共查询到20条相似文献，搜索用时 890 毫秒
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Inverse modeling is a useful tool in ground water flow modeling studies. The most frequent difficulties encountered when using this technique are the lack of conditioning information (e.g., heads and transmissivities), the uncertainty in available data, and the nonuniqueness of the solution. These problems can be addressed and quantified through a stochastic Monte Carlo approach. The aim of this work was to compare the applicability of two stochastic inverse modeling approaches in a field-scale application. The multi-scaling (MS) approach uses a downscaling parameterization procedure that is not based on geostatistics. The pilot point (PP) approach uses geostatistical random fields as initial transmissivity values and an experimental variogram to condition the calibration. The studied area (375 km2) is part of a regional aquifer, northwest of Montreal in the St. Lawrence lowlands (southern Québec). It is located in limestone, dolomite, and sandstone formations, and is mostly a fractured porous medium. The MS approach generated small errors on heads, but the calibrated transmissivity fields did not reproduce the variogram of observed transmissivities. The PP approach generated larger errors on heads but better reproduced the spatial structure of observed transmissivities. The PP approach was also less sensitive to uncertainty in head measurements. If reliable heads are available but no transmissivities are measured, the MS approach provides useful results. If reliable transmissivities with a well inferred spatial structure are available, then the PP approach is a better alternative. This approach however must be used with caution if measured transmissivities are not reliable. 相似文献
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The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor's series for the exponential terms introduced by sinks and sources or the Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity-denoted as ln(T)-perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can be performed. This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with an R2 coefficient = 0.96 for an ln(T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln(T) estimates, in comparison to simply interpolating the sparse ln(T) data alone. The new Bayesian code is also employed to calibrate a high-resolution finite difference MODFLOW model of the Edwards Aquifer in southwest Texas. The posterior ln(T) field from this application yields better head fit when compared to the prior ln(T) field determined from upscaling and cokriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers. 相似文献
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byGordon James MacMillan 《Ground water》2009,47(6):822-827
An analytical method is provided where the ground water practitioner can quickly determine the size (number of wells) and spacing of a well network capable of meeting a known ground water demand. In order to apply the method, two new parameters are derived that relate theoretical drawdown to the maximum drawdown that is achievable without mining the aquifer. The size of a well network is shown to be proportional to the ground water demand and inversely proportional to the transmissivity and available head. The spacing between wells in a supply well network is shown to be most sensitive to a derived parameter r HA/ 3 , which is related to the available head and the propagation of drawdown away from a theoretical well if the total ground water demand was applied to that well. The method can be used to quickly determine the required spacing between wells in well networks of various sizes that are completed in confined aquifers with no leakance. 相似文献
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In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2 /sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km. 相似文献
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Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error. 相似文献
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The variogram is a key parameter for geostatistical estimation and simulation. Preferential sampling may bias the spatial structure and often leads to noisy and unreliable variograms. A novel technique is proposed to weight variogram pairs in order to compensate for preferential or clustered sampling . Weighting the variogram pairs by global kriging of the quadratic differences between the tail and head values gives each pair the appropriate weight, removes noise and minimizes artifacts in the experimental variogram. Moreover, variogram uncertainty could be computed by this technique. The required covariance between the pairs going into variogram calculation, is a fourth order covariance that must be calculated by second order moments. This introduces some circularity in the calculation whereby an initial variogram must be assumed before calculating how the pairs should be weighted for the experimental variogram. The methodology is assessed by synthetic and realistic examples. For synthetic example, a comparison between the traditional and declustered variograms shows that the declustered variograms are better estimates of the true underlying variograms. The realistic example also shows that the declustered sample variogram is closer to the true variogram. 相似文献
8.
L. Jones 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(3):179-190
The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation. 相似文献
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Stauffer F 《Ground water》2005,43(6):843-849
A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers. 相似文献
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In this study, we examine the effects of conditioning spatially variable transmissivity fields using head and/or transmissivity measurements on well-capture zones. In order to address the challenge posed by conditioning a flow model with spatially varying parameters, an innovative inverse algorithm, the Representers method, is employed. The method explicitly considers this spatial variability.
A number of uniform measurement grids with different densities are used to condition transmissivity fields using the Representers method. Deterministic and stochastic analysis of well-capture zones are then examined. The deterministic study focuses on comparison between reference well-capture zones and their estimated mean conditioned on head data. It shows that model performance due to head conditioning on well-capture zone estimation is related to pumping rate. At moderate pumping rates transmissivity observations are more crucial to identify effects arising from small-scale variations in pore water velocity. However, with more aggressive pumping these effects are reduced, consequently model performance, through incorporating head observations, markedly improves. In the stochastic study, the effect of conditioning using head and/or transmissivity data on well-capture zone uncertainty is examined. The Representers method is coupled with the Monte Carlo method to propagate uncertainty in transmissivity fields to well-capture zones. For the scenario studied, the results showed that a combination of 48 head and transmissivity data could reduce the area of uncertainty (95% confidence interval) in well-capture zone location by over 50%, compared to a 40% reduction using either head or transmissivity data. This performance was comparable to that obtained through calibrating on three and a half times the number of head observations alone. 相似文献
14.
Carl Keller 《Ground water》2017,55(2):244-254
This study describes a new technique for measuring the head profile in a geologic formation. The technique provides rapid, low cost information on the depth of water‐producing zones and aquitards in heterogeneous aquifers, yielding estimates of hydraulic heads in each zone while identifying any potential for cross contamination between zones. The measurements can be performed in a typical borehole in just a few hours. The procedure uses both the continuous transmissivity profile obtained by the installation (eversion) of a flexible borehole liner into an open borehole and the subsequent removal (inversion) of the same liner from the borehole. The method is possible because of the continuous transmissivity profile (T profile described by Keller et al. 2014) obtained by measuring the rate of liner eversion under a constant driving head. The hydraulic heads of producing zones are measured using the reverse head profile (RHP) method (patent no. 9,008,971) based on a stepwise inversion of the borehole liner. As each interval of the borehole is uncovered by inversion of the liner, the head beneath the liner is allowed to equilibrate to a steady‐state value. The individual hydraulic heads contributing to each measurement are calculated using the measured transmissivity for each zone. Application of the RHP method to a sedimentary bedrock borehole in New Jersey verified that it reproduced the head distribution obtained the same day in the same borehole instrumented with a multilevel sampling system. 相似文献
15.
Many people in sub-Saharan Africa have to rely on meager water resources within mudstones for their only water supply. Although mudstones have been extensively researched for their low permeability behavior, little research has been undertaken to examine their ability to provide sustainable water supplies. To investigate the factors controlling the occurrence of usable ground water in mudstone environments, an area of Cretaceous mudstones in southeastern Nigeria was studied over a 3 yr period. Transmissivity (T) variations in a range of mudstone environments were studied. The investigations demonstrate that within the top 40 m of mudstones, transmissivity can be sufficient to develop village water supplies (T > 1 m2/d). Transmissivity is controlled by two factors: low-grade metamorphism and the presence of other, subordinate, lithologies within the mudstones. Largely unaltered mudstones (early diagenetic zone), comprising mainly smectite clays, are mostly unfractured and have a low T of < 0.1 m2/d. Mudstones that have undergone limited metamorphism (late diagenetic zone) comprise mixed layered illite/smectite clays, and ground water is found in widely spaced fracture zones (T > 1 m2/d in large fracture zones; T < 0.1 m2/d away from fracture zones). Mudstones that have been further altered and approach the anchizone comprise illite clays, are pervasively fractured, and have the highest transmissivity values (T > 4 m2/d). Dolerite intrusions in unaltered, smectitic mudstones are highly fractured with transmissivity in the range of 1 < T < 60 m2/d. Thin limestone and sandstone layers can also enhance transmissivity sufficiently to provide community water supplies. 相似文献
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This paper investigates the impact of heterogeneity of the transmissivity field on the interpretation of steady-state pumping test data from aquifer systems delimited by constant head boundaries such as aquifers adjacent to lakes or rivers. Spatially variable transmissivity fields are randomly generated and used to simulate the drawdown due to a pumping well located at different distances from a constant head boundary. The steady-state drawdown simulated at different observation wells are then interpreted using the Hantush method (Hantush 1959). The numerical simulations show that, in contrast to the case of infinite aquifer domains, the interpreted transmissivity varies depending on well locations and the separation distance between pumping well and boundary relative to the correlation length. The ensemble-averaged estimated transmissivity varies between the geometric mean and the arithmetic mean, and can even exceed the arithmetic mean in a narrow domain adjacent to the boundary. It approaches the geometric mean of the underlying transmissivity field only if the distance between the pumping well is more than 20 times the characteristic length of the transmissivity field. 相似文献
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This paper presents a geostatistical approach to multi-directional aquifer stimulation in order to better identify the transmissivity
field. Hydraulic head measurements, taken at a few locations but under a number of different steady-state flow conditions,
are used to estimate the transmissivity. Well installation is generally the most costly aspect of obtaining hydraulic head
measurements. Therefore, it is advantageous to obtain as many informative measurements from each sampling location as possible.
This can be achieved by hydraulically stimulating the aquifer through pumping, in order to set-up a variety of flow conditions.
We illustrate the method by applying it to a synthetic aquifer. The simulations provide evidence that a few sampling locations
may provide enough information to estimate the transmissivity field. Furthermore, the innovation of, or new information provided
by, each measurement can be examined by looking at the corresponding spline and sensitivity matrix. Estimates from multi-directional
stimulation are found to be clearly superior to estimates using data taken under one flow condition. We describe the geostatistical
methodology for using data from multi-directional simulations and address computational issues. 相似文献
18.
M. F. Snodgrass P. K. Kitanidis 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(5):299-316
This paper presents a geostatistical approach to multi-directional aquifer stimulation in order to better identify the transmissivity
field. Hydraulic head measurements, taken at a few locations but under a number of different steady-state flow conditions,
are used to estimate the transmissivity. Well installation is generally the most costly aspect of obtaining hydraulic head
measurements. Therefore, it is advantageous to obtain as many informative measurements from each sampling location as possible.
This can be achieved by hydraulically stimulating the aquifer through pumping, in order to set-up a variety of flow conditions.
We illustrate the method by applying it to a synthetic aquifer. The simulations provide evidence that a few sampling locations
may provide enough information to estimate the transmissivity field. Furthermore, the innovation of, or new information provided
by, each measurement can be examined by looking at the corresponding spline and sensitivity matrix. Estimates from multi-directional
stimulation are found to be clearly superior to estimates using data taken under one flow condition. We describe the geostatistical
methodology for using data from multi-directional simulations and address computational issues. 相似文献
19.
A conceptual model of anisotropic and dynamic permeability is developed from hydrogeologic and hydromechanical characterization of a foliated, complexly fractured, crystalline rock aquifer at Gates Pond, Berlin, Massachusetts. Methods of investigation include aquifer‐pumping tests, long‐term hydrologic monitoring, fracture characterization, downhole heat‐pulse flow meter measurements, in situ extensometer testing, and earth tide analysis. A static conceptual model is developed from observations of depth‐dependent and anisotropic permeability that effectively compartmentalizes the aquifer as a function of foliation intensity. Superimposed on the static model is dynamic permeability as a function of hydraulic head in which transient bulk aquifer transmissivity is proportional to changes in hydraulic head due to hydromechanical coupling. The dynamic permeability concept is built on observations that fracture aperture changes as a function of hydraulic head, as measured during in situ extensometer testing of individual fractures, and observed changes in bulk aquifer transmissivity as determined from earth tides during seasonal changes in hydraulic head, with higher transmissivity during periods of high hydraulic head, and lower transmissivity during periods of relatively lower hydraulic head. A final conceptual model is presented that captures both the static and dynamic properties of the aquifer. The workflow presented here demonstrates development of a conceptual framework for building numerical models of complexly fractured, foliated, crystalline rock aquifers that includes both a static model to describe the spatial distribution of permeability as a function of fracture type and foliation intensity and a dynamic model that describes how hydromechanical coupling impacts permeability magnitude as a function of hydraulic head fluctuation. This model captures important geologic controls on permeability magnitude, anisotropy, and transience and therefor offers potentially more reliable history matching and forecasts of different water management strategies, such as resource evaluation, well placement, permeability prediction, and evaluating remediation strategies. 相似文献
20.
MODFLOW 2000 head uncertainty,a first-order second moment method 总被引：1，自引：0，他引：1
A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MODFLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmissivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (transmissivity and recharge). 相似文献