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This study proposes a new analytical slug test model describing confined flow considering the effects of the formation damage and non‐Darcy flow near the wellbore. The former, primarily caused by drilling fluid invasion, introduces an extra wellbore head loss near the well screen. The latter, mainly resulting from the relatively high‐velocity flow across the gravel‐pack screen, adopts the Forchheimer equation to consider the joint effects of the laminar flow and non‐Darcy flow. The proposed model is nonlinear due to the quadratic term for non‐Darcy flow in the Forchheimer equation. The new solutions for head responses in the well and formation are derived using the Laplace transform method and integration by parts formula. Furthermore, the present solution is applied to estimate the aquifer parameters via analyzing the water level data from field slug tests conducted in the Minnelusa aquifer near Spearfish, South Dakota. We found that the present solution provides very good fit to the field data from tests in fractured aquifers, notably the data exhibits a rapid decline at late times on the normalized head vs. logarithmic time plots. Key Points: We present a slug test model by considering near‐well formation damage and nonlinear flowThe solution of the model is developed by Laplace transform method and integration by parts formulaPresent solution is used to analyze field water level data from three test wells in fractured aquifer for determining aquifer parameters [ABSTRACT FROM AUTHOR]

In the past, many mathematical models based on the dual‐porosity (DP) concept were developed to describe the groundwater flow in fractured aquifer systems. Most of them seemingly have problems in predicting accurate drawdown at the early and/or intermediate times as compared with field measured data. Thus, this study proposes a new analytical model with a generalized transfer term (GTT) to describe the flow induced by pumping in such systems. The new model is nonlinear because the GTT representing the matrix‐to‐fracture flux gives different weights to the fracture and matrix drawdowns. The GTT reduces to the existing first‐order transfer term if the weight equals zero and second‐order term if the weight is one. The present model also includes a leakage term accounting for flow from the overlain or underlain acquitard. The drawdown solution of the model is developed based on the Laplace transform method and integration by parts formula and then verified through the comparison with the finite‐element solution. The effect of different weight values in the GTT on the DP flow is investigated. Additionally, the sensitivity analysis is performed to assess the impact of the change in each of the aquifer parameters on the flow. Furthermore, the present solution is used to analyze two sets of pumping drawdown data from test sites in Canada and India. We found that the drawdown predictions from the present solution fit field measured data very well, suggesting that the present model can adequately describe the real‐world DP flow system. Key Points: A generalized nonlinear water transfer term is proposed for describing the matrix‐to‐fracture flux in a dual‐porosity (DP) system subject to pumpingThe present term reduces to the existing first‐order or second‐order transfer term for weighting factor of 0 or 1, respectivelyThe drawdown solution of the model is used to analyze field drawdown data for estimating the aquifer parameters [ABSTRACT FROM AUTHOR]

Vertical wells with radial extension at the well bottom can improve the rate of water production. No study has yet investigated the effects of the transient state and anisotropy in directional hydraulic conductivities on the wellbore flux rate for this type of well. This study derives a semianalytical transient drawdown solution for constant‐head pumping at a fully penetrating well radially extended at the bottom of a confined, anisotropic aquifer by applying Laplace transform and separation of variables as well as conducting a Fourier analysis. The results of this new solution indicate that transient and steady‐state wellbore flux rates can be increased by a factor of two for greater radial extension of the well. Compared with an isotropic aquifer (a ratio of vertical and horizontal hydraulic conductivities equal to one), an anisotropic aquifer with the ratio less than one may produce a higher transient wellbore flux rate and lower steady‐state wellbore flux rate. Moreover, the time required to achieve the steady‐state wellbore flux rate can be substantially affected by anisotropy of the aquifer. Article impact statement: A new solution for assessing transient and anisotropic effects on wellbore flux rate from a fully penetrating well with radial extension. [ABSTRACT FROM AUTHOR]

In the past, the analytical model developed for a radially divergent heat flow in an aquifer thermal energy storage (ATES) system considers only the process of either thermal conduction or thermal dispersion. In addition, the existing models commonly regarded the inner boundary at the injection well as the constant‐temperature condition, which does not meet the continuity condition of heat flux at the wellbore. We herein propose an analytical model for a realistic representation of heat flow in an ATES system by considering the effects of both thermal conduction and thermal dispersion in the heat transfer equation and a Robin‐type boundary condition at the injection well. The model consists of three heat flow equations depicting the temperature distributions in the confined aquifer and its underlying and overlying rocks. The Laplace transform method is applied to solve the proposed model. The solutions for the cases of dispersion‐ and conduction‐dominant flow fields are also developed and discussed. Comparisons between the present solutions with five existing solutions developed for similar heated water injection problems are made. A global sensitivity method is also performed to analyze the thermal response to the change in each of the aquifer parameters. Finally, our solution is validated through the comparison with the finite difference solution and observed data from an ATES experiment site in Mobile, Alabama. Key Points: A model for heat transfer includes the effects of both conduction and dispersion in ATES systemsThe Robin‐type boundary condition is set to keep the continuity of heat flux at the rim of the wellboreThe solution is validated by comparison with temperature data from an experimental ATES site [ABSTRACT FROM AUTHOR]

Oscillatory pumping tests (OPTs) provide an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters when OPT data are analyzed based on an associated analytical model coupled with an optimization approach. There are a large number of analytical models presented for the analysis of the OPT. The combined effects of delayed gravity drainage (DGD) and the initial condition regarding the hydraulic head are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by the OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of a static water table, Neumann boundary condition specified at the rim of a partially screened well, and a free surface equation describing water table motion with the DGD effect. The solution is derived using the Laplace, finite-integral, and Weber transforms. Sensitivity analysis is carried out for exploring head response to the change in each hydraulic parameter. Results suggest that the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when the dimensionless parameter a1=ϵSyb/Kz exceeds 500 with empirical constant ϵ , specific yield Sy , aquifer thickness b , and vertical hydraulic conductivity Kz. The water table can be regarded as a no-flow boundary when a1<10-2 and P<104 s, with P being the period of the oscillatory pumping rate. A pseudo-steady-state model without the initial condition causes a time-shift from the actual transient model in predicting simple harmonic motion of head fluctuation during a late pumping period. In addition, the present solution agrees well with head fluctuation data observed at the Savannah River site. Highlights. An analytical model of the hydraulic head due to oscillatory pumping in unconfined aquifers is presented. Head fluctuations affected by instantaneous and delayed gravity drainages are discussed. The effect of the initial condition on the phase of head fluctuation is analyzed. The present solution agrees well with head fluctuation data taken from field oscillatory pumping. [ABSTRACT FROM AUTHOR]

The issue of the groundwater fluctuation due to tidal effect in a two-dimensional coastal leaky aquifer system has attracted much attention in recent years. The predictions of head fluctuation play an important role in dealing with groundwater managements and contaminant remediation problems in costal aquifers. This article presents a two-dimensional analytical model describing the groundwater flow in a coastal leaky aquifer of wedge shape affected by the tides and bounded by two estuarine rivers with an arbitrary included angle. The solution of the model is derived in the Polar coordinates by the Hankel transform and finite sine transform. The head fluctuation predicted by this new solution is compared with that by an existing solution for groundwater flow in a non-L shaped tidal aquifer. The groundwater fluctuation due to the joint effect of estuarine tides is explored based on the present solution. Moreover, the influences of the parameters such as diffusion (Di), included angle (Ф), and tidal river coefficients (K1, K2) on the head fluctuation in the aquifer are also assessed and discussed. The results demonstrate that those parameters have significant effects on the head fluctuation in the leaky confined aquifer system. Moreover, the effect of Di increases with Ф, and the effects of K1 and K2 on the normalized amplitude and phase lag of the groundwater fluctuation are significant when both parameter values are larger than 10−5. [ABSTRACT FROM AUTHOR]

In the process of groundwater recharge, surface water usually enters an aquifer by passing an overlying unsaturated zone. Little attention has been given to the development of analytical solutions to a coupled unsaturated--saturated flow model due to localized recharge up to now. This paper develops a mathematical model to depict three-dimensional transient unsaturated--saturated flow in an unconfined aquifer with localized recharge on the ground surface. The model contains Richards' equation for unsaturated flow, a flow equation for saturated formation, and the Gardner constitutive model describing the behavior of unsaturated soil properties. Both flow equations are coupled through the continuity conditions of the head and flux at the water table. The semi-analytical solution to the coupled flow model is derived by the methods of Laplace transform and Fourier cosine transform. A sensitivity analysis is performed to explore the head response to the change in each of the aquifer parameters. A quantitative tool is presented to assess the recharge efficiency signifying the percentage of the water from the recharge to the aquifer. We found that the effect of unsaturated flow on the saturated hydraulic head is negligible if two criteria associated with the unsaturated soil properties and initial aquifer thickness are satisfied. The head distributions predicted from the present solution match well with those from finite-difference simulations. The predictions of the present solution also agree well with the observed data from a field experiment at an artificial recharge pond in Fresno County, California. [ABSTRACT FROM AUTHOR]

This study treats the catchment as a block box system with considering the rainfall input and runoff output being a stochastic process. The temporal rainfall-runoff relationship at the catchment scale is described by a convolution integral on a continuous time scale. Using the Fourier-Stieltjes representation approach, a frequency domain solution to the convolution integral is developed to the spectral analysis of runoff processes generated by temporal non-stationary rainfall events. It is shown that the characteristic time scale of rainfall process increases the runoff discharge variability, while the catchment mean travel time constant plays the role in reducing the variability of runoff discharge. Similar to the behavior of groundwater aquifers, catchments act as a low-pass filter in the frequency domain for the rainfall input signal. [ABSTRACT FROM AUTHOR]

Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops a model for describing flow induced by pumping in an L-shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two subregions and the continuity conditions of the hydraulic head and flux are imposed at the interface of the subregions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in the real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW is chosen to compare with the proposed head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007). [ABSTRACT FROM AUTHOR]

This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant-rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual-porosity model. The Laplace-domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time-domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer. [ABSTRACT FROM AUTHOR]

This study introduces an analytical approach to estimate drawdown induced by well extraction in a heterogeneous confined aquifer with an irregular outer boundary. The aquifer domain is divided into a number of zones according to the zonation method for representing the spatial distribution of a hydraulic parameter field. The lateral boundary of the aquifer can be considered under the Dirichlet, Neumann or Robin condition at different parts of the boundary. Flow across the interface between two zones satisfies the continuities of drawdown and flux. Source points, each of which has an unknown volumetric rate representing the boundary effect on the drawdown, are allocated around the boundary of each zone. The solution of drawdown in each zone is expressed as a series in terms of the Theis equation with unknown volumetric rates from the source points. The rates are then determined based on the aquifer boundary conditions and the continuity requirements. The estimated aquifer drawdown by the present approach agrees well with a finite element solution developed based on the Mathematica function NDSolve. As compared with the existing numerical approaches, the present approach has a merit of directly computing the drawdown at any given location and time and therefore takes much less computing time to obtain the required results in engineering applications. [ABSTRACT FROM AUTHOR]

Summary This work describes an investigation of the spatial statistical structure of specific discharge field and solute transport process of a nonreactive solute at the field scale through a heterogeneous deformable porous medium. The flow field is driven by a vertical gradient in the excess pore water pressure induced by a step increase in load applied on the upper part of a finite-thickness aquifer. The non-stationary spectral representation is adopted to characterize the spatial covariance of the specific discharge field necessary for the development of the solute particle trajectory statistics using the Lagrangian formalism. We show that the statistics of the specific discharge and particle trajectory derived herein are non-stationary and functions of the coefficient of soil compressibility, μ . The effect of μ on the relative variation of specific discharge and the solute particle trajectory statistics are analyzed upon evaluating our expressions. [ABSTRACT FROM AUTHOR]

The solid Earth's surface frequently experience changes in total stresses as a result of periodic loading. When the fluid-saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (ln K). It is important for the rational management of groundwater resources. A closed-form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of ln K process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Fluid-filled granular soils experience changes in total stress because of earth and oceanic tides, earthquakes, erosion, sedimentation, and changes in atmospheric pressure. The pore volume may deform in response to the changes in stress and this may lead to changes in pore fluid pressure. The transient fluid flow can therefore be induced by the gradient in excess pressure in a fluid-saturated porous medium. This work demonstrates the use of stochastic methodology in prediction of induced one-dimensional field-scale groundwater flow through a heterogeneous aquifer. A closed-form of mean groundwater flux is developed to quantify the induced field-scale mean behavior of groundwater flow and analyze the impacts of the spatial correlation length scale of log hydraulic conductivity and the pore compressibility. The findings provided here could be useful for the rational planning and management of groundwater resources in aquifers that contain lenses with large vertical aquifer matrix compressibility values. [ABSTRACT FROM AUTHOR]

Summary Due to the irregular distributions of aquifer hydraulic properties, the detail on the characterization of flow field cannot be anticipated. There can be a great degree of uncertainty in the prediction of heat transport processes anticipated in applying the traditional deterministic transport equation to field situations. This article is therefore devoted to quantification of uncertainty involving predictions over larger scales in terms of the temperature variance. A stochastic frame of reference is adopted to account for the spatial variability in hydraulic conductivity and specific discharge. Within this framework, the use of the first-order perturbation approximation and spectral representation leads to stochastic differential equations governing the mean behavior and perturbation of the temperature field in heterogeneous aquifers. It turns out that the mean equation developed in this sense is equivalent to the traditional deterministic transport equation and the temperature variance gives a measure of the prediction uncertainty from the traditional transport equation. The closed-form expression for the temperature variance developed here indicates that the controlling parameters such as the correlation scale of specific discharge, which measures the spatial persistence of the flow field, and the periodicity of the source term tend to increase the variability in temperature field in heterogeneous aquifers. The uncertainty of the traditional heat transport model increases as the penetration depth of thermal front through the aquifer increases. This suggests that prediction of temperature distribution using the traditional heat transport model in heterogeneous aquifers is expected to be subject to large uncertainty at a large depth (in the downstream region). For the management purpose, the variance of temperature could serve as a calibration target when applying the traditional model to field situations. It may be more reasonable to make conclusions from, say, the mean temperature with one or two standard deviations rather than only the mean temperature drawn from the traditional heat transport equation. [ABSTRACT FROM AUTHOR]

Summary This study develops a mathematical model for contaminant transport due to well injection in a radial two-zone confined aquifer system, which is composed of a wellbore skin zone and a formation zone. The model contains two transient equations describing the contaminant concentration distributions; one is for contaminant transport in the skin zone while the other is for transport in the formation zone. The contaminants are injected into the well with given dispersive and advective fluxes; therefore, the well boundary is treated as a third-type (Robin) condition. The solution of the model derived by the method of Laplace transforms can reduce to a single-zone solution in the absence of the skin zone. In addition, an approximate solution in the time domain is also developed by neglecting dispersion for the case that the contaminants move away from the injection well. Analysis of the semi-analytical solution showed that the influence of the skin zone on the concentration distribution decreases as time elapses. The distribution will be over-estimated near the wellbore if the constant concentration (Dirichlet) condition is adopted at the well boundary. The approximate solution has advantages of easy computing and yield reasonable predictions for Peclet numbers larger than 50, and thus is a practical extension to existing methods for designing aquifer remediation systems or performing risk assessments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In many practical applications, the rates for ground water recharge and discharge are determined based on the analytical solution developed by Bredehoeft and Papadopulos (1965) to the one-dimensional steady-state heat transport equation. Groundwater flow processes are affected by the heterogeneity of subsurface systems; yet, the details of which cannot be anticipated precisely. There exists a great deal of uncertainty (variability) associated with the application of Bredehoeft and Papadopulos' solution (1965) to the field-scale heat transport problems. However, the quantification of uncertainty involved in such application has so far not been addressed, which is the objective of this wok. In addition, the influence of the statistical properties of log hydraulic conductivity field on the variability in temperature field in a heterogeneous aquifer is also investigated. The results of the analysis demonstrate that the variability (or uncertainty) in the temperature field increases with the correlation scale of the log hydraulic conductivity covariance function and the variability of temperature field also depends positively on the position. [ABSTRACT FROM AUTHOR]

This study develops a mathematical model for simulating the hydraulic head distribution in response to pumping in a sloping fault zone aquifer under a water table boundary condition. A two-dimensional equation with a sink term representing the pumping is used for describing the head distribution in the aquifer. In addition, a first-order free surface equation is adopted to represent the change in water table at the outcrop. The analytical solution of the model, derived by the Laplace and finite Fourier cosine transforms, is expressed in terms of a double series. A finite difference solution within a deformable grid framework is developed to assess the solution obtained by specifying the free surface equation at the outcrop. Based on the analytical solution, we have found that the model's prediction tends to overestimate drawdown in a late pumping period. The temporal head distribution is independent of the aquifer slope if the water table change is small, and exhibits a double-humped shape due to the effect of the free surface. The temporal drawdown predicted from the analytical solution is further compared with those measured from a pumping test conducted in northern Portugal. [ABSTRACT FROM AUTHOR]

Highlights: [•] A model is developed to describe migration of contaminants in two-aquifer systems. [•] The model considers advection and diffusion in the aquitard between two aquifers. [•] The analytical results are compared with 2-D explicit finite difference solutions. [•] The concentration in lower aquifer will be underestimated if neglecting the aquitard advection. [ABSTRACT FROM AUTHOR]

After the end of pumping the water level in the observation well starts to recover and the reduced drawdown during the recovery period is named as the residual drawdown. Traditional approaches in analyzing the data of residual drawdown for estimating the aquifer hydraulic parameters are mostly based on the application of superposition principle and Theis equation. In addition, the effect of wellbore storage is commonly ignored in the evaluation even if the test well has a finite diameter. In this article, we develop a mathematical model for describing the residual drawdown with considering the wellbore storage effect and the existing drawdown distribution produced by the pumping part of the test. The Laplace-domain solution of the model is derived using the Laplace transform technique and the time-domain result is inverted based on the Stehfest algorithm. This new solution shows that the residual drawdown associated with the boundary and initial conditions are related to the well drawdown and the aquifer drawdown, respectively. The well residual drawdown will be overestimated by the Theis residual drawdown solution in the early recovery part if neglecting the wellbore storage. On the other hand, the Theis residual drawdown solution can be used to approximate the present residual drawdown solution in the late recovery part of the test. [ABSTRACT FROM AUTHOR]

Abstract: Well hydraulics is a discipline to understand the process of flow to the well in an aquifer which is regarded as a source of groundwater. A variety of analytical and numerical models have been developed over the last few decades to provide a framework for understanding and quantifying the flow behavior in aquifer systems. In this review, we first briefly introduce the background of the theory of well hydraulics and the concepts, methodologies, and applications of analytical, semi-analytical, numerical and approximate methods in solving the well-hydraulic problems. We then address the subjects of current interests such as the incorporation of effects of finite well radius, wellbore storage, well partial penetration, and the presence of skin into various practical problems of groundwater flow. Furthermore, we also summarize recent developments of flow modeling such as the flow in aquifers with horizontal wells or collector wells, the capture zone delineation, and the non-Darcian flow in porous media and fractured formations. Finally, we present a comprehensive review on the numerical calculations for five well functions frequently appearing in well-hydraulic literature and suggest some topics in groundwater flow for future research. [Copyright &y& Elsevier]

The solution describing the wellbore flow rate in a constant-head test integrated with an optimization approach is commonly used to analyze observed wellbore flow-rate data for estimating the hydrogeological parameters of low-permeability aquifers. To our knowledge, the wellbore flow-rate solution for the constant-head test in a two-zone finite-extent confined aquifer has never been reported so far in the literature. This article is first to develop a mathematical model for describing the head distribution in the two-zone aquifer. The Laplace domain solutions for the head distributions and wellbore flow rate in a two-zone finite confined aquifer are derived using the Laplace transform, and their corresponding time domain solutions are then obtained using the Bromwich integral method and residue theorem. These new solutions are expressed in terms of an infinite series with Bessel functions and not straightforward to calculate numerically. A large-time solution for the wellbore flow rate is therefore developed by employing the relationship of small Laplace variable versus large time variable and L'Hospital's rule. The result shows that the large-time solution is identical to the steady-state solution obtained after applying the Tauberian theorem into the Laplace domain solution. This large-time solution can reduce to the Thiem equation in the case of no skin. Finally, the newly developed solution is used to investigate the effects of outer boundary distance and conductivity ratio on the wellbore flow rate. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: An aquifer with a wellbore surrounded by a finite-thickness skin, such as a gravel pack, can be regarded as a radial two-zone system. In this study, a mathematical model is developed to describe contaminant transport in a radial two-zone confined aquifer system. The solution of the model equations can be used to delineate contaminant transport in such a two-zone aquifer system and to investigate the skin effect on the temporal and spatial concentration distribution. The present solution is shown to reduce to an existing solution for transport in a homogeneous aquifer in the case when there is no wellbore skin. The results predicted from the solution indicate that the skin effect has a significant impact on the concentration distribution at early time. But an abrupt change in the spatial concentration distribution may occur at the interface of the skin zone and aquifer formation zone. The results from a sensitivity analysis reveal that dispersivity in the formation zone has a more significant effect on the concentration distribution than do the effects of skin thickness and dispersivity in the skin zone. [Copyright &y& Elsevier]

SUMMARY This paper presents a stochastic analysis of the behaviour of heat transfer by soil moisture in a partially saturated heterogeneous aquifer. A spectral approach based on Fourier-Stieltjes representations for the perturbed quantities is used to develop closed-form expressions that describe the field-scale heat advection and the variability of temperature profile. It is shown that the field-scale heat advection is related to the variability of the specific discharge, which, in turn, is related to the variation of hydraulic conductivity. Our analysis is, therefore, focused on the impact of the correlation scale of the log saturated hydraulic conductivity field on these analytical results. It is found that the correlation scale of log saturated hydraulic conductivity has an influence on enhancing the heat advection and the variability of the mean temperature field. [ABSTRACT FROM AUTHOR]

We have developed a drawdown solution for a partially penetrating well under constant flux pumping in a confined aquifer with finite thickness. The predictions of our solution diverge from the predictions of Hantush's solution (), particularly for problems with low ratios of well screen length to aquifer thickness. Furthermore, the predicted drawdown from Hantush's solution () differs from that of Yang et al.'s solution Water Resour Res 42:W0552, () only near the well and at small time values as indicated in Yang et al. Water Resour Res 42:W0552, (). Our solution is based on Green's function with a columnar source (sink) that represents pumping from a finite-radius well. Hantush's solution () and Yang et al.'s solution Water Resour Res 42:W0552, (), however, were derived from Laplace transform techniques for pumping in a well with an infinitesimal and a finite radius, respectively. [ABSTRACT FROM AUTHOR]

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A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, confined aquifer, and an aquitard in between. The aquifer system has a tidal boundary at the seashore, a no flow boundary at remote inland side, and a confined aquifer extending under the sea and terminated with an outlet-capping. This new solution has shown to be a generalisation of most existing analytical solutions for a tidal aquifer system which includes single confined and leaky confined aquifers. In addition, the solution is used to explore the influences of the dimensionless leakance of the outlet-capping, the dimensionless hydraulic diffusivities, and the leakages of the inland and offshore aquitards on the head responses in the leaky confined aquifer. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Summary: An anticline, known as a convex-upward fold in layers of rock, commonly is formed during lateral compression, which may be elected as a potential site for carbon sequestration. A mathematical model is developed in this study for describing the steady-state drawdown distribution in an anticline aquifer in response to the constant-flux pumping. The topographical shape of the anticline is mimicked by three successive blocks. The solution is obtained by applying the infinite Fourier transform and the finite Fourier cosine transform in each blocks and acquiring the hydraulic continuities between the blocks. Simulated results reveal that the introduction of a thin-limbs or narrow-ridged anticline would produce a much greater head drop in the ridge zone. For a well of constant pumping rate, the dimensionless drawdown around the well increases with decreasing well screen length or/and aquifer anisotropy ratio. An examination of the effect of well location on the drawdown reveals that the partially penetrating well located at the top-middle of the ridge zone produces the largest drawdown. The simulation of the flow in an anticline aquifer based on MODFLOW results in slightly smaller drawdown values in most regions when compared with those predicted by the present solution. The present solution can also be used to simulate the flow in a slab-shaped aquifer or a hillslope aquifer. It can be applied to determine the aquifer parameters if coupled with an optimization scheme and to provide the basis for selecting a potential site for carbon sequestration in the future as well. [Copyright &y& Elsevier]

Summary: The problem of two-dimensional groundwater flow in a heterogeneous unconfined aquifer under periodic random forcing in time is analyzed from a stochastic point of view. It is assumed that the periodic random forcing, namely random recharge, can be represented by a sinusoidal function in time. Analytical solutions are developed through the nonstationary spectral approach in conjunction with the principle of superposition. The results, namely the variances of hydraulic head and specific discharge, are expressed in terms of statistical properties of hydraulic parameters and recharge field. It can be concluded from the analytical results that the mean recharge rate and integral scale of spatially random recharge fluctuations play essential roles in enhancing the variability of hydraulic head and specific discharges. [ABSTRACT FROM AUTHOR]

Abstract: The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view. [Copyright &y& Elsevier]

Abstract: This study develops a mathematical model for describing the steady-state head response to fluid injection into a fully penetrating well in a heterogeneous and anisotropic anticline reservoir. In the model, the upper boundary of the anticline reservoir is approximated by a form of step change in reservoir thickness and the domain of the reservoir is divided into two regions with different hydraulic conductivities. By virtue of the properties of Fourier series, the method of separation of variables is employed to develop the analytical solution of the model. This new solution can be applied to estimating head distributions or injection rates for various geometrical conditions of the reservoir. If the trap is absent, the solution can be utilized to analyze head distributions in the reservoir system with two concentric transmissivity zones. Moreover, if the upper boundary becomes flat and the reservoir is homogeneous and isotropic, the solution reduces to the Thiem equation. [Copyright &y& Elsevier]

The article presents a study to test a mathematical model that shows the drawdown distribution for a radial flow to a fully penetrating well of finite-thickness skin zone. The study developed a confined aquifer system in laplace domain and utilized a modified Crump algorithm. The study found that the drawdown for negative-skin case is very sensitive to a change in the formation of transmissivity while the positive-skin case is sensitive to a change in skin thickness.

Abstract: This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier–Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge. [Copyright &y& Elsevier]

Neglecting the effect of well radius may lead to a significant error in the predicted drawdown distribution near the pumping well area. New analytical solutions describing aquifer responses to a constant pumping or a constant head maintained at a finite-diameter well in a wedge-shaped aquifer are derived based on the image-well method and applicable to an arbitrarily located well in the system. The solutions are useful for quantifying groundwater exploitation from a wedge-shaped aquifer and for determining the hydrogeological parameters of a wedge-shaped aquifer in inverse problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84]. [Copyright &y& Elsevier]

Summary: This paper describes an investigation of the influence of uniformly distributed groundwater recharge on asymptotic macrodispersion in two-dimensional heterogeneous media. This is performed using a nonstationary spectral approach [Li, S.-G., McLaughlin, D., 1991. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour. Res. 27 (7), 1589–1605; Li, S.-G., McLaughlin, D., 1995. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour. Res. 31 (3), 541–551] based on Fourier–Stieltjes representations for the perturbed quantities. To solve the problem analytically, focus is placed on the case where the local longitudinal dispersivity α L is much smaller than the integral scale of log transmissivity λ (i.e., α L/λ ≪1). The closed-form expressions are obtained for describing the spectrum of flow velocity, the variability of flow velocity and asymptotic macrodispersion, in terms of the statistical properties and the integral scale of log transmissivity, local transport parameters and a parameter β [Rubin, Y., Bellin, A., 1994. The effects of recharge on flow nonuniformity and macrodispersion. Water Resour. Res. 30 (4), 939–948] used to characterize the degree of flow nonuniformity due to the groundwater recharge. The impact of β on these results is examined. [Copyright &y& Elsevier]

Summary: This paper presents a new analytical solution to describe the hydraulic head distribution and flow system in an anisotropic unconfined aquifer with a sloping bed and arbitrarily located multiwells under transient recharge. Unlike the existing analytical solutions for delineating the capture zones, the solution presented in this study is easy and convenient to calculate flow field in some complicated systems, and it can provide useful information for the pump-and-treat design. In addition, the presented solution may have the possible application in evaluating the sensitivity of hydrogeological parameters, or estimating the hydraulic parameters when coupled with an optimization approach to analyze the aquifer data. [Copyright &y& Elsevier]

Summary: Slug test is considered to reflect the hydraulic parameters in the vicinity of the test well. The aquifer parameters are usually identified by fitting an appropriate mathematical solution or graphical type curves with slug test data. In this paper, we developed an approach by combining [Moench, A.F., Hsieh, P.A., 1985. Analysis of slug test data in a well with finite-thickness skin. In: Memoirs of the 17th International Congress on the Hydrogeology of Rocks of Low Permeability, U.S.A. Members of the International Association of Hydrologists, Tucson, AZ, vol. 17, pp. 17–29] and simulated annealing (SA) approach to estimate five parameters, i.e., three skin parameters and two aquifer parameters. The three skin parameters are hydraulic conductivity, specific storage, and thickness of the wellbore-skin zone, while the two aquifer parameters are hydraulic conductivity and specific storage of the formation zone. It is worthy to note although the thickness of the wellbore-skin zone is usually taken as an input data for the data-analyzed software, it is actually an unknown parameter that cannot be measured directly. This paper proposes a methodology for estimating the thickness of the wellbore-skin zone with other hydraulic parameters at the same time. Eight sets of well water-level (WWL) data of aquifers with both positive and negative skins are generated by Moench and Hsieh [Moench and Hsieh, 1985] and four sets of standard normally distributed noise are then added to each set of WWL data. The results indicate that the negative-skin cases generally give a better estimated result than that of the positive-skin cases. Sensitivity analysis is also employed to demonstrate the physical behavior when slug test was performed under positive-skin effect. For the case of an aquifer with a positive-skin, the use of a longer series of WWL data for analysis is strongly recommended for better estimation of aquifer hydraulic conductivity. Analyzing the WWL data of the test and observation wells simultaneously could significantly improve the estimations on specific storages. Impetuously presuming an arbitrary value for the thickness of the wellbore-skin zone may lead to poor estimation for the other four parameters. [Copyright &y& Elsevier]

Summary: Generally, a pumping test requires a lot of effort and expense to perform the test and the drawdown is measured and analyzed for determining the aquifer parameters. The estimated aquifer parameters obtained from graphical approaches may not be in good accuracy if the pumping time is too short to give a good visual fit to the type curve. Yet, the problems of long pumping time and required efforts can be significantly reduced if the drawdown data are measured and the parameters are simultaneously estimated on-line. However, the drawdown behavior of the leaky and unconfined aquifers in response to the pumping may have a time lag and the time to terminate the estimation may not be easily and quickly to decide when applying a parameter estimation model (PEM) on-line to analyze the parameters. This study uses the sensitivity analysis to explore the influence period of each aquifer parameter to the pumping drawdown and the influence period is used as a guide in terminating the estimation when applying the PEM for on-line parameter identification. In addition, the sensitivity analysis is also used to study the effects of different value of S y and the distance between pumping well and observation well on the influence time of S y during the pumping. [Copyright &y& Elsevier]

Abstract??The slug test is a popular field method for estimating aquifer parameters. As a finite-thickness skin is present at a wellbore, the result of test-data analysis may represent average hydraulic properties of the skin and formation zones. Moench and Hsieh (Int. Assoc. of Hydrogeology, The IAH 17th International Congress on Hydrology of Rocks of Low Permeability, Int. Assoc. of Hydrogeology. Tucson, Arizona, 7?12 January) provided the Laplace-domain solution for a confined aquifer with a finite-thickness skin that satisfies the governing equations, boundary conditions, and continuity requirements at the interface of the skin and formation zones. Two new formulae presented here relate the modified zero-order Bessel functions of the first and second kinds to their first and second derivatives. Their solution is evaluated using the modified Crump approach for the Laplace inversion. The numerical values obtained by the modified Crump approach are compared with others based on finite-element modeling. The results indicate that the values based on finite-element modeling exhibit poor accuracy, attributed to errors in the mass balance equation and interface condition in their mathematical model. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical model is developed to investigate the effects of tidal fluctuations and leakage on the groundwater head of leaky confined aquifer extending an infinite distance under the sea. The leakages of the offshore and inland aquitards are two dominant factors controlling the groundwater fluctuation. The tidal influence distance from the coast decreases significantly with the dimensionless leakage of the inland aquitard (u i). The fluctuation of groundwater level in the inland part of the leaky confined aquifer increases significantly with the dimensionless leakage of the offshore aquitard (u o). The influence of the tidal propagation parameter of an unconfined aquifer on the head fluctuation of the leaky confined aquifer is comparatively conspicuous when u i is large and u o is small. In other words, ignoring water table fluctuation of the unconfined aquifer will give large errors in predicting the fluctuation, time lag, and tidal influence distance of the leaky confined aquifer for large u i and small u o. On the contrary, the influence of the tidal propagation parameter of a leaky confined aquifer on the head fluctuation of the leaky confined aquifer is large for large u o and small u i. [Copyright &y& Elsevier]

A mathematical model is presented for describing the groundwater flow in a radial two-layer confined aquifer system with a constant-flux pumping well that has a wellbore skin and finite well radius. The Laplace-domain solution for the model is first derived by the Laplace transforms; and the time-domain solution in terms of the aquifer drawdown is then obtained form the Laplace inversion using the Bromwich integral method. When neglecting the well radius, our Laplace-domain solution is shown to reduce to a Laplace-domain solution given by Butler [J. Hydrol. 101 (1988) 15]. A unified numerical approach including a root search approach, the Gaussian quadrature, and the Shanks method is employed for evaluating this time-domain solution. The evaluated results of the solution agree well with those of the Laplace-domain solution estimated by the modified Crump algorithm. This new solution can be used either to predict the spatial and temporal drawdown distributions in both the skin and formation zones or to investigate the effects of the skin type, skin thickness and well radius on the drawdown distribution. [Copyright &y& Elsevier]

Presents a study which derived a closed-form mathematical solution for transient flow rates across the wellbore when performing a constant-head test in a two-zone confined aquifer system. Use of a numerical approach to evaluate the derived solution; Information on the values of the transient flow rate; Identification of the effects of a skin with a finite thickness on the estimation of transient flow rates in a ground-water system.

The Laplace transform is applied to solve the groundwater flow equation with a boundary that is initially fixed but that starts to move at a constant rate after some fixed time. This problem arises in the study of pore water pressures due to erosional unloading where the aquifer lies underneath an unsaturated zone. We derive an analytic solution and examine the predicted pressure profiles and boundary fluxes. We calculate the negative pore water pressure in the aquifer induced by the initial erosion of the unsaturated zone and subsequent erosion of the aquifer. [ABSTRACT FROM AUTHOR]

Stream depletion due to groundwater extraction by wells may cause impact on aquatic ecosystem in streams, conflict over water rights, and contamination of water from irrigation wells near polluted streams. A variety of studies have been devoted to addressing the issue of stream depletion, but a fundamental framework for analytical modeling developed from aquifer viewpoint has not yet been found. This review shows key differences in existing models regarding the stream depletion problem and provides some guidelines for choosing a proper analytical model in solving the problem of concern. We introduce commonly used models composed of flow equations, boundary conditions, well representations and stream treatments for confined, unconfined, and leaky aquifers. They are briefly evaluated and classified according to six categories of aquifer type, flow dimension, aquifer domain, stream representation, stream channel geometry, and well type. Finally, we recommend promising analytical approaches that can solve stream depletion problem in reality with aquifer heterogeneity and irregular geometry of stream channel. Several unsolved stream depletion problems are also recommended. [ABSTRACT FROM AUTHOR]

A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang’s et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters. [ABSTRACT FROM AUTHOR]