共查询到20条相似文献，搜索用时 15 毫秒
1.
A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells. 相似文献
2.
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
3.
气压作用下, 井-含水层系统中地下水流是一类流体力学问题。 本文应用井壁水流通量边界条件和气压作用下井壁内外水(孔)压平衡条件, 提出了一个井水位随气压变化的解析公式。 解析式表明, 气压系数随时段长度增加而增大, 并趋于气压常数; 气压系数随时段长度的变化只依赖于导水系数与井半径平方的比值(T/r2w), 而与气压变化过程无关; 气压常数只与含水层的一维荷载效率(B)有关, 而与导水系数和井半径无关。 解析解所反映的气压系数与时段长度的关系, 与南溪井实测序列数据分析结果具有很好的一致性。 根据气压系数随时段长度变化过程, 提出了一个参数估计方法, 应用于估计南溪井含水层气压常数和导水系数, 并对本文提出的参数估计方法进行了讨论。 相似文献
4.
J. M. Roger De Wiest 《Pure and Applied Geophysics》1963,54(1):87-102
Summary An analytical solution is obtained for the flow to an eccentric well in a leaky circular aquifer with lateral replenishment, both for steady and unsteady cases. The flows for external boundary conditions of constant head and zero flux, which were treated previously, follow in the limit from a more general boundary condition. Graphs are developed to show the influence of vertical leakage and lateral replenishment on the relationship between drawdown at the well and eccentricity.Other symbols are defined in the text as they occur. 相似文献
5.
Lloyd Stewart 《Ground Water Monitoring & Remediation》2022,42(2):35-46
Soil vapor extraction (SVE) is widely used to remove volatile organic compounds from the vadose zone. Design of SVE systems rely largely upon vacuum responses and limited vapor concentration data measured during short-term soil gas extraction tests performed in single extraction wells. Interpretation of such vacuum data is often simply a rule of thumb as most field sites have layering complexity negating applicability of existing analytical models. This paper provides the derivation of an analytical model for steady, axisymmetric gas flow in heterogeneous (layered) soils from a single well. A general, variable flow boundary condition along the well screen represents actual conditions more closely than a uniform flow or uniform well pressure condition. Each soil layer is assumed homogeneous with anisotropic gas permeability. The solution is derived using the generalized integral transform technique and includes expressions for vacuum, velocities, and streamlines. The model is applied to the interpretation of multiple well tests at a field site and uses linear superposition to extend the flow model to multi-well extraction. The demonstration site included an array of vacuum monitoring data collected during nine individual well flow tests. A method of normalizing the vacuum data is illustrated that allowed the full data set to be employed in a single calibration effort. The test site also included a surface cap with an apparent vertical permeability two to three orders of magnitude smaller than the sands of the vadose zone. This large permeability contrast posed no difficulties in evaluating the solution. 相似文献
6.
Stephen P. Garabedian 《Ground water》2013,51(6):927-934
A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model. 相似文献
7.
《Advances in water resources》2006,29(1):89-98
We present explicit analytic solutions describing the hydraulic head and discharge vector for two-dimensional, steady groundwater flow past an impermeable barrier embedded in a regional flow field. We use the solution to investigate the effects of open vertical barriers on the flow field; in particular, we examine the hydraulic containment of contaminant plumes or source zones by combination of a vertical barrier wall and extraction wells. We quantify the local reduction in discharge rates due to the barrier wall and the local increase in the size of the capture zone of an extraction well near an open, up-gradient barrier. We find that the combination of an open vertical barrier with down-gradient extraction wells can be very effective in decreasing the well discharge rate necessary to control a contaminant plume or source area. Design charts are presented for quantifying the effects of the barrier wall on the hydraulic control of the groundwater flow field and for estimating the jump in head across a barrier. The charts are appropriate for use in the preliminary design and cost estimating of remedial systems, and for the design of dewatering systems. 相似文献
8.
An analytic element approach is presented for the modeling of steady groundwater flow through multi-aquifer systems with piecewise constant aquifer and leaky layer properties. Different properties may be specified for domains bounded by closed polygons, referred to as polygonal inhomogeneities. The boundary of these inhomogeneities is modeled with two types of high-order line elements. First, a string of single-aquifer line-doublets is used; these elements cut through all aquifers and are valid both inside and outside the inhomogeneity. Second, two strings of multi-aquifer line-sinks are used, one string that is valid inside the inhomogeneity and one string that is valid outside; the comprehensive extraction of these line-sinks is zero at any point along the string. The proposed approach results in a comprehensive flow field of which the component normal to the boundary of the inhomogeneity is continuous across the boundary at any point. Within each individual aquifer, continuity of head and the component of flow normal to the boundary are met approximately across the boundary; the accuracy increases when the order of the line elements is increased and/or when shorter line elements are used. The proposed analytic element approach produces results that are virtually identical to the exact solution for a cylindrical inhomogeneity, and a high-resolution MODFLOW2000 model of two rectangular inhomogeneities with a shared boundary. The practical application of the approach is demonstrated through the solution of a problem with an irregularly shaped inhomogeneity with rivers crossing the inhomogeneity boundary. 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.
Inflow to a tunnel is a great public concern and is closely related to groundwater hydrology, geotechnical engineering, and mining engineering, among other disciplines. Rapid computation of inflow to a tunnel provides a timely means for quickly assessing the inflow discharge, thus is critical for safe operation of tunnels. Dewatering of tunnels is another engineering practice that should be planned. In this study, an analytical solution of the inflow to a tunnel in a fractured unconfined aquifer is obtained. The solution takes into account either the spherical or slab-shaped matrix block and the unsteady state interporosity flow. The instantaneous drainage water table and anisotropic hydraulic conductivities of the fractures network are also considered. Both uniform flux and uniform head boundary condition are considered to simulate the constant head boundary condition in the tunnel. The effects of the hydraulic parameters of the fractured aquifer on the inflow variation of the tunnel are explored. The application of the presented solution to obtain the optimum location and discharge of the well to minimize the inflow to a tunnel is illustrated. 相似文献
11.
Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers 总被引：1，自引：0，他引：1
Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed. 相似文献
12.
The steady state two dimensional groundwater flow equation with constant transmissivities was studied by Whittle in 1954 as a stochastic Laplace equation. He showed that the correlation function consisted of a modified Bessel function of the second kind, order 1, multiplied by its argument. This paper uses this pioneering work of Whittle to fit an aquifer head field to unequally spaced observations by maximum likelihood. Observational error is also included in the model. Both the isotropic and anisotropic cases are considered. The fitted field is then calculated on a two dimensional grid together with its standard deviation. The method is closely related to the use of two-dimensional splines for fitting surfaces to irregularly spaced observations. 相似文献
13.
We present explicit analytical solutions to problems of steady groundwater flow to a pumping well in an aquifer divided by an infinite, linear fault. The transmissivity of the aquifer is allowed to jump from one side of the fault to the other to model the juxtaposition of host rocks with different hydrologic properties caused by faulting. The fault itself is represented as a thin anisotropic inhomogeneity; this allows the fault to act as a combined conduit–barrier to groundwater flow, as is commonly described in the literature. We show that the properties of the fault may be represented exactly by two lumped parameters—fault resistance and fault conductance—and that the effects of the fault on flow in the adjacent aquifer is independent of the fault width. We consider the limiting cases of a purely leaky and a purely conductive fault where the fault domain may be replaced exactly by internal boundary conditions, and we investigate the effects of fault properties on the flow behavior in the adjacent aquifers. We demonstrate that inferring fault properties based on field observations of head in the aquifer is inherently difficult, even when the fault may be described by one of the two limiting cases. In particular, the effects of a leaky fault and a conductive fault on heads and discharges in the aquifer opposite the fault from the well, are shown to be identical in some cases. 相似文献
14.
Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions 
下载免费PDF全文
下载免费PDF全文 A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements. 相似文献
15.
We consider common bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional, groundwater flow to a horizontal well near a river in an unconfined aquifer. For the boundary-value problem investigated, we find that a unique solution exists for all negative well discharges. For positive discharges, a maximum value exists which corresponds to the formation of a cusp on the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem. We use the solution to investigate the behavior of the free surface under varying well discharges to identify stable pumping rates and predict well yield. In particular, we examine the well yield and the stability of the free surface when the head in the horizontal well is maintained at the top of the well screen. This condition is shown to produce a stable free surface for a wide range of well radii; the stability is independent of the hydraulic conductivity of the aquifer, the location of the well, or the presence of a skin resistance at the well. 相似文献
16.
In this paper we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed. 相似文献
17.
The Analytic Element Method (AEM) provides a convenient tool for groundwater flow analysis in unbounded continuous domains. The AEM is based on the superposition of analytic functions, known as elements, useful at both regional and local scales. In this study, analytic elements for strip aquifers are presented. Such aquifers occur in riverine or coastal deposits and in outcrop zones of confined aquifers. Local flow field is modelled indirectly, using a reference plane related to the aquifer domain through the Schwarz‐Christoffel transform. The regional flow is obtained as a solution of the one‐dimensional flow equation. The proposed methodology was tested by modelling two hypothetical situations, which were compared to exact solutions. It is shown that regional boundaries can be reproduced exactly while local fields are adequately reproduced with analytic elements. The developed elements are applied to simulate a real flow field in northeastern Brazil showing good agreement with measured water levels. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
Bakker M 《Ground water》2006,44(1):81-85
An analytic element approach is presented for the modeling of multiaquifer domains embedded in a single-aquifer model. The inside of each domain may consist of an arbitrary number of aquifers separated by leaky layers. The analytic element solution is obtained through a combination of existing single-aquifer and multiaquifer analytic elements and allows for the analytic computation of head and leakage at any point in the aquifer. Along the boundary of an embedded multiaquifer domain, the normal flux is continuous everywhere; continuity of head across the boundary is met exactly at collocations points and approximately, but very accurately, in between. The analytic element solution compares well with an existing exact solution. A hypothetical example with a river intersecting two embedded domains illustrates the practical application of the proposed approach. 相似文献
19.
Steady flow to a well near a stream with a leaky bed 总被引：2，自引：0，他引：2
We present an explicit analytic solution for steady, two-dimensional ground water flow to a well near a leaky streambed that penetrates the aquifer partially. Leakage from the stream is approximated as occurring along the centerline of the stream. The problem domain is infinite and pumping on one side of the stream induces flow on the other side. The solution includes the effects of uniform flow in the far field and a sloping hydraulic head in the stream. We use the solution to investigate the interaction between ground water and surface water in the stream, the effects of pumping on the opposite side of the stream, and the effects of the leaky streambed on the capture zone envelope of the well. We develop a relationship between parameters such that the pumping well will not capture water from the stream, or from the opposite side of the stream. When the discharge of the well is large enough to capture water from the stream, the shape of the capture zone envelope depends on flow conditions on the side of the stream opposite the well. 相似文献
20.
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