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.     

Concentration Profiles in Screened Wells under Static and Pumped Conditions

Purge and pump samples from screened wells reflect concentration averaging and contaminant redistribution by wellbore flow. These issues were assessed in a screened well at the Hanford Site by investigating the vertical profile of a technetium-99 plume in a conventional well under static and pumped conditions. Specific conductance and technetium-99 concentrations were well correlated, and this enabled measurement of specific conductance to be used as a surrogate for technetium-99 concentration. Time-series measurements were collected during purging from three specific conductance probes installed in the well at 1.2, 3.1, and 4.9 m below the static water level in a 7.7-m-deep screened well. The vertical contaminant profile adjacent to the well in the aquifer was calculated using the concentration profile in the well during pumping, the pumping flow rate, and a wellbore flow and mixing model. The plume was found to be stratified in the aquifer—the highest concentrations occurred adjacent to the upper part of the screened interval. The purge and pump sample concentrations were 41% to 58% of the calculated peak concentration in the aquifer. Plume stratification in the aquifer adjacent to the well screen became more pronounced as pumping continued. Extended pumping may have partially reversed the effect of contaminant redistribution in the aquifer by wellbore flow and allowed the stratification of the plume to be more observable. It was also found that the vertical profile of contamination in the well under static (i.e., nonpumping conditions) was not representative of the profile in the aquifer. Thus, passive or micropurge sampling techniques, which sample the wellbore water at different depths, would not yield results representative of the aquifer in this well.     

A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.     

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.     

Travel-time distribution from a finite line contamination source to an extraction well with regional flow

Advective transport from a finite line contamination source to an extraction well with regional flow depends on interplay of radial and regional flows, a scheme commonly encountered in capture zone delineation. We have investigated travel-time distribution from a finite line contamination source and the associated breakthrough curves (BTCs) observed at an extraction well. The resulting travel-time distribution and BTCs depend on dimensionless source length, dimensionless pumping rate, and inclined angle of the source with respect to the regional flow, where the dimensionless terms are lumped parameters involving source length, pumping rate, distance between the source and the extraction well, aquifer thickness, and regional flow discharge. The observed concentration at the extraction well increases with time in a sub-linear manner. When the source orientation is perpendicular to the regional flow, the dimensionless first arrival time only depends on the dimensionless pumping rate whereas the dimensionless steady-state arrival time depends on both the dimensionless pumping rate and the dimensionless source length. The steady-state concentration at the extraction well is sensitive to the dimensionless source length and the inclined angle of the source with respect to the regional flow, but not sensitive to the dimensionless pumping rate. Two special cases where the extraction well is very close to the source and the regional flow can be negligible have also been discussed.     

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

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

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.     

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.     

Sustainable Capture: Concepts for Managing Stream‐Aquifer Systems

Most surface water bodies (i.e., streams, lakes, etc.) are connected to the groundwater system to some degree so that changes to surface water bodies (either diversions or importations) can change flows in aquifer systems, and pumping from an aquifer can reduce discharge to, or induce additional recharge from streams, springs, and lakes. The timescales of these interactions are often very long (decades), making sustainable management of these systems difficult if relying only on observations of system responses. Instead, management scenarios are often analyzed based on numerical modeling. In this paper we propose a framework and metrics that can be used to relate the Theis concepts of capture to sustainable measures of stream‐aquifer systems. We introduce four concepts: Sustainable Capture Fractions, Sustainable Capture Thresholds, Capture Efficiency, and Sustainable Groundwater Storage that can be used as the basis for developing metrics for sustainable management of stream‐aquifer systems. We demonstrate their utility on a hypothetical stream‐aquifer system where pumping captures both streamflow and discharge to phreatophytes at different amounts based on pumping location. In particular, Capture Efficiency (CE) can be easily understood by both scientists and non‐scientist alike, and readily identifies vulnerabilities to sustainable stream‐aquifer management when its value exceeds 100%.     

Multiple Working Transport Hypotheses in a Heterogeneous Glacial Aquifer System

Multiple working hypotheses can be used to evaluate permissible alternative hydrogeological interpretations at sites with limited subsurface control. This approach was applied to test the viability of three conceptual aquifer system architecture models coupled with three hypothesized source locations for a 1,4-dioxane plume in a heterogeneous glacial aquifer system in Washtenaw County, Michigan. The three alternative conceptual models characterized the site hydrogeology with increasingly complex distributions of hydrostratigraphic units: (A) an effective aquifer, (B) a layered confined aquifer, and (C) a discretely heterogeneous aquifer model. Each was incorporated into an independently calibrated numerical ground water flow (MODFLOW) model. Steady-state and transient flow simulations of the alternative models were evaluated using both hydraulic flow field characteristics observed under natural conditions and the perturbed response after local remedial pumping activity began. Three plausible locations where 1,4-dioxane could have entered the aquifer system were identified using historical information at the site: (1) manufacturing waste water disposal lagoons, (2) a 60 foot (18 m) deep kettle lake, and (3) a shallow impoundment on a local stream. Advective transport modeling (MODPATH) was used to assess the consistency of the hypothesized source locations with observed contaminant migration pathways inferred from the mapped location of the plume. Evaluation of the nine combinations of hydrogeologic conceptualizations and 1,4-dioxane source locations led to elimination of four working hypotheses and discounting of two others, leading to reduced overall uncertainty and the development of new insights into the system behavior.     

Multiscale characterization of a heterogeneous aquifer using an ASR operation

Heterogeneity in the physical properties of an aquifer can significantly affect the viability of aquifer storage and recovery (ASR) by reducing the recoverable proportion of low-salinity water where the ambient ground water is brackish or saline. This study investigated the relationship between knowledge of heterogeneity and predictions of solute transport and recovery efficiency by combining permeability and ASR-based tracer testing with modeling. Multiscale permeability testing of a sandy limestone aquifer at an ASR trial site showed that small-scale core data give lower-bound estimates of aquifer hydraulic conductivity (K), intermediate-scale downhole flowmeter data offer valuable information on variations in K with depth, and large-scale pumping test data provide an integrated measure of the effective K that is useful to constrain ground water models. Chloride breakthrough and thermal profiling data measured during two cycles of ASR showed that the movement of injected water is predominantly within two stratigraphic layers identified from the flowmeter data. The behavior of the injectant was reasonably well simulated with a four-layer numerical model that required minimal calibration. Verification in the second cycle achieved acceptable results given the model's simplicity. Without accounting for the aquifer's layered structure, high precision could be achieved on either piezometer breakthrough or recovered water quality, but not both. This study demonstrates the merit of an integrated approach to characterizing aquifers targeted for ASR.     

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.     

An analytical approach to capture zone delineation for a well near a stream with a leaky layer

Abstract

An analytical solution is developed to delineate the capture zone of a pumping well in an aquifer with a regional flow perpendicular to a stream, assuming a leaky layer between the stream and the aquifer. Three different scenarios are considered for different pumping rates. At low pumping rates, the capture zone boundary will be completely contained in the aquifer. At medium pumping rates, the tip of the capture zone boundary will intrude into the leaky layer. Under these two scenarios, all the pumped water is supplied from the regional groundwater flow in the aquifer. At high pumping rates, however, the capture zone boundary intersects the stream and pumped water is supplied from both the aquifer and the stream. The two critical pumping rates which separate these three scenarios, as well as the proportion of pumped water from the stream and the aquifer, are determined for different hydraulic settings.

Editor D. Koutsoyiannis; Associate editor A. Koussis

Citation Asadi-Aghbolaghi, M., Rakhshandehroo, G.R., and Kompani-Zare, M., 2013. An analytical approach to capture zone delineation for a well near a stream with a leaky layer. Hydrological Sciences Journal, 58 (8), 1813–1823.     

Modeling of Contaminant Movement Near Pumping Wells: Saturated-Unsaturated Flow with Particle Tracking

A transient axisymmetric saturated-unsaturated numerical flow model was coupled with a particle tracking model to investigate the movement of contaminants when a shallow unconfined aquifer is pumped at a constant rate. The particle tracking model keeps track of locations and masses of solutes in the aquifer, and the time of capture by the well. At the end of each time-step the flow model solves the Richard's equation for the hydraulic head distribution from which elemental velocities are calculated. Solutes are then displaced for a period equivalent to the time-step using both the magnitude and direction of the elemental velocities. Numerical experiments were performed to investigate effluent concentrations in wells with screens of different length and in different positions relative to zones of stratified contamination. At early times of pumping the effluent concentrations were similar to the concentrations adjacent to the well screen, but at late times, the concentrations approached the vertically averaged concentration in the aquifer. Time to attain the vertically averaged concentration was determined by the well geometry, initial location of the contaminant plume in relation to the well screen, and hydraulic properties of the aquifer. The results are consistent with the hydraulics of flow to a pumping well and of particular importance, they demonstrate that short-term pump tests could give erroneous design concentrations for pump-and-treat systems. The model provides a means of quantifying arrival times and mixing ratios. It could therefore provide a useful means of designing production wells in aquifers with stratified contamination and more efficient recovery systems for aquifer remediation.     

Temporal Changes in VOC Discharge to Surface Water from a Fractured Rock Aquifer During Well Installation and Operation, Greenville, South Carolina

Analysis of the vapor in passive vapor samplers retrieved from a streambed in fractured rock terrain implied that volatile organic carbon (VOC) discharge from ground water to surface water substantially increased following installation of a contaminant recovery well using air rotary drilling. The air rotary technique forced air into the aquifer near the stream. The injection produced an upward hydraulic gradient that appears to have transported water and contaminants from deeper parts of the aquifer through fractures into shallow parts of the aquifer. Once in the shallow flow regime, the contamination was transported to the stream, where it discharged during the next several weeks following well installation. After the recovery well was activated and began continuously pumping contaminated ground water to a treatment facility, the VOC concentrations in the stream bottom passive vapor samplers decreased to below detectable concentrations, suggesting that the withdrawal had captured the contaminated ground water that previously had discharged to the stream.     

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%.     

Evaluation of water‐use policies for baseflow recovery during droughts in an agricultural intensive karst watershed: Case study of the lower Apalachicola–Chattahoochee–Flint River Basin,southeastern United States

The lower Apalachicola–Chattahoochee–Flint River Basin in the Southeast United States represents a major agricultural area underlain by the highly productive karstic Upper Floridan aquifer (UFA). During El Niño Southern Oscillation‐induced droughts, intense groundwater withdrawal for irrigation lowers streamflow in the Flint River due to its hydraulic connectivity with the UFA and threatens the habitat of the federally listed and endangered aquatic biota. This study assessed the compounding hydrologic effects of increased irrigation pumping during drought years (2010–2012) on stream–aquifer water exchange (stream–aquifer flux) between the Flint River and UFA using the United States Geological Survey modular finite element groundwater flow model. Principal component and K‐means clustering analyses were used to identify critical stream reaches and tributaries that are adversely affected by irrigation pumping. Additionally, the effectiveness of possible water restriction scenarios on stream–aquifer flux was also analysed. Moreover, a cost–benefit analysis of acreage buyout procedure was conducted for various water restriction scenarios. Results indicate that increased groundwater withdrawal in Water Year 2011 decreased baseflow in the lower Apalachicola–Chattahoochee–Flint River Basin, particularly, in Spring Creek, where irrigation pumping during April, June, and July changed the creek condition from a gaining to losing stream. Results from sensitivity analysis and simulated water restrictions suggest that reducing pumping in selected sensitive areas is more effective in streamflow recovery (approximately 78%) than is reducing irrigation intensity by a prescribed percentage of current pumping rates, such as 15% or 30%, throughout the basin. Moreover, analysis of acreage buyout indicates that restrictions on irrigation withdrawal can have significant impacts on stream–aquifer flux in the Basin, especially in critical watersheds such as Spring and Ichawaynochaway Creeks. The proposed procedure for ranking of stream reaches (sensitivity analysis) in this study can be replicated in other study areas/models. This study provides useful information to policymakers for devising alternate irrigation water withdrawal policies during droughts for maintaining flow levels in the study area.     

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.     

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.