共查询到20条相似文献，搜索用时 31 毫秒
1.
In this work, a stochastic methodology is applied to analyze the variability of the poroelastic response of the heterogeneous medium at the field scale. To solve the problem analytically, we restrict our attention to the one-dimensional models, where fluid flow as well as deformation occurs in one direction only under a constant applied stress. Assuming statistic homogeneity, the closed-form solutions that describe the variability of fluid pressure head, and a solid's strain and displacement are developed using a spectral approach based on Fourier–Stieltjes representations for the perturbed quantities. The influence of the correlation length of the log hydraulic conductivity on these results is investigated. It is found that the variances of the solid's strain and displacement increase with the correlation length of the log hydraulic conductivity, while the correlation length of the log hydraulic conductivity plays the role in reducing the variability of the specific discharge. 相似文献
2.
This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous
media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic
representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media.
A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic
terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the
selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression
is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective
hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained.
The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous
limit. 相似文献
3.
Dionissios T. Hristopulos George Christakos 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(5):369-395
This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous
media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic
representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media.
A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic
terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the
selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression
is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective
hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained.
The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous
limit. 相似文献
4.
Localized, transient heterogeneity was studied in a sand aquifer undergoing benzene, toluene, ethylbenzene, and xylene bioremediation using a novel array of multilevel, in situ point velocity probes (PVPs). The experiment was conducted within a sheet-pile alleyway to maintain a constant average flow direction through time. The PVPs measured changes in groundwater velocity direction and magnitude at the centimeter scale, making them ideal to monitor small-scale changes in hydraulic conductivity (K). Velocities were shown to vary nonuniformly by up to a factor of 3 when a source of oxygen was established down-gradient of the petroleum spill. In spite of these local variations, the average groundwater velocity within the 7 m × 20 m sheet-piled test area only varied within ± 25%. The nonuniform nature of the velocity variations across the gate indicated that the changes were not due solely to seasonal hydraulic gradient fluctuations. At the conclusion of the experiment, microbial biomass levels in the aquifer sediments was approximately 1 order of magnitude higher in the oxygen-amended portion of the aquifer than at the edge of the plume or in locations up-gradient of the source. These data suggest that the transient velocities resulted, at least in part, from enhanced biological activity that caused transient heterogeneities in the porous medium. 相似文献
5.
Using the first-order analysis, we investigate the spatial cross-correlation between hydraulic conductivity variation and specific discharge (flux) as well as its components measured in a borehole under steady-state flow conditions during cross-hole pumping tests in heterogeneous aquifers. These spatial correlation patterns are found to be quite different from that between the hydraulic conductivity variation and the hydraulic head measurement in the same borehole. This finding suggests that a specific discharge measurement carries non-redundant information about the spatial distribution of heterogeneity, even this measurement is collected from the same location where the head measurement is taken. As such, specific discharge observations should be included in the analysis of hydraulic tomography to increase the resolution of estimated aquifer heterogeneity. Using numerical experiments, we demonstrate the effectiveness of the joint interpretation of both hydraulic heads and fluxes for mapping fracture distributions in a hypothetic geologic medium. 相似文献
6.
Illman and Tartakovsky (2005a, 2005b) developed a new approach for the interpretation of three-dimensional pneumatic well tests conducted in porous or fractured geologic media, which is based on a straight-line analysis of late-time data. We modify this approach to interpret three-dimensional well tests in the saturated zone and use it to analyze the cross-hole hydraulic test data collected in the Full-Scale Engineered Barrier Experiment gallery at the Grimsel Test Site in Switzerland. The equivalent hydraulic conductivity and specific storage obtained from our analysis increase with the radial distance between the centroids of the pumping and monitoring intervals. Since this scale effect is observed from a single test type (cross-hole tests), it is less ambiguous than scale effects typically inferred from laboratory and multiple types of hydraulic tests (e.g., slug, single- and cross-hole tests). The statistical analysis of the estimated hydraulic parameters shows a strong correlation between equivalent hydraulic conductivity and specific storage. 相似文献
7.
《Advances in water resources》2005,28(7):689-699
The analytic element method is well suited for the Gardner hydraulic conductivity function, but is limited in describing real soils. Therefore, parameter equivalence between the van Genuchten and Gardner hydraulic conductivity functions is explored for the case of steady vertical flow through a homogeneous medium with a single inclusion, i.e., a binary soil. The inclusion has different hydraulic parameters than the background medium. Equivalence is established using three methods: (1) effective capillary drive; (2) capillary length; (3) and a least-squares optimization method that aims to fit a Gardner function to a corresponding van Genuchten function by minimizing the difference in log conductivity over a specified pressure range. Comparisons between hydraulic models are made based on scatterplots of pressure head and the vertical Darcian flux obtained using a finite-element numerical solution with both constitutive relations. For applicability of an equivalent Gardner function over a broad range of pressure heads, the crossover pressure must be maintained between the two parametric functions. The crossover pressure is defined as the pressure in which the hydraulic conductivity of the inclusion is equal to the background. It can be shown that a hybrid methodology of preserving the crossover pressure exactly and using the effective capillary drive will result in hydraulic parameters that are easily obtained and provide good agreement between the conductivity functions of the GR model to the VG model. 相似文献
8.
Fluid‐filled granular soils experience changes in total stress because of earth and oceanic tides, earthquakes, erosion, sedimentation, and changes in atmospheric pressure. The pore volume may deform in response to the changes in stress and this may lead to changes in pore fluid pressure. The transient fluid flow can therefore be induced by the gradient in excess pressure in a fluid‐saturated porous medium. This work demonstrates the use of stochastic methodology in prediction of induced one‐dimensional field‐scale groundwater flow through a heterogeneous aquifer. A closed‐form of mean groundwater flux is developed to quantify the induced field‐scale mean behavior of groundwater flow and analyze the impacts of the spatial correlation length scale of log hydraulic conductivity and the pore compressibility. The findings provided here could be useful for the rational planning and management of groundwater resources in aquifers that contain lenses with large vertical aquifer matrix compressibility values. 相似文献
9.
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
10.
In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions. 相似文献
11.
The selective radius shift model was used to relate changes in mineral volume due to precipitation/dissolution reactions to changes in hydraulic properties affecting flow in porous media. The model accounts for (i) precipitation/dissolution taking place only in the water-filled part of the pore space and further that (ii) the amount of mineral precipitation/dissolution within a pore depends on the local pore volume. The pore bundle concept was used to connect pore-scale changes to macroscopic soil hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and, consequently, in the effective porosity. In a time step of the numerical model, mineral reactions lead to a discontinuous pore-size distribution because only the water-filled pores are affected. The pore-size distribution is converted back to a soil moisture characteristic function to which a new water retention curve is fitted under physically plausible constraints. The model equations were derived for the commonly used van Genuchten/Mualem hydraulic properties. Together with a mixed-form solution of Richards’ equation for aqueous phase flow, the model was implemented into the geochemical modelling framework PHREEQC, thereby making available PHREEQC’s comprehensive geochemical reactions. Example applications include kinetic halite dissolution and calcite precipitation as a consequence of cation exchange. These applications showed marked changes in the soil’s hydraulic properties due to mineral precipitation/dissolution and the dependency of these changes on water contents. The simulations also revealed the strong influence of the degree of saturation on the development of the saturated hydraulic conductivity through its quadratic dependency on the van Genuchten parameter α. Furthermore, it was shown that the unsaturated hydraulic conductivity at fixed reduced water content can even increase during precipitation due to changes in the pore-size distribution. 相似文献
12.
Stream water infiltration, bank storage, and storage zone changes due to stream-stage fluctuations 总被引：3，自引：0，他引：3
During a flood period, stream-stage increases induce infiltration of stream water into an aquifer; subsequent declines in stream stage cause a reverse motion of the infiltrated water. This paper presents the results of the water exchange rate between a stream and aquifer, the storage volume of the infiltrated stream water in the surrounding aquifer (bank storage), and the storage zone. The storage zone is the part of aquifer where groundwater is replaced by stream water during the flood. MODFLOW was used to simulate stream–aquifer interactions and to quantify rates of stream infiltration and return flow. MODPATH was used to trace the pathlines of the infiltrated stream water and to determine the size of the storage zone. Simulations were focused on the analyses of the effects of the stream-stage fluctuation, aquifer properties, the hydraulic conductivity of streambed sediments, regional hydraulic gradients, and recharge and evapotranspiration (ET) rates on stream–aquifer interactions. Generally, for a given stream–aquifer system, larger flow rates result from larger stream-stage fluctuations; larger storage volumes and storage zones are produced by larger and longer-lasting fluctuations. For a given stream-stage hydrograph, a lower-permeable streambed, an aquitard, or an anisotropic aquifer of low vertical hydraulic conductivity can significantly reduce the rate of infiltration and limit the size of the storage zone. The bank storage solely caused by the stage fluctuation differs slightly between gaining and losing streams. Short-term rainfall recharge and ET loss in the shallow groundwater slightly influence on the flow rate, but their effects on bank storage in a larger area for a longer period can be considerable. 相似文献
13.
Despite the presence of gas in river beds being a well known phenomenon, its potential feedbacks on the hydraulic and thermal dynamics of the hyporheic zone has not been widely studied. This paper explores hypotheses that the presence of accumulated gas impacts the hydraulic and thermal dynamics of a river bed due to changes in specific storage, hydraulic conductivity, effective porosity, and thermal diffusivity. The hypotheses are tested using data analysis and modelling for a study site on the urban River Tame, Birmingham, UK. Gas, predominantly attributed to microbial denitrification, was observed in the river bed up to around 14% by volume, and to at least 0.8 m depth below river bed. Numerical modelling indicates that, by altering the relative hydraulic conductivity distribution, the gas in the river bed leads to an increase of groundwater discharge from the river banks (relative to river bed) by a factor of approximately 2 during river low flow periods. The increased compressible storage of the gas phase in the river bed leads to an increase in the simulated volume of river water invading the river bed within the centre of the channel during storm events. The exchange volume can be more than 30% greater in comparison to that for water saturated conditions. Furthermore, the presence of gas also reduces the water-filled porosity, and so the possible depth of such invading flows may also increase markedly, by more than a factor of 2 in the observed case. Observed diurnal temperature variations within the gaseous river bed at 0.1 and 0.5 m depth are, respectively, around 1.5 and 6 times larger than those predicted for saturated sediments. Annual temperature fluctuations are seen to be enhanced by around 4 to 20% compared to literature values for saturated sediments. The presence of gas may thus alter the bulk thermal properties to such a degree that the use of heat tracer techniques becomes subject to a much greater degree of uncertainty. Although the likely magnitude of thermal and hydraulic changes due to the presence of gas for this site have been demonstrated, further research is needed into the origins of the gas and its spatial and temporal variability to enable quantification of the significance of these changes for chemical attenuation and hyporheic zone biology. 相似文献
14.
We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general. 相似文献
15.
Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling 总被引：3，自引：0，他引：3
The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [Water Resour. Res. 19 (1) (1983) 161]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1−2/dα<1 (where d is the actual medium dimension) in the geostatistical power average. 相似文献
16.
《Advances in water resources》2005,28(11):1159-1170
The paper concerns macroscopic modeling of water flow in an unsaturated double-porosity soil consisting of highly conductive inclusions embedded in a less conductive matrix. The flow at the local scale in both sub-domains is assumed to be governed by the Richards equation. Application of the asymptotic homogenization method leads to a macroscopic flow model in the form of a single equation with two effective parameters. The effective water capacity depends on the local capacities of both sub-domains and their volumetric fractions, while the effective conductivity depends on the conductivity of the porous matrix and the local geometry of the medium. The conductivity of the inclusions does not influence the calculation of the effective conductivity. The domain of validity of the model is defined. An example of numerical simulation is presented for 1D infiltration into initially dry soil. The local geometry of the considered medium is 2D. The results obtained from homogenization are close to the fine scale solution (SWMS_2D program), where the local heterogeneous structure of the medium is explicitly represented. 相似文献
17.
The deformation of the solid matrix affects the fluid pore pressure and flow by altering the pore volume. Such interaction in turn affects the storage of groundwater in the void space. Obviously, this subject is of interest in groundwater hydrology. This paper describes an investigation of the effect of aquifer heterogeneity on the variability of the fluid pressure head and solid's volume strain, where the assumption of a constant vertical total stress leads to a relatively simple relationship between changes in solid's volume strain and fluid pressure head. To solve the problem analytically, focus is placed on the one‐dimensional models. It is found from our closed‐form solutions that the variance and correlation length of the log hydraulic conductivity are important in increasing the variability of pressure head and solid's volume strain. It is hoped that our findings will provide a basic framework for understanding and quantifying field‐scale volume strain processes and be useful in stimulating further research in this area. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
A Laplace-transform analytic element method (LT-AEM) is described for the solution of transient flow problems in porous media. Following Laplace transformation of the original flow problem, the analytic element method (AEM) is used to solve the resultant time-independent modified Helmholtz equation, and the solution is inverted numerically back into the time domain. The solution is entirely general, retaining the mathematical elegance and computational efficiency of the AEM while being amenable to parallel computation. It is especially well suited for problems in which a solution is required at a limited number of points in space–time, and for problems involving materials with sharply contrasting hydraulic properties. We illustrate the LT-AEM on transient flow through a uniform confined aquifer with a circular inclusion of contrasting hydraulic conductivity and specific storage. Our results compare well with published analytical solutions in the special case of radial flow. 相似文献
19.
Interpretation of spring recession curves 总被引：4，自引：0，他引：4
Recession curves contain information on storage properties and different types of media such as porous, fractured, cracked lithologies and karst. Recession curve analysis provides a function that quantitatively describes the temporal discharge decay and expresses the drained volume between specific time limits (Hall 1968). This analysis also allows estimating the hydrological significance of the discharge function parameters and the hydrological properties of the aquifer. In this study, we analyze data from perennial springs in the Judean Mountains and from others in the Galilee Mountains, northern Israel. All the springs drain perched carbonate aquifers. Eight of the studied springs discharge from a karst dolomite sequence, whereas one flows out from a fractured, slumped block of chalk. We show that all the recession curves can be well fitted by a function that consists of two exponential terms with exponential coefficients alpha1 and alpha2. These coefficients are approximately constant for each spring, reflecting the hydraulic conductivity of different media through which the ground water flows to the spring. The highest coefficient represents the fast flow, probably through cracks, or quickflow, whereas the lower one reflects the slow flow through the porous medium, or baseflow. The comparison of recession curves from different springs and different years leads to the conclusion that the main factors that affect the recession curve exponential coefficients are the aquifer lithology and the geometry of the water conduits therein. In normal years of rainy winter and dry summer, alpha1 is constant in time. However, when the dry period is longer than usual because of a dry winter, alpha1 slightly decreases with time. 相似文献
20.
Fractures in porous media have been documented extensively. However, they are often omitted from groundwater flow and mass transport models due to a lack of data on fracture hydraulic properties and the computational burden of simulating fractures explicitly in large model domains. We present a MATLAB toolbox, FracKfinder, that automates HydroGeoSphere (HGS), a variably saturated, control volume finite-element model, to simulate an ensemble of discrete fracture network (DFN) flow experiments on a single cubic model mesh containing a stochastically generated fracture network. Because DFN simulations in HGS can simulate flow in both a porous media and a fracture domain, this toolbox computes tensors for both the matrix and fractures of a porous medium. Each model in the ensemble represents a different orientation of the hydraulic gradient, thus minimizing the likelihood that a single hydraulic gradient orientation will dominate the tensor computation. Linear regression on matrices containing the computed three-dimensional hydraulic conductivity (K) values from each rotation of the hydraulic gradient is used to compute the K tensors. This approach shows that the hydraulic behavior of fracture networks can be simulated where fracture hydraulic data are limited. Simulation of a bromide tracer experiment using K tensors computed with FracKfinder in HGS demonstrates good agreement with a previous large-column, laboratory study. The toolbox provides a potential pathway to upscale groundwater flow and mass transport processes in fractured media to larger scales. 相似文献