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1.
This paper proposes a multiscale flow and transport model which can be used in three-dimensional fractal random fields. The fractal random field effectively describes a field with a high degree of variability to satisfy the one-point statistics of Levy-stable distribution and the two-point statistics of fractional Levy motion (fLm). To overcome the difficulty of using infinite variance of Levy-stable distribution and to provide the physical meaning of a finite domain in real space, truncated power variograms are utilized for the fLm fields. The fLm model is general in the sense that both stationary and commonly used fractional Brownian motion (fBm) models are its special cases. When the upper cutoff of the truncated power variogram is close to the lower cutoff, the stationary model is well approximated. The commonly used fBm model is recovered when the Levy index of fLm is 2. Flow and solute transport were analyzed using the first-order perturbation method. Mean velocity, velocity covariance, and effective hydraulic conductivity in a three-dimensional fractal random field were derived. Analytical results for particle displacement covariance and macrodispersion coefficients are also presented. The results show that the plume in an fLm field moves slower at early time and has more significant long-tailing behavior at late time than in fBm or stationary exponential fields. The proposed fractal transport model has broader applications than those of stationary and fBm models. Flow and solute transport can be simulated for various scenarios by adjusting the Levy index and cutoffs of fLm to yield more accurate modeling results.  相似文献   

2.
Shlomo P. Neuman 《水文研究》2011,25(11):1837-1840
It has been previously demonstrated theoretically and numerically by the author that square or absolute increments of data sampled from fractional Brownian/Lévy motion (fBm/fLm), or of incremental data sampled from fractional Gaussian/Lévy noise (fGn/fLn), exhibit apparent/spurious multifractality. Here, we generalize these previous development in a way that (a) rigorously subordinates (truncated) fLn to fGn or, in a statistically equivalent manner, (truncated) fLm to fBm; (b) extends the analysis to a wider class of subordinated self‐affine processes; (c) provides a simple way to generate such processes and (d) explains why the distribution of corresponding increments tends to evolve from heavy tailed at small lags (separation distances or scales) to Gaussian at larger lags. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
Shlomo P. Neuman 《水文研究》2010,24(15):2056-2067
Many earth and environmental variables appear to be self‐affine (monofractal) or multifractal with spatial (or temporal) increments having exceedance probability tails that decay as powers of − α where 1 < α ≤ 2. The literature considers self‐affine and multifractal modes of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. We demonstrate theoretically that data having finite support, sampled across a finite domain from one or several realizations of an additive Gaussian field constituting fractional Brownian motion (fBm) characterized by α = 2, give rise to positive square (or absolute) increments which behave as if the field was multifractal when in fact it is monofractal. Sampling such data from additive fractional Lévy motions (fLm) with 1 < α < 2 causes them to exhibit spurious multifractality. Deviations from apparent multifractal behaviour at small and large lags are due to nonzero data support and finite domain size, unrelated to noise or undersampling (the causes cited for such deviations in the literature). Our analysis is based on a formal decomposition of anisotropic fLm (fBm when α = 2) into a continuous hierarchy of statistically independent and homogeneous random fields, or modes, which captures the above behaviour in terms of only E + 3 parameters where E is Euclidean dimension. Although the decomposition is consistent with a hydrologic rationale proposed by Neuman (2003), its mathematical validity is independent of such a rationale. Our results suggest that it may be worth checking how closely would variables considered in the literature to be multifractal (e.g. experimental and simulated turbulent velocities, some simulated porous flow velocities, landscape elevations, rain intensities, river network area and width functions, river flow series, soil water storage and physical properties) fit the simpler monofractal model considered in this paper (such an effort would require paying close attention to the support and sampling window scales of the data). Parsimony would suggest associating variables found to fit both models equally well with the latter. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

4.
In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.  相似文献   

5.
The effect of aquifer heterogeneity on flow and solute transport in two-dimensional isotropic porous media was analyzed using the Monte Carlo method. The two-dimensional logarithmic permeability (ln K) was assumed to be a non-stationary random field with its increments being a truncated fractional Lévy motion (fLm). The permeability fields were generated using the modified successive random additions (SRA) algorithm code SRA3DC [http://www.iamg.org/CGEditor/index.htm]. The velocity and concentration fields were computed respectively for two-dimensional flow and transport with a pulse input using the finite difference codes of MODFLOW 2000 and MT3DMS. Two fLm control parameters, namely the width parameter (C) and the Lévy index (α), were varied systematically to examine their effect on the resulting permeability, flow velocity and concentration fields. We also computed the first- and second-spatial moments, the dilution index, as well as the breakthrough curves at different control planes with the corresponding concentration fields. In addition, the derived breakthrough curves were fitted using the continuous time random walk (CTRW) and the traditional advection-dispersion equation (ADE). Results indicated that larger C and smaller α both led to more heterogeneous permeability and velocity fields. The Lévy-stable distribution of increments in ln K resulted in a Lévy-stable distribution of increments in logarithm of the velocity (ln v). Both larger C and smaller α created sharper leading edges and wider tailing edges of solute plumes. Furthermore, a relatively larger amount of solute still remained in the domain after a relatively longer time transport for smaller α values. The dilution indices were smaller than unity and increased as C increased and α decreased. The solute plume and its second-spatial moments increased as C increased and α decreased, while the first-spatial moments of the solute plume were independent of C and α values. The longitudinal macrodispersivity was scale-dependent and increased as a power law function of time. Increasing C and decreasing α both resulted in an increase in longitudinal macrodispersivity. The transport in such highly heterogeneous media was slightly non-Gaussian with its derived breakthrough curves being slightly better fitted by the CTRW than the ADE, especially in the early arrivals and late-time tails.  相似文献   

6.
Understanding the effects of contaminants that can diffuse into low-permeability (“low-k”) zones is crucial for effective groundwater remedial decision-making. Because low-k zones can serve as low-level sources of contamination to more transmissive zones over time, an accurate evaluation of the impacts of matrix diffusion at contaminated sites is vital. This study compared numerical groundwater flow and transport simulations using MODFLOW/RT3D at a hypothetical site using three cases, each with increasing discretization of the vertical 10-m thick domain: (1) a coarse multilayer heterogeneous grid based on one layer for each of four different hydrogeological units, (2) a “low-resolution” discretization approach where the low-k units were divided into several sublayers giving the model 10 layers, and (3) a “high-resolution” numerical model with 199 layers that are a few centimeters thick. When comparing the results of each case, significant differences were observed between the discretizations used, even though all other model input data were identical. The conventional grid models (Cases 1 and 2) appeared to underestimate groundwater plume concentrations by a factor ranging from 1.1 to 36 when compared to the high-resolution grid model (Case 3), and underestimated predicted cleanup times by more than a factor of 10 for some of the hypothetical sampling points in the modeling domain. These results validate the implication of Chapman et al. (2012), that conventional vertical discretization of numerical groundwater flow and transport models at contaminated sites (with layers that are greater than 1 m thick) can lead to significant errors when compared to more accurate high-resolution vertical discretization schemes (layers that are centimeters thick).  相似文献   

7.
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8.
Coastal wetlands are characterized by strong, dynamic interactions between surface water and groundwater. This paper presents a coupled model that simulates interacting surface water and groundwater flow and solute transport processes in these wetlands. The coupled model is based on two existing (sub) models for surface water and groundwater, respectively: ELCIRC (a three‐dimensional (3‐D) finite‐volume/finite‐difference model for simulating shallow water flow and solute transport in rivers, estuaries and coastal seas) and SUTRA (a 3‐D finite‐element/finite‐difference model for simulating variably saturated, variable‐density fluid flow and solute transport in porous media). Both submodels, using compatible unstructured meshes, are coupled spatially at the common interface between the surface water and groundwater bodies. The surface water level and solute concentrations computed by the ELCIRC model are used to determine the boundary conditions of the SUTRA‐based groundwater model at the interface. In turn, the groundwater model provides water and solute fluxes as inputs for the continuity equations of surface water flow and solute transport to account for the mass exchange across the interface. Additionally, flux from the seepage face was routed instantaneously to the nearest surface water cell according to the local sediment surface slope. With an external coupling approach, these two submodels run in parallel using time steps of different sizes. The time step (Δtg) for the groundwater model is set to be larger than that (Δts) used by the surface water model for computational efficiency: Δtg = M × Δts where M is an integer greater than 1. Data exchange takes place between the two submodels through a common database at synchronized times (e.g. end of each Δtg). The coupled model was validated against two previously reported experiments on surface water and groundwater interactions in coastal lagoons. The results suggest that the model represents well the interacting surface water and groundwater flow and solute transport processes in the lagoons. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

9.
Remediation of subsurface contamination requires an understanding of the contaminant (history, source location, plume extent and concentration, etc.), and, knowledge of the spatial distribution of hydraulic conductivity (K) that governs groundwater flow and solute transport. Many methods exist for characterizing K heterogeneity, but most if not all methods require the collection of a large number of small‐scale data and its interpolation. In this study, we conduct a hydraulic tomography survey at a highly heterogeneous glaciofluvial deposit at the North Campus Research Site (NCRS) located at the University of Waterloo, Waterloo, Ontario, Canada to sequentially interpret four pumping tests using the steady‐state form of the Sequential Successive Linear Estimator (SSLE) ( Yeh and Liu 2000 ). The resulting three‐dimensional (3D) K distribution (or K‐tomogram) is compared against: ( 1 ) K distributions obtained through the inverse modeling of individual pumping tests using SSLE, and ( 2 ) effective hydraulic conductivity (Keff) estimates obtained by automatically calibrating a groundwater flow model while treating the medium to be homogeneous. Such a Keff is often used for designing remediation operations, and thus is used as the basis for comparison with the K‐tomogram. Our results clearly show that hydraulic tomography is superior to the inversions of single pumping tests or Keff estimates. This is particularly significant for contaminated sites where an accurate representation of the flow field is critical for simulating contaminant transport and injection of chemical and biological agents used for active remediation of contaminant source zones and plumes.  相似文献   

10.
Anisotropy and heterogeneity of hydraulic conductivity (K) are seldom considered in models of mire hydrology. We investigated the effect of anisotropy and heterogeneity on groundwater flow in bog peat using a steady‐state groundwater model. In five model simulations, four sets of K data were used. The first set comprised measured K values from an anisotropic and heterogeneous bog peat. These data were aggregated to produce the following simplified data sets: an isotropic and heterogeneous distribution of K; an isotropic and homogeneous distribution; and an anisotropic and homogeneous distribution. We demonstrate that, where anisotropy and heterogeneity exist, groundwater flow in bog peat is complex. Fine‐scale variations in K have the potential to influence patterns and rates of groundwater flow. However, for our data at least, it is heterogeneity and not anisotropy that has the greater influence on producing complex patterns of groundwater flow. We also demonstrate that patterns and rates of groundwater flow are simplified and reduced when measured K values are aggregated to create a more uniform distribution of K. For example, when measured K values are aggregated to produce isotropy and homogeneity, the rate of modelled seepage is reduced by 28%. We also show that when measured K values are used, the presence of a drainage ditch can increase seepage through a modelled cross‐section. Our work has implications for the accurate interpretation of hydraulic head data obtained from peat soils, and also the understanding of the effect of drainage ditches on patterns and rates of groundwater flow. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

11.
ABSTRACT

The groundwater contamination risk in future climates was investigated at three locations in Sweden. Solute transport penetration depths were simulated using the HYDRUS-1D model using historical data and an ensemble of climate projections including two global climate models (GCMs), three emission scenarios and one regional climate model. Most projections indicated increasing precipitation and evapotranspiration until mid-century with a further increase at end-century. Results showed both increasing and decreasing groundwater contamination risks depending on emission scenario and GCM. Generally, the groundwater contamination risk is likely to be unchanged until mid-century, but higher at the end of the century. Soil and site specific relationships between Δ(P – PET) (i.e. change in the difference between precipitation, P, and potential evapotranspiration, PET) and changes in solute transport depths were determined. Using this, changes in solute transport depths for other climate projections can be assessed.  相似文献   

12.
We present the first demonstration of hydraulic tomography (HT) to estimate the three-dimensional (3D) hydraulic conductivity (K) distribution of a fractured aquifer at high-resolution field scale (HRFS), including the fracture network and connectivity through it. We invert drawdown data collected from packer-isolated borehole intervals during 42 pumping tests in a wellfield at the former Naval Air Warfare Center, West Trenton, New Jersey, in the Newark Basin. Five additional tests were reserved for a quality check of HT results. We used an equivalent porous medium forward model and geostatistical inversion to estimate 3D K at high resolution (K blocks <1 m3), using no strict assumptions about K variability or fracture statistics. The resulting 3D K estimate ranges from approximately 0.1 (highest-K fractures) to approximately 10−13 m/s (unfractured mudstone). Important estimated features include: (1) a highly fractured zone (HFZ) consisting of a sequence of high-K bedding-plane fractures; (2) a low-K zone that disrupts the HFZ; (3) several secondary fractures of limited extent; and (4) regions of very low-K rock matrix. The 3D K estimate explains complex drawdown behavior observed in the field. Drawdown tracing and particle tracking simulations reveal a 3D fracture network within the estimated K distribution, and connectivity routes through the network. Model fit is best in the shallower part of the wellfield, with high density of observations and tests. The capabilities of HT demonstrated for 3D fractured aquifer characterization at HRFS may support improved in situ remediation for contaminant source zones, and applications in mining, repository assessment, or geotechnical engineering.  相似文献   

13.
Changes in Entrapped Gas Content and Hydraulic Conductivity with Pressure   总被引：1，自引：0，他引：1  
Water table fluctuations continuously introduce entrapped air bubbles into the otherwise saturated capillary fringe and groundwater zone, which reduces the effective (quasi‐saturated) hydraulic conductivity, Kquasi, thus impacting groundwater flow, aquifer recharge and solute and contaminant transport. These entrapped gases will be susceptible to compression or expansion with changes in water pressure, as would be expected with water table (and barometric pressure) fluctuations. Here we undertake laboratory experiments using sand‐packed columns to quantify the effect of water table changes of up to 250 cm on the entrapped gas content and the quasi‐saturated hydraulic conductivity, and discuss our ability to account for these mechanisms in ground water models. Initial entrapped air contents ranged between 0.080 and 0.158, with a corresponding Kquasi ranging between 2 and 6 times lower compared to the Ks value. The application of 250 cm of water pressure caused an 18% to 26% reduction in the entrapped air content, resulting in an increase in Kquasi by 1.16 to 1.57 times compared to its initial (0 cm water pressure) value. The change in entrapped air content measured at pressure step intervals of 50 cm, was essentially linear, and could be modeled according to the ideal gas law. Meanwhile, the changes in Kquasi with compression–expansion of the bubbles because of pressure changes could be adequately captured with several current hydraulic conductivity models.  相似文献   

14.
Abstract

Wetting front instability (fingered flow) accelerates solute transport through the unsaturated zone to the groundwater table. Whether fingers widen or dissipate close to the groundwater is unclear. Water flow in a two-dimensional artificial capillary fringe below a dry layer exhibiting fingered flow was investigated. The flow diverged strongly in the wet soil, suggesting that fingers dissipate. Expressions for the finger radius in dry and wet soil were combined and adapted to a soil hydraulic property parameterization popular in numerical modelling. The modified equation provided finger radii for soils in humid and arid climates. The fingers in the arid soil were excessively wide. The finger radii were used to model solute transport, assuming fingers dissipated in the subsoil. Modelling was cumbersome for the arid climate. One shower may often be insufficient to trigger fingering in arid regions with short, heavy showers. In soils with shallow groundwater, the diverging subsoil flow determines solute leaching.  相似文献   

15.
Travel-time statistics for non-reacting tracers in fractal and multifractal media are addressed through numerical simulations. The logarithm of hydraulic conductivity is modeled using fractional Brownian motion (fBm) and more recently developed multifractal model based on bounded fractional Levy motion (bfLm). These models have been shown previously to accurately reproduce statistical properties of large conductivity datasets. The ensemble-mean travel time increases nearly linearly with travel distance and the variance in the travel time increases nearly parabolically with travel distance. This is consistent with near-field analytical approximations developed for non-fractal media and suggests that these analytical results may have some degree of robustness to non-ideal features in the random-field models. The magnitudes of the travel-time moments are dependent on the system size. For fBm media, this size dependence can be explained using an effective variance that increases with increasing size of the flow system. However, the magnitudes of the travel-time moments are also sensitive to other non-ideal effects such as deviations from Gaussian behavior. This sensitivity illustrates the need for careful aquifer characterization and conditional numerical simulation in practical situations requiring accurate estimates of uncertainty in the plume position.  相似文献   

16.
Peat soils are heterogeneous, anisotropic porous media. Compared to mineral soils, there is still limited understanding of physical and solute transport properties of fen peat soils. In this study, we aimed to explore the effect of soil anisotropy on solute transport in degraded fen peat. Undisturbed soil cores, taken in vertical and horizontal direction, were collected from one drained and one restored fen peatland both in a comparable state of soil degradation. Saturated hydraulic conductivity (K s) and chemical properties of peat were determined for all soil cores. Miscible displacement experiments were conducted under saturated steady state conditions using potassium bromide as a conservative tracer. The results showed that (1) the K s in vertical direction (K sv) was significantly higher than that in horizontal direction (Ksh), indicating that K s of degraded fen peat behaves anisotropically; (2) pronounced preferential flow occurred in vertical direction with a higher immobile water fraction and a higher pore water velocity; (3) the 5% arrival time (a proxy for the strength of preferential flow) was affected by soil anisotropy as well as study site. A strong correlation was found between 5% arrival time and dispersivity, K s and mobile water fraction; (4) phosphate release was observed from drained peat only. The impact of soil heterogeneity on phosphate leaching was more pronounced than soil anisotropy. The soil core with the strongest preferential flow released the highest amount of phosphate. We conclude that soil anisotropy is crucial in peatland hydrology but additional research is required to fully understand anisotropy effects on solute transport.  相似文献   

17.
Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models.  相似文献   

18.
Distributed watershed models are beneficial tools for the assessment of management practices on runoff and water‐induced erosion. This paper evaluates, by application to an experimental watershed, two promising distributed watershed‐scale sediment models in detail: the Kinematic Runoff and Erosion (KINEROS‐2) model and the Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model. The physics behind each model are to some extent similar, though they have different watershed conceptualizations. KINEROS‐2 was calibrated using three rainfall events and validated over four separate rainfall events. Parameters estimated by this calibration process were adapted to GSSHA. With these parameters, GSSHA generated larger and retarded flow hydrographs. A 30% reduction in both plane and channel roughness in GSSHA along with the assumption of Green‐Ampt conductivity KG‐A = Ks, where Ks is the saturated conductivity, resulted in almost identical hydrographs. Sediment parameters not common in both models were calibrated independently of KINEROS‐2. A comparative discussion of simulation results is presented. Even though GSSHA's flow component slightly overperformed KINEROS‐2, the latter outperformed GSSHA in simulations for sediment transport. In spite of the fact that KINEROS‐2 is not geared toward continuous‐time simulations, simulations performed with both models over a 1 month period generated comparable results. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

19.
The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees.  相似文献   

20.
Fluid flow exerts a critical impact on the convection of thermal energy in geological media, whereas heat transport in turn affects fluid properties, including fluid dynamic viscosity and density. The interplay of flow and heat transport also affects solute transport. To unravel these complex coupled flow, heat, and solute transport processes, here, we present a theory for the idealized scale‐dependent Poiseuille flow model considering a constant temperature gradient (?T) along a single fracture, where fluid dynamic viscosity connects with temperature via an exponential function. The idealized scale‐dependent model is validated based on the solutions from direct numerical simulations. We find that the hydraulic conductivity (K) of the Poiseuille flow either increases or decreases with scales depending on ?T > 0°C/m or ?T < 0°C/m, respectively. Indeed, the degree of changes in K depends on the magnitude of ?T and fracture length. The scale‐dependent model provides an alternative explanation for the well‐known scale‐dependent transport problem, for example, the dispersion coefficient increases with travel distance when ?T > 0°C/m according to the Taylor dispersion theory, because K (or equivalently flux through fractures) scales with fracture length. The proposed theory unravels intertwined interactions between flow and transport processes, which might shed light on understanding many practical geophysical problems, for example, geothermal energy exploration.  相似文献   

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