共查询到20条相似文献，搜索用时 15 毫秒
1.
Although recognized as important, measures of connectivity (i.e. the existence of high-conductivity paths that increase flow and allow for early solute arrival) have not yet been incorporated into methods for upscaling hydraulic conductivities of porous media. We present and evaluate a binary upscaling formula that utilizes connectivity information. The upscaled hydraulic conductivity (K) of binary media is determined as a function of the proportions and conductivities of the two materials, the geometry of the inclusions, and the mean distance between them. The use of a phase interchange theorem renders the formula equally applicable to two-dimensional media with inclusions of low K and high K as compared with the matrix. The new upscaling formula is tested on two-dimensional binary random fields spanning a broad range of spatial correlation structures and conductivity contrasts. The computed effective conductivities are compared to what is obtained using self-consistent effective medium theory, the coated ellipsoids approximation, and to a streamline approach. It is shown that, although simple, the proposed formula performs better than available methods for binary upscaling. The use of connectivity information leads to significantly improved behavior close to the percolation threshold. The proposed upscaling formula depends exclusively on parameters that are obtainable from field investigations. 相似文献
2.
The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity Keff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate Keff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function Keff (ψm) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent. 相似文献
3.
《Advances in water resources》2004,27(10):1017-1032
This paper presents a numerical solution for the effective conductivity of a periodic binary medium with cuboid inclusions located on an octahedral lattice. The problem is defined by five dimensionless geometric parameters and one dimensionless conductivity contrast parameter. The effective conductivity is determined by considering the flow through the “elementary flow domain” (EFD), which is an octant of the unitary domain of the periodic media. We derive practical bounds of interest for the six-dimensional parameter space of the EFD and numerically compute solutions at regular intervals throughout the entire bounded parameter space. A continuous solution of the effective conductivity within the limits of the simulated parameter space is then obtained via interpolation of the numerical results. Comparison to effective conductivities derived for random heterogeneous media demonstrate similarities and differences in the behavior of the effective conductivity in regular periodic (low entropy) vs. random (high entropy) media. The results define the low entropy bounds of effective conductivity in natural media, which is neither completely random nor completely periodic, over a large range of structural geometries. For aniso-probable inclusion spacing, the absolute bounds of Keff for isotropic inclusions are the Wiener bounds, not the Hashin-Shtrikman bounds. For isotropic inclusion and isoprobable conditions well below the percolation threshold, the results are in agreement with the self-consistent approach. For anisotropic cuboid inclusions, or at relatively close spacing in at least one direction (p > 0.2) (aniso-probable conditions), the effective conductivity of the periodic media is significantly different from that found in anisotropic random binary or Gaussian media. 相似文献
4.
This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
5.
《Advances in water resources》1998,22(3):223-238
Three-dimensional numerical simulations using a detailed synthetic hydraulic conductivity field developed from geological considerations provide insight into the scaling of subsurface flow and transport processes. Flow and advective transport in the highly resolved heterogeneous field were modeled using massively parallel computers, providing a realistic baseline for evaluation of the impacts of parameter scaling. Upscaling of hydraulic conductivity was performed at a variety of scales using a flexible power law averaging technique. A series of tests were performed to determine the effects of varying the scaling exponent on a number of metrics of flow and transport behavior. Flow and transport simulation on high-performance computers and three-dimensional scientific visualization combine to form a powerful tool for gaining insight into the behavior of complex heterogeneous systems.Many quantitative groundwater models utilize upscaled hydraulic conductivity parameters, either implicitly or explicitly. These parameters are designed to reproduce the bulk flow characteristics at the grid or field scale while not requiring detailed quantification of local-scale conductivity variations. An example from applied groundwater modeling is the common practice of calibrating grid-scale model hydraulic conductivity or transmissivity parameters so as to approximate observed hydraulic head and boundary flux values. Such parameterizations, perhaps with a bulk dispersivity imposed, are then sometimes used to predict transport of reactive or non-reactive solutes. However, this work demonstrates that those parameters that lead to the best upscaling for hydraulic conductivity and head do not necessarily correspond to the best upscaling for prediction of a variety of transport behaviors. This result reflects the fact that transport is strongly impacted by the existence and connectedness of extreme-valued hydraulic conductivities, in contrast to bulk flow which depends more strongly on mean values. It provides motivation for continued research into upscaling methods for transport that directly address advection in heterogeneous porous media.An electronic version of this article is available online at the journal's homepage at http://www.elsevier.nl/locate/advwatres or http://www.elsevier.com/locate/advwatres (see “Special section on vizualization”. The online version contains additional supporting information, graphics, and a 3D animation of simulated particle movement.©1998 Elsevier Science Limited. All rights reserved 相似文献
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Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales 总被引：1，自引：1，他引：0
Mohamad Reza Soltanian Robert Ritzi Zhenxue Dai Chaocheng Huang David Dominic 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):709-726
Solute transport in subsurface environments is controlled by geological heterogeneity over multiple scales. In reactive transport characterized by a low Damköhler number, it is also controlled by the rate of kinetic mass transfer. A theory for addressing the impact of sedimentary texture on the transport of kinetically sorbing solutes in heterogeneous porous formations is derived using the Lagrangian-based stochastic methodology. The resulting model represents the hierarchical organization of sedimentary textures and associated modes of log conductivity (K) for sedimentary units through a hierarchical Markov Chain. The model characterizes kinetic sorption using a spatially uniform linear reversible rate expression. Our main interest is to investigate the effect of sorption kinetics relative to the effects of K heterogeneity on the dispersion of a reactive plume. We study the contribution of each scale of stratal architecture to the dispersion of kinetically sorbing solutes in the case of a low Damköhler number. Examples are used to demonstrate the time evolution and relative contributions of the auto- and cross-transition probability terms to dispersion. Our analysis is focused on the model sensitivity to the parameters defined at each hierarchical level (scale) including the integral scales of K spatial correlation, the anisotropy ratio, the indicator correlation scales, and the contrast in mean K between facies defined at different scales. The results show that the anisotropy ratio and integral scales of K have negligible effect upon the longitudinal dispersion of sorbing solutes. Furthermore, dispersion of sorbing solutes depends mostly on indicator correlation scales, and the contrast of the mean conductivity between units at different scales. 相似文献
8.
Stochastic and deterministic upscaling techniques are developed that upscale saturated conductivity at the support of 0.04 m2 to representative actual infiltration (Ib) for support units (blocks) of 101–104 m2, as a function of steady state rainfall and runon to the block, under Hortonian runoff (infiltration excess overland flow). Parameters in the upscaling techniques represent the surface runoff flow pattern and the spatial probability distribution of saturated conductivity within the 101–104 m2 block. The stochastic upscaling technique represents the spatial process of infiltration and runoff using a simple process-imitating model, estimating Ib using Monte Carlo simulation. The deterministic upscaling technique aggregates these processes by a deterministic function relating rainfall and runon to Ib. The stochastic upscaling technique is shown to be capable to upscale saturated conductivity derived from ring infiltrometers to Ib values of plots (1 m2) corresponding to measured Ib values using rainfall simulators. It is shown that both upscaling techniques can be used to estimate Ib for each time step and each block in transient rainfall–runoff models, giving better estimates of cumulative runoff from a hillslope and a small catchment than model runs that do not use upscaling techniques. 相似文献
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You-Kuan Zhang Xiaoying Yang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(7):1043-1052
It was found in previous studies that groundwater levels may fluctuate as a temporal fractal. In this study numerical simulations
of groundwater level fluctuations in an unconfined aquifer near a river were conducted to investigate the effects of aquifer
heterogeneity and river stage variations on the fractal behavior of the water levels, h(t). Groundwater recharge was taken to be a white-noise process. The aquifer heterogeneity was simulated with a second-order
stationary field of hydraulic conductivity (K) with an exponential variogram model. The results showed that groundwater levels fluctuate as a temporal fractal in both
homogeneous and heterogeneous aquifers as long as K is less than 10 m/d. Most aquifers may indeed act as a fractal filter which takes a random non-fractal recharge inputs and
produces a fractal responses of groundwater level fluctuations. A crossover in temporal scaling of h(t) may appear in more permeable aquifers. Fluctuations of the groundwater level in a homogeneous aquifer are dominated by the
recharge process when the river stage is constant or by the river stage variations when the river stage varies in highly permeable
aquifers. Heterogeneity plays an important role in the temporal scaling of h(t) in more permeable aquifers: the stronger the heterogeneity, the stronger the temporal scaling of h(t). 相似文献
11.
《Advances in water resources》2004,27(4):445-464
The upscaling of dispersivity in solute transport in heterogeneous aquifers is addressed with a numerical stochastic formulation. This work represents progress toward converting theory into scalable numerical models that can be compared to laboratory experiments. Traditional global assumptions of low variance, ergodicity, single correlation scale, stationarity, and the like are avoided through the use of a flexible Lagrangian numerical, not analytical, framework, which allows assumptions to be local. A method of calculating grid-block upscaled dispersivities is presented. Computational results are obtained for a heterogeneous tank experiment, with reasonable behavior. 相似文献
12.
Numerical investigation of the anisotropic hydraulic conductivity behavior in heterogeneous porous media 总被引：1，自引：1，他引：0
The behavior of the mean equivalent hydraulic conductivity normal and parallel to stratification (K1, and K2, respectively) is studied here through Monte Carlo simulations of three-dimensional, steady-state flow in statistically anisotropic, bounded, and heterogeneous media. For water flow normal to stratification in strongly heterogeneous porous media (2Y=3) the value of K1 is not unique; it ranges from an arithmetic to a geometric, and finally, to a harmonic mean behavior depending on field dimensions, and medium anisotropy. For a fixed anisotropy ratio and variance of Y = ln K, the larger the distance, in the direction perpendicular to stratification, over which water flow takes place, the faster the rate at which, KH, behavior is approached. However, even for large anisotropy ratios, harmonic mean behavior appears to be a good approximation only for aquifer thickness L1 that is large enough to allow stratified flow to occur. For small aquifer thickness (L1/1<8, where 1 is the integral scale normal to stratification) the limiting behavior, for large anisotropy ratios, appears to be, instead, that of two-dimensional flow, i.e., water flows primarily parallel to the planes of stratification. When the aquifer thickness is very small compared to the horizontal dimensions (and with relative similar integral scales in the three directions) a behavior resembling arithmetic mean conditions is exhibited, i.e., water flow takes place through heterogeneous, vertical, soil volumes. The geostatistical expressions of Desbarats (1992a) for upscaling hydraulic conductivity values were utilized and closed form empirical relations were developed for the main components of the upscaled hydraulic conductivity tensor. 相似文献
13.
This paper presents a stochastic model for multicomponent competitive monovalent cation exchange in hierarchical porous media. Reactive transport in porous media is highly sensitive to heterogeneities in physical and chemical properties, such as hydraulic conductivity (K), and cation exchange capacity (CEC). We use a conceptual model for multimodal reactive mineral facies and develop a Eulerian-based stochastic theory to analyze the transport of multiple cations in heterogeneous media with a hierarchical organization of reactive minerals. Numerical examples investigate the retardation factors and dispersivities in a chemical system made of three monovalent cations (Na+, K+, and Cs+). The results demonstrate how heterogeneity influences the transport of competitive monovalent cations, and highlight the importance of correlations between K and CEC. Further sensitivity analyses are presented investigating how the dispersion and retardation of each cation are affected by the means, variances, and integral scales of K and CEC. The volume fraction of organic matter is shown to be another important parameter. The Eulerian stochastic framework presented in this work clarifies the importance of each system parameters on the migration of cation plumes in formations with hierarchical organization of facies types. Our stochastic approach could be used as an alternative to numerical simulations for 3D reactive transport in hierarchical porous media, which become prohibitively expensive for the multicomponent applications considered in this work. 相似文献
14.
Modeling dispersion in homogeneous porous media with the convection–dispersion equation commonly requires computing effective transport coefficients. In this work, we investigate longitudinal and transverse dispersion coefficients arising from the method of volume averaging, for a variety of periodic, homogeneous porous media over a range of particle Péclet (Pep) numbers. Our objective is to validate the upscaled transverse dispersion coefficients and concentration profiles by comparison to experimental data reported in the literature, and to compare the upscaling approach to the more common approach of inverse modeling, which relies on fitting the dispersion coefficients to measured data. This work is unique in that the exact microscale geometry is available; thus, no simplifying assumptions regarding the geometry are required to predict the effective dispersion coefficients directly from theory. Transport of both an inert tracer and non-chemotactic bacteria is investigated for an experimental system that was designed to promote transverse dispersion. We highlight the occurrence of transverse dispersion coefficients that (1) depart from power-law behavior at relatively low Pep values and (2) are greater than their longitudinal counterparts for a specific range of Pep values. The upscaling theory provides values for the transverse dispersion coefficient that are within the 98% confidence interval of the values obtained from inverse modeling. The mean absolute error between experimental and upscaled concentration profiles was very similar to that between the experiments and inverse modeling. In all cases the mean absolute error did not exceed 12%. Overall, this work suggests that volume averaging can potentially be used as an alternative to inverse modeling for dispersion in homogeneous porous media. 相似文献
15.
Vertically Integrated Hydraulic Conductivity: A New Parameter for Groundwater-Surface Water Analysis
Numerical modeling of groundwater-surface water interactions provides vital information necessary for determining the extent of nutrient transport, quantifying water budgets, and delineating zones of ecological support. The hydrologic data that drive these models are often collected at disparate scales and subsequently incorporated into numerical models through upscaling techniques such as piecewise constancy or geostatistical methods. However, these techniques either use basic interpolation methods, which often simplifies the system of interest, or utilize complex statistical methods that are computationally expensive, time consuming, and generate complex subsurface configurations. We propose a bulk parameter termed “vertically integrated hydraulic conductivity” (KV), and defined as the depth-integrated resistance to fluid flow sensed at the groundwater-surface water interface, as an alternative to hydraulic conductivity when investigating vertical fluxes across the groundwater-surface water interface. This bulk parameter replaces complex subsurface configurations in situations dominated by vertical fluxes and where heterogeneity is not of primary importance. To demonstrate the utility of KV, we extracted synthetic temperature time series data from a forward numerical model under a variety of scenarios and used those data to quantify vertical fluxes using the amplitude ratio method. These quantified vertical fluxes and the applied hydraulic head gradient were subsequently input into Darcy's Law and used to quantify KV. This KV was then directly compared to the equivalent hydraulic conductivity (KT) assuming an infinitely extending layer. Vertically integrated hydraulic conductivity allows for more accurate and robust flow modeling across the groundwater-surface water interface in instances where complex heterogeneities are not of primary concern. 相似文献
16.
《Advances in water resources》2007,30(4):772-793
A methodology for identifying the geometry of different materials in highly heterogeneous porous media in discrete inverse problems (DIP) is described. It applies a geostatistical approach within the differential system method (DSM). DSM calculates conductivity values along an integration path beginning at a point with known conductivity. In aquifers with zero source terms, DSM completely describes the conductivity field through a spatially distributed parameter depending on hydraulic head gradients and integration path. A factor analysis of the structural components of this parameter (i.e. coregionalisation analysis) was carried out to identify the geometry of different materials, corresponding to distinct statistically homogeneous areas. The equivalent conductivity values for homogeneous areas were estimated.This approach was applied for a synthetic aquifer. The identification of geometry was accurate and the estimates of equivalent parameters were good, compared with reference values. The accuracy of the results depended on errors in hydraulic gradients, compared with conductivity gradients. 相似文献
17.
为了定量地反映复杂非均匀介质非均匀地质体的尺度大小,本文利用统计学方法建立了能够很好地描述复杂非均匀介质特征的随机介质模型,模型参量自相关长度描述了非均匀介质横向和纵向上非均匀体的平均尺度。基于所建立的随机介质模型通过速度的横向变化和速度标准差分别探讨了自相关长度与非均匀体尺度之间的关系。对速度横向变化的研究表明:随机介质内速度具有一定均值和方差并呈随机扰动特征;随着模型自相关长度的增大,非均匀体尺度也随之增大。通过速度标准差的研究得出自相关长度与非均匀体尺度之间关系的拟合公式,利用此公式可以定量地获取非均匀体尺度的实际大小。 相似文献
18.
Interfacial error results from estimation of interblock conductivities related to the saturated–unsaturated interface. Both interfacial conductivity error (IEK) and interfacial pressure error (IEh) were analyzed under the arithmetic mean scheme while IEK was numerically investigated under the averaging schemes arithmetic, geometric and harmonic. IEK, dependent on the media pore size, is regularly less than zero while IEh, associated with the height of capillary fringe, may be greater than zero. An interfacial discretization technique was developed to add two complementary equations into the saturated–unsaturated model with respect to the interface. The proposed interfacial approach may eliminate interfacial error from the approximations of interblock conductivities. Underestimation of the water-table response to infiltration is related to the negative IEK. The water-table response error reaches −5.13% in our investigation, which is an accumulated result from IEK. 相似文献
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In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen–Loève decomposition is used to represent log hydraulic conductivity Y=lnKs. The hydraulic head h and average pore-velocity v are obtained by solving the continuity equation coupled with Darcy’s law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection–dispersion equation with stochastic average pore-velocity v computed from Darcy’s law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances. 相似文献