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1.
We conducted various field studies at the seawater intrusion monitoring wells located in the eastern part of Jeju Island, Korea, to observe the tidal effect on groundwater–seawater flow in the coastal aquifer. Studies included monitoring the fluctuations of groundwater and tide levels, electrical and temperature logging, and 2-D heat-pulse flowmeter tests. According to time-series analysis, tidal effects on groundwater level reached up to 3 km inland from the coastline. Water-level variation was more sensitive to tidal fluctuations near the coast, and more related to rainfall toward inland areas. Temporal and spatial variations in the shape and location of the freshwater–saltwater interface were analyzed using data from nine monitoring wells. The results indicated that the interface toe is located at a distance of 6–8 km from the coastline and its location was related to geological layers present. Long-term seasonal variations revealed no major changes in the interface; minor variations were due to moving boundary conditions induced by tidal fluctuations. Using the two-dimensional heat-pulse flowmeter, groundwater flow directions and velocities at four tidal stages were measured on three monitoring wells drilled into the multilayered aquifers. This direct measurement enabled us to relate the differences of flow velocities and directions with geology and tidal fluctuations. Combining the results of EC logging and flowmeter tests, we found a zone where freshwater and saltwater moved alternately in opposite directions, as influenced by the tidal fluctuations. Integrating various physical logging and flowmeter data with water-level fluctuations improved our understanding of the behavior of fresh and seawater flow in the coastal aquifers.  相似文献   

2.
Xun Zhou  Chao Song  Ting Li 《水文科学杂志》2013,58(13):2367-2375
ABSTRACT

The inland extending length of the freshwatersaltwater interface toe is useful in studies of seawater intrusion in coastal areas. The submarine fresh groundwater discharge in coastal zones is affected not only by hydraulic conductivity and hydraulic gradient of the aquifer, but also by the position of the interface. Two observation wells at different distances from the coast are required to calculate the fresh groundwater flow rate in coastal unconfined aquifers. By considering that the submarine groundwater discharge is equal to the groundwater flow rate, the length of the interface toe extending inland can be estimated when the groundwater flow is at a steady-flow state. Aquifers with horizontal and sloping confined beds and without/with unique surface vertical infiltration are considered. Examples used to illustrate the application of these methods indicate that the inland extending lengths of the interface toe in aquifers with vertical surface infiltration are much shorter than those in aquifers without vertical surface infiltration, and the length of the interface in aquifers with a horizontal confining lower bed are smaller than those in aquifers with a confining lower bed sloping towards the sea. The extent of the interface on the northwestern coast near the city of Beihai in southern Guangxi, China, on 18 January 2013 was estimated as 471478 m.
Editor M.C. Acreman Associate editor not assigned  相似文献   

3.
Physical barriers are widely used to control seawater intrusion (SWI). Amongst different kinds of physical barriers, mixed physical barriers (MPBs) are shown to be an effective approach to prevent SWI. However, the system may hinder the discharge of fresh groundwater and the removal of residual saltwater trapped in the inland aquifers of MPBs. Herein, using the validated numerical model, for the first time, we investigated the dynamics of residual saltwater and groundwater discharge after the installation of MPBs. For examining the applicability of MPB and its response to structural variations and hydraulic gradient, the comparison with traditional physical barriers and sensitivity analysis was also carried out. The MPB increased the mixing area of freshwater and saltwater at the beginning of the removal process, resulting in the reduction of the saltwater wedge length (RL) by 74.6% and the removal of total salt mass (RM) by 62.6% within the 4% of the total removal time. Meanwhile, the groundwater discharge (Q') rose rapidly after a sharp decline from 100% to 40% in the first stage. As the residual saltwater wedge was retreated, the mixing intensity and removal efficiency decreased substantially in the second stage. Similarly, Q' raised with a declining rate at this stage. The removal efficiency was positively correlated with wall depth and hydraulic gradient and there were optimal distance of the middle spacing and height of lower dam to reach the highest efficiency. The groundwater discharge reduced monotonously with the increase of dam height and wall depth as well as the decrease of barrier spacing and hydraulic gradient. Under certain conditions, the efficiency of MPB in removing residual saltwater could be 40%–100% and 0%–56% higher than that of traditional subsurface dam and cutoff wall, respectively. The laboratory scale conclusions provide valuable physical insight for the real field applications regarding dynamic mechanism and regularity. These findings will always help decision makers choose proper engineering measures and protect groundwater resources in coastal areas.  相似文献   

4.
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   

5.
The time domain electromagnetic method (TDEM) is applied to monitor, to delineate and to map the saltwater intrusion zones in the Mediterranean Plio‐Quaternary aquifer. Forty‐two TDEM soundings were carried out in the coastal plain of Nabeul–Hammamet region (NE Tunisia). TDEM resistivity data were correlated with the existing borehole logging data to assign them to a particular lithology and to provide information about the position of the freshwater–seawater transition zone. The geoelectric sections showing the vertical configuration of seawater intrusion, with the brackish‐salty‐saturated zones, have a resistivity ranging from ~0.1 to 5 Ω?m and are detected at a depth lower than 1.5 m. The salinized zones are located at Nabeul (Sidi Moussa, Sidi El Mahrsi, Al Gasba and Mrazgua) and at Hammamet (Touristic zone of Hammamet north and south, Baraket Essahel) and reached a distance of 4 km from the coastline, indicating a severe state for the aquifer in these zones. These TDEM results are confirmed by the increase of chloride concentration content in the analysed water samples of monitoring wells. Moreover, in the northeastern part, the presence of a saltwater front located far from the coast and along the NW–SE major surface fault can be explained by two hypothesis: (i) this fault seems to provide a conduit for seawater to move readily towards the water wells and (ii) the clay and gypsum infiltration of marine Messinian deposits through the fault plane leads to low resistivities. Finally, it comes out from this study that TDEM survey has successfully depicted salinized zones of this coastal aquifer. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

6.
Abstract

Parametric studies were carried out to analyse the effect on sea water intrusion of freshwater recharge through a finite width strip parallel to the coast. A vertically integrated one-dimensional finite element model was used for this purpose. The studies included the analysis of the effect of location, width, intensity and the period of recharge on sea water-freshwater interface motion. Relationships were established between the interface motion and the recharge parameters applicable to wide ranging practical cases. From the studies, the ideal location for recharge was identified to achieve the maximum repulsion of intrusion. The width of recharge also affects the interface motion and the widths greater than 2% of the initial intrusion length were effective in controlling the intrusion. The results indicated that the reduction of intrusion up to 30% could be achieved through strip recharge.  相似文献   

7.
Abstract

Saltwater intrusion is a naturally occurring phenomenon that is exacerbated significantly by excessive groundwater exploitation in coastal aquifers. In order to determine the extent of saltwater intrusion in a karstified coastal aquifer in Crete, Greece, a three-dimensional, density-dependent groundwater flow and transport model was developed and compared to the more traditional sharp-interface approach. The karstified medium was modelled using a combination of the equivalent porous medium approach (for lower-order fractures) and a discrete fracture approach (for the main fractures/faults). The model takes into consideration the geomorphologic characteristics of the karstic system, such as the depth and orientation of the fault network, and the diffusion phenomena associated with the variable densities of freshwater and saltwater—parameters that create a complex system, inducing uncertainty in the model. The model results showed that the orientation of the fractures, the pumping activity and the fluid density effects drive the seawater intrusion front asymmetrically inland.

Editor Z.W. Kundzewicz

Citation Dokou, Z. and Karatzas, G.P., 2012. Saltwater intrusion estimation in a karstified coastal system using density-dependent modelling and comparison with the sharp-interface approach. Hydrological Sciences Journal, 57 (5), 985–999.  相似文献   

8.
Studies investigating the effects of inland recharge on coastal groundwater dynamics were carried out typically in unconfined aquifers, with few in confined aquifers. This study focused on the groundwater dynamics in confined aquifers with seasonally sinusoidally fluctuated inland groundwater head and constant sea level by numerical simulations. It is known that the mixing zone (MZ) of saltwater wedge in response to the seasonal oscillations of inland groundwater head swings around the steady-state MZ. However, our simulation results indicate that even the most landward freshwater-saltwater interface over a year is seaward from the steady-state location when the hydraulic conductivity K is ≤10−4 m/s under certain boundary conditions with given parameter values. That is, seasonal oscillations of inland groundwater head may reduce seawater intrusion in confined coastal aquifers when K ≤ 10−4 m/s. Sensitivity analysis indicates that for aquifers of K ≤ 10−4 m/s, the larger the inland head fluctuation amplitude is, the less the seawater intrudes. This is probably due to the reason that the seawater intrusion time decreases with the increase of fluctuation amplitude when K ≤ 10−4 m/s. Numerical simulations demonstrate that seasonal inland groundwater head oscillations promote the annual averaged recirculated seawater discharge across the seaward boundary.  相似文献   

9.
The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer.  相似文献   

10.
11.
Marine intrusion is the most serious problem facing the coastal Jorf shallow aquifer, located in south‐eastern Tunisia on the Mediterranean Sea. Jorf Aquifer is intensively exploited to supply the growing needs of agriculture and domestic sectors. This work proposes a multidisciplinary investigation, involving hydro‐geochemical, geoelectrical survey and geostatistical techniques for modelling the saltwater intrusion. For this purpose, 36 water samples were conducted and analysed. Electric conductivity, pH, total dissolved solids and major ions were measured and analysed. Pie and Durov Diagrams, Q‐mode hierarchical cluster and geostatistical analysis were considered to identify the main groundwater mineralization processes. Results revealed that the Na‐Cl‐Ca‐SO4 is the dominant water type suggesting that dissolution of halite and gypsum was the main mineralization source of groundwater in the central and southern part of study area. However, saltwater intrusion was shown to control groundwater quality essentially in coastal areas. Variographic analyses were used to select the variographic model that best fits the spatial development of apparent resistivity. Kriged apparent resistivity profiles showed an abnormal decrease of resistivity values in the coastal zone, implying highly saline water because of seawater intrusion. Apparent resistivity values also decrease considerably in the faulted areas, suggesting a contribution of faults to seawater intrusion. Finally, saltwater mixing ratio was computed for each sample, and a refined seawater intrusion map was developed. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

12.
We use electrical resistivity tomography to obtain a 6.8‐km electrical resistivity image to a depth of approximately 150 m.b.s.l. along the coast of Monterey Bay. The resulting image is used to determine the subsurface distribution of saltwater‐ and freshwater‐saturated sediments and the geologic controls on fluid distributions in the region. Data acquisition took place over two field seasons in 2011 and 2012. To maximize our ability to image both vertical and horizontal variations in the subsurface, a combination of dipole–dipole, Wenner, Wenner‐gamma, and gradient measurements were made, resulting in a large final dataset of approximately 139,000 data points. The resulting resistivity section extends to a depth of 150 m.b.s.l., and is used, in conjunction with the gamma logs from four coastal monitoring wells to identify four dominant lithologic units. From these data, we are able to infer the existence of a contiguous clay layer in the southern portion of our transect, which prevents downward migration of the saltwater observed in the upper 25 m of the subsurface to the underlying freshwater aquifer. The saltwater and brackish water in the northern portion of the transect introduce the potential for seawater intrusion into the hydraulically connected freshwater aquifer to the south, not just from the ocean, but also laterally from north to south.  相似文献   

13.
This paper provides for the first time an experimental study where the impact of sea‐level fluctuations and inland boundary head‐level variations on freshwater–saltwater interface toe motion and transition zone dynamics was quantitatively analysed under transient conditions. The experiments were conducted in a laboratory flow tank where various (inland and coastal) head changes were imposed to the system and the response of the key seawater intrusion parameters was analysed with high spatial and temporal resolution. Two homogeneous aquifer systems of different grain size were tested. The numerical code SEAWAT was used for the validation. The results show that in cases of sea‐level variations, the intruding wedge required up to twice longer time to reach a new steady‐state condition than the receding wedge, which thereby extend the theory of timescale asymmetry between saltwater intrusion and retreat processes in scenarios involving sea‐level fluctuations. The intruding and receding rates of the saltwater wedge were respectively similar in the scenario involving sea‐level and the freshwater‐level changes, despite change in transmissivity. The results show that, during the intrusion phase, the transition zone remains relatively insensitive, regardless of where the boundary head change occurs (i.e., freshwater drop or sea‐level rise) or its magnitude. By contrast, a substantial widening of the transition zone was observed during the receding phase, with almost similar amplitude in the scenario involving a rise of the freshwater level compared with that caused by a drop of the saltwater level, provided that an equivalent absolute head change magnitude was used. This transition zone widening (occurring during saltwater retreat) was greater and extended over longer period in the low hydraulic conductivity aquifer, for both freshwater‐level rise and sea‐level drop scenarios. The concentration maps revealed that the widening mechanism was also enhanced by the presence of some freshwater sliding and into the wedge during saltwater retreat, which was thereafter sucked upward towards the interface because of density difference effects.  相似文献   

14.
Subsurface dams are rather effective and used for the prevention of saltwater intrusion in coastal regions around the world. We carried out the laboratory experiments to investigate the elevation of saltwater wedge after the construction of subsurface dams. The elevation of saltwater wedge refers to the upward movement of the downstream saltwater wedge because the subsurface dams obstruct the regional groundwater flow and reduce the freshwater discharge. Consequently, the saltwater wedge cannot further extend in the longitudinal direction but rises in the vertical profile resulting in significant downstream aquifer salinization. In order to quantitatively address this issue, field-scale numerical simulations were conducted to explore the influence of various dam heights, distances, and hydraulic gradients on the elevation of saltwater wedge. Our investigation shows that the upward movement of the saltwater wedge and its areal extension in the vertical domain of the downstream aquifer become more severe with a higher dam and performed a great dependence on the freshwater discharge. Furthermore, the increase of the hydraulic gradient and the dam distance from the sea boundary leads to a more pronounced wedge elevation. This phenomenon comes from the variation of the freshwater discharge due to the modification of dam height, location, and hydraulic gradient. Large freshwater discharge can generate greater repulsive force to restrain the elevation of saltwater wedge. These conclusions provide theoretical references for the behaviour of the freshwater–seawater interface after the construction of subsurface dams and help optimize the design strategy to better utilize the coastal groundwater resources.  相似文献   

15.
This study is aimed to understand the hydraulic mechanism of coastal aquifer systems that include highly permeable layers (HPLs). These hydrologic conditions can be found in many volcanic islands that are composed of a series of lava flows discharged into sea or other standing body of water. In the first part, we developed a numerical model based on the geologic and hydrologic data obtained from the eastern Jeju Island, Korea, of which the aquifer contains clinker and hyaloclastite layers. The simulation results reproduced spatial location of fresh‐saline water interface, especially the abrupt decline of interface at the inland part and the thickness variation of transition zone along the cross‐section observed at the eastern Jeju coastal aquifer. We were able to find out that these phenomena are strongly related to the presence of the HPL. In the second part, quantitative analyses were conducted with the use of hypothetical models in order to understand the dynamic characteristics of coastal system that includes HPLs. A series of sensitivity studies were conducted to assess the effect of the horizontal length and vertical depth of HPL on the spatial location of the interface toe and the configuration of transition zone. Various case studies have shown that the seawater intruded into the inland more as the horizontal length of HPL was increased and its vertical depth was decreased. In other simulations including two HPLs, the vertical distance between these two HPLs primarily controlled the flow regime, flux variations, and the configuration of the transition zone. Finally, we performed simulations to evaluate the effect of a rising sea‐level. This study provides more understanding of how the presence of HPL controls the seawater intrusion processes, and the spatial configurations of fresh‐saline water interface at coastal aquifers. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

16.
Storage of water in aquifers using injection wells is an efficient way for utilizing excess desalinated water in arid regions. In this investigation we estimate the benefits of optimally recharging seasonal surplus desalinated water into a strategic coastal aquifer already benefitting from natural recharge of flash-floods water by a recharge dam. Since, usually the buyers of desalinated water commit to purchase surplus desalinated water under take-or-pay contracts, any attempt in utilizing the paid water is beneficial. Coastal cities are observing an increased urbanization leaving limited space for aquifer recharge infrastructure. In order to determine the optimal location of wells and maximize the use of surplus desalinated water available in winter period, a decision tool combining a numerical groundwater flow simulation model (MODFLOW) with an optimization model is developed. The results of this study show that increasing the number of wells from the existing 45 wells to 173 would allow storing 31.4 million cubic meter per year of excess desalinated water into the aquifer that can be used during later during summer months. The net benefit would reach US$55 million/year while the cost of drilling the new wells is US$5.11 million.  相似文献   

17.
We examined the fire‐induced changes in groundwater recharge rate. This aspect is particularly important in the case of large forested areas growing over a coastal aquifer affected by saltwater intrusion. In the Ravenna coastal area (Italy), pine forests grow on coastal dune belts, overlying a sandy unconfined aquifer, which is strongly affected by marine ingression. Three groundwater profiles across the forest and perpendicular to the coastline were monitored for groundwater level, physical, and chemical parameters. The aims were to define groundwater quality, recharge rate, freshwater volume, and highlight change, which occurred after a forest fire with reference to pre‐fire conditions. Analytical solutions based on Darcy Law and the Dupuit Equation were applied to calculate unconfined flow and compare recharge rates among the profiles. The estimated recharge rates increased in the partially and completely burnt areas (219 and 511 mm year?1, respectively) compared with the pristine pine forest area (73 mm year?1). Although pre‐fire conditions were similar in all monitored profiles, a post‐fire decrease in salinity was observed across the burnt forest, along with an increase in infiltration and freshwater lens thickness. This was attributed to decrease canopy interception and evapotranspiration caused by vegetation absence after the fire. This research provided an example of positive forest fire feedback on the quantity and quality of fresh groundwater resources in a lowland coastal aquifer affected by saltwater intrusion, with limited availability of freshwater resources. The fire provided an opportunity to evaluate a new forest management approach and consider the restoration and promotion of native dune herbaceous vegetation.  相似文献   

18.
Coastal aquifers are at threat of salinization in most parts of the world. This work investigated the seasonal hydrochemical evolution of coastal groundwater resources in Urmia plain, NW Iran. Two recently proposed methods have been used to comparison, recognize and understand the temporal and spatial evolution of saltwater intrusion in a coastal alluvial aquifer. The study takes into account that saltwater intrusion is a dynamic process, and that seasonal variations in the balance of the aquifer cause changes in groundwater chemistry. Pattern diagrams, which constitute the outcome of several hydrochemical processes, have traditionally been used to characterize vulnerability to sea/saltwater intrusion. However, the formats of such diagrams do not facilitate the geospatial analysis of groundwater quality, thus limiting the ability of spatio-temporal mapping and monitoring. This deficiency calls for methodologies which can translate information from some diagrams such Piper diagram into a format that can be mapped spatially. Distribution of groundwater chemistry types in Urmia plain based on modified Piper diagram using GQIPiper(mix) and GQIPiper(dom) indices that Mixed Ca–Mg–Cl and Ca-HCO3 are the dominant water types in the wet and dry seasons, respectively. In this study, a groundwater quality index specific to seawater intrusion (GQISWI) was used to check its efficiency for the groundwater samples affected by Urmia hypersaline Lake, Iran. Analysis of the main processes, by means of the Hydrochemical Facies Evolution Diagram (HFE-Diagram), provides essential knowledge about the main hydrochemical processes. Subsequently, analysis of the spatial distribution of hydrochemical facies using heatmaps helps to identify the general state of the aquifer with respect to saltwater intrusion during different sampling periods. The HFE-D results appear to be very successful for differentiating variations through time in the salinization processes caused by saltwater intrusion into the aquifer, distinguishing the phase of saltwater intrusion from the phase of recovery, and their respective evolutions. Both GQI and HFE-D methods show that hydrochemical variations can be read in terms of the pattern of saltwater intrusion and groundwater quality status. But generally, in this case (i.e. saltwater and not seawater intrusion) the HFE-D method was presented better efficiency than GQI method (including GQIPiper and GQISWI).  相似文献   

19.
Impact of Sea-Level Rise on Sea Water Intrusion in Coastal Aquifers   总被引:17,自引:0,他引:17  
Despite its purported importance, previous studies of the influence of sea-level rise on coastal aquifers have focused on specific sites, and a generalized systematic analysis of the general case of the sea water intrusion response to sea-level rise has not been reported. In this study, a simple conceptual framework is used to provide a first-order assessment of sea water intrusion changes in coastal unconfined aquifers in response to sea-level rise. Two conceptual models are tested: (1) flux-controlled systems, in which ground water discharge to the sea is persistent despite changes in sea level, and (2) head-controlled systems, whereby ground water abstractions or surface features maintain the head condition in the aquifer despite sea-level changes. The conceptualization assumes steady-state conditions, a sharp interface sea water-fresh water transition zone, homogeneous and isotropic aquifer properties, and constant recharge. In the case of constant flux conditions, the upper limit for sea water intrusion due to sea-level rise (up to 1.5 m is tested) is no greater than 50 m for typical values of recharge, hydraulic conductivity, and aquifer depth. This is in striking contrast to the constant head cases, in which the magnitude of salt water toe migration is on the order of hundreds of meters to several kilometers for the same sea-level rise. This study has highlighted the importance of inland boundary conditions on the sea-level rise impact. It identifies combinations of hydrogeologic parameters that control whether large or small salt water toe migration will occur for any given change in a hydrogeologic variable.  相似文献   

20.
Explicit algebraic equations are derived to determine approximate maximum pumping rates or minimum injection rates to limit sea water intrusion to a prespecified distance from the coastline. The equations are based on Strack's (1976) single-potential solution. The maximum pumping rates and minimum injection rates applied at wells with uniform spacing to control the inland movement of the fresh water-salt water interface in a coastal aquifer could be calculated from Strack's (1976) solution without the need of a numerical optimization algorithm. When wells are distributed in a simple fashion, the maximum intrusion location can be identified precisely for pumping cases and approximately for injection cases. For pumping cases, critical points are the limit of allowable salt water intrusion, whereas no such limit exists for injection cases. Once an application site is identified, a series of design curves for pumping and injection rates can be developed for arbitrary intrusion limits. When a user is interested only in the largest pumping rates associated with critical points, one design curve can yield complete information.  相似文献   

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