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1.
A finite layer approach for the general problem of three‐dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three‐layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems. 相似文献
2.
Numerical approximation of head and flux covariances in three dimensions using mixed finite elements
《Advances in water resources》1999,22(7):729-740
A numerical method is developed for accurately approximating head and flux covariances and cross-covariances in finite two- and three-dimensional domains using the mixed finite element method. The method is useful for determining head and flux covariances for non-stationary flow fields, for example those induced by injection or extraction wells, impermeable subsurface barriers, or non-stationary hydraulic conductivity fields. Because the numerical approximations to the flux covariances are obtained directly from the solution to the coupled problem rather than having to differentiate head covariances, the approximations are in general more accurate than those obtained from conventional finite difference or finite element methods. Results for uniform flow example problems are consistent with results from previously published finite domain analyses and demonstrate that head variances and covariances are quite sensitive to boundary conditions and the size of the bounded domain. Flux variances and covariances are less sensitive to boundary conditions and domain size. Results comparing approximations from lower-order Raviart–Thomas–Nedelec and higher order Brezzi–Douglas–Marini[9] finite element spaces indicate that higher order element space improve the estimate of the flux covariances, but do not significantly affect the estimate of the head covariances. 相似文献
3.
《Advances in water resources》1999,22(7):697-710
Flownets are useful tools for the visualization of groundwater flow fields. Using orthogonal flownets as grids for transport modeling is an effective way to control numerical dispersion, especially transverse to the direction of flow. Therefore tools for automatic generation of flownets may be seen both as postprocessors for groundwater flow simulations and preprocessors for contaminant transport models. Existing methods to generate streamline-oriented grids suffer from drawbacks such as the inability to include sources in the interior of the grid. In this paper, we introduce a new method for the generation of streamline-oriented grids which handles wells in the grid interior, and which produces orthogonal grids for anisotropic systems. Streamlines are generated from an accurate velocity field obtained from the solution of the mixed-hybrid finite element method for flow, while pseudopotentials, which are orthogonal to the streamlines, are obtained by a standard finite element solution of the pseudopotential equation. A comprehensive methodology for the generation of orthogonal grids, including the location of stagnation points and dividing streamlines, is introduced. The effectiveness of the method is illustrated by means of examples. A related paper presents a compatible formulation of the solution for reactive transport, while a second related paper gives a detailed quantitative assessment of the various forms of modelled mixing and their effect on the accuracy of simulations of the biodegradation of groundwater contaminants. 相似文献
4.
A generalized transformation approach for simulating steady-state variably-saturated subsurface flow
A numerical method is proposed to accurately and efficiently compute a direct steady-state solution of the nonlinear Richards equation. In the proposed method, the Kirchhoff integral transformation and a complementary transformation are applied to the governing equation in order to separate the nonlinear hyperbolic characteristic from the linear parabolic part. The separation allows the transformed governing equation to be applied to partially- to fully-saturated systems with arbitrary constitutive relations between primary (pressure head) and secondary variables (relative permeability). The transformed governing equation is then discretized with control volume finite difference/finite element approximations, followed by inverse transformation. The approach is compared to analytical and other numerical approaches for variably-saturated flow in 1-D and 3-D domains. The results clearly demonstrate that the approach is not only more computationally efficient but also more accurate than traditional numerical solutions. The approach is also applied to an example flow problem involving a regional-scale variably-saturated heterogeneous system, where the vadose zone is up to 1 km thick. The performance, stability, and effectiveness of the transform approach is exemplified for this complex heterogeneous example, which is typical of many problems encountered in the field. It is shown that computational performance can be enhanced by several orders of magnitude with the described integral transformation approach. 相似文献
5.
Elena Zhebel Sara Minisini Alexey Kononov Wim A. Mulder 《Geophysical Prospecting》2014,62(5):1111-1125
The finite‐difference method on rectangular meshes is widely used for time‐domain modelling of the wave equation. It is relatively easy to implement high‐order spatial discretization schemes and parallelization. Also, the method is computationally efficient. However, the use of finite elements on tetrahedral unstructured meshes is more accurate in complex geometries near sharp interfaces. We compared the standard eighth‐order finite‐difference method to fourth‐order continuous mass‐lumped finite elements in terms of accuracy and computational cost. The results show that, for simple models like a cube with constant density and velocity, the finite‐difference method outperforms the finite‐element method by at least an order of magnitude. Outside the application area of rectangular meshes, i.e., for a model with interior complexity and topography well described by tetrahedra, however, finite‐element methods are about two orders of magnitude faster than finite‐difference methods, for a given accuracy. 相似文献
6.
地电磁场的直接求解法存在伪解现象,且电磁场分量在界面上的不连续性与节点型有限元的基本要求矛盾. 本文将Coulomb 规范下磁矢量势-电标量势与自适应有限元相结合,提出了地球物理电磁场计算的快速、高精度方法. 首先从地电磁场一般边值问题出发,给出了Coulomb 规范下磁矢量势-电标量势的公式系统,分析了求解域内势的连续性. 采用Galerkin 加权余值法推导出积分弱解形式和Delaunay非结构化四面体单元时Hierarchal 基函数的有限元方程. 基于超收敛恢复技术,提出了适用于电磁场的后验误差估计方法,阐述了地电磁场自适应计算的策略及迭代算法,分析了计算时间消耗和误差收敛性质,表明本文方法可以用最优的计算资源得到呈拟指数收敛到准确解的数值结果,从而为后续的数值计算奠定了理论基础. 相似文献
7.
The main goal of this work is to appraise the finite element method in the way it represents barotropic instabilities. To that end, three different formulations are employed. The free-surface formulation solves the primitive shallow-water equations and is of predominant use for ocean modeling. The vorticity–stream function and velocity–pressure formulations resort to the rigid-lid approximation and are presented because theoretical results are based on the same approximation. The growth rates for all three formulations are compared for hyperbolic tangent and piecewise linear shear flows. Structured and unstructured meshes are utilized. The investigation is also extended to time scales that allow for instability meanders to unfold, permitting the formation of eddies. We find that all three finite element formulations accurately represent barotropic instablities. In particular, convergence of growth rates toward theoretical ones is observed in all cases. It is also shown that the use of unstructured meshes allows for decreasing the computational cost while achieving greater accuracy. Overall, we find that the finite element method for free-surface models is effective at representing barotropic instabilities when it is combined with an appropriate advection scheme and, most importantly, adapted meshes. 相似文献
8.
9.
Delineating ground water recharge from leaking irrigation canals using water chemistry and isotopes 总被引：1，自引：0，他引：1
Across the Great Plains irrigation canals are used to transport water to cropland. Many of these canals are unlined, and leakage from them has been the focus of an ongoing legal, economic, and philosophical debate as to whether this lost water should be considered waste or be viewed as a beneficial and reasonable use since it contributes to regional ground water recharge. While historically there has been much speculation about the impact of canal leakage on local ground water, actual data are scarce. This study was launched to investigate the impact of leakage from the Interstate Canal, in the western panhandle of Nebraska, on the hydrology and water quality of the local aquifer using water chemistry and environmental isotopes. Numerous monitoring wells were installed in and around a small wetland area adjacent to the canal, and ground water levels were monitored from June 1992 until January 1995. Using the water level data, the seepage loss from the canal was estimated. In addition, the canal, the monitoring wells, and several nearby stock and irrigation wells were sampled for inorganic and environmental isotope analysis to assess water quality changes, and to determine the extent of recharge resulting from canal leakage. The results of water level monitoring within study wells indicates a rise in local ground water levels occurs seasonally as a result of leakage during periods when the canal is filled. This rise redirects local ground water flow and provides water to nearby wetland ecosystems during the summer months. Chemical and isotopic results were used to delineate canal, surface, and ground water and indicate that leaking canal water recharges both the surface alluvial aquifer and upper portions of the underlying Brule Aquifer. The results of this study indicate that lining the Interstate Canal could lower ground water levels adjacent to the canal, and could adversely impact the local aquifer. 相似文献
10.
The response of a reinforced concrete freeway structure damaged during the Northridge earthquake is determined using non-linear dynamic finite element analysis. The results obtained allow the ability of contemporary analysis techniques to predict the seismic response of such structures to be assessed and the critical aspects of the behaviour of the structure to be identified. Comparison is made with the response predicted using equivalent static analysis and more simplified dynamic analysis, from which the results of the more advanced analysis are shown to be superior. The influence of a number of modelling assumptions, principally with regard to boundary conditions, on the computed response is also assessed. From this, the disparity between the design conditions and those actually pertaining at the time of the earthquake are seen to play a crucial role in the mode of failure of the structure. It is concluded that, upon the development of an accurate structural model, the analytical results correlated well with the behaviour observed in post-earthquake reconnaissance. 相似文献
11.
标准升温条件下PEC柱耐火极限理论分析及简化计算 总被引：1，自引：0，他引：1
基于ABAQUS软件建立了标准升温条件下局部填充混凝土（Partially Encaed Concrete,简称PEC）柱抗火性能分析的有限元模型,计算了火灾下PEC柱的变形曲线及耐火极限,计算结果得到了已有试验数据的验证。利用上述模型分析了截面几何参数、材料物理参数、荷载比及偏心率等因素对耐火极限的影响。在参数分析的基础上,建立了标准升温条件下PEC耐火极限简化计算方法。结果表明：无耐火保护PEC柱的耐火极限一般达不到现有抗火标准的要求;荷栽比、长细比和截面周长是影响PEC柱耐火极限的主要因素;该耐火极限简化计算方法可供工程设计参考。 相似文献
12.
Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks. 相似文献
13.
Modeling Stream-Aquifer Interactions Under Seasonal Groundwater Pumping and Managed Aquifer Recharge
In South Korea, a significant amount of groundwater is used for the heating of water-curtain insulated greenhouses during the winter dry season, which had led to problems of groundwater depletion. A managed aquifer recharge (MAR) project is currently underway with the goal of preventing such groundwater depletion in a typical cultivation area, located on an alluvial aquifer near the Nam River. In the present study, FEFLOW, a three-dimensional finite element model, was used to evaluate different strategies for MAR of the cultivation areas. A conceptual model was developed to simulate the stream-aquifer dynamics under the influence of seasonal groundwater pumping and MAR. The optimal rates and duration of MAR were assessed by analyzing the recovery of the groundwater levels and the change in the groundwater temperature. The simulation results indicate that a MAR rate of 8000 m3/d effectively restores the groundwater level when the injection wells are located inside the groundwater depletion area. It is also demonstrated that starting the MAR before the beginning of the seasonal pumping is more effective. Riverbank filtration is preferable for securing the injection water owing to plentiful source of induced recharge from the river. Locating the pumping wells adjacent to the river where there are thick permeable layers could be a good strategy for minimizing decreases in the groundwater level and temperature. 相似文献
14.
Prediction of CO2 injection performance in deep subsurface porous media relies on the ability of the well to maintain high flow rates of carbon dioxide during several decades typically without fracturing the host formation or damaging the well. Dynamics of solid particulate suspensions in permeable media are recognized as one major factor leading to injection well plugging in sandstones. The invading supercritical liquid-like fluid can contain exogenous fine suspensions or endogenous particles generated in situ by physical and chemical interactions or hydrodynamic release mechanisms. Suspended solids can plug the pores possibly leading to formation damage and permeability reduction in the vicinity of the injector. In this study we developed a finite volume simulator to predict the injectivity decline near CO2 injection wells and also for production wells in the context of enhanced oil recovery. The numerical model solves a system of two coupled sets of finite volume equations corresponding to the pressure-saturation two-phase flow, and a second subsystem of solute and particle convection-diffusion equations. Particle transport equations are subject to mechanistic rate laws of colloidal, hydrodynamic release from pore surfaces, blocking in pore bodies and pore throats, and interphase particle transfer. The model was validated against available laboratory experiments at the core scale. Example results reveal that lower CO2 residual saturation and formation porosity enhance CO2-wet particle mobility and clogging around sinks and production wells. We conclude from more realistic simulations with heterogeneous permeability spanning several orders of magnitude that the control mode of mobilization, capture of particles, and permeability reduction processes strongly depends on the type of permeability distribution and connectivity between injection and production wells. 相似文献
15.
In our previous study, we developed the Stokes–Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers–Joseph (BJ) condition was used to describe the matrix–conduit interface. We also studied the mathematical well‐posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. In this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. Using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further model validation studies are based on the results of laboratory experiments. Comparing the results of computer simulations and experiments, we concluded that the SD model with the Beavers–Joseph interface condition is a valid model for conduit–matrix systems. On the other hand, the CCPF model with the value of the exchange parameter chosen within the range suggested in the literature perhaps does not result in good agreement with experimental observations. We then examined the sensitivity of the CCPF model with respect to the exchange parameter, concluding that, as has previously been noted, the model is highly sensitive for small values of the exchange parameter. However, for larger values, the model becomes less sensitive and, more important, also produces results that are in better agreement with experimental observations. This suggests that the CCPF model may also produce accurate simulation results, if one chooses larger values of the exchange parameter than those suggested in the literature. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
16.
The positive and negative difference of deep and shallow resisitivity in formation without invasion is caused mainly by the fixed two tool constants from numerical simulations. A dynamic calibration method for tool constants is proposed based on the effects of the mud and formation resisitivity ratio on the two constants calculated using the finite element method (FEM). Finally, four specific examples are given to validate the dynamic calibration method. It is an automatic borehole correction method and can give more accurate formation resistivity. The method is useful for dual laterolog logging. 相似文献
17.
带弹簧支撑的新型泥石流拦挡坝抗冲击性能研究 总被引：2，自引：0，他引：2
为了解决普通重力式泥石流拦挡坝在大规模泥石流发生时容易被大块石损毁的问题,提出带弹簧支撑的新型泥石流拦挡坝,并采用钢球代替泥石流中的大块石,运用有限元软件ANSYS/LS-DYNA对这种新型坝体进行泥石流大块石的冲击模拟,从坝体的变形、支反力、Von Mises应力、加速度和应变率5个方面与普通重力式拦挡坝进行对比分析。结果表明：与普通泥石流拦挡坝相比,带弹簧支撑的新型泥石流拦挡坝的支反力可减小3/4左右,钢球的冲击加速度可降到1/3.87,坝体的响应加速度可降到1/2.61,说明带弹簧支撑的新型泥石流拦挡坝具有非常好的抗冲击性能。 相似文献
18.
Plume containment using pump-and-treat (PAT) technology continues to be a popular remediation technique for sites with extensive groundwater contamination. As such, optimization of PAT systems, where cost is minimized subject to various remediation constraints, is the focus of an important and growing body of research. While previous pump-and-treat optimization (PATO) studies have used discretized (finite element or finite difference) flow models, the present study examines the use of analytic element method (AEM) flow models. In a series of numerical experiments, two PATO problems adapted from the literature are optimized using a multi-algorithmic optimization software package coupled with an AEM flow model. The experiments apply several different optimization algorithms and explore the use of various pump-and-treat cost and constraint formulations. The results demonstrate that AEM models can be used to optimize the number, locations and pumping rates of wells in a pump-and-treat containment system. Furthermore, the results illustrate that a total outflux constraint placed along the plume boundary can be used to enforce plume containment. Such constraints are shown to be efficient and reliable alternatives to conventional particle tracking and gradient control techniques. Finally, the particle swarm optimization (PSO) technique is identified as an effective algorithm for solving pump-and-treat optimization problems. A parallel version of the PSO algorithm is shown to have linear speedup, suggesting that the algorithm is suitable for application to problems that are computationally demanding and involve large numbers of wells. 相似文献
19.
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
20.
Dariusz Gąsiorowski 《Acta Geophysica》2013,61(3):668-689
In the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring to the procedure of spatial integration leads to a more general algorithm involving a weighting parameter. Time integration is carried out using a two-level difference scheme with the weighting parameter as well. The resulting tri-diagonal systems of nonlinear algebraic equations are solved using the Picard iterative method. For particular sets of the weighting parameters, the proposed method takes the form of a standard finite element method and various schemes of the finite difference method. On the other hand, for the linear version of the governing equation, the proper values of the weighting parameters ensure an approximation of 3rd order. Since the diffusive wave equation can be solved no matter whether the area is dry or wet, the numerical computations can be carried out over entire domain of solution without distinguishing a current position of the shoreline which is obtained as a result of solution. 相似文献