Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Seepage face height, water table position, and well efficiency at steady state

When a fully penetrating well pumps an ideal unconfined aquifer at steady state, the water table usually does not join the water level in the well. There is a seepage face inside the well, which is a key element in evaluating the well performance. This problem is analyzed using the finite-element method, solving the complete equations for saturated and unsaturated flow. The seepage face position is found to be almost independent of the unsaturated zone properties. The numerical results are used to test the validity of several analytic approximations. Equations are proposed to predict the seepage face position at the pumping well for any well drawdown, and the water table position at any distance from the pumping well for any in-well drawdown. Practical hints are provided for installing monitoring wells and evaluating well efficiency.     

Transient analysis of the source of water to wells: Cape Cod, Massachusetts

A transient flow modeling analysis for potential public-supply wells on western Cape Cod, Massachusetts, demonstrates the difference between transient and steady-state recharge areas can have important implications for wellhead protection. An example of a single pumping well illustrates that commonly used steady-state time-related capture areas do not represent the recharge area and travel times of water being pumped from the well until sufficient time has elapsed for steady-state flow conditions to be established. Until that time, transient recharge areas are needed to account for the portion of water discharging from the well that entered the aquifer before pumping started. An example of two pumping wells demonstrates the same area at the water table cannot supply water to more than one well under steady-state flow conditions. Transient recharge areas to multiple wells can overlap, however, until steady-state flow conditions are established. The same area can, therefore, be a source of water to more than one well during early pumping times, and the water pumped from a given well may derive from source areas, including contaminated areas, that do not lie within the well's steady-state recharge area.     

AQUIFER TEST AT A SITE ON THE MULLICA RIVER IN THE WHARTON TRACT,SOUTHERN NEW JERSEY

Abstract

A pumping test was conducted along the Mullica River in the Wharton Tract, New Jersey as part of a water-resources investigation. Impermeable bog iron caps parts of the flood plain and channel so that ground-water recharge moves directly into the river.

Observation wells on both sides of the river tapped water-bearing zones at 25 (shallow), 50 (medium), and 100 (deep) feet. A pumping well, screened in the medium zone, caused abrupt drawdowns which leveled off after a few minutes. Shape of the drawdown cone established early and changed little throughout the test. Piezometric surfaces were steepest on the southwest, indicating that most water came from there. Uninterrupted contour trends beneath the river show that here relatively little water entered the aquifer. Head differentials between the zones were greatest at the pumping well. Movement from the deep to medium zones was confined largely to the pumping-well vicinity. Pumping produced extensive reductions in the original areas of upward gradient between the medium and shallow zones; thus, areas of downward leakage became connected across the river. Piezometric head beneath the river was progressively lowered and caused the flood plain to dry; it became wet again when pumping stopped. The well field recovered to natural conditions in about 24 hours.

Lack of hydraulic continuity between the river and aquifer results from bog iron deposits. Their removal will improve the continuity, and it appears feasible to induce river recharge to nearby pumping wells.     

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.     

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.     

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.     

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.     

Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model

The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of K_sat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones).     

A method for evaluating horizontal well pumping tests

Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error.     

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.     

Empirical relationships for estimating stream depletion by a well pumping near a gaining stream

Siting wells near streams requires an accurate estimate of the quantity of water derived from the river due to pumping. A number of hydrogeological and hydraulic parameters influence this value. This study estimates stream depletion under steady-state conditions for a variety of hydrogeological systems. A finite differences model was used to analyze several hydrogeological situations, and for each of these the stream depletion was estimated using an advective transport method. An empirical equation for stream depletion was obtained for the case of a stream that partially penetrates the aquifer and a pumping well that is screened over a portion of the aquifer. The derived equation, which is valid for both isotropic and anisotropic conditions, expresses stream depletion as a function of the unit inflow to the river, the discharge of the pumping well, the well screen length, the distance between the river and pumping well, the wetted perimeter, and a new parameter called "overlap," which is defined to be the distance between the riverbed and the top of well screen. The overlap parameter makes it possible to consider indirectly the vertical component of flow, which is accentuated when the well is screened below the streambed. The formula proposed here should be useful in deciding where to locate a pumping well and to decide the appropriate length of its screen.     

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.     

Ground water flow in a desert basin: challenges of simulating transport of dissolved chromium

A large chromium plume that evolved from chromium releases in a valley near the Mojave River was studied to understand the processes controlling fate and migration of chromium in ground water and used as a tracer to study the dynamics of a basin and range ground water system. The valley that was studied is naturally arid with high evapotranspiration such that essentially no precipitation infiltrates to the water table. The dominant natural hydrogeologic processes are recharge to the ground water system from the Mojave River during the infrequent episodes when there is flow in the river, and ground water flow toward a playa lake where the ground water evaporates. Agricultural pumping in the valley from the mid-1930s to the 1970s significantly altered ground water flow conditions by decreasing water levels in the valley by more than 20 m. This pumping declined significantly as a result of dewatering of the aquifer, and water levels have since recovered modestly. The ground water system was modeled using MODFLOW, and chromium transport was simulated using MT3D. Several innovative modifications were made to these modeling programs to simulate important processes in this ground water system. Modifications to MODFLOW include developing a new well package that estimates pumping rates from irrigation wells at each time step based on available drawdown. MT3D was modified to account for mass trapped above the water table when the water table declines beneath nonirrigated areas and to redistribute mass to the system when water levels rise.     

Impacts of Seasonal Pumping on Stream‐Aquifer Interactions in Miryang,Korea

Large agricultural fields in South Korea are located mostly on alluvial plains, where a significant amount of groundwater is used for heating of water‐curtain insulated greenhouses. Such greenhouses are commonly used for crop cultivation during the winter dry season from November to March. After use the groundwater is discharged directly into streams, causing groundwater depletion. A hydrogeological study was carried out in a typical agricultural area of this type, located on an alluvial aquifer near the Nakdong River. Groundwater levels, chemical characteristics, and temperatures from 68 observation wells were analyzed to determine the impacts of seasonal groundwater pumping on the groundwater system and stream‐aquifer interactions. Our results show that the groundwater system has not yet reached a state of dynamic equilibrium. Decades of excessive seasonal pumping have caused a gradual decline of groundwater levels, leading to groundwater depletion, especially in areas further from the river. Seasonal pumping has also significantly affected groundwater quality in the aquifer near the river. Groundwater temperature is decreasing (in this case a disadvantage), and saline groundwater is being diluted by induced recharge. The results of this study provide a basic outline for effective integrated water management that is widely applicable in South Korea.     

Stream depletion in alluvial valleys using the SDF semianalytical model

A semianalytical method commonly used for quantifying stream depletion caused by ground water pumping was reviewed for applicability in narrow alluvial aquifers. This stream depletion factor (SDF) method is based on the analytic Glover model, but uses a numerical model-derived input parameter, called the SDF, to partly account for mathematically nonideal conditions such as variable transmissivity and nearby aquifer boundaries. Using the SDF can improve and simplify depletion estimates. However, the method's approximations introduce error that increases with proximity to the impermeable aquifer boundary. This article reviews the history of the method and its assumptions. New stream depletion response curves are presented as functions of well position within bounded aquifers. A simple modification to modeled SDF values is proposed that allows the impermeable boundary to be accounted for with image wells, but without overaccounting for boundary effects that are already reflected in modeled SDFs. It is shown that SDFs for locations closer to the river than to the aquifer boundary do not reflect impermeable-boundary effects, and thus need no modification, and boundary effects in the other portion of the aquifer follow a predictable removable pattern. This method is verified by comparing response curves using modified SDFs with response curves from an extensively calibrated numerical model of a managed ground water recharge site. The modification improves SDF-based stream depletion estimates in bounded aquifers while still benefiting from the additional information contained in SDF maps and retaining their value as standardized references for water rights administration.     

Influence of a thin veneer of low‐hydraulic‐conductivity sediment on modelled exchange between river water and groundwater in response to induced infiltration

A thin layer of fine‐grained sediment commonly is deposited at the sediment–water interface of streams and rivers during low‐flow conditions, and may hinder exchange at the sediment–water interface similar to that observed at many riverbank‐filtration (RBF) sites. Results from a numerical groundwater‐flow model indicate that a low‐permeability veneer reduces the contribution of river water to a pumping well in a riparian aquifer to various degrees, depending on simulated hydraulic gradients, hydrogeological properties, and pumping conditions. Seepage of river water is reduced by 5–10% when a 2‐cm thick, low‐permeability veneer is present on the bed surface. Increasing thickness of the low‐permeability layer to 0·1 m has little effect on distribution of seepage or percentage contribution from the river to the pumping well. A three‐orders‐of‐magnitude reduction in hydraulic conductivity of the veneer is required to reduce seepage from the river to the extent typically associated with clogging at RBF sites. This degree of reduction is much larger than field‐measured values that were on the order of a factor of 20–25. Over 90% of seepage occurs within 12 m of the shoreline closest to the pumping well for most simulations. Virtually no seepage occurs through the thalweg near the shoreline opposite the pumping well, although no low‐permeability sediment was simulated for the thalweg. These results are relevant to natural settings that favour formation of a substantial, low‐permeability sediment veneer, as well as central‐pivot irrigation systems, and municipal water supplies where river seepage is induced via pumping wells. Published in 2011 by John Wiley & Sons, Ltd.     

Atrazine in a Stream-Aquifer System: Estimation of Aquifer Properties from Atrazine Concentration Profiles

Lincolns municipal wellfield consists of 44 wells developed in an alluvial aquifer adjacent to the Platte River near Ashland, Nebraska Induced recharge from the river is the primary source of water for the wellfield. Wafer samples were collected on a periodic basis from the Platte River arid two transects of monitoring wells. These samples were analyzed for the herbicide atrazine, which was used as a tracer of induced recharge in this stream-aquifer system. Atrazine concentrations in the river and aquifer were much less than 1.0 ppb during late fall and winter, but increased to as high as 18.9 ppb during spring and summer, associated with runoff from upgradient agricultural lands. There was approximately a 21-day lag time from the first detection of increasing atrazine concentration in the river to the first detection in monitoring wells immediately adjacent to the river. This lag time was relatively constant throughout the year and from one year to the next, even with major fluctuations of river stage and wellfield production. This consistency of lag time indicated that the travel times from the river to the first set of monitoring wells immediately adjacent to the river were fairly constant.
Paths of preferential flow were identified in the aquifer at a depth of 25 to 35 feet below land surface. This aquifer zone appeared to play a significant role in movement of water from beneath the river into the wellfield.
Aquifer dispersivity was calculated using a method described by Hoehn and Santschi (1987). Macrodispersivity (A_L) was shown to increase linearly over the scale of the wellfield. Calculated values of A_L were within limits of other reported values for this type of aquifer material and agreed well with values reported by Hoehn and Santschi (1987); These findings will be extremely beneficial for planning and management of the municipal wellfield.     

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer’s permeability (semi-permeable and impermeable), of the boundary condition at the aquifer’s submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.