Leaky Aquifer Research Articles

Discussion of “Stream Depletion in a Two-Layer Leaky Aquifer System” by Bruce Hunt

Discussion of “Stream Depletion in a Two-Layer Leaky Aquifer System” by Bruce Hunt

Errata for “Approximation of Well Function and Identification of Leaky Aquifer Parameters” by Sushil K. Singh

Errata for “Approximation of Well Function and Identification of Leaky Aquifer Parameters” by Sushil K. Singh

Interaction between deep and shallow groundwater systems in areas affected by Quaternary tectonics (Central Italy): a geochemical and isotope approach

Hydro- and isotope geochemistry are used to refine groundwater conceptual models in two areas of central Italy (Acque Albule Basin and Velino River Valley) affected by extensional Quaternary tectonics, where deep and shallow groundwater flow systems are interacting. The role of geology, of recent deposits filling the plains and of main tectonic features controlling groundwater flowpaths and deep-seated fluids emergences are investigated and discussed. Environmental isotopes (2H and 18O) confirm recharge in the surrounding carbonate aquifers, and meteoric origin of both shallow and deep groundwater. Major ion chemistry indicates a mixing between shallow Ca-HCO3 groundwater from carbonate aquifers and deep Ca-HCO3-SO4 groundwater, characterised by higher salinity and temperature and high concentration in sulphates. Isotopic composition of dissolved sulphates (δ 34S and δ 18O) and dissolved inorganic carbon (δ 13C), henceforth indicated as DIC, are used to verify the presence of different sources of groundwater, and to validate the mixing model suggested by the major ion analyses. Sulphate isotope composition suggests a marine origin for the groundwater characterised by elevated sulphate concentration, whose source is present in the deep buried sequences. Carbon isotope composition confirms the role of a DIC source associated to CO2 degassing of a deep reservoir. Groundwater conceptual models are improved underlining the importance of Plio-Pleistocene sequences filling the tectonic depression. In the Acque Albule area, the travertine plateau represents a mixing stratified aquifer, where deep groundwater contribution is spread into the shallow aquifer. The alluvial–clastic–lacustrine leaky aquifer of Velino Valley enables a complete mixing of shallow and deep groundwater allowing spot-located discharge of deep groundwater along tectonic patterns and facilitating sulphate reduction in the lacustrine sediments, explaining locally the presence of H2S.

Three-Dimensional Semianalytical Solutions of Groundwater Flow to a Well in Fractured Wedge-Shaped Aquifers

The three-dimensional Laplace domain solutions of groundwater flow to a well in fractured double porosity confined, unconfined, and leaky wedge-shaped aquifers are developed. Three wedge boundary configurations: (1) two constant head zero drawdown; (2) two impermeable; and (3) one constant head zero drawdown and one impermeable wedge boundary are considered. Dimensionless drawdowns are obtained for different wedge boundary configurations to investigate flow system behavior. Lateral boundary dimensionless flux at a representative line is also calculated for two constant head zero drawdown configuration and its sensitivity to the matrix hydraulic parameters are investigated. Results of our study are presented in the form of dimensionless flux-dimensionless time and dimensionless drawdown-dimensionless time, type curves. The results are useful for evaluating the role of matrix hydraulic parameters on lateral boundary depletion rate and investigation of flow system behavior in double porosity wedge-shaped aquifers with different lateral boundary configurations. The presented analytical solutions can also be used in parameter identification, stream depletion rate estimation and numerical models verification.

Method to characterize aquitards above leaky aquifers with water supply wells

Leaky aquifers provide protected drinking water since the aquifer is overlain by an aquitard, and this study develops a method to estimate hydraulic properties of the latter deposit. Steady pumping, supply well shutdowns, and slug tests generate data in adjacent monitoring well clusters that characterize the aquitard. An existing steady model estimates a site-averaged value of the aquitard permeability k if its thickness is known, and this site-averaged estimate may be compared with local k estimates from conventional and extended slug tests. A shutdown attenuation model estimates a local value of the consolidation coefficient CV, which combines with the local k value to specify the compressibility α of the aquitard. The method is illustrated for the Fowl Meadow Aquifer, a stratified drift deposit used as a drinking water supply in eastern Massachusetts (USA), with an overlying silt aquitard of 10 m thickness. Steady data and theory suggest a site-averaged k of 2.3 × 10–17 m2 for the aquitard, while the shutdown attenuation model generates local CV values that vary from 10–5 to 10–3 m2/s. The slug tests yield a local k variation (10–17–10–13 m2) that brackets the site-averaged value, and an α range of 10–9–10–7 Pa–1.

On the use of analytical solutions to design pumping tests in leaky aquifers connected to a stream

Christensen et al. (2009) studied the optimal design of pumping tests whose goal is to estimate hydrogeologic parameters affecting stream depletion caused by pumping in a leaky aquifer. Their analysis relies on the analytical solutions of Zlotnik and Tartakovsky (2008), which are based on the assumptions of negligible drawdown in the source bed of a leaky aquifer and of horizontal flow in an aquifer of infinite extent. We conduct a series of two- and three-dimensional simulations to identify the validity and range of applicability of these assumptions, and to quantify their impact on estimation of aquifer drawdown, stream depletion, their sensitivities to the hydrogeologic parameters, and on selection of optimal locations to observe drawdown during a pumping test. Quantitative criteria for the use of these analytical solutions are formulated in terms of the source-bed transmissivity and the distance from the well to prescribed-head boundaries other than the stream.

Buoyancy driven flow from a waning source through a porous leaky aquifer

We develop a series of models to describe the migration of a buoyant fluid through a layered permeable rock following release from a localized waning source. In particular, if the fluid is injected into a high permeability layer, bounded above by a layer of lower permeability, a plume migrates along the interface, with some draining into the low permeability layer if the current is sufficiently deep to overcome the capillary entry pressure. We show the motion of the fluid is controlled by a number of key factors with the dominant dimensionless numbers being the time-scale for the source to decay compared to the time-scale for draining through the low permeability layer, the residual saturation of the gas and water in the formation as that phase is displaced by the other phase, and the capillary entry pressure, as measured by the critical depth of the current required for draining, as compared to the initial depth of the current. Simplified analytical models are presented to illustrate some of the key controls on and transitions in the flow, and the models are used to explore leakage and trapping prior to flow reaching a fault zone.

Closure to “Stream Depletion by Groundwater Pumping in Leaky Aquifers” by Vitaly A. Zlotnik and Daniel M. Tartakovsky

Closure to “Stream Depletion by Groundwater Pumping in Leaky Aquifers” by Vitaly A. Zlotnik and Daniel M. Tartakovsky

Discussion of “Stream Depletion by Groundwater Pumping in Leaky Aquifers” by Vitaly A. Zlotnik and Daniel M. Tartakovsky

Discussion of “Stream Depletion by Groundwater Pumping in Leaky Aquifers” by Vitaly A. Zlotnik and Daniel M. Tartakovsky

Discussion of “Stream Depletion by Groundwater Pumping in Leaky Aquifers” by Vitaly A. Zlotnik and Daniel M. Tartakovsky

The authors’ solution assumes that a pumped leaky aquifer is underlain by a source bed that has zero drawdown for all time. However, an actual source bed always has finite drawdown values after relatively long periods of time, and this means that the authors’ solution is valid only for a relatively short period of time after pumping starts. Since stream depletion solutions are almost always used to predict stream depletion values after long periods of time, this means that the solution obtained by the authors is of very limited use. In particular, steady-flow stream-depletion values predicted after an infinite period of pumping in the authors’ solution will always underestimate the actual stream depletion. Unfortunately, this means that their solution is in danger of being misapplied by anyone who wants to justify excessive well abstractions when applying for water right permits. In closing, it is worth pointing out that the equations solved by the authors are identical with Eqs. 18 – 21 in Hunt 2003 if S and in Hunt are replaced with the pumped aquifer specific yield and infinity, respectively. In other words, an appropriate choice of variables allows the Hunt 2003 solution to reproduce the solution obtained by the authors. It would be a misuse of this solution to do so, however, for the reason given above.

Optimal design of pumping tests in leaky aquifers for stream depletion analysis

s u m m a r y We analyze the optimal design of a pumping test for estimating hydrogeologic parameters that are subsequently used to predict stream depletion caused by groundwater pumping in a leaky aquifer. A global optimization method is used to identify the test’s optimal duration and the number and locations of observation wells. The objective is to minimize predictive uncertainty (variance) of the estimated stream depletion, which depends on the sensitivities of depletion and drawdown to relevant hydrogeologic parameters. The sensitivities are computed analytically from the solutions of Zlotnik and Tartakovsky [Zlotnik, V.A., Tartakovsky, D.M., 2008. Stream depletion by groundwater pumping in leaky aquifers. ASCE Journal of Hydrologic Engineering 13, 43‐50] and the results are presented in a dimensionless form, facilitating their use for planning of pumping test at a variety of sites with similar hydrogeological settings. We show that stream depletion is generally very sensitive to aquitard’s leakage coefficient and streambed’s conductance. The optimal number of observation wells is two, their optimal locations are one close to the stream and the other close to the pumping well. We also provide guidelines on the test’s optimal duration and demonstrate that under certain conditions estimation of aquitard’s leakage coefficient and stream-bed’s conductance requires unrealistic test duration and/or signal-to-noise ratio.

Simple Method for Quick Estimation of Leaky-Aquifer Parameters

Simple method and explicit equations are proposed for estimating the parameters of leaky aquifers from drawdown at an observation well, which avoid the curve matching or initial estimate of the parameter. The proposed method is computationally simple and the calculations can be performed even on a handheld calculator. The application of the methods is illustrated, using published data sets. The new method yields quick and accurate estimates of the leaky-aquifer parameters, if observed drawdowns do not contain large errors. The proposed method can also analyze the early drawdowns for accurate characteristics/parameters of a confined aquifer, if the conductance of the aquitard is assigned a zero value. It is hoped that the proposed method would be of help to field engineers and practitioners.

Reply

We thank Dr. Batu for his comments on our paper (Eaton et al. 2007) on three-dimensional ground water flow in the Maquoketa Aquitard. We agree that the classic analytical methods for leaky aquifer analysis, developed by Neuman and Witherspoon (see reference citations given by Batu) and others, are still relevant. However, indurated and fractured rock aquitards like the one we discussed present additional complexities for flow and hydrogeologic characterization. The objectives of our paper were to highlight these complexities and present a conceptual model that provides a better understanding of flow in these systems, which are very different from the unlithified, less heterogeneous aquifer-aquitard systems for which the classic analytical solutions were developed. We welcome the opportunity to provide additional discussion of our work. Dr. Batu discusses mainly the vertical flow assumption in aquitards, analytical solutions, aspects of the MODFLOW numerical code, and steady-state vs. transient conditions of the hydraulic head data. Notably absent from his comment is one of the main emphases of our work, which is that layered sedimentary bedrock is typically fractured. Preferential flow occurs along bedding-plane fractures; the mechanical stratigraphy inhibits propagation of vertical fractures. Although we refer to the classic aquitard framework to understand the bulk properties of the Maquoketa Formation, we also emphasize the role of bedding-plane fractures in the three-dimensional flow system (Figures 2 and 10 in Eaton et al. [2007]) and present an innovative application of thin model layers in our MODFLOW model (Table 1 in Eaton et al. [2007]). The presence of bedding plane fractures is supported by ground water geochemical data (Figure 7 in Eaton et al. [2007]). In response to Dr. Batu’s specific points, the tendency toward aquitard vertical flow due to hydraulic conductivity contrasts in layered systems is elementary both for analytical and numerical solutions, but our work adds to this framework the effect of the bedding plane fractures we describe. Of course, we recognize that analytical solutions for leaky aquifers are valid for both upward and downward flow through the aquitard and that both upward and downward flow occurs under field conditions (Figure 5 in Eaton et al. [2007]). We again refer interested readers to Eaton and Bradbury (2003), in which there is additional discussion of monotonic trends in hydraulic head profiles under transient conditions. We also recognize that the analytical solutions for leaky aquifers assume horizontal flow in the aquifers. We point out again that the main focus of our work is to present a conceptual model for three-dimensional flow in an aquitard. The possibility of three-dimensional flow in aquitards was recently recognized and analyzed analytically by Sepulveda (2008). Finally, we point out the distinction between steady-state conditions, which have apparently not been reached in the Maquoketa Aquitard, and equilibrated long-term values for the purpose of field data collection. As we stated, the hydraulic head data we used in our analysis of the Maquoketa Aquitard were collected over a period of years, not months.

Diagnostic Curves for Identifying Leaky Aquifer Parameters with or without Aquitard Storage

Two sets of unimodal diagnostic curves, one set assumes no aquitard storage and the other set assumes aquitard storage, are developed for identifying the parameter of leaky aquifers from early draw...

The leaky aquifer function revisited

AbstractThis article discusses the leaky aquifer function considered in a recent article by Frank Harris in the Journal of Computational and Applied Mathematics (2008). We describe the properties of an integral representing this function and give details on how to compute this function with a single algorithm for a wide range of the parameters. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Control of sea-water intrusion by salt-water pumping: Coast of Oman

A shallow alluvial coastal aquifer in the Batinah area of Oman, with sea-water intrusion that extends several kilometres inland, has been studied experimentally, analytically and numerically. The water table is proved to have a trough caused by intensive pumping from a fresh groundwater zone and evaporation from the saline phreatic surface. Resistivity traverses perpendicular to the shoreline indicated no fresh groundwater recharge into the sea. Using an analytical Dupuit-Forchheimer model, developed for the plain part of the catchment, explicit expressions for the water table, sharp interface location and stored volume of fresh water are obtained. It is shown that by the pumping of salt water from the intruded part of the aquifer, this intrusion can be mitigated. Different catchment sizes, intensities of fresh groundwater pumping, evaporation rates, water densities, sea level, incident fresh water level in the mountains and hydraulic conductivity are considered. SUTRA code is applied to a hypothetical case of a leaky aquifer with line sinks modeling fresh water withdrawal and evaporation. The numerical code also shows that pumping of saline water can pull the dispersion zone back to the shoreline.

Stream Depletion in a Two-Layer Leaky Aquifer System

A new semianalytical stream-depletion solution is obtained for pumping from a well beside a stream in a two-layer leaky aquifer system. The well abstracts water from an upper unconfined aquifer underlain by an aquitard and a second semiconfined aquifer. The governing equations reduce to the equations that describe flow in a Hantush-Jacob leaky aquifer, in which the bottom aquifer has zero drawdown for all time, when the storativity of the bottom aquifer becomes infinite. This allows a Hantush-Jacob leaky aquifer solution to be compared with the solution for a bottom aquifer with finite storativity, and this comparison shows that the Hantush-Jacob approximation significantly underestimates stream depletion at larger values of time. In addition, comparison of the two-aquifer solution with a stream-depletion solution for a single aquifer shows that a single-aquifer solution closely approximates the two-aquifer solution when the single-aquifer transmissivity is replaced with the sum of transmissivities for the two-layer system. This suggests that a similar approximation might be used in a previously obtained solution to obtain a very general stream depletion model for multiaquifer systems.

Approximation of Well Function and Identification of Leaky Aquifer Parameters

The existing equation for leaky aquifers is transformed into a nondimensional form using new parameters and a scaled well function for leaky aquifers is proposed. A computationally simple function is developed for accurately approximating the scaled well function for the practical range of the parameters. Utilizing this function (approximation), an optimization method is proposed for identifying the leaky-aquifer parameters from observed drawdowns. The new function has an enhanced utility when a repetitive numerical evaluation of the well function for leaky aquifers is needed, e.g., while estimating the aquifer parameters using optimization or Kalman filter or artificial neural network methods. The application of the proposed method is illustrated using a few sets of published data. The proposed method outperforms the extended Kalman filter method, based on the reported results in the literature.

An analytical solution and case study of groundwater head response to dual tide in an island leaky confined aquifer

This paper presents an analytical solution of groundwater head response to dual‐tide fluctuation in the transect of an island leaky aquifer system comprising a confined aquifer and its overlying semipermeable confining layer. Both layers terminate at the coastlines on two sides of the island. Solution analysis indicates that the tidal waves from the two sides of the island transect interfere at the middle of the island and the interference decreases to zero as the horizontal length of the aquifer increases to infinity. The leakage of the overlying confining layer enhances the landward attenuation of the tidal head fluctuation and shortens the time lag between the head and tide fluctuations. The solution agreed well with the observations in eight piezometers in Garden Island on the continental shelf of Western Australia reported by Trefry and Bekele (2004).

Influence of heterogeneity on the interpretation of pumping test data in leaky aquifers

Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred.