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1.
《Advances in water resources》2005,28(4):393-403
We consider the dynamics of a fluid interface in heterogeneous porous media, whose hydraulic properties are uncertain. Modeling hydraulic conductivity as a random field of given statistics allows us to predict the interface dynamics and to estimate the corresponding predictive uncertainty by means of statistical moments. The novelty of our approach to obtaining the interface statistics consists of dynamically mapping the Cartesian coordinate system onto a coordinate system associated with the moving front. This transforms a difficult problem of deriving closure relationships for highly nonlinear stochastic flows with free surfaces into a relatively simple problem of deriving stochastic closures for linear flows in domains with fixed boundaries. We derive a set of deterministic equations for the statistical moments of the interfacial dynamics, which hold in one and two spatial dimensions, and analyze their solutions for one-dimensional flow. 相似文献
2.
Two different deterministic and two alternative stochastic (i.e., geostatistical) approaches to modeling the distribution of hydraulic conductivity (K) in a nonuniform (sigma2ln(K)) = 0.29) glacial sand aquifer were used to explore the influence of conceptual model selection on simulations of three-dimensional tracer movement. The deterministic K models employed included a homogeneous effective K and a perfectly stratified 14 layer model. Stochastic K models were constructed using sequential Gaussian simulation and sequential i ndicator simulation conditioned to available K values estimated from measured grain size distributions. Standard simulation software packages MODFLOW, MT3DMS, and MODPATH were used to model three-dimensional ground water flow and transport in a field tracer test, where a pulse of bromide was injected through an array of three fully screened wells and extracted through a single fully screened well approximately 8 m away. Agreement between observed and simulated transport behavior was assessed through direct comparison of breakthrough curves (BTCs) and selected breakthrough metrics at the extraction well and at 26 individual multilevel sample ports distributed irregularly between the injection and extraction wells. Results indicate that conceptual models incorporating formation variability are better able to capture observed breakthrough behavior. Root mean square (RMS) error of the deterministic models bracketed the ensemble mean RMS error of stochastic models for simulated concentration vs. time series, but not for individual BTC characteristic metrics. The spatial variability models evaluated here may be better suited to simulating breakthrough behavior measured in wells screened over large intervals than at arbitrarily distributed observation points within a nonuniform aquifer domain. 相似文献
3.
C. -M. Chang M. W. Kemblowski 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(4):281-300
In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes. 相似文献
4.
E.R. Bayless Wayne A. Mandell James R. Ursic 《Ground Water Monitoring & Remediation》2011,31(2):48-62
Borehole flowmeters that measure horizontal flow velocity and direction of groundwater flow are being increasingly applied to a wide variety of environmental problems. This study was carried out to evaluate the measurement accuracy of several types of flowmeters in an unconsolidated aquifer simulator. Flowmeter response to hydraulic gradient, aquifer properties, and well‐screen construction was measured during 2003 and 2005 at the U.S. Geological Survey Hydrologic Instrumentation Facility in Bay St. Louis, Mississippi. The flowmeters tested included a commercially available heat‐pulse flowmeter, an acoustic Doppler flowmeter, a scanning colloidal borescope flowmeter, and a fluid‐conductivity logging system. Results of the study indicated that at least one flowmeter was capable of measuring borehole flow velocity and direction in most simulated conditions. The mean error in direction measurements ranged from 15.1° to 23.5° and the directional accuracy of all tested flowmeters improved with increasing hydraulic gradient. The range of Darcy velocities examined in this study ranged 4.3 to 155 ft/d. For many plots comparing the simulated and measured Darcy velocity, the squared correlation coefficient (r2) exceeded 0.92. The accuracy of velocity measurements varied with well construction and velocity magnitude. The use of horizontal flowmeters in environmental studies appears promising but applications may require more than one type of flowmeter to span the range of conditions encountered in the field. Interpreting flowmeter data from field settings may be complicated by geologic heterogeneity, preferential flow, vertical flow, constricted screen openings, and nonoptimal screen orientation. 相似文献
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A new method was developed for conducting aquifer tests in fractured-rock flow systems that have a pump-and-treat (P&T) operation for containing and removing groundwater contaminants. The method involves temporary shutdown of individual pumps in wells of the P&T system. Conducting aquifer tests in this manner has several advantages, including (1) no additional contaminated water is withdrawn, and (2) hydraulic containment of contaminants remains largely intact because pumping continues at most wells. The well-shutdown test method was applied at the former Naval Air Warfare Center (NAWC), West Trenton, New Jersey, where a P&T operation is designed to contain and remove trichloroethene and its daughter products in the dipping fractured sedimentary rocks underlying the site. The detailed site-scale subsurface geologic stratigraphy, a three-dimensional MODFLOW model, and inverse methods in UCODE_2005 were used to analyze the shutdown tests. In the model, a deterministic method was used for representing the highly heterogeneous hydraulic conductivity distribution and simulations were conducted using an equivalent porous media method. This approach was very successful for simulating the shutdown tests, contrary to a common perception that flow in fractured rocks must be simulated using a stochastic or discrete fracture representation of heterogeneity. Use of inverse methods to simultaneously calibrate the model to the multiple shutdown tests was integral to the effectiveness of the approach. 相似文献
7.
Information from an outcrop is used as an analogue of a natural heterogeneous aquifer in order to provide an exhaustive data set of hydraulic properties. Based on this data, two commonly used borehole based investigation methods are simulated numerically. For a scenario of sparse sampling of the aquifer, the process of regionalization of the borehole hydraulic conductivity values is simulated by application of a deterministic interpolation approach and conditioned stochastic simulations. Comparison of the cumulative distributions of particle arrival times illustrates the effects of the sparse sampling, the properties of the individual investigation methods and the regionalization methods on the ability to predict flow and transport behaviour in the real system (i.e. the exhaustive data set). 相似文献
8.
The large and diverse body of subsurface characterization data generated at a field research site near Oyster, Virginia, provides a unique opportunity to test the impact of conditioning data of various types on predictions of flow and transport. Bromide breakthrough curves (BTCs) were measured during a forced-gradient local-scale injection experiment conducted in 1999. Observed BTCs are available at 140 sampling points in a three-dimensional array within the transport domain. A detailed three-dimensional numerical model is used to simulate breakthrough curves at the same locations as the observed BTCs under varying assumptions regarding the character of hydraulic conductivity spatial distributions, and variable amounts and types of conditioning data. We present comparative results of six cases ranging from simple (deterministic homogeneous models) to complex (stochastic indicator simulation conditioned to cross-borehole geophysical observations). Quantitative measures of model goodness-of-fit are presented. The results show that conditioning to a large number of small-scale measurements does not significantly improve model predictions, and may lead to biased or overly confident predictions. However, conditioning to geophysical interpretations with larger spatial support significantly improves the accuracy and precision of model predictions. In all cases, the effects of model error appear to be significant in relation to parameter uncertainty. 相似文献
9.
We jointly invert field data of flowmeter and multiple pumping tests in fully screened wells to estimate hydraulic conductivity using a geostatistical method. We use the steady-state drawdowns of pumping tests and the discharge profiles of flowmeter tests as our data in the inference. The discharge profiles need not be converted to absolute hydraulic conductivities. Consequently, we do not need measurements of depth-averaged hydraulic conductivity at well locations. The flowmeter profiles contain information about relative vertical distributions of hydraulic conductivity, while drawdown measurements of pumping tests provide information about horizontal fluctuation of the depth-averaged hydraulic conductivity. We apply the method to data obtained at the Krauthausen test site of the Forschungszentrum Jülich, Germany. The resulting estimate of our joint three-dimensional (3D) geostatistical inversion shows an improved 3D structure in comparison to the inversion of pumping test data only. 相似文献
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This paper presents a Bayesian Monte Carlo method for evaluating the uncertainty in the delineation of well capture zones and its application to a wellfield in a heterogeneous, multiaquifer system. In the method presented, Bayes' rule is used to update prior distributions for the unknown parameters of the stochastic model for the hydraulic conductivity, and to calculate probability-based weights for parameter realizations using head residuals. These weights are then assigned to the corresponding capture zones obtained using forward particle tracking. Statistical analysis of the set of weighted protection zones results in a probability distribution for the capture zones. The suitability of the Bayesian stochastic method for a multilayered system is investigated, using the wellfield Het Rot at Nieuwrode, Belgium, located in a three-layered aquifer system, as an example. The hydraulic conductivity of the production aquifer is modeled as a spatially correlated random function with uncertain parameters. The aquitard and overlying unconfined aquifer are assigned random, homogeneous conductivities. The stochastic results are compared with deterministic capture zones obtained with a calibrated model for the area. The predictions of the stochastic approach are more conservative and indicate that parameter uncertainty should be taken into account in the delineation of well capture zones. 相似文献
12.
There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/S(s)) of fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard, and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model based on this conceptual model are consistent with field observations, which did not fit the typical conceptual model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting ground water flow and for planning and protecting water supplies. 相似文献
13.
The coupled flow-mass transport inverse problem is formulated using the maximum likelihood estimation concept. An evolutionary computational algorithm, the genetic algorithm, is applied to search for a global or near-global solution. The resulting inverse model allows for flow and transport parameter estimation, based on inversion of spatial and temporal distributions of head and concentration measurements. Numerical experiments using a subset of the three-dimensional tracer tests conducted at the Columbus, Mississippi site are presented to test the model's ability to identify a wide range of parameters and parametrization schemes. The results indicate that the model can be applied to identify zoned parameters of hydraulic conductivity, geostatistical parameters of the hydraulic conductivity field, angle of hydraulic conductivity anisotropy, solute hydrodynamic dispersivity, and sorption parameters. The identification criterion, or objective function residual, is shown to decrease significantly as the complexity of the hydraulic conductivity parametrization is increased. Predictive modeling using the estimated parameters indicated that the geostatistical hydraulic conductivity distribution scheme produced good agreement between simulated and observed heads and concentrations. The genetic algorithm, while providing apparently robust solutions, is found to be considerably less efficient computationally than a quasi-Newton algorithm. 相似文献
14.
H. J. W. M. Hendricks Franssen J. J. Gómez-Hernández 《Stochastic Environmental Research and Risk Assessment (SERRA)》2002,16(2):155-174
3D groundwater flow at the fractured site of Asp? (Sweden) is simulated. The aim was to characterise the site as adequately
as possible and to provide measures on the uncertainty of the estimates. A stochastic continuum model is used to simulate
both groundwater flow in the major fracture planes and in the background. However, the positions of the major fracture planes
are deterministically incorporated in the model and the statistical distribution of the hydraulic conductivity is modelled
by the concept of multiple statistical populations; each fracture plane is an independent statistical population. Multiple
equally likely realisations are built that are conditioned to geological information on the positions of the major fracture
planes, hydraulic conductivity data, steady state head data and head responses to six different interference tests. The experimental
information could be reproduced closely. The results of the conditioning are analysed in terms of ensemble averaged average
fracture plane conductivities, the ensemble variance of average fracture plane conductivities and the statistical distribution
of the hydraulic conductivity in the fracture planes. These results are evaluated after each conditioning stage. It is found
that conditioning to hydraulic head data results in an increase of the hydraulic conductivity variance while the statistical
distribution of log hydraulic conductivity, initially Gaussian, becomes more skewed for many of the fracture planes in most
of the realisations. 相似文献
15.
Convergence of deterministic and stochastic approaches in optimal remediation design of a contaminated aquifer 总被引：2，自引：2，他引：0
Nak-Youl Ko Kang-Kun Lee 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(3):309-318
The comparison between two series of optimal remediation designs using deterministic and stochastic approaches showed a number
of converging features. Limited sampling measurements in a supposed contaminated aquifer formed the hydraulic conductivity
field and the initial concentration distribution used in the optimization process. The deterministic and stochastic approaches
employed a single simulation–optimization method and a multiple realization approach, respectively. For both approaches, the
optimization model made use of a genetic algorithm. In the deterministic approach, the total cost, extraction rate, and the
number of wells used increase when the design must satisfy the intensified concentration constraint. Growing the stack size
in the stochastic approach also brings about same effects. In particular, the change in the selection frequency of the used
extraction wells, with increasing stack size, for the stochastic approach can indicate the locations of required additional
wells in the deterministic approach due to the intensified constraints. These converging features between the two approaches
reveal that a deterministic optimization approach with controlled constraints is achievable enough to design reliable remediation
strategies, and the results of a stochastic optimization approach are readily available to real contaminated sites. 相似文献
16.
Knowledge of site‐specific contaminant transport processes is an essential requirement for performing various tasks concerning the protection and management of groundwater resources. However, prediction of their behavior is often difficult, especially in heterogeneous aquifers because of the lack of information about flow‐ and transport‐governing subsurface structures and parameters. Hence, stochastic approaches have been developed and frequently used. However, extensive modeling studies on sedimentary structures have shown that consideration of hydrogeological subunits and their distribution can be essential for transport modeling. A case study from the intensely investigated Lauswiesen site is used to demonstrate that more accurate predictions are possible with improved knowledge of deterministic structures. Results of this case study using direct‐push injection logging (DPIL) provide a more reliable characterization of hydraulic conductivity than sieve and flow meter data. 相似文献
17.
The effect of random recharge on uniform steady free-surface flow in heterogeneous porous formations
The effect of parametric uncertainty in recharge rate and spatial variability of hydraulic conductivity upon free-surface flow is investigated in a stochastic framework. We examine the three-dimensional free-surface gravitational flow problem for sloped mean uniform flow in a randomly heterogeneous porous medium under the influence of random recharge. We develop analytic solutions for the variance of free-surface position, head, and specific discharge on the free surface. Additionally, we obtain semi-analytic solutions for the statistical moments of head and specific discharge beneath the free-surface. Statistical moments are derived using a first-order approximation and then compared with their parallel in an unbounded medium. The effect of recharge mean and variability on the statistical moments is analyzed. Results can be applied to more complex flows, slowly varying in the mean. 相似文献
18.
The impact of three-dimensional subsurface heterogeneity in the saturated hydraulic conductivity on hillslope runoff generated by excess infiltration (so-called Hortonian runoff) is examined. A fully coupled, parallel subsurface–overland flow model is used to simulate runoff from an idealized hillslope. Ensembles of correlated, Gaussian random fields of saturated hydraulic conductivity are used to create uncertainty in spatial structure. A large number of cases are simulated in a parametric manner with the variance of the hydraulic conductivity varied over orders of magnitude. These cases include rainfall rates above, equal and below the geometric mean of the hydraulic conductivity distribution. These cases are also compared to theoretical representations of runoff production based on simple assumptions regarding (1) the rainfall rate and the value of hydraulic conductivity in the surface cell using a spatially-indiscriminant approach; and (2) a percolation-theory type approach to incorporate so-called runon. Simulations to test the ergodicity of hydraulic conductivity on hillslope runoff are also performed. Results show that three-dimensional stochastic representations of the subsurface hydraulic conductivity can create shallow perching, which has an important effect on runoff behavior that is different than previous two-dimensional analyses. The simple theories are shown to be very poor predictors of the fraction of saturated area that might runoff due to excess infiltration. It is also shown that ergodicity is reached only for a large number of integral scales (∼30) and not achieved for cases where the rainfall rate is less than the geometric mean of the saturated hydraulic conductivity. 相似文献
19.
IINTRODUCTIONDependingonflowandoperatingconditions,navigationtrafficmaycausesignificantresuspensionofdepositedsediment.Jnanumberofsituationsresuspensionofdepositedsedimentcanhavesevereenvironmentalrepercussions.Forinstance,ifthesedimentcontainscontaminants,thecontaminantsmaybereentrainedwiththesediment,taintingthewaterquality(Erdmannetal.,1994).Inothersituations,..evedincreasesintheamountofcleansuspendedsedimentcanbedetrimentalforaquaticplantsandanimals(Garcfaetal.,1998).Inordertoassesst… 相似文献
20.
A rigorous and practical approach for interpretation of impeller flow log data to determine vertical variations in hydraulic conductivity is presented and applied to two well logs from a Chalk aquifer in England. Impeller flow logging involves measuring vertical flow speed in a pumped well and using changes in flow with depth to infer the locations and magnitudes of inflows into the well. However, the measured flow logs are typically noisy, which leads to spurious hydraulic conductivity values where simplistic interpretation approaches are applied. In this study, a new method for interpretation is presented, which first defines a series of physical models for hydraulic conductivity variation with depth and then fits the models to the data, using a regression technique. Some of the models will be rejected as they are physically unrealistic. The best model is then selected from the remaining models using a maximum likelihood approach. This balances model complexity against fit, for example, using Akaike's Information Criterion. 相似文献