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1.
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
2.
Hugo A. Loaiciga Roy B. Leipnik Paul F. Hudak Miguel A. Marino 《Mathematical Geology》1996,28(5):563-584
Starting with a stochastic differential equation with random coefficients describing steady-state flow, the effective hydraulic conductivity of 1-, 2-, and 3-dimensional aquifers is derived. The natural logarithm of hydraulic conductivity (lnK) is assumed to be heterogeneous, with a spatial trend, and isotropic. The effective conductivity relates the mean specific discharge in an aquifer to the mean hydraulic gradient, thus its importance in predicting Darcian discharge when field data represent mean or average values of conductivity or hydraulic head. Effective conductivity results are presented in exact form in terms of elementary functions after the introduction of special sets of coordinate transformations in two and three dimensions. It was determined that in one, two, and three dimensions, for the type of aquifer heterogeneity considered, the effective hydraulic conductivity depends on: (i) the angle between the gradient of the trend of lnK and the mean hydraulic gradient (which is zero in the one-dimensional situation); (2) (inversely) on the product of the magnitude of the trend gradient of lnK, b, and the correlation scale of lnK, and (3) (proportionally) on the variance of lnK,
f
2
. The productb plays a central role in the stability of the results for effective hydraulic conductivity. 相似文献
3.
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
4.
Hongbin Zhan 《Mathematical Geology》1999,31(1):113-134
Application of the ergodicity hypothesis to the stochastic subsurface hydrology has been checked by investigating the hydraulic conductivity field. The relative variance of the spatial average of conductivity, which is denoted as R, and the error index E.I. =
, were employed to justify the uncertainties and errors of using the ergodicity hypothesis. Six factors influence R: autocorrelation function; variance of logconductivity; spatial correlation scales of logconductivity; domain sizes; anisotropy; and dimensionality of the problem. Closed-form analytical solutions of R for the linear autocorrelation function were derived and the numerical integration of R for the exponential autocorrelation function for one-, two-, and three-dimensional problems calculated. It is easy to fulfill the ergodicity hypothesis under these conditions: weak heterogeneity and large ratio of domain size vs. correlation length (L/I). The uncertainties and errors of using this hypothesis increase rapidly when the variances of logconductivity increase and/or the ratios of L/I decrease. The ergodicity hypothesis has less error when applied to a problem with higher dimensionality. 相似文献
5.
通过模拟均质和非均质两种情形下非饱和-饱和系统中压力水头的时空变化,研究非饱和-饱和系统对水流波动的 阻尼作用和系统非均质性对水流波动的作用。结果显示,两种情形下非饱和-饱和系统对水流波动均有阻尼作用,随深度 增加,压力水头波动减弱,方差、自协方差和功率谱减小;压力水头在早期因初始条件做非平稳波动,而后随时间增长演 变为平稳波动;系统的非均质性加剧了压力水头的波动,是波动的主要来源,使得压力水头方差、自协方差和功率谱增 大;非均质性减小压力水头波动的短期相关性。 相似文献
6.
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
7.
Temporary dams can be formed by the sudden injection of debris flow into main streams by some favorable geomorphologic and
hydraulic conditions, resulting in extensive inundations upstream and catastrophic floods downstream due to dam breaches and
consequently dramatic changes of channels and valleys. Expeditious means of assessing dam-forming potential are necessary,
particularly in geologically active regions. Complete blockages or dam formations are significantly related to the discharge
ratio and velocity ratio between the tributary and the main stream, the bulk density of the debris flow, confluent angles
and the degree of unevenness of grain sizes. In order to set up a critical index/C for dam formation, 19 groups of flume tests were conducted. The results showed that there were three types of blockage in
the intersections, and dam-forming processes were mainly controlled by the product of the dimensionless momentum ratio and
the degree of unevenness of grain sizes in the debris flow. Complete blockages or dam formations occurred when C > 83.4, whereas semi-blockages were formed or no dams were formed when C < 71.5, which had been judged to be feasible by historical instances of dam formation in China. Dam failures commonly resulted
from overtopping. No piping was observed in the course of dam failure, and the time elapsed between dams can be denoted by
a linear relation with the momentum ratio. 相似文献
8.
区域尺度上含水层非均质具有复杂的结构性和随机性,难以准确刻画,造成非均质对区域地下水流系统的影响机制研究不够深入。本文以鄂尔多斯盆地白垩系地下水流系统为研究实例,选择典型剖面,采用剖面二维随机数值模拟方法,通过对比不同非均质刻画方法下地下水流场的变化,探讨含水层层状非均质对地下水流系统的影响机制。结果显示,均质条件下模型各向异性（含水层水平和垂向渗透系数比值Kh/Kv）取值为1000时,地下水流场与实际条件较为接近;非均质条件下,渗透系数方差取值0.91,水平相关长度取值5000 m,Kh/Kv取值150时,接近实际条件。研究表明,在大尺度地下水流模拟研究中,采用水平相关长度、渗透系数方差和各向异性值三个变量生成的随机场能很好地刻画含水层的层状非均质特征及其对水流系统的影响控制作用。由于含水层不同尺度层状非均质的叠加效应,采用均质各向异性介质等效概化含水层层状非均质性会造成等效各向异性值偏大失真的效应。 相似文献
9.
Regional scale models of groundwater flow and transport often employ domain discretizations with grid blocks larger than typical scales of field data. For heterogeneous formations, this difference in scales is often handled by using effective (upscaled) parameters. We investigate the problem of upscaling hydraulic conductivity and transmissivity from a small scale of measurement to a larger scale of grid blocks. Transmissivity statistics is expressed in terms of statistics of hydraulic conductivity, and expressions for the effective (upscaled) hydraulic conductivity K
eff and transmissivity T
eff for steady state flow in confined heterogeneous aquifers are derived by means of stochastic averaging and perturbation analysis. These expressions reveal that the commonly used relation T
eff = BK
eff, where B is the confined aquifer thickness, is not generally valid. 相似文献
10.
Gregory D. Lazear 《Hydrogeology Journal》2006,14(8):1582-1598
The Tongue Creek watershed lies on the south flank of Grand Mesa in western Colorado, USA and is a site with 1.5 km of topographic relief, heat flow of 100 mW/m2, thermal conductivity of 3.3 W m–1 °C–1, hydraulic conductivity of 10-8 m/s, a water table that closely follows surface topography, and groundwater temperatures 3–15°C above mean surface temperatures. These data suggest that convective heat transport by groundwater flow has modified the thermal regime of the site. Steady state three-dimensional numerical simulations of heat flow, groundwater flow, and convective transport were used to model these thermal and hydrological data. The simulations provided estimates for the scale of hydraulic conductivity and bedrock base flow discharge within the watershed. The numerical models show that (1) complex three-dimensional flow systems develop with a range of scales from tens of meters to tens of kilometers; (2) mapped springs are frequently found at locations where contours of hydraulic head indicate strong vertical flow at the water table, and; (3) the distribution of groundwater temperatures in water wells as a function of surface elevation is predicted by the model. 相似文献
11.
We continue the work that was initiated in (K. H. Karlsen, K.-A. Lie, and N. H. Risebro. A fast marching method for reservoir
simulation. Comp. Geo., 4(2) (2000)185–206) on a marching method for simulating two-phase incompressible immiscible flow of water and oil in a porous
medium. We first present an alternative derivation of the marching method that reveals a strong connection to modern streamline
methods. Then, through the study of three numerical test cases we present two deficiencies: (i) the original marching algorithm
does not always compute the correct solution of the underlying difference equations, and (ii) the method gives largely inaccurate
arrival times in the presence of large jumps within the upwind difference stencil. As a remedy of the first problem, we present
a new advancing-front method, which is faster than the original marching method and guarantees a correct solution of the underlying
discrete linear system. To cure the second problem, we present two adaptive strategies that avoid the use of finite-difference
stencils containing large jumps in the arrival times. The original marching method was introduced as a fast tool for simulating
two-phase flow scenarios in heterogeneous formations. The new advancing-front method has limited applicability in this respect,
but may rather be used as a fast and relatively accurate method for computing arrival times and derived quantities in heterogeneous
media. 相似文献
12.
Extenuating the parameters using HEC-HMS hydrological model for ungauged catchment in the central Omo-Gibe Basin of Ethiopia 
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下载免费PDF全文 Demisse Habtamu Semunigus Ayalew Abebe Temesgen Ayana Melkamu Teshome Lohani Tarun Kumar 《地下水科学与工程》2021,9(4):317-325
Characteristics of ungauged catchments can be studied from the hydrological model parameters of gauged catchments. In this research, discharge prediction was carried out in ungauged catchments using HEC-HMS in the central Omo-Gibe basin. Linear regression, spatial proximity, area ratio, and sub-basin mean were amalgamated for regionalization. The regional model parameters of the gauged catchment and physical characteristics of ungauged catchments were collated together to develop the equations to predict discharge from ungauged catchments. From the sensitivity analysis, crop coefficient (CC), storage coefficient (R), constant rate (CR), and time of concentration (TC) are found to be more sensitive than others. The model efficiency was evaluated using Nash–Sutcliffe Efficiency (NSE) which was greater than 0.75, varying between ?10% and +10% and the coefficient of determination (R2) was approximated to be 0.8 during the calibration and validation period. The model parameters in ungauged catchments were determined using the regional model (linear regression), sub-basin mean, area ratio, and spatial proximity methods, and the discharge was simulated using the HEC-HMS model. Linear regression was used in the prediction where p-value ≤ 0.1, determination coefficient (R2) = 0.91 for crop coefficient (CC) and 0.99 for maximum deficit (MD). Constant rate (CR), maximum storage (MS), initial storage (IS), storage coefficient (R), and time of concentration (TC) were obtained. The result is that an average of 30 m3/s and 15 m3/s as the maximum monthly simulated flow for ungauged sub-catchments, i.e. Denchiya and Mansa of the main river basin . 相似文献
13.
将土壤或含水层的介质参数视为随机分布,建立了饱和非饱和水流运动的随机微分方程,利用随机数值求解方法,得到各种随机参数对水头分布和含水量空间变异性的影响。分析结果表明,随着渗透系数空间变异性和相关尺度的增大,含水层水头分布的变异性增大;对于区域内有抽水井分布的问题,在井点附近区域,z向水流速度空间变异性大,而在井点处变异性较小。当采用Gardner-Russo模型描述非饱和水分特征时,其非饱和土壤介质参数α的变异性对土壤负压和含水量变异性的影响大于饱和渗透系数,土壤含水量越小,含水量的空间变异性越大。初步讨论了根据随机数值方法研究地下水运动问题的可靠性分析方法。 相似文献
14.
15.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
16.
L.B. Reid G. Bloomfield L.P. Ricard C. Botman P. Wilkes 《Australian Journal of Earth Sciences》2013,60(7):1033-1048
Exploration of Perth's geothermal potential has been performed by the Western Australian Geothermal Centre of Excellence (WAGCoE). Detailed vertical temperature and gamma ray logging of 17 Western Australia Department of Water's (DoW) Artesian Monitoring (AM) wells was completed throughout the Perth Metropolitan Area (PMA). In addition, temperature logs from 53 DoW AM wells measured in the 1980s were digitised into LAS format. The logged data are available in the WAGCoE Data Catalogue. Analysis of the gamma ray logs yielded the first estimates of radiogenic heat production in Perth Basin formations. Values by formation ranged between 0.24 and 1.065 μW m?3. The temperature logs provide a picture of true formation temperatures within shallow sediments in the Perth Basin. A three-dimensional model of the temperature distribution was used to produce maps of temperature at depth and on the top of the Yarragadee aquifer. The temperature data were interpreted with a one-dimensional conductive heat model. Significant differences between the model and the observations was indicative of heat moving via non-conductive mechanisms, such as advection or convection. Evidence of non-conductive or advective heat flow is demonstrated in most formations in the region, with significant effects in the aquifers. Average conductive geothermal gradients range from 13°C km?1 to 39°C km?1, with sandstone formations exhibiting average gradients of approximately 25°C km?1, while insulating silt/shale formations show higher average gradients of over 30°C km?1. To produce preliminary heat flow estimates, temperature gradients were combined with thermal conductivities measured elsewhere. The geometric mean heat flow estimates range between 64 mW m?2 to 91 mW m?2, with the standard deviation of the arithmetic mean heat flow ranging between 15 and 23 mW m?2. The study characterises the shallow temperature regime in the Perth Metropolitan Area, which is of direct relevance towards developing commercial geothermal projects. 相似文献
17.
K. Muthukrishnavellaisamy G. C. Mishra M. L. Kansal N. C. Ghosh 《Environmental Geology》2009,57(4):899-908
For predicting and forecasting fate of non-conservative pollutants downstream from source using advection–dispersion–decay
equation (ADDE), estimation of three parameters; mean flow velocity (U), longitudinal dispersion co-efficient (D
L) and decay rate co-efficient (λ), is required a priori. In this three parameters model, estimation of D
L holds difficulties and draws interest towards it. The empirical formulae use the field and experimental data of channel and
flow characteristics to estimate D
L. In this paper, an innovative approach has been proposed towards the estimation of D
L using regime channel concept. Having known discharge of flow and silt factor of the riverbed material, hydraulic parameters
of the channel can be determined theoretically, which in turn can be used to estimate D
L appropriately making use of a suitable empirical formula. 相似文献
18.
Assessment of porous aquifer hydrogeological parameters using automated groundwater level measurements in Greece 下载免费PDF全文
下载免费PDF全文 Kirlas Marios C 《地下水科学与工程》2021,9(4):269-278
In this paper, the hydrogeological parameters of a confined aquifer, such as transmissivity (T), storativity (S) and radius of influence (R), have been assessed using real groundwater level measurements recorded by a monitoring network, consisting of automated municipal water supply boreholes at Nea Moudania aquifer, Chalkidiki, Greece. Particularly, the paper focused on the correlation between the drawdown and the constant flow rate during pumping time. So the Cooper-Jacob and the recovery test method were applied in order to delineate if turbulent head losses occur, as well as the impact of incorrect measurements of the radial distance (r) in the accuracy of estimating S values. The results show that a) the occurrence of a linear correlation between s and Q indicates a negligible turbulent head loss in the pumping wells and thus a reasonable flow rate usage, b) the validity of storativity values could be compromised if the r value is not accurately measured, and c) recovery test method can be used as an indicator of residual drawdown (s’) caused by previous pumping cycles, when the straight line intersecting the logarithmic t/t’ axis has a value greater than 1. 相似文献
19.
A new approach is proposed to analyze the surface flow and subsurface flow passing over a pervious ground under a uniform rainfall excess. The flow field is divided into two regions that are called water layer and soil layer. To figure out the hydraulic behavior of overland flow on an inclined plane under a rainfall event, the simplified Navier–Stokes equations are employed for the surface water flow, and the flow inside the soil layer is porous media flow, which is governed by Biot's (1956, 1962) theory of poroelasticity. The velocity distribution of overland flow is nonzero at the ground surface. The relation between water depth and slope length was developed first. The profile of surface water flow was then found backwards from the downstream end of the flow section by the Runge–Kutta method. After that, the flow velocity and flow discharge of each layer could also be obtained via the water depth. Finally, the variation of fluid shear stress inside the soil layer is also discussed. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
20.
Groundwater pollution due to discharge of industrial effluents in Venkatapuram area, Visakhapatnam, Andhra Pradesh, India 总被引：1，自引：0，他引：1
Hindustan Polymers Limited was established in the Venkatapuram area in the northwestern part of Visakhapatnam urban agglomeration.
Untreated industrial effluent from the plant is discharged with total dissolved solids concentrations reaching up to 6500 mg/l.
The groundwater pollution was identified as early as 1981 and a hydrogeologic and water-quality database is available from
1981. The groundwater quality in the plant environs is found to be in the range of 3500–4500 mg/l. Major chemical constituents
of industrial-waste waters consist of Na, Cl, and SO4. Some characteristic parameters of the aquifer were estimated. The available hydrogeologic and hydrologic data was analyzed
to conceptualize the groundwater regime. A mathematical groundwater flow model was constructed to compute the hydraulic head
at the center of finite-difference grid. The computed head distribution and effective porosity of the formations were used
to calculate the groundwater flow velocity. The computed velocity field was ultimately used to prognose the pollutant migration
in groundwater accounting for the advection and dispersion processes in the mass transport model and for determining the time-dependent
pathlines of pollutant. Areal migration of pollutants from the source was predicted up to year 2002.
Received: 23 December 1996 · Accepted: 9 September 1997 相似文献