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1.
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. 相似文献
2.
《Advances in water resources》2004,27(10):981-990
The Theis equation has been widely used to study the transient movement of groundwater as a result of pumping in a confined aquifer. It is well known that the observed drawdown at early times has an obvious departure from the theoretical drawdown based on the Theis equation. The Theis equation was derived under the assumption that total stress in the aquifer was constant and the mechanical behavior of the confining unit was neglected. However, most geological formations, especially those which are well consolidated, have rigidity and therefore may bend like a plate to a certain extent. The increase in the effective stress in the aquifer due to pumping may not contribute entirely to the compression of the aquifer, but may be partially cancelled out by bending of the overlying aquitard. This means only a part of the total stress is used to compact the aquifer, or the aquifer cannot produce as much water as estimated from the Theis equation. This paper investigated the impact of the bending effect of the confining unit on drawdown. An analytical model which couples flow in the aquifer and bending of the confining unit was presented. The theory is based on elastic plates and solutions were given to the drawdown of groundwater level and deflection of the overlying formation. The drawdown estimated from the new equation was compared with that from the Theis equation. It can be concluded that drawdown from the Theis equation is less than the drawdown predicted by including the bending effect of the confining unit. Both a hypothetical example and a field pumping test in Shandong Province, China, were used to demonstrate the bending effect of the confining unit in the analysis of pumping test data. This paper demonstrated that the initial disagreement between observed drawdown and the Theis solution could be caused by the bending effect of the confining unit, a phenomenon not well addressed in traditional pumping test analysis. A quantitative understanding of this phenomenon can provide improved guidelines for analyzing drawdown data in a confined aquifer. 相似文献
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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
5.
This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values. 相似文献
7.
Detecting and quantifying small drawdown at observation wells distant from the pumping well greatly expands the characterized aquifer volume. However, this detection is often obscured by water level fluctuations such as barometric and tidal effects. A reliable analytical approach for distinguishing drawdown from nonpumping water‐level fluctuations is presented and tested here. Drawdown is distinguished by analytically simulating all pumping and nonpumping water‐level stresses simultaneously during the period of record. Pumping signals are generated with Theis models, where the pumping schedule is translated into water‐level change with the Theis solution. This approach closely matched drawdowns simulated with a complex three‐dimensional, hypothetical model and reasonably estimated drawdowns from an aquifer test conducted in a complex hydrogeologic system. Pumping‐induced changes generated with a numerical model and analytical Theis model agreed (RMS as low as 0.007 m) in cases where pumping signals traveled more than 1 km across confining units and fault structures. Maximum drawdowns of about 0.05 m were analytically estimated from field investigations where environmental fluctuations approached 0.2 m during the analysis period. 相似文献
8.
Tomas Perina 《Ground water》2021,59(3):438-442
Time-domain analytical solution for groundwater flow to a fully penetrating flowing well is derived using the same substitution technique used to re-derive (Perina 2010) the Theis (1935) equation and the approximate solution by Mishra and Guyonnet (1992) is confirmed. The exponential integral-based flowing well function is a computationally effective alternative to the original Jacob and Lohman (1952) solution in integral form. For a constant drawdown test, the ratio of drawdown at an observation well to the flowrate is equivalent to drawdown response to pumping at unit constant rate; the transformed observations can be analyzed using the Theis (1935) function. Analysis of field test shows that simultaneous fitting to measurements of flow from the test well and drawdown at an observation well results in more accurate and better resolved estimates of aquifer properties than fitting to flow observations only. 相似文献
9.
An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data. 相似文献
10.
An analysis method for slug tests performed in a partially penetrating well within a vertical cutoff wall is presented. A steady‐state shape factor for evaluating hydraulic conductivity of the material within the wall was derived by applying the method of images to the previously developed analytical solution of Zlotnik et al. (2010) for an infinite aquifer. Two distinct boundary conditions were considered: constant‐head boundary for the case of direct contact between the wall and the aquifer, and no‐flux boundary representing an impermeable filter cake on the sides of the wall. The constant‐head and no‐flux boundary conditions yield significantly higher and lower shape factors, respectively, than those for the infinite aquifer. Consequently the conventional line‐fitting method for slug test analysis would yield an inaccurate estimate of the hydraulic conductivity of a vertical cutoff wall. 相似文献
11.
Renard P 《Ground water》2005,43(3):439-442
The calculation of the discharge to a constant drawdown well or tunnel in the presence of an infinite linear constant head boundary in an ideal confined aquifer usually relies on the numerical inversion of a Laplace transform solution. Such a solution is used to interpret constant head tests in wells or to roughly estimate ground water inflow into tunnels. In this paper, a simple approximate solution is proposed. Its maximum relative error is on the order of 2% as compared to the exact analytical solution. The approximation is a weighted mean between the early-time and late-time asymptotes. 相似文献
12.
We have investigated non‐Darcian flow to a vertical fracture represented as an extended well using a linearization procedure and a finite difference method in this study. Approximate analytical solutions have been obtained with and without the consideration of fracture storage based on the linearization procedure. A numerical solution for such a non‐Darcian flow case has also been obtained with a finite difference method. We have compared the numerical solution with the approximate analytical solutions obtained by the linearization method and the Boltzmann transform. The results indicate that the linearized solution agrees generally well with the numerical solution at late times, and underestimates the dimensionless drawdown at early times, no matter if the fracture storage is considered or not. When the fracture storage is excluded, the Boltzmann transform solution overestimates the dimensionless drawdown during the entire pumping period. The dimensionless drawdowns in the fracture with fracture storage for different values of dimensionless non‐Darcian hydraulic conductivity β approach the same asymptotic value at early times. A larger β value results in a smaller dimensionless drawdown in both the fracture and the aquifer when the fracture storage is included. The dimensionless drawdown is approximately proportional to the square root of the dimensionless time at late times. 相似文献
13.
Serdar Korkmaz 《Ground water》2013,51(3):432-441
In this study, the well‐known Hantush solution procedure for groundwater mounding under infinitely long infiltration strips is extended to finite and semi‐infinite aquifer cases. Initially, the solution for infinite aquifers is presented and compared to those available in literature and to the numerical results of MODFLOW. For the finite aquifer case, the method of images, which is commonly used in well hydraulics, is used to be able to represent the constant‐head boundaries at both sides. It is shown that a finite number of images is enough to obtain the results and sustain the steady state. The effect of parameters on the growth of the mound and on the time required to reach the steady state is investigated. The semi‐infinite aquifer case is emphasized because the growth of the mound is not symmetric. As the constant‐head boundary limits the growth, the unbounded side grows continuously. For this reason, the groundwater divide shifts toward the unbounded side. An iterative solution procedure is proposed. To perform the necessary computations a code was written in Visual Basic of which the algorithm is presented. The proposed methodology has a wide range of applicability and this is demonstrated using two practical examples. The first one is mounding under a stormwater dispersion trench in an infinite aquifer and the other is infiltration from a flood control channel into a semi‐infinite aquifer. Results fit very well with those of MODFLOW. 相似文献
14.
Aquifer parameter estimation using an incremental area method 总被引：2，自引：0，他引：2
Theoretical well functions have been derived over the years to predict ground water level behaviour in aquifer systems under stress owing to groundwater extraction. The drawdown data collected during pump tests are typically analysed using graphical curve‐matching procedures to estimate aquifer parameters based on these well functions. Difficulty in aquifer characteristic identification and parameter estimation may arise when the field data do not perfectly match the drawdown curves obtained from the well functions. The present study provides a new method for the interpretation of aquifer pump tests which supplements the existing curve‐matching procedures in case ideal conditions do not exist; the proposed method provides a greater degree of flexibility in the data analysis for diagnostic tool purposes. The method, referred to as the Incremental Area Method (IAM) is based on integrating the logarithmic‐based drawdown curves within a discrete time and matching the results with a corresponding time integral of the Theis ( 1935 ) Well Function which governs ideal confined aquifers. The application of the proposed method to synthetically generated data and field data showed that IAM represents a viable method which yields information on potential non‐idealness of the aquifer and provides aquifer parameter estimates thus potentially overcoming drawdown data curve‐matching difficulties. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
In this study, we investigate the accuracy of approximating constant‐Q wave propagation by series of Zener or standard linear solid (SLS) mechanisms. Modelling in viscoacoustic and viscoelastic media is implemented in the time domain using the finite‐difference (FD) method. The accuracy of numerical solutions is evaluated by comparison with the analytical solution in homogeneous media. We found that the FD solutions using three SLS relaxation mechanisms as well as a single SLS mechanism, with properly chosen relaxation times, are quite accurate for both weak and strong attenuation. Although the RMS errors of FD simulations using a single relaxation mechanism increase with increasing offset, especially for strong attenuation (Q = 20), the results are still acceptable for practical applications. The synthetic data of the Marmousi‐II model further illustrate that the single SLS mechanism, to model constant Q, is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in computer time and memory. 相似文献
16.
Zhixue Zhao Xiaoguang Wang Yonghong Hao Tongke Wang Abderrahim Jardani Herve Jourde Tian‐Chyi Jim Yeh Ming Zhang 《水文研究》2019,33(19):2551-2560
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
17.
Uniform head in horizontal and vertical wells 总被引：1，自引：0，他引：1
The steady-state head within a fully penetrating well may be estimated by evaluating the Thiem equation at the radius of the well. A method is presented here to extend results from the Thiem equation to horizontal wells and to partially penetrating wells. The particular model used in this investigation is based upon the analytic element method; it accurately reproduces a boundary condition of uniform head along the cylindrical surface at the perforated face of the well. This model is exercised over a representative range of parameters including the well's length, radius, and pumping rate, and the aquifer's hydraulic conductivity and thickness. Results are presented in a set of figures and tables that compare the well's drawdown to the drawdown that would have been obtained using the Thiem solution with the same pumping rate and radius. A methodology is presented to estimate the head within a horizontal or partially penetrating well by adding a correction term to results that can be readily obtained from computer models of vertical fully penetrating wells. This approach may also be used to contrast the differences in head between horizontal and vertical wells of various lengths, radii, and placement elevations. 相似文献
18.
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
19.
Underdamped slug tests with unsaturated‐saturated flows by considering effects of wellbore skins 
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下载免费PDF全文 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
20.
Starting from the equations of Theis and Cooper-Jacob, two new mathematical methods are proposed for interpreting the residual drawdown data for an infinite confined aquifer. Under Theis' assumptions and using the Cooper-Jacob approximation, the principal aquifer characteristics of transmissivity, pumping storativity, and recovery storativity are expressed without any correction or additional assumption. An actual case is used for illustration and confirms the validity of proposed equations and methods. 相似文献