共查询到20条相似文献，搜索用时 15 毫秒
1.
With most existing methods, transverse dispersion coefficients are difficult to determine. We present a new, simple, and robust approach based on steady-state transport of a reacting agent, introduced over a certain height into the porous medium of interest. The agent reacts with compounds in the ambient water. In our application, we use an alkaline solution injected into acidic ambient water. Threshold values of pH are visualized by adding standard pH indicators. Since aqueous-phase acid-base reactions can be considered practically instantaneous and the only process leading to mixing of the reactants is transverse dispersion, the length of the plume is controlled by the ratio of transverse dispersion to advection. We use existing closed-form expressions for multidimensional steady-state transport of conservative compounds in order to evaluate the concentration distributions of the reacting compounds. Based on these results, we derive an easy-to-use expression for the length of the reactive plume; it is proportional to the injection height squared, times the velocity, and inversely proportional to the transverse dispersion coefficient. Solving this expression for the transverse dispersion coefficient, we can estimate its value from the length of the alkaline plume. We apply the method to two experimental setups of different dimension. The computed transverse dispersion coefficients are rather small. We conclude that at slow but realistic ground water velocities, the contribution of effective molecular diffusion to transverse dispersion cannot be neglected. This results in plume lengths that increase with increasing velocity. 相似文献
2.
The influence of source zone concentration reduction on solute plume detachment and recession times in fractured rock was investigated using new semianalytical solutions to transient solute transport in the presence of advection, dispersion, sorption, matrix diffusion, and first-order decay. Novel aspects of these solutions are: (1) the source zone concentration behavior is simulated using a constant concentration with the option for either an instantaneous reduction to zero concentration or an exponentially decaying source zone concentration initiated at some time (t*) after the source is introduced, and (2) different biodegradation rates in the fracture and rock matrix. These solutions were applied for sandstone bedrock and revealed that biodegradation in the matrix, not the fracture, may be the most significant attenuation mechanism and therefore may dictate remediation time scales. Also, instantaneous and complete source concentration reduction in aged plumes may not be beneficial with respect to plume response because back-diffusion can sustain plume migration for long periods of time. Moderate source zone concentration reduction has a similar impact on the rate of advance of the leading edge of the plume as aggressive concentration reduction. If the source zone concentration reduction half-life is less than the plume decay half-life, then volatile organic compound (VOC) mass sequestered in the rock matrix will ultimately dictate plume persistence and not the presence of the source zone. 相似文献
3.
This work presents analytical models which are able to predict contours of concentrations and isotope ratios of organic pollutants in homogeneous aquifers. Four analytical solutions of the advective–dispersive transport equation for reactive transport from the literature differing in assumptions regarding biodegradation kinetics were used. Stable isotope ratios are computed after modelling the individual reactive transport of isotopic species in the aquifer, which respond differently to fractionation by biodegradation or sorption. The main finding of this study is that the isotope ratios in the plumes are very sensitive to the assumptions underlying the biodegradation kinetics in the models. When biodegradation occurs throughout the core of the plume as first-order reaction, the transversal gradients in isotope ratios are smooth. When biodegradation occurs in a bi-molecular reaction with an electron acceptor (modelled by double-Monod kinetics), steep transversal isotope gradients are predicted. When the reaction rates approach instantaneous reaction along the plume fringes, isotope shifts in the core of the plume disappear. A model incorporating plume and fringe degradation produces the most plausible predictions of isotope ratios in this study. It is shown furthermore that isotope fractionation by sorption causes an even different pattern of isotope ratios, with positive shifts restricted to near the forerunning front of an expanding plume. The models developed in this work can serve for the validation of numerical models and may be incorporated in natural attenuation support systems such as e.g. BIOSCREEN. 相似文献
4.
5.
This study describes the development of a general model for reaction in and performance of spatially heterogeneous bioreactors such as treatment wetlands. The modeled domain possesses local-scale velocities, reaction rates and transverse dispersion coefficients that are functions of an underlying heterogeneity variate representing one or more controlling biophysical attributes, for example, reactive surface area (submerged plant) density. Reaction rate coefficients are treated as related to local velocities in an inverse square fashion via their mutual dependence upon the variate. The study focuses on the solution for the steady-state case with constant inlet concentration. Results compare well with exact solutions developed for laterally-bounded systems in which the heterogeneity is represented explicitly. Employing the bicontinuum analogue of a second-order model, an expression for an effective longitudinal dispersion coefficient as a function of travel distance is developed using the method of moments. The result provides insights into the behavior of concentration as transverse mixing drives the system asymptotically toward Fickian longitudinal dispersion. The model may represent an improvement over other approaches for characterizing treatment wetland performance because it accounts for evolving shear flow dispersion, and because parameters are few in number, physically based, and invariant with mean velocity. 相似文献
6.
《Advances in water resources》2007,30(6-7):1421-1431
Recent studies indicate that during in situ bioremediation of contaminated groundwater, degradation occurs primarily along transverse mixing zones. Classical reactive-transport models overpredict the amount of degradation because solute spreading and mixing are not distinguished. Efforts to correct this have focused on modifying both dispersion and reaction terms, but no consensus on the best approach has emerged. In this work, a pore-scale model was used to simulate degradation along a transverse mixing zone between two required nutrients, and a continuum model with fitted parameters was used to match degradation rates from the pore-scale model. The pore-scale model solves for the flow field, concentration field, and biomass development within pore spaces of porous medium. For the continuum model, the flow field and biomass distributions are assumed to be homogeneous, and the fitting parameters are the transverse dispersion coefficient (DT) and maximum substrate utilization rate (kS,c). Results from the pore-scale model show that degradation rates near the system inlet are limited by the reaction rate, while degradation rates downgradient are limited by transverse mixing. For the continuum model, the value of DT may be adjusted so that the degradation rate with distance matches that from the pore-scale model in the mixing-limited region. However, adjusting the value of kS only improves the fit to pore-scale results within the reaction-limited region. Comparison with field and laboratory experiments suggests that the length of the reaction rate-limited region is small compared to the length scale over which degradation occurs. This indicates that along transverse mixing zones in the field, values of kS are unimportant and only the value of DT must be accurately fit. 相似文献
7.
《Advances in water resources》2007,30(6-7):1618-1629
Residual dense non-aqueous liquids (NAPLs) in aquifers constitute a great challenge for groundwater cleanup. Active engineered treatment of regions that contain residual NAPLs is often required to shorten the long-term impact of NAPLs on groundwater quality. Enhanced residual NAPL cleanup can be achieved by promoting biodegradation of NAPL components in the aqueous phase, thereby increasing contaminant fluxes from the NAPL phase. Reaction-enhanced NAPL dissolution is often mathematically simulated under the assumption that lumped mass transfer coefficients, used to describe the dissolution behavior of the NAPL phase, are independent of the reactions. However, this assumption is not warranted because reactions occurring near the water–NAPL interface can reduce characteristic mass transfer lengths, which tend to enhance mass transfer over the no-reaction case.In this study, we mathematically investigated the connections between lumped mass transfer coefficients and reaction kinetics over an idealized residual NAPL domain. Since mass transfer is frequently a scale-dependent process, we also examined the influence of system extent on mass transfer coefficients. For our idealized domain with an assumed first-order decay reaction, the results show that lumped mass transfer coefficients depend on reaction kinetics and system scale. The mass transfer coefficient derived from the non-reactive case cannot properly represent the mass transfer process under the reactive conditions. When the advection time scale is long in comparison to the transverse dispersion time scale in the system, a fast reaction can increase significantly the lumped mass transfer coefficient. The mass transfer coefficient used for simulation was also found to be affected by the nature of the numerical scheme used. 相似文献
8.
A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number. 相似文献
9.
Andrzej Aniszewski 《Acta Geophysica》2009,57(2):435-453
The paper addresses the 2D mathematical equation of conservative contaminant transport in an aquifer for chosen contaminants.
The contaminants (chlorides and sulfates) are subject to instantaneous reversible part of sorption process. The term of instantaneous
reversible sorption in the presented equation has been described by the non-linear Freundlich adsorption isotherm, widely
applied in practice in relation to static processes (for local equilibrium). The numerical solution (using the finite difference
method) has been based on the previously calculated values of longitudinal and transverse dispersion coefficients and the
non-linear adsorption parameters for the chosen contaminants. Based on this model, the values of chloride and sulfate concentration
isolines have been calculated and compared with the measured maximal concentrations in the chosen natural aquifer (installed
piezometers). Additionally, the values of chloride concentrations have been calculated taking into account the influence of
radioactive decay term, using the numerical value of the firstorder decay rate constant for an adopted theoretical radionuclide. 相似文献
10.
Analytical Solutions of Three‐Dimensional Contaminant Transport Models with Exponential Source Decay 
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下载免费PDF全文 Despite the availability of numerical models, interest in analytical solutions of multidimensional advection‐dispersion systems remains high. Such models are commonly used for performing Tier I risk analysis and are embedded in many regulatory frameworks dealing with groundwater contamination. In this work, we develop a closed‐form solution of the three‐dimensional advection‐dispersion equation with exponential source decay, first‐order reaction, and retardation, and present an approach based on some ease of use diagrams to compare it with the integral open form solution and with earlier versions of the closed‐form solution. The comparison approach focuses on the relative differences associated with source decay and the effect of simulation time. The analysis of concentration contours, longitudinal sections, and transverse sections confirms that the closed‐form solutions studied can be used with acceptable approximation in the central area of a plume bound transversely within the source width, both behind and beyond the advective front and for concentration values up to two orders of magnitude less than the initial source concentration. As the proposed closed‐form model can be evaluated without nested numerical computations and with simple mathematical functions, it can be very useful in risk assessment procedures. 相似文献
11.
Pore-scale dispersion (PSD), aquifer heterogeneity, sampling volume, and source size influence solute concentrations of conservative tracers transported in heterogeneous porous formations. In this work, we developed a new set of analytical solutions for the concentration ensemble mean, variance, and coefficient of variation (CV), which consider the effects of all these factors. We developed these models as generalizations of the first-order solutions in the log-conductivity variance of point concentration proposed by [Fiori A, Dagan G. Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J Contam Hydrol 2000;45(1–2):139–163]. Our first-order solutions compare well with numerical simulations for small and moderate formation heterogeneity and from small to large sampling and source volumes. However, their performance deteriorates for highly heterogeneous formations. Successively, we used our models to study the interplay among sampler size, source volume, and PSD. Our analysis shows a complex and important interaction among these factors. Additionally, we show that the relative importance of these factors is also a function of plume age, of aquifer heterogeneity, and of the measurement location with respect to the mean plume center of gravity. We found that the concentration moments are chiefly controlled by the sampling volume with pore-scale dispersion playing a minor role at short times and for small source volumes. However, the effect of the source volume cannot be neglected when it is larger than the sampling volume. A different behavior occurs for long periods, which may be relevant for old contaminations, or for small injection volumes. In these cases, PSD causes a significant dilution, which is reflected in the concentration statistics. Additionally, at the center of the mean plume, where high concentrations are most likely to occur, we found that sampling volume and PSD are attenuating mechanisms for both concentration ensemble mean and coefficient of variation, except at very large source and sampler sizes, where the coefficient of variation increases with sampler size and PSD. Formation heterogeneity causes a faster reduction of the ensemble mean concentrations and a larger uncertainty at the center of the mean plume. Therefore, our results highlight the importance of considering the combined effect of formation heterogeneity, exposure volume, PSD, source size, and measurement location in performing risk assessment. 相似文献
12.
We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general. 相似文献
13.
《Advances in water resources》2004,27(11):1045-1059
Transient and steady-state analytical solutions are derived to investigate solute transport in a fractured porous medium consisting of evenly spaced, parallel discrete fractures. The solutions incorporate a finite width strip source, longitudinal and transverse dispersion in the fractures, source decay, aqueous phase decay, one-dimensional diffusion into the matrix, sorption to fracture walls, and sorption within the matrix. The solutions are derived using Laplace and Fourier transforms, and inverted by interchanging the order of integration and utilizing a numerical Laplace inversion algorithm. The solutions are verified for simplified cases by comparison to solutions derived by Batu [Batu V. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type condition at the source. Wat Resour Res 1989;25(6):1125] and Sudicky and Frind [Sudicky EA, Frind EO. Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Wat Resour Res 1982;18(6):1634]. The application of the solutions to a fractured sandstone demonstrates that narrower source widths and larger values of transverse dispersivity both lead to lower downstream concentrations in the fractures and shorter steady-state plumes. The incorporation of aqueous phase decay and source concentration decay both lead to lower concentrations and shorter plumes, with even moderate amounts of decay significantly shortening the persistence of contamination. 相似文献
14.
Monte Carlo simulations are conducted to evaluate microbial-mediated contaminant reactions in an aquifer comprised of spatially variable microbial biomass concentrations, aquifer hydraulic conductivities, and initial electron donor/acceptor concentrations. A finite element simulation model is used that incorporates advection, dispersion, and Monod kinetic expressions to describe biological processes. Comparisons between Monte Carlo simulations of heterogeneous systems and simulations using homogeneous formulation of the same two-dimensional transport problem are presented. For the assumed set of parameters, physical aquifer heterogeneity is found to have a minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system; however, it noticeably changes the dispersion, skewness, and peakness of contaminant concentration distributions. Similarly, for low microbial growth rate, given favorable microbial growth characteristics, biological heterogeneity has minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system. On the other hand, when higher effective growth rates are assumed, biological heterogeneity and spatial heterogeneities in essential electron donor/acceptors reduce the efficiency of biotic contaminant reactions; consequently, model simulations derived from heterogeneous biomass distributions predict remediation time scales that are longer than those simulated for homogeneous systems. When correlations between physical aquifer and biological heterogeneities are considered, the assumed correlation affects predicted mean and variance of contaminant concentration and biomass distributions. For example, an assumed negative correlation between hydraulic conductivity and the initial biomass distribution produces a plume where less efficient biotic contaminant reactions occur at the leading edge of the plume; this is consistent with less degradation/transformation occurring over regions of higher groundwater velocities. However, the presence and absence of these correlations do not appear to affect the efficiency of microbial-mediated contaminant attenuation. 相似文献
15.
Falta RW 《Ground water》2008,46(2):272-285
It is often difficult at contaminated sites to decide whether remediation effort should be focused on the contaminant source, the dissolved plume, or on both zones. The decision process at these sites is hampered by a lack of quantitative tools for comparing remediation alternatives. A new screening-level mass balance approach is developed for simulating the transient effects of simultaneous ground water source and plume remediation. The contaminant source model is based on a power function relationship between source mass and source discharge, and it can consider partial source remediation at any time after the initial release. The source model serves as a time-dependent mass flux boundary condition to a new analytical plume model, where flow is assumed to be one dimensional, with three-dimensional dispersion. The plume model simulates first-order sequential decay and production of several species, and the decay rates and parent/daughter yield coefficients are variable functions of time and distance. This new method allows for flexible simulation of natural attenuation or remediation efforts that enhance plume degradation. The plume remediation effort may be temporary or delayed in time, limited in space, and it may have different chemical effects on different contaminant species in the decay chain. 相似文献
16.
《Advances in water resources》1998,22(2):103-116
We consider a one-dimensional model biodegradation system consisting of two reaction–advection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting biomass kinetics to equilibrium. We derive closed form solutions for constant speed traveling fronts for the reduced two component models and compare their profiles in homogeneous media. For a spatially random velocity field, we introduce travel time and study statistics of degradation fronts via representations in terms of the travel time probability density function (pdf) and the traveling front profiles. The travel time pdf does not vary with the nutrient and pollutant concentrations and only depends on the random water velocity. The traveling front profiles are expressed analytically or semi-analytically as functions of the travel time. The problem of nonlinear transport by a random velocity reduces to two subproblems: one being nonlinear transport by a known (unit) velocity, and the other being linear (advective) transport by a random velocity. The approach is illustrated through some examples where the randomness in velocity stems from the spatial variability of porosity. 相似文献
17.
Transport of three herbicides in ground water at Twin Lake test site,Chalk River,Ontario, Canada 总被引：2，自引：0，他引：2
A field tracer test performed under natural flow conditions at the Twin Lake test site, Chalk River Laboratories of the Atomic Energy of Canada Ltd. in Chalk River, Ontario, Canada, using tritium and three herbicides (Chlortoluron, Terbuthylazine, and Pendimethalin) was interpreted using the dispersion equation with a combined reaction model. The reaction model couples an instantaneous equilibrium reaction governed by a linear adsorption isotherm with a reversible or irreversible kinetic reaction of the first order, and decay. An improved interpretation method consists of a simultaneous fitting of theoretical concentration and mass-recovery curves to the experimental data, which leads to a more reliable determining of reaction models and improves the accuracy of fitting. Tritium served as the reference tracer to determine the flow velocity, dispersivity, and the recovery of the herbicides. Chlortoluron was slightly delayed by equilibrium exchange with strongly reduced concentration due to an irreversible kinetic reaction and/or decay. Terbuthilazine was slightly delayed by equilibrium exchange, with strongly reduced concentration due to a reversible kinetic reaction with some influence of decay. A strong equilibrium reaction and a strong reversible kinetic reaction without degradation governed the transport of Pendimethalin, reducing considerably its concentration. The results obtained show that simulations based only on Kd and decay constant, especially if these parameters are found in the laboratory, may considerably differ from those performed with reaction parameters determined in properly performed field tests. The dominant reaction types, and the values of parameters found in the study, supply useful information on the transport of the investigated herbicides in sandy aquifers under natural flow conditions. 相似文献
18.
Modelling adsorptive solute transport in soils needs a number of parameters to describe its reaction kinetics and the values of these parameters are usually determined from batch and displacement experiments. Some experimental results reveal that when describing the adsorption as first-order kinetics, its associated reaction rates are not constants but vary with pore water velocity. Explanation of this varies but an independent verification of each explanation is difficult because simultaneously measuring the spatiotemporal distributions of dissolved and adsorbed solutes in soils is formidable. Pore-scale modelling could play an important role to address this gap and has received increased attention over the past few years. This paper investigated the transport of adsorptive solute in a simple porous medium using pore-scale modelling. Fluid flow through the void space of the medium was assumed to be laminar and in saturated condition, and solute transport consisted of advection and molecular diffusion; the sorption and desorption occurring at the fluid–solid interface were modelled as linear first-order kinetics. Based on the simulated spatiotemporal distribution of dissolved and adsorbed solutes at pore scale, volumetric-average reaction kinetics at macroscopic scale and its associated reactive parameters were measured. Both homogeneous adsorption where the reaction rates at microscopic scale are constant, and heterogeneous adsorption where the reaction rates vary from site to site, were investigated. The results indicate that, in contrast to previously thought, the macroscopic reaction rates directly measured from the pore-scale simulations do not change with pore velocity under both homogeneous and heterogeneous adsorptions. In particular, we found that for the homogeneous adsorption, the macroscopic adsorption remains first-order kinetic and can be described by constant reaction rates, regardless of flow rate; whilst for the heterogeneous adsorption, the macroscopic adsorption kinetics continues not to be affected by flow rate but is no longer first-order kinetics that can be described by constant reaction rates. We discuss how these findings could help explain some contrary literature reports over the dependence of reaction rates on pore water velocity. 相似文献
19.
We analyze the impact of conditioning to measurements of hydraulic transmissivity on the transport of a conservative solute. The effects of conditioning on solute transport are widely discussed in the literature, but most of the published works focuses on the reduction of the uncertainty in the prediction of the plume dispersion. In this study both ensemble and effective plume moments are considered for an instantaneous release of a solute through a linear source normal to the mean flow direction, by taking into account different sizes of the source. The analysis, involving a steady and spatially inhomogeneous velocity field, is developed by using the stochastic finite element method. Results show that conditioning reduces the ensemble moment in comparison with the unconditioned case, whereas the effective dispersion may increase because of the contribution of the spatial moments related to the lack of stationarity in the flow field. As the number of conditioning points increases, this effect increases and it is significant in both the longitudinal and transverse directions. Furthermore, we conclude that the moment derived from data collected in the field can be assessed by the conditioned second-order spatial moment only with a dense grid of measured data, and it is manifest for larger initial lengths of the plume. Nevertheless, it seems very likely that the actual dispersion of the plume may be underestimated in practical applications. 相似文献