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1.
Heterogeneity is prevalent in aquifers and has an enormous impact on contaminant transport in groundwater. Numerical simulations are an effective way to deal with heterogeneity directly by assigning different hydraulic property values to each numerical grid block. Because hydraulic properties vary on different scales, but they cannot be sampled exhaustively and the number of numerical grid blocks is limited by computational considerations, the dispersive effects of unmodeled heterogeneity need to be accounted for. Dispersion tensors can be used to model the dispersion caused by unmodeled heterogeneity. The concept of block-effective macrodispersion tensors for modeling the effects of small-scale variability on solute transport introduced by Rubin et al. [Rubin Y, Sun A, Maxwell R, Bellin A. The concept of block-effective macrodispersivity and a unified approach for grid-scale- and plume-scale-dependent transport. J Fluid Mech 1999;395:161–80] is extended in this paper for use with reactive solutes. The tensors are derived for reactive solutes with spatially variable retardation factors and for solutes experiencing spatially uniform rate-limited sorption. The longitudinal block-effective macrodispersion coefficient is largest for perfect negative correlation between the log-hydraulic conductivity and the retardation factor. Because dispersion tensors, as they are usually implemented in numerical simulations, produce symmetric spreading, the applicability of the concept depends on the portion of the plume asymmetry caused by small-scale variability. The presented results show that the concept is applicable for rate-limited sorption for block sizes of one and two integral scales. 相似文献
2.
Flow against dispersion in two-dimensional regions 总被引：1，自引：0，他引：1
In field applications, upstream spreading of contaminant plumes may be controlled by the flow of fresh water in a direction opposite to the dispersive expansion direction of the plume. In the current literature this type of control is identified as flow against dispersion or contrary flow. In this study analytic methods are used to investigate contrary flow conditions for two-dimensional applications. In particular, special attention is given to the dispersive spread of the contaminant plume in the transverse direction under equilibrium flow against dispersion. Typical problems analyzed emphasize the effect of adsorption and transverse dispersion on the overall control process. Problems analyzed indicate that equilibrium flow velocities deduced from one-dimensional analysis, which may balance the dispersive spread of the plume in the longitudinal direction, represent an over design condition when these equilibrium velocities are compared with the conditions generated from a two-dimensional model for a downstream source which is finite in the transverse direction. 相似文献
3.
The rate of biodegradation in contaminated aquifers depends to a large extent on dispersive mixing processes that are now generally accepted to result from spatial variations in the velocity field. It has been shown, however, that transient flow fields can also contribute to dispersive mixing. The influence of transient flow on biodegrading contaminants is particularly important since it can enhance mixing with electron acceptors, further promoting the reactive process. Using numerical simulations, the effect of transient flow on the behavior of a biodegradable contaminant is evaluated here both with respect to the development of apparently large horizontal transverse dispersion and also with respect to enhanced mixing between the substrate (electron donor) and electron acceptor. The numerical model BIO3D, which solves for advective-dispersive transport coupled with Monod-type biodegradation of substrates in the presence of an electron acceptor, was used for the simulations. The model was applied in a two-dimensional plan view mode considering a single substrate. Transient flow fields were found to yield larger apparent transverse dispersion because the longitudinal dispersivity also acts transverse to the mean flow direction. In the reactive case, the transient flow field increases substrate-oxygen mixing, which in turn enhances the overall rate of biodegradation. The results suggest that in the case of moderate changes of flow directions, a steady-state flow field can be justified, thereby avoiding the higher computational costs of a fully transient simulation. The use of a higher transverse horizontal dispersivity in a steady flow field can, under these conditions, adequately forecast plume development. 相似文献
4.
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
5.
A number of experimental studies have tackled the issue of solute transport parameter assessments either in the laboratory or in the field. But yet, the behavior of a plume in the field under density driven forces, is not well known due to possible development of instabilities. Some field tracer tests on the fate of plumes denser than native groundwater such as those encountered under waste disposal facilities, have pointed out the processes of sinking and splitting at the early stage of migration. The process of dispersion was widely investigated, but the range of dispersivity values obtained from either experimental tests, or numerical and theoretical calculations is still very large, even for the same type of aquifers. These discrepancies were considered to be essentially caused by soil heterogeneities and scale effects. In the meantime, studies on the influence of sinking and fingering have remained more scarce. The objective of the work is to analyze how transport parameters such as dispersivities can be affected by unstable conditions, which lead to plume sinking and fingering. A series of tracer tests were carried out to study under natural conditions, the transport of a dense chloride solution injected in a shallow two-layered aquifer. Two types of experiments were performed: in the first type, source injection was such that the plume could travel downward from one layer to the other of higher pore velocity, and in the second one, the migration took place only in the faster layer. The results suggest some new insights in the processes occurring at the early stages of a dense plume migration moving in a stratified aquifer under groundwater fluctuations, which can be summarized through the following points: (i) Above a stability criterion threshold, a fingering process and a multi modal plume transport take place, but local dispersivities can be cautiously derived, using breakthrough curves matching. (ii) When water table is subject to some cycling or rising, the plume can be significantly distorted in the transverse direction, leading to unusual values of the ratio between longitudinal and transverse dispersivities. (iii) Under stable conditions, for example in the case of straightforward injection in the faster aquifer layer, longitudinal dispersivity is greater than the transverse component as usually encountered, and the obtained transport parameters are closed to macro dispersivity values, which reach their asymptotic limit at very short distances. (iv) The classical scale effect about the varying dispersivity at short distances could be a process mainly due to the distance required for a plume stabilization. 相似文献
6.
The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT‐MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach. An alternative for all types of media is the capture probability (CP) approach, which is based on the solution of the standard advection‐dispersion equation in a backward mode, making use of the analogy between forward and backward transport processes. Within this context, we review the current controversy about the correct form of the conceptual model for transport, finding that the advection‐diffusion model, which represents the diffusive interchange between streamtubes with differing velocities, is more physically realistic than the conventional advection‐dispersion model. For mildly to moderately heterogeneous materials, stochastic theories and simulation experiments show that this process converges at the field scale to an effective advection‐dispersion process that can be simulated with conventional transport models using appropriate macrodispersivity values. For highly heterogeneous materials, stochastic theories do not yet exist but there is no reason why the process should not converge naturally as well. Macrodispersivities appear to be formation‐specific. The advection‐dispersion model can be used for capture zone delineation in heterogeneous granular media. For fractured porous systems, hybrid equivalent porous medium and discrete fracture network or CP‐based approaches may have potential. In general, capture zones delineated by PT without MC will always be too small and should not be used as a basis for land‐use decisions. 相似文献
7.
Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport 
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下载免费PDF全文 Numerical transport models based on the advection‐dispersion equation (ADE) are built on the assumption that sub‐grid cell transport is Fickian such that dispersive spreading around the average velocity is symmetric and without significant tailing on the front edge of a solute plume. However, anomalous diffusion in the form of super‐diffusion due to preferential pathways in an aquifer has been observed in field data, challenging the assumption of Fickian dispersion at the local scale. This study develops a fully Lagrangian method to simulate sub‐grid super‐diffusion in a multidimensional regional‐scale transport model by using a recent mathematical model allowing super‐diffusion along the flow direction given by the regional model. Here, the time randomizing procedure known as subordination is applied to flow field output from MODFLOW simulations. Numerical tests check the applicability of the novel method in mapping regional‐scale super‐diffusive transport conditioned on local properties of multidimensional heterogeneous media. 相似文献
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9.
《Advances in water resources》2001,24(6):607-619
Solute discharge moments (mean and variance) are computed using numerical modeling of flow and advective transport in two-dimensional heterogeneous aquifers and are compared to theoretical results. The solute discharge quantifies the temporal evolution of the total contaminant mass crossing a certain compliance boundary. In addition to analyzing the solute discharge moments within a classical absolute dispersion framework, we also analyze relative dispersion formulation, whereby plume meandering (deviation from mean flow path caused by velocity variations at scales larger than plume size) is removed. This study addresses some important issues related to the computation of solute discharge moments from random walk particle tracking experiments, and highlights some of the important differences between absolute and relative dispersion frameworks. Relative dispersion formulation produces maximum uncertainty that coincides with the peak mean discharge. Absolute dispersion, however, results in earlier arrival of the uncertainty peak as compared to the first moment peak. Simulations show that the standard deviation of solute discharge in a relative dispersion framework requires increasingly large temporal sampling windows to smooth out some of the large fluctuations in breakthrough curves associated with advective transport. Using smoothing techniques in particle tracking to distribute the particle mass over a volume rather than at a point significantly reduces the noise in the numerical simulations and removes the need to use large temporal windows. Same effect can be obtained by adding a local dispersion process to the particle tracking experiments used to model advective transport. The effect of the temporal sampling window bears some relevance and important consequences for evaluating risk-related parameters. The expected value of peak solute discharge and its standard deviation are very sensitive to this sampling window and so will be the risk distribution relying on such numerical models. 相似文献
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11.
Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments. 相似文献
12.
Subsurface fluid flow and solute transport take place in a multiscale heterogeneous environment. Neither these phenomena nor their host environment can be observed or described with certainty at all scales and locations of relevance. The resulting ambiguity has led to alternative conceptualizations of flow and transport and multiple ways of addressing their scale and space–time dependencies. We focus our attention on four approaches that give rise to nonlocal representations of advective and dispersive transport of nonreactive tracers in randomly heterogeneous porous or fractured continua. We compare these approaches theoretically on the basis of their underlying premises and the mathematical forms of the corresponding nonlocal advective–dispersive terms. One of the four approaches describes transport at some reference support scale by a classical (Fickian) advection–dispersion equation (ADE) in which velocity is a spatially (and possibly temporally) correlated random field. The randomness of the velocity, which is given by Darcy’s law, stems from random fluctuations in hydraulic conductivity (and advective porosity though this is often disregarded). Averaging the stochastic ADE over an ensemble of velocity fields results in a space–time-nonlocal representation of mean advective–dispersive flux, an approach we designate as stnADE. A closely related space–time-nonlocal representation of ensemble mean transport is obtained upon averaging the motion of solute particles through a random velocity field within a Lagrangian framework, an approach we designate stnL. The concept of continuous time random walk (CTRW) yields a representation of advective–dispersive flux that is nonlocal in time but local in space. Closely related to the latter are forms of ADE entailing fractional derivatives (fADE) which leads to representations of advective–dispersive flux that are nonlocal in space but local in time; nonlocality in time arises in the context of multirate mass transfer models, which we exclude from consideration in this paper. We describe briefly each of these four nonlocal approaches and offer a perspective on their differences, commonalities, and relative merits as analytical and predictive tools. 相似文献
13.
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
14.
Lessons Learned from 25 Years of Research at the MADE Site 总被引：2，自引：0，他引：2
Field studies at well‐instrumented research sites have provided extensive data sets and important insights essential for development and testing of transport theories and mathematical models. This paper provides an overview of over 25 years of research and lessons learned at one of such field research sites on the Columbus Air Force Base in Mississippi, commonly known as the Macrodispersion Experiment (MADE) site. Since the mid‐1980s, field data from the MADE site have been used extensively by researchers around the world to explore complex contaminant transport phenomena in highly heterogeneous porous media. Results from field investigations and modeling analyses suggested that connected networks of small‐scale preferential flow paths and relative flow barriers exert dominant control on solute transport processes. The classical advection‐dispersion model was shown to inadequately represent plume‐scale transport, while the dual‐domain mass transfer model was found to reproduce the primary observed plume characteristics. The MADE site has served as a valuable natural observatory for contaminant transport studies where new observations have led to better understanding and improved models have sprung out analysis of new data. 相似文献
15.
Solute transport in heterogeneous media: The impact of anisotropy and non-ergodicity in risk assessment 总被引：1，自引：1，他引：0
X. Sánchez-Vila J. Solís-Delfín 《Stochastic Environmental Research and Risk Assessment (SERRA)》1999,13(5):365-379
Conceptual model selection is a key issue in risk assessment studies. We analyze the effect of a number of conceptual aspects
related to solute transport in two-dimensional heterogeneous media. The main issues addressed are non-ergodicity, anisotropy
in the correlation structure of the transmissivity field, and dispersion at the local scale. In particular, we study the development
of a solute plume when mean flow is oriented at an angle with respect to the principal directions of anisotropy. The study
is carried out in a Lagrangian framework using Monte Carlo analysis.
Of special interest is the evolution of individual plumes. A number of aspects are analyzed, namely the location of the center
of mass for each plume and the different ways to compute the angles that the main axes of the plume develop with respect to
the direction of the mean flow. Stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean
flow direction. In our non-ergodic simulations, the mean of the offset angles, for each individual plume in each particular
realization, is offset from the mean flow direction towards the direction of maximum anisotropy. If, instead, the analysis
is performed on the ensemble plume (superposition of all different simulations), it is then found oriented closer to the direction
of the mean flow than the average offset angle for the different plumes considered separately. This last result adds an extra
word of caution to the use of ensemble averaged values in solute transport studies.
Serious implications for risk assessment follow from the conceptual model adopted. First, in any single realization there
will a large uncertainty in locating the plume at any given time; second, real dilution would be less than what would be expected
if the macrodispersion values obtained for ergodic conditions were applied; third, the volume that is affected by a non-zero
concentration is smaller than that predicted from macrodispersion concepts; fourth, the orientation of the plume does not
correspond to that of the mean flow; and fifth, accounting for local dispersion helps reducing uncertainty. 相似文献
16.
The transport of instantaneously injected conservative solute through a well in the formation of random conductivity is analyzed. The solute is advected by the recharging well flow with the uniform background gradient. The longitudinal trajectory variance is derived for the central mean streamline. It is shown that the solute is spread as in a radial flow at small travel distances and as in a uniform flow far from the well. Closed form expressions of the longitudinal trajectory variance and macrodispersivity are derived for the case of small scale heterogeneity. It is shown that the macrodispersivity is bounded between the asymptotic macrodispersivities pertinent to the well and uniform flows. 相似文献
17.
James N. Carleton 《水文研究》2015,29(6):1198-1212
Models that simulate loadings of pollutants from agricultural landscapes to surface waters often operate at time scales that are relatively coarse (e.g. daily) compared with how fast water moves in streams, suggesting a commensurate physical scale that is substantially larger than typical agricultural fields. In general, as pollutants enter water and move downstream, longitudinal dispersive effects and travel time de‐synchronization tend to cause flattening and broadening of concentration peaks—an effect with implications for potential impacts on ecological and human health, and for which adequate representation is thus important for risk assessment. In‐stream transport is often approximated in practice using numerical implementation of the one‐dimensional advection–dispersion equation (ADE), with streams discretized into linked homogeneous segments. However, when a daily time step is employed, limitations inherent in the finite difference methodology may constrain simulated dispersion in lotic waters to unrepresentative or unrealistic magnitudes. In this paper, a convolution‐based approach to surface water transport is suggested as an alternative to the ADE, for use in combination with daily input loading models. This approach offers the advantage of greater flexibility in representing longitudinal mixing by using impulse response functions (IRF) to represent inter‐segment transport. Networks of stream segments are represented using nested convolutions, implemented using forward and inverse discrete Fourier transform to simplify calculations. Enhanced representational flexibility arises from the freedom afforded the modeller in selecting each segment's IRF, which may be chosen to represent dispersive regimes ranging from pure advection (plug flow) to compete mixing, and beyond to the sort of long‐tailed mixing characterized by fractal inverse frequency power‐law scaling. The approach is explored in proof‐of‐concept exercises that make use of atrazine monitoring data sets collected over common time periods from upstream and downstream locations within the same watersheds. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. 相似文献
18.
Kaili Wang Guanhua Huang 《Advances in water resources》2011,34(6):671-683
The effect of aquifer heterogeneity on flow and solute transport in two-dimensional isotropic porous media was analyzed using the Monte Carlo method. The two-dimensional logarithmic permeability (ln K) was assumed to be a non-stationary random field with its increments being a truncated fractional Lévy motion (fLm). The permeability fields were generated using the modified successive random additions (SRA) algorithm code SRA3DC [http://www.iamg.org/CGEditor/index.htm]. The velocity and concentration fields were computed respectively for two-dimensional flow and transport with a pulse input using the finite difference codes of MODFLOW 2000 and MT3DMS. Two fLm control parameters, namely the width parameter (C) and the Lévy index (α), were varied systematically to examine their effect on the resulting permeability, flow velocity and concentration fields. We also computed the first- and second-spatial moments, the dilution index, as well as the breakthrough curves at different control planes with the corresponding concentration fields. In addition, the derived breakthrough curves were fitted using the continuous time random walk (CTRW) and the traditional advection-dispersion equation (ADE). Results indicated that larger C and smaller α both led to more heterogeneous permeability and velocity fields. The Lévy-stable distribution of increments in ln K resulted in a Lévy-stable distribution of increments in logarithm of the velocity (ln v). Both larger C and smaller α created sharper leading edges and wider tailing edges of solute plumes. Furthermore, a relatively larger amount of solute still remained in the domain after a relatively longer time transport for smaller α values. The dilution indices were smaller than unity and increased as C increased and α decreased. The solute plume and its second-spatial moments increased as C increased and α decreased, while the first-spatial moments of the solute plume were independent of C and α values. The longitudinal macrodispersivity was scale-dependent and increased as a power law function of time. Increasing C and decreasing α both resulted in an increase in longitudinal macrodispersivity. The transport in such highly heterogeneous media was slightly non-Gaussian with its derived breakthrough curves being slightly better fitted by the CTRW than the ADE, especially in the early arrivals and late-time tails. 相似文献
19.
20.
《Advances in water resources》2007,30(4):851-865
Groundwater flow and chemical transport in subterranean estuaries are poorly understood despite their potentially important implications for chemical fluxes from aquifers to coastal waters. Here, a numerical study of the dynamics in a subterranean estuary subject to tidal forcing is presented. Simulations show that salt transport associated with tidally driven seawater recirculation leads to the formation of an upper saline plume in the intertidal region. Computed transit times and flow velocities indicate that this plume represents a more active zone for mixing and reaction than the dispersion zone of the lower, classical salt wedge. Proper conceptualisation of this surficial mixing zone extends our understanding of processes within the subterranean estuary. Numerical tracer simulations reveal that tidal forcing may reduce the threat of a land-derived contaminant discharging to the marine environment by modifying the subsurface transport pathway and local geochemical conditions. Mixing and stratification in the subterranean estuary are strongly affected by both inland and tidal forcing. Based on the estuarine analogy we present a systematic classification of subterranean estuaries. 相似文献