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.     

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.     

An innovative methodology for analyzing digital visibility images in an urban environment

A novel methodology combining digital imaging, conventional fixed visibility monitors, and solar radiation monitors has been developed to characterize the visual air quality of the El Paso and Ciudad Juarez urban vista. The authors have found that the digital image quality is reproducible and useful for quantitative analysis of visibility conditions. Regions of interest were selected in images along view paths of interest and values for a contrast variable of interest, typically the coefficient of variation or contrast ratio (CR) for discrete targets, were computed. Both of these indices are bounded at 0 and 1 and are scaled to the "clean day" maxima for a given date, time, and selected view paths. This produces a relative visibility index for various view paths. With the siting of a Belfort (6230A) visibility monitor at a central location, it has been possible to initiate contrast analysis of various targets in current and archived camera images obtained near this monitor. For uniformly "clean" days, as indicated by fine particulate matter observations and visual inspection, the authors have been able to use the extinction coefficient (Bext) derived from the 6230A to put the relative visibility index, based on CR, on an absolute basis in terms of an ideal target located at a given distance. This permits the generation of contrast extinction, Bext/C, for each view path that is independent of the actual target intrinsic contrast (within limits) and allows the comparison of Bext/C along different view paths with other air quality indices. Multiple linear regression was used to derive a relationship between the CR-based Bext/C value and air quality parameters. Visibility attenuation because of sulfate particles was found to have the highest correlation with Bext/C. In addition, solar radiation was observed to be a significant predictor of visibility in the urban region.     

Analytical solutions for multiple species reactive transport in multiple dimensions

Many numerical computer codes used to simulate multi-species reactive transport and biodegradation have been developed in recent years. Such numerical codes must be validated by comparison of the numerical solutions with an analytical solution. In this paper, a method for deriving analytical solutions of the partial differential equations describing multiple species multi-dimensional transport with first-order sequential reactions is presented. Although others have developed specific solutions of multi-species transport equations, here a more general analytical approach, capable of describing any number of reactive species in multiple dimensions is derived. A substitution method is used to transform the multi-species reactive transport problem to one that can be solved using previously published single-species solutions for various initial and boundary conditions. One- and three-dimensional examples are presented to illustrate the steps involved in extending single-species solutions to a four-species system with sequential first-order reactions.     

A methodology for the estimation of road transport air emissions in urban areas of Italy

This paper focuses on the top–down approach for estimating road transport emissions at a local level. A bottom–up approach is preferable where the data and information required by estimation methodologies are available at regional territorial level. In the absence of this regional data, emissions are adapted from national to smaller levels by means of proxy variables. This study highlights the importance of an improvement of the top–down methodology and identifies a corrective index to better characterise road transport emissions at a local level. A set of indicators related to transport activities is selected in order to identify homogeneous areas in the Italian territory. For each area, COPERT (Computer Programme to estimate Emissions from Road Traffic) methodology is applied to estimate the atmospheric emissions of different pollutants; the same methodology is used to calculate road transport emissions at a national level. The results, calculated according to vehicle category and driving mode, are compared with those deriving from a spatial disaggregation of national data by means of simple surrogate variables.     

Concentration statistics for mixing-controlled reactive transport in random heterogeneous media

Uncertainty in the distribution of hydraulic parameters leads to uncertainty in flow and reactive transport. Traditional stochastic analysis of solute transport in heterogeneous media has focused on the ensemble mean of conservative-tracer concentration. Studies in the past years have shown that the mean concentration often is associated with a high variance. Because the range of possible concentration values is bounded, a high variance implies high probability weights on the extreme values. In certain cases of mixing-controlled reactive transport, concentrations of conservative tracers, denoted mixing ratios, can be mapped to those of constituents that react with each other upon mixing. This facilitates mapping entire statistical distributions from mixing ratios to reactive-constituent concentrations. In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used. We demonstrate that the second-order perturbative approximation leads to erroneous or even physically impossible estimates of mean reactive-constituent concentrations when the variance of the mixing ratio is high and the relationship between the mixing ratio and the reactive-constituent concentrations strongly deviates from a quadratic function. The latter might be the case in biokinetic reactions or in equilibrium reactions with small equilibrium constant in comparison to the range of reactive-constituent concentrations. When only the mean and variance of the mixing ratio is known, we recommend assuming a distribution that meets the known bounds of the mixing ratio, such as the beta distribution, and mapping the assumed distribution of the mixing ratio to the distributions of the reactive constituents.     

A triple-continuum approach for modeling flow and transport processes in fractured rock

This paper presents a triple-continuum conceptual model for simulating flow and transport processes in fractured rock. Field data collected from the unsaturated zone of Yucca Mountain, a repository site of high-level nuclear waste, show a large number of small-scale fractures. The effect of these small fractures has not been considered in previous modeling investigations within the context of a continuum approach. A new triple-continuum model (consisting of matrix, small-fracture, and large-fracture continua) has been developed to investigate the effect of these small fractures. This paper derives the model formulation and discusses the basic triple-continuum behavior of flow and transport processes under different conditions, using both analytical solutions and numerical approaches. The simulation results from the site-scale model of the unsaturated zone of Yucca Mountain indicate that these small fractures may have an important effect on radionuclide transport within the mountain.     

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.     

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.     

Analytical solutions for reactive transport under an infiltration-redistribution cycle

Transport of reactive solute in unsaturated soils under an infiltration-redistribution cycle is investigated. The study is based on the model of vertical flow and transport in the unsaturated zone proposed by Indelman et al. [J. Contam. Hydrol. 32 (1998) 77], and generalizes it by accounting for linear nonequilibrium kinetics. An exact analytical solution is derived for an irreversible desorption reaction. The transport of solute obeying linear kinetics is modeled by assuming equilibrium during the redistribution stage. The model which accounts for nonequilibrium during the infiltration and assumes equilibrium at the redistribution stage is termed partial equilibrium infiltration-redistribution model (PEIRM). It allows to derive approximate closed form solutions for transport in one-dimensional homogeneous soils. These solutions are further applied to computing the field-scale concentration by adopting the Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979) 461] column model. The effect of soil heterogeneity on the solute spread is investigated by modeling the hydraulic saturated conductivity as a random function of horizontal coordinates. The quality of the PEIRM is illustrated by calculating the critical values of the Damk?hler number which provide the achievable accuracy in estimating the solute mass in the mobile phase. The distinguishing feature of transport during the infiltration-redistribution cycle as compared to that of infiltration only is the finite depth of solute penetration. For irreversible desorption, the maximum solute penetration W/theta(r) is determined by the amount of applied water W and the residual water content theta(r). For sorption-desorption kinetics, the maximum depth of penetration z(r)(e, infinity ) also depends on the ratio between the rate of application and the column-saturated conductivity. It is shown that z(r)(e, infinity ) is bounded between the depths W/(theta(r)+K(d)) and W/theta(r) corresponding to the maximum solute penetration for equilibrium transport and for irreversible desorption, respectively. This feature of solute penetration explains the unusual phenomena of plume contraction after an initial period of spreading [Lessoff, S.C., Indelman, P., Dagan, G., 2002. Solute transport in infiltration-redistribution cycles in heterogeneous soils. In Raats, P.A.C., Smiles, D.,Warrick, A.W. (Eds), Environmental Mechanics: Water, Mass and Energy Transport in the Biosphere. American Geophysical Union, pp. 133-144]. Unlike transport under equilibrium conditions, when the solute is completely concentrated at the front, the solute under nonequilibrium conditions is spread out behind the front. Heterogeneity leads to additional spreading of the plume.     

Theory for reactive solute transport through clay membrane barriers

The theoretical development for one-dimensional, coupled migration of solutes with different ionic mobilities through clay soils that behave as ion-restrictive membranes, referred to as clay membrane barriers (CMBs), is presented. The transport formulation is based on principles of irreversible thermodynamics and accounts explicitly for coupling effects of hyperfiltration (ultrafiltration) and chemico-osmotic counter-advection associated with clay membrane behavior in the absence of electrical current. Since, by definition, no solute can enter a "perfect" or "ideal" membrane, the concept of an implicit coupling effect, such that the effective salt-diffusion coefficient, Ds* approaches zero as the chemico-osmotic efficiency coefficient, omega approaches unity is introduced. The theoretical development also illustrates that, even in the absence of membrane behavior, traditional advective-dispersive transport theory based on a constant value of Ds* for the solutes may not be appropriate for simulating transient transport in reactive (ion exchanging) systems. This potential limitation is illustrated through simulations for solute mass flux involving the migration of a binary salt solution (KCl) through a clay barrier with exchange sites saturated with a single exchangeable cation (e.g., Na+) that enters the pore solution upon ion exchange with the salt cation (K+).     

Gas phase transport in gravity sewers--A methodology for determination of horizontal gas transport and ventilation.

A method was developed for determination of horizontal gas transport and ventilation in gravity sewers. This was achieved by changing the composition of the sewer atmosphere by pulse injection of oxygen gas and subsequently measuring the oxygen concentration in a downstream manhole. Conventional tracer techniques may require sampling and may also affect the environment. The method developed is simple, based on direct monitoring and without environmental or toxic effects. The method was developed based on measurements in an intercepting gravity sewer. The horizontal gas transport processes were quantified by measuring the velocity and dispersion of the gas in the sewer atmosphere. Based on 54 measurements, the gas velocity was found to vary between 0.05 and 0.22 m/s. The coefficients of dispersion were calculated to be in the range 0.05 to 1.1 m2/s. Climatic conditions did not significantly influence the gas phase transport.     

A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.     

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.     

微环境新风量的检测原理及方法研究

新风量是评价室内微环境空气卫生质量的主要卫生指标之一,也是计算室内某种气体单位时间排放量的重要参数。以CO2作为示踪气体,利用于冰升华和人体呼吸产生CO2示踪气体两种测量方法对室内和车内微环境进行了检测,并考虑室内人呼出CO2量的影响,运用箱子模式的各种推导公式（稳态法、解析解法和差分法）对新风量进行了计算,并对结果进行了讨论。结果表明,没有人存在下,用箱子模式的解析解法和差分法计算的新风量值没有明显的统计差异;微环境内有人时必须考虑人释放的影响,这样箱子模式的各种推导公式都可以计算新风量值,且结果准确,准确度高。利用人体呼吸产生CO2示踪气体法,用差分法计算结果不理想,偏差很大;用稳态法计算重现性高,结果可靠。     

A review on reactive transport model and porosity evolution in the porous media

Environmental Science and Pollution Research - This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and...     

Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions

The couplings among chemical reaction rates, advective and diffusive transport in fractured media or soils, and changes in hydraulic properties due to precipitation and dissolution within fractures and in rock matrix are important for both nuclear waste disposal and remediation of contaminated sites. This paper describes the development and application of LEHGC2.0, a mechanistically based numerical model for simulation of coupled fluid flow and reactive chemical transport, including both fast and slow reactions in variably saturated media. Theoretical bases and numerical implementations are summarized, and two example problems are demonstrated. The first example deals with the effect of precipitation/dissolution on fluid flow and matrix diffusion in a two-dimensional fractured media. Because of the precipitation and decreased diffusion of solute from the fracture into the matrix, retardation in the fractured medium is not as large as the case wherein interactions between chemical reactions and transport are not considered. The second example focuses on a complicated but realistic advective-dispersive-reactive transport problem. This example exemplifies the need for innovative numerical algorithms to solve problems involving stiff geochemical reactions.     

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.     

Analytical solutions for flow fields near continuous wall reactive barriers

Permeable reactive barriers (PRBs) are widely applied for in-situ remediation of contaminant plumes transported by groundwater. Besides the goal of a sufficient contaminant remediation inside the reactive cell (residence time) the width of plume intercepted by a PRB is of critical concern. A 2-dimensional analytical approach is applied to determine the flow fields towards rectangular PRBs of the continuous wall (CW) configuration with and without impermeable side walls (but yet no funnel). The approach is based on the conformal mapping technique and assumes a homogeneous aquifer with a uniform ambient flow field. The hydraulic conductivity of the reactive material is furthermore assumed to exceed the conductivity of the aquifer by at least one order of magnitude as to neglect the hydraulic gradient across the reactor. The flow fields are analyzed regarding the widths and shapes of the respective capture zones as functions of the dimensions (aspect ratio) of the reactive cell and the ambient groundwater flow direction. Presented are an improved characterization of the advantages of impermeable side walls, a convenient approach to improved hydraulic design (including basic cost-optimization) and new concepts for monitoring CW PRBs. Water level data from a CW PRB at the Seneca Army Depot site, NY, are used for field demonstration.     

A mountain-scale thermal-hydrologic model for simulating fluid flow and heat transfer in unsaturated fractured rock

A multidimensional, mountain-scale, thermal-hydrologic (TH) numerical model is presented for investigating unsaturated flow behavior in response to decay heat from the proposed radioactive waste repository in the Yucca Mountain unsaturated zone (UZ), The model, consisting of both two-dimensional (2-D) and three-dimensional (3-D) representations of the UZ repository system, is based on the current repository design, drift layout, thermal loading scenario, and estimated current and future climate conditions. This mountain-scale TH model evaluates the coupled TH processes related to mountain-scale UZ flow. It also simulates the impact of radioactive waste heat release on the natural hydrogeological system, including heat-driven processes occurring near and far away from the emplacement tunnels or drifts. The model simulates predict thermally perturbed liquid saturation, gas- and liquid-phase fluxes, and water and rock temperature elevations, as well as the changes in water flux driven by evaporation/condensation processes and drainage between drifts. These simulations provide insights into mountain-scale thermally perturbed flow fields under thermal loading conditions.