Leaky Aquifer Research Articles

Low velocity non-Darcian flow to a well fully penetrating a confined aquifer in the first kind of leaky aquifer system

In this study, we use a finite difference method to solve low velocity non-Darcian flow to a well in the first kind of leaky aquifer system. Flow in the confined aquifer is assumed to be Darcian and horizontal, whereas flow in the aquitard is assumed to be non-Darcian and vertical. The threshold hydraulic gradient existence of non-Darcian flow in low permeability porous media is employed to describe the non-Darcian flow in the aquitard. A numerical solution has been obtained by using a finite difference method. This solution is compared with the previous solution for Darcian flow case in leaky aquifer system. The error has been analyzed. The comparison of this study and Darcian flow case (Hantush and Jacob, 1955) in leaky aquifer system indicates that the error is very small and can be neglected. However, the hydrogeological parameter calculation of leaky aquifer system is remarkably influenced by low velocity non-Darcian flow in aquitard. For the inflection point method (Hantush, 1956), the absolute values of estimated errors for coefficient of transmissibility of confined aquifer and vertical hydraulic conductivity of aquitard show negative relationship with the pumping rate. For the type curve-fitting method (Walton, 1962), the estimated errors for coefficient of transmissibility and elastic drainable porosity of confined aquifer are very small under small pumping rate. In general, the estimated errors for coefficient of transmissibility and elastic drainable porosity of confined aquifer can be controlled under certain level through adjusting pumping rate. The estimated error of vertical hydraulic conductivity of aquitard is quite large no matter which method is used, even up to nearly 300%.

A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative

A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative

Management of BWRO systems using long-term monitoring of feed water quality to avoid future membrane process failure

Pumping of wells from aquifers that are used to supply brackish-water reverse osmosis (BWRO) treatment systems commonly causes increases of water salinity in time. Some key aspects of assuring operational security are the magnitude of the water quality changes to assure that treatment can continue without failure of the process, reduction in installed capacity, or the necessity to modify the process by increasing the operational pressure and changing the membranes. An example of a BWRO system that uses a leaky aquifer system as a source of feed water located in Florida shows that careful monitoring of the well water quality and individual well pumping rates over a 10-year operating period can be used to assess the projected long-term changes in water quality with regard to the treatment facility design. The total dissolved solids concentration of the wellfield began with an average TDS of 2,461 mg/L which changed over 10 years to an average of 2,855 mg/L. The variation in time is linear and the projected average change for the next 20 years shows that the average TDS for the current pumping rate will increase to 3,611 mg/L which is well below the design maximum TDS treatment ability of 8,129 mg/L.

Development of semi-analytical solution for recharging through multiple well points system under constant head conditions

Under natural geographical settings, there are numerous regions where freshwater floats in layers on the native brackish groundwater. Skimming of these floating freshwater layers for fulfilling water needs using lesser capacity wells is a proven technology and is popularly known as multiple well points system (MWPS). Excessive exploitation of water is thinning these freshwater layers. Therefore, for reducing stress on existing freshwater layers due to pumping and/or retaining the fresh–brackish water interface at desired depth, it is mandatory to maintain adequate recuperation rate. For this purpose, the most convenient way is to use the existing MWPSs for recharging these aquifers when quality potable water is available in excess during the monsoon season. However, prior information regarding the performance of MWPSs during recharging operation is of much significance while planning of any recharging project. Therefore, by incorporating the principle of superposition and Darcy–Weisbach relation-based newly developed position-oriented opportunistic proportion equation, a semi-analytical solution for evaluating hydraulic head distribution and recharge rate in a single leaky aquifer while recharging the freshwater under constant head conditions through MWPS has been developed. A close conformity of the computed results with the field observations describes the potential of the developed solution.

An exact solution for the discharge potential of a linear sink feature in a leaky rectangular aquifer

This paper presents the exact solution of the 2D modified Helmholtz equation which governs the discharge potential for a semi-confined rectangular aquifer with leakage due to line elements and imposing no-flow conditions on the boundaries. An application example is given for a constant straight line-sink at the centre of the aquifer and a rapidly convergent series representation of the solution is obtained involving only elementary functions. A precise comparison is performed with the Bessel function-based solutions usually derived assuming the aquifer of an infinite extent.

Aquifer assessment for agriculture through geophysical, hydrochemical and hydrogeological approaches around Perumattunallur lake, Southern India

This study mainly focused on aquifer assessment using 2-D Electrical Resistivity Imaging (ERI), hydrochemical, Geographic Information System (GIS)-based analysis and aquifer yield test for agriculture around Perumattunallur lake, Southern India. It comprises on quantifying aquifer thickness and yields with groundwater quality. The 2-D ERI technique was an attempt to study the geological structural and compare with borewell lithologs. The litho units encompass clay, calcrete weathered gneiss rock and charnockites. It shows that the resistivity of the top layer covered by clay/calcrete with kankar ranges of 1–12 Ωm followed by fine sand with a resistivity range of (10–20 Ωm) and calcrete mixed with gneissic rocks with a resistivity range of 20–120 Ωm. The massive charnockite with a resistivity range of >200 Ωm is observed in the hill ranges, present in the NE–SW direction. The hydrochemical study was attempted for the parameters (i.e., TDS, pH, Na+, K+, Ca2+, Mg2+ and Cl−) from bore well water samples briefly displayed by GIS-based geospatial analysis. The geochemical facies analysis of rock–water interaction study was used for the groundwater quality for agriculture. The pumping test helped to determine the aquifer yields with exact determination of the estimation of groundwater supply for agricultural use. The NW side of the wall is a high yield of water discharge from the lake. The average water yield of the study area is about 245.8 m3/day in summer and 310.6 m3/day in winter through the selected 7 bore wells. The alluvium clay with a calcrete layer occurs at the SE part and the results show as a low yield due to poor porosity. The radius influence of each well to be taken as 150 m was identified using the pumping test. The pumping test gives details about an aquifer of leaky aquifer with complex structure of gneissic rock with fracture/fault zone help for aquifer types. The results of the geophysical, hydrochemical and water yield test are used for groundwater quality and quantity for agriculture purpose and domestic use for the sustainable development of groundwater resources in the surroundings of the lake.

Approximation of the exponential integral (well function) using sampling methods

• This study proposes a new method for exponential integral approximation. • The methods are based on probabilistic sampling. • Three different sampling methods have been used; LHS, OA and MCS. • The results of sampling methods are good and accurate compared to other methods. Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E−08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.

A new formulation for steady multiaquifer flow: An analytic element for piecewise constant infiltration

AbstractThis paper contains a new formulation for infiltration inside domains bounded by polygons and its application to problems of steady multiaquifer flow, using the Dupuit‐Forchheimer approximation and assuming vertical flow in the separating layers. An alternative formulation is presented for leaky aquifer systems where infiltration or extraction is given. Existing formulations of multiaquifer flow involve a system of equations that must be solved for the heads in the aquifers. These formulations are abstract, and the relation between the parameters in the solution and physical quantities is hidden. The formulation in the paper aims at linking the system of equations to physical quantities; we have done this in two ways. First, we formulate the problem in terms of leakage potentials, related directly to the leakage through the leaky layers. Second, we introduce the concept of “equilibrated leakage,” leakage that is either the result of infiltration or of some disturbance in the flow pattern, such as that caused by a well. The leakage through the leaky layers tends to some constant value far from a disturbance, e.g., a well, or the boundary of an area of constant infiltration. This concept of equilibrated leakage is useful in practice and helps in understanding the distribution of leakage; we explain this in detail in the paper. The study of problems of steady flow in leaky aquifer systems is inspired by problems of groundwater sustainability, where the overall distribution of flow over long periods of time is important, rather than detailed information.

Exact solution of the time-fractional groundwater flow equation within a leaky aquifer equation

The concern of this work was first to extend the model describing the groundwater flowing within a leaky aquifer to the scope of the fractional order derivative. We first derive the solution of the extended equation with an iteration method. We presented the stability of the method and also the uniqueness of the special solution. We further make use of the Laplace transform, the Boltzmann and the separation methods to derive the exact solution of the extended equation.

Groundwater Response to Tidal Fluctuation in an Inhomogeneous Coastal Aquifer-Aquitard System

This paper investigates tide-induced groundwater fluctuation and submarine groundwater discharge (SGD) in a leaky inhomogeneous coastal aquifer system with an upper unconfined aquifer, a lower confined aquifer, and an aquitard between them. The upper left aquifer is formed due to land reclamation. The SGD defined as the groundwater flow from land into the sea is controlled mainly by the hydraulic gradient between land and sea. An analytical expression is developed to discuss and assess the effect of inhomogeneity on the groundwater head fluctuation in the leaky aquifer system. Joint effects of aquifers’ parameters such as leakage and hydraulic diffusivity on the groundwater head fluctuation and SGD are investigated. The predicted results from the analytical expression indicate that the groundwater head fluctuation in both unconfined and confined aquifers is dependent on dimensionless leakages and increases with dimensionless hydraulic diffusivity.

Stream filtration induced by pumping in a confined, unconfined or leaky aquifer bounded by two parallel streams or by a stream and an impervious stratum

summary A mathematical model is developed for describing three-dimensional groundwater flow induced by a fully-penetrating vertical well in aquifers between two parallel streams. A general equation is adopted to represent the top boundary condition which is applicable to either a confined, unconfined or leaky aquifer. The Robin (third-type) boundary condition is employed to represent the low-permeability streambeds. The Laplace-domain head solution of the model is derived by the double-integral and Laplace transforms. The Laplace-domain solution for a stream depletion rate (SDR) describing filtration from the streams is developed based on Darcy’s law and the head solution and inverted to the timedomain result by the Crump method. In addition, the time-domain solution of SDR for the confined aquifer is developed analytically after taking the inverse Laplace transform and the time-domain solutions of SDR for the leaky and unconfined aquifers are developed using the Pade approximation. Both approximate solutions of SDR are expressed in terms of simple series and give fairly good match with the Laplace-domain SDR solution and measured data from a field experiment in New Zealand. The uncertainties in SDR predictions for the aquifers are assessed by performing the sensitivity analysis and Monte Carlo simulation. With the aid of the time-domain solutions, we have found that the effect of the vertical groundwater flow on the temporal SDR for a leaky aquifer is dominated by two lumped parameters: j ¼ Kv x

General well function for soil vapor extraction

This paper develops a well function applicable to extraction of groundwater or soil vapor from a well under the most common field test conditions. The general well function (Perina and Lee, 2006) [12] is adapted to soil vapor extraction and constant head boundary at the top. For groundwater flow, the general well function now applies to an extraction well of finite diameter with uniform drawdown along the screen, finite-thickness skin, and partially penetrating an unconfined, confined, and leaky aquifer, or an aquifer underneath a reservoir. With a change of arguments, the model applies to soil vapor extraction from a vadose zone with no cover or with leaky cover at the ground surface. The extraction well can operate in specified drawdown (pressure for soil vapor) or specified flowrate mode. Frictional well loss is computed as flow-only dependent component of the drawdown inside the extraction well. In general case, the calculated flow distribution is not proportional to screen length for a multiscreen well.

Questioning the applicability of the areal leakage factor as a constant hydro-geological parameter

The differential equation of the flow through a leaky aquifer considers the leakage factor a constant hydro-geological parameter. The purpose of this research paper is to examine the suitability of this constant for the simulation of the distribution of the piezometric heads through leaky aquifers. To perform this task, a proposed explicit finite difference scheme for the determination of the hydrostatic distribution of the simulated piezometric heads was designed and verified against the maximum historical field measurements of the piezometric heads recorded during June 1977 of a four months irrigation season of the leaky aquifer of Dujailah, Iraq. Best fits between the simulated and measured piezometric heads were obtained at leakage factors B ranging between B >= 150 m and B < =200 m. Model results validated the applicability of the leakage factor as a hydro-geological constant and the good hydraulic communication between the upper and lower parts of the Dujailah aquifer.

Analytical solution for capture and catchment zones of a well located on a groundwater divide

[1] An analytical solution is presented for capture and catchment zones of a well located on a groundwater divide in a recharged aquifer. The analytical solution is derived for a homogeneous, isotropic, and uniformly thick leaky aquifer. It is shown that streamlines and well-catchment area have elongated shapes tending to infinity along the groundwater divide, and do not depend on any aquifer property, but only on the ratio of the well-pumping rate and aquifer recharge flux. Isochrones delineating capture zones also depend on the mean residence time of the groundwater, which is independent of the well-pumping rate. The capture and catchment zones differ significantly in both size and shape from the classical theory that ignores recharge. In particular, the catchment zone is wider and has a finite extent.

A Study on Unsaturated Zone Characterization and Feasibility of Soil Vapor Extraction at a DNAPL-contaminated Site in Korea

This study aimed at characterizing unsaturated zone at the source zone area contaminated by DNAPL and investigating feasibility of soil vapor extraction (SVE). Five boreholes with three multi-level screens at the depth of 3.0~4.5 m, 5.5~7.0 m, and 8.0~12.0 m were installed at the source zone. Pneumatic tests were performed to determine the permeability of porous medium. Permeability was estimated to be 81.6 to 203.7 darcy, depending on the applied solutions, which was contradicted by grain size analysis of cored soil samples leading to 3.51 darcy. This is due to air flow through gravel pack during the early stage of pneumatic test. Pressure-drawdown curve in the late stage also well showed the leaky aquifer type, indicating air leakage to the ground. Air flow tests were also carried out to investigate air flow connectivity between multi-level wells, indicating that the horizontal air flow was well developed between the lower screens of the wells, not between the upper and middle screens due to the leakage to the surface. For the SVE test, there was no noticeable variation in TCE vapor concentration between three different test runs: 1. 8 hours daily for 5 days, 2. 24 hours together with air blowing at another well (BH1), 3. five consecutive days. Even for five-day consecutive test, total amount of removed TCE was estimated only to be as low as 46.5 g.

An analytical study of groundwater fluctuations in unconfined leaky aquifers induced by multiple localized recharge and withdrawal

&lt;p&gt;Commonly used analytical methods for assessing the effects of recharge and withdrawal on the groundwater flow system are based on an idealistic assumption that the aquifer&amp;rsquo;s base is fully impervious. In reality, the hydrostratigraphic conditions are often complex and involve leakage induced flow between aquifer and the confining layers. In this study, a simple analytical procedure is presented for determining the spatial and temporal distribution of water head in an unconfined aquifer system due to multiple localized recharge and withdrawal at time-varying rates. A new transient function is introduced that can conveniently approximate the rising and recession limbs of any single recharge hydrograph. Solution of linearized two-dimensional groundwater flow equation under Dirichlet and Neumann boundary conditions is obtained using finite Fourier cosine transform with analytic inversion. The study has at least one clear advantage over the existing solutions that it accounts for the vertical leakage in water table buildup and drawdown analysis. A computational example demonstrates that the leakage induced flow plays an important role in recharge and withdrawal processes of unconfined aquifer system. The model results can be used for estimating aquifer&amp;rsquo;s hydraulic properties and validation of numerical models.&lt;/p&gt;

Hydraulics of a multi-section screened well while draining ponded land in a leaky aquifer

A transient semi-analytical solution is developed for evaluating hydraulic head distribution in a leaky aquifer while draining the surface ponded water under constant-head conditions through a well having multi-section screen. Integral transform techniques such as Laplace and finite Fourier cosine are used for deriving the semi-analytical solution. Applicability of the derived solution is verified using the field data. The developed hydraulics is used to demonstrate the effect of multi-section screen on head distribution within the aquifer. A new term, radius of partial-screening influence (R ps), is introduced in the present study. The R ps of a single/multi-section screen depends on the position(s) of the screen section(s) within the aquifer. Analyses of the results show that the radial distance beyond which the influence of multi-section (m sections, say) well screen fully penetrating the aquifer (but only partially screening it) vanishes is equal to 1/m times the aquifer thickness for the screen sections that are positioned symmetrically with reference to the mid-lines of their respective aquifer portions hypothetically divided into m equal depths, whereas this radial distance ranges from 1 to 2 times the aquifer thickness for the screen having asymmetrically positioned screen section(s). Analyses for various screen thicknesses show that the prominence of the edge effect(s) of screen-section(s) increases with the increase in screen thickness.

Hydraulics of a Drainage Well Fully Penetrating a Leaky Aquifer through a Multisection Screen

AbstractThe authors develop a transient semianalytical solution for evaluating the hydraulic head distribution in a leaky aquifer under constant surface-ponding conditions while draining through a fully penetrating multisection screen of an injection well. The authors use integral transform techniques such as Laplace and finite Fourier cosine for solving the said problem analytically. The solution in the Laplace domain is inverted to the time domain numerically. The authors test the performance of the derived semianalytical solution by comparing its results with field data. Subsequently, they use the solution to evaluate the hydraulic head distribution within the flow medium for a drainage event. Analyses show that the hydraulic head distribution within the radius of partial screening influence (Rps) in the aquifer is controlled by both the radial distance from the well and the monitoring depth but only by the radial distance beyond Rps. Further, the Rps does not depend on the screen sections’ lengths and...

Determining the optimal pumping duration of transient pumping tests for estimating hydraulic properties of leaky aquifers using global curve-fitting method: a simulation approach

Global curve-fitting method (GCFM) is regarded as an effective approach in hydrogeological parameter estimation, as it integrates and uses pumping data and water recovery data of a transient pumping test for parameter estimation. The impacts of pumping duration on hydrogeological parameter estimation by GCFM were investigated in the present study using 2 in situ pumping tests and 24 simulated transient pumping tests. Empirical formulas for determining the optimal pumping duration were derived. The study results suggest that pumping duration will have impacts on the accuracy of hydrogeological parameter estimation. When pumping duration is longer than a certain period, relative errors of hydrogeological parameter estimation keep relatively stable within an acceptable limit. Therefore, it is unnecessary to continue the pumping for a very long time after the groundwater level has become stable. When the change rate of drawdown over time (γ) in an observation well located within a distance of 100 m to the pumping well reaches 0.134, the pumping can be stopped. If there are more than one observation wells in a pumping test, the smallest γ value should be selected to determine the optimal pumping duration. This research is meaningful in the instruction of pumping tests, and will reduce test costs greatly.

Comparison of three methods of hydrogeological parameter estimation in leaky aquifers using transient flow pumping tests

AbstractAccurate knowledge of hydrogeological parameters is essential for groundwater modeling, protection and remediation. Three methods (type curve fitting method, inflection point method and global curve‐fitting method (GCFM)) which are frequently applied in the estimation of leaky aquifer parameters were compared using synthetic pumping tests. The results revealed GCFM could provide best parameter estimation among the three methods with fewer uncertainties associated with the processes of parameter estimation. GCFM was also found to be both time saving and of low cost and is thus more preferable for hydrogeological parameter estimation than the other two methods. Copyright © 2013 John Wiley &amp; Sons, Ltd.