spatial and temporal variations in environmental conditions. Constraint-based genome-scale microbial in silico models, using genomic data and multiple-pathway reaction networks, have been shown to be able to simulate transient metabolism of some well studied microorganisms and identify growth rate, substrate uptake rates, and byproduct rates under different growth conditions. These rates can be identified and used to replace specific microbially-mediated reaction rates in a reactive transport model using local geochemical conditions as constraints. We previously demonstrated the potential utility of integrating a constraint-based microbial metabolism model with a reactive transport simulator as applied to bioremediation of uranium in groundwater. However, that work relied on an indirect coupling approach that was effective for initial demonstration but may not be extensible to more complex problems that are of significant interest (e.g., communities of microbial species and multiple constraining variables). Here, we extend that work by presenting and demonstrating a method of directly integrating a reactive transport model (FORTRAN code) with constraint-based in silico models solved with IBM ILOG CPLEX linear optimizer base system (C library). The models were integrated with BABEL, a language interoperability tool. The modeling system is designed in such a way that constraint-based models targeting different microorganisms or competing organism communities can be easily plugged into the system. Constraint-based modeling is very costly given the size of a genome-scale reaction network. To save computation time, a binary tree is traversed to examine the concentration and solution pool generated during the simulation in order to decide whether the constraint-based model should be called. We also show preliminary results from the integrated model including a comparison of the direct and indirect coupling approaches and evaluated the ability of the approach to simulate field experiment.     

Biodegradation during contaminant transport in porous media: 1. mathematical analysis of controlling factors

Interest in coupled biodegradation and transport of organic contaminants has expanded greatly in the past several years. In a system in which biodegradation is coupled with solute transport, the magnitude and rate of biodegradation is influenced not only by properties of the microbial population and the substrate, but also by hydrodynamic properties (e.g., residence time, dispersivity). By nondimensionalizing the coupled-process equations for transport and nonlinear biodegradation, we show that transport behavior is controlled by three characteristic parameters: the effective maximum specific growth rate, the relative half-saturation constant, and the relative substrate-utilization coefficient. The impact on biodegradation and transport of these parameters, which constitute various combinations of factors reflecting the influences of biotic and hydraulic properties of the system, are examined numerically. A type-curve diagram based on the three characteristic parameters is constructed to illustrate the conditions under which steady and non-steady transport is observed, and the conditions for which the linear, first-order approximation is valid for representing biodegradation. The influence of constraints to microbial growth and substrate utilization on contaminant transport is also briefly discussed. Additionally, the impact of biodegradation, with and without biomass growth, on spatial solute distribution and moments is examined.     

Stochastic-convective transport with nonlinear reaction and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media

Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.     

Modelling geochemical and microbial consumption of dissolved oxygen after backfilling a high level radiactive waste repository

Dissolved oxygen (DO) left in the voids of buffer and backfill materials of a deep geological high level radioactive waste (HLW) repository could cause canister corrosion. Available data from laboratory and in situ experiments indicate that microbes play a substantial role in controlling redox conditions near a HLW repository. This paper presents the application of a coupled hydro-bio-geochemical model to evaluate geochemical and microbial consumption of DO in bentonite porewater after backfilling of a HLW repository designed according to the Swedish reference concept. In addition to geochemical reactions, the model accounts for dissolved organic carbon (DOC) respiration and methane oxidation. Parameters for microbial processes were derived from calibration of the REX in situ experiment carried out at the Asp? underground laboratory. The role of geochemical and microbial processes in consuming DO is evaluated for several scenarios. Numerical results show that both geochemical and microbial processes are relevant for DO consumption. However, the time needed to consume the DO trapped in the bentonite buffer decreases dramatically from several hundreds of years when only geochemical processes are considered to a few weeks when both geochemical reactions and microbially-mediated DOC respiration and methane oxidation are taken into account simultaneously.     

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.     

Multicomponent simulation of wastewater-derived nitrogen and carbon in shallow unconfined aquifers. I. Model formulation and performance

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. The objectives of this study are to develop and assess the performance of a mechanistic flow and reactive transport model which couples the most relevant physical, geochemical and biochemical processes involved in wastewater plume evolution in sandy aquifers. The numerical model solves for variably saturated groundwater flow and reactive transport of multiple carbon- and nitrogen-containing species in a three-dimensional porous medium. The reactive transport equations are solved using the Strang splitting method which is shown to be accurate for Monod and first- and second-order kinetic reactions, and two to four times more efficient than sequential iterative splitting. The reaction system is formulated as a fully kinetic chemistry problem, which allows for the use of several special-purpose ordinary differential equation (ODE) solvers. For reaction systems containing both fast and slow kinetic reactions, such as the combined nitrogen-carbon system, it is found that a specialized stiff explicit solver fails to obtain a solution. An implicit solver is more robust and its computational performance is improved by scaling of the fastest reaction rates. The model is used to simulate wastewater migration in a 1-m-long unsaturated column and the results show significant oxidation of dissolved organic carbon (DOC), the generation of nitrate by nitrification, and a slight decrease in pH.     

Reactive transport modelling of biogeochemical processes and carbon isotope geochemistry inside a landfill leachate plume

The biogeochemical processes governing leachate attenuation inside a landfill leachate plume (Banisveld, the Netherlands) were revealed and quantified using the 1D reactive transport model PHREEQC-2. Biodegradation of dissolved organic carbon (DOC) was simulated assuming first-order oxidation of two DOC fractions with different reactivity, and was coupled to reductive dissolution of iron oxide. The following secondary geochemical processes were required in the model to match observations: kinetic precipitation of calcite and siderite, cation exchange, proton buffering and degassing. Rate constants for DOC oxidation and carbonate mineral precipitation were determined, and other model parameters were optimized using the nonlinear optimization program PEST by means of matching hydrochemical observations closely (pH, DIC, DOC, Na, K, Ca, Mg, NH4, Fe(II), SO4, Cl, CH4, saturation index of calcite and siderite). The modelling demonstrated the relevance and impact of various secondary geochemical processes on leachate plume evolution. Concomitant precipitation of siderite masked the act of iron reduction. Cation exchange resulted in release of Fe(II) from the pristine anaerobic aquifer to the leachate. Degassing, triggered by elevated CO2 pressures caused by carbonate precipitation and proton buffering at the front of the plume, explained the observed downstream decrease in methane concentration. Simulation of the carbon isotope geochemistry independently supported the proposed reaction network.     

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.     

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.     

Coupling air quality and land use modeling within an optimization framework

Land use regulations and air quality standards can be effective tools to control air pollution. Atmospheric transport/chemistry simulation models could be used to develop suitable regulations and standards; however, these models are not as efficient as air quality management models developed from embedding governing equations for atmospheric transport/chemistry into an optimization framework. Formulations of two steady-state air quality management models are presented to facilitate the development or evaluation of land use strategies to protect regional air quality from pollution generated from distributed point or nonpoint sources. Both models are linear programs constructed with equations that describe steady-state atmospheric pollutant fate and transport. The first model determines feasible pollutant loading patterns for multiple land use activities to accommodate the greatest regional population. The second model ascertains patterns of expanded land use which have a minimum impact on air quality. The primary goal of this paper is to explain how air pollution and land use modeling may be coupled to create an effective management tool to aid scientists and engineers with decisions affecting air quality and land use. The secondary goal is to show the types of air quality and regulatory information which could be obtained from these models. This latter goal is attained with general conclusions as consequence of applying ‘duality theory.’     

The Langmuir two-surface equation as a model for cadmium adsorption on peat

The Langmuir isotherm equation is often used to describe the adsorption of cadmium on peat. If the total surface onsists of two or more populations of sites with different bonding energies, it is proposed that the Langmuir two-surface equation be used. The effects of the contact time and pH on adsorption were investigated in batch experiments. Adsorption batch isotherm studies were carried out by using 12 solutions with initial concentrations of 5–110 mg/l. The samples were analysed by using axial ICP-AES. Adsorption data were compared using four different linearizations (Lineweaver-Burk, Eadie-Hofstee, Scatchard and Langmuir linearizations). Better results among linearizations were found with the Langmuir linearization, but the results obtained by using the nonlinear regression were still the best. A new, nonlinear regression method for the calculation of the equation constants was created by using the system of equations and these findings were compared to the results found using earlier methods.     

Numerical methods for describing chemical transport in the unsaturated zone of the subsurface

Finite-difference and finite-element methods of approximation have been extended to solve the one-dimensional nonlinear partial differential equations that describe the simultaneous transport of heat, moisture and chemical in the unsaturated zone. Especially for chemical transport, nodal spacing criteria are required to minimize numerical dispersion and oscillatory behavior in the solution vector for chemical concentration. Conservative criteria for nodal spacing for saturated flow can be used to set nodal spacing for unsaturated zone transport. When nodal spacing criteria are satisfied, for the same set of transport and boundary conditions, chemical concentration profiles calculated by the two numerical methods will be almost the same. A situation that is simulated very well with one-dimensional models, is the application of chemicals to land surfaces. To compare and contrast the characteristics of solutions given by the two numerical methods, moisture content, temperature and chemical concentration profiles for a 75-day period after application in the unsaturated zone are calculated for two representative types of organic chemicals. In the first, the chemical is very slowly degraded in the subsurface environment but strongly sorbed to soil surfaces. In the second, the chemical is rapidly degraded but weakly sorbed to soil surfaces. Because of differences in sorption coefficients and mechanisms of degradation, for the same set of hydrodynamic properties of the subsurface, the weakly sorbed chemical is more widely distributed throughout the unsaturated zone, whereas the strongly sorbed chemical stays very close to where it is put initially with little penetration into the subsurface. Satisfying nodal spacing criteria minimizes the impact of the method of approximation on the calculated solutions of the transport equations. For better model predictive performance, however, there are needs for more fundamental information on processes governing transport in the subsurface.     

Numerical simulations of pyrite oxidation and acid mine drainage in unsaturated waste rock piles

Numerical simulations of layered, sulphide-bearing unsaturated waste rock piles are presented to illustrate the effect of coupled processes on the generation of acid mine drainage (AMD). The conceptual 2D systems were simulated using the HYDRUS model for flow and the POLYMIN model for reactive transport. The simulations generated low-pH AMD which was buffered by sequential mineral dissolution and precipitation. Sulphide oxidation rates throughout the pile varied by about two orders of magnitude (0.004-0.4 kg m-3 year-1) due to small changes in moisture content and grain size. In the fine-grained layers, the high reactive surface area induced high oxidation rates, even though capillary forces kept the local moisture content relatively high. In waste rock piles with horizontal layers, most of the acidity discharged through vertical preferential flow channels while with inclined fine grained layers, capillary diversion channeled the AMD to the outer slope boundary, keeping the pile interior relatively dry. The simulation approach will be useful for helping evaluate design strategies for controlling AMD from waste rock.     

Reactive transport of 85Sr in a chernobyl sand column: static and dynamic experiments and modeling

The effects of nonlinear sorption and competition with major cations present in the soil solution on radioactive strontium transport in an eolian sand were examined. Three laboratory techniques were used to identify and quantify the chemical and hydrodynamic processes involved in strontium transport: batch experiments, stirred flow-through reactor experiments and saturated laboratory columns. The major goal was to compare the results obtained under static and dynamic conditions and to describe in a deterministic manner the predominant processes involved in radioactive strontium transport in such systems. Experiments under dynamic conditions, namely flow-through reactor and column experiments, were in very good agreement even though the solid/liquid ratio was very different. The experimental data obtained from the flow-through reactor study pointed to a nonlinear, instantaneous and reversible sorption process. Miscible displacement experiments were conducted to demonstrate the competition between stable and radioactive strontium and to quantify its effect on the 85Sr retardation factor. The results were modeled using the PHREEQC computer code. A suitable cation-exchange model was used to describe the solute/soil reaction. The model successfully described the results of the entire set of miscible displacement experiments using the same set of parameter values for the reaction calculations. The column study revealed that the stable Sr aqueous concentration was the most sensitive variable of the model, and that the initial state of the sand/solution system had also to be controlled to explain and describe the measured retardation factor of radioactive strontium. From these observations, propositions can be made to explain the discrepancies observed between some data obtained from static (batches) and dynamic (reactor and column) experiments. Desorbed antecedent species (stable Sr) are removed from the column or reactor in the flow system but continue to compete for sorption sites in the batch system. Batch experiments are simple and fast, and provide a very useful means of multiplying data. However, interpretation becomes difficult when different species compete for sorption sites in the soil/solution system. A combination of batches, flow-through reactor and column experiments, coupled with hydrogeochemical modeling, would seem to offer a very powerful tool for identifying and quantifying the predominant processes on a cubic decimeter scale (dm3) and for providing a range of radioactive strontium retardation factor as a function of the geochemistry of the soil/solution system.     

Sorption of hydrophobic organic pollutants in saturated soil systems

Sorption equilibria and rates were characterized for a matrix of four aquifer sands and two slightly to moderately hydrophobic organic solutes (nitrobenzene and lindane), and the effects of sorption on the behavior of these solutes in saturated systems of the soils were determined. Experimental data were used to test and evaluate a variety of mathematical models for predicting contaminant fate and transport in groundwater systems.Observed equilibrium relationships between soil and solution phase solute concentrations were found to be described best by the nonlinear Freundlich isotherm model. It was further determined that the sorption process in the systems tested is rate controlled, requiring several days to approach equilibrium in completely mixed batch reactors. Subsequent modeling of solute transport in continuous flow soil column reactors was found to be most successful when rate-controlled models were used, the best results were obtained with a dual-resistance model incorporating the coupled mass transport steps of boundary-layer and intraparticle diffusion.     

Effect of initial sulfide concentration on sulfide and phenol oxidation under denitrifying conditions

The objective of this work was to evaluate the effect of the initial sulfide concentration on the kinetics and metabolism of phenol and sulfide in batch bioassays using nitrate as electron acceptor. Complete oxidation of sulfide (20 mg L(-1) of S(2-)) and phenol (19.6 mg L(-1)) was linked to nitrate reduction when nitrate was supplemented at stoichiometric concentrations. At 32 mg L(-1) of sulfide, oxidation of sulfide and phenol by the organo-lithoautotrophic microbial culture was sequential; first sulfide was rapidly oxidized to elemental sulfur and afterwards to sulfate; phenol oxidation started once sulfate production reached a maximum. When the initial sulfide concentration was increased from 20 to 26 and finally to 32 mg L(-1), sulfide oxidation was inhibited. In contrast phenol consumption by the denitrifying culture was not affected. These results indicated that sulfide affected strongly the sulfide oxidation rate and nitrate reduction.     

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.