Detecting Drawdowns Masked by Environmental Stresses with Water‐Level Models

Detecting and quantifying small drawdown at observation wells distant from the pumping well greatly expands the characterized aquifer volume. However, this detection is often obscured by water level fluctuations such as barometric and tidal effects. A reliable analytical approach for distinguishing drawdown from nonpumping water‐level fluctuations is presented and tested here. Drawdown is distinguished by analytically simulating all pumping and nonpumping water‐level stresses simultaneously during the period of record. Pumping signals are generated with Theis models, where the pumping schedule is translated into water‐level change with the Theis solution. This approach closely matched drawdowns simulated with a complex three‐dimensional, hypothetical model and reasonably estimated drawdowns from an aquifer test conducted in a complex hydrogeologic system. Pumping‐induced changes generated with a numerical model and analytical Theis model agreed (RMS as low as 0.007 m) in cases where pumping signals traveled more than 1 km across confining units and fault structures. Maximum drawdowns of about 0.05 m were analytically estimated from field investigations where environmental fluctuations approached 0.2 m during the analysis period.     

The unusual and large drawdown response of buried-valley aquifers to pumping

The buried-valley aquifers that are common in the glacial deposits of the northern hemisphere are a typical case of the strip aquifers that occur in many parts of the world. Pumping from a narrow strip aquifer leads to much greater drawdown and much more distant drawdown effects then would occur in a sheet aquifer with a similar transmissivity and storage coefficient. Widely used theories for radial flow to wells, such as the Theis equation, are not appropriate for narrow strip aquifers. Previously published theory for flow to wells in semiconfined strip aquifers is reviewed and a practical format of the type curves for pumping-test analysis is described. The drawdown response of strip aquifers to pumping tests is distinctive, especially for observation wells near the pumped well. A case study is presented, based on extensive pumping test experience for the Estevan Valley Aquifer in southern Saskatchewan, Canada. Evaluation of groundwater resources in such buried-valley aquifers needs to take into account the unusually large drawdowns in response to 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.     

An analytical solution for non-Darcian flow in a confined aquifer using the power law function

We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r¹⁻ⁿ, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t^{(1−n)/(3−n)}, where t is the time.     

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.     

Solutions for Non‐Darcian Flow to an Extended Well in Fractured Rock

We have investigated non‐Darcian flow to a vertical fracture represented as an extended well using a linearization procedure and a finite difference method in this study. Approximate analytical solutions have been obtained with and without the consideration of fracture storage based on the linearization procedure. A numerical solution for such a non‐Darcian flow case has also been obtained with a finite difference method. We have compared the numerical solution with the approximate analytical solutions obtained by the linearization method and the Boltzmann transform. The results indicate that the linearized solution agrees generally well with the numerical solution at late times, and underestimates the dimensionless drawdown at early times, no matter if the fracture storage is considered or not. When the fracture storage is excluded, the Boltzmann transform solution overestimates the dimensionless drawdown during the entire pumping period. The dimensionless drawdowns in the fracture with fracture storage for different values of dimensionless non‐Darcian hydraulic conductivity β approach the same asymptotic value at early times. A larger β value results in a smaller dimensionless drawdown in both the fracture and the aquifer when the fracture storage is included. The dimensionless drawdown is approximately proportional to the square root of the dimensionless time at late times.     

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.     

Flow to a well in a five-layer system with application to the Oxnard Basin

Nearly 40 years ago, Neuman (1968) developed an analytical solution for drawdown in a system of three aquifers separated by two aquitards when one of the aquifers is pumped at a constant rate. Whereas the simpler case of two aquifers separated by one aquitard has been presented by Neuman and Witherspoon (1969a), the full five-layer solution has not been previously evaluated. We do so here using numerical inversion of its Laplace-transformed version and present selected results graphically in dimensionless form. The solution demonstrates that the effect of pumping propagates across all five layers, adding emphasis to a question previously raised by Neuman and Witherspoon about the validity of leaky aquifer theories that disregard drawdowns in unpumped aquifers. A large-scale, long-term pumping test spanning three aquifers separated by two aquitards near Oxnard, California, has been conducted and analyzed by Neuman and Witherspoon (1972). They evaluated the vertical hydraulic diffusivities of the aquitards using the Neuman-Witherspoon ratio method and their specific storage values on the basis of laboratory consolidation tests. We reinterpret the Oxnard pumping test by coupling the five-layer analytical solution of Neuman (1968) with the parameter estimation code PEST (Doherty 2002) and validate our results against drawdowns from a subsequent pumping test at the site. Our parameter estimates compare favorably with those of Neuman and Witherspoon (1972).     

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.     

Flowing Well—Time-Domain Solution and Inverse Problem Revisited

Time-domain analytical solution for groundwater flow to a fully penetrating flowing well is derived using the same substitution technique used to re-derive (Perina 2010) the Theis (1935) equation and the approximate solution by Mishra and Guyonnet (1992) is confirmed. The exponential integral-based flowing well function is a computationally effective alternative to the original Jacob and Lohman (1952) solution in integral form. For a constant drawdown test, the ratio of drawdown at an observation well to the flowrate is equivalent to drawdown response to pumping at unit constant rate; the transformed observations can be analyzed using the Theis (1935) function. Analysis of field test shows that simultaneous fitting to measurements of flow from the test well and drawdown at an observation well results in more accurate and better resolved estimates of aquifer properties than fitting to flow observations only.     

Evaluation of Pumping Induced Flow in Observation Wells During Aquifer Testing

The vertical variation of drawdown around pumping wells generates an induced flow in the observation wells. A set of governing equations is presented to couple the drawdown variation and the vertical flux distribution in observation wells. A numerical example is performed to justify the governing equations and to verify the solution methods used by the simulation software WT. The example analyzes the effect of skin loss, wellbore storage, and vertical segmentation on the drawdown and induced flow in observation well during pumping. The evaluation of the Fairborn pumping test involves a vertically homogeneous and anisotropic water table aquifer, uniform well‐face drawdown conditions in the pumping well and simulation of the drawdown evolution in the observation well with and without the effect of induced flow. The computer calibrations resulted in small differences between the measured and simulated drawdown curves.     

Modeling a Large-Scale Historic Aquifer Test: Insight into the Hydrogeology of a Regional Fault Zone

Faults can act as flow barriers or conduits to groundwater flow by introducing heterogeneity in permeability. We examine the hydrogeology of the Sandwich Fault Zone, a 137 km long zone of high-angle faults in northern Illinois, using a large-scale historic aquifer test. The fault zone is poorly understood at depth due to the majority of the faults being buried by glacial deposits and its near-vertical orientation which limits geologic sampling across faults. The aquifer test—perhaps one of the largest in terms of overall withdrawal in North American history—was conducted in 1942 at a facility adjacent to the fault zone. More than 34,000 m³/day was pumped for 37 days from nine multiaquifer wells open to the stratified Cambrian-Ordovician sandstone aquifer system. We modeled the aquifer test using a transient MODFLOW-USG model and simulated pumping wells with the CLN package. We tested numerous fault core/damage zone conceptualizations and calibrated to drawdown values recorded at production and observation wells. Our analysis indicates that the fault zone is a low-permeability feature that inhibits lateral movement of groundwater and that there is at least an order of magnitude decrease in horizontal hydraulic conductivity in the fault core compared to the undeformed sandstone. Large head declines have occurred north of the fault zone (over 300 m since predevelopment conditions) and modifying fault zone parameters significantly affects calibration to regional drawdown on a decadal scale. The flow-barrier behavior of the fault zone has important implications for future groundwater availability in this highly stressed region.     

A Novel Semi-Analytical Solution of Over-Damped Slug Test in a Three-Layered Aquifer System

The slug test has been commonly used to estimate aquifer parameters. Previous studies on the slug test mainly focused on a single-layer aquifer. However, understanding the interaction between layers is particularly important when assessing aquifer parameters under certain circumstances. In this study, a new semi-analytical model on transient flow in a three-layered aquifer system with a partially penetrating well was developed for the slug test. The proposed model was solved using the Laplace transform method and the Goldstein-Weber transform method, where the semi-analytical solution for the model was obtained. The drawdowns of the proposed model were analyzed to understand the impacts of the different parameters on the drawdowns in a three-layered aquifer system. The results indicated that groundwater interactions between the layers have a significant impact on the slug test. In addition, a shorter and deeper well screen as well as a greater permeability ratio between the layers creates a greater interface flow between them, leading to a higher drawdown in the slug test. Finally, a slug test in a three-layered aquifer system was conducted in our laboratory to validate the new model, which indicated that the proposed model performed better in the interpretation of the experimental data than a previous model proposed by Hyder et al. (1994). We also proposed an empirical relationship to qualitatively identify the errors in the application of single-layer model for the analysis of response data in a three-layered aquifer system.     

Bootstrap confidence intervals for design storms from exceedance series

Abstract

An approach for better understanding of the physical implication of estimated aquifer parameters is demonstrated by analysing the pumping test data at Cottam in the Nottingham aquifer, UK. A sensitivity analysis showed that the area represented by the estimated parameters was much smaller than the area covered by the depression cone. After parameters are estimated, further research should be carried out to understand what portions of the aquifer the parameters represent. The parameters estimated at Cottam represented mainly aquifer features between roughly 100 and 2000 m. The sensitivity analysis also showed that the observed drawdown being satisfactorily matched by a model with uniform parameters does not prove that the aquifer is homogeneous. Slightly anomalous data may imply the existence of large anomalous zones. Although the drawdowns at Cottam could be ‘satisfactorily’ fitted by a model with uniform parameters, the fit could be improved by a model using a more permeable aquifer but with a zone about 700 m wide and with 42% less transmissivity.     

Effect of wellbore storage and finite thickness skin on flow to a partially penetrating well in a phreatic aquifer

An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown–time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown–time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

Air and water flows induced by pumping tests in unconfined aquifers with low‐permeability zones

Air flows from the atmosphere into an unconfined aquifer when the water table falls during pumping tests. Pumping test results in unconfined aquifers may be significantly affected by low‐permeability zones (LPZs) near the initial water table position, because they restrict the downward movement of air. A transient, three‐dimensional air–water two‐phase flow model is employed to investigate numerically the effects of local heterogeneity on pumping test results in unconfined aquifers. Two cases of local heterogeneities are considered herein: a LPZ around the pumping well and on one side of the pumping well. Results show that the drawdown with the LPZ is significantly greater than that of the homogeneous aquifer. The differences in drawdown are the most significant at intermediate times and gradually diminish at later times. The LPZ significantly reduces air flow from the atmosphere to the aquifer. The pore air velocity in the LPZ is very low. The air pressure at the observation point under the LPZ when air begins to enter is significantly lower than the air pressure of the homogeneous aquifer at the same point. After that, the air pressure increases quickly and then increases slowly. The time for the air pressure to reach the atmospheric pressure is significantly longer. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Aquifer Studies Using Flow Simulations

Flow simulations supplemented resource evaluation studies of the Lower Greensand aquifer. The annual recharge has hitherto been considered to be the resource available for development although a large confined storage exists. Pumping is principally in urban areas but recent monitoring suggests that the aquifer may have suffered excessive drawdowns. Therefore, simulation studies were carried out to refine the annual recharge estimate, to define the past effects of pumping and to obtain an indication of future trends. Catchment water balance indicates average annual recharge of 28 × 10⁶ m³. One-dimensional (ID) ground-water flow simulation suggests that regional abstractions affect outcrop-water levels. The study showed that the aquifer reached a new equilibrium with the current pumping regime. An improved insight to the aquifer has permitted the formulation of strategies for future resource development.     

The impact of well drawdowns on the mixing process of river water and groundwater and water quality in a riverside well field,Northeast China

Riverbank filtration (RBF) has been widely used throughout the world as an effective means to regulate surface water and groundwater resources and pretreat raw water for municipal water supply. The quality of the water from a riverside well field and the mixing ratios of surface water and groundwater is primarily impacted by the hydrodynamic processes in the RBF system. The RBF system is largely controlled by the water exploiting system in addition to the natural hydrologic condition of the river–aquifer system. As one of the most important design parameters of the riverside well field, the drawdown of groundwater level greatly determines the water head differences between the river water and groundwater as well as the field flow net, which subsequently impacts the mixing of river water and groundwater and water quality significantly. This study aimed to improve the understanding of the mixing process between the surface water and groundwater and estimate the impact of the RBF on the mixing ratio of surface water–groundwater and water quality quantitatively. A set of field pumping tests with various groundwater level drawdowns were carried out independently and successively at a riverside field with a single pumping well near the Songhua River in Northeast China in August 2017. During these tests, the water levels and hydrochemical parameters of the Songhua River, the adjacent aquifer, and the pumping well were monitored. The dynamic mixing process of the river water and groundwater and water quality under various drawdown conditions were analysed systematically using analytical methods. The results obtained from Dupuit method and the Mirror Image method in conjunction with the Hydrochemical Tracing method showed that the pumping water directly from the river water reached 60% ± 10% after a steady flow net was established. The larger the proportion of the pumping water captured from the river, the better quality of the pumping water was, because the quality of the river water (only limited to some water quality parameters monitored which were minority) was better than that of the groundwater. The results also showed that total Fe, TDS, total hardness, COD_Mn, and K⁺ were relatively sensitive to the changes of groundwater drawdown, and their concentrations decreased with an increase in the groundwater drawdown. It can be concluded that both the mixing ratio of the surface water and the groundwater and the water quality of the riverside well field can be regulated through adjusting the designed drawdown of the groundwater level, which is helpful for the design and the optimization of the riverside well water intake engineering.