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1.
Modeling transport of contaminants in the earths subsurface relies on numerical solutions over grids with blocks larger than Darcys scale. The hydraulic conductivity is homogenized over the grid blocks and the plumes spreading is reduced as a consequence of the wiped-out variability. To compensate for this loss Rubin et al. (1999) proposed to augment mixing by block-effective dispersion coefficients, and Rubin et al. (2003) showed, by means of two dimensional simulations, how this concept can be applied in practice. In this paper, we present new solutions of the block-effective dispersion tensor for an axisymmetric exponential covariance model. In addition, we discuss the influence of pore-scale dispersion in both two- and three-dimensional applications.  相似文献   

2.
I. Haltas 《水文研究》2012,26(22):3448-3458
Recognizing the spatial heterogeneity of hydraulic parameters, many researchers have studied the solute transport by both groundwater and channel flow in a stochastic framework. One of the methodologies used to up‐scale the stochastic solute transport equation, from a point‐location scale to a grid scale, is the cumulant expansion method combined with the calculus for the time‐ordered exponential and the calculus for the Lie operator. When the point‐location scale transport equation is scaled up to the grid scale, using the cumulant expansion method, a new dispersion coefficient emerges in the dispersive term of the solute transport equation in addition to the molecular dispersion coefficient. This velocity driven dispersion is called ‘macrodispersion’. The macrodispersion coefficient is the integral function of the time‐ordered covariance of the random velocity field. The integral is calculated over a Lagrangian trajectory of the flow. The Lagrangian trajectory depends on the following: (i) the spatial origin of the particle; (ii) the time when the macrodispersion is calculated; and (iii) the mean velocity field along the trajectory itself. The Lagrangian trajectory is a recursive function of time because the location of the particle along the trajectory at a particular time depends on the location of the particle at the previous time. This recursive functional form of the Lagrangian trajectory makes the calculation of the macrodispersion coefficient difficult. Especially for the unsteady, spatially non‐stationary, non‐uniform flow field, the macrodispersion coefficient is a highly complex expression and, so far, calculated using numerical methods in the discrete domains. Here, an analytical method was introduced to calculate the macrodispersion coefficient in the discrete domain for the unsteady and steady, spatially non‐stationary flow cases accurately and efficiently. This study can fill the gap between the theory of the ensemble averaged solute transport model and its numerical implementations. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
The U.S. Department of Energy is currently studying Yucca Mountain, Nevada, as a potential site for a geological high-level waste repository. In the current conceptual models of radionuclide transport at Yucca Mountain, part of the transport path to pumping locations would be through an alluvial aquifer. Interactions with minerals in the alluvium are expected to retard the downstream migration of radionuclides, thereby delaying arrival times and reducing ground water concentrations. We evaluate the effectiveness of the alluvial aquifer as a transport barrier using the stochastic Lagrangian framework. A transport model is developed to account for physical and chemical heterogeneities and rate-limited mass transfer between mobile and immobile zones. The latter process is caused by small-scale heterogeneity and is thought to control the macroscopic-scale retardation in some field experiments. A geostatistical model for the spatially varying sorption parameters is developed from a site-specific database created from hydrochemical measurements and a calibrated modeling approach (Turner and Pabalan 1999). Transport of neptunium is considered as an example. The results are sensitive to the rate of transfer between mobile and immobile zones, and to spatial variability in the hydraulic conductivity. Chemical heterogeneity has only a small effect, as does correlation between hydraulic conductivity and the neptunium distribution coefficient. These results illustrate how general sensitivities can be explored with modest effort within the Lagrangian framework. Such studies complement and guide the application of more detailed numerical simulations.  相似文献   

4.
Solute transport in subsurface environments is controlled by geological heterogeneity over multiple scales. In reactive transport characterized by a low Damköhler number, it is also controlled by the rate of kinetic mass transfer. A theory for addressing the impact of sedimentary texture on the transport of kinetically sorbing solutes in heterogeneous porous formations is derived using the Lagrangian-based stochastic methodology. The resulting model represents the hierarchical organization of sedimentary textures and associated modes of log conductivity (K) for sedimentary units through a hierarchical Markov Chain. The model characterizes kinetic sorption using a spatially uniform linear reversible rate expression. Our main interest is to investigate the effect of sorption kinetics relative to the effects of K heterogeneity on the dispersion of a reactive plume. We study the contribution of each scale of stratal architecture to the dispersion of kinetically sorbing solutes in the case of a low Damköhler number. Examples are used to demonstrate the time evolution and relative contributions of the auto- and cross-transition probability terms to dispersion. Our analysis is focused on the model sensitivity to the parameters defined at each hierarchical level (scale) including the integral scales of K spatial correlation, the anisotropy ratio, the indicator correlation scales, and the contrast in mean K between facies defined at different scales. The results show that the anisotropy ratio and integral scales of K have negligible effect upon the longitudinal dispersion of sorbing solutes. Furthermore, dispersion of sorbing solutes depends mostly on indicator correlation scales, and the contrast of the mean conductivity between units at different scales.  相似文献   

5.
We investigate the impact of injection mode (flux and resident injection) and heterogeneity in hydraulic properties on dispersion of advecting particles in two-dimensional discrete fracture network models, using a Monte Carlo method. We find that the injection mode has a significant effect on dispersion: The resident injection mode exhibits anomalous features of transport whereas the flux injection mode tends to Gaussian transport; this observation is easily understood by considering phase diagrams where a limited number of particles entering low velocity fractures greatly increase macrodispersion. In spite of a sizeable portion of negative longitudinal velocities, it is shown that multiple crossings are negligible when quantifying longitudinal macrodispersion. A simple probabilistic expression of particle mass balance is shown to predict well the spatial distribution of advecting particles.  相似文献   

6.
This paper addresses the question of how spatial variability in the hydraulic and chemical properties of groundwater systems affects the transport and sorption behavior of pollutants at the field scale. In this paper, we limit our investigations on pollutants that adsorb according to an equilibrium controlled nonlinear Freundlich sorption isotherm. The new contribution of this paper is take into account not only spatially variable Freundlich distribution coefficients KSKS but spatially variable Freundlich nonlinearity parameters p as well. Using a homogenization theory approach, we shortly review the impact of spatially variable hydraulic properties on the transport and extend the theory to spatially variable chemical properties. We show that spatially variable Freundlich exponents cause a very different field scale transport and sorption behavior than spatial variations in the distribution coefficients only since in the first case field scale Freundlich parameters and field scale dispersion coefficients become concentration dependent. In particular, field scale retardation is much larger than small-scale retardation.  相似文献   

7.
Transport of sorbing solutes in 2D steady and heterogeneous flow fields is modeled using a particle tracking random walk technique. The solute is injected as an instantaneous pulse over a finite area. Cases of linear and Freundlich sorption isotherms are considered. Local pore velocity and mechanical dispersion are used to describe the solute transport mechanisms at the local scale. This paper addresses the impact of the degree of heterogeneity and correlation lengths of the log-hydraulic conductivity field as well as negative correlation between the log-hydraulic conductivity field and the log-sorption affinity field on the behavior of the plume of a sorbing chemical. Behavior of the plume is quantified in terms of longitudinal spatial moments: center-of-mass displacement, variance, 95% range, and skewness. The range appears to be a better measure of the spread in the plumes with Freundlich sorption because of plume asymmetry. It has been found that the range varied linearly with the travelled distance, regardless of the sorption isotherm. This linear relationship is important for extrapolation of results to predict behavior beyond simulated times and distances. It was observed that the flow domain heterogeneity slightly enhanced the spreading of nonlinearly sorbing solutes in comparison to that which occurred for the homogeneous flow domain, whereas the spreading enhancement in the case of linear sorption was much more pronounced. In the case of Freundlich sorption, this enhancement led to further deceleration of the solute plume movement as a result of increased retardation coefficients produced by smaller concentrations. It was also observed that, except for plumes with linear sorption, correlation between the hydraulic conductivity and the sorption affinity fields had minimal effect on the spatial moments of solute plumes with nonlinear sorption.  相似文献   

8.
Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.  相似文献   

9.
A generalized dual porosity method (GDPM) has been developed to incorporate sub-grid scale heterogeneity into large-scale flow and transport simulations. The method is spatially variable in the sense that the method can be applied with different levels of resolution for different spatial nodes in the simulation. The method utilizes the nodal connectivity structure and linear equation solvers of unstructured grids like those used in the finite element method, and can be applied to any problem without externally modifying the numerical grid. The algorithm scales linearly in CPU time and storage with the number of GDPM nodes. We demonstrate the utility and computational efficiency of the technique with two verification problems and an example problem of a field site.  相似文献   

10.
A recursion formulation for the transport of linearly sorbing solutes undergoing non-equilibrium sorption is developed. Constant or spatially varying sorption kinetics can be modeled using the recursion approach. The sorption and desorption rates are modeled as two independent random processes with a prescribed mean and covariance structure with spatial variability in the rate parameters included as well. The recursion solution, in terms of the probability density function for solute travel times, is derived by specifying transition probabilities for moving between the aqueous and sorbed phases. A few simple examples are used to illustrate the approach. The computer implementation leads to a very rapid algorithm that is easily extended to cover cases beyond the basic model presented here.  相似文献   

11.
Cosler DJ 《Ground water》2004,42(2):203-222
Nonequilibrium concentration type curves are numerically developed and sensitivity analyses are performed to examine the relationships between effluent concentrations in partially penetrating monitoring/extraction wells, the vertical plume shape, and the mass transfer characteristics of the aquifer. The governing two-dimensional, axisymmetric nonequilibrium solute transport equation is solved in three stages using an operator-splitting approach. In the first two stages, the advection and dispersion terms are solved with the Eulerian-Lagrangian method, based on the backward method of characteristics for advection and the standard implicit Galerkin finite element method for dispersion. In the third step, the first-order, immobile-mobile domain mass transfer term is computed analytically for both two-site and lognormally distributed, multirate models. Effluent concentration variations with time and contour plots of the pore water concentration distribution in the aquifer are compared for a wide range of field- and laboratory-measured mass transfer rates, various plume shapes, and relevant physical/chemical parameter values, including pumping rate, vertical anisotropy ratio, retardation factor, and porosity. The simulation results show that rate-limited mass transfer can have a significant impact on sample and aquifer pore water concentrations during three-dimensional transport to a partially penetrating well. An alternative dimensionless form of the nonequilibrium solute transport equation is derived to illustrate the key parameter groupings that quantify rate-limited sorption effects and show the relative importance of individual parameters. A hypothetical field application example demonstrates the fitting of dimensional type curves to discrete-interval sampling data in order to evaluate the mass transfer characteristics of an aquifer and shows how type curve superposition can be used to model complex plume shapes.  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.
We present a sequence of purely advective transport models that demonstrate the influence of small-scale geometric inhomogeneities on contaminant transport in fractured crystalline rock. Special weight is placed on the role of statistically generated variable fracture apertures. The fracture network geometry and the aperture distribution are based on information from an in situ radionuclide retardation experiment performed at Grimsel test site (Swiss Alps). The obtained breakthrough curves are fitted with the advection dispersion equation and continuous-time random walks (CTRW). CTRW is found to provide superior fits to the late-arrival tailing and is also found to show a good correlation with the velocity distributions obtained from the hydraulic models. The impact of small-scale heterogeneities, both in fracture geometry and aperture, on transport is shown to be considerable.  相似文献   

14.
Solute leaching in unsaturated soil is influenced by the variability in hydraulic functions (water retention and conductivity) that govern the flow process. Variability in measured soil hydraulic functions of a coarse-, medium- and fine-textured soil group was quantified with the scaling theory of similar media. Solute leaching in these soils was calculated with Monte Carlo simulation assuming, successively, hydraulic conductivity, K, volumetric water content, 0, and pressure head, h, to be constant. In addition to variability in hydraulic functions, variability in the solute retardation factor was also taken into account. To examine this effect five solutes were considered: a conservative solute (chloride), a non-retarded solute subject to decay (nitrate), a retarded solute that does not decay (cadmium) and two organic solutes which are retarded but have different sorption and decay parameters (the pesticide atrazine and a chlorinated hydrocarbon). The numerical results obtained with Monte Carlo simulation were in a number of instances verified with analytical solutions. The three soil groups distinguished showed considerable differences in vulnerability for leaching of the five solutes, emphasizing the importance of the effect of variability in soil hydraulic functions when studying solute leaching. Numerical and analytical results showed good agreement. Therefore, in relatively simple situations analytical solutions are attractive. However, in complicated situations, analytical solutions are cumbersome and numerical solutions are the only realistic alternative.  相似文献   

15.
Three-dimensional numerical simulations using a detailed synthetic hydraulic conductivity field developed from geological considerations provide insight into the scaling of subsurface flow and transport processes. Flow and advective transport in the highly resolved heterogeneous field were modeled using massively parallel computers, providing a realistic baseline for evaluation of the impacts of parameter scaling. Upscaling of hydraulic conductivity was performed at a variety of scales using a flexible power law averaging technique. A series of tests were performed to determine the effects of varying the scaling exponent on a number of metrics of flow and transport behavior. Flow and transport simulation on high-performance computers and three-dimensional scientific visualization combine to form a powerful tool for gaining insight into the behavior of complex heterogeneous systems.Many quantitative groundwater models utilize upscaled hydraulic conductivity parameters, either implicitly or explicitly. These parameters are designed to reproduce the bulk flow characteristics at the grid or field scale while not requiring detailed quantification of local-scale conductivity variations. An example from applied groundwater modeling is the common practice of calibrating grid-scale model hydraulic conductivity or transmissivity parameters so as to approximate observed hydraulic head and boundary flux values. Such parameterizations, perhaps with a bulk dispersivity imposed, are then sometimes used to predict transport of reactive or non-reactive solutes. However, this work demonstrates that those parameters that lead to the best upscaling for hydraulic conductivity and head do not necessarily correspond to the best upscaling for prediction of a variety of transport behaviors. This result reflects the fact that transport is strongly impacted by the existence and connectedness of extreme-valued hydraulic conductivities, in contrast to bulk flow which depends more strongly on mean values. It provides motivation for continued research into upscaling methods for transport that directly address advection in heterogeneous porous media.An electronic version of this article is available online at the journal's homepage at http://www.elsevier.nl/locate/advwatres or http://www.elsevier.com/locate/advwatres (see “Special section on vizualization”. The online version contains additional supporting information, graphics, and a 3D animation of simulated particle movement.©1998 Elsevier Science Limited. All rights reserved  相似文献   

16.
We present a new streamline-based numerical method for simulating reactive solute transport in porous media. The key innovation of the method is that both longitudinal and transverse dispersion are incorporated accurately without numerical dispersion. Dispersion is approximated in a flow-oriented grid using a combination of a one-dimensional finite difference scheme and a meshless approximation. In contrast to previous hybrid alternatives to incorporate dispersion in streamline-based simulations, the proposed scheme does not require a grid and, hence, it does not introduce numerical dispersion. In addition, the proposed scheme eliminates numerical oscillations and negative concentration values even when the dispersion tensor includes the off-diagonal coefficients and the flow field is non-uniform. We demonstrate that for a set of two- and three-dimensional benchmark problems, the new proposed streamline-based formulation compares favorably to two state of the art finite volume and hybrid Eulerian–Lagrangian solvers.  相似文献   

17.
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   

18.
The relationship between the longitudinal dispersion (DL) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the DL and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the DL from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the DL and Pe revealed that the longitudinal dispersivity αL increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of αL and the secondary roughness played a significant role in enhancing the αL. As the Taylor dispersion mechanism dominated, the αL was insensitive to the influence of multiscale roughness in variable‐aperture fractures.  相似文献   

19.
In the Hanford Reach of the Columbia River, a thin layer of recent alluvium overlies the sedimentary formations that comprise the unconfined groundwater aquifer. Experimental and modelling studies have demonstrated that this alluvial layer exerts significant control on the exchange of groundwater and surface water (hydrologic exchange flux), and is associated with elevated levels of biogeochemical activity. This layer is also observed to be strongly heterogeneous, and quantifying the spatial distribution of properties over the range of scales of interest is challenging. Facies are elements of a sediment classification scheme that groups complex geologic materials into a set of discrete classes according to distinguishing features. Facies classifications have been used as a framework for assigning heterogeneous material properties to grid cells of numerical models of flow and reactive transport in subsurface media. The usefulness of such an approach hinges on being able to relate facies to quantitative properties needed for flow and reactive transport modelling, and on being able to map facies over the domain of interest using readily available information. Although aquifer facies have been used in various modelling contexts, application of this concept to riverbed sediments is relatively new. Here, we describe an approach for categorizing and mapping recent alluvial (riverbed) sediments based on the integration of diverse observations with numerical simulations of river hydrodynamics. The facies have distinct distributions of sediment texture that correspond to variations in hydraulic properties, and therefore provide a useful framework for assigning heterogeneous properties in numerical simulations of hydrologic exchange flows and biogeochemical processes.  相似文献   

20.
This is Part-II of a two-part article that presents analytical solutions to multi-species reactive transport equations coupled through sorption and sequential first-order reactions. In Part-I, we provide the mathematical derivations and in this article we discuss the computational techniques for implementing these solutions. We adopt these techniques to develop a general computer code and use it to verify the solutions. We also simplify the general solutions for various special-case transport scenarios involving zero initial condition, identical retardation factors and zero advection. In addition to this, we derive specialized solution expressions for zero dispersion and steady-state conditions. Whereever possible, we compare these special-case solutions against previously published analytical solutions to establish the validity of the new solution. Finally, we test the new solution against other published analytical and semi-analytical solutions using a set of example problems.  相似文献   

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