共查询到20条相似文献，搜索用时 421 毫秒
1.
Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media 总被引：4，自引：0，他引：4
A. J. Desbarats 《Mathematical Geology》1992,24(3):249-267
Numerical models of groundwater flow require the assignment of hydraulic conductivities to large grid blocks discretizing the flow domain; however, conductivity data is usually available only at the much smaller scale of core samples. This paper describes a geostatistical model for hydraulic conductivity at both the core or point scale and that of grid blocks. Conductivity at the block scale is obtained empirically as a spatial power-average of point scale values. Assuming a multivariate Gaussian model for point log-conductivity, expressions are derived for the ensemble mean and variance of block conductivity. The expression for the ensemble mean of block scale conductivity is found to be similar to an expression for the ensemble effective conductivity of an infinite field derived analytically by earlier authors. Here, block conductivities obtained by power averaging are compared with effective conductivities obtained from a numerical flow model and are found to be in excellent agreement for a suitably chosen averaging exponent. This agreement deteriorates gradually as the log variance of conductivity increases beyond 2. For arbitrary flow field geometry and anisotropic conductivity covariances, the averaging exponent can be calibrated by recourse to numerical flow experiments. For cubic fields and an isotropic spatial covariance, the averaging exponent is found to be 1/3. In this particular case, it was found that flow field discretization at the block scale through local averaging of point conductivities gave similar results to those obtained directly using a point scale discretization of the flow field. 相似文献
2.
In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation. 相似文献
3.
4.
Modern geostatistical techniques allow the generation of high-resolution heterogeneous models of hydraulic conductivity containing millions to billions of cells. Selective upscaling is a numerical approach for the change of scale of fine-scale hydraulic conductivity models into coarser scale models that are suitable for numerical simulations of groundwater flow and mass transport. Selective upscaling uses an elastic gridding technique to selectively determine the geometry of the coarse grid by an iterative procedure. The geometry of the coarse grid is built so that the variances of flow velocities within the coarse blocks are minimum. Selective upscaling is able to handle complex geological formations and flow patterns, and provides full hydraulic conductivity tensor for each block. Selective upscaling is applied to a cross-bedded formation in which the fine-scale hydraulic conductivities are full tensors with principal directions not parallel to the statistical anisotropy of their spatial distribution. Mass transport results from three coarse-scale models constructed by different upscaling techniques are compared to the fine-scale results for different flow conditions. Selective upscaling provides coarse grids in which mass transport simulation is in good agreement with the fine-scale simulations, and consistently superior to simulations on traditional regular (equal-sized) grids or elastic grids built without accounting for flow velocities. 相似文献
5.
Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling. 相似文献
6.
In the framework of various studies to characterize the aquifer at the groundwater experimental field near Montalto Uffugo, Italy, the present work estimates the spatial distribution of hydraulic conductivity of the unconsolidated deposits that underlie the area, by applying the geostatistical technique of kriging with external drift to electrical-resistivity and hydraulic-conductivity data. The reliability of the estimation method was tested by implementing a model, based on the method of cells, that simulates groundwater flow, with the estimated values of hydraulic conductivity. The results obtained indicate that the estimation method used has an acceptable degree of reliability. 相似文献
7.
8.
Marijke Huysmans Philippe Orban Elke Cochet Mathias Possemiers Benedicta Ronchi Katherine Lauriks Okke Batelaan Alain Dassargues 《Mathematical Geosciences》2014,46(5):519-537
This study investigates the effect of fine-scale clay drapes on tracer transport. A tracer test was performed in a sandbar deposit consisting of cross-bedded sandy units intercalated with many fine-scale clay drapes. The heterogeneous spatial distribution of the clay drapes causes a spatially variable hydraulic conductivity and sorption coefficient. A fluorescent tracer (sodium naphthionate) was injected in two injection wells and ground water was sampled and analyzed from five pumping wells. To determine (1) whether the fine-scale clay drapes have a significant effect on the measured concentrations and (2) whether application of multiple-point geostatistics can improve interpretation of tracer tests in media with complex geological heterogeneity, this tracer test is analyzed with a local three-dimensional ground-water flow and transport model in which fine-scale sedimentary heterogeneity is modeled using multiple-point geostatistics. To reduce memory needs and calculation time for the multiple-point geostatistical simulation step, this study uses the technique of direct multiple-point geostatistical simulation of edge properties. Instead of simulating pixel values, model cell edge properties indicating the presence of irregularly shaped surfaces are simulated using multiple-point geostatistical simulations. Results of a sensitivity analysis show under which conditions clay drapes have a significant effect on the concentration distribution. Calibration of the model against measured concentrations from the tracer tests reduces the uncertainty on the clay-drape parameters. The calibrated model shows which features of the breakthrough curves can be attributed to the geological heterogeneity of the aquifer and which features are caused by other processes. 相似文献
9.
Sabine Attinger 《Computational Geosciences》2003,7(4):253-273
This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric
head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found
for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric
head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are
resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure
is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations.
In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which
are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented
in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group
analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid
for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992).
The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions
for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different
scales and for reduction of grid-block resolution in numerical modeling.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
Estimation of regional-scale groundwater flow properties in the Bengal Basin of India and Bangladesh
Quantitative evaluation of management strategies for long-term supply of safe groundwater for drinking from the Bengal Basin aquifer (India and Bangladesh) requires estimation of the large-scale hydrogeologic properties that control flow. The Basin consists of a stratified, heterogeneous sequence of sediments with aquitards that may separate aquifers locally, but evidence does not support existence of regional confining units. Considered at a large scale, the Basin may be aptly described as a single aquifer with higher horizontal than vertical hydraulic conductivity. Though data are sparse, estimation of regional-scale aquifer properties is possible from three existing data types: hydraulic heads, 14C concentrations, and driller logs. Estimation is carried out with inverse groundwater modeling using measured heads, by model calibration using estimated water ages based on 14C, and by statistical analysis of driller logs. Similar estimates of hydraulic conductivities result from all three data types; a resulting typical value of vertical anisotropy (ratio of horizontal to vertical conductivity) is 104. The vertical anisotropy estimate is supported by simulation of flow through geostatistical fields consistent with driller log data. The high estimated value of vertical anisotropy in hydraulic conductivity indicates that even disconnected aquitards, if numerous, can strongly control the equivalent hydraulic parameters of an aquifer system. 相似文献
11.
12.
P. Juan J. Mateu M.M. Jordan J. Mataix-Solera I. Meléndez-Pastor J. Navarro-Pedreño 《Journal of Geochemical Exploration》2011
The problem of estimating and predicting spatial distribution of a spatial stochastic process, observed at irregular locations in space, is considered in this paper. Environmental variables usually show spatial dependencies among observations, with lead one to use geostatistical methods to model the spatial distributions of those observations. This is particularly important in the study of soil properties and their spatial variability. In this study geostatistical techniques were used to describe the spatial dependence and to quantify the scale and intensity of spatial variations of soil properties, which provide the essential spatial information for local estimation. In this contribution, we propose a spatial Gaussian linear mixed model that involves (a) a non-parametric term for accounting deterministic trend due to exogenous variables and (b) a parametric component for defining the purely spatial random variation due possibly to latent spatial processes. We focus here on the analysis of the relationship between soil electrical conductivity and Na content to identify spatial variations of soil salinity. This analysis can be useful for agricultural and environmental land management. 相似文献
13.
D.M. Finlayson 《Tectonophysics》1982,84(2-4)
Cannikin atomic bomb recordings indicate that there are differences in travel-times from the Aleutian Islands test site to Phanerozoic and Precambrian provinces in Australia of up to 1.1 s. Explosion seismic studies in central and southeastern Australia enable travel-time corrections for crustal and upper mantle structure to be made to recordings of such teleseismic events. Structure in the upper 60 km can account for, at most, about 0.2 s of the residual difference, but attempts to constrain the remaining residual time to the region above the Lehmann discontinuity at about 200 km depth are difficult to reconcile with explosion seismic models. Regional differences in seismic velocity structure between Phanerozoic and Precambrian Australia therefore appear to exist at depths greater than 200 km.Electrical conductivities within the mantle have been investigated using two methods. Long-period electromagnetic depth sounding using magnetometer arrays demonstrates that conductivities increase at about 200 km under Phanerozoic Australia but not until about 500 km depth under Precambrian Australia. Shorter period magnetotelluric measurements can only resolve shallower structures; these too indicate a similar trend but with sub-crustal conductivities increasing at less than 100 km under Phanerozoic Australia. Magma at these depths and shallower may be the source for Cainozoic volcanism in eastern Australia. Under Precambrian central and northern Australia magnetotelluric investigations indicate that pronounced conductivity increases do not occur until depths of 150–200 km are reached.Oceanic magnetic observations indicate that the Australian lithospheric plate as a whole is separating from Antarctica at a rate of about 7 cm/yr. The seismic and conductivity structures under the continental region of this plate indicate that lateral inhomogeneities possibly extend to depths as great as 500 km and are probably caused by the passage of eastern Australia over a hot spot. Hawaiian studies indicate that hot spots are not local features but result from large scale disturbances in the mantle. Conductivity increases commencing in the depth range 100–250 km may give an indication of uppermost zones within which the Palaeozoic lithospherc has been substantially modified resulting in elevated surface heat flow, volcanism and seismic travel-time anomalies. 相似文献
14.
Stochastic analysis of the effect of spatial variability of diffusion parameters on radionuclide transport in a low permeability clay layer 总被引：1，自引：0，他引：1
Most studies that incorporate subsurface heterogeneity in groundwater flow and transport models only analyze and simulate the spatial variability of hydraulic conductivity. Heterogeneity of the other flow and transport parameters are usually neglected. This approach is often justified, but there are, however, cases in which disregarding the heterogeneity of the other flow and transport parameters can be questionable. In low permeability media, for instance, diffusion is often the dominant transport mechanism. It therefore seems logical to incorporate the spatial variability of the diffusion parameters in the transport model. This study therefore analyses and simulates the spatial variability of the effective diffusion coefficient and the diffusion accessible porosity with geostatistical techniques and incorporates their heterogeneity in the transport model of a low permeability formation. The formation studied was Boom clay (Belgium), a candidate host rock for the deep geological disposal of high-level radioactive waste. The calculated output radionuclide fluxes of this model are compared with the fluxes calculated with a homogeneous model and a model with a heterogeneous hydraulic conductivity distribution. This analysis shows that the heterogeneity of the diffusion parameters has a much larger effect on the calculated output radionuclide fluxes than the heterogeneity of hydraulic conductivity in the low permeability medium under study. 相似文献
15.
Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium) 总被引：3，自引：1，他引：2
Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport. 相似文献
16.
Integration of Tracer Test Data to Refine Geostatistical Hydraulic Conductivity Fields Using Sequential Self-Calibration Method 总被引：3，自引：0，他引：3
On the basis of local measurements of hydraulic conductivity,geostatistical methods have been found to be useful in heterogeneity characterization of a hydraulic conductivity field on a regional scale. However,the methods are not suited to directly integrate dynamic production data,such as,hydraulic head and solute concentration,into the study of conductivity distribution. These data,which record the flow and transport processes in the medium,are closely related to the spatial distribution of hydraulic conductivity. In this study,a three-dimensional gradient-based inverse method-the sequential self-calibration (SSC) method-is developed to calibrate a hydraulic conductivity field,initially generated by a geostatistical simulation method,conditioned on tracer test results. The SSC method can honor both local hydraulic conductivity measurements and tracer test data. The mismatch between the simulated hydraulic conductivity field and the reference true one,measured by its mean square error (MSE),is reduced through the SSC conditional study. In comparison with the unconditional results,the SSC conditional study creates the mean breakthrough curve much closer to the reference true curve,and significantly reduces the prediction uncertainty of the solute transport in the observed locations. Further,the reduction of uncertainty is spatially dependent,which indicates that good locations,geological structure,and boundary conditions will affect the efficiency of the SSC study results. 相似文献
17.
B. Shifteh Some’e F. Hassanpour A. Ezani S. R. Miremadi H. Tabari 《Environmental Earth Sciences》2011,64(7):1849-1864
Analysis of the spatial variability of soil properties is important to explain the site-specific ecosystems. Spatial patterns
of some soil properties such as soil texture, exchangeable sodium percentage (ESP), electrical conductivity (ECe), soil pH
and cation exchange capacity (CEC) were analyzed in salt and sodic affected soils in the south of the Ardabil province, in
the northwest of Iran, to identify their spatial distribution for performance of a site-specific management. Soil samples
were collected from 0 to 30, 30 to 60, 60 to 90, 90 to 120 and 120 to 150 cm soil depths at sampling sites. Data were investigated
both statistically and geostatistically on the basis of the semivariogram. The spatial distribution model and spatial dependence
level varied in the study area. Among the considered parameters, maximum and minimum spatial variability were observed in
EC and pH parameters, respectively. Soil properties showed moderate to strong spatial dependence, except for a few. ECe was
strongly spatially dependent in the total soil depth and clay was strongly spatially dependent at the first depth. Sand and
pH were moderately spatially dependent for three of the five depths. ESP was strongly spatially dependent and silt was moderate
in the total soil depths, except at 90–120 cm depth. Furthermore, CEC had strong spatial dependence for three of the five
depths. All geostatistical range values were >1,389 m in this study. It was concluded that the strong spatial dependency of
soil properties would lead to extrinsic factors such as bedrock, agricultural pollution, drainage and ground water level. 相似文献
18.
A procedure to estimate the probability of intercepting a contaminant groundwater plume for monitoring network design has been developed and demonstrated. The objective of the procedure is to use all available information in a method that accounts for the heterogeneity of the aquifer and the paucity of data. The major components of the procedure are geostatistical conditional simulation and parameter estimation that are used sequentially to generate flow paths from a suspected contaminant source location to a designated monitoring transect. From the flow paths, a histogram is constructed that represents the spatial probability distribution of plume centerlines. With an independent estimate of the plume width, a relationship between the total cost and the probability of detecting a plume can be made. The method uses geostatistical information from hydraulic head measurements and is conditioned by the data and the physics of groundwater flow. This procedure was developed specifically for the design of monitoring systems at sites where very few, if any, hydraulic conductivity data are available. 相似文献
19.
Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity. 相似文献
20.
The Lynx mine, currently inactive, has produced copper and zinc concentrates from massive sulfide deposits on a lease within the rainy, mountainous interior of Vancouver Island. Tailings, used to back-fill a mined-out stope, are being leached by percolating groundwater and the resulting acidic, metal-laden drainage is discharging from the portal of the 8-Level adit. Temporal variations in the flow rate, specific conductance and temperature of the discharge were monitored continuously over a 2-year period while effluent chemistry was sampled weekly. Conductivity was relatively constant throughout most of the year but peaked with the first autumn storm events as accumulated soluble sulfide oxidation products were flushed from the workings. Concentrations of sulfate and most metals were closely correlated with conductivity as were low pH values as stored acidity was released along with dissolved species. Variations in pH controlled the speciation and partitioning of metals between dissolved and particulate phases. 相似文献