Successive identification of biodegradation rates for multiple sequentially reactive contaminants in groundwater.

At the field scale, the biodegradation rate is usually estimated from analytical solutions to single species transport with first-order reactions, using measured data as input. Because many contaminants, e.g., chlorinated solvents, are degraded in a sequential pattern, with degradation products further reacting to produce new species, it is of great interest to quantify the transformation rate of every reaction. The conventional inverse solutions for identifying the transformation rates are limited to single species problems. In the present study, we propose a successive optimization approach to identify the biodegradation rate for each species by using a previously developed analytical solution to multi-species first-order reactive transport using data obtained at the field scale. By specifying a link between analytical solutions to sequentially reactive transport problems and optimization methods and assuming constant transport parameters (velocity, dispersivities, and retardation factors), the first-order transformation rates are optimized successively from parent species to its daughter species.     

单井捕获地下水污染羽的优化方法

针对不同抽水井捕获半径及驻点获取方法存在局限性和误差的问题,以潜水、承压水2个类型污染场地为例,分别采用实测法、解析解公式法、数值模拟法3种方法计算单井捕获半径及驻点值;通过对比分析,研究了不同条件下3种方法的局限性及精确度;探讨了不同类型污染场地获取捕获半径及驻点的最适宜方法。结果表明：对于承压水类型,解析解计算值与实际观测值误差较小,为3.2%;对于水位降深相对于含水层厚度不可忽略的潜水类型,解析解计算值与实际观测值误差较大,为80.7%;在充分掌握水文地质条件时,数值模型模拟结果与实际观测误差值不超过10%。因此,当场地水文地质情况符合解析解公式假设条件时,可采用解析解公式法获取单井捕获半径及驻点,否则须利用数值模拟方法或实测法获取相关参数。研究成果为不同类型污染场地选择合适方法获取捕获半径及驻点提供了参考。     

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.     

Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in sigmaY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999-3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019-3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139-193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit-Forchheimer assumption holds.     

Displacement and sweep efficiencies in a DNAPL recovery test using micellar and polymer solutions injected in a five-spot pattern

Soil washing with micellar solutions is a promising alternative for the remediation of DNAPL source zones. As with any flushing technology, the success of soil washing with micellar solutions depends in a very large part on the ability of the solution to contact the contaminant (sweep efficiency) and then on the efficiency of contaminant removal once this contact is made (displacement efficiency). We report here on a field test where a micellar solution was used to recover a DNAPL in an open five-spot pattern in which polymer solutions were also injected before and after the washing solution to improve sweep efficiency. The washing solution formulation was optimised in the laboratory prior to the test to obtain good dissolution capacity. For a high-concentration and low-volume soil flushing remediation test such as the one performed (0.8 pore volumes of actual washing solution injected), slug sizing of the washing solution is critical. It was evaluated by an analytical solution. In a five-spot pattern, the displacement efficiency of the washing solution was observed to vary in the porous medium as a function of the radial distance from the injection well because: (1) the volume of the washing solution flowing through a section of the test cell changes (maximum close to the injection well and minimal at the pumping wells); (2) the in situ velocity changes (maximum at the wells and minimum between the wells) and; (3) the contact time of the washing solution with the NAPL changes as a function of the distance from the injection well. The relative importance of the recovery mechanisms, mobilisation and dissolution, was also observed to vary in the test cell. The reduced velocity increased the contact time of the washing solution with the DNAPL enhancing its dissolution, but the decrease of the capillary number caused less mobilisation. The washing process is much more extensive around the injection well. The use of an injection-pumping pattern allowing a complete sweep of the remediated area is essential. Following a comprehensive characterisation, modeling is an efficient tool to design the injection-pumping scheme and to optimise injection and pumping rates providing the best areal sweep. The vertical sweep can be controlled by using a polymer solution (Xanthan gum). The polymer solution also has a positive effect on front stability between the solutions injected. The injection rate of the polymer solution that follows the washing solution must be kept minimal initially to prevent dilution of the washing solution by fingering.     

Two analytical solutions to the linear transport diffusion equation for a parallel plate precipitator

An analytical solution is derived for the linear transport-diffusion equation with boundary conditions appropriate to an electrostatic precipitator. The dependence of precipitator performance on along flow diffusion is shown to be minimal. Accordingly a second solution is developed, taking this factor to be zero, which is found to encapsulate the results of the earlier model. The latter solution provides a suitable basis for a piecewise analytic model which permits account to be taken of changes in the governing variables, with distance through the precipitator.The analytical solutions are used to explore the dependence of precipitator performance on geometry, flow properties and particle migration velocity. It is found to be possible to express this concisely in terms of dimensionless groups.The results illustrate the sensitivity of precipitator performance to lateral diffusivity and hence the importance of correctly representing this factor in mathematical models and the potential benefit flowing from practical designs which minimize turbulence.     

Analytical formulas for the below-cloud scavenging coefficient of an irreversibly soluble gas: a quantitative evaluation for HNO3

In the present paper, analytical expressions are derived for the below-cloud gas scavenging coefficient, considering various functions that can be found in the literature to describe raindrop populations and terminal velocities. Three primary cases have been identified where an analytical solution exists: (i) a raindrop size distribution described by a gamma function and raindrop terminal velocity by a power function of raindrop size; (ii) a raindrop size distribution described by a gamma function and raindrop terminal velocity by an exponential function; and (iii) a raindrop size distribution described by a log–normal function and raindrop terminal velocity by a power function. In addition, in case (i), the gas scavenging coefficient is expressed analytically as a function of rain intensity. The derived analytical expressions are subsequently used to compute the scavenging coefficients of HNO₃ for different parameterizations of the raindrop size distribution and terminal velocity functions. In order to broaden the sensitivity test of HNO3 scavenging coefficients on parameterizations, scavenging coefficients of HNO₃ are also computed numerically for the raindrop terminal velocity as a function of raindrop size and atmospheric conditions. The results show that there is a relative variation in the values of the gas scavenging coefficient up to 50% for the parameterization considered in this study, and that the overestimation given by the analytical formulas is not important for cut-off limits of raindrop spectra below 0.2 mm.     

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.     

A model for contaminant mass flux in capped sediment under consolidation

The paper presents a model for contaminant transport and flux through a consolidating subaqueous sediment and overlying cap. The formulation is based on the effect of consolidation and excess pore pressure dissipation on transient, nonlinear advective component of transport through sediment and the cap. The consolidation is induced by the buoyant weight of the cap when it is placed on the contaminated sediments. One equation is presented for advective-diffusive transport through the sediment that is dependent upon soil/contaminant properties and transient advective velocity, which is calculated from a second equation based on the Terzaghi consolidation theory. A third equation is provided to describe the transport of contaminants in the cap. The parameters, including advective velocity, and boundary conditions used for contaminant transport through the cap are derived from the solution of the first two equations. The finite difference method is used to solve the system of equations for consolidation and contaminant transport. A hypothetical case is analyzed to demonstrate the formulation, and the results show that advection due to consolidation can accelerate breakthrough of contaminant through the cap by orders of magnitude. The derivation and results show that consolidation should be included for cap design, and that reactive caps are essential for delaying and reducing dissolved contaminant flux.     

An analytical solution for vertical transport of volatile chemicals in the vadose zone

An analytical solution is presented for one-dimensional vertical transport of volatile chemicals through the vadose zone to groundwater. The solution accounts for the important transport mechanisms of the steady advection of water and gas, diffusion and dispersion in water and gas, as well as adsorption, and first-order degradation. By assuming a linear, equilibrium partitioning between water, gas and the adsorbed chemical phases, the dependent variable in the mathematical model becomes the total resident concentration. The general solution was derived for cases having a constant initial total concentration over a discrete depth interval and a zero initial total concentration elsewhere. A zero concentration gradient is assumed at the groundwater table. Examples are given to demonstrate the application of the new solution for calculating the case of a non-uniform initial source concentration, and estimating the transport of chemicals to the groundwater and the atmosphere. The solution was also used to verify a numerical code called VLEACH. We discovered an error in VLEACH, and found that the new solution agreed very well with the numerical results by corrected VLEACH. A simplified solution to predict the migration of volatile organic chemical due to the gas density effect has shown that a high source concentration may lead to significant downward advective gas-phase transport in a soil with a high air-permeability.     

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).     

Stepwise superposition approach for the analytical solutions of multi-dimensional contaminant transport in finite- and semi-infinite aquifers

Analytical solutions of contaminant transport in multi-dimensional media are significant for theoretical and practical purposes. However, due to the problems for which the solutions are sought which are complex in most of the cases, most available analytical solutions in multi-dimensional media are not given in their closed forms. Integrals are often included in the solution expressions, which may limit the practitioners to use the solutions. In addition, available multi-dimensional solutions for the third-type sources in bounded media are fairly limited. In this paper, a stepwise superposition approach for obtaining approximate multi-dimensional transport solutions is developed. The approach is based on the condition that the one-dimensional solution along the flow direction is known. The solutions are expressed in their closed forms without integrals. The transport media to the solutions are flexible and can be finite, semi-infinite, or infinite in the transverse directions. The solutions subject to the first- and third-type boundary conditions at the inlet with a distributed source over the domain are obtained. The integrals in some known solutions can also be evaluated by the approach if they can be derived to include known longitudinal integrals with respect to time. The accuracy and efficiency of the solutions proposed in this paper are verified through test problems and calculation examples.     

Contributions of advective and diffusive oxygen transport through multilayer composite caps over mine waste

The relative contributions of four mechanisms of oxygen transport in multilayer composite (MLC) caps placed over oxygen-consuming mine waste were evaluated using numerical and analytical methods. MLC caps are defined here as caps consisting of earthen and geosynthetic (polymeric) components where a composite barrier layer consisting of a geomembrane (1-2 mm thick polymeric sheet) overlying a clay layer is the primary barrier to transport. The transport mechanisms that were considered are gas-phase advective transport, gas-phase diffusive transport, liquid-phase advective transport via infiltrating precipitation and liquid-phase diffusive transport. A numerical model was developed to simulate gas-phase advective-diffusive transport of oxygen through a multilayer cap containing seven layers. This model was also used to simulate oxygen diffusion in the liquid phase. An approximate analytical method was used to compute the advective flux of oxygen in the liquid phase. The numerical model was verified for limiting cases using an analytical solution. Comparisons were also made between model predictions and field data for earthen caps reported by others. Results of the analysis show that the dominant mechanism for oxygen transport through MLC caps is gas-phase diffusion. For the cases that were considered, the gas-phase diffusive flux typically comprises at least 99% of the total oxygen flux. Thus, designers of MLC caps should focus on design elements and features that will limit diffusion of gas-phase oxygen.     

Monitoring groundwater contamination and delineating source zones at industrial sites: uncertainty analyses using integral pumping tests

Field-scale characterisations of contaminant plumes in groundwater, as well as source zone delineations, are associated with uncertainties that can be considerable. A major source of uncertainty in environmental datasets is due to variability of sampling results, as a direct consequence of the heterogeneity of environmental matrices. We develop a methodology for quantifying uncertainties in field-scale mass flow and average concentration estimations, using integral pumping tests (IPTs), where the contaminant concentration is measured as a function of time in a pumping well. This procedure increases the sampling volume and reduces the effect of small-scale variability that may bias point-scale measurements. In particular, using IPTs, the interpolation uncertainty of conventional point-scale measurements is transformed to a quantifiable uncertainty related to the (unknown) plume position relative to the pumping well. We show that this plume position uncertainty generally influenced the predicted mass flows and average concentrations (of acenapthene, benzene and CHCs) to a greater extent than a boundary condition uncertainty related to the local water balance, considering 19 control planes at a highly heterogeneous industrial site in southwest Germany. Furthermore, large (order of magnitude) uncertainties only occurred if the conditions were strongly heterogeneous in the nearest vicinity of the well. We also develop a consistent methodology for an assessment of the combined effect of uncertainty in hydraulic conditions and uncertainty in reactive transport parameters for delimiting of both contaminant source zones and zones absent of source, based on (downgradient) IPTs.     

Predicting natural attenuation of xylene in groundwater using a numerical model.

The aquifer beneath an abandoned refinery in the Lower Rhine area, Germany, was contaminated with a number of different mineral oil products. Groundwater sampling in the area around the former xylene plant revealed that a xylene plume had developed in the underlying groundwater, and moreover, that there is strong evidence for in situ microbial xylene degradation with oxygen, nitrate, sulfate and ferric iron as electron acceptors. In order to prevent further xylene spreading, three pumping wells extracting contaminated water were installed downgradient of the spill zone. The numerical reactive transport code Transport Biochemisty Chemistry (TBC) was applied to this situation to quantify the relation of microbial degradation to xylene removal by the pumping wells. It could be shown that the unamended in situ degradation was an appreciable xylene removal process that contributed to about one-third to the total xylene removal (degradation plus extraction). A further objective of the model application was to predict xylene spreading under regional flow conditions, i.e. without operation of the three pumping wells, to consider the possible effects of natural xylene attenuation. To accomplish this, the model calibrated for the situation with operating wells was transferred to the hydraulic situation of regional flow while retaining the parameters of the biochemical model. It turned out that the xylene plume that is expected to develop downgradient of the source area will be limited to an extension of not more than 1000 m. An interesting feature of the simulations results was that xylene degradation under iron-reducing conditions, which was of minor importance for the situation with operating pumping wells, becomes the dominant degradation mechanism under regional flow conditions. Moreover, iron reduction will be the key process in controlling plume evolution. The model application illustrates that multi-species reactive transport models are needed to adequately transfer reactive processes from one hydraulic situation to another, while single species models are not suited for this predictive task.     

Dissolved plume attenuation with DNAPL source remediation, aqueous decay and volatilization--analytical solution, model calibration and prediction uncertainty

A vertically-integrated analytical model for dissolved phase transport is described that considers a time-dependent DNAPL source based on the upscaled dissolution kinetics model of Parker and Park with extensions to consider time-dependent source zone biodecay, partial source mass reduction, and remediation-enhanced source dissolution kinetics. The model also considers spatial variability in aqueous plume decay, which is treated as the sum of aqueous biodecay and volatilization due to diffusive transport and barometric pumping through the unsaturated zone. The model is implemented in Excel/VBA coupled with (1) an inverse solution that utilizes prior information on model parameters and their uncertainty to condition the solution, and (2) an error analysis module that computes parameter covariances and total prediction uncertainty due to regression error and parameter uncertainty. A hypothetical case study is presented to evaluate the feasibility of calibrating the model from limited noisy field data. The results indicate that prediction uncertainty increases significantly over time following calibration, primarily due to propagation of parameter uncertainty. However, differences between the predicted performance of source zone partial mass reduction and the known true performance were reasonably small. Furthermore, a clear difference is observed between the predicted performance for the remedial action scenario versus that for a no-action scenario, which is consistent with the true system behavior. The results suggest that the model formulation can be effectively utilized to assess monitored natural attenuation and source remediation options if careful attention is given to model calibration and prediction uncertainty issues.     

A model of oscillatory transport in granular soils, with application to barometric pumping and earth tides

A simple algebraic model is proposed to estimate the transport of a volatile or soluble chemical caused by oscillatory flow of fluid in a porous medium. The model is applied to the barometric pumping of vapors in the vadose zone, and to the transport of dissolved species by earth tides in an aquifer. In the model, the fluid moves sinusoidally with time in the porosity of the soil. The chemical concentration in the mobile fluid is considered to equilibrate with the concentration in the surrounding matrix according to a characteristic time governed by diffusion, sorption, or other rate processes. The model provides a closed form solution, to which barometric pressure data are applied in an example of pore gas motion in the vadose zone. The model predicts that the additional diffusivity due barometric pumping in an unfractured vadose zone would be comparable to the diffusivity in stagnant pore gas if the equilibration time is 1 day or longer. Water motion due to the M2 lunar tide is examined as an example of oscillatory transport in an aquifer. It is shown that the tidal motion of the water in an aquifer might significantly increase the vertical diffusivity of dissolved species when compared to diffusion in an absolutely stagnant aquifer, but the hydrodynamic dispersivity due to tidal motion or gravitational flow would probably exceed the diffusivity due to oscillatory advection.     

Transport of a decay chain in homogenous porous media: analytical solutions

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.     

An analytical model for the transport,dispersion and elimination of air pollutants emitted from a point source

The solution of the complete transport diffusion equation with a first order reaction term is obtained for a continuous source. A deposition velocity boundary condition is met at the ground and, optionally, a similar leakage velocity boundary condition can be met at the base of a superjacent layer. The identification of a preliminary transformation of the dependent variable that eliminates the transport and sink terms permits particularly simple analytic solutions to be obtained by means of conventional Laplace transform, Green's function methods. Prior solutions are compared with these results. A linearisation of the solution without an overlying layer provides a simple extension of the conventional Gaussian plume result that permits account to be taken of pollutant settling velocity, of absorption at the ground and of a first order reaction. The accuracy of this linearisation is assessed. Examples of the application of the methods to calculation of the distribution of particulates and of the formation of nitrogen dioxide in a plume are given.     

The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport

In this study, the potential effects of coupled transport phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay in Switzerland, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), are addressed. The solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters. shows that thermal osmosis is the only coupled transport mechanism that could, on its own, have a strong effect on repository performance. Based on the results from the analytical model, two-dimensional finite-difference models incorporating advection and thermal osmosis, and taking conservation of fluid mass into account, have been formulated. The results show that, under the conditions in the vicinity of the repository at the time scales of interest, and due to the constraints imposed by conservation of fluid mass, the advective component of flow will oppose and cancel the thermal-osmotic component. The overall conclusion is that coupled phenomena will only have a very minor impact on radionuclide transport in the Opalinus Clay, in terms of fluid and solute fluxes, at least under the conditions prevailing at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years).