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1.
A main purpose of groundwater inverse modeling lies in estimating the hydraulic conductivity field of an aquifer. Traditionally, hydraulic head measurements, possibly obtained in tomographic setups, are used as data. Because the groundwater flow equation is diffusive, many pumping and observation wells would be necessary to obtain a high resolution of hydraulic conductivity, which is typically not possible. We suggest performing heat tracer tests using the same already installed pumping wells and thermometers in observation planes to amend the hydraulic head data set by the arrival times of the heat signals. For each tomographic combinations of wells, we recommend installing an outer pair of pumping wells, generating artificial ambient flow, and an inner well pair in which the tests are performed. We jointly invert heads and thermal arrival times in 3-D by the quasi-linear geostatistical approach using an efficiently parallelized code running on a mid-range cluster. In the present study, we evaluate the value of heat tracer versus head data in a synthetic test case, where the estimated fields can be compared to the synthetic truth. Because the sensitivity patterns of the thermal arrival times differ from those of head measurements, the resolved variance in the estimated field is 6 to 10 times higher in the joint inversion in comparison to inverting head data only. Also, in contrast to head measurements, reversing the flow field and repeating the heat-tracer test improves the estimate in terms of reducing the estimation variance of the estimate. Based on the synthetic test case, we recommend performing the tests in four principal directions, requiring in total eight pumping wells and four intersecting observation planes for heads and temperature in each direction. 相似文献
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3.
The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks’ method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer. 相似文献
4.
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
5.
In this paper, we present a conceptual‐numerical model that can be deduced from a calibrated finite difference groundwater‐flow model, which provides a parsimonious approach to simulate and analyze hydraulic heads and surface water body–aquifer interaction for linear aquifers (linear response of head to stresses). The solution of linear groundwater‐flow problems using eigenvalue techniques can be formulated with a simple explicit state equation whose structure shows that the surface water body–aquifer interaction phenomenon can be approached as the drainage of a number of independent linear reservoirs. The hydraulic head field could be also approached by the summation of the head fields, estimated for those reservoirs, defined over the same domain set by the aquifer limits, where the hydraulic head field in each reservoir is proportional to a specific surface (an eigenfunction of an eigenproblem, or an eigenvector in discrete cases). All the parameters and initial conditions of each linear reservoir can be mathematically defined in a univocal way from the calibrated finite difference model, preserving its characteristics (geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses). We also demonstrated that, in practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. The reduced computational cost of these solutions can help to integrate the groundwater component within conjunctive use management models. Conceptual approximation also facilitates understanding of the physical phenomenon and analysis of the factors that influence it. A simple synthetic aquifer has been employed to show how the conceptual model can be built for different spatial discretizations, the parameters required, and their influence on the simulation of hydraulic head fields and stream–aquifer flow exchange variables. A real‐world case was also solved to test the accuracy of the proposed approaches, by comparing its solution with that obtained using finite‐difference MODFLOW code. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
Post VE 《Ground water》2012,50(5):785-792
Groundwater density is an important parameter in the interpretation of flow patterns. This paper investigates the relationship between electrical conductivity (EC) and groundwater density in coastal aquifers and evaluates the suitability of the UNESCO 1980 equation of state, developed for the world's oceans, for determining the density of groundwater based on its EC. To achieve this aim, a dataset of groundwater samples from four different types of coastal aquifers was collected. It is found that the density of a sample can be estimated to a good approximation on the basis of its EC using the UNESCO 1980 equation of state. Deviations from the equation of state were found to be due to the changes in EC and the density caused by geochemical reactions, such as the dissolution of carbonates, degradation of organic carbon, cation exchange, and sulfate loss. Owing to these deviations, the UNESCO 1980 equation of state may underestimate the density by up to 1.5 kg/m(3). The effect of this uncertainty on the correction terms applied to the hydraulic head required for a proper interpretation of groundwater flow patterns and rates is quantified. It was found that the fresh water head may be wrong by centimeters to a few decimeters. From this it is concluded that, unless the purpose of a groundwater investigation requires great accuracy, the equation of state provides an efficient and inexpensive way to estimate density from EC. 相似文献
7.
As a result of rock dissolution processes, karst aquifers exhibit highly conductive features such as caves and conduits. Within these structures, groundwater flow can become turbulent and therefore be described by nonlinear gradient functions. Some numerical groundwater flow models explicitly account for pipe hydraulics by coupling the continuum model with a pipe network that represents the conduit system. In contrast, the Conduit Flow Process Mode 2 (CFPM2) for MODFLOW-2005 approximates turbulent flow by reducing the hydraulic conductivity within the existing linear head gradient of the MODFLOW continuum model. This approach reduces the practical as well as numerical efforts for simulating turbulence. The original formulation was for large pore aquifers where the onset of turbulence is at low Reynolds numbers (1 to 100) and not for conduits or pipes. In addition, the existing code requires multiple time steps for convergence due to iterative adjustment of the hydraulic conductivity. Modifications to the existing CFPM2 were made by implementing a generalized power function with a user-defined exponent. This allows for matching turbulence in porous media or pipes and eliminates the time steps required for iterative adjustment of hydraulic conductivity. The modified CFPM2 successfully replicated simple benchmark test problems. 相似文献
8.
Franklin W. Koch Emily B. Voytek Frederick D. Day‐Lewis Richard Healy Martin A. Briggs John W. Lane Jr. Dale Werkema 《Ground water》2016,54(3):434-439
A new version of the computer program 1DTempPro extends the original code to include new capabilities for (1) automated parameter estimation, (2) layer heterogeneity, and (3) time‐varying specific discharge. The code serves as an interface to the U.S. Geological Survey model VS2DH and supports analysis of vertical one‐dimensional temperature profiles under saturated flow conditions to assess groundwater/surface‐water exchange and estimate hydraulic conductivity for cases where hydraulic head is known. 相似文献
9.
Emily B. Voytek Anja Drenkelfuss Frederick D. Day‐Lewis Richard Healy John W. Lane Jr. Dale Werkema 《Ground water》2014,52(2):298-302
A new computer program, 1DTempPro, is presented for the analysis of vertical one‐dimensional (1D) temperature profiles under saturated flow conditions. 1DTempPro is a graphical user interface to the U.S. Geological Survey code Variably Saturated 2‐Dimensional Heat Transport (VS2DH), which numerically solves the flow and heat‐transport equations. Pre‐ and postprocessor features allow the user to calibrate VS2DH models to estimate vertical groundwater/surface‐water exchange and also hydraulic conductivity for cases where hydraulic head is known. 相似文献
10.
Steady interface flow in heterogeneous aquifer systems is simulated with single‐density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m3). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi‐aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben‐Herzberg formula. The transformed problem may be solved with a single‐density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi‐aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached. 相似文献
11.
G. Christakos C. T. Miller D. Oliver 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(3):213-239
As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations. 相似文献
12.
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
13.
《Advances in water resources》2006,29(1):89-98
We present explicit analytic solutions describing the hydraulic head and discharge vector for two-dimensional, steady groundwater flow past an impermeable barrier embedded in a regional flow field. We use the solution to investigate the effects of open vertical barriers on the flow field; in particular, we examine the hydraulic containment of contaminant plumes or source zones by combination of a vertical barrier wall and extraction wells. We quantify the local reduction in discharge rates due to the barrier wall and the local increase in the size of the capture zone of an extraction well near an open, up-gradient barrier. We find that the combination of an open vertical barrier with down-gradient extraction wells can be very effective in decreasing the well discharge rate necessary to control a contaminant plume or source area. Design charts are presented for quantifying the effects of the barrier wall on the hydraulic control of the groundwater flow field and for estimating the jump in head across a barrier. The charts are appropriate for use in the preliminary design and cost estimating of remedial systems, and for the design of dewatering systems. 相似文献
14.
G. Christakos D. T. Hristopulos 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(2):117-138
In earlier publications, certain applications of space transformation operators in subsurface hydrology were considered. These operators reduce the original multi-dimensional problem to the one-dimensional space, and can be used to study stochastic partial differential equations governing groundwater flow and solute transport processes. In the present work we discuss developments in the theoretical formulation of flow models with space-dependent coefficients in terms of space transformations. The formulation is based on stochastic Radon operator representations of generalized functions. A generalized spectral decomposition of the flow parameters is introduced, which leads to analytically tractable expressions of the space transformed flow equation. A Plancherel representation of the space transformation product of the head potential and the log-conductivity is also obtained. A test problem is first considered in detail and the solutions obtained by means of the proposed approach are compared with the exact solutions obtained by standard partial differential equation methods. Then, solutions of three-dimensional groundwater flow are derived starting from solutions of a one-dimensional model along various directions in space. A step-by-step numerical formulation of the approach to the flow problem is also discussed, which is useful for practical applications. Finally, the space transformation solutions are compared with local solutions obtained by means of series expansions of the log-conductivity gradient. 相似文献
15.
《Advances in water resources》1998,21(7):591-604
A heuristic algorithm is presented for problems which are formulated to find an optimal groundwater remediation strategy with constraints on confined groundwater flow and contaminant transport. The problem is simplified by decoupling the transport constraints from the hydraulic constraints to produce a linear hydraulic control optimization problem. The solution is obtained by an iterative process in which the constraints on hydraulic gradient are updated, using information from transport simulation, and the hydraulic control problem is solved repeatedly. In effect, the transport simulation is used to calibrate the head difference constraint values of the hydraulic control problem. The algorithm is described in detail and its convergence is demonstrated on several examples. The advantages and limitations of the algorithm are discussed. 相似文献
16.
Fine‐scale dynamics of groundwater flow were studied in a 1·5 ha peatland in central New York. Measurements of the hydraulic head throughout a detailed network of piezometer clusters revealed spatial and temporal variability in the direction of groundwater flow at a very fine (within a few metres) scale of analysis. Within the small wetland, there were areas of groundwater recharge, discharge and lateral flow. Such patterns of groundwater flow frequently reversed or changed due to fluctuations of only a few centimetres in hydraulic head. Specific conductance, deuterium signatures and calcium concentrations of groundwater corroborated the groundwater flow patterns determined with hydraulic head measurements and illustrated the influence of source water chemistry and evaporation on different layers in the peat column. The control of peat chemistry by such fine‐scale groundwater flow may have important implications for plant community composition and diversity in groundwater‐fed peatlands. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
17.
An investigation of seepage below floodwater-retarding structures conducted by the U.S.D.A. Science and Education Administration Federal Research resulted in a method for estimating seepage from a reservoir based upon change in head. A typical structure was selected for the study and physiographic and geologic features of the site were identified. Extensive hydrologic and hydrogeologic data were collected and analyzed for the site. A major inflow event was recorded in the reservoir in September 1965 and data from that event were used to develop an equation for estimating the amount of seepage lost from the structure in relation to the hydraulic head behind the structure. The method presented by the authors provides a physically based method for estimating the impact of a reservoir on the groundwater flow system assuming variable reservoir head conditions. 相似文献
18.
Abstract The distribution of major geological units, static water level data, water chemistry data, and observations of surface features influenced by groundwater seepage were used to ascertain the nature of groundwater occurrence and flow pattern in the Enugu coal field, Nigeria. Considerations of the geological units, the static groundwater levels and groundwater seepages in the mines indicate that the coal sequence is a multiaquifer system in which sandstone and coal aquifers alternate with shale aquitards. Based on the hydraulic head data, the groundwater flow is predominantly downwards. Groundwater velocity calculation across the multiaquifer system using the Darcy equation gave a flow velocity of about 1 m day?1. For groundwater systems, such a calculated velocity is considered high. The high velocity is most probably due to the high fracture porosity as well as the presence of other stratigraphic and structural features such as alluvial fills that provide high hydraulic conductivity pathways across the aquifer system. The pattern of groundwater inflow into the mines is also influenced by these stratigraphie and structural features. 相似文献
19.
Combination of FEM and CMA‐ES algorithm for transmissivity identification in aquifer systems 
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下载免费PDF全文 In this paper, we propose a coupling of a finite element model with a metaheuristic optimization algorithm for solving the inverse problem in groundwater flow (Darcy's equations). This coupling performed in 2 phases is based on the combination of 2 codes: This is the HySubF‐FEM code (hydrodynamic of subsurface flow by finite element method) used for the first phase allowing the calculation of the flow and the CMA‐ES code (covariance matrix adaptation evolution strategy) adopted in the second phase for the optimization process. The combination of these 2 codes was implemented to identify the transmissivity field of groundwater by knowing the hydraulic head in some point of the studied domain. The integrated optimization algorithm HySubF‐FEM/CMA‐ES has been validated successfully on a schematic case offering an analytical solution. As realistic application, the integrated optimization algorithm HySubF‐FEM/CMA‐ES was applied to a complex groundwater in the north of France to identify the transmissivity field. This application does not use zonation techniques but solves an optimization problem at each internal node of the mesh. The obtained results are considered excellent with high accuracy and fully consistent with the hydrogeological characteristics of the studied aquifer.However, the various numerical simulations performed in this paper have shown that the CMA‐ES algorithm is time‐consuming. Finally, the paper concludes that the proposed algorithm can be considered as an efficient tool for solving inverse problems in groundwater flow. 相似文献
20.
In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhars work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio. 相似文献