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1.
A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

2.
The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

3.
An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin.  相似文献   

4.
Groundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

5.
An aquifer containing a skin zone is considered as a two-zone system. A mathematical model describing the head distribution is presented for a slug test performed in a two-zone confined aquifer system. A closed-form solution for the model is derived by Laplace transforms and Bromwich integral. This new solution is used to investigate the effects of skin type, skin thickness, and the contrast of skin transmissivity to formation transmissivity on the distributions of dimensionless hydraulic head. The results indicate that the effect of skin type is marked if the slug-test data is obtained from a radial two-zone aquifer system. The dimensionless well water level increases with the dimensionless positive skin thickness and decreases as the dimensionless negative skin thickness increases. In addition, the distribution of dimensionless well water level due to the slug test depends on the hydraulic properties of both the wellbore skin and formation zones.  相似文献   

6.
Y. C. Chang  H. D. Yeh  G. Y. Chen 《水文研究》2010,24(11):1496-1503
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7.
The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.  相似文献   

8.
This paper presents an analytical solution to tide‐induced head fluctuations in a two‐dimensional estuarine‐coastal aquifer system that consists of an unconfined aquifer and a heterogeneous confined aquifer extending under a tidal river with a semipermeable layer between them. This study considers the joint effects of tidal‐river leakage, inland leakage, dimensionless transmissivity between the tidal‐river and inland confined aquifer, and transmissivity anisotropic ratios. The analytical solution for this model is obtained via the separation of variables method. Three existing solutions related to head fluctuation in one‐ or two‐dimensional leaky confined aquifers are considered as special cases in the present solution. This study shows that there is a threshold of tidal‐river confined aquifer length. When the tidal‐river length is greater than the threshold length, the inland head fluctuations remain sensitive to the leakage effect but become insensitive to the tidal‐river width and dimensionless transmissivity. Considering leakage and transmissivity anisotropy, this study also demonstrates that at a location farther from the river–inland boundary, head fluctuations increase with increasing leakage and transmissivity anisotropy; the maximum head fluctuation occurs when leakage and transmissivity anisotropy are both at their maximum values. The combined action of the 3 effects of loading, tidal‐river aquifer leakage, and inland aquifer leakage differs significantly according to various aquifer parameters. The analytical solution in this paper can be applied to demonstrate the behaviours of the head fluctuations of an estuarine‐coastal aquifer system, and the head fluctuations can be clearly described when the tidal and hydrogeological parameters are derived from field measurement data or hypothetical cases.  相似文献   

9.
A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions.  相似文献   

10.
The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.  相似文献   

11.
This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

12.
We present an analytical solution of groundwater head response to tidal fluctuation in a coastal multilayered aquifer system consisting of an unconfined aquifer, a leaky confined aquifer and a semi‐permeable layer between them. The submarine outcrop of the confined aquifer is covered by a thin silt layer. A mathematical model and the analytical solution of this model are given. The silt layer reduces the amplitude of the hydraulic head fluctuation by a constant factor, and shifts the phase by a positive constant (time lag), both of which depend on the leakances of the silt layer and the semi‐permeable layer. The time lag is less than 1·5 h and 3·0 h for semi‐diurnal and diurnal sea tides respectively. When the leakance of the semi‐permeable layer or the silt layer assumes certain special values, the solution becomes the existing solutions derived by previous researchers. The amplitude of the hydraulic head fluctuation in the confined aquifer increases with the leakance of the silt layer and decreases with the leakance of the semi‐permeable layer, whereas the phase shift of the fluctuation decreases with both of them. A hypothetical example shows that neglecting the silt layer may result in significant parameter estimation discrepancy between the amplitude attenuation and the time‐lag fittings. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

13.
The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.  相似文献   

14.
In this paper, we present a conceptual‐numerical model that can be deduced from a calibrated finite difference groundwater‐flow model, which provides a parsimonious approach to simulate and analyze hydraulic heads and surface water body–aquifer interaction for linear aquifers (linear response of head to stresses). The solution of linear groundwater‐flow problems using eigenvalue techniques can be formulated with a simple explicit state equation whose structure shows that the surface water body–aquifer interaction phenomenon can be approached as the drainage of a number of independent linear reservoirs. The hydraulic head field could be also approached by the summation of the head fields, estimated for those reservoirs, defined over the same domain set by the aquifer limits, where the hydraulic head field in each reservoir is proportional to a specific surface (an eigenfunction of an eigenproblem, or an eigenvector in discrete cases). All the parameters and initial conditions of each linear reservoir can be mathematically defined in a univocal way from the calibrated finite difference model, preserving its characteristics (geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses). We also demonstrated that, in practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. The reduced computational cost of these solutions can help to integrate the groundwater component within conjunctive use management models. Conceptual approximation also facilitates understanding of the physical phenomenon and analysis of the factors that influence it. A simple synthetic aquifer has been employed to show how the conceptual model can be built for different spatial discretizations, the parameters required, and their influence on the simulation of hydraulic head fields and stream–aquifer flow exchange variables. A real‐world case was also solved to test the accuracy of the proposed approaches, by comparing its solution with that obtained using finite‐difference MODFLOW code. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

15.
Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.  相似文献   

16.
Analytical solutions for contaminant transport in a non‐uniform flow filed are very difficult and relatively rare in subsurface hydrology. The difficulty is because of the fact that velocity vector in the non‐uniform flow field is space‐dependent rather than constant. In this study, an analytical model is presented for describing the three‐dimensional contaminant transport from an area source in a radial flow field which is a simplest case of the non‐uniform flow. The development of the analytical model is achieved by coupling the power series technique, the Laplace transform and the two finite Fourier cosine transform. The developed analytical model is examined by comparing with the Laplace transform finite difference (LTFD) solution. Excellent agreements between the developed analytical model and the numerical model certificate the accuracy of the developed model. The developed model can evaluate solution for Peclet number up to 100. Moreover, the mathematical behaviours of the developed solution are also studied. More specifically, a hypothetical convergent flow tracer test is considered as an illustrative example to demonstrate the three‐dimensional concentration distribution in a radial flow field. The developed model can serve as benchmark to check the more comprehensive three‐dimensional numerical solutions describing non‐uniform flow contaminant transport. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

17.
Steady interface flow in heterogeneous aquifer systems is simulated with single‐density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m3). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi‐aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben‐Herzberg formula. The transformed problem may be solved with a single‐density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi‐aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached.  相似文献   

18.
This article investigates the quantity of submarine groundwater discharge (SGD) from a coastal multi‐layered aquifer system in response to constant rainfall infiltration. The system comprises an unconfined aquifer, a leaky confined aquifer and an aquitard between them and terminates at the coastline. An approximate analytical solution is derived based on the following assumptions: (i) flow is horizontal in the aquifers and vertical in the aquitard, and (ii) flow in the unconfined aquifer is described by nonlinear Boussinesq equation. The analytical solution is compared with numerical solutions of the strictly two‐dimensional nonlinear model to validate the model assumptions used for the analytical solution. The SGD from the leaky confined aquifer increases with the inland rainfall infiltration recharge and the specific leakage of aquitard. The maximum SGD ranges from 1·87 to 10·37 m3 per day per meter of shoreline when rainfall infiltration ranges from 18·2 to 182 mm/year and the specific leakage of aquitard varies from 10?9 to 10?1 l/day. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

19.
In alluvial coastal aquifers, finer sediments are preferentially deposited along the downstream direction, so the hydraulic conductivity is generally heterogeneous and changes with distance from the coastline. To investigate the influence of aquifer heterogeneity on seawater‐groundwater interaction, a new two‐dimensional model characterising groundwater flow in an aquifer‐aquitard system was developed assuming that the hydraulic conductivity of the aquifer linearly increases with the distance from the coastline along the inland direction. A closed‐form analytical solution was derived using the separation‐of‐variables method. Comparing the new solution with the numerical solution by comsol Multiphysics (Sweden) based on the finite‐element method, one can see that the new solution agreed with the numerical solution very well except at the early time. We found that both aquitard leakance and the heterogeneity factor (b) could result in the propagation bias. The propagation bias represents the inconsistency between the theoretical calculation and the observed strong attenuation and small time lag between the head and tide fluctuations. The attenuation decreased with perpendicular distance from the coastline (x‐axis), whereas the time lag increased with distance along the x‐axis. The relationship between the time lag and the distance along the x‐axis seemed to be linear when b was 0.001 m?1, whereas it obeyed a power function when b was greater than 0.01 m?1. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown–time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown–time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.  相似文献   

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