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1.
Concurrent existence of confined and unconfined zones of an aquifer can arise owing to ground water withdrawal by pumping. Using Girinskii's potential function, Chen (1974, 1983) developed an approximate analytical solution to analyze transient ground water flow to a pumping well in an aquifer that changes from an initially confined system to a system with both unconfined and confined regimes. This article presents the details of the Chen model and then compares it with the analytical model developed by Moench and Prickett (1972) for the same problem. Hypothetical pumping test examples in which the aquifer undergoes conversion from confined to water table conditions are solved by the two analytical models and also a numerical model based on MODFLOW. Comparison of the results suggests that the solutions of the Chen model give better results than the Moench and Prickett model except when the radial distance is very large or aquifer thickness is large compared with drawdown. 相似文献
2.
Stephen P. Garabedian 《Ground water》2013,51(6):927-934
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
3.
Narayan C. Ghosh Govinda C. Mishra Cornelius S. S. Sandhu Thomas Grischek Vikrant V. Singh 《Ground water》2015,53(5):794-805
The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified. 相似文献
4.
In this study, we attempted to analyse a drawdown pattern around a pumping well in an unconfined sandy gravelly aquifer constructed in a laboratory tank by means of both experimental and numerical modelling of groundwater flow. The physical model consisted of recharge, aquifer and discharge zones. Permeability and specific yield of the aquifer material were determined by Dupuit approximation under steady‐state flow and stepwise gravitational drainage of groundwater, respectively. The drawdown of water table in pumping and neighbouring observation wells was monitored to investigate the effect of no‐flow boundary on the drawdown pattern during pumping for three different boundary conditions: (i) no recharge and no discharge with four no‐flow boundaries (Case 1); (ii) no recharge and reservoir with three no‐flow boundaries (Case 2); (iii) recharge and discharge with two no‐flow boundaries (Case 3). Based on the aquifer parameters, numerical modelling was also performed to compare the simulated drawdown with that observed. Results showed that a large difference existed between the simulated drawdown and that observed in wells for all cases. The reason for the difference could be explained by the formation of a curvilinear type water table between wells rather than a linear one due to a delayed response of water table in the capillary fringe. This phenomenon was also investigated from a mass balance study on the pumping volume. The curvilinear type of water table was further evidenced by measurement of water contents at several positions in the aquifer between wells using time domain reflectometry (TDR). This indicates that the existing groundwater flow model applicable to an unconfined aquifer lacks the capacity to describe a slow response of water table in the aquifer and care should be taken in the interpretation of water table formation in the aquifer during pumping. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort. 相似文献
6.
An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation. 相似文献
7.
Jacob Zaidel 《Ground water》2013,51(6):952-959
Known analytical solutions of groundwater flow equations are routinely used for verification of computer codes. However, these analytical solutions (e.g., the Dupuit solution for the steady‐state unconfined unidirectional flow in a uniform aquifer with a flat bottom) represent smooth and continuous water table configurations, simulating which does not pose any significant problems for the numerical groundwater flow models, like MODFLOW. One of the most challenging numerical cases for MODFLOW arises from drying‐rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. Numerical solutions of groundwater flow equations cannot be rigorously verified for such cases due to the lack of corresponding exact analytical solutions. Analytical solutions of the steady‐state Boussinesq equation, associated with the discontinuous water table configurations over a stairway impervious base, are presented in this article. Conditions resulting in such configurations are analyzed and discussed. These solutions appear to be well suited for testing and verification of computer codes. Numerical solutions, obtained by the latest versions of MODFLOW (MODFLOW‐2005 and MODFLOW‐NWT), are compared with the presented discontinuous analytical solutions. It is shown that standard MODFLOW‐2005 code (as well as MODFLOW‐2000 and older versions) has significant convergence problems simulating such cases. The problems manifest themselves either in a total convergence failure or erroneous results. Alternatively, MODFLOW‐NWT, providing a good match to the presented discontinuous analytical solutions, appears to be a more reliable and appropriate code for simulating abrupt changes in water table elevations. 相似文献
8.
Air and water flows induced by pumping tests in unconfined aquifers with low‐permeability zones 
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下载免费PDF全文 Air flows from the atmosphere into an unconfined aquifer when the water table falls during pumping tests. Pumping test results in unconfined aquifers may be significantly affected by low‐permeability zones (LPZs) near the initial water table position, because they restrict the downward movement of air. A transient, three‐dimensional air–water two‐phase flow model is employed to investigate numerically the effects of local heterogeneity on pumping test results in unconfined aquifers. Two cases of local heterogeneities are considered herein: a LPZ around the pumping well and on one side of the pumping well. Results show that the drawdown with the LPZ is significantly greater than that of the homogeneous aquifer. The differences in drawdown are the most significant at intermediate times and gradually diminish at later times. The LPZ significantly reduces air flow from the atmosphere to the aquifer. The pore air velocity in the LPZ is very low. The air pressure at the observation point under the LPZ when air begins to enter is significantly lower than the air pressure of the homogeneous aquifer at the same point. After that, the air pressure increases quickly and then increases slowly. The time for the air pressure to reach the atmospheric pressure is significantly longer. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers 下载免费PDF全文
下载免费PDF全文 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
10.
Underdamped slug tests with unsaturated‐saturated flows by considering effects of wellbore skins 下载免费PDF全文
下载免费PDF全文 An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin. 相似文献
11.
An Explicit Finite Difference Model for Unconfined Aquifers 总被引：2，自引：0，他引：2
Most of the current simulation models for unconfined aquifers are based on the assumption that the free surface variation is small so that it can be combined with permeability to reduce the nonlinear Boussinesq equation to a linear partial differential equation (PDE). One of the most obvious reasons for using the linearization assumption is for the ease of numerical solution. This work presents a simpler alternative which permits an easy direct solution of the Boussinesq equation. A forward in time, central in space (FTCS) explicit finite difference method is used in the simulation model. The model was first validated by comparing its results with known analytical solution. It was then applied to an actual situation in which the short-term responses (from pumping) of an unconfined aquifer were simulated. The study shows that the stability of the model can be easily controlled, and because of the simple algorithm used, the code can be expeditiously developed and economically run on smaller machines. Due to the uncertainties in the calibration results, it is recommended here that more data be collected to improve the calibration before the model is used as a real-time simulation tool. 相似文献
12.
Xunhong Chen Jerry F. Ayers David C. Gosselin 《Ground Water Monitoring & Remediation》1998,18(4):148-156
AGalerkin finite-element model coupled with a particle tracking routine was developed to analyze the flow and transport dynamics near a high-capacity irrigation well. The model was used to compute the head distribution around the pumping well, to determine the area of influence, and to define ground water flowlines during short-term pumping periods typical of those used to collect water quality samples from high-capacity wells. In addition to hypothetical example results, the model was used to qualitatively analyze data obtained from pump-and-sample experiments conducted in an unconfined alluvial aquifer within the Platte River valley of south-central Nebraska where nitrate-nitrogen (NO3 -N) contamination is prevalent.
Simulation results of both the hypothetical and field cases suggest that short-term pumping events, impact a limited volume of aquifer. The area of influence and flowlines are affected by aquifer anisotropy, pumping rate, and well construction characteristics). Ground water above or below the screened intervals does not enter a partially penetrating well in anisotropic aquifers. In aquifers where NO3 -N concentration varies vertically and horizontally, waler quality samples from an irrigation, or other high-capacity, well provide only limited information about ground water contamination. A numerical model is thus recommended for calculating the area of influence and determining flowlines around high-capacity wells so that information derived from water quality samples collected at the wellhead can be better interpreted. 相似文献
Simulation results of both the hypothetical and field cases suggest that short-term pumping events, impact a limited volume of aquifer. The area of influence and flowlines are affected by aquifer anisotropy, pumping rate, and well construction characteristics). Ground water above or below the screened intervals does not enter a partially penetrating well in anisotropic aquifers. In aquifers where NO
13.
Analytical studies for well design adjacent to river banks are the most significant practical task in cases involving the efficiency of riverbank filtration systems. In times when high pollution of river water is joined with increasing water demand, it is necessary to design pumping wells near the river that provide acceptable amounts of river water with minimum contaminant concentrations. This will guarantee the quality and safety of drinking water supplies. This article develops an analytical solution based on the Green's function approach to solve an inverse problem: based on the required level of contaminant concentration and planned pumping time period, the shortest distance to the riverbank that has the maximum percentage of river water is determined. This model is developed in a confined and homogenous aquifer that is partially penetrated by the stream due to the existence of clogging layers. Initially, the analytical results obtained at different pumping times, rates and with different values of initial concentration are checked numerically using the MODFLOW software. Generally, the distance results obtained from the proposed model are acceptable. Then, the model is validated by data related to two pumping wells located at the first riverbank filtration pilot project conducted in Malaysia. 相似文献
14.
Detecting and quantifying small drawdown at observation wells distant from the pumping well greatly expands the characterized aquifer volume. However, this detection is often obscured by water level fluctuations such as barometric and tidal effects. A reliable analytical approach for distinguishing drawdown from nonpumping water‐level fluctuations is presented and tested here. Drawdown is distinguished by analytically simulating all pumping and nonpumping water‐level stresses simultaneously during the period of record. Pumping signals are generated with Theis models, where the pumping schedule is translated into water‐level change with the Theis solution. This approach closely matched drawdowns simulated with a complex three‐dimensional, hypothetical model and reasonably estimated drawdowns from an aquifer test conducted in a complex hydrogeologic system. Pumping‐induced changes generated with a numerical model and analytical Theis model agreed (RMS as low as 0.007 m) in cases where pumping signals traveled more than 1 km across confining units and fault structures. Maximum drawdowns of about 0.05 m were analytically estimated from field investigations where environmental fluctuations approached 0.2 m during the analysis period. 相似文献
15.
16.
The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins. 相似文献
17.
Analytical solutions of groundwater travel time to a pumping well in an unconfined aquifer have been developed in previous studies, however, the change in evapotranspiration was not considered. Here, we develop a mathematical model of unconfined flow toward a discharge well with redistribution of groundwater evapotranspiration for travel time analysis. Dependency of groundwater evapotranspiration on the depth to water table is described using a linear formula with an extinction depth. Analytical solutions of groundwater level and travel time are obtained. For a typical hypothetical example, these solutions perfectly agree with the numerical simulation results based on MODFLOW and MODPATH. As indicated in a dimensionless framework, a lumped parameter which is proportional to the pumping rate controls the distributions of groundwater evapotranspiration rate and the travel time along the radial direction. 相似文献
18.
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
19.
Water level changes in wells provide a direct measure of the impact of groundwater development at a scale of relevance for management activities. Important information about aquifer dynamics and an aquifer's future is thus often embedded in hydrographs from continuously monitored wells. Interpretation of those hydrographs using methods developed for pumping‐test analyses can provide insights that are difficult to obtain via other means. These insights are demonstrated at two sites in the High Plains aquifer in western Kansas. One site has thin unconfined and confined intervals separated by a thick aquitard. Pumping‐induced responses in the unconfined interval indicate a closed (surrounded by units of relatively low permeability) system that is vulnerable to rapid depletion with continued development. Responses in the confined interval indicate that withdrawals are largely supported by leakage. Given the potential for rapid depletion of the unconfined interval, the probable source of that leakage, it is likely that large‐scale irrigation withdrawals will not be sustainable in the confined interval beyond a decade. A second site has a relatively thick unconfined aquifer with responses that again indicate a closed system. However, unlike the first site, previously unrecognized vertical inflow can be discerned in data from the recovery periods. In years of relatively low withdrawals, this inflow can produce year‐on‐year increases in water levels, an unexpected occurrence in western Kansas. The prevalence of bounded‐aquifer responses at both sites has important ramifications for modeling studies; transmissivity values from pumping tests, for example, must be used cautiously in regional models of such systems. 相似文献
20.
Wells in aquifers of loose collapsible sediment are cased so that they have a blind wall and gain water only from the bottom. The hydraulic gradient established at the bottom of these wells during pumping brings the aquifer materials in a quicksand state, which may cause abrasion of pipes and pumps and even the destruction of well structure. To examine the quicksand occurrence, an analytical solution for the steady flow to a partially penetrating blind‐wall well in a confined aquifer is developed. The validity of the proposed solution is evaluated numerically. The sensitivity of maximum vertical gradient along the well bottom in response to aquifer and well parameters is examined. The solution is presented in the form of dimensionless‐type curves and equations that can be easily used to design the safe pumping rate and optimum well geometry to protect the well against sand production. The solution incorporates the anisotropy of aquifer materials and can also be used to determine the hydraulic conductivity of the aquifer. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献