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1.
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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2.
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
3.
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
4.
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
5.
Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples. 相似文献
6.
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
7.
J.A. Barker 《Advances in water resources》1982,5(2):98-104
The main processes affecting the migration of a solute in a fissured aquifer will be advection and dispersion in the fissures, diffusion into the porous matrix; and adsorption. This paper considers solute transport in an idealized fissured aquifer consisting of slabs of saturated rock-matrix separated by equally spaced, planar fissures. The solution of the transport equations is developed as far as Laplace transforms of the solute concentrations in the fissure and matrix water. Numerical inversion of the transforms is used to investigate characteristic behaviour of the model for a number of special cases. 相似文献
8.
A 5-m radius magma-filled conduit will solidify in much less than one year if heat losses to the conduit wall are not offset by some form of forced or free convection of magma from some source body through the conduit. If the forced convection of magma from a source through the conduit is either too weak or is prevented by closure of the conduit at the end nearest the surface, only free convective circulations between the source chamber and conduit are available to balance the wall heat loss. Using an integral approach, the efficiency of free convection is investigated for conduits emplaced in both conductive and hydrothermally convective host rock environments. The results of the model strongly suggest that free circulations within conduits of large aspect ratio provide an efficient mechanism for offsetting heat losses to the conduit wall. The model provides a possible explanation for the occurrence of periodic eruptions from a conduit when the periodicity greatly exceeds the time scale for the cooling of a quiescent conduit by heat loss through the wall. 相似文献
9.
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
10.
The use of electrical resistivity surveys to locate karst conduits has shown mixed success. However, time‐lapse electrical resistivity imaging combined with salt injection improves conduit detection and can yield valuable insight into solute transport behaviour. We present a proof of concept above a known karst conduit in the Kentucky Horse Park (Lexington, Kentucky). A salt tracer solution was injected into a karst window over a 45‐min interval, and repeat resistivity surveys were collected every 20 min along a 125‐m transect near a monitoring well approximately 750 m downgradient from the injection site. In situ fluid conductivity measurements in the well peaked at approximately 25% of the initial value about 3 h after salt injection. Time‐lapse electrical resistivity inversions show two broad zones at the approximate conduit depth where resistivity decreased and then recovered in general agreement with in situ measurements. Combined salt injection and electrical resistivity imaging are a promising tool for locating karst conduits. The method is also useful for gaining insight into conduit geometry and could be expanded to include multiple electrical resistivity transects. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
A pilot-scale nutrient injection will (NIW) (4 m by 4 m by 1 m) was installed in the Borden Aquifer lo serve as a pulsed injection source of a potassium acetate solution for the stimulation of anaerobic microbial activity. The success of the flushing procedure was evaluated by monitoring the breakthrough of the acetate solution at several multilevel piezometers installed in the wall. Although some variation in the ground water velocity was observed with depth, the wall was flushed with reasonable uniformity after about six hours of injection and withdrawal, representing about one pore volume, Calculations bused on head level data collected during the flush, and on the solute breakthrough curves, indicated that about 90% of the flow induced by the pumping and injecting was confined to the permeable wall. These results show that a permeable wall injection system is a viable method of introducing solutes uniformly to a cross section of aquifer, with minimal perturbation of the natural flow system. In addition lo its importance for the biostimulation system tested in this project the flushing of permeable walls may have applications in other semi-passive remedial systems, such as the rejuvenation of reactive barriers. 相似文献
12.
A steady-state, one-dimensional, and nonhomogeneous two-phase flow model was developed for the prediction of local flow properties in volcanic conduits. The model incorporates the effects of relative velocity between the phases and for the variable magma viscosity. The resulting set of nonlinear differential equations was solved by a stiff numerical solver and the results were verified with the results of basaltic fissure eruptions obtained by a homogeneous two-phase flow model, before applying the model to the eruptions of Mt. St. Helens and Vesuvius volcanoes. This verification, and a study of the sensitivity of several modeling parameters, proved effective in establishing the confidence in the predicted nonequilibrium results of flow distribution in the conduits when the mass flow rate is critical or maximum. The application of the model to the plinian eruptions of Mt. St. Helens on May 18, 1980, and Vesuvius in AD 79, demonstrates the sensitivity of the magma discharge rate and distributions of pressure, volumetric fraction, and velocities of phases, on the hydrous magma viscosity feeding the volcanic conduits. Larger magma viscosities produce smaller mass discharge rates (or greater conduit diameters), smaller exit pressures, larger disequilibrium between the phases, and larger difference between the local lithostatic and fluid pressures in the conduit. This large pressure difference occurs when magma fragments and may cause a rupture of the conduit wall rocks, producing a closure of the conduit and cessation of the volcanic eruption, or water pouring into the conduit from underground aquifers leading to phreatomagmatic explosions. The motion of the magma fragmentation zone along a conduit during an eruption can be caused by the varying viscosity of magma feeding the volcanic conduit and may cause intermittent phreatomagmatic explosions during the plinian phases as different underground aquifers are activated at different depths. The variation of magma viscosity during the eruptions of Mt. St. Helens in 1980 and Vesuvius in AD 79 is normally associated with the tapping of magmas from different depths of the magma chambers. This variation of viscosity, which can include different crystal and dissolved water contents, can also produce conduit wall erosion, the onset and collapse of volcanic columns above the vent, and the onset and cessation of pyroclastic flows and surges. 相似文献
13.
J.-F. Girard M. Boucher A. Legchenko J.-M. Baltassat 《Journal of Applied Geophysics》2007,63(3-4):103-116
Karstic conduits play a crucial role for water supply in many parts of the world. However, the imaging of such targets is generally a difficult task for most geophysical methods. Magnetic Resonance Sounding (MRS) is a geophysical method designed for imaging of water bearing structures. Initially, MRS was developed for characterizing horizontally stratified aquifers. However, when applying a 1D MRS measuring setup to the imaging of 2D–3D targets, the size of which may be much smaller than the loop, the accuracy and the lateral resolution may not be sufficient. We have studied the possibility of simultaneously processing several MRS aligned along a profile to perform a Magnetic Resonance Tomography (MRT). This work emphasizes the gain of resolution for 2D–3D imagery of MRT versus the interpolation of 1D inversion results of MRS along the same profile. Numerical modelling results show that the MRT response is sensitive to the size and location of the 2D target in the subsurface. Sensitivity studies reveal that by using the coincident transmitting/receiving (TX/RX) setup and shifting the loop around the anomaly area, the depth, section and position of a single karstic conduit with a size smaller than the MRS loop size can be resolved. The accuracy of the results depends on the noise level and signal level, the latter parameter being linked to the depth and volume of the karstic conduit and the water content in the limestone matrix. It was shown that when applying MRT to the localization of 2D anomalies such as karstic conduits, the inclination of the geomagnetic field, the orientation of the MRT profile and the angle of crossover of the conduit by the MRT profile must be taken into account. Otherwise additional errors in interpretation should be expected. A 2D inversion scheme was developed and tested. Both numerical and experimental results confirm the efficiency of the developed approach. 相似文献
14.
《Journal of Applied Geophysics》2008,64(3-4):103-116
Karstic conduits play a crucial role for water supply in many parts of the world. However, the imaging of such targets is generally a difficult task for most geophysical methods. Magnetic Resonance Sounding (MRS) is a geophysical method designed for imaging of water bearing structures. Initially, MRS was developed for characterizing horizontally stratified aquifers. However, when applying a 1D MRS measuring setup to the imaging of 2D–3D targets, the size of which may be much smaller than the loop, the accuracy and the lateral resolution may not be sufficient. We have studied the possibility of simultaneously processing several MRS aligned along a profile to perform a Magnetic Resonance Tomography (MRT). This work emphasizes the gain of resolution for 2D–3D imagery of MRT versus the interpolation of 1D inversion results of MRS along the same profile. Numerical modelling results show that the MRT response is sensitive to the size and location of the 2D target in the subsurface. Sensitivity studies reveal that by using the coincident transmitting/receiving (TX/RX) setup and shifting the loop around the anomaly area, the depth, section and position of a single karstic conduit with a size smaller than the MRS loop size can be resolved. The accuracy of the results depends on the noise level and signal level, the latter parameter being linked to the depth and volume of the karstic conduit and the water content in the limestone matrix. It was shown that when applying MRT to the localization of 2D anomalies such as karstic conduits, the inclination of the geomagnetic field, the orientation of the MRT profile and the angle of crossover of the conduit by the MRT profile must be taken into account. Otherwise additional errors in interpretation should be expected. A 2D inversion scheme was developed and tested. Both numerical and experimental results confirm the efficiency of the developed approach. 相似文献
15.
H. C. Hardee 《Bulletin of Volcanology》1982,45(1):41-49
An analytical solution for periodic magma intrusions in conduits was developed to study the onset of shallow magma chamber formation. The solution is based on determining when a repetitive series of intrusions can cause the wall rock of a conduit to reach its melt temperature. The results show that magma chamber formation in conduits is a strong function of the volume rate of intrusion and that magma chamber formation is likely when the intrusion rate exceeds 10?3 km3/ yr. which agrees with observations by other investigators. Once this critical value of intrusion rate is reached, magma chambers are likely to begin forming after only a few intrusive pulses (less than ten). Results for both cylindrical conduits and dikes show cylindrical conduits are more favourable for the formation of shallow magma chambers. 相似文献
16.
C. C. Smart 《水文研究》1988,2(1):31-41
Discharge exceedance probabilities are calculated for a simple model karst aquifer composed of a few multilevel conduits with recharge from a single sinking stream with an exponential flow exceedance distribution. It is assumed that outflow instantaneously matches inflow, so that the conduit volume is constant but discharge is governed by the head in a volumeless shaft at the top end of the system. It is shown that small single conduit aquifers will frequently overflow at the surface during floods and the exceedance probability of flow through the aquifer and over the surface can be defined as a function of the inflow distribution and the form of the aquifer. Systems with multiple conduits will overflow less frequently, but each conduit will exhibit a flow distribution characteristic of its form and position in the vertical hierarchy. Comparison of these findings with actual flow data from a conduit aquifer shows that the approach is valid, although imprecise. The model is unlikely to be applied directly, as it requires unusually detailed data. However, it provides for the first time an indication of typical flow durations for surface overflows and individual conduits in a karst aquifer. Contrasts in flow duration will have a profound influence on solutional and sedimentary processes in the karst system. 相似文献
17.
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
18.
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
19.
The Pinacate volcanic field, Sonora, Mexico, contains 400 cinder cones and eight maars. It is noteworthy that most of the maar-forming, phreatomagmatic eruptions were immediately preceded by effusive and Strombolian activity rather than occurring when magma first approached the surface. The Strombolian activity may have facilitated access of groundwater to the conduits in this arid region. The field evidence suggests that phreatomagmatism is inhibited unless the magma flux is low relative to the rate of water supply and unless the top of the magma column has subsided, probably below the water table. The latter condition is difficult to prove in the absence of direct observation, and alternative hypotheses involving disturbance of the conduit system are considered. The spatial distribution of maars in the Pinacate and the lithology of their associated tuffaceous ejecta both may reflect the course of an ancient river channel whose permeable gravels were pierced by the magmatic conduits. 相似文献
20.
We apply geospatial analysis to borehole imagery in an effort to develop new techniques to evaluate the spatial distribution and internal structure of karst conduits. Remote sensing software is used to classify a high resolution, digital borehole image of limestone bedrock from the Biscayne aquifer (South Florida, USA) into a binary image divided into cells of rock matrix and pores. Within a GIS, 2D porosity is calculated for a series of rectangular sampling windows placed over the binary image and then plotted as a function of depth. Potential conduits that intersect the borehole are identified as peaks of high porosity. A second GIS technique identifies a conduit as a continuous object that spans the entire borehole width. According to these criteria, geospatial analysis reveals ∼10 discrete conduits along the ∼15 m borehole image. Continuous sampling of the geologic medium intersected by the borehole provides insight into the internal structure of karst aquifers and the evolution of karst features. Most importantly, this pilot study demonstrates that GIS-based techniques are capable of quantifying the depths, dimensions, shapes, apertures and connectivity of potential conduits, physical attributes that impact flow in karst aquifers. 相似文献