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1.
In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity kD results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter BD results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered. 相似文献
2.
AbstractAn analytical solution is developed to delineate the capture zone of a pumping well in an aquifer with a regional flow perpendicular to a stream, assuming a leaky layer between the stream and the aquifer. Three different scenarios are considered for different pumping rates. At low pumping rates, the capture zone boundary will be completely contained in the aquifer. At medium pumping rates, the tip of the capture zone boundary will intrude into the leaky layer. Under these two scenarios, all the pumped water is supplied from the regional groundwater flow in the aquifer. At high pumping rates, however, the capture zone boundary intersects the stream and pumped water is supplied from both the aquifer and the stream. The two critical pumping rates which separate these three scenarios, as well as the proportion of pumped water from the stream and the aquifer, are determined for different hydraulic settings.Editor D. Koutsoyiannis; Associate editor A. KoussisCitation Asadi-Aghbolaghi, M., Rakhshandehroo, G.R., and Kompani-Zare, M., 2013. An analytical approach to capture zone delineation for a well near a stream with a leaky layer. Hydrological Sciences Journal, 58 (8), 1813–1823. 相似文献
3.
Abstract This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated. Editor D. Koutsoyiannis; Associate editor J. Simunek Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172. 相似文献
4.
We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r1−n, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t(1−n)/(3−n), where t is the time. 相似文献
5.
We have derived an analytical solution for two-region flow toward a well in a confined aquifer based on a linearization method. The two-region flow includes Izbash non-Darcian flow near the well and Darcian flow in the rest of the aquifer. The wellbore storage is also considered. The type curves in the non-Darcian and Darcian flow domains are obtained by a numerical Laplace inversion method incorporated in MATLAB programs. We have compared our results with the one-region Darcian flow model (Theis). Our solutions agree with those of Sen [Sen Z. Type curves for two-region well flow. J Hydr Eng 1988;114(12):1461–84] which were obtained using the Boltzmann transform at late times for fully turbulent flow, while some difference has been found at early and moderate times. We have defined a dimensionless non-Darcian hydraulic conductivity term which is shown to be a key parameter for analyzing the two-region flow. A smaller dimensionless non-Darcian hydraulic conductivity results in a larger drawdown in the non-Darcian flow region at late times. However, the dimensionless non-Darcian hydraulic conductivity does not affect the slope of the dimensionless drawdown versus the logarithmic dimensionless time in the non-Darcian flow region at late times. The dimensionless non-Darcian hydraulic conductivity does not affect the late time drawdown in the Darcian flow region. 相似文献
6.
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 (ui). The fluctuation of groundwater level in the inland part of the leaky confined aquifer increases significantly with the dimensionless leakage of the offshore aquitard (uo). The influence of the tidal propagation parameter of an unconfined aquifer on the head fluctuation of the leaky confined aquifer is comparatively conspicuous when ui is large and uo 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 ui and small uo. 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 uo and small ui. 相似文献
7.
J. Zhu M. G. Satish 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(3):228-243
Stochastic analysis of one- and two-dimensional flow through a shallow semi-confined aquifer with spatially variable hydraulic
conductivity K represented by a stationary (statistically homogeneous) random process is carried out by using the spectral technique. The
hydraulic head covariance functions for flows in a semi-confined aquifer bounded by a leaky layer above and an impervious
stratum below are derived by assuming that the randomness forcing the head variation to originate from the hydraulic conductivity
field of the aquifer. The head covariance functions are studied using two convenient forms of the logarithmic hydraulic conductivity
process. The results demonstrate the significant reduction in the head variances and covariances due to the presence of a
leaky layer. The hydraulic head correlation distance is also reduced greatly due to the presence of the leaky layer. 相似文献
8.
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
9.
A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type-curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume. 相似文献
10.
Jacob Bear 《Advances in water resources》1977,1(1):15-23
A general methodology is presented for describing transport phenomena in porous media at a macroscopic level. Then, these macroscopic balance equations are integrated (or averaged) along the vertical for confined, leaky and phreatic aquifers.The results are employed to derive (averaged) aquifer equations for the flow of water and of a solute (hydrodynamic dispersion). It is shown that in all cases, the resulting equation is identical to that derived on the basis of an assumption of horizontal flow (the Dupuit assumption).Macrodispersion, occurring at the aquifer level, is discussed and appropriate coefficients are proposed. 相似文献
11.
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
12.
《水文科学杂志》2013,58(3):481-486
Abstract Explicit algebraic expressions of influence coefficients of an aquifer system are addressed. The methodology is straightforwardly exemplified using a one-dimensional (1D) semi-confined homogeneous aquifer model. It consists of the integration of the governing equation from two different viewpoints. On the one hand, the analytical solution to the governing equation is presented under an integral form involving the appropriate Green function. On the other hand, equations resulting from a finite difference discretization are processed to deduce a fully explicit algebraic expression of the nodal hydraulic head. This latter, arranged after the previously developed continuum solution, helps with deriving an explicit algebraic expression of influence coefficients corresponding to the studied aquifer model. Finally, the study is extended to an inhomogeneous aquifer model. 相似文献
13.
《水文科学杂志》2013,58(4):868-882
Abstract Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. 相似文献
14.
Travel time of marked fluid particles along arbitrary streamlines in arbitrary porous streamtubes is estimated from below based on the Cauchy–Bunyakovskii (Schwartz) and Jensen inequalities. In homogeneous media the estimate is strict and expressed through the length of the streamline, hydraulic conductivity, porosity and the head fall. The minimum is attained at streamlines of unidirectional flow. The bounds for heterogeneous soils, non-Darcian flows and unsaturated media are also written. If such bounds are attained the corresponding trajectories become brachistochrones. For example, in a two-layered aquifer and seepage perpendicular to the layers there is a unique conductivity–porosity ratio which makes a broken streamline brachistocronic. Similarly, if conductivities of two layers are fixed there is a unique incident angle between flow in one medium and the interface which makes a refracted streamline brachistocronic. 相似文献
15.
Existing analytical procedures for nonsteady flow in a leaky confined aquifer assume that the aquifer system is areally infinite. A technique is presented that treats a leaky confined aquifer system of finite configuration. By means of a discrete space continuous time (DSCT) modeling approach, the partial differential equation governing the flow system is transformed into a set of ordinary differential equations that can be easily integrated numerically on a high speed digital computer using available scientific subroutines. The finite difference formulation is in effect an explicit scheme. A criterion is developed for which the scheme is computationally stable. A numerical example is presented. 相似文献
16.
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
17.
Prof. M. PARDÉ 《水文科学杂志》2013,58(2):17-35
Abstract The “non-Darcian” behaviour of water in soils is discussed considering the coupling that can arise between the different transport phenomena. In general, it is shown that there is a reason to expect that a difference in osmotic pressure will arise when solutions flow through porous media, and that due to that difference the resulting flow be related in a non-linear fashion to the applied pressure difference. Several numerical examples are presented illustrating this behaviour. 相似文献
18.
C. J. Hemker 《Ground water》1985,23(2):247-253
Abstract. Although determination of aquifer characteristics from pumping test data is generally carried out using type curves or other graphical techniques, a number of computer methods have been developed recently for this purpose. Based on the principle of least squares, these methods of nonlinear regression analysis can be applied to any flow system for which analytical expressions of the drawdown distribution are known. In view of the growing general interest in the application of microcomputers in ground-water hydrology, a BASIC routine has been developed for estimating any number of aquifer parameters. The least squares solution is calculated by Marquardt's algorithm, using the singular-value decomposition of the Jacobian matrix. The robust computing method obtained can be applied to all kinds of pumping tests. Aquifer characteristics as well as their standard deviations are computed with optimal speed and accuracy. The technique is demonstrated by a simple application to steady flow in a leaky aquifer and an example is provided. Other applications are easily implemented and programs for unsteady-state aquifer tests, recovery tests and multiple aquifer tests are available. 相似文献
19.
This paper derives an equivalent of Darcian Theis solution for non-Darcian flow induced by constant rate pumping of a well in a confined aquifer. The derivation, which is valid at later times only, is original. It utilizes Izbash's equation. This introduces an additional parameter to Darcian condition, namely, empirical exponent. The solution is a non-Drcian equivalent of Jacob straight line method for analyzing pumping tests at late times. It can be used to determine aquifer parameters: storativity, analogous hydraulic conductivity, and empirical exponent. However, while the Jacob method requires a minimum of only one pumping test with one observation well, the additional parameter in the present solution means that a minimum of two observation wells in one test or two pumping tests at different rates with one observation well are required. The derived solution is applied to a case study at Plomeur in Brittany, France, and is shown to provide a practical and efficient method for analyzing pumping tests where non-Darcian groundwater flow occurs. 相似文献
20.
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