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1.
A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.  相似文献   

2.
Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

3.
Simple closed‐form approximations are presented for calculating the steady‐state groundwater age distribution in two‐dimensional vertical cross sections of idealized fresh water lenses overlying salt water, for aquifers that are vertically semi‐infinite and of finite thickness. The approximations are developed on the basis of existing one‐dimensional analytical solutions for travel‐time calculation in fresh water lenses and approximate streamline formulations. The two‐dimensional age distributions based on the closed‐form solutions match convincingly with numerical simulations. As expected, notable deviations from the numerical solution are encountered at the groundwater flow divide and when submarine groundwater discharge occurs. Ratios of recharge over hydraulic conductivities are varied to explore how the magnitude of the deviations changes, and it is found that the approximate closed‐form solutions perform well over a range of conditions found in natural systems.  相似文献   

4.
Saltwater intrusion problems have been usually tackled through analytical models because of its simplicity, easy implementation and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (?). We propose to approach also the transient problem solving a single potential equation (using also the ? variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

5.
Methods of estimation of the location of a sharp fresh water–salt water interface with hydraulic heads or pressures are relatively simple and are widely used. Progress has been made in the recent decade toward the mathematical relations describing the position of the sharp interface using hydraulic heads or pressures in coastal zones. This paper reviews several methods for estimation of the location of fresh water–salt water interface in coastal aquifers, including the classical Ghyben–Herzberg relation. The location of the fresh water–salt water interface in a coastal homogeneous, isotropic unconfined aquifer can be estimated based on piezometric heads at two points in the same vertical line tapping, respectively, the salt water zone (including the interface) and the fresh water zone (from the water table to the interface) when the groundwater flow system is in a steady state and satisfies the Dupuit assumption. If pressures are measured at two points in the fresh water and salt water zones in the same vertical line in the coastal aquifer under the same assumption, then the position of the interface can still be estimated with the pressure data. If the Dupuit assumption is not met in coastal aquifers and the vertical fresh water head gradients can be approximated with a straight line, the position of the interface can roughly be estimated by using the water level data in a partially penetrating well during drilling of the well.  相似文献   

6.
A new operational paradigm is presented for small‐scale aquifer storage and recovery systems (ASR) in saline aquifers. Regular ASR is often not feasible for small‐scale storage in saline aquifers because fresh water floats to the top of the aquifer where it is unrecoverable. In the new paradigm, fresh water storage is combined with salt water extraction from below the fresh water cone. The salt water extraction counteracts the buoyancy due to the density difference between fresh water and salt water, thus preventing the fresh water from floating up. The proposed approach is applied to assess the feasibility of ASR for the seasonal storage of fresh water produced by desalination plants in tourist resorts along the Egyptian Red Sea coast. In these situations, the continuous extraction of salt water can be used for desalination purposes. An analytical Dupuit solution is presented for the steady flow of salt water toward a well with a volume of fresh water floating on top of the cone of depression. The required salt water discharge for the storage of a given volume of fresh water can be computed with the analytical solution. Numerical modeling is applied to determine how the stored fresh water can be recovered. Three recovery approaches are examined. Fresh water recovery rates on the order of 70% are achievable when salt water is extracted in high volumes, subsurface impermeable barriers are constructed at a distance from the well, or several fresh water recovery drains are used. The effect of ambient flow and interruptions of salt water pumping on the recovery efficiency are reported.  相似文献   

7.
We consider 3D steady flow of fresh water over a salt water body in a confined aquifer of constant thickness D, with application to a pumping well in a coastal aquifer. With neglect of mixing, a sharp interface separates the two fluid bodies and an existing analytical solution, based on the Dupuit assumption, is adopted. The aim is to solve for the mixing between the fresh and salt waters for αT/D  1 (αT transverse dispersivity), as field studies indicate that αT = O(10−3 − 10−2 m). The mixing zone around the interface is narrow and solutions by existing codes experience numerical difficulties. The problem is solved by the boundary layer (BL) approximation, extending a method, applied previously to two-dimensional flows. The BL equations of variable-density flow are solved by using the Von Karman integral method, to determine the BL thickness and the rate of entrainment of salt water along the interface. Application to the pumping well problem yields the salinity of the pumped water, as function of the parameters of the problem (well discharge, seaward discharge, well distance from the coast and density difference).  相似文献   

8.
In regions with saline groundwater, fresh water lenses may develop due to rainwater infiltration. The amount of fresh water that is available for e.g. agricultural crops depends on the thickness of the lens and the extent of mixing between fresh and saline water. In this paper, we consider the mixing of fresh water and upward moving saline ground water in low-lying deltaic areas. The parameters that dominate the flow and transport problem are investigated using dimensionless groups and scaled sensitivities. We characterize the numerically simulated thicknesses of the lens and of the mixing zone by spatial moments. Rayleigh number and mass flux ratio, which is the ratio of the salt water seepage and the precipitation, determine the thickness of the fresh water lens. The local thickness of the mixing zone is mainly influenced by the dispersive/diffusive groups and the mass flux ratio. In addition, convergence of streamlines towards an outflow boundary affects the thickness, particularly in the vicinity of this boundary.Analytical and numerical steady state solutions for lens thickness are compared, taking into account upward seepage, for the two cases with and without a density difference between lens and underlying groundwater. Agreement between the numerical and analytical solutions for the lens thickness is good except when the mass flux ratio becomes small. For zero mass flux ratio, it is implicitly assumed in the analytical solution that salt water is stagnant, and that is unrealistic. Relative contributions of longitudinal and transversal hydrodynamic dispersion and diffusion to the thickness of the mixing zone are quantified numerically for different phases of lens formation. Longitudinal dispersion dominates in the early stages of lens formation, while diffusion and transversal dispersion dominate at steady state.  相似文献   

9.
A Python Script to Compute Isochrones for MODFLOW   总被引：1，自引：0，他引：1       下载免费PDF全文
  相似文献   

10.
Effects of sea-level rise on ground water flow in a coastal aquifer system   总被引：5，自引：0，他引：5  
The effects of sea-level rise on the depth to the fresh water/salt water interface were simulated by using a density-dependent, three-dimensional numerical ground water flow model for a simplified hypothetical fresh water lens that is similar to shallow, coastal aquifers found along the Atlantic coast of the United States. Simulations of sea-level rise of 2.65 mm/year from 1929 to 2050 resulted in an increase in water levels relative to a fixed datum, yet a net decrease in water levels relative to the increased sea-level position. The net decrease in water levels was much greater near a gaining stream than farther from the stream. The difference in the change in water levels is attributed to the dampening effect of the stream on water level changes in response to sea-level rise. In response to the decreased water level altitudes relative to local sea level, the depth to the fresh water/salt water interface decreased. This reduction in the thickness of the fresh water lens varied throughout the aquifer and was greatly affected by proximity to a ground water fed stream and whether the stream was tidally influenced. Away from the stream, the thickness of the fresh water lens decreased by about 2% from 1929 to 2050, whereas the fresh water lens thickness decreased by about 22% to 31% for the same period near the stream, depending on whether the stream was tidally influenced. The difference in the change in the fresh water/salt water interface position is controlled by the difference in the net decline in water levels relative to local sea level.  相似文献   

11.
Sea water intrusion into aquifers is problematic in many coastal areas. The physics and chemistry of this issue are complex, and sea water intrusion remains challenging to quantify. Simple assessment tools like analytical models offer advantages of rapid application, but their applicability to field situations is unclear. This study examines the reliability of a popular sharp‐interface analytical approach for estimating the extent of sea water in a homogeneous coastal aquifer subjected to pumping and regional flow effects and under steady‐state conditions. The analytical model is tested against observations from Canada, the United States, and Australia to assess its utility as an initial approximation of sea water extent for the purposes of rapid groundwater management decision making. The occurrence of sea water intrusion resulting in increased salinity at pumping wells was correctly predicted in approximately 60% of cases. Application of a correction to account for dispersion did not markedly improve the results. Failure of the analytical model to provide correct predictions can be attributed to mismatches between its simplifying assumptions and more complex field settings. The best results occurred where the toe of the salt water wedge is expected to be the closest to the coast under predevelopment conditions. Predictions were the poorest for aquifers where the salt water wedge was expected to extend further inland under predevelopment conditions and was therefore more dispersive prior to pumping. Sharp‐interface solutions remain useful tools to screen for the vulnerability of coastal aquifers to sea water intrusion, although the significant sources of uncertainty identified in this study require careful consideration to avoid misinterpreting sharp‐interface results.  相似文献   

12.
Steady interface flow in heterogeneous aquifer systems is simulated with single‐density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m3). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi‐aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben‐Herzberg formula. The transformed problem may be solved with a single‐density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi‐aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached.  相似文献   

13.
A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

14.
In this study, we examine the maximum net extraction rate from the novel arrangement of an injection‐extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation‐point locations and recirculation ratio, assuming steady‐state, sharp‐interface conditions. The injection‐extraction well‐pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m2/d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well‐pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.  相似文献   

15.
This study employed a coupled water-air two-phase flow and salt water transport model to analyze the behaviors of generated airflow in unsaturated zones and the fluctuations of salinity at the salt–fresh water interface in a two-layered unconfined aquifer with a sloping beach surface subjected to tidal oscillations. The simulation results show that as the new dynamic steady state including effects of tidal fluctuations is reached through multiple tidal cycles, the dispersion zone in the lower salt water wedge is broadened because fresh water/salt water therein flows continuously landward or seaward during tidal cycles. The upper salt–fresh water interface exhibits more vulnerable to the tidal fluctuations, and the variation of salinity therein is periodic, which is irrelevant to the hydraulic head but is influenced by the direction and velocity of surrounding water-flow. With the tidal level fluctuating, airflow is mainly concentrated in the lower permeable layer due to the restraint of the upper semi-permeable layer, and the time-lag between the pore-air pressure and the tidal level increases with distance from the coastline. The effect of airflow in unsaturated zones can be transmitted downward, causing both the magnitude of salinity and its amplitude in the upper salt–fresh water interface to be smaller for the case with airflow than without airflow due to the resistance of airflow to water-flow. Sensitivity analysis reveal that distributions of airflow in unsaturated zones are affected by the permeability of the upper/lower layer and the van Genuchten parameter of the lower layer, not by the van Genuchten parameter of the upper layer, whereas the salinity fluctuations in the salt–fresh water interface are affected only by soil parameters of the lower layer.  相似文献   

16.
Regular aquifer storage recovery, ASR, is often not feasible for small‐scale storage in brackish or saline aquifers because fresh water floats to the top of the aquifer where it is unrecoverable. Flow barriers that partially penetrate a brackish or saline aquifer prevent a stored volume of fresh water from expanding sideways, thus increasing the recovery efficiency. In this paper, the groundwater flow and mixing is studied during injection, storage, and recovery of fresh water in a brackish or saline aquifer in a flow‐tank experiment and by numerical modeling to investigate the effect of density difference, hydraulic conductivity, pumping rate, cyclic operation, and flow barrier settings. Two injection and recovery methods are investigated: constant flux and constant head. Fresh water recovery rates on the order of 65% in the first cycle climbing to as much as 90% in the following cycles were achievable for the studied configurations with constant flux whereas the recovery efficiency was somewhat lower for constant head. The spatial variation in flow velocity over the width of the storage zone influences the recovery efficiency, because it induces leakage of fresh water underneath the barriers during injection and upconing of salt water during recovery.  相似文献   

17.
The change of the salinity distribution in coastal aquifers due to pumpage is often described as an upconing of the interface between saline and fresh water. Sea and fresh water are miscible fluids, however. Therefore, dispersion of salinity in the aquifer affects the upconing process. An estimate of the effect of salinity dispersion on the dynamics of the flow as well as on the salinity distribution in the aquifer is presented in this study. The phenomenon is described as a migration of a sharp interface perturbed by small disturbances due to salinity dispersion. The creation of the mixing zone between fresh and saline water is described as a formation of a boundary layer in the vicinity of the sharp interface. This method is primarily recommended for flow fields in which simple representation of the sharp interface migration is obtainable.  相似文献   

18.
Abstract A numerical model (NEWVAR) to simulate the transient movement of a discrete interface between salt water and fresh water has been developed. NEWVAR is designed to allow the analysis of a regional two-dimensional ground-water flow in coastal aquifers. The numerical solution permits the prediction of both regional fresh-water levels and two-dimensional fresh-water/salt-water interface by using nested square meshes.
The numerical solution is based on the finite-difference method; the Gauss-Jordan direct method is used for solving steady- and unsteady-state linear equations. Different procedures are used to avoid numerical difficulties in the transient position of the interface toe for two-dimensional areal flow.
The numerical solution was tested against the analytical ones for the cases of an advancing interface and of a floating fresh-water lens over sea water. These tests showed good agreement, thus verifying the finite-difference approximation. The results of an application of this model to a real aquifer are discussed in a companion paper entitled: "A Compatible Single-Phase/Two-Phase Numerical Model 2. Application to a Coastal Aquifer in Mexico."  相似文献   

19.
This proposed technique allows sensible and numerically stable behavior in multilayer analytic element models when layers dewater. When saturated thickness approaches zero in an unconfined or fresh/salt interface domain, the domain transitions to a very thin confined domain with a minimum saturated thickness M. M is an adjustable input parameter, so you can make the horizontal flow in dewatered domains negligibly small by making the minimum saturated thickness very small. Vertical flows can pass through a dewatered domain, whether it is near the surface or at depth. For example, recharge may pass through a shallow dewatered layer to a deeper layer that is not dewatered. This approach is examined in detail in an example multilayer model of mine dewatering.  相似文献   

20.
The fresh groundwater lenses (FGLs) of small islands can be highly vulnerable to climate change impacts, including sea‐level rise (SLR). Many real cases of atoll or sandy islands involve two‐layer hydrogeological conceptualizations. In this paper, the influential factors that affect FGLs in two‐layer small islands subject to SLR are investigated. An analytical solution describing FGLs in circular islands, composed of two geological layers, is developed for the simplified case of steady‐state and sharp‐interface conditions. An application of the developed model is demonstrated to estimate the FGL thickness of some real‐world islands by comparison with existing FGL thickness data. Furthermore, numerical modelling is applied to extend the analysis to consider dispersion effects and to confirm comparable results for both cases. Sensitivity analyses are used to assess the importance of land‐surface inundation caused by SLR, relative to other parameters (i.e. thickness of aquifer layers, hydraulic conductivity, recharge rate and land‐surface slope) that influence the FGL. Dimensionless parameters are used to generalize the findings. The results demonstrate that land‐surface inundation has a considerable impact on a FGL influenced by SLR, as expected, although the FGL volume is more sensitive to recharge, aquifer thickness and hydraulic conductivity than SLR impacts, considering typical parameter ranges. The methodology presented in this study provides water resource managers with a rapid‐assessment tool for evaluating the likely impacts of SLR and accompanying LSI on FGLs.  相似文献   

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