Upscaling heterogeneity in aquifer reactivity via the exposure-time concept: inverse model

A novel inverse technique is proposed to quantitatively characterize macroscopic variability in aquifer reactivity in a Lagrangian representation. Reactivity heterogeneity is expressed in terms of distributions of flux over cumulative time of exposure of the solution to reactive surface area, termed here 'cumulative reactivity'. In cases involving single aqueous species the combined effects of physical and reactivity heterogeneity on reactive solute transport can often be established and further investigated through joint distributions of flux over travel time and cumulative reactivity. The inverse technique requires the breakthrough curve of a passive tracer to determine the distribution of flux over travel time, and additional breakthrough curves of reactive tracers provide additional moments of the distribution of flux over cumulative reactivity given travel time. Thus breakthroughs of one passive and two reactive tracers can provide the mean and variance of the distribution of flux over cumulative reactivity. This Lagrangian characterization is achieved with knowledge of the types of reactive surfaces present, but not their spatial locations. The distributions can subsequently be applied via forward modeling using the same technique to predict breakthrough curves of other solutes undergoing first-order reactions in similar physically and chemically heterogeneous configurations.     

Turbulence effects on chemical reactions in smog chamber flows

Turbulent mixing effects on the reaction rate of a non-premixed flow are presented for a moderately slow second-order irreversible chemical reaction. The turbulent mixing process leads to inhomogeneities in the concentration of the reactants. Chemical reactions are normally highly non-linear and large errors can result from using average concentrations in the computation of mean reaction rates. A brief review of the literature on this problem and its application areas is made with particular emphasis placed on near isothermal flows where the fluctuation in the reaction rate constant can be neglected. The reaction between mixing air jets containing dilute nitric oxide, NO, and ozone, O₃, is studied in a large Turbulent Smog Chamber (TSC) under conditions of high Reynolds number, three-dimensional flow. The measured reactant concentrations, obtained with good time and space resolution, are used to investigate the effects of the reactant species concentration fluctuations on the mean reactant species concentration field through their contribution to the mean reaction rate. Two flow geometries have been studied: two opposed jets issuing into a large chamber and a plume-like source issuing into a turbulent background flow. A three-dimensional finite-difference computation has been carried out for the flow in the chamber using the k-ε-g model of turbulence and mixing. The reacting species concentration field is calculated by considering the transport of a ‘perturbation variable’ equal to the mean of the difference between the species concentration and its corresponding fast chemistry value. A closure for the mean chemical reaction rate based on this quantity is presented and its experimental validation discussed.     

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.     

Choice of dispersion coefficients in reactive transport calculations on smoothed fields

Local dispersion dominates the mixing of compounds that are introduced separately into the subsurface and do not partition into any other than the aqueous phase. Thus, reactions between these compounds are controlled by dispersive mixing if they are not limited by kinetics. I quantify longitudinal dispersive mixing by the longitudinal effective dispersion coefficient of a conservative tracer introduced by a point-like injection [Water Resour. Res. 36 (12) (2000) 3591-3604]. In the upscaling of mixing-controlled reactive transport, I apply the mean velocity and the effective dispersion coefficient to the macroscopic transport calculations, whereas the reactive parameters on the macro-scale are identical to those on the local scale. The applicability of the approach is demonstrated for the transport of compounds undergoing a second-order irreversible bimolecular reaction. Ten realizations of a two-dimensional heterogeneous log-conductivity field are considered. Using the effective dispersion parameters, the overall mass balance is met in the ensemble average, whereas solute spreading is underestimated. I assess the lack of spreading by the difference between the expected macrodispersion and effective dispersion coefficients. I extend the approach to simulations on log-conductivity fields obtained by kriging of regularly spaced conductivity measurements. These fields contain the large-scale features of the true fields but do not resolve the small-scale variability. For the calculations on the kriged fields, the corresponding conditional covariance is substituted into the analytical expressions of effective dispersion, yielding a correction effective dispersion coefficient. The comparison between simulations on the fully resolved fields and on the kriged fields indicates that the approach is valid for wide plumes meeting the ergodicity condition. The high variability of mixing on small scales unresolved by kriging, however, leads to severe uncertainty when mixing-controlled reactions are predicted for narrow plumes.     

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.     

Relationships between emission sources and air mass characteristics in East Asia during the TRACE-P period

Long-range transport of pollutants influenced by anthropogenic and natural emission sources in East Asia is investigated by using backward trajectory analysis along the NASA TRACE-P flight tracks and a numerical simulation with the three-dimensional chemical transport model (STEM-2k1). Observation-based regional distributions of trace gases are reconstructed using the observations obtained by measurements on board the DC-8 and P3-B aircrafts. Systematic features of the spatial distribution for each species are identified. It is found that the observed concentrations of CO and some NMHCs, and the ratios between these species, are highly associated with the source distribution features and their regional characteristics. Reconstructed fields of the observed and modeled ethane/CO and ethane/propane are found to reproduce well the estimated emission ratios in East Asia. We also investigated the time rate of change of the concentration of species and their ratio along the trajectory. From this analysis the propane/ethane and propane/acetylene ratios are shown to preserve their emission ratios during regional transport. However systematic differences in the propane vs. acetylene/CO relationships are found between the model and observation values. This analysis suggests that further efforts are needed to improve the estimates of biomass burning emissions in SE Asia. The results presented in this paper also suggest ways to further extend the capabilities to derive observation-based inventories.     

New particle formation in the Midwestern USA: Event characteristics,meteorological context and vertical profiles

Two years of continuous particle size distribution measurements at three heights over and in a deciduous forest in southern Indiana exhibit evidence of particle nucleation on 46% of classifiable days, and clear nucleation with consistent subsequent growth on 14% of days. Events characterized by high ultra-fine particle production and clear growth are most frequent in spring. These events most frequently follow cold front passages and exhibit a higher frequency of northerly back-trajectories. Local meteorological conditions, as described using the Nucleation Parameter (NP) of Boy and Kulmala (2002) and stability indices, indicate a significant association with ultra-fine particle concentrations, and specifically that nucleation was frequently preceded by destabilization of the atmosphere consistent with entrainment of elevated pollution layers. There appears to be little or no dependence of nucleation frequency or intensity on the in situ condensational sink particularly during spring, which is consistent with very high regional emissions of the precursors of ternary nucleation. Vertical gradients of particle size distributions exhibit evidence for nucleation being focused above canopy and accordingly mean ratios of above and below canopy concentrations of ultra-fine particles (6–30 nm) just subsequent to nucleation are 1.8 and 1.7 respectively during leaf-on and leaf-off periods. The difference in vertical concentration ratios during leaf-on and leaf-off are used to infer that of the order of 25% of ultra-fine particles are captured by foliar elements in the canopy during turbulent mixing through the canopy.     

On the seasonal variation of the surface ozone in Athens,Greece

An attempt has been made to examine the seasonal variation of the surface ozone mixing ratio in Athens, Greece during the periods 1901–1940 and 1987–1998. The first finding is that in July and August while the daytime surface ozone mixing ratio from the beginning until the end of the 20th century has increased by approximately 1.8 times, the nighttime surface ozone mixing ratio remained approximately at the same level. The second finding is that the increase in the mean daytime mixing ratio during the transition period from winter to summer is equal to the increase in the maximum daytime mixing ratios, whilst the enhancement of the nighttime surface ozone maxima is stronger than that of the nighttime mean surface ozone mixing ratio. Plausible explanation for this finding is given through mechanisms like long-range transport and photochemical processes occurring in the boundary layer, free troposphere and lower stratosphere.     

Vertical distributions of aerosols under different weather conditions: Analysis of in-situ aircraft measurements in Beijing,China

In this study, aerosol vertical distributions of 17 in-situ aircraft measurements during 2005 and 2006 springs are analyzed. The 17 flights are carefully selected to exclude dust events, and the analyses are focused on the vertical distributions of aerosol particles associated with anthropogenic activities. The results show that the vertical distributions of aerosol particles are strongly affected by weather and meteorological conditions, and 3 different types of aerosol vertical distributions corresponding to different weather systems are defined in this study. The measurement with a flat vertical gradient and low surface aerosol concentrations is defined as type-1; a gradual decrease of aerosols with altitudes and modest surface aerosol concentrations is defined as type-2; a sharp vertical gradient (aerosols being strongly depressed in the PBL) with high surface aerosol concentrations is defined as type-3. The weather conditions corresponding to the 3 different aerosol types are high pressure, between two high pressures, and low pressure systems (frontal inversions), respectively. The vertical mixing and horizontal transport for the 3 different vertical distributions are analyzed. Under the type-1 condition, the vertical mixing and horizontal transport were rapid, leading to strong dilution of aerosols in both vertical and horizontal directions. As a result, the aerosol concentrations in PBL (planetary boundary layer) were very low, and the vertical distribution was flat. Under the type-2 condition, the vertical mixing was strong and there was no strong barrier at the PBL height. The horizontal transport (wind flux) was modest. As a result, the aerosol concentrations were gradually reduced with altitude, with modest surface aerosol concentrations. Under the type-3 condition, there was a cold front near the region. As a result, a frontal inversion associated with weak vertical mixing appeared at the top of the inversion layer, forming a very strong barrier to prevent aerosol particles being exchanged from the PBL height to the free troposphere. As a result, the aerosol particles were strongly depressed in the PBL height, producing high surface aerosol concentrations. The measured vertical aerosol distributions have important implications for studying the effects of aerosols on photochemistry. The J[O₃] values are reduced by 11%, 48%, and 50%, under the type-1, type-2, and type-3 conditions, respectively. This result reveals that atmospheric oxidant capacity (OH concentrations) is modestly reduced under the type-1 condition, but is significantly reduced under the type-2 and type-3 conditions. This result also suggests that the effect of aerosol particles on surface solar flux is an integrated column effect, and detailed vertical distributions of aerosol particles are very important for assessing the impacts of aerosol on photochemistry.     

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.     

Groundlevel concentration fluctuations from a buoyant and a non-buoyant source within a laboratory convectively mixed layer

With the use of mixed-layer scaling, the near-surface mean concentration and the concentration fluctuations at moderate distances downwind of a stack emitting a highly buoyant effluent are obtained and compared quantitatively with those from a non-buoyant source that is otherwise identical. The environment is a laboratory mixed layer in a state of free convection with mean wind simulated by towing the stack along a horizontal line. Although the buoyant effluent has a much smaller maximum mean groundlevel concentration occurring at a greater downwind distance than the non-buoyant effluent, the decay of mean concentration from that point downwind is found to be exceedingly slow in the buoyant case.The cumulative frequency distributions of sampled concentrations greater than zero for these same two cases are found to be log-normal in only a bimodal sense, with the weaker concentrations having a greater logarithmic range in amplitude than the stronger concentrations. The ratio of the root-mean-square (r.m.s.) concentration fluctuation to the mean concentration, in the central portion of the mean plume, is found to decay with downwind distance. Homogenization associated with both downstream and vertical mixing is believed responsible for the rapid decay observed.     

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.     

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.     

Atmospheric phase distribution of oxidized and reduced nitrogen at a forest ecosystem research site

Atmospheric concentrations of gaseous NH3 and HNO3 and of particulate NH4+ and NO3- were measured during various seasons at a forest ecosystem research site in the "Fichtelgebirge" mountains in Central Europe. Air masses arriving at this site were highly variable with respect to trace compound concentration levels and their concentration ratios. However, the distributions of NH4+ and NO3- within the aerosol particle size spectra exhibited some very consistent patterns, with the former dominating the fine particle concentrations, and the latter dominating the coarse particles range, respectively. Overall, the particulate phase (NH4+ + NO3-) dominated the atmospheric nitrogen budget (particulate and gas phase, NH4+ + NO3- + NH3 + HNO3) by more than 90% of the median total mixing ratio in winter, and by more than 60% in summer. The phase partitioning varied significantly between the winter and summer seasons, with higher relative importance of the gaseous species during summer, when air temperatures were higher and relative humidities lower as compared to the winter season. Reduced nitrogen dominated over oxidized nitrogen, indicating the prevailing influence of emissions from agricultural activity as compared to traffic emissions at this mountainous site. A model has been successfully applied in order to test the hypothesis of thermodynamic equilibrium between the particulate and gas phases.     

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.     

Scavenging of atmospheric formaldehyde by wet precipitation

Despite the great importance that formaldehyde has in atmospheric photochemistry, few studies have been reported on rain water. In this paper, concentrations of HCHO in rain fractions within rain events are presented. Two sampling sites were chosen: one at Mexico City, a great polluted urban area, and the second at Rancho Viejo, a forested area under the meteorological influence of the city. The results show a general decrease during the early portion of the rain event. This seems to indicate that below-cloud scavenging is the most important mechanism while, from the small variations observed in the latter portion of the rainfall, it is possible to assume within-cloud scavenging as the predominant mechanism. Using the HCHO concentrations in rain water, the mixing ratios were estimated for the two sampling sites. The values were 0.68 ppb and 0.44 ppb at Mexico City and Rancho Viejo, respectively. Measurements at ground level in Mexico City gave a mean HCHO concentration in air of 24 ppb, much higher than the estimated mixing ratio. The high levels of HCHO found in ambient air and in rain water reflect anthropogenic emissions as the potential atmospheric sources.     

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.     

Nighttime variations in HO2 radical mixing ratios at Rishiri Island observed with elevated monoterpene mixing ratios

HO₂ radical concentrations were measured by a laser-induced fluorescence instrument for three nighttime periods during the intensive field campaign at Rishiri Island, Japan, in June 2000. The HO₂ mixing ratio had temporal variations around its average of 4.2±1.2 (1σ) pptv and showed a positive correlation with the summed mixing ratio of four monoterpene species, α-pinene, β-pinene, camphene, and limonene, that sometimes reached 1 ppbv. Our model calculations suggested that ozonolysis reactions of monoterpenes were the main source of nighttime radicals and they explained 58% of measured HO₂ concentration levels. The model roughly reproduced the dependence of the HO₂ mixing ratio on the square root of the radical production rate due to the ozonolysis reactions of the monoterpenes. However, the absolute HO₂ mixing ratio was significantly underpredicted by the model. We discuss possible reasons in terms of misunderstood RO₂ chemistry, RO₂ interference with HO₂ observations, unknown radical production process associated by high NO₂ mixing ratio, and the contribution of unmeasured olefinic species to radical production via their reactions with ozone.     

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.     

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.