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At least 1,441 records · Page 80Linked to original sources

Groundwater transport of strontium 90 in a glacial outwash environment

As part of the investigation of groundwater contamination at a uranium-scrap recovery plant at Wood River Junction, Rhode Island, laboratory experiments led to the development of a model for predicting the transport of strontium 90 in glacial outwash sediments based on an approximate mechanism for ion exchange. The multicomponent system was simplified to two components by regarding all exchangeable cations other than strontium 90 as a single component. The binary ion-exchange parameter was a function of the variable, total ion concentration. A one-dimensional solute transport model was formulated to evaluate the time necessary for natural groundwater flow to remove the strontium 90 contamination plume from the groundwater system to the Pawcatuck River. The finite difference transport equations were solved sequentially for total ion concentrations, then strontium 90 concentrations. Clay-free quartz and feldspar sands at the study site have little potential for strontium 90 sorption, and high calcium, magnesium, and sodium concentrations compete for the few ion exchange sites. As the total ion concentration plume moves out of the system, ion exchange of strontium 90 increases, reducing the strontium 90 concentration in the groundwater. Cleanout times predicted using the binary ion exchange mechanism were about two thirds of those predicted using a constant distribution coefficient. It is suggested that this type of model can simulate solute transport more realistically in many groundwater systems where the total ion concentration is not constant.

Rhode Island↗

Regression approximations for transport model constraint sets in combined aquifer simulation-optimization studies

Problems involving the combined use of contaminant transport models and nonlinear optimization schemes can be very expensive to solve. This paper explores the use of transport models with ordinary regression and regression on ranks to develop approximate response functions of concentrations at critical locations as a function of pumping and recharge at decision wells. These response functions combined with other constraints can often be solved very easily and may suggest reasonable starting points for combined simulation-management modeling or even relatively efficient operating schemes in themselves.

Water Resources Research↗

Stochastic analysis of three-dimensional flow in a bounded domain

A commonly accepted first-order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of Poisson's equation. This form allows for the advantageous use of Green's functions to solve for the random output (hydraulic heads) in terms of a convolution over the random input (the logarithm of hydraulic conductivity). A solution for steady state three- dimensional flow in an aquifer bounded above and below is presented; consideration of these boundaries is made possible by use of Green's functions to solve Poisson's equation. Within the bounded domain the medium hydraulic conductivity is assumed to be a second-order stationary random process as represented by a simple three-dimensional covariance function. Upper and lower boundaries are taken to be no-flow boundaries; the mean flow vector lies entirely in the horizontal dimensions. The resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions. Comparisons are made with existing infinite domain solutions.

Water Resources Research↗

A comparison of several methods for the solution of the inverse problem in two-dimensional steady state groundwater flow modeling

Two geostatistical approaches for the estimation of hydraulic conductivity and hydraulic head from hydraulic conductivity and hydraulic head measurements are developed for two-dimensional steady flow with sinks. For both approaches the field of the logarithm of hydraulic conductivity (log-conductivity) is represented as a random field with mean θ 1 +θ 2 x +θ 3 y where x and y denote Cartesian coordinates, variance σ 2 , and covariance σ 2 , exp (−α R ), σ 2 , exp (−α R 2 ), or, σ 2 Δ R r where α, Δ, and r are constants and R is separation distance. The first approach uses linearization of the discretized flow equations to allow the construction of the joint covariance matrix of the hydraulic head and log-conductivity measurements as functions of the parameters θ, θ 2 , θ 3 , σ 2 , and α or Δ. It then uses maximum likelihood estimation to obtain these parameters and also a parameter associated with log-conductivity measurement error. Having found values for the parameters, it then uses kriging to form predictors for log-conductivity and hydraulic head from measured values of hydraulic conductivity and hydraulic head. The second approach uses kriging to form a parameter-dependent predictor for log-conductivity from measured hydraulic conductivity, and then uses this predicted log-conductivity placed into the discretized flow equations to compute hydraulic head. The parameters are determined by the minimization of the sum of the squares of the difference between the measured and computed hydraulic heads. A third approach simply allows the hydraulic conductivity field to be a step function with a different value for hydraulic conductivity assigned to each of several chosen regions in the two-dimensional aquifer. The assigned hydraulic conductivities are determined by the minimization of the sum of the squares of the difference between the measured and computed hydraulic heads. The three approaches are tested for hydraulic head prediction accuracy on two generated test problems, one of which is statistically generated, and also on a field problem. The third approach, despite its simplicity, performs as well or better than the other approaches.

Water Resources Research↗

Simulation of fluid flow and energy transport processes associated with high-level radioactive waste disposal in unsaturated alluvium

Many parts of the Great Basin have thick zones of unsaturated alluvium which might be suitable for disposing of high-level radioactive wastes. A mathematical model accounting for the coupled transport of energy, water (vapor and liquid), and dry air was used to analyze one-dimensional, vertical transport above and below an areally extensive repository. Numerical simulations were conducted for a hypothetical repository containing spent nuclear fuel and located 100 m below land surface. Initial steady state downward water fluxes of zero (hydrostatic) and 0.0003 m yr −1 were considered in an attempt to bracket the likely range in natural water flux. Predicted temperatures within the repository peaked after approximately 50 years and declined slowly thereafter in response to the decreasing intensity of the radioactive heat source. The alluvium near the repository experienced a cycle of drying and rewetting in both cases. The extent of the dry zone was strongly controlled by the mobility of liquid water near the repository under natural conditions. In the case of initial hydrostatic conditions, the dry zone extended approximately 10 m above and 15 m below the repository. For the case of a natural flux of 0.0003 m yr −1 the relative permeability of water near the repository was initially more than 30 times the value under hydrostatic conditions, consequently the dry zone extended only about 2 m above and 5 m below the repository. In both cases a significant perturbation in liquid saturation levels persisted for several hundred years. This analysis illustrates the extreme sensitivity of model predictions to initial conditions and parameters, such as relative permeability and moisture characteristic curves, that are often poorly known.

Water Resources Research↗

The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

Water Resources Research↗

Ground-water flow in low permeability environments

Certain geologic media are known to have small permeability; subsurface environments composed of these media and lacking well developed secondary permeability have groundwater flow sytems with many distinctive characteristics. Moreover, groundwater flow in these environments appears to influence the evolution of certain hydrologic, geologic, and geochemical systems, may affect the accumulation of pertroleum and ores, and probably has a role in the structural evolution of parts of the crust. Such environments are also important in the context of waste disposal. This review attempts to synthesize the diverse contributions of various disciplines to the problem of flow in low-permeability environments. Problems hindering analysis are enumerated together with suggested approaches to overcoming them. A common thread running through the discussion is the significance of size- and time-scale limitations of the ability to directly observe flow behavior and make measurements of parameters. These limitations have resulted in rather distinct small- and large-scale approaches to the problem. The first part of the review considers experimental investigations of low-permeability flow, including in situ testing; these are generally conducted on temporal and spatial scales which are relatively small compared with those of interest. Results from this work have provided increasingly detailed information about many aspects of the flow but leave certain questions unanswered. Recent advances in laboratory and in situ testing techniques have permitted measurements of permeability and storage properties in progressively “tighter” media and investigation of transient flow under these conditions. However, very large hydraulic gradients are still required for the tests; an observational gap exists for typical in situ gradients. The applicability of Darcy's law in this range is therefore untested, although claims of observed non-Darcian behavior appear flawed. Two important nonhydraulic flow phenomena, osmosis and ultrafiltration, are experimentally well established in prepared clays but have been incompletely investigated, particularly in undisturbed geologic media. Small-scale experimental results form much of the basis for analyses of flow in low-permeability environments which occurs on scales of time and size too large to permit direct observation. Such large-scale flow behavior is the focus of the second part of the review. Extrapolation of small-scale experimental experience becomes an important and sometimes controversial problem in this context. In large flow systems under steady state conditions the regional permeability can sometimes be determined, but systems with transient flow are more difficult to analyze. The complexity of the problem is enhanced by the sensitivity of large-scale flow to the effects of slow geologic processes. One-dimensional studies have begun to elucidate how simple burial or exhumation can generate transient flow conditions by changing the state of stress and temperature and by burial metamorphism. Investigation of the more complex problem of the interaction of geologic processes and flow in two and three dimensions is just beginning. Because these transient flow analyses have largely been based on flow in experimental scale systems or in relatively permeable systems, deformation in response to effective stress changes is generally treated as linearly elastic; however, this treatment creates difficulties for the long periods of interest because viscoelastic deformation is probably significant. Also, large-scale flow simulations in argillaceous environments generally have neglected osmosis and ultrafiltration, in part because extrapolation of laboratory experience with coupled flow to large scales under in situ conditions is controversial. Nevertheless, the effects are potentially quite important because the coupled flow might cause ultra long lived transient conditions. The difficulties associated with analysis are matched by those of characterizing hydrologic conditions in tight environments; measurements of hydraulic head and sampling of pore fluids have been done only rarely because of the practical difficulties involved. These problems are also discussed in the second part of this paper.

Water Resources Research↗

A statistical methodology for estimating transport parameters: Theory and applications to one-dimensional advectivec-dispersive systems

A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.

Water Resources Research↗

Groundwater Seepage Vectors and the Potential for Hillslope Failure and Debris Flow Mobilization

Insight for understanding the effect of groundwater flow on the potential for hillslope failure and liquefaction is provided by a novel limit‐equilibrium analysis of infinite slopes with steady, uniform Darcian seepage of arbitrary magnitude and direction. Normalization of the limit‐equilibrium solution shows that three dimensionless parameters govern completely the Coulomb failure potential of saturated, cohesionless, infinite homogeneous hillslopes: (1) the ratio of seepage force magnitude to gravitational body force magnitude; (2) the angle θ − Φ, where θ is the surface slope angle and Φ is the angle of internal friction of the soil; and (3) the angle λ + Φ, where λ is the angle of the seepage vector measured with respect to an outward‐directed surface‐normal vector. An additional dimensionless parameter affects the solution if soil cohesion is included in the analysis. Representation of the normalized solution as a single family of curves shows that minimum slope stability universally occurs when the seepage direction is given by λ = 90° − Φ. It also shows that for some upward seepage conditions, slope stability is limited by static liquefaction rather than by Coulomb failure. Close association between these liquefaction conditions and certain Coulomb failure conditions indicates that slope failure in such instances could be responsible for nearly spontaneous mobilization of destructive flowing soil masses on hillslopes.

Water Resources Research↗

A new formula for the analytical solution of the radial dispersion problem

A new formula is presented for the analytical solution of the radial dispersion problem, which analyzes the dispersive transport of a tracer in radial flow from a recharge well. This formula is simpler than a solution presented by previous investigators, but the two solutions are shown to be equivalent. Because the analytical solution consists of an integral of an oscillatory function, it is evaluated as an alternating series, the terms of which are the integrals over successive half cycles of the integrand. An efficient algorithm is used to accelerate convergence of the series. The accuracies of previous solutions obtained by finite difference, numerical Laplace transform, and perturbation methods are examined by comparison with the analytical solution. Numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes.

Water Resources Research↗

On tide-induced Lagrangian residual current and residual transport: 1. Lagrangian residual current

Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k , which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.

Water Resources Research↗

Manganese biogeochemistry in a small Adirondack forested lake watershed

I n September and October 1981, manganese (Mn) concentrations and p H were intensively monitored in a small forested lake watershed in the west-central Adirondack Mountains, New York, during two large acidic storms (each ∼5 cm rainfall, p H 4.61 and 4.15). The data were evaluated to identify biogeochemical pathways of Mn and to assess how these pathways are altered by acidic atmospheric inputs. Concentrations of Mn averaged 1.1 μg/L in precipitation and increased to 107 μg/L in canopy throughfall, the enrichment reflecting active biological cycling of Mn. Rain p H and throughfall Mn were negatively correlated, suggesting that foliar leaching of Mn was enhanced by rainfall acidity. The pulselike input of Mn to the forest floor in the high initial concentrations in throughfall (∼1000 μg/L) did not affect Mn concentrations in soil water (< 20 μg/L) or groundwater (usually < 40 μg/L), which varied little with time. In the inlet stream, Mn concentrations remained constant at 48 μg/L as discharge varied from 1.1 to 96 L/s. Manganese was retained in the vegetative cycle and regulated in the stream by adsorption in the soil organic horizon. The higher Mn levels in the stream may be linked to its high acidity (pH 4.2–4.3). Mixing of Mn-rich stream water with neutral lake water ( p H 7.0) caused precipitation of Mn and deposition in lake sediment.

New York↗

Nonlinear-regression groundwater flow modeling of a deep regional aquifer system

A nonlinear regression groundwater flow model, based on a Galerkin finite-element discretization, was used to analyze steady state two-dimensional groundwater flow in the areally extensive Madison aquifer in a 75,000 mi 2 area of the Northern Great Plains. Regression parameters estimated include intrinsic permeabilities of the main aquifer and separate lineament zones, discharges from eight major springs surrounding the Black Hills, and specified heads on the model boundaries. Aquifer thickness and temperature variations were included as specified functions. The regression model was applied using sequential F testing so that the fewest number and simplest zonation of intrinsic permeabilities, combined with the simplest overall model, were evaluated initially; additional complexities (such as subdivisions of zones and variations in temperature and thickness) were added in stages to evaluate the subsequent degree of improvement in the model results. It was found that only the eight major springs, a single main aquifer intrinsic permeability, two separate lineament intrinsic permeabilities of much smaller values, and temperature variations are warranted by the observed data (hydraulic heads and prior information on some parameters) for inclusion in a model that attempts to explain significant controls on groundwater flow. Addition of thickness variations did not significantly improve model results; however, thickness variations were included in the final model because they are fairly well defined. Effects on the observed head distribution from other features, such as vertical leakage and regional variations in intrinsic permeability, apparently were overshadowed by measurement errors in the observed heads. Estimates of the parameters correspond well to estimates obtained from other independent sources.

Great Plains, Madison aquifer↗

Unsaturated flow in a centrifugal field: Measurement of hydraulic conductivity and testing of Darcy's Law

A method has been developed to establish steady state flow of water in an unsaturated soil sample spinning in a centrifuge. Theoretical analysis predicts moisture conditions in the sample that depend strongly on soil type and certain operating parameters. For Oakley sand, measurements of flux, water content, and matric potential during and after centrifugation verify that steady state flow can be achieved. Experiments have confirmed the theoretical prediction of a nearly uniform moisture distribution for this medium and have demonstrated that the flow can be effectively one-dimensional. The method was used for steady state measurements of hydraulic conductivity K for relatively dry soil, giving values as low as 7.6 × 10 −11 m/s with data obtained in a few hours. Darcy's law was tested by measuring K for different centrifugal driving forces but with the same water content. For the sand at a bulk density of 1.82 Mg/m 3 and 27% saturation, results were consistent with Darcy's law for K equal to 5.22 × 10 −10 m/s and forces ranging from 216 to 1650 times normal gravity.

Water Resources Research↗

Tidal and tidally averaged circulation characteristics of Suisun Bay, California

Availability of extensive field data permitted realistic calibration and validation of a hydrodynamic model of tidal circulation and salt transport for Suisun Bay, California. Suisun Bay is a partially mixed embayment of northern San Francisco Bay located just seaward of the Sacramento-San Joaquin Delta. The model employs a variant of an alternating direction implicit finite-difference method to solve the hydrodynamic equations and an Eulerian-Lagrangian method to solve the salt transport equation. An upwind formulation of the advective acceleration terms of the momentum equations was employed to avoid oscillations in the tidally averaged velocity field produced by central spatial differencing of these terms. Simulation results of tidal circulation and salt transport demonstrate that tides and the complex bathymetry determine the patterns of tidal velocities and that net changes in the salinity distribution over a few tidal cycles are small despite large changes during each tidal cycle. Computations of tidally averaged circulation suggest that baroclinic and wind effects are important influences on tidally averaged circulation during low freshwater-inflow conditions. Exclusion of baroclinic effects would lead to overestimation of freshwater inflow by several hundred m 3 /s for a fixed set of model boundary conditions. Likewise, exclusion of wind would cause an underestimation of flux rates between shoals and channels by 70–100%.

California↗

A compositional multiphase model for groundwater contamination by petroleum products: 1. Theoretical considerations

A mathematical model is developed to describe the fate of hydrocarbon constituents of petroleum products introduced to soils as an immiscible liquid from sources such as leaking underground storage tanks and ruptured pipelines. The problem is one of multiphase transport (oil (immiscible), air, and water phases) of a reactive contaminant with constituents such as benzene, toluene, and xylene found in refined petroleum products like gasoline. In the unsaturated zone, transport of each constituent can occur as a solute in the water phase, vapor in the air phase, and as an unaltered constituent in the oil phase. Additionally, the model allows for adsorption. Molecular transformations, microbially mediated or abiotic, are incorporated as sink terms in the conservation of mass equations. An equilibrium approximation, applicable to any immiscible organic contaminant is applied to partition constituent mass between the air, oil, water, and adsorbed phases for points in the region where the oil phase exists. Outside the oil plume the equilibrium approximation takes on a simpler form to partition constituent mass between the air, water, and adsorbed phases only. Microbial degradation of petroleum products is first discussed in a general model, then the conservation of mass equation for oxygen is incorporated into the analysis which takes advantage of the key role played by oxygen in the metabolism of hydrocarbon utilizing microbes in soil environments. Approximations to two subproblems, oil plume establishment in the unsaturated zone, and solute and vapor transport subsequent to immiscible plume establishment are then developed from the general model.

Water Resources Research↗

A compositional multiphase model for groundwater contamination by petroleum products: 2. Numerical solution

In this paper we develop a numerical solution to equations developed in part 1 (M. Y. Corapcioglu and A. L. Baehr, this issue) to predict the fate of an immiscible organic contaminant such as gasoline in the unsaturated zone subsequent to plume establishment. This solution, obtained by using a finite difference scheme and a method of forward projection to evaluate nonlinear coefficients, provides estimates of the flux of solubilized hydrocarbon constituents to groundwater from the portion of a spill which remains trapped in a soil after routine remedial efforts to recover the product have ceased. The procedure was used to solve the one-dimensional (vertical) form of the system of nonlinear partial differential equations defining the transport for each constituent of the product. Additionally, a homogeneous, isothermal soil with constant water content was assumed. An equilibrium assumption partitions the constituents between air, water, adsorbed, and immiscible phases. Free oxygen transport in the soil was also simulated to provide an upper bound estimate of aerobic biodgradation rates. Results are presented for a hypothetical gasoline consisting of eight groups of hydrocarbon constituents. Rates at which hydrocarbon mass is removed from the soil, entering either the atmosphere or groundwater, or is biodegraded are presented. A significant sensitivity to model parameters, particularly the parameters characterizing diffusive vapor transport, was discovered. We conclude that hydrocarbon solute composition in groundwater beneath a gasoline contaminated soil would be heavily weighted toward aromatic constituents like benzene, toluene, and xylene.

Water Resources Research↗

Behavior of sensitivities in the one-dimensional advection-dispersion equation: Implications for parameter estimation and sampling design

The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one-dimensional form of the advection-dispersion equation. When parameters are estimated in regression models of one-dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) Information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance. (3) The frequency of sampling must be “in phase” with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters. (8) The time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system.

Water Resources Research↗