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1.
A Lagrangian perturbation method is applied to develop a method of moments for solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity stems from medium nonstationarity and internal and external boundaries of the study domain. The solute flux is described as a space-time process where time refers to the solute flux breakthrough through a control plane (CP) at some distance downstream of the solute source and space refers to the transverse displacement distribution at the CP. The analytically derived moment equations for solute transport in a nonstationarity flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The developed method is applied to study the effects of heterogeneity and nonstationarity of the hydraulic conductivity and chemical sorption coefficient on solute transport. The study results indicate all these factors will significantly influence the mean and variance of solute flux. 相似文献
2.
A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field. 相似文献
3.
Jichun Wu Bill X. Hu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(6):665-682
The unconditional stochastic studies on groundwater flow and solute transport in a nonstationary conductivity field show that
the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values (Zhang et al.
in Water Resour Res 36:2107–2120, 2000; Wu et al. in J Hydrol 275:208–228, 2003; Hu et al. in Adv Water Resour 26:513–531, 2003). In this study, we develop a numerical method of moments conditioning on measurements of hydraulic conductivity and head
to reduce the variances of the head and the solute flux. A Lagrangian perturbation method is applied to develop the framework
for solute transport in a nonstationary flow field. Since analytically derived moments equations are too complicated to solve
analytically, a numerical finite difference method is implemented to obtain the solutions. Instead of using an unconditional
conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment
for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity
and head at some points. The developed theory is applied in several case studies to investigate the influences of the measurements
of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary
flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Since the
hydraulic head measurement points are treated as the interior boundary (Dirichlet boundary) conditions, conditioning on both
the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for
reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant. 相似文献
4.
Hu BX 《Ground water》2006,44(2):222-233
A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects. 相似文献
5.
We analyze the impact of a linear trend in the mean log-conductivity on the transport of a conservative tracer in a bounded domain. The effects of such a linear trend on solute transport were analyzed in depth for unbounded domains (Rubin and Seong, Water Resour Res 30(11):2901–2911, 1994; Indelman and Rubin, Water Resour Res 31(5):1257–1265, 1995; Water Resour Res 32(5):1257–1265, 1996), whereas studies concerning this special case of medium nonstationarity in finite domains usually focus on head or flow statistics (Guadagnini et al., Stoch Environ Res Risk Assess, 17:394–407, 2003). In this study both ensemble and effective plume moments are provided 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 velocity field spatially nonstationary is developed by using the stochastic finite element method. Results show that ensemble moments are affected by increasing trends both parallel and normal to the mean flow direction, but the impact on effective plume moments is very different. A parallel trend does not seem to influence the effective second moments; while a normal trend, although modifies the transverse effective moment only weakly, strongly increases the longitudinal one, especially for large initial sizes of the source. Furthermore, the increase of the particle displacement variance produced by a parallel trend in the finite domain disagrees with the results obtained in an unbounded domain, due to the boundary conditions here considered making both head and velocity moments nonstationary and nonsymmetric. 相似文献
6.
Z. J. Kabala 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(4):331-348
Under the assumption that local solute dispersion is negligible, a new general formula (in the form of a convolution integral)
is found for the arbitrary k-point ensemble moment of the local concentration of a solute convected in arbitrary m spatial
dimensions with general sure initial conditions. From this general formula new closed-form solutions in m=2 spatial dimensions
are derived for 2-point ensemble moments of the local solute concentration for the impulse (Dirac delta) and Gaussian initial
conditions. When integrated over an averaging window, these solutions lead to new closed-form expressions for the first two
ensemble moments of thevolume-averaged solute concentration and to the corresponding concentration coefficients of variation (CV). Also, for the impulse (Dirac delta) solute concentration
initial condition, the second ensemble moment of thesolute point concentration in two spatial dimensions and the corresponding CV are demonstrated to be unbound. For impulse initial conditions the CVs
for volume-averaged concentrations axe compared with each other for a tracer from the Borden aquifer experiment. The point-concentration
CV is unacceptably large in the whole domain, implying that the ensemble mean concentration is inappropriate for predicting
the actual concentration values. The volume-averaged concentration CV decreases significantly with an increasing averaging
volume. Since local dispersion is neglected, the new solutions should be interpreted as upper limits for the yet to be derived
solutions that account for local dispersion; and so should the presented CVs for Borden tracers. The new analytical solutions
may be used to test the accuracy of Monte Carlo simulations or other numerical algorithms that deal with the stochastic solute
transport. They may also be used to determine the size of the averaging volume needed to make a quasi-sure statement about
the solute mass contained in it. 相似文献
7.
Analysis of macrodispersion through volume averaging: comparison with stochastic theory 总被引：2，自引：1，他引：1
Jie Wang Peter K. Kitanidis 《Stochastic Environmental Research and Risk Assessment (SERRA)》1999,13(1-2):66-84
Velocity variability at scales smaller than the size of a solute plume enhances the rate of spreading of the plume around
its center of mass. Macroscopically, the rate of spreading can be quantified through macrodispersion coefficients, the determination
of which has been the subject of stochastic theories. This work compares the results of a volume-averaging approach with those
of the advection dominated large-time small-perturbation theory of Dagan [1982] and Gelhar and Axness [1983]. Consider transport
of an ideal tracer in a porous medium with deterministic periodic velocity. Using the Taylor-Aris-Brenner method of moments,
it has been previously demonstrated [Kitanidis, 1992] that when the plume spreads over an area much larger than the period,
the volume-averaged concentration satisfies the advection-dispersion equation with constant coefficients that can be computed.
Here, the volume-averaging analysis is extended to the case of stationary random velocities. Additionally, a perturbation
method is applied to obtain explicit solutions for small-fluctuation cases, and the results are compared with those of the
stochastic macrodispersion theory. It is shown that the method of moments, which uses spatial averaging, for sufficiently
large volumes of averaging yields the same result as the stochastic theory, which is based on ensemble averaging. The result
is of theoretical but also practical significance because the volume-averaging approach provides a potentially efficient way
to compute macrodispersion coefficients. The method is applied to a simplified representation of the Borden aquifer.
Received: December 28, 1998 相似文献
8.
Chunlin Huang Bill X. Hu Xin Li Ming Ye 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(8):1155-1167
Hydraulic conductivity distribution and plume initial source condition are two important factors affecting solute transport
in heterogeneous media. Since hydraulic conductivity can only be measured at limited locations in a field, its spatial distribution
in a complex heterogeneous medium is generally uncertain. In many groundwater contamination sites, transport initial conditions
are generally unknown, as plume distributions are available only after the contaminations occurred. In this study, a data
assimilation method is developed for calibrating a hydraulic conductivity field and improving solute transport prediction
with unknown initial solute source condition. Ensemble Kalman filter (EnKF) is used to update the model parameter (i.e., hydraulic
conductivity) and state variables (hydraulic head and solute concentration), when data are available. Two-dimensional numerical
experiments are designed to assess the performance of the EnKF method on data assimilation for solute transport prediction.
The study results indicate that the EnKF method can significantly improve the estimation of the hydraulic conductivity distribution
and solute transport prediction by assimilating hydraulic head measurements with a known solute initial condition. When solute
source is unknown, solute prediction by assimilating continuous measurements of solute concentration at a few points in the
plume well captures the plume evolution downstream of the measurement points. 相似文献
9.
10.
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
11.
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
12.
Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples. 相似文献
13.
Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant. 相似文献
14.
《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
15.
The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-θ schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect. 相似文献
16.
Antonio Coppola Alessandro ComegnaGiovanna Dragonetti Miles DyckAngelo Basile Nicola LamaddalenaMohamed Kassab Vincenzo Comegna 《Advances in water resources》2011,34(6):747-759
Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include information from different scales of heterogeneities. 相似文献
17.
Experimental and analytical studies of solute transport during run‐off over vegetated surfaces 
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下载免费PDF全文 Solute transport in overland flow is considered as one of the main contributors to water pollution. Although many models of pollutant transport mechanism from soil to run‐off water have been proposed, the characteristics of solute transport accompanying the water run‐off over vegetated surface have not been well studied. In this study, a series of laboratory experiments were conducted to study the solute transport over vegetated surfaces. Based on the experimental results, an idea of the “stationary water layer” in run‐off was proposed. Applying the complete mixing theory in the stationary water layer, an analytical solute transport model was developed with the assumption that the upper run‐off completely mixes with the underlying water in the stationary water layer for each site. The results show that the predictions made by the present model are in good agreement with the measured experimental data. For the vegetated surfaces, the depth of stationary water layer is related to the rainfall intensity, bed slope, and vegetation density. The analytical solution shows that the maximum solute transport occurs at the time of concentration. This study advances our understanding of the mechanisms of solute transport over vegetated areas. 相似文献
18.
径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制. 相似文献
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20.
Quantifying hyporheic solute dynamics has been limited by our ability to assess the magnitude and extent of stream interactions with multiple domains: mobile subsurface storage (MSS, e.g., freely flowing pore water) and immobile subsurface storage (ISS, e.g., poorly connected pore water). Stream-tracer experiments coupled with solute transport modeling are frequently used to characterize lumped MSS and ISS dynamics, but are limited by the ability to sample only “mobile” water and by window of detection issues. Here, we couple simulations of near-surface electrical resistivity (ER) methods with conservative solute transport to directly compare solute transport with ER interpretations, and to determine the ability of ER to predict spatial and temporal trends of solute distribution and transport in stream–hyporheic systems. Results show that temporal moments from both ER and solute transport data are well correlated for locations where advection is not the dominant solute transport process. Mean arrival time and variance are especially well-predicted by ER interpretation, providing the potential to estimate rate-limited mass transport (i.e. diffusive) parameters from these data in a distributed domain, substantially increasing our knowledge of the fate and transport of subsurface solutes. 相似文献