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1.
Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions. 相似文献
2.
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
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.
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:
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5.
Hydrological and biogeochemical processes in karst environments are strongly controlled by heterogeneous fracture-conduit networks. Quantifying the spatio-temporal variability of water transit time and young water fractions in such heterogeneous hydrogeological systems is fundamental to linking discharge and water quality dynamics in the karst critical zone. We used a tracer-aided conceptual hydrological model to track the fate of each hour of rain input individually. Using this approach, the variability of transit time distributions and young water fraction were estimated in the main landscape units in a karst catchment of Chenqi in Guizhou Province, Southwest China. The model predicted that the mean young water (i.e., <~2 months old) fraction of ground conduit flow is 0.31. Marked seasonal variabilities in water storage and hydrological connectivity between the conduit network and fractured matrix, as well as between hillslopes and topographic depression, drive the dynamics of young water fraction and travel time distributions in each landscape unit. Especially, the strong hydrological connectivity between the land surface and underground conduits caused by the direct infiltration through large fractures and sinkholes, leads the drastic increasement in young water fraction of runoff after heavy rain. Even though the contribution of young water to runoff is greater, the strong mixing and drainage of small fractures accelerate the old water release during high flows during the wet season. It is notable that the young water may sometimes be the most contaminated component contributing to the underground conduit network in karst catchments, because of the direct transfer of contaminants from the ground surface with rain water via large fractures and sinkholes. 相似文献
6.
South China karst aquifer storm-scale hydrochemistry 总被引：7，自引：0，他引：7
7.
by Guangquan Li 《Ground water》2009,47(5):714-722
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
8.
《Advances in water resources》2001,24(8):877-885
Based on a dye tracer experiment in a sand tank we addressed the problem of local dispersion of conservative tracers in the unsaturated zone. The sand bedding was designed to have a defined spatial heterogeneity with a strong anisotropy. We estimated the parameters that characterize the local dispersion and dilution from concentration maps of a high spatial and temporal resolution obtained by image analysis. The plume spreading and mixing behavior was quantified on the basis of the coefficient of variation of the concentration and of the dilution index. The heterogeneous structure modified the flow pattern depending on water saturation. The shape of the tracer plumes revealed the structural signature of the sand bedding at low saturation only. In this case pronounced preferential flow was observed. At higher flow rates the structure remained hidden by a spatially almost homogeneous behavior of the plumes. In this context, we mainly discuss the mechanism of re-distributing a finite mass of inert solutes over a large volume, due to macro- and micro-heterogeneities of the structure. 相似文献
9.
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
10.
A method to estimate reactive transport parameters as well as geometric conduit parameters from a multitracer test in a karst aquifer is provided. For this purpose, a calibration strategy was developed applying the two-region nonequilibrium model CXTFIT. The ambiguity of the model calibration was reduced by first calibrating the model with respect to conservative tracer breakthrough and later transferring conservative transport parameters to the reactive model calibration. The reactive transport parameters were only allowed to be within a defined sensible range to get reasonable calibration values. This calibration strategy was applied to breakthrough curves obtained from a large-scale multitracer test, which was performed in a karst aquifer of the Swabian Alb, Germany. The multitracer test was conducted by the simultaneous injection of uranine, sulforhodamine G, and tinopal CBS-X. The model succeeds to represent the tracer breakthrough curves (TBCs) of uranine and sulforhodamine G and verifies that tracer-rock interactions preferably occur in the immobile fluid region, although the fraction of this region amounts to only 3.5% of the total water. However, the model failed to account for the long tailing observed in the TBC of tinopal CBS-X. Sensitivity analyses reveal that model results for the conservative tracer transport are most sensitive to average velocity and volume fraction of the mobile fluid region, while dispersion and mass transfer coefficients are least influential. Consequently, reactive tracer calibration allows the determination of sorption sites in the mobile and immobile fluid region at small retardation coefficients. 相似文献
11.
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
12.
This pore-scale modeling study in saturated porous media shows that compound-specific effects are important not only at steady-state and for the lateral displacement of solutes with different diffusivities but also for transient transport and solute breakthrough. We performed flow and transport simulations in two-dimensional pore-scale domains with different arrangement of the solid grains leading to distinct characteristics of flow variability and connectivity, representing mildly and highly heterogeneous porous media, respectively. The results obtained for a range of average velocities representative of groundwater flow (0.1–10 m/day), show significant effects of aqueous diffusion on solute breakthrough curves. However, the magnitude of such effects can be masked by the flux-averaging approach used to measure solute breakthrough and can hinder the correct interpretation of the true dilution of different solutes. We propose, as a metric of mixing, a transient flux-related dilution index that allows quantifying the evolution of solute dilution at a given position along the main flow direction. For the different solute transport scenarios we obtained dilution breakthrough curves that complement and add important information to traditional solute breakthrough curves. Such dilution breakthrough curves allow capturing the compound-specific mixing of the different solutes and provide useful insights on the interplay between advective and diffusive processes, mass transfer limitations, and incomplete mixing in the heterogeneous pore-scale domains. The quantification of dilution for conservative solutes is in good agreement with the outcomes of mixing-controlled reactive transport simulations, in which the mass and concentration breakthrough curves of the product of an instantaneous transformation of two initially segregated reactants were used as measures of reactive mixing. 相似文献
13.
The advection–dispersion equation with spatially variable coefficients does not have an exact analytical solution and is therefore solved numerically. However, solutions obtained with several of the traditional finite difference or finite element techniques typically exhibit spurious oscillation or numerical dispersion when advection is dominant. The mixing cell and semi-analytical solution methods proposed in this study avoid such oscillation or numerical dispersion when advection dominates. Both the mixing cell and semi-analytical solution methods calculate the spatial step size by equating numerical dispersion to physical dispersion. Because of the spatial variability of the coefficients the spatial step size varies in space. When the time step size Δt→0, the mixing cell method reduces to the semi-analytical solution method. The results of application to two cases show that the mixing cell and semi-analytical solution methods are better than a finite difference method used in the study. © 1998 John Wiley & Sons, Ltd. 相似文献
14.
Scott C. James Tanya K. Bilezikjian Constantinos V. Chrysikopoulos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2005,19(4):266-279
A quasi-three-dimensional particle tracking model is developed to characterize the spatial and temporal effects of advection, molecular diffusion, Taylor dispersion, fracture wall deposition, matrix diffusion, and co-transport processes on two discrete plumes (suspended monodisperse or polydisperse colloids and dissolved contaminants) flowing through a variable aperture fracture situated in a porous medium. Contaminants travel by advection and diffusion and may sorb onto fracture walls and colloid particles, as well as diffuse into and sorb onto the surrounding porous rock matrix. A kinetic isotherm describes contaminant sorption onto colloids and sorbed contaminants assume the unique transport properties of colloids. Sorption of the contaminants that have diffused into the matrix is governed by a first-order kinetic reaction. Colloids travel by advection and diffusion and may attach onto fracture walls; however, they do not penetrate the rock matrix. A probabilistic form of the Boltzmann law describes filtration of both colloids and contaminants on fracture walls. Ensemble-averaged breakthrough curves of many fracture realizations are used to compare arrival times of colloid and contaminant plumes at the fracture outlet. Results show that the presence of colloids enhances contaminant transport (decreased residence times) while matrix diffusion and sorption onto fracture walls retard the transport of contaminants. Model simulations with the polydisperse colloids show increased effects of co-transport processes. 相似文献
15.
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
16.
Calculation of ground water ages--a comparative analysis 总被引：1，自引：0，他引：1
Ground water age is a fundamental, yet complex, concept in ground water hydrology. Discrepancies between results obtained through different modeling approaches for ground water age calculation have been reported, in particular, between ground water ages modeled by advection and direct simulation of ground water ages (e.g., age-mass approach), which includes effects of advection and dispersion. Here, through a series of two-dimensional (2D) simulations, the impact of water mixing through advection and dispersion on modeled 14C and directly simulated ground water ages is assessed. Impact of dispersion on modeled ages is systematically stronger in areas where water velocities are smaller and far more pronounced on 14C ages. This effect is also observed in one-dimensional models. 2D simulations show that longitudinal dispersion generally acts as a "source" of 14C, while vertical dispersion acts as a "sink," leading to apparent younger or older modeled 14C ages as compared to advective and directly simulated ground water ages. The presence of permeable and impermeable faults provides an equally important source for discrepancies, leading to major differences in modeled ages among the three methods considered. Overall, our results show that a 14C modeling approach using a solute transport model for calculating ground water age appears to be more reliable in ground water systems without faults and where water velocities are relatively high than in systems that are relatively more heterogeneous and those where faults are present. Among the three modeling approaches considered here, direct simulation of ground water age seems to yield the most consistent results in complex, heterogeneous ground water flow systems, giving a vertical age structure consistent with ages expected from consideration of the flow system. 相似文献
17.
Exchange of water between conduits and matrix is an important control on regional chemical compositions, karstification, and quality of ground water resources in karst aquifers. A sinking stream (Santa Fe River Sink) and its resurgence (River Rise) in the unconfined portion of the Floridan Aquifer provide the opportunity to monitor conduit inflow and outflow. The use of temperature as a tracer allows determination of residence times and velocities through the conduit system. Based on temperature records from two high water events, flow is reasonably represented as pipe flow with a cross-sectional area of 380 m2, although this model may be complicated by losses of water from the conduit system at higher discharge rates. Over the course of the study year, the River Rise discharged a total of 1.9 x 10(7) m3 more water than entered the River Sink, reflecting net contribution of ground water from the matrix into the conduit system. However, as River Sink discharge rates peaked following three rainfall events during the study period, the conduit system lost water, presumably into the matrix. Surface water in high flow events is typically undersaturated with respect to calcite and thus may lead to dissolution, depending on its residence time in the matrix. A calculation of local denudation is larger than other regional estimates, perhaps reflecting return of water to conduits before calcite equilibrium is reached. The exchange of matrix and conduit water is an important variable in karst hydrology that should be considered in management of these water resources. 相似文献
18.
Richard Hoffmann Jean-Christophe Maréchal Adrien Selles Alain Dassargues Pascal Goderniaux 《Ground water》2022,60(2):192-209
Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures. 相似文献
19.
In this paper, five model approaches with different physical and mathematical concepts varying in their model complexity and requirements were applied to identify the transport processes in the unsaturated zone. The applicability of these model approaches were compared and evaluated investigating two tracer breakthrough curves (bromide, deuterium) in a cropped, free-draining lysimeter experiment under natural atmospheric boundary conditions. The data set consisted of time series of water balance, depth resolved water contents, pressure heads and resident concentrations measured during 800 days. The tracer transport parameters were determined using a simple stochastic (stream tube model), three lumped parameter (constant water content model, multi-flow dispersion model, variable flow dispersion model) and a transient model approach. All of them were able to fit the tracer breakthrough curves. The identified transport parameters of each model approach were compared. Despite the differing physical and mathematical concepts the resulting parameters (mean water contents, mean water flux, dispersivities) of the five model approaches were all in the same range. The results indicate that the flow processes are also describable assuming steady state conditions. Homogeneous matrix flow is dominant and a small pore volume with enhanced flow velocities near saturation was identified with variable saturation flow and transport approach. The multi-flow dispersion model also identified preferential flow and additionally suggested a third less mobile flow component. Due to high fitting accuracy and parameter similarity all model approaches indicated reliable results. 相似文献
20.
Karst spring responses examined by process-based modeling 总被引：8，自引：0，他引：8
Ground water in karst terrains is highly vulnerable to contamination due to the rapid transport of contaminants through the highly conductive conduit system. For contamination risk assessment purposes, information about hydraulic and geometric characteristics of the conduits and their hydraulic interaction with the fissured porous rock is an important prerequisite. The relationship between aquifer characteristics and short-term responses to recharge events of both spring discharge and physicochemical parameters of the discharged water was examined using a process-based flow and transport model. In the respective software, a pipe-network model, representing fast conduit flow, is coupled to MODFLOW, which simulates flow in the fissured porous rock. This hybrid flow model was extended to include modules simulating heat and reactive solute transport in conduits. The application of this modeling tool demonstrates that variations of physicochemical parameters, such as solute concentration and water temperature, depend to a large extent on the intensity and duration of recharge events and provide information about the structure and geometry of the conduit system as well as about the interaction between conduits and fissured porous rock. Moreover, the responses of solute concentration and temperature of spring discharge appear to reflect different processes, thus complementing each other in the aquifer characterization. 相似文献