Showing papers in "Water Resources Research in 1988"
TL;DR: In this paper, a method is presented for developing probability density functions for parameters of soil moisture relationships of capillary head [h(θ)] and hydraulic conductivity [K(α), which are required for the assessment of water flow and solute transport in unsaturated media.
Abstract: A method is presented for developing probability density functions for parameters of soil moisture relationships of capillary head [h(θ)] and hydraulic conductivity [K(θ)]. These soil moisture parameters are required for the assessment of water flow and solute transport in unsaturated media. The method employs a statistical multiple regression equation proposed in the literature for estimating [h(θ)] or [K(θ)] relationships using the soil saturated water content and the percentages of sand and clay. In the absence of known statistical distributions for either [h(θ)] or [K(θ)] relationships, the method facilitates modeling by providing variability estimates that can be used to examine the uncertainty associated with water flow or solute transport in unsaturated media.
2,050 citations
TL;DR: In this paper, a Lagrangian model for fractal heterogeneity is proposed, which exhibits a pattern (over a large range of scales) that is independent of the scale of observation and will possess a very large correlation scale.
Abstract: Stochastic transport theories rely on the assumptions that the principles of stationarity and ergodicity are satisfied. These assumptions imply that the pattern of heterogeneity can be viewed as being spatially periodic, thus yielding a finite correlation scale. We examine a type of heterogeneity which does not satisfy these principles: self-similar, or fractal heterogeneity, which exhibits a pattern (over a large range of scales) that is independent of the scale of observation and thus will possess a very large correlation scale. We review the basic concepts of fractal geometry and develop scaling relationships for fractal travel distance versus scale of observation. We then develop Lagrangian models for dispersion in a single fractal streamtube and for a set (or bundle) of fractal streamtubes. The results are compared to classical one-dimensional advection-dispersion theory, existing fractal and stochastic theories, and to a summary of field-measured dispersivity data. For the single streamtube model, field-measured dispersivity is proportional to the straight-line travel distance raised to a power of D - 1, where D is the fractal dimension. For the set of fractal streamtubes, field-measured dispersivity is proportional to the straight-line travel distance raised to a power of 2D - 1. The analytical expressions are verified and elaborated by a fractal random walk computer model. The computer model is used to show the self-similar nature of heterogeneity that is independent of the scale of observation. Comparisons of the field dispersivity data with our fractal models indicate that most tracer tests have been performed in media that approximate a set of fractal streamtubes.
433 citations
TL;DR: In this paper, it was shown that the network as a whole, although composed of nearly linear members, is practically space filling with fractal dimension near 2, and the empirical results are backed by a theoretical analysis based on long-standing hydrologic concepts describing the geometric similarity of river networks.
Abstract: Ever since Mandelbrot (1975, 1983) coined the term, there has been speculation that river networks are fractals. Here we report analyses done on river networks to determine their fractal structure. We find that the network as a whole, although composed of nearly linear members, is practically space filling with fractal dimension near 2. The empirical results are backed by a theoretical analysis based on long-standing hydrologic concepts describing the geometric similarity of river networks. These results advance our understanding of the geometry and composition of river networks.
431 citations
TL;DR: In this article, a generalized radial flow model for hydraulic test data is presented, which considers the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically.
Abstract: Models commonly used for the analysis of hydraulic test data are generalized by regarding the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically. Mathematical solutions for this generalized radial flow model are derived for the standard test conditions: constant rate, constant head, and slug tests. Solutions for the less common, sinusoidal test are contained within the general solutions given. Well bore storage and skin are included and the extension to dual-porosity media outlined. The model is presented as a model of fractured media, for which it is most likely to find application because of the problem of choosing the appropriate flow dimension.
391 citations
TL;DR: In this article, the authors examined the physics governing the emplacement and movement of a separate phase in porous media, the role of sorption, and the conditions necessary to mobilize a separatephase.
Abstract: Groundwater contamination by nonaqueous liquids such as organic solvents and petroleum hydrocarbons frequently occurs as a result of surface spills, tank leaks, and improper disposal practices. This first of two papers examines the physics governing the emplacement and movement of a separate phase in porous media, the role of sorption, and the conditions necessary to mobilize a separate phase. The movement of the separate phase is controlled by capillary forces, and ganglia displacement by groundwater is not possible under reasonable hydraulic gradients. In addition, because of mass transfer limitations in liquid phase dissolution, groundwater extraction at contaminated sites is shown to be ineffective in removing the nonaqueous contaminant within a reasonable time frame. Therefore other means of mobilizing the trapped second phase are needed, steam displacement is proposed and steam front propagation through contaminated porous media is evaluated. The results of laboratory experiments supporting some of these analytical results are presented in the second paper (Hunt et al., this issue).
387 citations
TL;DR: In this article, the flow and solute transport through a single rough-surfaced fracture were carried out using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length.
Abstract: Calculations for the flow and solute transport through a single rough-surfaced fracture were carried out. The fracture plane was discretized into a square mesh to which variable apertures were assigned. The spatially varying apertures of each single fracture were generated using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length. Constant head boundary conditions were assumed for the flow in the x direction of a single fracture with no flow boundaries in the y direction. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Our calculations showed that fluid flow occurs predominantly in a few preferred paths. Hence, the large range of apertures in the single fracture gives rise to flow channeling. The solute transport was calculated using a particle tracking method. Both the spatial and time variations of tracer breakthrough results are presented. The spatial variation of tracer transport between a line of injection points and a line of observation points are displayed in contour plots which we labeled “transfer matrix.” Our results indicate that such plots can give information on the spatial correlation length of the heterogeneity in the fracture. The tracer breakthrough curve obtained from a line of point measurements is shown to be controlled by the aperture density distribution and is insensitive to statistical realization and spatial correlation length. These results suggest the importance of making line measurements in the laboratory and the field. Sensitivity of our results on parameter variations was also investigated.
370 citations
TL;DR: In this article, three different models were considered: those of van Genuchten (VG) and Brooks and Corey (BC) model, and the exponential model of Gardner for the hydraulicconductivity-soil-water-pressure relationships, coupled with a new expression for the soil-water content-soIL-water pressure relationship (GR model).
Abstract: Parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties. One of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties. Three different models were considered: those of van Genuchten (VG) and Brooks and Corey (BC) model, and the exponential model of Gardner for the hydraulic-conductivity-soil-water-pressure relationships, coupled with a new expression for the soil-water-content-soil-water-pressure relationship (GR model). For a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of −15,000 cm H2O, using the parameter estimation procedure of Kool et al. (1985a) and data from two soils: a hypothetical sandy loam soil (assumed to be described by the VG model) and a silt loam soil. Model validation tests were performed, and the most appropriate model was selected from the candidate models by discrimination tests using the Akaike Information Criterion (AIC). In the case of the hypothetical sandy loam, the VG model was found to be the most accurate and most consistent with the data. The performance of both the BC and the GR models (in terms of the AIC) was less good but very similar to each other. In the case of the silt loam soil, the VG model with additional parameter m, which accounts for the correlation between pores and for the flow path tortuosity (m=2.02) rather than a constant m=0.5, was found to be most accurate and most consistent with the data. The performance of the BC and the GR models was similar when m was considered as an unknown parameter instead of a constant.
357 citations
TL;DR: In this paper, the expected second-order moments of a solute body transported by groundwater are derived for flow through heterogeneous formations of a stationary random anisotropic structure based on a general formulation.
Abstract: The expected values of the spatial second-order moments of a solute body transported by groundwater are derived for flow through heterogeneous formations of a stationary random anisotropic structure They are based on a general formulation, which reduces to most existing results in the literature as particular cases Detailed results are given for the spatial variance as a function of time in the case of axisymmetric anisotropy, average flow parallel to the plane of isotropy, first-order approximation in the log conductivity variance sigma/sub Y//sup 2/, and high Peclet numbers These results fill the gap existing between the studies of Dagan (1982, 1984), on one hand, and those of Gelhar and Axness (1983) and Neuman et al (1987), on the other A preliminary investigation of the higher-order effects in sigma/sub Y//sup 2/ suggests that the use of the first-order approximations is warranted, at present, only for sigma/sub Y//sup 2/ << 1 The impact of the errors of estimation of the parameters on which transport depends is briefly analyzed
352 citations
TL;DR: In this paper, analytical solutions for a nonlinear diffusion-convection model describing constant rate rainfall infiltration in uniform soils and other porous materials are presented for a Darcy-Buckham approach to unsaturated water flow and assume simple functional forms for the soil water diffusivity D(θ) and hydraulic conductivity K(δ) which depend on a single free parameter C and readily measured soil hydraulic properties.
Abstract: Analytic solutions are presented for a nonlinear diffusion-convection model describing constant rate rainfall infiltration in uniform soils and other porous materials. The model is based on the Darcy-Buckingham approach to unsaturated water flow and assumes simple functional forms for the soil water diffusivity D(θ) and hydraulic conductivity K(θ) which depend on a single free parameter C and readily measured soil hydraulic properties. These D(θ) and K(θ) yield physically reasonable analytic moisture characteristics. The relation between this model and other models which give analytic solutions is explored. As C→ ∞, the model reduces to the weakly nonlinear Burgers' equation, which has been applied in certain field situations. At the other end of the range as C→1, the model approaches a Green-Ampt-like model. A wide range of realistic soil hydraulic properties is encompassed by varying the C parameter. The general features of the analytic solutions are illustrated for selected C values. Gradual and steep wetting profiles develop during rainfall, aspects seen in the laboratory and field. In addition, the time-dependent surface water content and surface water pressure potential are presented explicitly. A simple traveling wave approximation is given which agrees closely with the exact solution at comparatively early infiltration times.
296 citations
TL;DR: In this article, the authors extend the work of Gilliom and Helsel (1986) on procedures for estimating descriptive statistics of water quality data that contain "less than" observations and investigate the performance of estimators for data that have multiple detection limits.
Abstract: This paper extends the work of Gilliom and Helsel (1986) on procedures for estimating descriptive statistics of water quality data that contain “less than” observations. Previously, procedures were evaluated when only one detection limit was present. Here we investigate the performance of estimators for data that have multiple detection limits. Probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use. Therefore simple substitution procedures (e.g., substitution of the detection limit) should be avoided. Probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown. When utilized correctly, less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them.
296 citations
TL;DR: The concept of time stability as defined by Vachaud et al. (1985) is expanded to include general linear transformations in time and to account for the occurrence of spatial scale dependency as discussed by the authors.
Abstract: The concept of time stability as defined by Vachaud et al. (1985) is expanded to include general linear transformations in time and to account for the occurrence of spatial scale dependency. Time stability is described as the temporal persistence of a spatial pattern and is evaluated using correlation analysis of successive measurement dates. Spatial coherency analysis is suggested as a method for examining the temporal persistence of a spatial pattern as a function of spatial scale. Spatial coherency analysis was used to examine the temporal persistence of soil water storage (0–1.7 m) measured every 10 m in a 720-m-long transect for drying and recharge events. Soil water recharge altered the spatial pattern of water storage at small scales which was significantly related to surface (topographic) curvature. Drying did not alter the spatial pattern of soil water storage. The study supports the concept that soil water storage at a point is the product of hydrologic processes operating at different spatial scales. The analysis can be used to relate the spatial scale of processes to independent factors.
TL;DR: In this article, the simultaneous measurement of water content and electrical conductivity of soils and KCl solutions was achieved using time domain reflectometry (TDR) using Coaxial transmission lines varying in length from 90 to 300 mm.
Abstract: The simultaneous measurement of water content and electrical conductivity of soils and KCl solutions was achieved using time domain reflectometry (TDR). Coaxial transmission lines varying in length from 90 to 300 mm contained either KCl solutions or soil of varied water and salt content. The water content of soil or dielectric constant of the water solutions was determined from the travel time. The measured dielectric constant of KCl solutions was unchanged from that of pure water (81) at those concentrations where there was sufficient reflected signal for measurement. Two analyses were used for determination of electrical conductivity, one based on signal attenuation after one “round-trip” and the second based on a thin sample approximation for the signal reflection and attenuation. Reference measurements of conductivity were made on the same samples using low-frequency conductance bridge measurements. These analyses of the TDR traces showed that for water solution both the thin sample analysis and the analysis after a signal had traversed one round-trip yielded conductivity in agreement with bridge conductivity values. This indicated that the imaginary part of the complex dielectric constant was negligible. For soils the thin sample analysis was in general agreement with the bridge measurements. From the analysis of signal after one round-trip in soils there was indication that the imaginary part of the dielectric constant should not be assumed negligible. Further investigation of the frequency dependence of the dielectric constant and attenuation will be required to identify the relative contributions of the real and imaginary parts of the dielectric constant to measurement by TDR. The effect of impedance-matching transformers on conductivity measurements in the field has yet to be ascertained.
TL;DR: In this paper, the inverse problem of determining unsaturated soil hydraulic properties from one-dimensional, transient infiltration and redistribution events is analyzed using an efficient Levenberg-Marquardt algorithm.
Abstract: The inverse problem of determining unsaturated soil hydraulic properties from one-dimensional, transient infiltration and redistribution events is analyzed. Hydraulic properties are assumed to be described by an extension of van Genuchten's (1980) model which allows for hysteresis in the retention function and air entrapment. Unknown parameters in the model are estimated from observed water contents and heads during transient flow by numerical inversion of the unsaturated flow equation. The inverse problem is formulated as a weighted least squares problem and solved using an efficient Levenberg-Marquardt algorithm. The flow event consists of ponded infiltration followed by gravity drainage with evaporation at the soil surface. Sensitivity analyses indicate that observations during ponded infiltration should be made near the position of the wetting front. The location of observation points during the drying stage is less critical than during the infiltration stage, but for the relatively high imposed evaporative flux sensitivity of pressure head is highest near the soil surface. Large differences in sensitivity are observed among the various model parameters. Unknown evaporative fluxes are approximated in the inverse solution as an equivalent first-type boundary condition requiring only periodic measurements of surface water content during the drying stage. Little error is incurred provided accurate measurements are possible. Corruption of input data with random error is shown to have a larger effect on the predicted conductivity function than on the retention function and more effect on the wetting branch of the hysteretic retention function than on the drying. When measurements are subject to error and the assumed parametric model for water retention and conductivity relations is not exact, it may no longer be possible to detect hysteresis in the retention function.
TL;DR: In this article, a critical literature review on the different soil solution samplers is given, and the differences among the various soil solution sampling techniques and their relative advantages and limitations are discussed.
Abstract: Soil interstitial waters are an extremely important facet of many environmental studies. The biogeochemical cycles of important nutrients, metal migration across the landscape, and pollutant movement to groundwater are highly affected by the water flow characteristics in soils and sediments. The purpose of this review is to evaluate the various soil solution sampling techniques. There is no single device that will perfectly sample soil solution in all conditions encountered in the field; hence a critical literature review on the different soil solution samplers is given. The differences among the various soil solution samplers and their relative advantages and limitations are discussed. The problems involved in using these samplers are assessed and plausible solutions are presented.
TL;DR: In this article, the authors used Monte Carlo simulation to assess the effect of realistically specified intersite dependence on the regional probability weighted moment algorithm, a robust and efficient procedure for regional flood frequency analysis.
Abstract: Regional flood frequency analysis usually assumes that flood records from different sites are statistically independent. This assumption is unlikely to be valid in practice, so it is important to know how intersite dependence affects flood quantile estimates obtained by regional analysis. We use Monte Carlo simulation to assess the effect of realistically specified intersite dependence on the regional probability weighted moment algorithm, a robust and efficient procedure for regional flood frequency analysis. Our principal conclusions are as follows. Any bias in flood quantile estimates is unchanged by the presence of intersite dependence. The accuracy of flood quantile estimates decreases when intersite dependence is present, but this effect is less important for practical applications than the bias in flood quantile estimates due to heterogeneity (inequality of the flood frequency distributions in the region). Even when both heterogeneity and intersite dependence are present and the form of the flood frequency distribution is misspecified, regional flood frequency analysis is more accurate than at-site analysis.
TL;DR: In this paper, a model to simulate organic carbon biodegradation by facultative bacteria in saturated porous media using oxygen-and/or nitrate-based respiration is developed, which is highly resistant to numerical dispersion and oscillation when applied to the advection-dispersion equation, even for large Peclet numbers.
Abstract: A model to simulate organic carbon biodegradation by facultative bacteria in saturated porous media using oxygen- and/or nitrate-based respiration is developed. Basic assumptions incorporated into the model concept include a simulated particle-bound microbial population comprised of heterotrophic, facultative bacteria in which metabolism is controlled by lack of either an organic carbon-electron donor source (substrate), electron acceptor (O/sub 2/ and/or NO/sub 3//sup -/), or mineral nutrient (NH/sub 4//sup +/), or all three simultaneously. A system of nine coupled nonlinear equations is developed that describe the processes of transport, degradation, and microbial growth and decay. The solution technique is highly resistant to numerical dispersion and oscillation when applied to the advection-dispersion equation, even for large Peclet numbers (100). Microbial utilization of materials is assumed to occur by intrapore scale diffusion of materials across a diffusion boundary layer separating the particle-bound microcolonies of bacteria from the pore fluid. Denitrifying enzyme inhibition is modeled as a function of the oxygen concentration associated with the biomass. Simulations of oxygen-based, nitrate-based, and multiple-electron acceptor respiration are presented for a hypothetical experiment using kinetic parameter value estimates available from the literature.
TL;DR: In this article, two nonlinear optimization formulations are proposed which model the design process for the location and pump rates of injection and extraction wells in an aquifer cleanup system, and derive a general relationship for computing the derivatives of an arbitrary function of the simulation outputs with respect to model inputs.
Abstract: The problem of designing contaminated groundwater remediation systems using hydraulic control is addressed. Two nonlinear optimization formulations are proposed which model the design process for the location and pump rates of injection and extraction wells in an aquifer cleanup system. The formulations are designed to find a pumping system which (1) removes the most contaminant over a fixed time period and (2) reduces contaminant concentration to specified levels by the end of a fixed time period at least cost. The formulations employ a two-dimensional Galerkin finite element simulation model of steady state groundwater flow and transient convective-dispersive transport. To make the optimization problems computationally tractable sensitivity theory is used to derive a general relationship for computing the derivatives of an arbitrary function of the simulation outputs with respect to model inputs. This relationship is then applied to the convective-dispersive transport equation.
TL;DR: In this paper, a simulation model incorporating a groundwater flow model and sediment transport relationships closely replicates the observed evolution of sapping erosion in a two-dimensional tank filled with noncohesive sand subjected to lateral groundwater flow.
Abstract: Surface grains of noncohesive sediment eroded by emerging groundwater are acted upon by three forces, the tractive force of the cumulative surface flow contributed by upslope seepage, the local seepage force, and gravity. The balance of the force moments determines the mode and rate of transport. Seepage forces are strong in a narrow “sapping zone” at the upstream end of the emerging flow, where erosion occurs by mass movement and the surface gradient is determined by the balance of the seepage and gravity moments. Most of the erosion occurs in this zone, and the resultant backcutting triggers intermittent failure of overlying slopes in a “undermining zone” maintained at the angle of repose of the dry or damp sediment. In the “fluvial zone” downstream from the sapping zone the seepage force is small compared to the tractive force, and transport occurs by normal fluvial traction. The overall rate of sapping erosion in noncohesive sediments is determined by the capacity of fluvial transport to remove sediment eroded in the sapping zone. Prediction of sapping rates is complicated by the interaction between the geometry of the fluvial and sapping zones and the quantity and spatial distribution of seepage. A simulation model incorporating a groundwater flow model and sediment transport relationships closely replicates the observed evolution of sapping erosion in a two-dimensional tank filled with noncohesive sand subjected to lateral groundwater flow.
TL;DR: In this paper, a macroscopic approach and a microscopic approach are used to evaluate water movement in a fractured rock mass, assuming that the pressure head in the fractures and the matrix are identical in a plane perpendicular to flow.
Abstract: The movement of fluids in a fractured, porous medium has been the subject of considerable study. This paper presents a continuum model that may be used to evaluate the isothermal movement of water in an unsaturated, fractured, porous medium under slowly changing conditions. This continuum model was developed for use in evaluating the unsaturated zone at the Yucca Mountain site as a potential repository for high-level nuclear waste. Thus its development has been influenced by the conditions thought to be present at Yucca Mountain. A macroscopic approach and a microscopic approach are used to develop a continuum model to evaluate water movement in a fractured rock mass. Both approaches assume that the pressure head in the fractures and the matrix are identical in a plane perpendicular to flow. Both approaches lead to a single-flow equation for a fractured rock mass. The two approaches are used to calculate unsaturated hydrologic properties, i.e., relative permeability and saturation as a function of pressure head, for several types of tuff underlying Yucca Mountain, using the best available hydrologic data for the matrix and the fractures. Rock mass properties calculated by both approaches are similar.
TL;DR: In this paper, the authors used cross-spectral estimation to fit the response to atmospheric loading of three water wells to the theoretical curves in order to yield estimates of three dimensionless parameters.
Abstract: The water level in a well that taps a partially confined aquifer is often sensitive to atmospheric loading. The magnitude and character of this response is partly governed by the well radius, the lateral hydraulic diffusivity of the aquifer, the thickness and vertical pneumatic diffusivity of the unsaturated zone, and the thickness and vertical hydraulic diffusivity of the saturated zone overlying the aquifer. These key elements can be combined into five dimensionless parameters that partly govern the phase and attenuation of the response. In many cases, the response of a well to atmospheric loading can be broken up into a high-, intermediate-, and low-frequency response. The high-frequency response is governed largely by the well radius and lateral diffusivity of the aquifer. The intermediate-frequency response is governed by the loading efficiency of the aquifer. The low-frequency response is governed by the vertical pneumatic diffusivity and thickness of the unsaturated zone and the vertical hydraulic diffusivity and thickness of the saturated material above the aquifer. Cross-spectral estimation is used to fit the response to atmospheric loading of three water wells to the theoretical curves in order to yield estimates of three of the key dimensionless parameters. These estimates then are used to make estimates or place bounds on the vertical pneumatic diffusivity of the unsaturated zone, the lateral permeability of the aquifer, and the composite vertical hydraulic diffusivity of the overlying saturated materials.
TL;DR: In this paper, the authors investigated the longitudinal advective solute movement in heterogeneous porous media by considering the solute arrival time at a plane perpendicular to the mean fluid velocity, defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field.
Abstract: Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux-averaged concentration is specified by introducing the moments of the arrival time into a probability density function for the arrival time. The quadratic dependence of the arrival time variance on position in the vicinity of an injection point is indicative of a nondiffusive process. For the assumed spatial correlation of the hydraulic conductivity, the variance of the arrival time asymptotically approaches a linear dependence on the position from the injection point similar to a diffusion process. The impact of assuming solute movement to be a diffusive process from the onset of the solute injection causes erroneous estimates of flux-averaged concentrations at distances from the injection point that are of the order of the correlation length of the hydraulic conductivity. The arrival time analysis and the particle position analysis given in Dagan (1982, 1984) are complementary interpretations of advective solute movement that yield different definitions of the solute concentration; the position analysis intrinsically defines the resident or volume-averaged concentration, while the flux-averaged concentration is defined from the arrival time analysis. The temporal variation of the resident and flux-averaged concentration are similar at a given position for small values of the variance of the hydraulic conductivity, or at distances from the solute injection point that are large relative to correlation length of the hydraulic conductivity.
TL;DR: In this paper, the authors examined some conditions under which contaminant transport in fractured porous rocks can be described by an equivalent porous medium (single continuum) model and showed that within the range of considered parameter values, and except for the region close to the source, a single continuum model is sufficient for modelling the movement of contaminants.
Abstract: This work examines some conditions under which contaminant transport in fractured porous rocks can be described by an equivalent porous medium (single continuum) model. For this purpose, a two-dimensional mathematical and numerical model for flow and contaminant transport was developed. The model allows for contaminant transport by advection, diffusion, and dispersion in both fractures and porous blocks. Concentration distributions were calculated for different flow conditions and medium properties. The resulting S-shaped breakthrough curves, characteristic of ordinary porous media, indicated the possibility of regarding the fractured porous medium as a single (equivalent) continuum. The results were compared to an existing analytical solution for contaminant movement in ordinary porous media. Analysis showed that within the range of considered parameter values, and except for the region close to the source, a single continuum model is sufficient for modelling the movement of contaminants. In such cases, application of the equivalent porous medium model is an actual field situation requires knowledge of the “equivalent” porosity and the equivalent coefficient of dispersion appearing in the governing transport equation. In practice, these coefficients must be determined by analysis of breakthrough curves obtained from field tests.
TL;DR: In this article, the governing equations for the flow of salt solution with significant density variations through a porous medium are discussed for the finite element groundwater code NAMMU and applied to test case 5 of level 1 of the international HYDROCOIN project.
Abstract: The governing equations are discussed for the flow of salt solution with significant density variations through a porous medium. Equations for mass conservation, salt conservation, and momentum conservation are formulated in terms of the mass fraction weighted average velocity and the mass fraction of concentrated salt solution, and the underlying approximations are considered. These equations are incorporated in the finite element groundwater code NAMMU and applied to test case 5 of level 1 of the international HYDROCOIN project. This test case proposed to model the groundwater flow over a hypothetical salt dome. The nonlinearities arising from the density variation and from a velocity-dependent dispersion tensor made the problem very hard: we had to use special techniques including mixed interpolation finite elements and parameter stepping. Starting from a related problem involving a large diffusivity we obtained a series of solutions at successively smaller values of dispersion. Our final solution is to a physically realistic problem very similar to that specified. We draw general conclusions relevant to modeling these flows and have built confidence in our numerical code.
TL;DR: Moreno et al. as discussed by the authors proposed a theoretical approach to interpret flow and transport through a two- or three-dimensional fractured medium in terms of a system of statistically equivalent one-dimensional channels.
Abstract: Field evidences indicate that the bulk of water flow in fractured crystalline rock often occurs in preferred flow paths, or channels. A theoretical approach was proposed by Tsang and Tsang (1987) to interpret flow and transport through a two- or three-dimensional fractured medium in terms of a system of statistically equivalent one-dimensional channels. The apertures along the flow channels are characterized by an aperture density distribution and a spatial correlation length. In this paper, we present detailed studies on the properties of these channels: channel volume, channel residence time, and channel volumetric flow rate. We also calculated the dispersion in tracer transport through groups of statistically equivalent channels. The one-dimensional channel model is then applied to breakthrough data from transport in a two-dimensional single fracture (Moreno et al., this issue) in both a forward and an inverse calculation. We show from the inverse calculation that the aperture density distribution parameters of the one-dimensional flow channels may be estimated from the dispersion and mean residence time of the tracer data. The tracer breakthrough curve should be obtained from line measurements with tracer sampled over several spatial correlation lengths of the variable apertures. This is in contrast to conventional point tracer measurements which is expected to fluctuate with statistical realization and may not yield pertinent information on the flow system. Based on the insight gained in such calculations, design, and analysis of field measurements are discussed. Both tracer breakthrough measurements and flow rate measurements are needed to obtain the aperture parameters of the flow systems. The permeability measurements alone are controlled by the small constrictions along the flow paths and therefore do not yield a good measure of the mean aperture in channel.
TL;DR: In this article, a general definition of initial motion in mixed-size sediment is presented that allows the characteristic differences between the results to be explained in terms of sampling and scaling considerations inherent in the mixed size initial motion problem.
Abstract: Two methods are commonly used to estimate the critical shear stress of individual fractions in mixed-size sediment, one using the largest grain displaced, the other using the shear stress that produces a small value of transport rate for each fraction. The initial-motion results produced by the two methods are typically different: largest-grain critical shear stresses vary with roughly the square root of grain size, and reference transport critical shear stresses show little variation with grain size. Comparison of the two methods is seldom possible because both methods can rarely be applied to the same data. The one case known for which both methods can be used suggests that the typical differences in initial-motion results reflect more methodological influence than real differences in the initial motion of different sediments. Although the two classes of methods may not be directly compared, a general definition of initial-motion in mixed-size sediment is presented that allows the characteristic differences between the results to be explained in terms of sampling and scaling considerations inherent in the mixed-size initial-motion problem. The initial-motion criterion defined also provides a rational basis for collecting comparable and reproducible data using the two classes of method.
TL;DR: In this article, two water recirculating sediment feed flumes were used: one with a 6 m long and 0.15 m wide channel and other with an 11 m long channel with widths of 0.74 m and0.53 m.
Abstract: Flume experiments were conducted to investigate the mechanisms of transport of a gravel-sand mixture by shallow unidirectional flows. Two water recirculating sediment feed flumes were used: one with a 6 m long and 0.15 m wide channel and other with an 11 m long channel with widths of 0.74 m and 0.53 m. The sediment, poorly sorted gravel with a mean size of 3 mm, was fed at the upstream end of the channel at steady rates from 0.03 kg s−1 m−1 to 1.0 kg s−1 m−1. Sediment transport rate out of the channel varied in all runs, at approximate periods of 3 min in the runs with high transport rates to 14 min in the runs with low transport rates. The runs with low transport rates also showed fluctuations in total transport rate at periods of about 25 min. Transport rates of each size fraction varied with time in a distinctive pattern in all runs. The time variations were caused by the migration of very long and low bed load sheets in the runs with low to moderate transport rates and dunelike bed forms in the run with the highest transport rate. The bed surface in all runs was coarser in size than the original sediment mix except that with the highest transport rate (run H5) in which the size distribution was nearly the same as the original.
TL;DR: In this article, the critical shear stress for incipient motion of the individual size fractions within these sediments was estimated as that shear stressed that produced a small dimensionless transport rate.
Abstract: Transport rates of five sediments were measured in a laboratory flume. Three of these sediments had the same mean size, the same size distribution shape, and different values of grain size distribution standard deviation. The critical shear stress for incipient motion of the individual size fractions within these sediments was estimated as that shear stress that produced a small dimensionless transport rate. The sorting of the sediment mixture had little effect on the critical shear stress of individual fractions, once the median size (D50) of the mixture and a fraction's relative size (Di/D50) are accounted for. Our data, combined with previously published data, show a remarkably consistent relation between the critical shear stress of individual fractions and the fraction's relative grain size, despite a broad variation in the available data of mixture sorting, grain size distribution shape, mean grain size, and grain shape. All fractions in a size mixture begin moving at close to the same value of bed shear stress during steady state transport conditions. This result is apparently true for transport systems where the transport rates of individual fractions are determined solely by the flow and bed sediment (recirculating systems), as well as for systems where the fractional transport rates are imposed on the system (feed systems). This equivalence in initial-motion results is important because natural transporting systems often show attributes of both types of behavior in an unknown combination.
TL;DR: In this article, the authors derived exact analytical expressions for the Y, H moments, which account for the presence of a given head boundary in a half plane, and examined the effects of boundaries on the semivariogram of H and on the Y-H cross covariance.
Abstract: The spatial variability of log transmissivity Y and head H in aquifers assumes a major role in determining the solutions of the direct flow problem, as well as of the inverse problem. Investigation of the joint Y, H variability has been cast in the past in numerical and analytic frames. Analytic solutions for the Y, H statistical moments in two dimensions assumed the flow to occur in an unbounded domain. In this study, exact analytical expressions for the Y, H moments are derived, which account for the presence of a given head boundary in a half plane. This result is achieved by a first-order approximation and for an exponential Y covariance. The result offers the opportunity to examine the effects of boundaries on the semivariogram of H and on the Y, H cross covariance. The assumption of unbounded domain is examined and shown to be accurate at distances larger than two Y integral scales from the boundary. By using conditional probabilities, a general and simple method to estimate the moments close to the boundary is presented. It requires the knowledge of the moments of Y and H in the unbounded domain only. The method is compared with the exact analytic solution, showing excellent results.
TL;DR: In this article, the relationship between base flow recession characteristics in steep watersheds and geomorphologic and soil parameters is investigated by means of a hydraulic approach applied to a simple conceptual model for a hillslope.
Abstract: The relationship between base flow recession characteristics in steep watersheds and geomorphologic and soil parameters is investigated. The formulation for the groundwater outflow was obtained by means of a hydraulic approach applied to a simple conceptual model for a hillslope. Long-term flow data of 19 representative basins in the Allegheny Mountain section of the Appalachian Plateaus were analyzed on the basis of this formulation. Results showed that the reaction factor, which is a time scale of base flow recession, is dependent on the mean land slope, the drainage density, and the ratio (K/f) of the hydraulic conductivity and the drainable porosity. On account mainly of the nonuniform distribution of the physical characteristics within a basin, the reaction factor for a given watershed is somewhat variable with time, but the adoption of a constant value is useful to represent average conditions for a recession period. Analysis of the (K/f) dependency showed that macropores and other structural features may greatly affect the watershed base flow. Evaporation from groundwater appears to constitute only a minor portion of overall basin evaporation.
TL;DR: In this article, a method for locating wells in a monitoring network under conditions of uncertainty is presented, which couples the use of a simulation model of contaminant transport and a facility location model.
Abstract: A method is presented for locating wells in a monitoring network under conditions of uncertainty. The method couples the use of a simulation model of contaminant transport and a facility location model. The Monte Carlo technique is used with the simulation model to translate uncertainty in the simulation model parameters into uncertainty in the contaminant concentration distribution. The simulation model determines which well locations would detect a given realization of a contaminant plume with a concentration above a specified limit. The facility location model is then used to select a fixed number of well locations so that a maximum number of such plume realizations are detected. The selected well network maximizes the probability of detection. The method is applied to an example problem. Although the technique is computationally intensive, the results indicate that practical problems are tractable.