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1.
The permeable conduit wall in a karst aquifer allows for water and solute to be exchanged between conduits and the limestone matrix. Contaminant sequestered in the limestone matrix is flushed into conduits following flood events. The contaminant released from the permeable wall will then mix with conduit water and will be transported downgradient in the conduit. A one-dimensional advection-dispersion equation is presented to describe this mixing-transport incorporating water flow and solute flux through the conduit wall. An analytical solution ignoring conduit dispersion is derived using the method of characteristics. Scale analysis is performed to provide a general guideline to estimate when conduit dispersion can be neglected. The solution also can be used to compute the distribution of solute in the matrix before flushing.  相似文献   

2.
Exact analytical solutions for two-dimensional advection-dispersion equation (ADE) in cylindrical coordinates subject to the third-type inlet boundary condition are presented in this study. The finite Hankel transform technique in combination with the Laplace transform method is adopted to solve the two-dimensional ADE in cylindrical coordinates. Solutions are derived for both continuous input and instantaneous slug input. The developed analytical solutions are compared with the solutions for first-type inlet boundary condition to illustrate the influence of the inlet condition on the two-dimensional solute transport in a porous medium system with a radial geometry. Results show significant discrepancies between the breakthrough curves obtained from analytical solutions for the first-type and third-type inlet boundary conditions for large longitudinal dispersion coefficients. The developed solutions conserve the solute mass and are efficient tools for simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment or an in situ infiltration test with a tracer.  相似文献   

3.
In karst aquifers with significant matrix permeability, water and solutes are exchanged between the conduits and carbonate matrix. Transport through the matrix increases the spread of solutes and increases travel times. This study numerically evaluates advective solute transport in synthetic karst systems that contain 3D branching conduit networks. Particle tracking is performed to analyze the spatial and temporal transport history of solute that arrives at the conduit outlet. Three measures of transport connectivity are used to quantify the solute migration behavior: the skewness of the particle arrival time distribution, the normalized fifth percentile of arrival times, and the fraction of the total travel time that occurs within conduits. All three of these metrics capture the influence of conduit network geometry on solute transport. A more tortuous network leads to enhanced conduit-matrix mixing, which reduces the transport connectivity and yields a broader distribution of solute arrival times. These results demonstrate that the conduit network geometry is an important control on solute transport in karst systems with a permeable matrix.  相似文献   

4.
Process-based interpretation of tracer tests in carbonate aquifers   总被引：6，自引：0，他引：6  
Birk S  Geyer T  Liedl R  Sauter M 《Ground water》2005,43(3):381-388
A tracer test in a carbonate aquifer is analyzed using the method of moments and two analytical advection-dispersion models (ADMs) as well as a numerical model. The numerical model is a coupled continuum-pipe flow and transport model that accounts for two different flow components in karstified carbonate aquifers, i.e., rapid and often turbulent conduit flow and Darcian flow in the fissured porous rock. All techniques employed provide reasonable fits to the tracer breakthrough curve (TBC) measured at a spring. The resulting parameter estimates are compared to investigate how each conceptual model of flow and transport processes that forms the basis of the analyses affects the interpretation of the tracer test. Numerical modeling results suggest that the method of moments and the analytical ADMs tend to overestimate the conduit volume because part of the water discharged at the spring is wrongly attributed to the conduit system if flow in the fissured porous rock is ignored. In addition, numerical modeling suggests that mixing of the two flow components accounts for part of the dispersion apparent in the measured TBC, while the remaining part can be attributed to Taylor dispersion. These processes, however, cannot reasonably explain the tail of the TBC. Instead, retention in immobile-fluid regions as included in a nonequilibrium ADM provides a possible explanation.  相似文献   

5.
This article outlines analytical solutions to quantify the length scale associated with “upstream dispersion,” the artificial movement of solutes in the opposite direction to groundwater flow, in solute transport models. Upstream dispersion is an unwanted artifact in common applications of the advection-dispersion equation (ADE) in problems involving groundwater flow in the direction of increasing solute concentrations. Simple formulae for estimating the one-dimensional distance of upstream dispersion are provided. These show that under idealized conditions (i.e., steady-state flow and transport, and a homogeneous aquifer), upstream dispersion may be a function of only longitudinal dispersivity. The scale of upstream dispersion in a selection of previously presented situations is approximated to highlight the utility of the presented formulae and the relevance of this ADE anomaly in common transport problems. Additionally, the analytical solution is applied in a hypothetical scenario to guide the modification of dispersion parameters to minimize upstream dispersion.  相似文献   

6.
A benchmark test for flow in karstic aquifers is presented in the form of an exact solution of the harmonic variations of water flux and head within a karst conduit that is imbedded within a three-dimensional porous matrix having a free surface. The variations are driven by a prescribed variation of head applied at one end of the conduit. The benchmark consists of expressions for the spring discharge as a function of time and the conduit head and flux as functions of distance along the conduit and time. These expressions contain three dimensionless parameters, permitting development of a wide range of specific benchmark tests. The expressions are particularly simple in the case of an infinitely deep aquifer. This limiting solution should provide the most severe test for two-dimensional models of karst aquifer flow. Another limiting case of interest is that in which the conduit diameter is equal to the water depth. This limiting solution should provide the easiest test for two-dimensional models.  相似文献   

7.
 The advection-dispersion equation (ADE) is inadequate for describing tails in solute breakthrough curves. Re-examination of solute breakthrough curves from one-dimensional experiments in porous media and channel flow literature shows a consistent discrepancy compared with solutions to the ADE. The leading tail of breakthrough curves is sharper, and the trailing tail is longer and smoother, than best fitting, least-squares ADE solutions. A random particle simulation exercise shows that the ADE may firstly be erroneous because of the assumption of time steps over which random solute movements are considered independent. Definition of such time steps hinges upon the slowest random movements, such as those predominantly by molecular diffusion. A second potential source of error is the highly skewed nature of the inverse distribution of underlying, micro-scale velocities, which causes slow convergence to normality under the central limit theorem.  相似文献   

8.
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   

9.
A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one‐dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production‐value problem. Both nonuniform cross‐section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two‐way transfer between conduit water and matrix water is also investigated by using the solution for the production‐value problem as a first‐order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring‐breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Highlights:
    相似文献   

10.
Transport processes in heterogeneous porous media are often treated in terms of one-equation models. Such treatment assumes that the velocity, pressure, temperature, and concentration can be represented in terms of a single large-scale averaged quantity in regions having significantly different mechanical, thermal, and chemical properties. In this paper we explore the process of single-phase flow in a two-region model of heterogeneous porous media. The region-averaged equations are developed for the case of a slightly compressible flow which is an accurate representation for a certain class of liquid-phase flows. The analysis leads to a pair of transport equations for the region averaged pressures that are coupled through a classic exchange term, in addition to being coupled by a diffusive cross effect. The domain of validity of the theory has been identified in terms of a series of length and timescale constraints.In Part II the theory is tested, in the absence of adjustable parameters, by comparison with numerical experiments for transient, slightly compressible flow in both stratified and nodular models of heterogeneous porous media. Good agreement between theory and experiment is obtained for nodular and stratified systems, and effective transport coefficients for a wide range of conditions are presented on the basis of solutions of the three closure problems that appear in the theory. Part III of this paper deals with the principle of large-scale mechanical equilibrium and the region-averaged form of Darcy's law. This form is necessary for the development and solution of the region-averaged solute transport equations that are presented in Part IV. Finally, in Part V we present results for the dispersion tensors and the exchange coefficient associated with the two-region model of solute transport with adsorption.  相似文献   

11.
This review focuses on investigations of groundwater flow and solute transport in karst aquifers through laboratory scale models (LSMs). In particular, LSMs have been used to generate new data under different hydraulic and contaminant transport conditions, testing of new approaches for site characterization, and providing new insights into flow and transport processes through complex karst aquifers. Due to the increasing need for LSMs to investigate a wide range of issues, associated with flow and solute migration karst aquifers this review attempts to classify, and introduce a framework for constructing a karst aquifer physical model that is more representative of field conditions. The LSMs are categorized into four groups: sand box, rock block, pipe/fracture network, and pipe-matrix coupling. These groups are compared and their advantages and disadvantages highlighted. The capabilities of such models have been extensively improved by new developments in experimental methods and measurement devices. Newer technologies such as 3D printing, computed tomography scanning, X-rays, nuclear magnetic resonance, novel geophysical techniques, and use of nanomaterials allow for greater flexibilities in conducting experiments. In order for LSMs to be representative of karst aquifers, a few requirements are introduced: (1) the ability to simulate heterogeneous distributions of karst hydraulic parameters, (2) establish Darcian and non-Darcian flow regimes and exchange between the matrix and conduits, (3) placement of adequate sampling points and intervals, and (4) achieving some degree of geometric, kinematic, and dynamic similitude to represent field conditions.  相似文献   

12.
Li G 《Ground water》2011,49(4):584-592
Often the water flowing in a karst conduit is a combination of contaminated water entering at a sinkhole and cleaner water released from the limestone matrix. Transport processes in the conduit are controlled by advection, mixing (dilution and dispersion), and retention-release. In this article, a karst transport model considering advection, spatially varying dispersion, and dilution (from matrix seepage) is developed. Two approximate Green's functions are obtained using transformation of variables, respectively, for the initial-value problem and for the boundary-value problem. A numerical example illustrates that mixing associated with strong spatially varying conduit dispersion can cause strong skewness and long tailing in spring breakthrough curves. Comparison of the predicted breakthrough curve against that measured from a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida, shows that the conduit dispersivity can be as large as 400 m. Such a large number is believed to imply strong solute interaction between the conduit and the matrix and/or multiple flow paths in a conduit network. It is concluded that Taylor dispersion is not dominant in transport in a karst conduit, and the complicated retention-release process between mobile- and immobile waters may be described by strong spatially varying conduit dispersion.  相似文献   

13.
To more accurately predict the migration behavior of pollutants in porous media, we conduct laboratory scale experiments and model simulation. Aniline (AN) is used in one-dimensional soil column experiments designed under various media and hydrodynamic conditions. The advection-dispersion equation (ADE) and the continuous-time random walk (CTRW) were used to simulate the breakthrough curves (BTCs) of the solute transport. The results show that the media and hydrodynamic conditions are two important factors affecting solute transport and are related to the degree of non-Fickian transport. The simulation results show that CTRW can more effectively describe the non-Fickian phenomenon in the solute transport process than ADE. The sensitive parameter in the CTRW simulation process is , which can reflect the degree of non-Fickian diffusion in the solute transport. Understanding the relationship of with velocity and media particle size is conducive to improving the reactive solute transport model. The results of this study provide a theoretical basis for better prediction of pollutant transport in groundwater.  相似文献   

14.
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile–immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection–dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests.  相似文献   

15.
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.  相似文献   

16.
Tracer breakthrough curves provide valuable information about the traced media, especially in inherently heterogeneous karst aquifers. In order to study the effect of variations in hydraulic gradient and conduit systems on breakthrough curves, a bench scale karst model was constructed. The bench scale karst model contains both matrix and a conduit. Eight tracing tests were conducted under a wide range of hydraulic gradients from 1 to greater than 5 for branchwork and network-conduit systems. Sampling points at varying distances from the injection point were utilized. Results demonstrate that mean tracer velocities, tracer mass recovery and linear rising slope of the breakthrough curves were directly controlled by hydraulic gradient. As hydraulic gradient increased, both one half the time for peak concentration and one fifth the time for peak concentration decreased. The results demonstrate the variations in one half the time for peak concentration and one fifth the time for peak concentration of the descending limb for different sampling points under differing hydraulic gradients are mainly controlled by the interactions of advection with dispersion. The results are discussed from three perspectives: different conduit systems, different hydraulic-gradient conditions, and different sampling points. The research confirmed the undeniable role of hydrogeological setting (i.e., hydraulic gradient and conduit system) on the shape of the breakthrough curve. The extracted parameters (mobile-fluid velocity, tracer-mass recovery, linear rising limb, one half the time for peak concentration, and one fifth the time for peak concentration) allow for differentiating hydrogeological settings and enhance interpretations the tracing tests in karst aquifers.  相似文献   

17.
Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scale-dependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.  相似文献   

18.
Modeling flow and transport using both temperature and dye tracing provides constraints that can improve understanding of karst networks. A laminar flow and transport model using the finite element subsurface flow model simulated the conduit connection between a sinking stream and spring in central Pennsylvania to evaluate how conduit morphology might affect dye transport. Single and overly tortuous conduit models resulted in high concentrations as dye flowed back into the conduit from the matrix after dye injections ceased. A forked conduit model diverted flow from the main conduit, reducing falling limb dye concentration. Latin hypercube sampling was performed to evaluate the sensitivity of 52 parameter combinations (conduit hydraulic conductivity, conduit cross-sectional area, matrix transmissivity, matrix porosity, and dispersivity) for four conduit geometry scenarios. Sensitivity of arrival time for 50% of the dye indicated no parameter combinations which simulate falling limb dye concentrations for tortuous geometries, confirming the importance of the forked geometry regardless of other parameters. Temperature data from high-resolution loggers were then incorporated into the forked conduit model to reproduce seasonal spring temperature using variable sink inflow. Unlike the dye trace models, the thermal models were sensitive to other model parameters, such as conduit cross-sectional area and matrix transmissivity. These results showed this dual approach (dye and temperature) to karst network modeling is useful for (1) exploring the role of conduit and matrix interaction for contaminant storage, (2) constraining karst conduit geometries, which are often poorly understood, and (3) quantifying the effect of seasonal trends on karst aquifers.  相似文献   

19.
Many studies indicate that small‐scale heterogeneity and/or mobile–immobile mass exchange produce transient non‐Fickian plume behavior that is not well captured by the use of the standard, deterministic advection‐dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non‐Fickian transport coupled with simultaneous sequential first‐order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed‐form, steady‐state, multi‐species analytical solutions are also derived for non‐Fickian transport in highly heterogeneous aquifers with linear sorption–desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi‐species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over‐estimate cleanup rates and under‐predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.  相似文献   

20.
The geochemical computer model PHREEQC can simulate solute transport in fractured bedrock aquifers that can be conceptualized as dual-porosity flow systems subject to one-dimensional advective-dispersive transport in the bedrock fractures and diffusive transport in the bedrock matrix. This article demonstrates how the physical characteristics of such flow systems can be parameterized for use in PHREEQC, it provides a method for minimizing numerical dispersion in PHREEQC simulations, and it compares PHREEQC simulations with results of an analytical solution. The simulations assumed a dual-porosity conceptual model involving advective-reactive-dispersive transport in the mobile zone (bedrock fracture) and diffusive-reactive transport in the immobile zone (bedrock matrix). The results from the PHREEQC dual-porosity transport model that uses a finite-difference approach showed excellent agreement compared with an analytical solution.  相似文献   

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