Boundary condition effects on maximum groundwater withdrawal in coastal aquifers

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

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.     

Constraints on hydraulic parameters and implications for groundwater flux across the upland–estuary interface

Analyses of independent laboratory- and field-scale measurements from two sites on Sapelo Island, Georgia reveal heterogeneity in hydraulic parameters across the upland–estuary interface. Regardless of the method used (short-duration pumping tests, amplitude attenuation of tidal pumping data, sediment grain size distributions, and falling head permeameter tests), we obtain hydraulic conductivity of 10⁻⁴ m s⁻¹ for the fine-grained, well-sorted, clean sands that make up the upland areas. Proximal to the upland–estuary boundary, the tidal pumping analyses and permeameter tests suggest that hydraulic conductivities decrease by more than two orders of magnitude, a result consistent with the presence of a clogging layer. Such a clogging layer may arise due to a variety of physical, chemical, or biological processes. The extent and orientation of the layers of reduced hydraulic conductivity near the upland–estuary boundary influence the nature of the aquifer's response to tidal forcing. Where the lower conductivity layer forms a relatively flat creek bank, tidal pumping produces a primarily mechanical response in the adjacent aquifer. Where the creek bank is nearly vertical, there is a more direct hydraulic connection between the tidal creek and the adjacent aquifer. The clogging layer likely contributes to the development of complicated flow pathways across the upland–estuary boundary. Effective flow paths calculated from tidal pumping data terminate within the marsh, beyond the boundary of the upland aquifer, suggesting a diffuse regime of groundwater discharge in the marsh. We postulate that, in many settings, submarsh flow may be as important as seepage faces for groundwater discharge into the marsh–estuary complex.     

A new method to characterize hydraulic short-circuits in defective borehole seals

A new approach has been developed to detect, characterize, and quantify hydraulic short-circuits in boreholes with faulty seals. The methodology, applicable to an aquifer-aquitard-aquifer system, involves a series of successive, constant-rate pumping tests in the lower aquifer while determining the leakage rate with a simultaneous nonreactive tracer test. During each pumping step, the tracer is injected under constant concentration and constant hydraulic head from a piezometer in the upper aquifer. If a seal defect exists, the tracer will follow the leak and will be recovered from the pumped water. The theoretical equations relate the leakage rate, the pumping rate, the concentration of the injected tracer, and the recovered concentration. Leakage rates can be determined for any pumping rate. The theory is tested using numerical analysis and a full-scale field test.     

Small‐Scale ASR Between Flow Barriers in a Saline Aquifer

Regular aquifer storage recovery, ASR, is often not feasible for small‐scale storage in brackish or saline aquifers because fresh water floats to the top of the aquifer where it is unrecoverable. Flow barriers that partially penetrate a brackish or saline aquifer prevent a stored volume of fresh water from expanding sideways, thus increasing the recovery efficiency. In this paper, the groundwater flow and mixing is studied during injection, storage, and recovery of fresh water in a brackish or saline aquifer in a flow‐tank experiment and by numerical modeling to investigate the effect of density difference, hydraulic conductivity, pumping rate, cyclic operation, and flow barrier settings. Two injection and recovery methods are investigated: constant flux and constant head. Fresh water recovery rates on the order of 65% in the first cycle climbing to as much as 90% in the following cycles were achievable for the studied configurations with constant flux whereas the recovery efficiency was somewhat lower for constant head. The spatial variation in flow velocity over the width of the storage zone influences the recovery efficiency, because it induces leakage of fresh water underneath the barriers during injection and upconing of salt water during recovery.     

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.     

On Simulation and Analysis of Variable‐Rate Pumping Tests

Analytical solutions for constant‐rate pumping tests are widely used to infer aquifer properties. In this note, we implement a methodology that approximates the time‐varying pumping record as a series of segments with linearly varying pumping rates. We validate our approach using an analytical solution for a sinusoidally varying pumping test. We also apply our methodology to analyze synthetic test data and compare the results with those from a commonly used method where rate variations are represented by a series of constant‐rate steps.     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

The Effects of Fault-Zone Cementation on Groundwater Flow at the Field Scale

Fault zones are an important control on fluid flow, affecting groundwater supply, contaminant migration, and carbon storage. However, most models of fault seal do not consider fault zone cementation, despite the recognition that it is common and can dramatically reduce permeability. In order to study the field-scale hydrogeologic effects of fault zone cementation, we conducted a series of aquifer pumping tests in wells installed within tens of meters of the variably cemented Loma Blanca Fault, a normal fault in the Rio Grande Rift. In the southern half of the study area, the fault zone is cemented by calcite; the cemented zone is 2-8 m wide. In the center of the study area, the cemented fault zone is truncated at a buttress unconformity that laterally separates hydrostratigraphic units with a ∼40X difference in permeability. The fault zone north of the unconformity is not cemented. Constant rate pumping tests indicate that where the fault is cemented, it is a barrier to groundwater flow. This is an important demonstration that a fault with no clay in its core and similar sediment on both sides can be a barrier to groundwater flow by virtue of its cementation; most conceptual models for the hydrogeology of faults would predict that it would not be a barrier to groundwater flow. Additionally, the lateral permeability heterogeneity across the unconformity imposes another important control on the local flow field. This permeability discontinuity acts as either a no-flow boundary or a constant head boundary, depending on the location of pumping.     

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

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

Analytical and Semi‐Analytical Tools for the Design of Oscillatory Pumping Tests

Oscillatory pumping tests—in which flow is varied in a periodic fashion—provide a method for understanding aquifer heterogeneity that is complementary to strategies such as slug testing and constant‐rate pumping tests. During oscillatory testing, pressure data collected at non‐pumping wells can be processed to extract metrics, such as signal amplitude and phase lag, from a time series. These metrics are robust against common sensor problems (including drift and noise) and have been shown to provide information about aquifer heterogeneity. Field implementations of oscillatory pumping tests for characterization, however, are not common and thus there are few guidelines for their design and implementation. Here, we use available analytical solutions from the literature to develop design guidelines for oscillatory pumping tests, while considering practical field constraints. We present two key analytical results for design and analysis of oscillatory pumping tests. First, we provide methods for choosing testing frequencies and flow rates which maximize the signal amplitude that can be expected at a distance from an oscillating pumping well, given design constraints such as maximum/minimum oscillator frequency and maximum volume cycled. Preliminary data from field testing helps to validate the methodology. Second, we develop a semi‐analytical method for computing the sensitivity of oscillatory signals to spatially distributed aquifer flow parameters. This method can be quickly applied to understand the “sensed” extent of an aquifer at a given testing frequency. Both results can be applied given only bulk aquifer parameter estimates, and can help to optimize design of oscillatory pumping test campaigns.     

Assessing Lakebed Hydraulic Conductivity and Seepage Flux by Potentiomanometer

Potentiomanometers (PMs) are commonly used to determine flux directions across interfaces between surface waters and aquifers. We describe a complementary function: estimating small‐scale hydraulic conductivity (K) in a lakebed, using the constant‐head injection test (CHIT) by Cardenas and Zlotnik (2003) with the PM designed by Winter et al. (1988). A piezometer with a small screen is inserted into the lakebed. Local head potential is obtained by measuring the head difference between the test point and the aquifer interface. The piezometer is then used for water injection. This technique is illustrated by measurements taken from Alkali Lake in the Sand Hills, Nebraska, United States. Lakebed K and seepage fluxes ranged from 0.037 to 0.090 m/d and Darcy velocities ranged from 0.004 to 0.027 m/d. Results were consistent with the supplementary data gathered using a modified CHIT and a cone penetrometer. The compact size of the device and the small volumes used for injection enable this method to estimate lakebed K values as low as 0.01 to 0.1 m/d, a range seldom explored in lake‐aquifer interface systems.     

Obtaining the steady‐state drawdown solutions of constant‐head and constant‐flux tests

The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Maximizing Net Extraction Using an Injection‐Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection‐extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation‐point locations and recirculation ratio, assuming steady‐state, sharp‐interface conditions. The injection‐extraction well‐pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m²/d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well‐pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.     

Field Demonstration of Permeable Wall Flushing for Biostimulation of a Shallow Sandy Aquifer

A pilot-scale nutrient injection will (NIW) (4 m by 4 m by 1 m) was installed in the Borden Aquifer lo serve as a pulsed injection source of a potassium acetate solution for the stimulation of anaerobic microbial activity. The success of the flushing procedure was evaluated by monitoring the breakthrough of the acetate solution at several multilevel piezometers installed in the wall. Although some variation in the ground water velocity was observed with depth, the wall was flushed with reasonable uniformity after about six hours of injection and withdrawal, representing about one pore volume, Calculations bused on head level data collected during the flush, and on the solute breakthrough curves, indicated that about 90% of the flow induced by the pumping and injecting was confined to the permeable wall. These results show that a permeable wall injection system is a viable method of introducing solutes uniformly to a cross section of aquifer, with minimal perturbation of the natural flow system. In addition lo its importance for the biostimulation system tested in this project the flushing of permeable walls may have applications in other semi-passive remedial systems, such as the rejuvenation of reactive barriers.     

A Simplified Solution Using Izbash's Equation for Non-Darcian Flow in a Constant Rate Pumping Test

This paper derives an equivalent of Darcian Theis solution for non-Darcian flow induced by constant rate pumping of a well in a confined aquifer. The derivation, which is valid at later times only, is original. It utilizes Izbash's equation. This introduces an additional parameter to Darcian condition, namely, empirical exponent. The solution is a non-Drcian equivalent of Jacob straight line method for analyzing pumping tests at late times. It can be used to determine aquifer parameters: storativity, analogous hydraulic conductivity, and empirical exponent. However, while the Jacob method requires a minimum of only one pumping test with one observation well, the additional parameter in the present solution means that a minimum of two observation wells in one test or two pumping tests at different rates with one observation well are required. The derived solution is applied to a case study at Plomeur in Brittany, France, and is shown to provide a practical and efficient method for analyzing pumping tests where non-Darcian groundwater flow occurs.     

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.     

Analysis of continuous and pulsed pumping of a phreatic aquifer

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

Three-Dimensional Numerical Investigation of Pore Water Pressure and Deformation of Pumped Aquifer Systems

Excessive groundwater withdrawal has caused severe land subsidence worldwide. The pore water pressure and the deformation of pumped hydrostratigraphic units are complex. A fully coupled three-dimensional numerical simulation was carried out for different pumping plans in this paper. When groundwater is pumped from a confined aquifer, the great compaction occurs in the pumped aquifer and its upper and lower adjacent aquitard units. Land subsidence is smaller and the area affected by land subsidence is greater when groundwater is pumped from the deeper confined aquifer. The pore water pressure in the pumped confined aquifer changes immediately with pumpage. In the adjacent aquitard units, however, the pore water pressure increases in the early pumping time and decreases in the early recharging time. The decrease in the pore water pressure vertically spreads from the interface between aquitard and pumped aquifer to the other surface of the aquitard. The pumped aquifer compacts and rebounds immediately with pumping and non-pumping or recharging actions, while the compaction and rebounding of the aquitard units clearly lag behind. The compaction of the adjacent aquitard unit first occurs near the interface between aquitard and pumped aquifer units, and the compaction zone spreads outward as the pumping goes on. The aquitards may expand vertically within some zones. Due to the inelastic deformation of soil skeleton, different pumping plans result in different land subsidence. For the same net pumpage, maximal land subsidence and horizontal displacement are the smallest for constant discharge and the greatest for recharge-discharge cycle.