Drawdown and stream depletion produced by pumping in the vicinity of a partially penetrating stream

Commonly used analytical approaches for estimation of pumping-induced drawdown and stream depletion are based on a series of idealistic assumptions about the stream-aquifer system. A new solution has been developed for estimation of drawdown and stream depletion under conditions that are more representative of those in natural systems (finite width stream of shallow penetration adjoining an aquifer of limited lateral extent). This solution shows that the conventional assumption of a fully penetrating stream will lead to a significant overestimation of stream depletion (> 100%) in many practical applications. The degree of overestimation will depend on the value of the stream leakance parameter and the distance from the pumping well to the stream. Although leakance will increase with stream width, a very wide stream will not necessarily be well represented by a model of a fully penetrating stream. The impact of lateral boundaries depends upon the distance from the pumping well to the stream and the stream leakance parameter. In most cases, aquifer width must be on the order of hundreds of stream widths before the assumption of a laterally infinite aquifer is appropriate for stream-depletion calculations. An important assumption underlying this solution is that stream-channel penetration is negligible relative to aquifer thickness. However, an approximate extension to the case of nonnegligible penetration provides reasonable results for the range of relative penetrations found in most natural systems (up to 85%). Since this solution allows consideration of a much wider range of conditions than existing analytical approaches, it could prove to be a valuable new tool for water management design and water rights adjudication purposes.     

Stream-aquifer interactions: evaluation of depletion volume and residual effects from ground water pumping

Numerical modeling techniques were used to simulate stream-aquifer interactions from seasonal ground water pumping. We used stream-aquifer models in which a shallow stream penetrates the top of an aquifer that discharges ground water to the stream as base flow. Because of the pumping, the volume of base flow discharged to the stream was reduced, and as the pumping continued, infiltration from the stream to the aquifer was induced. Both base-flow reduction and stream infiltration contributed to total stream depletion. We analyzed the depletion rates and volumes of the reduced base flow and induced stream infiltration during pumping and postpumping periods. Our results suggested that for a shallow penetrating stream with a low streambed conductance, base-flow reduction accounts for a significant percentage of the total stream depletion. Its residual effects in postpumping can last very long and may continue into the next pumping season for areas where recharge is nominal. In contrast, the contribution of the induced stream infiltration to the total stream depletion is much smaller, and its effects often become negligible shortly after pumping was stopped. For areas where surface recharge replenishes the aquifer, the residual effects of base-flow reduction and thus its depletion volume will be significantly reduced. A stream of large conductance has a high hydraulic connection to the aquifer, but the relationship between stream conductance and stream depletion is not linear.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

Semianalytical solutions for stream depletion in partially penetrating streams

In the analysis of streamflow depletion, the Hunt (1999) solution has an important advantage because it considers a partially penetrating stream. By extending the Hunt drawdown solution, this paper presents semianalytical solutions for gaining streams that evaluate the induced stream infiltration and base flow reduction separately. Simulation results show that for a given deltah (the initial hydraulic head difference between stream and aquifer beneath the channel), the base flow reduction is in direct proportion to the product of streambed leakage (lambda) and the distance between pumping well and stream (L), and the induced stream infiltration is in inverse proportion to lambdaL. Deltah has a significant effect on the ratio of stream infiltration to base flow reduction. The results from the semianalytical solutions agree well with those from MODFLOW simulations. The semianalytical solutions are useful in the verification of numerical simulations and in the analysis of stream-aquifer interactions where water quantity or quality is concerned.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Modified Theis equation by considering the bending effect of the confining unit

The Theis equation has been widely used to study the transient movement of groundwater as a result of pumping in a confined aquifer. It is well known that the observed drawdown at early times has an obvious departure from the theoretical drawdown based on the Theis equation. The Theis equation was derived under the assumption that total stress in the aquifer was constant and the mechanical behavior of the confining unit was neglected. However, most geological formations, especially those which are well consolidated, have rigidity and therefore may bend like a plate to a certain extent. The increase in the effective stress in the aquifer due to pumping may not contribute entirely to the compression of the aquifer, but may be partially cancelled out by bending of the overlying aquitard. This means only a part of the total stress is used to compact the aquifer, or the aquifer cannot produce as much water as estimated from the Theis equation. This paper investigated the impact of the bending effect of the confining unit on drawdown. An analytical model which couples flow in the aquifer and bending of the confining unit was presented. The theory is based on elastic plates and solutions were given to the drawdown of groundwater level and deflection of the overlying formation. The drawdown estimated from the new equation was compared with that from the Theis equation. It can be concluded that drawdown from the Theis equation is less than the drawdown predicted by including the bending effect of the confining unit. Both a hypothetical example and a field pumping test in Shandong Province, China, were used to demonstrate the bending effect of the confining unit in the analysis of pumping test data. This paper demonstrated that the initial disagreement between observed drawdown and the Theis solution could be caused by the bending effect of the confining unit, a phenomenon not well addressed in traditional pumping test analysis. A quantitative understanding of this phenomenon can provide improved guidelines for analyzing drawdown data in a confined aquifer.     

Monitoring of drawdown pattern during pumping in an unconfined physical aquifer model

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.     

Migration of induced-infiltrated stream water into nearby aquifers due to seasonal ground water withdrawal

Analysis of stream-aquifer interaction due to ground water extraction has traditionally focused on the determination of the amount of water depleted in the stream. Less attention has been paid to the movement of infiltrated stream water inside aquifer, particularly for agricultural areas. This paper presents a method of using particle-tracking techniques to evaluate the transport of the leaked stream water in the nearby aquifers. Simple stream-aquifer conditions are used to demonstrate the usefulness of the analysis. Travel times, pathlines, and influence zones of stream water were determined between a stream and nearby pumping wells for seasonal ground water extraction areas. When water quantity is a concern, the analyses provide additional information about stream depletion; when water quality is an issue, they offer information for wellhead protection. Analyses were conducted for transient conditions, and both pumping and nonpumping periods were considered. According to the results from the simulation examples, migration of infiltrated stream water into the nearby aquifers is generally slow and most infiltrated stream water does not arrive at the pumping well at the end of a 90-day irrigation season. Infiltrated stream water may remain in the aquifer for several years before arriving at the pumping well. For aquifers with a regional hydraulic gradient toward streams, part of the infiltrated stream water may discharge back to streams during a recovery period.     

Radial groundwater flow to a finite diameter well in a leaky confined aquifer with a finite‐thickness skin

A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Pumping induced depletion from two streams

We have proved that the Hantush’s model [Hantush MS. Wells near streams with semipervious beds. J Geophys Res 1965;70:2829–38] in a half-domain can be extended to a whole-domain and becomes identical to that of Hunt [Hunt B. Unsteady stream depletion from ground water pumping. Ground Water 1999;37(1):98–102] for a shallow and infinitely narrow stream, provided that the Dupuit assumption is adopted. This proof helps correct a false concept that regards the Hantush’s model as less useful because of its fully penetrating stream assumption. This study deals with interaction of an aquifer with two parallel streams based on the Hantush’s model. Semi-analytical solutions are obtained based on rigorous mass conservation requirement by maintaining continuity of flux and head along the aquifer–streambed boundaries. This study shows that the hydraulic conductivity ratio of the two streambeds appears to be the most important factor controlling the stream–aquifer interaction, followed by a less important role played by the thickness ratio of the two streambeds. When the low-permeability streambeds do not exist, the steady-state stream depletion from one stream is linearly proportional to the ratio of the shortest distance from the pumping well to the other stream over the shortest distance between the two streams. When the low-permeability streambeds are presented, similar conclusion can be drawn except that the stream depletion now also strongly depends on the hydraulic conductivity ratio of the two streambeds. When the values of the hydraulic conductivity of the two streambeds are different by an order of magnitude, the location of the pumping well that receives equal flux from two streams can be off the middle-line between the two streams by nearly 90%.     

Stream depletion by a pumping well including the effects of nonlinear variation of captured evaporation from a phreatic aquifer / Vidange en cours d’eau par puits de pompage incluant les effets de la variation non-linéaire de l’évaporation capturée d’une nappe à surface libre

Abstract

Abstract A study was made to develop a model that can be used to predict the steady-state stream depletion rates caused by a continuous pumping well located in a water table aquifer. The effects of nonlinear variation of evaporation with the depth to water table on steady-state stream depletion rate were investigated using model results. Dimensional analysis was used to determine the relationship between the scaled steady-state stream depletion, the scaled pumping distance, the scaled hydraulic conductivity, and the scaled initial depth to the water table. A dimensionless graph was developed for a wide range of these parameters. Analysis of this graph showed that the steady-state stream depletion rate decreases as the pumping distance between the well and the stream increases. The dimensionless graph also showed that steady-state stream depletion rates strongly depended on the initial position of the water table. Analysis indicated that, as the saturated conductivity increased, the effect of the initial position of the water table on the magnitude of stream depletion rate was more influential. Analysis also showed that, as the value of saturated conductivity decreased, the relative error produced by the assumption that at steady state all the pumped water is captured from the evaporation, also decreased.     

Flow depletion in a small stream caused by ground water abstraction from wells

The interaction between a gaining stream and a water-table aquifer is studied at an outwash plain. The aquifer is hydraulically well connected to the stream. Pumping tests were carried out in 1997 and 1998 in two wells 60 m from the stream, screening different depths of the aquifer. Drawdown was measured on both sides of the stream. Hydraulic head, drawdown, and stream depletion data were analyzed using numerical flow models. Similar models were fitted to each of two different data sets: Model A was fitted to steady-state hydraulic head and streamflow gain data not influenced by pumping; and model B was fitted to drawdown data measured during the 1998 pumping test. Each calibrated model closely fits its calibration data; however, predictions were biased if model A was used to predict the calibration data of model B, and vice versa. To further test the models, they were used to predict streamflow depletion during the two pumping tests as well as the drawdown during the 1997 test. Neither of these data were used for calibration. Model A predicted the measured depletions fairly accurately during both tests, whereas the predicted drawdowns in 1997 were significantly larger than actually measured. Contrary to this, the 1997 drawdowns predicted by model B were nearly unbiased; the predicted depletions deviate significantly from the measured depletions in 1997, but they compare well with the observations in 1998. Thus, although field work and analyses were extensive and done carefully to develop a ground water flow model that could predict both drawdown and streamflow depletion, the model predictions are biased. Analyses indicate that the deviations between model and data may be because of error in the models' representations of either the release of water from storage or of the hydrology in the riparian zone.     

Modeling Stream-Aquifer Interactions Under Seasonal Groundwater Pumping and Managed Aquifer Recharge

In South Korea, a significant amount of groundwater is used for the heating of water-curtain insulated greenhouses during the winter dry season, which had led to problems of groundwater depletion. A managed aquifer recharge (MAR) project is currently underway with the goal of preventing such groundwater depletion in a typical cultivation area, located on an alluvial aquifer near the Nam River. In the present study, FEFLOW, a three-dimensional finite element model, was used to evaluate different strategies for MAR of the cultivation areas. A conceptual model was developed to simulate the stream-aquifer dynamics under the influence of seasonal groundwater pumping and MAR. The optimal rates and duration of MAR were assessed by analyzing the recovery of the groundwater levels and the change in the groundwater temperature. The simulation results indicate that a MAR rate of 8000 m³/d effectively restores the groundwater level when the injection wells are located inside the groundwater depletion area. It is also demonstrated that starting the MAR before the beginning of the seasonal pumping is more effective. Riverbank filtration is preferable for securing the injection water owing to plentiful source of induced recharge from the river. Locating the pumping wells adjacent to the river where there are thick permeable layers could be a good strategy for minimizing decreases in the groundwater level and temperature.     

Propagation of seasonal temperature signals into an aquifer upon bank infiltration

Infiltrating river water carries the temperature signal of the river into the adjacent aquifer. While the diurnal temperature fluctuations are strongly dampened, the seasonal fluctuations are much less attenuated and can be followed into the aquifer over longer distances. In one-dimensional model with uniform properties, this signal is propagated with a retarded velocity, and its amplitude decreases exponentially with distance. Therefore, time shifts in seasonal temperature signals between rivers and groundwater observation points may be used to estimate infiltration rates and near-river groundwater velocities. As demonstrated in this study, however, the interpretation is nonunique under realistic conditions. We analyze a synthetic test case of a two-dimensional cross section perpendicular to a losing stream, accounting for multi-dimensional flow due to a partially penetrating channel, convective-conductive heat transport within the aquifer, and heat exchange with the underlying aquitard and the land surface. We compare different conceptual simplifications of the domain in order to elaborate on the importance of different system elements. We find that temperature propagation within the shallow aquifer can be highly influenced by conduction through the unsaturated zone and into the underlying aquitard. In contrast, regional groundwater recharge has no major effect on the simulated results. In our setup, multi-dimensionality of the flow field is important only close to the river. We conclude that over-simplistic analytical models can introduce substantial errors if vertical heat exchange at the aquifer boundaries is not accounted for. This has to be considered when using seasonal temperature fluctuations as a natural tracer for bank infiltration.     

Hydrologic trade-offs in conjunctive use management

An aquifer, in a stream/aquifer system, acts as a storage reservoir for groundwater. Groundwater pumping creates stream depletion that recharges the aquifer. As wells in the aquifer are moved away from the stream, the aquifer acts to filter out annual fluctuations in pumping; with distance the stream depletion tends to become equal to the total pumping averaged as an annual rate, with only a small fluctuation. This is true for both a single well and an ensemble of wells. A typical growing season in much of the western United States is 3 to 4 months. An ensemble of irrigation wells spread more or less uniformly across an aquifer several miles wide, pumping during the growing season, will deplete the stream by approximately one-third of the total amount of water pumped during the growing season. The remaining two-thirds of stream depletion occurs outside the growing season. Furthermore, it takes more than a decade of pumping for an ensemble of wells to reach a steady-state condition in which the impact on the stream is the same in succeeding years. After a decade or more of pumping, the depletion is nearly constant through the year, with only a small seasonal fluctuation: ±10%. Conversely, stream depletion following shutting down the pumping from an ensemble of wells takes more than a decade to fully recover from the prior pumping. Effectively managing a conjunctive groundwater and surface water system requires integrating the entire system into a single management institution with a long-term outlook.     

Non-Darcian flow to a well in an aquifer–aquitard system

In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity k_D results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter B_D results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered.     

Adjoint simulation of stream depletion due to aquifer pumping

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.