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1.
《Advances in water resources》2004,27(3):207-222
An Eulerian perturbation approach was applied to develop a method of moment for solute transport in a nonstationary, fractured medium. The conceptualized fractured medium is described through a dual-porosity model. Stochastic governing equations for mean concentration and concentration covariance were analytically derived to the first-order accuracy of log-conductivity variance and solved with a numerical method––a finite difference method. The developed method is called a numerical Eulerian method of moment (NEMM). This method was compared with the stationary transport theory [Water Resour. Res. 36(7) (2000) 1665] for predicting mean concentration and its spatial moments. The comparison indicated that the two methods matched very well in predicting first and second spatial moments. NEMM solutions were also compared with Monte Carlo simulations for solute transport in stationary fractured media. The results of the two methods were consistent for calculating small log conductivity variance. The theory was then used to study effects of various parameters and nonstationarity of the medium on flow and transport processes. Results indicated that medium nonstationarity would significantly influence the solute transport process. The nonstationary transport theory relaxes many assumptions adopted in stationary theories and paves the way for applying the NEMM to many environmental projects, especially in analyzing uncertainty of solute transport. 相似文献
2.
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
3.
《Advances in water resources》1996,19(4):193-206
This study deals with a method to solve the transport equations for a kinetically adsorbing solute in a porous medium with spatially varying velocity field and dispersion coefficients. Making use of the stochastic nature of a first-order kinetic process, we show that the advection-dispersion equation and the adsorption isotherm can be decoupled. Once the solution for a non-adsorbing solute is known, the method provides an exact solution for the kinetically adsorbing solute. The method is worked out in four examples. In particular we demonstrate how the method can be applied simultaneously with a numerical transport code: the advective-dispersive transport is computed numerically, whereas kinetic effects are incorporated analytically. The proposed approach may be useful in field scale applications with complex flow patterns. 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.
Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media 
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下载免费PDF全文 Farzaneh MahmoodPoor Dehkordy Martin A. Briggs Frederick D. Day‐Lewis Amvrossios C. Bagtzoglou 《水文研究》2018,32(13):2030-2043
Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales. 相似文献
6.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 下载免费PDF全文
下载免费PDF全文 In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field. 相似文献
7.
Boundary conditions are required to close the mathematical formulation of unstable density‐dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density‐dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams‐Bashford/Backward Trapezoidal time integration approach in comparison to the Euler‐Backward/Euler‐Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density‐dependent flow. 相似文献
8.
The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity. 相似文献
9.
Hillel Rubin 《Advances in water resources》1983,6(2):96-105
Stratification of the density in groundwater flow stems from the contact between water which contains minerals in low concentration with water containing a high concentration of minerals. The flow in such a flow field should be simulated by solving simultaneously the equations of continuity, motion and solute transport, because solute concentration affects the dynamics of the flow. Such an approach is generally associated with complicated calculations and numerical schemes subject to problems of convergence and stability, as the basic equations are highly nonlinear.This study applies the phenomenological boundary layer approximation, and suggests a reference to three different zones in the flow field: (a) fresh water zone, (b) transition zone, and (c) mineralized water zone. In zones (a) and (c) it is assumed that the potential flow theory can be applied. In zone (b) the flow is nonpotential but the basic similarity conditions typical to boundary layers exist.The approach suggested in this study simplifies the mathematical models that should be used for the flow field simulation. This approach is especially attractive in cases where the Dupuit approximation is applicable. In such cases very often analytical solutions can be obtained for unidirectional flows. In cases that are too complicated for representation by analytical solutions, the method can be used for the creation of simplified numerical schemes.Various examples in this study demonstrate the application of the method for various field problems associated with steady state as well as unsteady state conditions.The simplicity of the method makes it useful for variety of problems. It can be used even by small institutions and small consulting firms, who have usually access to minicomputers and microprocessors. 相似文献
10.
V. D. Cvetkovic G. Dagan A. M. Shapiro 《Stochastic Environmental Research and Risk Assessment (SERRA)》1991,5(1):45-54
The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity. 相似文献
11.
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
12.
13.
Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport 下载免费PDF全文
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
14.
The heterogeneity of the solute flux field in the horizontal plane at the field scale has been documented in several field studies. On the other hand, little information is available on the persistence of certain solute transport scenarios over consecutive infiltration cycles. This study was initiated to analyse the recurrence of solute leaching behaviour as estimated in two soil column tests emphasizing the preferential flow phenomenon. Twenty-four small-sized soil samples were subjected to two consecutive unsaturated steady-state flow leaching experiments with bromide as tracer. Observed breakthrough curves (BTCs) were analysed by the method of moments and by the advection–dispersion equation (ADE) to classify solute behaviour. Frequency distributions of the parameters indicating the solute velocity were heavily skewed or bimodal, reflecting the broad variability of the leaching scenarios, including some with pronounced preferential solute breakthrough. Exclusion of the preferential flow columns from our calculations revealed an average amount of 37% of immobile water. The large-scale BTCs derived from assembling the individual concentration courses of each run showed similar features, such as an early bromide breakthrough. However, two distinct apices, viz. one preferential and one matrix, were observed only in the first run, whereas the concentration decrease between the peaks was missing from the second run. A change in soil structure with continuous leaching was presumed to modify the interplay of the various flow domains, thereby altering the spreading of the BTCs. Correlation analysis between parameters of both tests suggests that preferential transport conditions are likely to occur at the same locations in the field over several infiltration cycles, whereas the ‘classical’ or expected matrix flow is time variant and therefore seems to be hardly predictable. © 1998 John Wiley & Sons, Ltd. 相似文献
15.
The finite-element method based on a Galerkin technique was used to formulate the problem of simulating the two-dimensional (cross-sectional) transient movement of water and solute in saturated or partially saturated nonuniform porous media. The numerical model utilizes linear triangular elements. Nonreactive, as well as reactive solutes whose behaviour can be described by a distribution coefficient or first-order reaction term were considered. The flow portion of the model was tested by comparison of the model results with experimental and finite-difference results for transient flow in an unsaturated sand column and the solute transport portion of the model was tested by comparison with analytical solution results. The model was applied to a hypothetical case involving movement of water and solutes in tile-drained soils. The simulation results showed the development of distinct solute leaching patterns in the soil as drainage proceeded. Although applied to a tile drainage problem in this study, the model should be equally useful in the study of a wide range of two-dimensional water and solute migration problems. 相似文献
16.
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
17.
A novel solute-flux measuring technique has been developed and a limited but successful field study was carried out. The technique involves the emplacement of perspex columns containing ion-exchange resin into the soil to abstract the solute flux from soilwater flowing through the column. Column construction and emplacement procedures have been developed to minimise soilwater flow disturbance in and around soil-emplaced columns. Some disturbance must occur, however, the technique can be seen as a practical compromise which offers some improvement over conventional solute-flux measurement techniques.
The technique, using linear arrays of columns, was used to compare solute fluxes at two positions on a hillslope segment, underlain by Millstone Grit in the Pennines. Using a random-position technique for emplacement, consistent fluxes between downslope positions were separated from random lateral fluxes within locations at the same slope position. 相似文献
18.
The removal of chemicals in solution by overland flow from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface‐mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
Jos C. van Dam 《水文研究》2000,14(6):1101-1117
Single domain models may seriously underestimate leaching of nutrients and pesticides to groundwater in clay soils with shrinkage cracks. Various two‐domain models have been developed, either empirical or physically based, which take into account the effects of cracks on water flow and solute transport. This paper presents a model concept that uses the clay shrinkage characteristics to derive crack volume and crack depth under transient field conditions. The concept has been developed to simulate field average behaviour of a field with cracks, rather than flow and transport at a small plot. Water flow and solute transport are described with basic physics, which allow process and scenario analysis. The model concept is part of the more general agrohydrological model SWAP, and is applied to a field experiment on a cracked clay soil, at which water flow and bromide transport were measured during 572 days. A single domain model was not able to mimic the field‐average water flow and solute transport. Incorporation of the crack concept considerably improved the simulation of water content and bromide leaching to the groundwater. Still deviations existed between the measured and simulated bromide concentration profiles. The model did not reproduce the observed bromide retardation in the top layer and the high bromide dispersion resulting from water infiltration at various soil depths. A sensitivity analysis showed that the amounts of bromide leached were especially sensitive to the saturated hydraulic conductivity of the top layer, the solute transfer from the soil matrix to crack water flow and the mean residence time of rapid drainage. The shrinkage characteristic and the soil hydraulic properties of the clay matrix showed a low sensitivity. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
20.
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