Operator-splitting errors in coupled reactive transport codes for transient variably saturated flow and contaminant transport in layered soil profiles

One possible way of integrating subsurface flow and transport processes with (bio)geochemical reactions is to couple by means of an operator-splitting approach two completely separate codes, one for variably-saturated flow and solute transport and one for equilibrium and kinetic biogeochemical reactions. This paper evaluates the accuracy of the operator-splitting approach for multicomponent systems for typical soil environmental problems involving transient atmospheric boundary conditions (precipitation, evapotranspiration) and layered soil profiles. The recently developed HP1 code was used to solve the coupled transport and chemical equations. For steady-state flow conditions, the accuracy was found to be mainly a function of the adopted spatial discretization and to a lesser extent of the temporal discretization. For transient flow situations, the accuracy depended in a complex manner on grid discretization, time stepping and the main flow conditions (infiltration versus evaporation). Whereas a finer grid size reduced the numerical errors during steady-state flow or the main infiltration periods, the errors sometimes slightly increased (generally less than 50%) when a finer grid size was used during periods with a high evapotranspiration demand (leading to high pressure head gradients near the soil surface). This indicates that operator-splitting errors are most significant during periods with high evaporative boundary conditions. The operator-splitting errors could be decreased by constraining the time step using the performance index (the product of the grid Peclet and Courant numbers) during infiltration, or the maximum time step during evapotranspiration. Several test problems were used to provide guidance for optimal spatial and temporal discretization.     

Process-based reactive transport modeling of a permeable reactive barrier for the treatment of mine drainage

Reactive transport modeling of a permeable reactive barrier for the treatment of mine drainage was used to integrate a comprehensive data set including pore water chemistry and solid phase data from several sampling events over a >3-year time period. The simulations consider the reduction of sulfate by the organic carbon-based treatment material and the removal of sulfate and iron by precipitation of reduced mineral phases including iron monosulfides and siderite. Additional parameters constraining the model include dissolved H2S, alkalinity and pH, as well as a suite of solid phase S-fractions identified by extractions. Influences of spatial heterogeneity necessitated the use of a 2-dimensional modeling approach. Simulating observed seasonal fluctuations and long-term changes in barrier reactivity required the use of temperature dependent rate coefficients and a multimodal Monod-type rate expression accounting for the variable reactivity of different organic carbon fractions. Simulated dissolved concentrations of SO4, Fe, H2S, alkalinity and pH, as well as solid phase accumulations of reduced sulfur phases generally compare well to observed trends over 23 months. Spatial variations, seasonal fluctuations and the time-dependent decline in reactivity were also captured. The modeling results generally confirm, and further strengthen, the existing conceptual model for the site. Overall sulfate reduction and S-accumulation rates are constrained with confidence within a factor of 1.5.     

Three-dimensional density-dependent flow and multicomponent reactive transport modeling of chlorinated solvent oxidation by potassium permanganate

A popular method for the treatment of aquifers contaminated with chlorinated solvents is chemical oxidation based on the injection of potassium permanganate (KMnO₄). Both the high density (1025 gL^− 1) and reactivity of the treatment solution influence the fate of permanganate (MnO₄) in the subsurface and affect the degree of contaminant treatment. The MIN3P multicomponent reactive transport code was enhanced to simulate permanganate-based remediation, to evaluate the pathways of MnO₄ utilization, and to assess the role of density contrasts for the delivery of the treatment solution. The modified code (MIN3P-D) provides a direct coupling between density-dependent fluid flow, solute transport, contaminant treatment, and geochemical reactions. The model is used to simulate a field trial of TCE oxidation in a sandy aquifer that is underlain by an aquitard. Three-dimensional simulations are conducted for a coupled reactive system comprised of ten aqueous components, two mineral phases, TCE (dissolved, adsorbed, and NAPL), reactive organic matter, and including ion exchange reactions. Model parameters are constrained by literature data and a detailed data set from the field site under investigation. The general spatial and transient evolution in observed concentrations of the oxidant, dissolved TCE, and reaction products are adequately reproduced by the simulations. The model elucidates the important role of density-induced flow and transport on the distribution of the treatment solution into NAPL containing regions located at the aquifer–aquitard interface. Model results further suggest that reactions that do not directly affect the stability of MnO₄ have a negligible effect on solution density and MnO₄ delivery.     

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.     

Reactive transport modeling of processes controlling the distribution and natural attenuation of phenolic compounds in a deep sandstone aquifer

Reactive solute transport modeling was utilized to evaluate the potential for natural attenuation of a contaminant plume containing phenolic compounds at a chemical producer in the West Midlands, UK. The reactive transport simulations consider microbially mediated biodegradation of the phenolic compounds (phenols, cresols, and xylenols) by multiple electron acceptors. Inorganic reactions including hydrolysis, aqueous complexation, dissolution of primary minerals, formation of secondary mineral phases, and ion exchange are considered. One-dimensional (1D) and three-dimensional (3D) simulations were conducted. Mass balance calculations indicate that biodegradation in the saturated zone has degraded approximately 1-5% of the organic contaminant plume over a time period of 47 years. Simulations indicate that denitrification is the most significant degradation process, accounting for approximately 50% of the organic contaminant removal, followed by sulfate reduction and fermentation reactions, each contributing 15-20%. Aerobic respiration accounts for less than 10% of the observed contaminant removal in the saturated zone. Although concentrations of Fe(III) and Mn(IV) mineral phases are high in the aquifer sediment, reductive dissolution is limited, producing only 5% of the observed mass loss. Mass balance calculations suggest that no more than 20-25% of the observed total inorganic carbon (TIC) was generated from biodegradation reactions in the saturated zone. Simulations indicate that aerobic biodegradation in the unsaturated zone, before the contaminant entered the aquifer, may have produced the majority of the TIC observed in the plume. Because long-term degradation is limited to processes within the saturated zone, use of observed TIC concentrations to predict the future natural attenuation may overestimate contaminant degradation by a factor of 4-5.     

Large-scale modeling of reactive solute transport in fracture zones of granitic bedrocks

Final disposal of high-level radioactive waste in deep repositories located in fractured granite formations is being considered by several countries. The assessment of the safety of such repositories requires using numerical models of groundwater flow, solute transport and chemical processes. These models are being developed from data and knowledge gained from in situ experiments such as the Redox Zone Experiment carried out at the underground laboratory of Äspö in Sweden. This experiment aimed at evaluating the effects of the construction of the access tunnel on the hydrogeological and hydrochemical conditions of a fracture zone intersected by the tunnel. Most chemical species showed dilution trends except for bicarbonate and sulphate which unexpectedly increased with time. Molinero and Samper [Molinero, J. and Samper, J. Groundwater flow and solute transport in fracture zones: an improved model for a large-scale field experiment at Äspö (Sweden). J. Hydraul. Res., 42, Extra Issue, 157–172] presented a two-dimensional water flow and solute transport finite element model which reproduced measured drawdowns and dilution curves of conservative species. Here we extend their model by using a reactive transport which accounts for aqueous complexation, acid–base, redox processes, dissolution–precipitation of calcite, quartz, hematite and pyrite, and cation exchange between Na⁺ and Ca²⁺. The model provides field-scale estimates of cation exchange capacity of the fracture zone and redox potential of groundwater recharge. It serves also to identify the mineral phases controlling the solubility of iron. In addition, the model is useful to test the relevance of several geochemical processes. Model results rule out calcite dissolution as the process causing the increase in bicarbonate concentration and reject the following possible sources of sulphate: (1) pyrite dissolution, (2) leaching of alkaline sulphate-rich waters from a nearby rock landfill and (3) dissolution of iron monosulphides contained in Baltic seafloor sediments. Based on these results, microbially mediated processes are postulated as the most likely hypothesis to explain the measured increase of dissolved bicarbonates and sulphates after tunnel construction.     

Present state and future directions of modeling of geochemistry in hydrogeological systems

A first step towards understanding and controlling the fate and dissemination of radioactive waste is to create a concise and comprehensive theoretical framework for the rather non-linear processes involved--hence, the need for geochemical models. Two classes of geochemical models are commonly used, i.e., static and hydrodynamic models. In contrast to static models, hydrodynamic models combine geochemical reactions with hydrogeological processes such as ground-water flow, diffusion and dispersion. In this review, we examine the present state of geochemical models in terms of included processes, thermodynamic databases, missing phenomena, numerical behavior and performance. It is shown that over the past decade, significant progress has been made with respect to modeling of geochemistry in hydrodynamic systems: this is illustrated by describing several applications. Finally, we focus on the perspectives of geochemical modeling in the assessment of the safety of nuclear waste disposal.     

Variably saturated flow and multicomponent biogeochemical reactive transport modeling of a uranium bioremediation field experiment

Three-dimensional, coupled variably saturated flow and biogeochemical reactive transport modeling of a 2008 in situ uranium bioremediation field experiment is used to better understand the interplay of transport and biogeochemical reactions controlling uranium behavior under pulsed acetate amendment, seasonal water table variation, spatially variable physical (hydraulic conductivity, porosity) and geochemical (reactive surface area) material properties. While the simulation of the 2008 Big Rusty acetate biostimulation field experiment in Rifle, Colorado was generally consistent with behaviors identified in previous field experiments at the Rifle IFRC site, the additional process and property detail provided several new insights. A principal conclusion from this work is that uranium bioreduction is most effective when acetate, in excess of the sulfate-reducing bacteria demand, is available to the metal-reducing bacteria. The inclusion of an initially small population of slow growing sulfate-reducing bacteria identified in proteomic analyses led to an additional source of Fe(II) from the dissolution of Fe(III) minerals promoted by biogenic sulfide. The falling water table during the experiment significantly reduced the saturated thickness of the aquifer and resulted in reactants and products, as well as unmitigated uranium, in the newly unsaturated vadose zone. High permeability sandy gravel structures resulted in locally high flow rates in the vicinity of injection wells that increased acetate dilution. In downgradient locations, these structures created preferential flow paths for acetate delivery that enhanced local zones of TEAP reactivity and subsidiary reactions. Conversely, smaller transport rates associated with the lower permeability lithofacies (e.g., fine) and vadose zone were shown to limit acetate access and reaction. Once accessed by acetate, however, these same zones limited subsequent acetate dilution and provided longer residence times that resulted in higher concentrations of TEAP reaction products when terminal electron donors and acceptors were not limiting. Finally, facies-based porosity and reactive surface area variations were shown to affect aqueous uranium concentration distributions with localized effects of the fine lithofacies having the largest impact on U(VI) surface complexation. The ability to model the comprehensive biogeochemical reaction network, and spatially and temporally variable processes, properties, and conditions controlling uranium behavior during engineered bioremediation in the naturally complex Rifle IFRC subsurface system required a subsurface simulator that could use the large memory and computational performance of a massively parallel computer. In this case, the eSTOMP simulator, operating on 128 processor cores for 12h, was used to simulate the 110-day field experiment and 50 days of post-biostimulation behavior.     

A sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite

We performed a sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite through model calibration and validation. Based on some solid phase analysis data and kinetic batch experimental results, we hypothesized three two-site sorption models in the LEHGC reactive transport model to fit the breakthrough curves (BTCs) from the corresponding column experiments. The analysis of breakthrough curves shows that both the empirical two-site kinetic linear sorption model and the semi-mechanistic/semi-empirical two-site kinetic surface complexation model, regardless of their complexity, can match our experimental data fairly well under given test conditions. A numerical experiment to further compare the two models shows that they behave differently when the pore velocity is not of the same order of magnitude as our test velocities. This result indicates that further investigations to help determine a better model are needed. We suggest that a multistage column experiment, which tests over the whole range of practical flow velocities, should be conducted to help alleviate inadequate hypothesized models.     

Natural attenuation of chlorinated ethene compounds: model development and field-scale application at the Dover site

A multi-dimensional and multi-species reactive transport model was developed to aid in the analysis of natural attenuation design at chlorinated solvent sites. The model can simulate several simultaneously occurring attenuation processes including aerobic and anaerobic biological degradation processes. The developed model was applied to analyze field-scale transport and biodegradation processes occurring at the Area-6 site in Dover Air Force Base, Delaware. The model was calibrated to field data collected at this site. The calibrated model reproduced the general groundwater flow patterns, and also, it successfully recreated the observed distribution of tetrachloroethene (PCE), trichloroethene (TCE), dichloroethylene (DCE), vinyl chloride (VC) and chloride plumes. Field-scale decay rates of these contaminant plumes were also estimated. The decay rates are within the range of values that were previously estimated based on lab-scale microcosm and field-scale transect analyses. Model simulation results indicated that the anaerobic degradation rate of TCE, source loading rate, and groundwater transport rate are the important model parameters. Sensitivity analysis of the model indicated that the shape and extent of the predicted TCE plume is most sensitive to transmissivity values. The total mass of the predicted TCE plume is most sensitive to TCE anaerobic degradation rates. The numerical model developed in this study is a useful engineering tool for integrating field-scale natural attenuation data within a rational modeling framework. The model results can be used for quantifying the relative importance of various simultaneously occurring natural attenuation processes.     

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

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

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.     

Inverse modeling of multicomponent reactive transport through single and dual porosity media

Compacted bentonite is foreseen as buffer material for high-level radioactive waste in deep geological repositories because it provides hydraulic isolation, chemical stability, and radionuclide sorption. A wide range of laboratory tests were performed within the framework of FEBEX (Full-scale Engineered Barrier EXperiment) project to characterize buffer properties and develop numerical models for FEBEX bentonite. Here we present inverse single and dual-continuum multicomponent reactive transport models of a long-term permeation test performed on a 2.5 cm long sample of FEBEX bentonite. Initial saline bentonite porewater was flushed with 5.5 pore volumes of fresh granitic water. Water flux and chemical composition of effluent waters were monitored during almost 4 years. The model accounts for solute advection and diffusion and geochemical reactions such as aqueous complexation, acid-base, cation exchange, protonation/deprotonation by surface complexation and dissolution/precipitation of calcite, chalcedony and gypsum. All of these processes are assumed at local equilibrium. Similar to previous studies of bentonite porewater chemistry on batch systems which attest the relevance of protonation/deprotonation on buffering pH, our results confirm that protonation/deprotonation is a key process in maintaining a stable pH under dynamic transport conditions. Breakthrough curves of reactive species are more sensitive to initial porewater concentration than to effective diffusion coefficient. Optimum estimates of initial porewater chemistry of saturated compacted FEBEX bentonite are obtained by solving the inverse problem of multicomponent reactive transport. While the single-continuum model reproduces the trends of measured data for most chemical species, it fails to match properly the long tails of most breakthrough curves. Such limitation is overcome by resorting to a dual-continuum reactive transport model.     

Intercomparison of reactive transport models applied to UO2 oxidative dissolution and uranium migration

Oxidative dissolution of uranium dioxide (UO₂) and the subsequent migration of uranium in a subsurface environment and an underground waste disposal have been simulated with reactive transport models. In these systems, hydrogeological and chemical processes are closely entangled and their interdependency has been analyzed in detail, notably with respect to redox reactions, kinetics of mineralogical evolution and hydrodynamic migration of species of interest.Different codes, where among CASTEM, CHEMTRAP and HYTEC, have been used as an intercomparison and verification exercise. Although the agreement between codes is satisfactory, it is shown that the discretization method of the transport equation (i.e. finite elements (FE) versus mixed-hybrid FE and finite differences) and the sequential coupling scheme may lead to systematic discrepancies.     

Long-term geochemical evolution of the near field repository: insights from reactive transport modelling and experimental evidences

The KBS-3 underground nuclear waste repository concept designed by the Swedish Nuclear Fuel and Waste Management Co. (SKB) includes a bentonite buffer barrier surrounding the copper canisters and the iron insert where spent nuclear fuel will be placed. Bentonite is also part of the backfill material used to seal the access and deposition tunnels of the repository. The bentonite barrier has three main safety functions: to ensure the physical stability of the canister, to retard the intrusion of groundwater to the canisters, and in case of canister failure, to retard the migration of radionuclides to the geosphere. Laboratory experiments (< 10 years long) have provided evidence of the control exerted by accessory minerals and clay surfaces on the pore water chemistry. The evolution of the pore water chemistry will be a primordial factor on the long-term stability of the bentonite barrier, which is a key issue in the safety assessments of the KBS-3 concept.In this work we aim to study the long-term geochemical evolution of bentonite and its pore water in the evolving geochemical environment due to climate change. In order to do this, reactive transport simulations are used to predict the interaction between groundwater and bentonite which is simulated following two different pathways: (1) groundwater flow through the backfill in the deposition tunnels, eventually reaching the top of the deposition hole, and (2) direct connection between groundwater and bentonite rings through fractures in the granite crosscutting the deposition hole. The influence of changes in climate has been tested using three different waters interacting with the bentonite: present-day groundwater, water derived from ice melting, and deep-seated brine. Two commercial bentonites have been considered as buffer material, MX-80 and Deponit CA-N, and one natural clay (Friedland type) for the backfill. They show differences in the composition of the exchangeable cations and in the accessory mineral content. Results from the simulations indicate that pore water chemistry is controlled by the equilibrium with the accessory minerals, especially carbonates. pH is buffered by precipitation/dissolution of calcite and dolomite, when present. The equilibrium of these minerals is deeply influenced by gypsum dissolution and cation exchange reactions in the smectite interlayer. If carbonate minerals are initially absent in bentonite, pH is then controlled by surface acidity reactions in the hydroxyl groups at the edge sites of the clay fraction, although its buffering capacity is not as strong as the equilibrium with carbonate minerals. The redox capacity of the bentonite pore water system is mainly controlled by Fe(II)-bearing minerals (pyrite and siderite). Changes in the groundwater composition lead to variations in the cation exchange occupancy, and dissolution–precipitation of carbonate minerals and gypsum. The most significant changes in the evolution of the system are predicted when ice-melting water, which is highly diluted and alkaline, enters into the system. In this case, the dissolution of carbonate minerals is enhanced, increasing pH in the bentonite pore water. Moreover, a rapid change in the population of exchange sites in the smectite is expected due to the replacement of Na for Ca.     

Uranium removal from groundwater via in situ biostimulation: Field-scale modeling of transport and biological processes

During 2002 and 2003, bioremediation experiments in the unconfined aquifer of the Old Rifle UMTRA field site in western Colorado provided evidence for the immobilization of hexavalent uranium in groundwater by iron-reducing Geobacter sp. stimulated by acetate amendment. As the bioavailable Fe(III) terminal electron acceptor was depleted in the zone just downgradient of the acetate injection gallery, sulfate-reducing organisms came to dominate the microbial community. In the present study, we use multicomponent reactive transport modeling to analyze data from the 2002 field experiment to identify the dominant transport and biological processes controlling uranium mobility during biostimulation, and determine field-scale parameters for these modeled processes. The coupled process simulation approach was able to establish a quantitative characterization of the principal flow, transport, and reaction processes based on the 2002 field experiment, that could be applied without modification to describe the 2003 field experiment. Insights gained from this analysis include field-scale estimates of the bioavailable Fe(III) mineral threshold for the onset of sulfate reduction, and rates for the Fe(III), U(VI), and sulfate terminal electron accepting processes.     

Influence of variable chemical conditions on EDTA-enhanced transport of metal ions in mildly acidic groundwater

Adsorption of Ni and Pb on aquifer sediments from Cape Cod, Massachusetts, USA increased with increasing pH and metal-ion concentration. Adsorption could be described quantitatively using a semi-mechanistic surface complexation model (SCM), in which adsorption is described using chemical reactions between metal ions and adsorption sites. Equilibrium reactive transport simulations incorporating the SCMs, formation of metal-ion-EDTA complexes, and either Fe(III)-oxyhydroxide solubility or Zn desorption from sediments identified important factors responsible for trends observed during transport experiments conducted with EDTA complexes of Ni, Zn, and Pb in the Cape Cod aquifer. Dissociation of Pb-EDTA by Fe(III) is more favorable than Ni-EDTA because of differences in Ni- and Pb-adsorption to the sediments. Dissociation of Ni-EDTA becomes more favorable with decreasing Ni-EDTA concentration and decreasing pH. In contrast to Ni, Pb-EDTA can be dissociated by Zn desorbed from the aquifer sediments. Variability in adsorbed Zn concentrations has a large impact on Pb-EDTA dissociation.     

Quantifying the physical and chemical mass transfer processes for the fate and transport of Co(II)EDTA in a partially-weathered limestone-shale saprolite

The objective of the research is to quantify the relative contributions of physical and chemical mass transfer to the movement of Co(II/III)EDTA (chelates of Cobalt and Ethylene Diamine Tetraacetic Acid or EDTA) through a limestone-shale saprolite soil. Saprolite is a collective term referring to partially-weathered bedrock. It exists extensively in the subsurface. Because the parent bedding structures are maintained during the weathering process, saprolite soils are characterized by intensive fractures and secondary deposits of minerals such as Al-, Fe- and Mn-oxides on the fracture surfaces. Movement of reactive species through the soils may be influenced by diffusion into the rock matrix, a physical mass transfer (PMT) process, and interfacial chemical reactions, a chemical mass transfer (CMT) process. The PMT and CMT processes are phenomenologically similar but mechanistically different. In this research, previous laboratory observations from a Br and Co(II)EDTA tracer injection into an undisturbed saprolite soil column were used. Mechanistic reactive transport models were formulated to quantify the PMT and CMT processes. The PMT process was independently characterized by using the non-reactive tracer Br. Model parameters thus obtained were subsequently used as constraints to quantify the CMT processes involving Co(II)EDTA and its oxidation product Co(III)EDTA. Our calculations indicated that the PMT rates of the less reactive Co(III)EDTA were comparable with their theoretical CMT rates. In contrast, for the more reactive species Co(II)EDTA, CMT rates are higher than PMT rates. Evaluations of alternative CMT process models further confirmed one of our hypotheses on the basis of previous experimental understandings. The hypothesis suggested that competition from Fe-oxide for Co(II)EDTA may account for the majority of the decrease of Co(III)EDTA effluent concentrations that resulted in the separation of total Co and Co(III)EDTA breakthrough curves. Because Co(III)EDTA is more mobile than Co(II)EDTA in the subsurface, the results of this research suggest independent quantifications of CoEDTA PMT and CMT processes if laboratory results are to be interpreted correctly and scaled up for field and predictive uses.     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

Two modelling approaches to water-quality simulation in a flooded iron-ore mine (Saizerais, Lorraine, France): a semi-distributed chemical reactor model and a physically based distributed reactive transport pipe network model

The flooding of abandoned mines in the Lorraine Iron Basin (LIB) over the past 25 years has degraded the quality of the groundwater tapped for drinking water. High concentrations of dissolved sulphate have made the water unsuitable for human consumption. This problematic issue has led to the development of numerical tools to support water-resource management in mining contexts. Here we examine two modelling approaches using different numerical tools that we tested on the Saizerais flooded iron-ore mine (Lorraine, France). A first approach considers the Saizerais Mine as a network of two chemical reactors (NCR). The second approach is based on a physically distributed pipe network model (PNM) built with EPANET 2 software. This approach considers the mine as a network of pipes defined by their geometric and chemical parameters. Each reactor in the NCR model includes a detailed chemical model built to simulate quality evolution in the flooded mine water. However, in order to obtain a robust PNM, we simplified the detailed chemical model into a specific sulphate dissolution-precipitation model that is included as sulphate source/sink in both a NCR model and a pipe network model. Both the NCR model and the PNM, based on different numerical techniques, give good post-calibration agreement between the simulated and measured sulphate concentrations in the drinking-water well and overflow drift. The NCR model incorporating the detailed chemical model is useful when a detailed chemical behaviour at the overflow is needed. The PNM incorporating the simplified sulphate dissolution-precipitation model provides better information of the physics controlling the effect of flow and low flow zones, and the time of solid sulphate removal whereas the NCR model will underestimate clean-up time due to the complete mixing assumption. In conclusion, the detailed NCR model will give a first assessment of chemical processes at overflow, and in a second time, the PNM model will provide more detailed information on flow and chemical behaviour (dissolved sulphate concentrations, remaining mass of solid sulphate) in the network. Nevertheless, both modelling methods require hydrological and chemical parameters (recharge flow rate, outflows, volume of mine voids, mass of solids, kinetic constants of the dissolution-precipitation reactions), which are commonly not available for a mine and therefore call for calibration data.