Aquifer Properties Determined from Two Analytical Solutions

In the analysis of pumping test data, the quality of the determined aquifer parameters can be greatly improved by using a proper model of the aquifer system. Moench (1995) provided an analytical solution for flow to a well partially penetrating an unconfined aquifer. His solution, in contrast to the Neuman solution (1974), accounts for the noninstantaneous decline of the water table (delayed yield). Consequently, the calculated drawdown in these two solutions is different under certain circumstances, and this difference may therefore affect the computation of aquifer properties from pumping test data. This paper uses an inverse computational method to calculate four aquifer parameters as well as a delayed yield parameter, α₁ from pumping test data using both the Neuman (1974) and Moench (1995) solutions. Time-drawdown data sets from a pumping test in an unconfined alluvial aquifer near Grand Island, Nebraska, were analyzed. In single-well analyses, horizontal hydraulic conductivity values derived from the Moench solution are lower, but vertical hydraulic conductivity values are higher than those calculated from the Neuman solution. However, the hydraulic conductivity values in composite-well analyses from both solutions become very close. Furthermore, the Neuman solution produces similar hydraulic conductivity values in the single-well and composite-well analyses, but the Moench solution does not. While variable α₁, seems to play a role in affecting the computation of aquifer parameters in the single-well analysis, a much smaller effect was observed in the composite-well analysis. In general, specific yield determined using the Moench solution could be slightly higher than the values from the Neuman solution; however, they are still lower than the realistic values for sand and gravel aquifers.     

Unsteady flow to wells in layered and fissured aquifer systems

A solution has been developed for the calculation of drawdowns in leaky and confined multiaquifer systems, pumped by a well of constant discharge penetrating one or more of the aquifers. In contrast to earlier solutions the effects of elastic storage in separating and bounding aquitards have now completely been accounted for.

The computing technique is based on the numerical inversion of the Laplace transform. Two different methods are used and results are compared with an analytical solution. Both Stehfest's¹ algorithm and Schapery's² least squares method yield accurate results in a fraction of the computation time required for the analytical evaluation.

Selected sets of time-drawdown and distance-drawdown curves are plotted to illustrate multiple-aquifer well flow and to compare new solutions with results which were previously published. The analogy with flow is unconfined and fissured aquifers is demonstrated by multilayer models, representing multiple-porosity formations with linear and diffusive crossflow.     

Hydraulic parameters of a multilayered aquifer system in Kuwait City

The Kuwait Group consists mainly of clastic sediments overlying unconformably the Dammam Formation of Tertiary age. The Kuwait Group is generally divided into three main hydrostratigraphic units: the upper and lower aquifers separated by an aquitard. The upper aquifer is further divided into the water table aquifer, an aquitard and a semiconfined aquifer. This semiconfined unit was pumped and the drawdowns were observed in piezometers screened in various subunits of the Kuwait Group. Some pumping tests of short duration were carried out in the top water table aquifer as well. These tests showed that the subunits of the Kuwait Group are hydraulically interconnected to a varying degree.

The pumping test data were analysed using conventional analytical solutions. The semiconfined pumping test was also simulated by a quasi-three-dimensional model using a leaky multiaquifer modelling technique. The initial hydraulic parameters were improved manually in the model till best fit drawdowns were obtained.

The final parameters obtained by simulation of the pumping tests were used in designing a pilot drainage system for the control of a rising groundwater table in parts of Kuwait City.     

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.     

Analytical methods for transient flow to a well in a confined-unconfined aquifer

Concurrent existence of confined and unconfined zones of an aquifer can arise owing to ground water withdrawal by pumping. Using Girinskii's potential function, Chen (1974, 1983) developed an approximate analytical solution to analyze transient ground water flow to a pumping well in an aquifer that changes from an initially confined system to a system with both unconfined and confined regimes. This article presents the details of the Chen model and then compares it with the analytical model developed by Moench and Prickett (1972) for the same problem. Hypothetical pumping test examples in which the aquifer undergoes conversion from confined to water table conditions are solved by the two analytical models and also a numerical model based on MODFLOW. Comparison of the results suggests that the solutions of the Chen model give better results than the Moench and Prickett model except when the radial distance is very large or aquifer thickness is large compared with drawdown.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

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

Regional Flow and Deformation Analysis of Basin‐Fill Aquifer Systems Using Stress‐Dependent Parameters

Changes in effective stress due to water pressure variations modify the intrinsic hydrodynamic properties of aquifers and aquitards. Overexploited groundwater systems, such as basins with heavy pumping, are subject to nonrecoverable modifications. This results in loss of permeability, porosity, and specific storage due to system consolidation. This paper presents (1) the analytical development of model functions relating effective stress to hydrodynamic parameters for aquifers and aquitards constituted of unconsolidated granular sediments, and (2) a modeling approach for the analysis of aquifer systems affected by effective stress variations, taking into account the aforementioned dependency. The stress‐dependent functions were fit to laboratory data, and used in the suggested modeling approach. Based on only few unknowns, this approach is computationally simple, efficiently captures the hydromechanical processes that are active in regional aquifer systems under stress, and readily provides an estimate of their consolidation.     

Poroelastic Effects on Fracture Characterization

Reverse water‐level fluctuations have been widely observed in aquitards or aquifers separated from a pumped confined aquifer (Noordbergum effect) immediately after the initiation of pumping. This same reverse fluctuation has been observed in a fractured crystalline‐rock aquifer at the Coles Hill uranium site in Virginia in which the reverse water‐level response occurs within a pumped fracture and results from an instantaneous strain response to pumping that precedes the pore‐pressure response in observation wells of sufficient distance from the pumped well. This response is referred to as the Mandel‐Cryer effect. The unique aspect of this water level rise during a controlled 24 h pumping test was that the reverse water levels lasted for approximately 100 min and reached a magnitude of nearly 1 cm prior to a typical drawdown response. The duration and magnitude of the response reflects the poromechanical properties of the fractured host rock and hydraulic properties of the pumped fracture. An axisymmetric flow and deformation model were developed using Biot2 in an effort to simulate the observed water‐level response along an assumed 0.5 to 1.0 cm aperture horizontal fracture 176 m from the pumping well and to identify the importance of the poroelastic effect. Results indicate that traditional aquifer‐testing methods that ignore the poromechanical response are not significantly different than results that include the response. However, the poroelastic effect allows for more accurate and efficient parameter calibration.     

A Comparative Study of Specific Yield Determinations for a Shallow Sand Aquifer

Using the type-curve methods of Boulton (1963) and Neuman (1972), and comparisons, at various times, of the cumulative volume of water pumped to the volume of the water-table drawdown cone (volume-balance method), values of specific yield were obtained from pumping test data from numerous piezometers in an unconfined sand aquifer. The long-term value of specific yield for the aquifer was determined from measurements of the laboratory drainage curve of the aquifer material. The volume-balance method gave specific yield values of 0.02, 0.05, 0.12, 0.20, 0.23, and 0.25 at times of 0.25, 0.66, 10, 26, 45, and 65 hours, respectively, indicating a gradual increase in specific yield and an asymptotic approach to the long-term value of 0.30 determined from the laboratory method. The type-curve methods provided values of 0.07 and 0.08, which correspond to the volume-balance values at early times, but which are less than one-third of the value obtained from the laboratory method and from the volume-balance method applied at the end of the pumping test (2.7 days). The type-curve procedures therefore provide unrealistically low values of specific yield for application to problems concerning the long-term yield characteristics of the aquifer. The observed trend towards increasing values of specific yield with increasing duration of pumping, and the vertical hydraulic head profiles that were measured during the pumping test indicate that both delayed drainage from above the water table and downward hydraulic gradients in the saturated zone can be important hydraulic effects contributing to the delayed-drawdown segment that is characteristic of time-drawdown graphs for unconfined aquifers.     

Numerical simulation of the Rhade effect in layered aquifer systems due to groundwater pumping shutoff

A series of numerical simulations using a fully coupled poroelastic numerical model is performed to analyze the so-called Rhade effect. A three-layer aquifer system composed of two aquifers separated by an aquitard, and a corresponding single-layer aquifer system composed of an equivalent lumped material are simulated for the purpose of comparison. In the numerical simulation of the layered aquifer system, the Rhade effect is observed in the aquitard and upper aquifer immediately after the stop of groundwater pumping from the lower aquifer. In contrast, the numerical simulation results of the lumped aquifer system do not show such Rhade effect throughout the entire domain during the groundwater pumping shutoff period. These numerical simulation results strongly suggest that hydraulically less permeable and mechanically more deformable aquitards that generally exist in layered aquifer systems particularly play an important role in causing the Rhade effect at the end of groundwater pumping. The Rhade effect is caused by two mechanisms: a slower hydraulic propagation (head recovery) of the unpumping stress than its mechanical propagation (extension) from the pumped aquifer into the adjacent aquitard and unpumped aquifer due to the relatively lower hydraulic conductivity of the aquitard, and an amplification of the faster mechanical propagation (excessive extension) in the lower part of the aquitard due to its relatively higher deformability. However, the unpumping stress is evenly distributed throughout the entire domain of the lumped aquifer system over time without such hydrogeomechanical mechanisms since it does not have an aquitard and hence is hydraulically and mechanically homogeneous.     

Use of Groundwater Level Fluctuations near an Operating Water Supply Well to Estimate Aquifer Transmissivity

We developed a method to estimate aquifer transmissivity from the hydraulic-head data associated with the normal cyclic operation of a water supply well thus avoiding the need for interrupting the water supply associated with a traditional aquifer test. The method is based on an analytical solution that relates the aquifer's transmissivity to the standard deviation of the hydraulic-head fluctuations in one or more observation wells that are due to the periodic pumping of the production well. We analyzed the resulting analytical solution and demonstrated that when the observation wells are located near the pumping well, the solution has a simple, Dupuit like form. Numerical analysis demonstrates that the analytical solution can also be used for a quasi-periodic pumping of the supply well. Simulation of cyclic pumping in a statistically heterogeneous medium confirms that the method is suitable for analyzing the transmissivity of weakly or moderately heterogeneous aquifers. If only one observation well is available, and the shift in the phase of hydraulic-head oscillations between the pumping well and the observation well is not identifiable. Prior knowledge of aquifer's hydraulic diffusivity is required to obtain the value of the aquifer transmissivity.     

Theoretical analysis and field evidence of reciprocity gaps during interference pumping tests

We address the question of the reciprocity of drawdowns observed during a sequence of interference pumping tests performed within a porous medium, in the context of different conceptual models of subsurface flow. We provide a generalization of the work by Bruggeman (1972) [5], extending his results obtained in 1972 for Darcian flows in an unbounded, heterogeneous porous medium. We then analyze reciprocity within a dual-continuum conceptualization, where the medium is viewed as being composed of two overlapping continua, representing the porous matrix and embedded fractures, respectively. We show theoretically, and demonstrate numerically, that only drawdowns associated with the fracture continuum display reciprocity under transient flow conditions. Conversely, non-flowing matrix and fracture continua display reciprocity behavior under steady-state conditions. We then provide field evidence of the insurgence of reciprocity gaps by analyzing interference test data from the karstic limestone aquifer of the Hydrogeological Experimental Site (HES) in Poitiers, France. On the basis of our theoretical results and experimental observations, we discuss different interpretations of the observed reciprocity gaps. These include (a) non-linear dependencies of local hydraulic parameters, (b) occurrence of internal boundaries within the domain, (c) inertial effects that develop through open conduits within the rock matrix, (d) modifications of the aquifer properties between subsequent pumping tests, and (e) significant contribution of the matrix pressure in monitored wells when the behavior of the aquifer is conceptualized by a dual-continuum approach.     

Groundwater modelling and marine intrusion in the semi‐arid systems (Cap‐Bon,Tunisia)

This article studies the effect of drought and pumping discharge on groundwater supplies and marine intrusion in the Korba aquifer (Cap‐Bon peninsula, Tunisia). The Groundwater Modelling System has been used to model the groundwater flow and to simulate the seawater intrusion. The calibration is based on the groundwater levels in the steady state from 1963, and in the transient state from the groundwater levels from 1963 to 2005. The main objective is to quantify the components of the groundwater mass balance and to estimate the hydraulic conductivity distribution. The impact of pumping discharge on the groundwater level evolution has been examined by two pumping scenarios P1 (no. 8420) and P2 (no. 8862) wells. The hydrodynamic modelling shows the increasing drawdowns after 14 years of pumping: 4 m in P1 well and about 5 m in P2 well below sea level. The drawdowns are accompanied by the inverse hydraulic gradient. The numerical model was used to discuss the management of the groundwater resources of Cap‐Bon. As the population continues to grow and the demand for groundwater pumping intensifies beyond the 1963 level, it can be expected that the actual extent of seawater intrusion in the future would be more severe than the model prediction. Better strategies for groundwater development and management will be necessary to protect the freshwater aquifers to the marine intrusion. Copyright © 2011 John Wiley & Sons, Ltd.     

Fracture control of ground water flow and water chemistry in a rock aquitard

There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/S(s)) of fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard, and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model based on this conceptual model are consistent with field observations, which did not fit the typical conceptual model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting ground water flow and for planning and protecting water supplies.     

Leaky Aquifer Models to Simulate the Well Flow in Fractured Aquifers with Linear Interporosity Flow

Following Hemker and Maas (1987) the models of two or three leaky aquifers are applied to simulate the flow to vertical wells operating in the fractured or dual porosity aquifers. The software WellTest (WT) (Székely 2015) is used for calculating the drawdown and discharge rate variation. The comparative analysis with the independent analytical solutions by Boulton and Streltsova-Adams (1978), Warren and Root (1963), Kazemi et al. (1969) concluded with acceptable agreement between the WT simulation and the alternate calculation methods. The selected field tests have been conducted in fractured limestone aquifers. The pumping test west of Copenhagen shows an example of fractured aquifer with considerable negative skin effect at the well face. The flowing well Wafra W1 in Kuwait operates in the two-zone aquifer exhibiting sufficient vertical recharge via leakage beyond a circular domain of estimated radius of 2460 m.     

Interpreting a Pumping Test Influenced by Another Well in an Anisotropic Aquifer

In confined aquifers the influence of neighboring active wells is often neglected when interpreting a pumping test. This can, however, lead to an erroneous interpretation of the pumping test data. This article presents simple methods to evaluate the transmissivity tensor and storativity of an anisotropic confined aquifer when there is an interfering well in the neighborhood of the tested well. Two methods have been developed depending on whether the tested well or the interfering well is the first in operation. These new methods yield better estimates of the hydraulic parameters than when the influence of the interfering well is neglected. These methods have then been used on data obtained from numerical models with an interfering well and the results have been compared to an analytical method that neglects the influence of the interfering well. The methods require knowledge of the pumping rate of the interfering well and the time elapsed since the pumping started in each well. If the interfering well started pumping before the tested well, the method does not require knowledge of the aquifer piezometric level at the beginning of the test, which is often unknown in this case. As for the method without interference, at least three monitoring wells (MWs) are needed, the position of which influences the accuracy of the estimated parameters. Some recommendations concerning MWs position have been given to get more accurate results according to the sought parameter.     

Observed Drawdown Pattern Around a Well Partially Penetrating a Vertically Extensive Water-Table Aquifer

In order to understand the flow pattern around a pumping well partially penetrating a vertically extensive aquifer, a specially designed pumping test was carried out in Pakistan. In this paper salient features of the test have been described. The spatial distributions of drawdown have been shown graphically. Some of the preliminary conclusions made from the drawdown pattern include:

• • The distance beyond which the flow is likely to be horizontal increases with decrease in the degree of aquifer penetration.
• • In equidistant observation wells open at different depths, (1) the drawdowns tend to merge at larger times, provided the observation point is located within the screened section of the aquifer; (2) the less the depth of penetration is, the earlier the drawdowns start merging; and (3) the initial rate of drawdown near the aquifer top is slow but catches up with time to exceed those at deeper points.

     

Conceptualizing leakage and storage contributions from long open interval wells in regional deep basin flow models

Deep basin aquifers are increasingly used in water‐stressed areas, though their potential for sustainable development is inhibited by overlying aquitards and limited recharge rates. Long open interval wells (LOIWs)—wells uncased through multiple hydrostratigraphic units—are present in many confined aquifer systems and can be an important mechanism for deep basin aquifers to receive flow across aquitards. LOIWs are a major control on flow in the deep Cambrian–Ordovician sandstone aquifers of the upper Midwest, USA, providing a source of artificial leakage from shallow bedrock aquifers and equilibrating head within the sandstone aquifers despite differential pumpage. Conceptualizing and quantifying this anthropogenic flow has long been a challenge for groundwater flow modellers, particularly on a regional scale. Synoptic measurements of active production wells and well completion data for northeast Illinois form the basis for a transient, head‐specified MODFLOW model that determines mass balance contributions to the region and estimates LOIW leakage to the aquifers. Using this insight, transient LOIW leakage was simulated using transiently changing K_V zones in a traditional, Q‐specified MODFLOW‐USG model, a novel approach that allows the K_V in a cell containing a LOIW to change transiently by use of the time‐variant materials (TVM) package. With this modification, we achieved a consistent calibration through time, averaging 19.9 m root mean squared error. This model indicates that artificial leakage via LOIWs contributed a minimum of 10–13% of total flow to the sandstone aquifers through the entire history of pumping, up to 50% of flow around 1930. Removal from storage exceeds 40% of flow during peak withdrawals, much of this flow sourced from units other than the primary sandstone aquifers via LOIWs. As such, understanding the timing and magnitude of LOIW leakage is essential for predicting future water availability in deep basin aquifers.