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1.
Due to changes in lithostatic pressure, differential fracturing across bedding planes and irregularities in depositional environments, hydraulic conductivity exhibits heterogeneities and trends at various spatial scales. Using spectral theory, we have examined the effect of trends in hydraulic conductivity on (1) the solution of the mean equation for hydraulic head, (2) the covariance of hydraulic head, (3) the cross-covariances of hydraulic head and log-hydraulic conductivity perturbations and their gradients, and (4) the effective hydraulic conductivity. It is shown that the field of hydraulic head is sensitive to the presence of trends in ways that cannot be predicted by the classical analysis based on stationary hydraulic conductivity fields. The controlling variables for the second moments of hydraulic head are the mean hydraulic gradient, the correlation scale of log-hydraulic conductivity and its variance, and the slope of the trend in log-hydraulic conductivity. The mean hydraulic gradient introduces complications in the analysis since it is, in general, spatially variable. In this respect, our results are approximate, yet indicative of the true role of spatially variable patterns of log-hydraulic conductivity on groundwater flow systems.  相似文献   

2.
We present a second-order analytic solution [in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions.  相似文献   

3.
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4.
Analytical studies on release/capture zones are often limited to a uniform background groundwater flow. In fact, for basin-scale problems, the undulating water table would lead to the development of hierarchically nested flow systems, which are more complex than a uniform flow. Under the premise that the water table is a replica of undulating topography and hardly influenced by wells, an analytical solution of hydraulic head is derived for a two-dimensional cross section of a drainage basin with horizontal injection/pumping wells. Based on the analytical solution, distributions of hydraulic head, stagnation points and flow systems (including release/capture zones) are explored. The superposition of injection/pumping wells onto the background flow field leads to the development of new internal stagnation points and new flow systems (including release/capture zones). Generally speaking, the existence of n injection/pumping wells would result in up to n new internal stagnation points and up to 2n new flow systems (including release/capture zones). The analytical study presented, which integrates traditional well hydraulics with the theory of regional groundwater flow, is useful in understanding basin-scale groundwater flow influenced by human activities.  相似文献   

5.
Conservative tracer experiments can provide information useful for characterizing various subsurface transport properties. This study examines the effectiveness of three different types of transport observations for sensitivity analysis and parameter estimation of a three-dimensional site-specific groundwater flow and transport model: conservative tracer breakthrough curves (BTCs), first temporal moments of BTCs (m 1), and tracer cumulative mass discharge (M d) through control planes combined with hydraulic head observations (h). High-resolution data obtained from a 410-day controlled field experiment at Vandenberg Air Force Base, California (USA), have been used. In this experiment, bromide was injected to create two adjacent plumes monitored at six different transects (perpendicular to groundwater flow) with a total of 162 monitoring wells. A total of 133 different observations of transient hydraulic head, 1,158 of BTC concentration, 23 of first moment, and 36 of mass discharge were used for sensitivity analysis and parameter estimation of nine flow and transport parameters. The importance of each group of transport observations in estimating these parameters was evaluated using sensitivity analysis, and five out of nine parameters were calibrated against these data. Results showed the advantages of using temporal moment of conservative tracer BTCs and mass discharge as observations for inverse modeling.  相似文献   

6.
水平井的水力特征及其解析解的适用条件   总被引：3，自引：0，他引：3  
利用自制的水平井砂槽模型, 进行了一系列不同流量条件下的水平井抽水试验, 结果表明: (1)在不同出流条件下, 水平井井管中可以同时出现层流-粗糙紊流多种不同流态; (2) 水平井出流条件下, 井管中的水头损失既不能忽略, 也不服从线性变化规律.它与井管中的水流流态有关.用“等水头井壁”或“等强度线汇”来刻画水平井井壁边界条件是不全面的.根据“等强度线汇”理论得到的解析解与试验结果对比发现, 本试验条件下解析解的近似适用条件是: 水平井管中的水流全部为层流(Re < 2 320)或者层流和层流-光滑紊流过渡区(Re < 4 000)同时并存的情况.当水平井管中出现光滑紊流区(Re> 4 000), 即同时有层流、层流-光滑紊流过渡态和光滑紊流或更多种流态时, 解析解已不再适用, 此时必须用新的层流-管流耦合模型来求解.   相似文献   

7.
Transmissivity (T) is a basic hydraulic parameter of an aquifer that is utilized in most groundwater flow equations to understand the flow dynamics and is generally estimated from pumping tests. However, the cost of performing a large number of aquifer tests is expensive and time consuming. The fact that specific capacity (S c) is correlated with hydraulic flow properties of aquifers simplifies parameter estimation mainly because specific capacity values are more abundant in groundwater databases than values of transmissivity and they offer another approach to estimate hydraulic parameters of aquifers. In this study, an empirical relation is derived using 214 pairs of transmissivity and specific capacity values that are obtained from pumping tests conducted on water wells penetrating the complex volcanic aquifers of Upper Awash Basin, central Ethiopia. Linear and logarithmic regression functions have been performed and it is found that the logarithmic relationship predicting transmissivity from specific capacity data has a better correlation (R = 0.97) than the linear relationship (R = 0.79). The two parameters are log-normally distributed, in which the logarithmic relation is also better statistically justified than the linear relation. Geostatistical estimations of the transmissivity were made using different inputs and methods. Measured and supplemented transmissivity data obtained from estimates using the derived empirical relation were krigged and cokrigged, spherical and exponential models were fitted to the experimental variograms. The cross-validation results showed that the best estimation is provided using the kriging procedure, the transmissivity field represented by the measured transmissivity data and the experimental variogram fitted with the exponential model. Based on the geostatistical approach, the transmissivity map of the aquifer is produced, which will be used for groundwater flow modeling of the study area that will follow this analysis.  相似文献   

8.
A hierarchical geostatistical analysis is conducted on a high-resolution, multiscale hydraulic conductivity (ln K) map, created by scaling up an experimental stratigraphy. Unlike a previous study which evaluates ln K variograms within individual depositional environments, this study analyzes deposits (or samples) that incorporate multiple depositional environments. Based on conductivity cutoffs selected from a global ln K histogram, an indicator map is created to divide the deposits into 4 categories: sand, silty sand, clayey silt, and clay (Hierarchy-I). Based on facies and facies assemblage types selected using geological criteria, two more indicator maps are created at a higher hierarchy (Hierarchy-II) to divide the deposits into 14 units and 2 units, respectively. For each sample, its experimental ln K variogram is decomposed into 4 auto- and cross-transition component variograms. The decomposition characteristics are then evaluated against the underlying heterogeneity and specific division rule. The analysis reveals that: (1) ln K cutoffs (sand contents of the physical stratigraphy) can be used to distinguish the shifts in dominant deposition mode; (2) sample univariate modes depend on the choice of hierarchical division; (3) sample variograms exhibit smooth-varying correlation structures (exponential-like variograms are observed in samples with a large variance in mean facies length); (4) the decomposition characteristics are sensitive to the division based on conductivity cutoffs, but not sensitive to the division based on depositional environment (For all samples, with appropriate division, the sample variogram is closely approximated by the sum of the cross-transition component variograms.); and (5) at the Hierarchy-II level, the 2-unit division gives similar decomposition characteristics as the 14-unit division. For the select samples, parsimony in hierarchical division is achieved at the facies assemblage scale.  相似文献   

9.
A mathematical model describing the hydraulic head distribution for a constant‐head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer‐region transmissivity to patch‐region transmissivity as α. The dimensionless hydraulic head for α=0.1 case is about 2.72 times to that for α=10 case at dimensionless large time (e.g. τ?106) when the dimensionless distance (ρ) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two‐zone formations. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

10.
We shall consider diffusion or single-phase flow in a multiscale porous medium which represents an infinite set of self-similar double-porosity media. At each scale, the medium consists of a highly permeable network of connected channels and low-permeable blocks. The characteristic scale of heterogeneity is ε at the highest level of hierarchy, wherein ε is a small parameter. The ratio between the channel and block permeability at each scale is ε 2. The process analyzed is described using a diffusion equation with an oscillating multiscale diffusion parameter. The macroscale behavior is of interest. The transition to the macroscale is performed by means of the two-scale homogenization procedure. One step of averaging at each level of hierarchy leads to the appearance of the memory terms in the averaged equation. The successive averaging steps lead to progressive memory accumulation, so at each step of averaging, the macroscale model changes its type, and even the result of the second step is unknown a priori. The objective was to determine the macroscopic limit model for the infinite number of scales. By the method of induction, we obtained the macroscale model for an arbitrary number of scales and its limit for the infinite hierarchy. The limit model represents the system of two equations with memory terms. The kernel of the memory operator is the solution of a nonlinear integro-differential equation. Its solution is obtained through Laplace transform.  相似文献   

11.
We consider groundwater steady flow in a heterogeneous porous formation of random and stationary log-conductivity Y = ln K, characterized by the mean 〈Y〉, and the two point correlation function C Y which in turn has finite, and different horizontal and vertical integral scales I and I v , respectively. The fluid velocity V, driven by a given head drop applied at the boundary, has constant mean value U ≡ (U, 0, 0). Approximate explicit analytical expressions for transverse velocity covariances are derived. The adopted methodology follows the approach developed by Dagan and Cvetkovic (Spatial moments of kinetically sorbing plume in a heterogeneous aquifers, Water Resour. Res. 29 (1993) 4053) to obtain a similar result for the longitudinal velocity covariance. Indeed, the approximate covariances of transverse velocities are determined by requiring that they have the exact first order variances as well as zero integral scale (G. Dagan, Flow and Transport in Porous Formations (Springer, 1989)) , and provide the exact asymptotic limits of the displacement covariance of the fluid particles obtained by Russo (On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations 1. Saturated flow, Water Resour. Res., 31 (1995) 129). Comparisons with numerical results show that the proposed expressions compare quite well in the early time regime, and for Ut/I >100. Since most of the applications, like assessing the effective mobility of contaminants or quantifying the potential hazards of nuclear repositories, require predictions over higher times the proposed approximate expressions provide acceptable results. The main advantage related to such expressions is that they allow obtaining closed analytical forms of spatial moments pertaining to kinetically sorbing contaminant plumes avoiding the very heavy computational effort which is generally demanded. For illustration purposes, we consider the movement of one contaminant species, and show how our approximate spatial moments compare with the numerical simulations.  相似文献   

12.
Open boreholes in fractured rock often cross-connect fractures with differing hydraulic head and the head differences between these fractures cause vertical flow in the water column. This cross-connection has potential to bias transmissivity (T) values obtained from straddle packer tests. This study demonstrates how measurements of the blended head in the open-hole segments above and below the straddle-packer test interval can be used to correct packer tests for cross-connection effects. A pressure response observed in the open-hole segment above and/or below the packers isolating a test interval during a hydraulic test indicates short-circuiting of water from the injection interval through the vertically connected fracture network to the open-hole segments, resulting in the overestimation of T. A method is presented using blended head concepts to minimize this error using a trial-and-error procedure to determine the short-circuiting flow rate to account for the head conditions in the open-hole segments during each hydraulic test. Observed differences between the measured head and the calculated blended head in the open-hole segments above and below the test interval are attributed to cross-connection effects around the 1-m-long packers. The head and corrected T values determined from packer tests are used to estimate the flow in and out of the open hole at each of the intervals tested for assessing the cross-connection effects under open borehole conditions. Understanding open-hole flow dynamics gives insight about the potential for vertical cross connection of chemical constituents caused by the open hole.  相似文献   

13.
This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K s and the shape parameter vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented.  相似文献   

14.
水平面渗流有限元中利用接触单元模拟悬挂式阻水结构   总被引：1，自引：0，他引：1  
骆冠勇  曹洪  房营光 《岩土力学》2007,28(12):2691-2697
区域性渗流场由于范围大,通常忽略掉竖向的水头损失而用水平面二维有限元进行分析,但在城区区域渗流场中悬挂式阻水结构物量多,竖向绕流现象突出,用一般水平面二维有限元进行分析将产生较大的偏差。针对这一问题在悬挂式结构体周边引入一层无厚度界面接触单元。在水平面有限元中利用它考虑因竖向绕流产生的局部水头损失。利用阻力系数的方法和二维状态下截面突变流道流动的解析解,同时考虑防渗墙本身的弱透水性,推导了接触单元的导水矩阵。应用接触单元编制了相关程序,在水平面有限元中利用接触单元对悬挂式阻水结构进行分析,并将结果与三维有限元进行比较,两者的计算结果在流量上保持一致,在水头上前者是后者在同一位置处沿高程方向平均值。提出的该计算方法,对于用水平面二维有限元分析含有悬挂式阻水结构的大区域渗流问题,是一个有效的手段。  相似文献   

15.
The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater interface below mean sea level follows from the Dupuit–Ghyben–Herzberg relation. The method of solution presented in this work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping.  相似文献   

16.
Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K v, plays a more prominent role than the fractal dimension, D a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D a1d and K v, D a1d × K v, is suggested to capture the aperture anisotropy.  相似文献   

17.
Assessment of the sampling variance of the experimental variogram is an important topic in geostatistics as it gives the uncertainty of the variogram estimates. This assessment, however, is repeatedly overlooked in most applications mainly, perhaps, because a general approach has not been implemented in the most commonly used software packages for variogram analysis. In this paper the authors propose a solution that can be implemented easily in a computer program, and which, subject to certain assumptions, is exact. These assumptions are not very restrictive: second-order stationarity (the process has a finite variance and the variogram has a sill) and, solely for the purpose of evaluating fourth-order moments, a Gaussian distribution for the random function. The approach described here gives the variance–covariance matrix of the experimental variogram, which takes into account not only the correlation among the experiemental values but also the multiple use of data in the variogram computation. Among other applications, standard errors may be attached to the variogram estimates and the variance–covariance matrix may be used for fitting a theoretical model by weighted, or by generalized, least squares. Confidence regions that hold a given confidence level for all the variogram lag estimates simultaneously have been calculated using the Bonferroni method for rectangular intervals, and using the multivariate Gaussian assumption for K-dimensional elliptical intervals (where K is the number of experimental variogram estimates). A general approach for incorporating the uncertainty of the experimental variogram into the uncertainty of the variogram model parameters is also shown. A case study with rainfall data is used to illustrate the proposed approach.  相似文献   

18.
Inversion methods that rely on measurements of the hydraulic head h cannot capture the fine-scale variability of the hydraulic properties of an aquifer. This is particularly true for direct inversion methods, which have the further limitation of providing only deterministic results. On the other hand, stochastic simulation methods can reproduce the fine-scale heterogeneity but cannot directly incorporate information about the hydraulic gradient. In this work, a hybrid approach is proposed to join a direct inversion method (the comparison model method, CMM) and multiple-point statistics (MPS), for determination of a hydraulic transmissivity field T from a map of a reference hydraulic head \(h^\mathrm {(ref)}\) and a prior model of the heterogeneity (a training image). The hybrid approach was tested and compared with pure MPS and pure CMM approaches in a synthetic case study. Also, sensitivity analysis was performed to test the importance of the acceptance threshold \(\delta \), a simulation parameter that allows one to tune the influence of \(h^\mathrm {(ref)}\) on the final results. The transmissivity fields T obtained using the hybrid approach take into account information coming from the hydraulic gradient while simultaneously reproducing some of the fine-scale features provided by the training image. Furthermore, many realizations of T can be obtained thanks to the stochasticity of MPS. Nevertheless, it is not straightforward to exploit the correlation between the T maps provided by the CMM and the prior model introduced by the training image, because the former depends on the boundary conditions and flow settings. Another drawback is the growing number of simulation parameters introduced when combining two diverse methods. At the same time, this growing complexity opens new possibilities that deserve further investigation.  相似文献   

19.
程大伟  陈茜  安鹏  郭鸿  郑睿 《岩土力学》2015,36(10):2951-2954
渗流场水头分布计算是进行渗流量和渗流水力坡降计算的基础,准确、有效地求取渗流场水头分布是渗流计算的关键环节。对均质非饱和土体一维稳态流的流动方程进行分析,考虑到渗透系数是与基质吸力相关的函数,通过数学变换,给出了稳定渗流场的解析通式,并基于渗透性函数中的Gardner模型,给出了非饱和土一维稳态流水头垂直分布的解析解。该解析通式表明,均质非饱和土一维稳态流水头垂直分布主要受地表水头、深度和流动率3个因素控制。分别计算了一维稳态蒸发条件下粉土和黏土两种典型土类水头沿垂直方向的分布。计算结果表明：稳态蒸发条件下粉土层和黏土层内的水头分布表现出相似的变化规律,即自地表至地下水位处随着土层深度的增加,水头分布呈现出加速递减的趋势;在相同的蒸发条件下,对于相同深度处的黏土和粉土而言,黏土层内水头更高些;对同一种土类而言,在较大的蒸发状态下同一深度处土层内水头更高。反之,则较低。  相似文献   

20.
Here, I describe a theoretical approach to the structure and chemical composition of minerals based on their bond topology. This approach allows consideration of many aspects of minerals and mineral behaviour that cannot be addressed by current theoretical methods. It consists of combining the bond topology of the structure with aspects of graph theory and bond-valence theory (both long range and short range), and using the moments approach to the electronic energy density-of-states to interpret topological aspects of crystal structures. The structure hierarchy hypothesis states that higher bond-valence polyhedra polymerize to form the (usually anionic) structural unit, the excess charge of which is balanced by the interstitial complex (usually consisting of large low-valence cations and (H2O) groups). This hypothesis may be justified within the framework of bond topology and bond-valence theory, and may be used to hierarchically classify oxysalt minerals. It is the weak interaction between the structural unit and the interstitial complex that controls the stability of the structural arrangement. The principle of correspondence of Lewis acidity–basicity states that stable structures will form when the Lewis-acid strength of the interstitial complex closely matches the Lewis-base strength of the structural unit, and allows us to examine the factors that control the chemical composition and aspects of the structural arrangements of minerals. It also provides a connection between a structure, the speciation of its constituents in aqueous solution and its mechanism of crystallization. The moments approach to the electronic energy density-of-states provides a link between the bond topology of a structure and its thermodynamic properties, as indicated by correlations between average anion coordination number and reduced enthalpy of formation from the oxides for [6]Mg m [4] Si n O(m+2n) and MgSO4(H2O) n .  相似文献   

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