Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

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.     

A Model to Simulate Pumping Tests in Wells with High Loss and Backflow

Traditional methods of analyzing pumping tests in single wells fail when the well loss is very high due to a low transmissivity skin. Because of the restricted rate at which water can enter a high loss well from the aquifer, well casing storage becomes a significant factor. Additionally, if a slug of water enters the well from the pump column immediately after the pump is switched off, it has a long‐lasting significant effect on the recovering water level in the well because it cannot be absorbed rapidly by the aquifer. A theoretical model is derived here that simulates the water level in a well in these circumstances. In the model, the continuously changing rate of water inflow from the aquifer to the well is approximated by a step function with a finite difference time step. It is demonstrated by a real example that the model can be applied easily to analyze pumping tests, including tests with a varying pumping rate. The analysis confirms suspected high well loss, calculates the unknown rate of backflow, and determines the aquifer's transmissivity.     

Boundary condition effects on maximum groundwater withdrawal in coastal aquifers

Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.     

Optimized system to improve pumping rate stability during aquifer tests

Aquifer hydraulic properties are commonly estimated using aquifer tests, which are based on an assumption of a uniform and constant pumping rate. Substantial uncertainties in the flow rate across the borehole-formation interface can be induced by dynamic head losses, caused by rapid changes in borehole water levels early in an aquifer test. A system is presented that substantially reduces these sources of uncertainty by explicitly accounting for dynamic head losses. The system which employs commonly available components (including a datalogger, pressure transducers, a variable-speed pump motor, a flow controller, and flowmeters), is inexpensive, highly mobile, and easily set up. It optimizes the flow rate at the borehole-formation interface, making it suitable for any type of aquifer test, including constant, step, or ramped withdrawal and injection, as well as sinusoidal. The system was demonstrated for both withdrawal and injection tests in three aquifers at the Savannah River Site. No modifications to the control system were required, although a small number of characteristics of the pumping and monitoring system were added to the operating program. The pumping system provided a statistically significant, constant flow rate with time. The range in pumping variability (95% confidence interval) was from +/- 2.58 x 10(-4) L/sec to +/- 9.07 x 10(-4) L/sec, across a wide range in field and aquifer conditions.     

Reverse Water‐Level Fluctuations Associated with Fracture Connectivity

Reverse water‐level fluctuations (RWFs), a phenomenon in which water levels rise briefly in response to pumping, were detected in monitoring wells in a fractured siliciclastic aquifer system near a deep public supply well. The magnitude and timing of RWFs provide important information that can help interpret aquifer hydraulics near pumping wells. A RWF in a well is normally attributed to poroelastic coupling between the solid and fluid components in an aquifer system. In addition to revealing classical pumping‐induced poroelastic RWFs, data from pressure transducers located at varying depths and distances from the public supply well suggest that the RWFs propagate rapidly through fractures to influence wells hundreds of meters from the pumping well. The rate and cycling frequency of pumping is an important factor in the magnitude of RWFs. The pattern of RWF propagation can be used to better define fracture connectivity in an aquifer system. Rapid, cyclic head changes due to RWFs may also serve as a mechanism for contaminant transport.     

Optimizing Wellfield Operation in a Variable Power Price Regime

Wellfield management is a multiobjective optimization problem. One important objective has been energy efficiency in terms of minimizing the energy footprint (EFP) of delivered water (MWh/m³). However, power systems in most countries are moving in the direction of deregulated markets and price variability is increasing in many markets because of increased penetration of intermittent renewable power sources. In this context the relevant management objective becomes minimizing the cost of electric energy used for pumping and distribution of groundwater from wells rather than minimizing energy use itself. We estimated EFP of pumped water as a function of wellfield pumping rate (EFP‐Q relationship) for a wellfield in Denmark using a coupled well and pipe network model. This EFP‐Q relationship was subsequently used in a Stochastic Dynamic Programming (SDP) framework to minimize total cost of operating the combined wellfield‐storage‐demand system over the course of a 2‐year planning period based on a time series of observed price on the Danish power market and a deterministic, time‐varying hourly water demand. In the SDP setup, hourly pumping rates are the decision variables. Constraints include storage capacity and hourly water demand fulfilment. The SDP was solved for a baseline situation and for five scenario runs representing different EFP‐Q relationships and different maximum wellfield pumping rates. Savings were quantified as differences in total cost between the scenario and a constant‐rate pumping benchmark. Minor savings up to 10% were found in the baseline scenario, while the scenario with constant EFP and unlimited pumping rate resulted in savings up to 40%. Key factors determining potential cost savings obtained by flexible wellfield operation under a variable power price regime are the shape of the EFP‐Q relationship, the maximum feasible pumping rate and the capacity of available storage facilities.     

A CONSTANT DISCHARGE DEVICE FOR AQUIFER TESTS ON LARGE-DIAMETER WELLS

Abstract. The discharge in pumping tests conducted on large-diameter wells declines with the fall of water level. This violates the basic requirement of pumping tests that the discharge should remain constant. A simple device to keep the discharge constant has therefore been developed. This device is also useful in keeping the discharge much lower than the rated capacity of the farmer's pump, and thus in increasing the total test period.
The discharge from the farmer's pump is released in a barrel having a V-notch at the top and an arrangement for returning a part of the discharge to the well. The return flow is gradually reduced through a control valve, and thus the net outflow is kept constant.
This device has been used for conducting pumping tests on several dug wells.     

Evaluation of long-term groundwater level data in regular monitoring wells,Barka, Sultanate of Oman

A detailed investigation was carried out to evaluate long-term groundwater level fluctuation in regular monitoring wells constructed by the Ministry of Water Resources in Barka, Sultanate of Oman. For this study, groundwater level data for 71 wells and rainfall data from six stations were collected from 1984 to 2003 and analysed. Based on long-term water level fluctuation, groundwater wells are classified into three groups. In group 1, water level shows a long-term cyclic trend without yearly fluctuation whereas in group 2 the water level declined continuously until 1995 followed by a constant water level. In group 3, water level decreases continuously throughout the study periods with rapid annual cyclic variation. Group 1 wells show high water-level fluctuations (5 to 10 m) and seem to be regulated by discharge (lateral flow) from this aquifer and recharge from the adjacent Jabal Akhdar mountainous region. Constant trend in water level after 1995 in group 2 wells illustrates the advancement of saline–fresh water interface to the inland due to heavy pumping which is justified by higher electrical conductivity and Cl/HCO₃ ratio. In group 3 wells, the water level dropped continuously due to overabstraction by agricultural farms and human settlements. In addition, wells existing near the recharge dams express the influences of recharge dams and rainfall, and exhibit high water-level fluctuations during heavy rainfall periods. The long-term regional variation indicates that water level drops continuously in the coastal and central parts of the study region. Linear regression analysis revealed that the decline in water level is 0·3–0·4 m year⁻¹ near the coastal and central parts of the study area and is almost constant in the remaining area. We conclude that the contribution of man-made activities on groundwater level is well compared with natural factors. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of analytical solution for stream depletion due to groundwater pumping in Gapcheon watershed,South Korea

A number of groundwater wells for agricultural activity, including rice farming and greenhouses, have been developed near streams over the past 20 years in South Korea. The result of a stream depletion calculation using an analytical solution of complimentary error function shows that groundwater pumping at 1949 wells drilled in the Gapcheon watershed can produce stream depletion. This amount is estimated at about 7% of annual baseflow and reaches as high as 18% of monthly baseflow during the maximum agricultural water consumption period in May. Agricultural wells have a larger effect on stream depletion than domestic wells because of their higher pumping rate. Stream depletion from agricultural wells located within 200 m from a stream represents 65% of the total depletion rate. Agricultural water policy for water use at nearby streams should be changed to reduce stream depletion and thereby maintain sustainable water development in South Korea. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of Methods for Sampling Dissolved Nitrogen in a Fractured Carbonate-Rock Aquifer

As part of an agricultural non-point-source study in the Conestoga River head waters area in Pennsylvania, different methods for collecting ground water samples from a fractured carbonate-rock aquifer were compared. Samples were collected from seven wells that had been cased to bedrock and drilled as open holes to the first significant water-bearing zone. All samples were analyzed for specific conductance, dissolved oxygen, and dissolved-nitrogen species. Water samples collected by a point sampler without pumping the well were compared to samples collected by a submersible pump and by a point sampler after pumping the well. Samples collected by using a point sampler, adjacent to major water-bearing zones in an open borehole without pumping the well, were not statistically different from samples collected from the pump discharge or from point samples collected adjacent to major water-bearing zones after pumping the well. Samples collected by using a point sampler without pumping the well at depths other than those adjacent to the water-bearing zones did not give the same results as the other methods, especially when the water samples were collected from within the well casings. It was concluded that, for the wells at this site, sampling adjacent to major water-bearing zones by using a point sampler without pumping the well provides samples that are as representative of aquifer conditions as samples collected from the pump discharge after reaching constant temperature and specific conductance, and by using a point sampler after pumping the well.     

A critical review of groundwater budget myth, safe yield and sustainability

The principle of water balance is well known, but its application often causes controversy. One recent debate is the use of the water balance equation to determine the safe yield and sustainable yield. Two extreme opinions exist on natural groundwater recharge. One misconception is that the development of groundwater is considered to be safe if the pumping rate does not exceed the rate of natural recharge. Another is that the sustainable pumping rate has nothing to do with natural recharge, but depends on the increased recharge and decreased discharge (called capture) induced by pumping. The truth is that both the natural recharge and dynamic development of the capture determine the safe yield or sustainable yield of a groundwater basin. This paper clarifies the water budget controversy and uses the water balance equation to critically analyse the concepts of safe yield and sustainable yield. Numerical simulation of a hypothetical case was used to demonstrate the natural groundwater balance, effects of pumping and the dynamic development of the capture.     

Analysis of continuous and pulsed pumping of a phreatic aquifer

In a phreatic aquifer, fresh water is withdrawn by pumping from a recovery well. As is the case here, the interfacial surface (air/water) is typically assumed to be a sharp boundary between the regions occupied by each fluid. The pumping efficiency depends on the method by which the fluid is withdrawn. We consider the efficiency of both continuous and pulsed pumping. The maximum steady pumping rate, above which the undesired fluid will break through into the well, is defined as critical pumping rate. This critical rate can be determined analytically using an existing solution based on the hodograph method, while a Boundary Element Method is applied to examine a high flow rate, pulsed pumping strategy in an attempt to achieve more rapid withdrawal. A modified kinematic interface condition, which incorporates the effect of capillarity, is used to simulate the fluid response of pumping. It is found that capillarity influences significantly the relationship between the pumping frequency and the fluid response. A Hele-Shaw model is set up for experimental verification of the analytical and numerical solutions in steady and unsteady cases for pumping of a phreatic aquifer. When capillarity is included in the numerical model, close agreement is found in the computed and observed phreatic surfaces. The same model without capillarity predicts the magnitude of the free surface fluctuation induced by the pulsed pumping, although the phase of the fluctuation is incorrect.     

Two-stage aquifer pumping subject to slow desorption and persistent sources

This work focuses on improving pump-and-treat remediation by optimizing a two-stage operational scheme to reduce volumes extracted when confronted with nonequilibrium desorption, low-permeability units, and continuous contaminant sources such as non-aqueous phase liquids (NAPL). Q1 and Q2 are the initial short-term high pumping rate and later long-term low pumping rate, respectively. A two-dimensional ground water flow and transport management model was used to test the proposed strategy for plumes developed from finite (NAPL-free) and continuous (NAPL-driven) contaminant sources in homogeneous and nonhomogeneous (zoned) aquifers. Remediation scenarios were simulated over durations of 2000, 6000, and 15,000 d to determine (1) the optimal time to switch from a preset Q1 to Q2 and (2) the value of Q2. The problem was constrained by mass removal requirements, maximum allowable downgradient concentrations, and practical bounds on Q2. Q1 was fixed at preset values 50% to 200% higher than the single-stage pumping rates (i.e., steady pumping rates during entire remediation period) necessary to achieve a desired cleanup level and capture the plume. Results for the NAPL-free homogeneous case under nonequilibrium desorption conditions achieved the same level of cleanup as single-stage pumping, while reducing extracted volumes by up to 36%. Comparable savings were obtained with NAPL-driven sources only when the source concentration was reduced by at least 2 orders of magnitude. For the zoned aquifer, the proposed strategy provided volume savings of up to 24% under NAPL-free and reduced source conditions.     

Strategies for offsetting seasonal impacts of pumping on a nearby stream

Ground water pumping from aquifer systems that are hydraulically connected to streams depletes streamflow. The amplitude and timing of stream depletion depend on the stream depletion factor (SDF(i)) of the pumping wells, which is a function of aquifer hydraulic characteristics and the distance from the wells to the stream. Wells located at different locations, but having the same SDF and the same rate and schedule of pumping, will deplete streamflow equally. Wells with small SDF(i) deplete streamflow approximately synchronously with pumping. Wells with large SDF(i) deplete streamflow at approximately a constant rate throughout the year, regardless of the pumping schedule. For large values of SDF(i), artificial recharge that occurs on a different schedule from pumping can offset streamflow depletion effectively. The requirements are (1) that the pumping and recharge wells both have the same SDF(i) and (2) that the annual total quantities of recharge and pumping be equal. At larger SDF(i) values, it takes longer for pumping to impact streamflow in a wide aquifer than it does in a narrow aquifer. In basins that are closed to further withdrawals because streamflow is fully allocated, water-use changes replace new allocations as the source of water for new developments. Ground water recharge can be managed to offset the impacts of new ground water developments, allowing for changes in the timing and source of withdrawals from a basin without injuring existing users or instream flows.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

2016年衡水冀16井水位变化分析

衡水冀16井水位2016年经常出现有规律的大幅度异常波动变化,具有小幅下降—持续上升—小幅上升—持续下降变化形态,日变最大幅度0.73 m。通过现场核实,发现观测仪器工作正常,附近鱼场地下水开采量增加。增加辅助观测仪器同井对比水位观测,并对鱼场2口冷水井进行抽水试验,分析衡水冀16井水位异常变化原因。结果显示,衡水冀16井水位大幅波动异常变化可能因冷水井1抽水所致,冷水井2无影响。     

Controls of Wellbore Flow Regimes on Pump Effluent Composition

Where well water and formation water are compositionally different or heterogeneous, pump effluent composition will vary due to partial mixing and transport induced by pumping. Investigating influences of purging and sampling methodology on composition variability requires quantification of wellbore flow regimes and mixing. As a basis for this quantification, analytical models simulating Poiseuille flow were developed to calculate flow paths and travel times. Finite element modeling was used to incorporate influences of mixing. Parabolic velocity distributions within the screened interval accelerate with cumulative inflow approaching the pump intake while an annulus of inflowing formation water contracts uniformly to displace an axial cylinder of pre‐pumping well water as pumping proceeds. Increased dispersive mixing forms a more diffuse formation water annulus and the contribution of formation water to pump effluent increases more rapidly. Models incorporating viscous flow and diffusion scale mixing show that initially pump effluent is predominantly pre‐pumping well water and compositions vary most rapidly. After two screen volumes of pumping, 94% of pump effluent is inflowing formation water. Where the composition of formation water and pre‐pumping well water are likely to be similar, pump effluent compositions will not vary significantly and may be collected during early purging or with passive sampling. However, where these compositions are expected to be considerably different or heterogeneous, compositions would be most variable during early pumping, that is, when samples are collected during low‐flow sampling. Purging of two screen volumes would be required to stabilize the content and collect a sample consisting of 94% formation water.     

Cautions and Suggestions for Geochemical Sampling in Fractured Rock

Collecting water samples for geochemical analyses in open bedrock boreholes or in discrete intervals of boreholes intersected by multiple fractures is likely to yield ambiguous results for ground water chemistry because of the variability in the transmissivity, storativity, and hydraulic head of fractures intersecting the borehole. Interpreting chemical analyses of water samples collected in bedrock boreholes requires an understanding of the hydraulic conditions in the borehole under the ambient flow regime in the aquifer as well as during sampling. Pumping in open boreholes, regardless of the pumping rate and the location of the pump intake, first draws water from the borehole and then from fractures intersecting the borehole. The time at which the volumetric rate of water entering the borehole from fractures is approximately equal to the pumping rate can be identified by monitoring the logarithm of drawdown in the borehole as a function of the logarithm of time. Mixing of water entering the borehole from fractures with water in the borehole must be considered in estimating the time at which the pump discharge is representative of aquifer water. In boreholes intersected by multiple fractures, after the contribution from the borehole volume has diminished, the contribution of fractures to the pump discharge will be weighted according to their transmissivity, regardless of the location of the pump intake. This results in a flux-averaged concentration in the pump discharge that is biased by the chemical signature of those fractures with the highest transmissivity. Under conditions where the hydraulic head of fractures varies over the length of the borehole, open boreholes will be subject to ambient flow in the water column in the borehole. In some instances, the magnitude of the ambient flow may be similar to the designated pumping rate for collecting water samples for geochemical analyses. Under such conditions, the contributions to the pump discharge from individual fractures will be a function not only of the transmissivity of the fractures, but also of the distribution of hydraulic head in fractures intersecting the borehole. To reduce or eliminate the deleterious effects of conducting geochemical sampling in open boreholes, a straddle-packer apparatus that isolates a single fracture or a series of closely spaced fractures is recommended. It is also recommended that open boreholes be permanently outfitted with borehole packers or borehole liners in instances where maintaining the hydraulic and chemical stratification in the aquifer is of importance. In a field example, a comparison of results from sampling in an open borehole and in discrete intervals of the same borehole showed dramatic differences in the concentrations of chemical constituents in the water samples, even though chemical field parameters stabilized prior to both open borehole and discrete interval sampling.     

INFLUENCE OF PUMPING ON FOUR-COMPONENT BOREHOLE STRAIN AT TAI'AN SEISMIC STATION AND ITS INTERFERENCE MECHANISM

Four-component borehole strainmeter (FCBS) is one kind of high-precision borehole strain observation instruments invented in China. As a kind of near-surface deformation observation instrument, FCBS is also easily disturbed by the external environment factors. As a common factor, pumping has significant influence on FCBS observation. Existing studies mostly identify the pumping interference from the perspective of observation curve morphology, relatively few studies focus on its interference mechanism. In order to truly capture earthquake precursor information, it is necessary to study the interference mechanism. In recent years, RZB-3 type FCBS at Tai'an seismic station has been seriously affected by pumping, so it is necessary and also feasible to study the interference mechanism of pumping. Since the influence of pumping interference on borehole strainmeter is common, this work would be very practical and be used for reference by other borehole strain observation stations. We find that the original observation curves and observed surface strain, shear strain from RZB-3 type FCBS at Tai'an seismic station have the characteristics of synchronous change with the borehole water level, in which the linear correlation coefficient between the two observed shear strain curves and borehole water level reached 0.70 and 0.82 respectively. We further find that the principal strain direction of borehole and borehole water level after normalization meet the nonlinear function as y=1.217arctan(x)^0.224-0.284. The above phenomenon indicates that the observation of RZB-3 type FCBS at Tai'an seismic station is significantly affected by the borehole water level, and the influence is more obvious and the gradient is larger at the stage of low water level. Pumping interference often appears in low water level stage and changes the rock pore pressure state. Statistics show that pumping interference affects the borehole strain state. To investigate the interference mechanism of pumping to RZB-3 type FCBS at Tai'an seismic station, we take a known pumping as an example, in which we study the principal strain state of the borehole in three periods of normal pumping, interruption of pumping and resuming pumping respectively. During each period, we solve 3 parameters of the principal plane strain state, i.e. the maximum principal strain rate, the minimum principal strain rate and the maximum principal strain direction from four observation equations of FCBS by nonlinear iterative least squares algorithm. On the other hand, concentrated load model (CLM) is used to simulate the mechanical mechanism of pumping. Firstly, the depth of FCBS relative to pumping source and the concentrated load at pumping source are inversed, then, the strain state surrounding the pumping well, including the state at RZB-3 borehole, is simulated by forward modeling. By comparing these results, we find that: (1)The concentrated load at pumping source inversed by CLM during periods of normal pumping and resuming pumping are both located at or near the bottom of the pumping well, which is consistent with the actual situation, indicating that mechanism and degree of the influence of pumping on borehole strain are well simulated by CLM. (2)The observed strain state is consistent with the simulation result of pumping interference by forward modeling, indicating that the principal strain state of borehole calculated based on observation of FCBS reflects the true strain state of borehole under different pumping states.(3)The inversed concentrated load at pumping source during pumping periods is significant greater than the load of the pumped water, indicating that the pumping process has more significant influence on the pore pressure of rocks than the load of the pumped water. Even though CLM is an approximate simulation since it's based on some elastic assumptions, the interference mechanism of pumping on RZB-3 type FCBS at Tai'an seismic station is well explained, which is maybe very helpful for studying the influence of pumping interference on other deformation instruments, locating the unknown pumping source and studying the characteristics of pore pressure of rocks.     

Using Alternate Pumping and Cooperative Game Theory to Reduce Sea Water Intrusion

In this article, alternate pumping is studied as a means used to reduce the salinity concentration in coastal aquifers, pumped using a system of wells. This approach has been applied to a hypothetical confined coastal aquifer. Flow has been modeled, using SEAWAT. Two strategies are proposed based on cooperative game theory, to promote alternate pumping. In both strategies an external player will compensate the users that will pump during an unpopular pumping period. In the first strategy it is supposed that this external player aims at protecting a critical well, e.g. a municipal well, reducing its maximum salinity concentration by pumping alternately. In the second strategy proposed, the target is to reduce the overall salinity of the water pumped by the wells. In applying the cooperative game theory, the Shapley value is used to distribute the benefits of cooperation between the players (well users), according to their marginal contribution. Overall, well users can reduce sea water intrusion by cooperatively changing their pumping time schedules. The game theoretical model developed is a useful tool to promote cooperation toward this direction. The methods applied in the hypothetical aquifer, can be tested in actual aquifers to reduce sea water intrusion.