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1.
《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   

2.
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   

3.
Remediation of subsurface contamination requires an understanding of the contaminant (history, source location, plume extent and concentration, etc.), and, knowledge of the spatial distribution of hydraulic conductivity (K) that governs groundwater flow and solute transport. Many methods exist for characterizing K heterogeneity, but most if not all methods require the collection of a large number of small‐scale data and its interpolation. In this study, we conduct a hydraulic tomography survey at a highly heterogeneous glaciofluvial deposit at the North Campus Research Site (NCRS) located at the University of Waterloo, Waterloo, Ontario, Canada to sequentially interpret four pumping tests using the steady‐state form of the Sequential Successive Linear Estimator (SSLE) ( Yeh and Liu 2000 ). The resulting three‐dimensional (3D) K distribution (or K‐tomogram) is compared against: ( 1 ) K distributions obtained through the inverse modeling of individual pumping tests using SSLE, and ( 2 ) effective hydraulic conductivity (Keff) estimates obtained by automatically calibrating a groundwater flow model while treating the medium to be homogeneous. Such a Keff is often used for designing remediation operations, and thus is used as the basis for comparison with the K‐tomogram. Our results clearly show that hydraulic tomography is superior to the inversions of single pumping tests or Keff estimates. This is particularly significant for contaminated sites where an accurate representation of the flow field is critical for simulating contaminant transport and injection of chemical and biological agents used for active remediation of contaminant source zones and plumes.  相似文献   

4.
《Advances in water resources》2007,30(6-7):1571-1582
It has been widely observed in field experiments that the apparent rate of bacterial attachment, particularly as parameterized by the collision efficiency in filtration-based models, decreases with transport distance (i.e., exhibits scale-dependency). This effect has previously been attributed to microbial heterogeneity; that is, variability in cell–surface properties within a single monoclonal population. We demonstrate that this effect could also be interpreted as a field-scale manifestation of local-scale correlation between physical heterogeneity (hydraulic conductivity variability) and reaction heterogeneity (attachment rate coefficient variability). A field-scale model of bacterial transport developed for the South Oyster field research site located near Oyster, Virginia, and observations from field experiments performed at that site, are used as the basis for this study. Three-dimensional Monte Carlo simulations of bacterial transport were performed under four alternative scenarios: (1) homogeneous hydraulic conductivity (K) and attachment rate coefficient (Kf); (2) heterogeneous K, homogeneous Kf; (3) heterogeneous K and Kf with local correlation based on empirical and theoretical relationships; and (4) heterogeneous K and Kf without local correlation. The results of the 3D simulations were analyzed using 1D model approximations following conventional methods of field data analysis. An apparent decrease with transport distance of effective collision efficiency was observed only in the case where the local properties were both heterogeneous and correlated. This effect was observed despite the fact that the local collision efficiency was specified as a constant in the 3D model, and can therefore be interpreted as a scale effect associated with the local correlated heterogeneity as manifested at the field scale.  相似文献   

5.
Systematic experimental deviations from theoretical predictions derived for water retention characteristics of fractal porous media have previously been interpreted in terms of continuum percolation theory (at low moisture contents, below the critical volume fraction of water, αc capillary flow ceases). In other work, continuum percolation theory was applied to find the hydraulic conductivity as a function of saturation for saturations high enough to guarantee percolation of capillary flow. Now these two problems are further linked, using percolation theory to estimate non-equilibrium water retention at matric potential values such that the equilibrium water content is too low for percolation of capillary flow paths. In particular, a procedure for developing a time-dependent moisture content is developed for experimental time scales long enough that film flow can provide an alternate mechanism for equilibrating when continuous capillary flow is not possible. The time scales are defined in terms of moisture-dependent length scales and film flow and capillary flow hydraulic conductivities. Imbibition is treated in the extreme case of no film-flow contribution to equilibration. In another application at higher matric potentials, recursive relations are derived for the water content of porous media during drying when external pressures are changed at rates too rapid for equilibrium to be attained by capillary flow.  相似文献   

6.
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7.
We consider heterogeneous media whose properties vary in space and particularly aquifers whose hydraulic conductivity K may change by orders of magnitude in the same formation. Upscaling of conductivity in models of aquifer flow is needed in order to reduce the numerical burden, especially when modeling flow in heterogeneous aquifers of 3D random structure. Also, in many applications the interest is in average values of the dependent variables over scales larger or comparable to the conductivity length scales. Assigning values of the conductivity Kb to averaging domains, or computational blocks, is the topic of a large body of literature, the problem being of wide interest in various branches of physics and engineering. It is clear that upscaling causes loss of information and at best it can render a good approximation of the fine scale solution after averaging it over the blocks.The present article focuses on upscaling approaches dealing with random media. It is not meant to be a review paper, its main scope being to elucidate a few issues of principle and to briefly discuss open questions. We show that upscaling can be usually achieved only approximately, and the result may depend on the particular upscaling scheme adopted. The typically scarce information on the statistical structure of the fine-scale conductivity imposes a strong limitation to the upscaling problem. Also, local upscaling is not possible in nonuniform mean flows, for which the upscaled conductivity tensor is generally nonlocal and it depends on the domain geometry and the boundary conditions. These and other limitations are discussed, as well as other open topics deserving further investigation.  相似文献   

8.
Streambed hydraulic conductivity is one of the main factors controlling variability in surface water‐groundwater interactions, but only few studies aim at quantifying its spatial and temporal variability in different stream morphologies. Streambed horizontal hydraulic conductivities (Kh) were therefore determined from in‐stream slug tests, vertical hydraulic conductivities (Kv) were calculated with in‐stream permeameter tests and hydraulic heads were measured to obtain vertical head gradients at eight transects, each comprising five test locations, in a groundwater‐dominated stream. Seasonal small‐scale measurements were taken in December 2011 and August 2012, both in a straight stream channel with homogeneous elevation and downstream of a channel meander with heterogeneous elevation. All streambed attributes showed large spatial variability. Kh values were the highest at the depositional inner bend of the stream, whereas high Kv values were observed at the erosional outer bend and near the middle of the channel. Calculated Kv values were related to the thickness of the organic streambed sediment layer and also showed higher temporal variability than Kh because of sedimentation and scouring processes affecting the upper layers of the streambed. Test locations at the channel bend showed a more heterogeneous distribution of streambed properties than test locations in the straight channel, whereas within the channel bend, higher spatial variability in streambed attributes was observed across the stream than along the stream channel. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

9.
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   

10.
This paper presents a dual-percolation model coupling the percolation theory and the fracture percolation theory to study the conductivity of the fractured porous media. The Monte-Carlo method is used in the numerical simulation. First an appropriate computing scale by considering the calculation precision and elapsed time together is validated. Then, two parameters, A 0 and D are presented in this model to determine the conductivity of the media. Generally the media can be blocked by itself in the condition of D > 2. However, the increase of pore connection and the randomness of fracture direction may release the selfblockage, increase the conductivity and make the dual porous media dissipated. A few long fractures can play a great role in the connection of media.  相似文献   

11.
The effects of vegetation root distribution on near‐surface water partitioning can be two‐fold. On the one hand, the roots facilitate deep percolation by root‐induced macropore flow; on the other hand, they reduce the potential for deep percolation by root‐water‐uptake processes. Whether the roots impede or facilitate deep percolation depends on various conditions, including climate, soil, and vegetation characteristics. This paper examines the effects of root distribution on deep percolation into the underlying permeable bedrock for a given soil profile and climate condition using HYDRUS modelling. The simulations were based on previously field experiments on a semiarid ponderosa pine (Pinus ponderosa) hillslope. An equivalent single continuum model for simulating root macropore flow on hillslopes is presented, with root macropore hydraulic parameterization estimated based on observed root distribution. The sensitivity analysis results indicate that the root macropore effect dominates saturated soil water flow in low conductivity soils (Kmatrix below 10?7 m/s), while it is insignificant in soils with a Kmatrix larger than 10?5 m/s, consistent with observations in this and other studies. At the ponderosa pine site, the model with simple root‐macropore parameterization reasonably well reproduces soil moisture distribution and some major runoff events. The results indicate that the clay‐rich soil layer without root‐induced macropores acts as an impeding layer for potential groundwater recharge. This impeding layer results in a bedrock percolation of less than 1% of the annual precipitation. Without this impeding layer, percolation into the underlying permeable bedrock could be as much as 20% of the annual precipitation. This suggests that at a surface with low‐permeability soil overlying permeable bedrock, the root penetration depth in the soil is critical condition for whether or not significant percolation occurs. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

12.
Connectivity of high conductivity (K) paths is important because it can lead to channeling, i.e. flow along preferential paths, which can reduce travel times very significantly. Nevertheless, limited effort has been devoted to defining the concept quantitatively. We propose and evaluate nine indicators of connectivity. Three account for the presence of flow connectivity, that is, the flow rate increase caused by preferential flow paths. Two account for the presence of transport connectivity, that is, the existence of fast paths allowing early solute arrival. The remaining four are statistical indicators based on two- and multiple-point statistics. We test these indicators on heterogeneous conductivity fields with different visual connectivity. The indicators of flow connectivity and one of the transport connectivity indicators succeed in identifying the increased presence of connected high-K features. The two-point statistical indicators fail to do so. The directional multi-point statistical indicator performs better. None of the statistical indicators correlate with the flow and transport indicators. We find only weak dependence between the flow and transport indicators. Our results suggest that transport connectivity is much less sensitive to barriers, which control flow connectivity. Instead, transport connectivity appears to be controlled by the existence of narrow, possibly discontinuous high-K paths. Therefore, we conclude that connectivity is a process-dependent concept.  相似文献   

13.
Electromagnetic induction (EMI) instruments provide rapid, noninvasive, and spatially dense data for characterization of soil and groundwater properties. Data from multi-frequency EMI tools can be inverted to provide quantitative electrical conductivity estimates as a function of depth. In this study, multi-frequency EMI data collected across an abandoned uranium mill site near Naturita, Colorado, USA, are inverted to produce vertical distribution of electrical conductivity (EC) across the site. The relation between measured apparent electrical conductivity (ECa) and hydraulic conductivity (K) is weak (correlation coefficient of 0.20), whereas the correlation between the depth dependent EC obtained from the inversions, and K is sufficiently strong to be used for hydrologic estimation (correlation coefficient of ? 0.62). Depth-specific EC values were correlated with co-located K measurements to develop a site-specific ln(EC)–ln(K) relation. This petrophysical relation was applied to produce a spatially detailed map of K across the study area. A synthetic example based on ECa values at the site was used to assess model resolution and correlation loss given variations in depth and/or measurement error. Results from synthetic modeling indicate that optimum correlation with K occurs at ~ 0.5 m followed by a gradual correlation loss of 90% at 2.3 m. These results are consistent with an analysis of depth of investigation (DOI) given the range of frequencies, transmitter–receiver separation, and measurement errors for the field data. DOIs were estimated at 2.0 ± 0.5 m depending on the soil conductivities. A 4-layer model, with varying thicknesses, was used to invert the ECa to maximize available information within the aquifer region for improved correlations with K. Results show improved correlation between K and the corresponding inverted EC at similar depths, underscoring the importance of inversion in using multi-frequency EMI data for hydrologic estimation.  相似文献   

14.
An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum Kmax/Kmin tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.  相似文献   

15.
Magmas often contain multiple interacting phases of embedded solid and gas inclusions. Multiphase percolation theory provides a means of modeling assemblies of these different classes of magmatic inclusions in a simple, yet powerful way. Like its single phase counterpart, multiphase percolation theory describes the connectivity of discrete inclusion assemblies as a function of phase topology. In addition, multiphase percolation employs basic laws to distinguish separate classes of objects and is characterized by its dependency on the order in which the different phases appear. This paper examines two applications of multiphase percolation theory: the first considers how the presence of bubble inclusions influences yield stress onset and growth in a magma's crystal network; the second examines the effect of bi-modal bubble-size distributions on magma permeability. We find that the presence of bubbles induces crystal clustering, thereby 1) reducing the percolation threshold, or critical crystal volume fraction, ?c, at which the crystals form a space-spanning network providing a minimum yield stress, and 2) resulting in a larger yield stress for a given crystal volume fraction above ?c. This increase in the yield stress of the crystal network may also occur when crystal clusters are formed due to processes other than bubble formation, such as heterogeneous crystallization, synneusis, and heterogeneity due to deformation or flow. Further, we find that bimodal bubble size distributions can significantly affect the permeability of the system beyond the percolation threshold. This study thus demonstrates that larger-scale structures and topologies, as well as the order in which different phases appear, can have significant effects on macroscopic properties in multiphase materials.  相似文献   

16.
Gerard Govers  Jan Diels 《水文研究》2013,27(25):3777-3790
Experimental work has clearly shown that the effective hydraulic conductivity (Ke) or effective infiltration rate (fe) on the local scale of a plot cannot be considered as constant but are dependent on water depth and rainfall intensity because non‐random microtopography‐related variations in hydraulic conductivity occur. Rainfall–runoff models generally do not account for this: models assume that excess water is uniformly spread over the soil surface and within‐plot variations are neglected. In the present study, we propose a model that is based on the concepts of microtopography‐related water depth‐dependent infiltration and partial contributing area. Expressions for the plot scale Ke and fe were developed that depend on rainfall intensity and runon from upslope (and thus on water depth). To calibrate and validate the model, steady state infiltration experiments were conducted on maize fields on silt loam soils in Belgium, with different stages and combinations of rainfall intensity and inflow, simulating rainfall and runon. Water depth–discharge and depth–inundation relationships were established and used to estimate the effect of inundation on Ke. Although inflow‐only experiments were found to be unsuitable for calibration, the model was successfully calibrated and validated with the rainfall simulation data and combined rainfall–runon data (R²: 0.43–0.91). Calibrated and validated with steady state infiltration experiments, the model was combined with the Green–Ampt infiltration equation and can be applied within a two‐dimensional distributed rainfall–runoff model. The effect of water depth–dependency and rainfall intensity on infiltration was illustrated for a hillslope. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

17.
《Journal of Hydrology》2006,316(1-4):184-194
A semi-analytical model for the estimate of expected areal-average infiltration rate at hillslope scale is presented. It accounts for spatial heterogeneity of the saturated hydraulic conductivity, Ks, and rainfall rate, r. The Ks field is characterized by a lognormal probability density function while the rainfall rate r is represented by a uniform distribution between two extreme values. The model formulation relies upon the use of cumulative infiltration as the independent variable which is then expressed as a function of an expected time for use in practical applications. The solution is applicable for those ranges of r and Ks that allow for neglecting the infiltration of surface water running downslope into pervious soils (run-on process). The model was tested by comparisons with Monte Carlo simulations carried out for a variety of coefficients of variation of r and Ks over a clay loam soil and a sandy loam soil. The model was found to be very reliable both with coupled spatial variability of r and Ks and when only one variable is characterized by spatial heterogeneity while the other is uniform.  相似文献   

18.
In this study, we derive analytical solutions of the first two moments (mean and variance) of pressure head for one-dimensional steady state unsaturated flow in a randomly heterogeneous layered soil column under random boundary conditions. We first linearize the steady state unsaturated flow equations by Kirchhoff transformation and solve the moments of the transformed variable up to second order in terms of σY and σβ, the standard deviations of log hydraulic conductivity Y=ln(Ks) and of the log pore size distribution parameter β=ln(α). In addition, we also give solutions for the mean and variance of the unsaturated hydraulic conductivity. The analytical solutions of moment equations are validated via Monte Carlo simulations.  相似文献   

19.
Management of water resources in alluvial aquifers relies mainly on understanding interactions between hydraulically connected streams and aquifers. Numerical models that simulate this interaction often are used as decision support tools for water resource management. However, the accuracy of numerical predictions relies heavily on unknown system parameters (e.g., streambed conductivity and aquifer hydraulic conductivity), which are spatially heterogeneous and difficult to measure directly. This paper employs an ensemble smoother to invert groundwater level measurements to jointly estimate spatially varying streambed and alluvial aquifer hydraulic conductivity along a 35.6‐km segment of the South Platte River in Northeastern Colorado. The accuracy of the inversion procedure is evaluated using a synthetic experiment and historical groundwater level measurements, with the latter constituting the novelty of this study in the inversion and validation of high‐resolution fields of streambed and aquifer conductivities. Results show that the estimated streambed conductivity field and aquifer conductivity field produce an acceptable agreement between observed and simulated groundwater levels and stream flow rates. The estimated parameter fields are also used to simulate the spatially varying flow exchange between the alluvial aquifer and the stream, which exhibits high spatial variability along the river reach with a maximum average monthly aquifer gain of about 2.3 m3/day and a maximum average monthly aquifer loss of 2.8 m3/day, per unit area of streambed (m2). These results demonstrate that data assimilation inversion provides a reliable and computationally affordable tool to estimate the spatial variability of streambed and aquifer conductivities at high resolution in real‐world systems.  相似文献   

20.
This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably saturated flow in actual or realistic hypothetical heterogeneous porous media. Statistical properties of unsaturated hydraulic conductivity, soil water tension, and soil water flux in heterogeneous soils are investigated through high resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in analytical stochastic models of unsaturated flow, hydraulic conductivity and soil water tension are found to be lognormally and normally distributed, respectively. In contrast, simulations indicate that in moderate to strong variable conductivity fields, longitudinal flux is highly skewed. Transverse flux distributions are leptokurtic. the moments of the probability distributions obtained from Monte Carlo simulations are compared to modified first-order analytical models. Under moderate to strong heterogeneous soil flux conditions (σ2y≥1), analytical solutions overestimate variability in soil water tension by up to 40% as soil heterogeneity increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well with the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flow in heterogeneous soils.©1998 Elsevier Science Limited. All rights reserved  相似文献   

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