Flow Depletion Induced by Pumping Well from Finite Length of Stream

A procedure for calculating the flow depletion from a finite length of a stream induced by a pumping well in an adjacent aquifer is developed. Four management cases of finite length of the stream including a basic case are considered. A “basic flow depletion factor” is defined, in terms of which the flow depletion factors for all cases are expressed. The basic flow depletion factor is twice the Hantush M function. A computationally simple and accurate practical approximation of the basic flow depletion factor is presented that encompasses the full practical range of the solutions. Using this approximation, an optimization method is proposed for the estimation of the aquifer hydraulic diffusivity and effective distance from the pumping well to the line of recharge from the measured temporal variation of stream flow depletion between two sections. During optimization, repeated computation of stream flow depletion is required; use of the proposed approximation simplifies the computation.     

Analytical Ground-Water Flow Solutions for Channel-Aquifer Interaction

A general solution scheme for determining ground-water levels for channel∕group-water systems with recharge is developed and verified. The analytical solution uses the Laplace transform method to solve a linearized form of the Boussinesq equation. Unlike other solutions, this scheme allows for both boundaries and sources∕sinks to vary as a function of time and space. To verify the analytical scheme, three one-dimensional case studies of flow between two line sources in an unconfined aquifer were explored through a base run and a set of sensitivity analyses. These runs involved comparisons to MODFLOW and changes in the boundary conditions and dimensions. As noted, the flow equations were linearized about a point called the representative flow depth. A value of havg, defined as the average water depth between the initial and steady flow conditions, was used as the representative flow depth. Results of the proposed method matched very well with MODFLOW solutions for all times and locations using an optimal linearization point. In addition, using havg improved the solutions compared to those obtained previously.     

Theory of Seepage into an Auger Hole in a Confined Aquifer

A steady-state theory is presented for predicting flow into an auger hole partially penetrating a homogeneous and anisotropic confined aquifer that is underlain by an impermeable layer. The developed equations can be directly applied (i.e., without resorting to a coordinate transformation) to translate the rate of rise of the water in a pumped auger hole into directional conductivities of soil. The study shows that the conductivity values calculated by neglecting the confining pressure of an artesian aquifer (i.e., by applying the existing unconfined auger-hole seepage theories to experimental auger data obtained from a confined aquifer) may lead to serious error; hence, the confining head of an aquifer must be considered while the conductivity values are computed. Further, the distance of the outer layer also plays an important role in determining the flow to an auger hole penetrating a confined aquifer, and this parameter must therefore be included in the theoretical analysis of the problem. The validity of the proposed theory is checked by comparing a few results obtained from the theory with corresponding results obtained from numerical and analytical works. The developed theory is an addition to already existing auger-hole seepage theories for water-table aquifers; together with the available theories, the proposed solution is expected to cover the most commonly encountered auger hole experimental flow situations in the field.     

Transient Flow into a Partially Penetrating Well during the Constant-Head Test in Unconfined Aquifers

This study derives a semianalytical solution for drawdown distribution during a constant-head test at a partially penetrating well in an unconfined aquifer. The constant-head condition is used to describe the boundary along the screen. In addition, a free-surface condition is used to delineate the upper boundary of the unconfined aquifer. The Laplace-domain solution is then derived using separation of variables and Laplace transform. This solution can be used to identify the aquifer parameters from the data of the constant-head test when integrated with an optimization scheme or to investigate the effects of vertical flow caused by the partially penetrating well and free-surface boundary in an unconfined aquifer.     

Development of Management Models for Sustainable Use of Coastal Aquifers

A number of nonlinear optimization-based multiple-objective management models for sustainable utilization of coastal aquifers are formulated and solved. The management objectives represent plausible scenarios for planned withdrawal and salinity control in coastal aquifers. The first multiple-objective management model is developed for spatial and temporal control of aquifer salinity through planned pumping (withdrawal) from locations closest to the ocean boundary. The second multiple-objective management model is useful for maximizing sustainable water withdrawal from the aquifer for beneficial uses, while limiting the maximum salinity in the aquifer. The third multiple-objective management model is developed for maximizing sustainable water withdrawal from the aquifer for beneficial uses and minimizing the total pumping at locations adjacent to the ocean boundary to control the salinity in the aquifer. The nonlinear finite-difference form of the steady-state density-dependent miscible flow and salt transport model for seawater intrusion in coastal aquifers is embedded within the constraints of the management model. The constraint method of generating noninferior solutions is used to solve the multiple-objective management problems. The management models are solved for a hypothetical unconfined coastal aquifer system. The projected augmented Lagrangian method of nonlinear programming is used to solve the resulting large-scale optimization problem. The solution results demonstrate the feasibility of the developed optimization models and also the conflicting nature of the various objectives of coastal aquifer management.     

Interaction of Stream and Sloping Aquifer Receiving Constant Recharge

An analytical solution and finite-element numerical solution of a linearized and nonlinear Boussinesq equation, respectively, were obtained to describe water table variation in a semi-infinite sloping∕horizontal aquifer caused by the sudden rise or fall of the water level in the adjoining stream. Transient water table profiles in recharging and discharging aquifers having 0, 5, and 10% slopes and receiving zero or constant replenishment from the land surface were computed for t = 1 and 5 days by employing analytical and finite-element numerical solutions. The effect of linearization of the nonlinear governing equation, recharge, and slope of the impermeable barrier on water table variation in a semi-infinite flow region was illustrated with the help of a numerical example. Results suggest that linearization of the nonlinear equation has only a marginal impact on the predicted water table heights (with or without considering constant replenishment). The relative errors between the analytical and finite-element numerical solution varied in the range of ?0.39 to 1.59%. An increase in slope of the impermeable barrier causes an increase in the water table height at all the horizontal locations, except at the boundaries for the recharging case and a decrease for the discharging case.     

Flow Depletion of Semipervious Streams Due to Unsteady Pumping Discharge

Analytical expressions for rate and volume of flow depletion of semipervious streams due to sinusoidal variation in pumping rate are obtained. An analytical but approximate method is developed for obtaining the rate and volume of stream flow depletion due to arbitrary unsteady pumping discharge. The method uses the ramp kernel and convolution. The use of ramp kernels permits linear interpolation between two consecutive discretized discharge values. The analytical equations for the ramp kernels for the rate and volume of stream flow depletion are derived. The proposed method is applicable for homogeneous and isotropic aquifers that are hydraulically connected to streams.     

Solution for Flow Rates across the Wellbore in a Two-Zone Confined Aquifer

A closed-form solution for transient flow rates across the wellbore in a confined aquifer is derived from a two-zone radial ground-water flow equation subject to the boundary condition of keeping a constant head at the well radius. An aquifer may be considered as a two-zone system if the formation properties near the wellbore are significantly changed due to the well construction and/or well development. An efficient numerical approach is used to evaluate this newly derived solution. Values of the transient flow rate are provided in a tabular form and compared with those obtained by numerical inversion for the Laplace-domain solution. The results show that the two solutions are in good agreement. This newly derived solution can be used not only for predicting the transient flow rate across the wellbore but also for identifying the effects of a skin with a finite thickness on the estimation of transient flow rates in a ground-water system with two different formation properties.     

Simulation of Radial Collector Well in Shallow Alluvial Riverbed Aquifer Using Analytic Element Method

To withdraw large quantities of groundwater from the alluvial aquifers for various uses near riverbeds, radial collector (RC) wells are often preferable to the installation of several small diameter tube wells. In regions where rivers are not perennial or have low flow conditions during most part of the year, the RC wells are placed in the riverbed to obtain uninterrupted supply of naturally filtered groundwater through highly permeable saturated riverbed aquifers. Due to the complexities of flow, no exact analytical solution exists to provide steady state discharge drawdown relationship for RC well. Numerical model construction using finite difference or finite element method is quite cumbersome because of the radial orientation of laterals. To overcome these difficulties, in this study a steady state simulation model based on analytic element method (AEM) is developed to simulate the discharge-drawdown relation for RC well in an unconfined riverbed aquifer. In the model, line-sink elements are used to represent stream as well as radial laterals with specified conductance. The model is used to study the effects of different lateral configurations, hydraulic conductivity of riverbed aquifer, radius of influence and conductance of laterals on the well discharge, and consequent drawdown. Further based on the results of simulations using the AEM model, an approximate empirical equation is developed to obtain the discharge of RC well readily for design purpose. Further, the developed model has been applied to a field study and results are obtained for different plausible configurations of radial wells. The proposed methodology based on the application of AEM modeling tool, has been found to be efficient in constructing riverbed aquifer model with RC well. The proposed model is recommended in designing new collector well by providing minimum length of laterals for the sustained yield.     

Aquifer Response to Sinusoidal or Arbitrary Stage of Semipervious Stream

Analytical expressions for the aquifer responses, viz., groundwater head, rate of flow and cumulative volume of flow, to a generalized sinusoidal stage of semipervious streams considering the stream boundary resistance, are derived. The analytical aquifer responses to a linear stream stage and to a typical analytical flood wave that was used by Cooper and Rorabaugh, are also derived. For a zero-stream resistance, the aquifer responses converge to those for a fully penetrating stream. Also, two analytical methods, a “ramp kernel method” and a “Fourier series method,” for obtaining the aquifer responses to an arbitrary temporal stage of sempervious stream, are developed. The analytical expressions of the ramp kernels for different aquifer responses are developed. The ramp kernel method is found superior to the conventional convolution that uses numerical integration or pulse kernels for obtaining the convolution integral. In the Fourier series method, the aquifer responses to sinusoidal stage are used along with Fourier series. The results obtained using both methods are in close agreement. The new methods are also applicable to fully penetrating streams by assigning a zero value to the stream resistance.     

Leaky One-Dimensional Flow with Storage and Skin Effect in Finite-Width Sink

One-dimensional horizontal flow in a semiinfinite confined aquifer can be described in terms of mathematical solutions that relate drawdown in the aquifer to aquifer parameters and flow into or out of a line sink. A new solution that considers the effects of a low-permeability skin along with storage in a finite-width sink is developed for the leaky-aquifer case. A coefficient Sk is defined to represent the skin effect for one-dimensional flow. The transient solution, which is obtained by inverting the Laplace-space solution using the Stehfest numerical algorithm, calculates drawdowns in the sink as well as in the aquifer. A nondimensional drain function D(u,x/B,A/x,Sk/x)q is defined based on the solution. Selected type curves for the drain function are plotted, and a match-point procedure is described that is based on matching observed drawdowns at observation wells to an appropriate type curve. The match-point procedure is illustrated by fitting simulated drawdown data to a type curve and determining the aquifer parameters. The drawdown solution is also represented by dimensional time–drawdown plots, which can be used to determine aquifer parameters by adjusting the parameters until model-calculated drawdowns match observed values. This new solution can be used to analyze drawdowns that result from a canal pumping test in which the discharge from the canal is derived from water stored in the canal and from a leaky aquifer and in which the drawdowns are affected by storage and a low-permeability skin in the canal.     

Water Table Fluctuation in the Presence of a Time-Varying Exponential Recharge and Depth-Dependent ET in a Two-Dimensional Aquifer System with an Inclined Base

An analytical solution is presented for water table fluctuation between ditch drains in presence of exponential recharge and depth-dependent evapotranspiration (ET) from groundwater table in a two-dimensional gently sloping aquifer. The groundwater head above the drain is small compared to the saturated thickness of the aquifer. A sound mathematical transformation is devised to transform the two-dimensional groundwater flow equation into a simple form, which makes possible to obtain an analytical solution. The transient midpoint water table variations from the proposed solution compare well with the already existing solutions for horizontal aquifer. A numerical example is used to illustrate the combined effect of depth-dependent ET coupled with a time-varying exponential recharge on the water table fluctuation. The inclusion of a depth-dependent ET in the solution results in water table decline at a faster rate as compared to the case when ET is not considered. With an increase in slope of the aquifer base, water table profiles become asymmetric and the water table divide shifts towards the lower drain. The height of the water table profiles increases on moving away from the boundary of the aquifer and the highest level of the ground water table is obtained in the central portion of the aquifer basin due to the presence of drainage ditches on the aquifer boundary. When the effect of ET is incorporated in combination with recharge, the analytical solution results in accurate and reliable estimates of water table fluctuations under situations subjected to a number of controlling factors. This study will be useful for alleviation of drainage problems of the aquifers receiving surface recharge and surrounded by streams.     

Water Table Rise in Sloping Aquifer due to Canal Seepage and Constant Recharge

Analytical solutions of the linearized Boussinesq equation and a fully implicit finite-difference numerical solution of the nonlinear Boussinesq equation were obtained to study transient and steady-state water table rise in a homogeneous, isotropic, and incompressible unconfined sloping aquifer. The rise was due to seepage from two canals located at different elevations above the sloping impermeable barrier and constant recharge from the land surface. Proposed analytical solutions were verified with existing analytical solutions for a horizontal aquifer and were found in close agreement. The effect of recharge and slope of the impermeable barrier on water table rise predicted by both analytical and numerical solutions was studied by considering a numerical example. The effect of the linearization of the Boussinesq equation on water table rise was also studied by comparing the water table heights predicted by the numerical solution with those computed from the analytical solution. The analytical solution overestimates water table elevations compared to those obtained from the numerical solution, and the difference in water table in the middle region decreases with increase in time.     

Approximation of M Function for Partially Penetrating Wells

A computationally simple approximation of the Hantush M function is proposed. Using this approximation, an optimization method is proposed for identifying the aquifer parameters from early drawdowns around partially penetrating wells. The aquifer parameters are hydraulic conductivity and specific storage. The application of the method is illustrated using a field example. The proposed method results in a 120-fold saving in time when compared to the prior method. It is hoped that the proposed approximation and method will be of help to the field engineers and practitioners.     

Transient Head Development due to Flood Induced Seepage under Levees

The purpose of this study was to predict the uplift force during floods on confining layers that overlay extensive horizontal confined aquifers that intersect a large river in response to the water level changes that occur with time in a flooding river. Transient flow of water through the confined aquifer was described by a diffusion type of equation with a boundary condition at the river in which the river head varied with time. The transient head distribution developed from the unsteady flow model applied to the aquifer was compared with the hydraulic head distributions obtained from U.S. Army Corps of Engineers steady-state flow model and a finite-element seepage model. This study concluded that the transient flow model has the potential to analyze time lag in head development, and to predict the seepage condition and heaving potential at various times and distances landside of a levee during a flood cycle, but additional case histories are needed to justify widespread use of the model.     

Groundwater Flow from Fractured Layer to Porous-Media Blind Variable Large Diameter Well

In this paper, unconfined porous medium is considered to drain vertically to an underlying fractured aquifer, which leads groundwater to a variable large diameter well blind to porous medium. Such cases are quite common in arid regions, where the geological layers have top to bottom sequence as quaternary sedimentary layer (porous-unconfined aquifer), weathered and/or fractured underlying layers (fractured-confined aquifer), which are underlain by impervious rock formation. The necessary type curves are provided both for the fractured (pumped) and overlying porous (unpumped) media. Initially, the effect of varying well diameter on the drawdown is explained. The general groundwater movement equation for this configuration yields to well known Theis, Hantush, and Jacob solutions. It is also indicated that at large times, classical Jacob straight line is not valid in every case, because there is a set of other straight lines with different slopes. The application of the methodology is presented for an aquifer test in the Kingdom of Saudi Arabia.     

Stream Multiaquifer Well Interactions

In this paper, unsteady flow into a multiaquifer well due to stream stage changes and varying pumping rate is analyzed. The well is located at such a distance that the radius of influence touches the stream boundary; hence, pumping induces seepage from the stream to the aquifer. The discrete kernel approach, which is based on Duhamel’s principle, has been applied to find the interaction among stream, aquifers, and pumping well for constant as well as varying stream stage. The analytical expression for a damped sinusoidal flood wave passing in a fully penetrating stream has been used for obtaining the aquifer response. By applying image-well theory, the finite aquifer and well system has been transformed into an infinite aquifer and well system. The principle of superposition, which is applicable to a linear system, has been used to analyze the interaction processes among the three components of the system. The interaction of the stream, aquifers, and well with each other are analyzed during pumping, after stoppage of pumping, as well as during passage of a flood wave in the stream.     

Tide-Induced Water Table Fluctuations in Coastal Aquifers Bounded by Rhythmic Shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer’s properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.     

Rate and Volume of Stream Flow Depletion due to Unsteady Pumping

Analytical but approximate methods are developed for obtaining pumping induced rate and volume of stream flow depletion, which can account for unsteady (any variation) pumping discharge and are also applicable for intermittent pumping and recovery. Exact analytical solutions for a sinusoidal variation in the pumping discharge are proposed; the proposed methods are verified using these solutions. The proposed methods use ramp kernels that give results superior to the conventional convolution. These ramp kernels assume the linear variation in pumping discharge between the two consecutive discretized points as opposed to the uniform variation assumed in the conventional convolution. The proposed solutions are applicable for homogeneous and isotropic aquifers hydraulically connected to streams.     

Simple Model for Analyzing Transient Pumping from Two Aquifers without Cross Flow

A computationally simple semianalytical model is proposed for calculating the drawdown due to pumping a well tapping two aquifers separated by an aquiclude with no cross flow. The new model can take into account the transient pumping discharge. Equations are proposed for calculating the transient contributions of the aquifers to the pumped discharge and drawdowns in aquifers. The residual drawdowns in the aquifers and the aquifer contributions during recovery period can also be obtained using the proposed model. Based upon a similar principle, another model is also developed that can consider the effect of the well storage. The proposed models can be used to calculate drawdowns neglecting or considering the well storage, in the case of transient pumping from two aquifers having different values of transmissivity and storage coefficient. It is hoped that the new models would be of help to the field engineers and practitioners.