bluuebunny/crossref_metadata_2025 huggingface dataset:
Analysis and interpretation of single‐well tracer tests in stratified aquifers
Authors: Güven O. , Falta R. W. , Molz F. J. , Melville J. G.
Published: February 2008

This study deals with the definition and measurement of the dispersive properties of a stratified aquifer based on the single‐well tracer test. Knowledge of such dispersive properties are of fundamental importance to the evaluation, analysis, and simulation of contaminant migration in groundwater, a subject of great interest in recent years. In the single‐well test, tracer is pumped into the formation for a period of time and then pumped out. Concentration data are obtained from the injection‐withdrawal well and from one or more sampling‐observation wells which may be multilevel. Our analysis of such a test is based on a Lagrangian‐Eulerian numerical model which considers the depth‐dependent advection in the radial direction and local hydrodynamic dispersion in the vertical and radial directions. Results show that the movement of an injected tracer in a stratified aquifer may be accurately simulated without resorting to the use of a scale‐dependent, full aquifer dispersivity if the flow field is known in sufficient detail. When the advection process is simulated accurately, the values of local dispersivity will be small, constant, and on the order of those measured in the field or laboratory at individual levels in the aquifer. The full‐aquifer breakthrough curves measured in observation wells in a single‐well test in a stratified aquifer are determined by the hydraulic conductivity profile in the region between the injection‐withdrawal well and the observation well if the travel distance between these wells is typical of most test geometries. However, the relative concentration versus time data recorded at the injection‐withdrawal well during the withdrawal phase is primarily a measure of mixing in the aquifer due to local dispersion which has taken place during the experiment. The amount of mixing will depend on both the hydraulic conductivity distribution in the aquifer and the size of the experiment. As the experiment scale increases, the effects of local vertical dispersion will become larger compared to the effects of local radial dispersion. Local vertical dispersion will cause a solute traveling in a high‐conductivity layer in an aquifer to migrate into adjacent low‐conductivity layers where its movement will be relatively slow in comparison. In the initial design of a tracer test it is important to have some idea of the type of nonhomogeneity with which one is dealing. More information of a broad nature concerning the types or classifications of nonhomogeneities that exist in natural aquifers would be very useful. Future research in this area is needed.
A Quantitative Analysis of the Lassen Hydrothermal System, North Central California
Authors: Ingebritsen S. E. , Sorey M. L.
Published: February 2008

Our conceptual model of the Lassen system is termed a liquid‐dominated hydrothermal system with a parasitic vapor‐dominated zone. The essential feature of this model is that steam and steam‐heated discharge at relatively high altitudes in Lassen Volcanic National Park (LVNP) and liquid discharge with high chloride concentrations at relatively low altitudes outside LVNP are both fed by an upflow of high‐enthalpy two‐phase fluid within the Park. Liquid flows laterally away from the upflow area toward the areas of high‐chloride discharge, and steam rises through a vapor‐dominated zone to feed the steam and steam‐heated features. Numerical simulations show that several conditions are necessary for the development of this type of system, including (1) large‐scale topographic relief; (2) an initial period of convective heating within an upflow zone followed by (3) a change in hydrologic or geologic conditions that initiates drainage of liquid from portions of the upflow zone; and (4) low‐permeability barriers that inhibit the movement of cold water into the vapor zone. Simulations of thermal fluid withdrawal south of LVNP, carried out in order to determine the effects of such withdrawal on portions of the hydrothermal system within the Park, generally showed decreases in pressure and liquid saturation beneath the vapor zone which resulted in temporary increases and subsequent decreases in the rate of upflow of steam. A generalized production‐injection scenario that could mitigate the effects of development on both the high‐chloride and steam‐fed features was identified.
Discrimination of Soil Physical Parameters, Thermal Inertia, and Soil Moisture from Diurnal Surface Temperature Fluctuations
Authors: Van De Griend A. A. , Camillo P. J. , Gurney R. J.
Published: February 2008

A coupled heat and moisture flux model was used to study the influence of soil physical parameters and moisture content on diurnal surface temperature fluctuations. The study was performed for a grass cover under summer and autumn conditions for four soil types, ranging from sand to clay. The results show that it may be possible to use the daily maximum and minimum surface temperature measurements to discriminate several soil physical characteristics, including soil moisture. Further, ignoring the lower boundary heat flux, as is usually done in thermal inertia mapping but which can vary substantially in relation to different hydrological recharge and discharge areas, may lead to significant errors in the interpretation of soil moisture, thermal inertia, and transpiration.
Comparative Study of Green and Ampt Analysis for a Falling Water Table in a Homogeneous Sand Profile
Authors: Watson K. K. , Awadalla S. A.
Published: February 2008

Equations are developed for a Green and Ampt type analysis for a falling water table regime in an initially saturated homogeneous profile of porous material both with and without the presence of an applied surface flux of constant magnitude. The predictive capability of these Green and Ampt equations for a homogeneous medium sand is then tested against results obtained from a computer‐based numerical analysis of the differential equation describing water movement in unsaturated porous media. Three simulations with different rates of water table fall are described for the zero surface flux case with one of these rates also being used when an applied surface infiltration flux is included in the system. Comparisons with Green and Ampt results are then made for these simulations in terms of the discharge‐time relationship, the position of the draining front with time, and the thickness of the draining capillary fringe with time. In certain cases the approximate analysis is shown to agree with the numerical simulations quite satisfactorily while in others, notably those involving a more rapid water table fall, the differences are significant.
Type Curve Analysis of Inertial Effects in the Response of a Well to a Slug Test
Authors: Kipp Kenneth L.
Published: February 2008

The water level response to a slug or bailer test in a well completed in a confined aquifer has been evaluated taking into account well‐bore storage and inertial effects of the water column in the well. The response range, from overdamped with negligible inertial effects to damped oscillation, was covered employing numerical inversions of the Laplace‐transform solution. By scaling the time with respect to the undamped natural period of the well‐aquifer system and by using the damping parameter for a second‐order damped, inertial‐elastic system, a set of type curves was constructed that enables water level response data from a slug or bailer test to be analyzed under conditions where the inertial parameter is large. Values of transmissivity and effective static water column length can be determined when an estimate of storage coefficient is available. The numerical solution and resulting type curves cover the transition range between the limiting cases of negligible inertial effects and of damped oscillation that have been treated by others. Two examples of slug test analysis show that precise results depend on accurate measurements of water level displacement (±1% of initial value).
Models for Evaluating Flow Conveyance Reliability of Hydraulic Structures
Authors: Tung Yeou‐Koung
Published: February 2008

Two generalized dynamic reliability models (integrating both hydrologic and hydraulic uncertainties) based on binomial and Poisson distributions are developed for evaluating flow conveyance reliability of hydraulic structures. The two generalized models correct the deficiencies of dynamic reliability models developed previously. Relative performance of the generalized models and two conventional reliability models were examined. It is found that the total risk is significantly underestimated by the conventional approaches when hydraulic uncertainty is moderate or large.
The Role of Organic Acids in the Acid‐Base Status of Surface Waters at Bickford Watershed, Massachusetts
Authors: Eshleman K. N. , Hemond H. F.
Published: February 2008

An experimental field study of the alkalinity and major ion budgets of Bickford watershed in central Massachusetts indicates that organic acid production by the ecosystem contributes measurably to surface water acidification. Applying the concepts of alkalinity, electroneutrality of solutions, and mass balance, organic acids were found to comprise 20% of all strong acid sources on one subcatchment annually, a value half as large as the measured bulk mineral acid deposition. Inorganic cation to anion ratios in Provencial Brook varied between 1.0 in winter and 1.6 during summer, suggesting the presence of up to 100 μeq/L of unmeasured charge from organic anions during the growing season. Base titrations and ultraviolet photooxidation experiments confirmed the existence of low pKa (3.5–5.0) acidic functional groups. A positive linear relationship between dissolved organic carbon (DOC) and anion deficit for a group of surface and groundwater samples indicates the DOC contains about 7.5 meq carboxylic groups per gram C. Biological factors related to both upland and wetland carbon metabolism apparently control this natural acidification phenomenon, which has not been documented on other watersheds in the northeastern United States for which annual alkalinity budgets have been determined.
Modeling the Effects of Acid Deposition: Estimation of Long‐Term Water Quality Responses in a Small Forested Catchment
Authors: Cosby B. J. , Wright R. F. , Hornberger G. M. , Galloway J. N.
Published: February 2008

Research in recent years has led to conceptualizations of the long‐term responses of catchment surface water quality to acidic deposition. That research has focused attention on certain soil processes as likely keys to catchment responses (anion retention, cation exchange, primary mineral weathering, aluminum dissolution, and CO2 solubility). We present a mathematical model which uses quantitative descriptions of these soil chemical processes to estimate the long‐term chemical changes that occur in the soil, soil water, and surface waters of catchments in response to changes in atmospheric deposition. The model is applied to a small forested catchment in the Shenandoah National Park, Virginia. Historical changes in surface water quality are reconstructed for the catchment for the last 140 years. The model indicates that alkalinity of surface waters in the catchment may have been reduced by as much as 50%. Water quality is forecast for the catchment under three different scenarios of future changes in atmospheric deposition. The model indicates that all but very large reductions in deposition will result in further deterioration of the catchment water quality. The process‐oriented, lumped‐parameter approach used is consistent with all currently available observations of water quality in the catchment. Due to the lack of long‐term records of catchment water quality, strict verification of the model estimates and an assessment of the model validity is problematic. This is the case for all models of long‐terrn catchment chemical responses to acid deposition. Nonetheless, the model provides a means of integrating the results of individual process level laboratory and field studies. Used this way, the model becomes a vehicle for examining the interactions and long‐term implications of our conceptualization of the acidification process.
Field Determination of the Three‐Dimensional Hydraulic Conductivity Tensor of Anisotropic Media: 2. Methodology and Application to Fractured Rocks
Authors: Hsieh Paul A. , Neuman Shlomo P. , Stiles Gary K. , Simpson Eugene S.
Published: February 2008

The analytical solutions developed in the first paper can be used to interpret the results of cross‐hole tests conducted in anisotropic porous or fractured media. In the particular case where the injection and monitoring intervals are short relative to the distance between them, the test results can be analyzed graphically. From the transient variation of hydraulic head in a given monitoring interval, one can determine the directional hydraulic diffusivity, Kd(e)/Ss, and the quantity D/Ss, by curve matching. (Here Kd(e) is directional hydraulic conductivity parallel to the unit vector, e, pointing from the injection to the monitoring interval, Ss is specific storage, and D is the determinant of the hydraulic conductivity tensor, K.) The principal values and directions of K, together with Ss, can then be evaluated by fitting an ellipsoid to the square roots of the directional diffusivities. Ideally, six directional measurements are required. In practice, a larger number of measurements is often necessary to enable fitting an ellipsoid to the data by least squares. If the computed [Kd(e)/ss]½ values fluctuate so severely that a meaningful least squares fit is not possible, one has a direct indication that the subsurface does not behave as a uniform anisotropic medium on the scale of the test. Test results from a granitic rock near Oracle in southern Arizona are presented to illustrate how the method works for fractured rocks. At the site, the Oracle granite is shown to respond as a near‐uniform, anisotropic medium, the hydraulic conductivity of which is strongly controlled by the orientations of major fracture sets. The cross‐hole test results are shown to be consistent with the results of more than 100 single‐hole packer tests conducted at the site.
Incorporation of Point Sources in Numerical Transport Schemes
Authors: McBride G. B.
Published: February 2008

Numerical experiments with the Stone‐Brian numerical transport scheme for a continuous point source injection into steady uniform flow show that substantial oscillations can be generated upstream of the fixed steep front at the source location. These occur because this scheme does not possess the transportive property. Oscillations are most severe when the point source massflow is all allocated to a single grid node, in which case they can lead to gross mass conservation errors if the upstream boundary condition is not specified carefully. Incorporation of point sources in schemes that lack the transportive property is not trivial.
Numerical Modeling of Immiscible Organic Transport at the Hyde Park Landfill
Authors: Osborne M. , Sykes J.
Published: February 2008

In this paper, a two‐dimensional two‐phase mathematical model based on Darcy's law and conservation of mass for each liquid is presented. The numerical model is based on a generalized method of weighted residuals in conjunction with the finite element method and linear quadrilateral isoparametric elements. To alleviate numerical problems associated with hyperbolic equations, upstream weighting of the spatial terms in the model has been incorporated. The theoretical and numerical accuracy of the model is verified by comparison of simulation results with those from an existing one‐dimensional two‐phase flow simulator. The finite element model is used to simulate the migration of an immiscible organic solvent in groundwater, from a chemical waste disposal site located north of Niagara Falls, New York. The effects of uncertainty regarding porous media heterogeneities and anisotropy are examined, and it is concluded that the extent of immiscible contaminant migration is greatly sensitive to these parameters.
A Porous Flow Model for Steady State Transport of Radium in Groundwater
Authors: Davidson M. R. , Dickson B. L.
Published: February 2008

The quasi‐steady variation of uranium and radium isotopes from the decay of 238U, 235U, and 232Th has been determined along an idealized, one‐dimensional aquifer which is a distributed source of activity and from which the transfer of radionuclides to solution occurs by alpha recoil and chemical exchange. The model includes the effects of dispersive flow and retardation by adsorption. The importance of these effects on the variation of U and Ra activity ratios along the model aquifer is shown. Predicted limiting activity ratios (for large flow times) of 226Ra/223Ra, 224Ra/228Ra, and 226Ra/228Ra are 21.4, 1.5, and (∼1.7–2.0) (U/Th)s, respectively (where (U/Th)s is the activity ratio 238U/232Th in the aquifer rocks), although in many cases, an aquifer may not be long enough for the ratios involving 226Ra to achieve their limiting values.
Estimation of Distributional Parameters for Censored Trace Level Water Quality Data: 1. Estimation Techniques
Authors: Gilliom Robert J. , Helsel Dennis R.
Published: February 2008

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored‐sample estimates of the four distributional parameters over all simulation conditions was the log‐probability regression method. With this method, censored observations are assumed to follow the zero‐to‐censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log‐probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.
Optimal Management of Large‐Scale Aquifers: Methodology and Applications
Authors: Wanakule Nisai , Mays Larry W. , Lasdon Leon S.
Published: February 2008

A methodology is developed for determining optimal pumping and recharge of large scale artesian and/or nonartesian aquifers. This methodology couples optimization techniques with existing groundwater simulation models. It can be applied to both groundwater policy evaluation (allocation) such as large‐scale aquifers and to hydraulic management problems such as the dewatering of mining or excavation sites. The state variables which represent the heads and the control variables which represent the pumpages are implicitly related through the groundwater simulator. The simulator equations are used to express the states in terms of the controls, yielding a much smaller reduced problem. Techniques for computing gradients of reduced problem functions are described. The reduced problem is solved by combining augmented Lagrangian and reduced gradient procedures. The optimization‐groundwater simulation system is referred to as GWMAN. Two small examples are solved in addition to both steady state and transient type dewatering problems. Also, an application to the Edwards Aquifer in Texas is presented.
A Programming Model for Analysis of the Reliability, Resilience, and Vulnerability of a Water Supply Reservoir
Authors: Moy Wai‐See , Cohon Jared L. , ReVelle Charles S.
Published: February 2008

Reliability in water supply reservoir operation is commonly thought of as the probability of failing to achieve some target release. Here we explore two additional proposed descriptions of reservoir performance: the maximum shortfall from the target (system vulnerability) and the maximum number of consecutive periods of deficit during a record (system resilience). The larger the maximum shortfall, the greater the vulnerability. The shorter the maximum length of deficits, the more resilient the system. Using multiobjective mixed‐integer, linear programming, the tradeoffs between reliability, vulnerability, and resilience are examined. It is found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.
Parameter Uncertainty in Estimation of Spatial Functions: Bayesian Analysis
Authors: Kitanidis Peter K.
Published: February 2008

Linear estimation has found many applications in the inference of spatial functions in surface and subsurface hydrology. The effect of parameter uncertainty is examined in a Bayesian framework with emphasis on the derivation of the Bayesian distribution (and its first two moments) of unknown quantities given some measurements. This distribution accounts not only for natural variability but also for parameter uncertainty. For known covariance parameters the Bayesian distribution is Gaussian (for Gaussian processes) with the mean being a given linear function of the data. This linear estimator is equivalent to the conventional Gaussian conditional mean estimator for a priori known drift coefficients and is the same with kriging for diffuse prior distribution of the drift coefficients; however, the developed procedure is more general. When both drift and covariance function parameters are uncertain, the Bayesian distribution is generally not Gaussian, and the Bayesian conditional mean is a nonlinear estimator. The case of diffuse priors is examined in some detail; it is shown that the posterior distribution of the covariance function parameters is given by the restricted likelihood function, i.e., the likelihood function of generalized increments. The results provide insight into the applicability of maximum likelihood versus restricted maximum likelihood parameter estimation, and conventional linear versus kriging estimation. A more general procedure which includes these methods as special cases is presented.
Radionuclide Migration in Strongly Fissured Zones: The Sensitivity to Some Assumptions and Parameters
Authors: Rasmuson Anders , Neretnieks Ivars
Published: February 2008

Radionuclides escaping from a repository for high‐level nuclear waste in crystalline rock may eventually be carried by the flowing water in fissure zones. In such zones the rock is broken into blocks of varying sizes and shapes. Also, the water velocity may vary considerably in such zones. A previously developed model which lumps the different blocks into a single PSEUDOBODY is tested by comparing it with an exact analytical solution which can account for the diffusion into blocks of any size distribution. The approximate simplified model, which is based on a numerical scheme, and thus is more versatile, gives errors which are small compared to the “normal” variation in observed block size distributions and other data. A method for determining an “average” Peclet number (or dispersion length) in a strongly varying velocity field is tested arid found to give small errors compared to the present confidence limits in predicting dispersion data for large migration distances. A simple criterion is proposed for defining the cutoff limit in the block size distribution, below which the blocks can be modeled as if they were in equilibrium with the flowing water. A simple sensitivity analysis shows that much can be gained if the confidence limits for block size distribution, water flow rate, dispersion data, sorption data, and matrix diffusion data can be narrowed down.
An Orthogonal‐Upstream Finite Element Approach to Modeling Aquifer Contaminant Transport
Authors: Yeh G. T.
Published: February 2008

An orthogonal‐upstream weighting (OUW) finite element scheme, which will result in a matrix amenable to point successive overrelaxation (SOR) solution strategies, is presented for approximating the aquifer contaminant‐transport equation. This scheme differs from the standard Galerkin weighting (GW) and nonorthogonal‐upstream weighting (NUW) schemes in that the set of weighting functions is required to be orthogonal to the set of basis functions. These weighting functions are referred to as OUW functions and are developed for line, quadrilateral, and triangular elements. Numerical results have been obtained for two examples and are compared with results obtained through analytical solutions (AS) and the Galerkin and/or NUW schemes. The direct elimination solutions of the OUW finite element equations yield results comparable to those obtained by the direct solution of the Galerkin and/or NUW finite element equations. The SOR computations of the OUW finite element scheme generate convergent solutions for all cases. In contrast, the SOR calculations of the Galerkin and/or NUW finite element schemes result in convergent solutions for dispersion‐dominant cases but produce divergent results for advection‐dominant cases. For small problems when the central processing unit (CPU) memory is not a consideration, the direct elimination solutions of the Galerkin and NUW finite element methods are the most efficient schemes. For large problems, when one wish to use point SOR iteration to solve the matrix equation because of CPU memory limitations, the OUW scheme provides an alternative because it gives convergent SOR computations for all Peclet numbers. Even when CPU memory is not a consideration, one may still prefer OUW to Galerkin or NUW because of its susceptibility to the SOR iteration for all grid Peclet numbers, especially for large problems when the SOR iteration will be much more efficient than the direct elimination solution.
Steady Infiltration From Buried Discs and Other Sources
Authors: Philip J. R.
Published: February 2008

Scattering analog techniques are used to analyze steady quasilinear infiltration from buried discs and to develop related results. The exact solution involves spheroidal wave functions; but, more usefully, we express the far‐field wetting function and the discharge function as expansions appropriate for small and large values of s, the dimensionless disc radius. Other simple techniques for estimating the moisture field include boundary layer and Green's function methods. Further aspects of the study include: useful comparisons with Wooding's classical results for the surface disc; and small s expansions, not hitherto available, for steady infiltration from cylindrical and spherical cavities. Buried discs (with aspect ratio h = 0), oblate spheroids (0 < h < 1), spheres (h = 1), and prolate spheroids (h > 1) form an ordered sequence. Both capillary effects and the difficulty of matching small and large s expansions increase markedly with h. The surface disc is an exceptional “least capillarity” case. The foregoing considerations lead to design principles for permeameters to measure the saturated hydraulic conductivity of unsaturated field soils. The customary borehole permeameter has h large and consequently strong capillary effects; but saturated conductivity has greatest influence on permeameter discharge when capillary effects are least. Accordingly, the optimal design is the surface disc permeameter, with h = 0 and minimal capillary effects.
Sediment Transport Capacity of Sheet and Rill Flow: Application of Unit Stream Power Theory
Authors: Moore I. D. , Burch G. J.
Published: February 2008

Theoretical equations for calculating the unit stream power of both sheet and rill flow were developed and used to predict the sediment transport capacity of such flows. Independent data sets from three sources representing both finely aggregated clay soils and coarse textured nonaggregated soils, sheet, rill, and composite sheet rill flow systems, and a range of slopes were used to test the utility of the method. The results were very good and demonstrated the simplicity and robustness of the method. For shallow overland flow the best results were obtained when the critical unit stream power at incipient sediment motion was treated as a constant value that was independent of slope. The results also suggest that a unique value of critical unit stream power for rill initiation exists that is independent of soil type. For noncohesive loams or fine sands and finely aggregated clay soils the sediment transport capacity can be accurately predicted from a knowledge of the physical characteristics of the soil or bed material alone. For aggregated clay soils this requires information on the aggregate size distribution and the effects of soil particle size differentiation as flow rates and unit stream powers increase with the transition from sheet to rill flow.
Water and Air Intake of Surface‐Exposed Rock Fractures in Situ
Authors: Kilbury Richard K. , Rasmussen Todd C. , Evans Daniel D. , Warrick A. W.
Published: February 2008

The siting and reclamation of hazardous waste disposal facilities may require the examination of solute transport through networks of fractures within lithic units. Water intake at the surface of a fractured rock medium may provide a transport mechanism for the movement of hazardous wastes. A dual‐chambered fractured rock infiltrometer (FRI) is used to provide in situ measurements of water and air intake rates for isolated fracture segments. The FRI is used to apply a known head to an exposed fracture segment and to provide a precise means for measuring the intake rate. Water intake rates for fractures in an exposed, densely welded tuff are highest at early time, then fall to a constant rate. Analytical procedures are developed to estimate fracture apertures using the Green and Ampt model and Poiseuille's law. Calculated fracture apertures from water intake data range from 1.0 to 33.7 μm and are approximately lognormally distributed. An analytical expression relating air intake data to fracture aperture is derived using the Schwartz‐Christoffel transformation. Estimated apertures using this experimental technique range from 10.0 to 37.2 μm and appear to fit the same lognormal distribution.
Deterministic and Stochastic Analyses of Dispersion in an Unbounded Stratified Porous Medium
Authors: Güven Oktay , Molz Fred J.
Published: February 2008

The dispersion of a conservative solute released instantaneously from a finite or point source in an unbounded, nonrandom periodically stratified porous medium is examined theoretically by applying the moment method of R. Aris (1956) and P. G. Saffman (1962). The governing moment equations are derived for a general stratified medium and then applied to study the detailed time‐dependent variations of various low‐order spatial moments of the three‐dimensional concentration distribution in a particular periodic (sinusoidal) stratified medium, both for the general case when the mean flow direction is inclined to the stratification as well as for the special case of flow parallel to the stratification. The present results confirm the previous results of V. K. Gupta and K. N. Bhattacharya (1986) regarding the asymptotic (large‐time) large‐scale dispersion coefficients for such a periodic medium. The present results which are obtained through a deterministic analysis are compared also with the results which would be obtained by using the previous stochastic theories of G. Matheron and G. deMarsily (1980) and L. W. Gelhar et al. (1979). The comparison reveals several similarities as well as some important differences between the results of the deterministic and stochastic analyses.
An Upstream Weight Multiple‐Cell Balance Finite‐Element Method for Solving Three‐Dimensional Convection‐Dispersion Equations
Authors: Wang Chuching , Sun Ne‐Zheng , Yeh William W‐G.
Published: February 2008

An upstream weight multiple‐cell balance finite‐element method is developed to simulate the three‐dimensional contaminant transport in aquifers. The method combines the concepts of local mass balance and finite‐element approximations. When convective transport dominates the dispersive transport, the proposed technique effectively eliminates the oscillation of numerical solutions with only a nominal increase of formulation effort over that of the general Galerkin finite‐element method. Two numerical examples for which analytical solutions exist are used to verify the proposed numerical solutions. An additional example is presented to demonstrate the practical applicability of the proposed method.
A New Formula for the Analytical Solution of the Radial Dispersion Problem
Authors: Hsieh Paul A.
Published: February 2008

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.
Linearized unsteady multidimensional infiltration
Authors: Philip J. R.
Published: February 2008

The parameters in the linearized multidimensional unsteady equation for unsaturated flow in homogeneous soils can be chosen so that small time flow rates are given correctly, with the quasi‐linear steady solution as the large time limit. Matched in this way, the linearized equation offers insight into the time course of multidimensional infiltration. The Laplace transform reduces the equation and its governing conditions into forms similar to those for quasi‐linear steady flows. The problems of unsteady infiltration from buried spherical and cylindrical cavities are solved. In many cases the solutions are approximately reducible to the product of the steady solution and a function only of time and radial coordinate. Theorems show that approximate product solutions apply not only to these configurations but generally to multidimensional cavities of arbitrary shape. Multidimensional infiltration from finite supply surfaces involves two characteristic lengths and two characteristic times, one set deriving from the capillarity gravity interaction and the other from the capillarity‐geometry interaction. We explore the influence of the two characteristic times on the time scales of approach to steady moisture distribution near the supply surface and to steady discharge. The analysis provides explanation of the relatively rapid approach to the steady state observed in three‐dimensional infiltration from small supply surfaces.
Particle transport through porous media
Authors: McDowell‐Boyer Laura M. , Hunt James R. , Sitar Nicholas
Published: February 2008

Transport of suspended participate matter is widely recognized to occur in subsurface environments. Field data indicate that viruses, bacteria, and clay minerals can migrate considerable distances and that small particles and macromolecules are implicated in the transport of organic contaminants and radio‐nuclides. Furthermore, media permeability can be significantly altered by changes in aqueous chemistry through particle release and capture. Quantitative models for predicting particle transport are available within the water filtration literature that account for the mechanisms of particle‐media collisions and the conditions for attachment. Predictions from the filtration models are used to analyze particle migration through porous media at typical groundwater flow velocities. As particles accumulate within media pores, available models become less predictive because of the coupling between particle retention and permeability reduction. An examination of filtration data reveals that retention of a relatively small solid volume within media pores can reduce media permeability by orders of magnitude. The fact that contaminants adsorbed to particles are mobile has important implications in understanding and predicting contaminant transport. The design of laboratory experiments and the collection of field samples often neglect contaminants transported by suspended colloids and particles.
Predicting mass transport in discrete fracture networks with the aid of geometrical field data
Authors: Andersson Johan , Thunvik Roger
Published: February 2008

The importance of knowing the details of the fracture network geometry when predicting mass transport in discrete fractured media is investigated in this study. It is assumed that some information of the fractured medium is known, such as the location and direction of fractures that intersect drill cores in the investigated region and the overall conductivity of the fracture network in this region. In comparison, individual fracture properties are assumed to be unknown, apart from the assumption that they follow specified stochastic distributions. A two‐dimensional test problem is analyzed with the Monte Carlo technique. Reality is there represented by a hypothetical fracture network. On this real network, cores are drilled and the thereby intersected fractures recorded. On the basis of the data obtained, realizations of fracture networks that might represent reality are generated. The data from the real network will limit the variability of the possible realizations of fracture networks. A problem of mass transport is solved on the real network and on each of the generated ones, using a particle tracing technique. By comparing the real transport time with the estimated transport time as is obtained from the Monte Carlo runs, the advantage of increasing the measurements (for example, drilling more holes) is analyzed. It is found that introducing more cores will decrease the estimated uncertainty but that the fracture lengths, the fracture line density, and the spatial correlation of the aperture along the fracture influence the value of the geometrical information. The estimated uncertainty is less in networks with long fractures combined with a high line density and little spatial correlation of the apertures. It is also noted that if the fracture apertures are adjusted so that all conditional networks have the same hydraulic conductivity, the estimated uncertainty in transport times is reduced substantially.
Chlorine 36 dating of very old groundwater: 2. Milk River Aquifer, Alberta, Canada
Authors: Phillips Fred M. , Bentley Harold W. , Davis Stanley N. , Elmore David , Swanick Gerald B.
Published: February 2008

The Milk River aquifer in southern Alberta, Canada, consists of sandstone interbedded between thick shale units. The groundwater is confined and discharges by both upward and downward leakage through the shales. The concentration of Cl− increases by about 2 orders of magnitude downgradient through the aquifer. This Cl−increase complicates 36Cl dating of the system. Climatic changes, flushing of connate water, introduction of Cl− from older water below the aquifer, and ion filtration have been proposed as possible explanations for the increase. The 36Cl data show a consistent decrease of the 36Cl/Cl ratio downgradient, but an increase in the 36Cl concentration downgradient in certain parts of the aquifer. Dates calculated from the 36Cl/Cl ratio show a reasonable distribution in light of the hydraulic controls on the system, whereas dates calculated from the 36Cl concentration give negative ages. This suggests that ion filtration is responsible for the Cl− increase and that the 36Cl/Cl dates are to be preferred. We estimate water ages to be more than 2 m.y. near the distal end of the aquifer.
Chaparral conversion and streamflow: Nitrate increase is balanced mainly by a decrease in bicarbonate
Authors: Davis Edwin A.
Published: February 2008

Converting Arizona chaparral watersheds to grass by controlling the brush with herbicides increases water yield as subsurface runoff to streams. The increased stream discharge is accompanied by several hundredfold increases in the nitrate concentration of the stream water. Nitrate concentrations remained 46–69 fold above normal for 11 years or more. Nitrate ion concentration increases were balanced mainly by bicarbonate ion concentration decreases, with little change in the concentration of other anions or cations. One mechanism suggested to explain the decrease in bicarbonate that balances the increase in nitrate is the reaction of H+ NO3− with HCO3− to give carbon dioxide and water.
Saltwater intrusion in aquifers: Development and testing of a three‐dimensional finite element model
Authors: Huyakorn Peter S. , Andersen Peter F. , Mercer James W. , White Harold O.
Published: February 2008

A three‐dimensional finite element model is developed for the simulation of saltwater intrusion in single and multiple coastal aquifer systems with either a confined or phreatic top aquifer. The model formulation is based on two governing equations, one for fluid flow and the other for salt transport. Density coupling of these equations is accounted for and handled using a Picard sequential solution algorithm with special provisions to enhance convergence of the iterative solution. Flexibility in the formulation allows for either three‐dimensional simulations or quasi three‐dimensional simulations, where flow and transport in aquitards are treated using one‐dimensional analytical and/or numerical approximations. Spatial discretization of three‐dimensional regions is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuity. This approach is effectively combined with the use of simple linear elements such as rectangular and triangular prisms, and composite hexahedra and pentahedra made up of tetrahedra. For these elements, computation of element matrices can be performed efficiently using influence coefficient formulas that avoid numerical integration. New transport influence coefficient formulas are presented for rectangular and triangular prism elements. Matrix assembly is performed slice by slice, and the matrix solution is achieved using a slice successive relaxation scheme. This permits a fairly large number of nodal unknowns (of the order of five to ten thousand) to be handled conveniently on small or medium‐size minicomputers. Flexibility of the formulation and matrix handling procedures also allows two‐dimensional and axisymmetric problems to be solved efficiently using single slice representations. Four examples are presented to demonstrate the model verification and utility. These problems represent a fair range of physical conditions. Where possible, simulation results are compared with previously published solutions.
Depth‐averaging effects on hydraulic head for media with stochastic hydraulic conductivity
Authors: Naff R. L. , Vecchia A. V.
Published: February 2008

Hydraulic conductivity of a porous medium frequently is considered to be a single realization of a three‐dimensional spatial stochastic process. The most common observations of flow in porous media are hydraulic‐head measurements obtained from wells which are screened over extensive sections of the medium. These measurements represent, approximately, a one‐dimensional spatial average of the actual three‐dimensional head distribution, the actual head distribution being a stochastic process resulting from flow through a random hydraulic‐conductivity field. This paper examines, via ensemble averages, the effect of such spatial averages of groundwater flow on the spatial autocovariance function for a simple, yet viable, stochastic model of a bounded medium. The model is taken to be three‐dimensional flow in a medium that is bounded above and below and in which the hydraulic conductivity is a second‐order stationary stochastic process. Spatial averaging of the hydraulic heads is considered to take place over the entire thickness of the medium. Ensemble variances and autocorrelations for depth‐averaged heads are computed for the resulting two‐dimensional flow system and compared with those from a fully three‐dimensional flow system.
The estimation of the generalized covariance when it is a linear combination of two known generalized covariances
Authors: Barendregt L. G.
Published: February 2008

In order to be able to perform a spatial interpolation according to the kriging method, one must know the generalized covariance of the underlying intrinsic random field. Recently, P. K. Kitanidis (1983) described how this generalized covariance can be estimated by making use of the maximum likelihood method. Here, it will be described how this estimation can be simplified if the model for the generalized covariance is linear with two parameters. The computations are based on a particular set of generalized increments, the so‐called principal increments. These increments can also serve as a starting point for a study of the mathematical properties of the maximum likelihood estimators.
Measuring recreation benefits: Conceptual and empirical issues
Authors: Brookshire David S. , Smith V. Kerry
Published: February 2008

The focus of this special section is the conceptual and empirical issues associated with the development of water‐based recreation benefit estimation methodologies. The papers address two themes in the ongoing development of modeling the demand for outdoor recreation. The issues of characterizing and estimating nonuse (existence) values are discussed by K. J. Boyle and R. C. Bishop (this issue) and B. Madariaga and K. E. McConnell (this issue). R. Mendelsohn (this issue) and N. E. Bockstael et al. (this issue) address the problem of developing consistent methodologies for modeling the household's recreation decisions. This paper attempts to identify and highlight the issues and interrelationships of both sets of papers. An attempt is made to identify remaining research issues.
Nonlinear flood routing with multilinear models
Authors: Becker Alfred , Kundzewicz Zbigniew W.
Published: February 2008

The category of multilinear models is analyzed that embraces several approaches developed in apparently independent references. Multilinear modeling is a means of describing a nonlinear system with a set of linear models. This is performed by distributing the inflow to the system (river reach) into inflows to submodels and treating these inflows with a family of different linear operators. The models considered are nearly as simple as linear models and almost as accurate as nonlinear hydrodynamical models.