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At least 883 records · Page 49Linked to original sources
USGS2010

Simulation of calcite dissolution and porosity changes in saltwater mixing zones in coastal aquifers

Thermodynamic models of aqueous solutions have indicated that the mixing of seawater and calcite-saturated fresh groundwater can produce a water that is undersaturated with respect to calcite. Mixing of such waters in coastal carbonate aquifers could lead to significant amounts of limestone dissolution. The potential for such dissolution in coastal saltwater mixing zones is analyzed by coupling the results from a reaction simulation model (PHREEQE) with a variable density groundwater flow and solute transport model. Idealized cross sections of coastal carbonate aquifers are simulated to estimate the potential for calcite dissolution under a variety of hydrologic and geochemical conditions. Results show that limestone dissolution in mixing zones is strongly dependent on groundwater flux and nearly independent of the dissolution kinetics of calcite. The amount of dissolution varies within a mixing zone, depending on the properties, physical dimensions, and boundary conditions of the aquifer system. Nearly all of the dissolution occurs in the fresher side of the mixing zone, with the maximum dissolution occurring in water that is fresher than that predicted solely by geochemical reaction models. The greatest porosity and permeability development occur at the toe and at the top of the mixing zone. If permeability increases as porosity increases, asymmetry in the dissolution causes the mixing zone to migrate landward over time. Dissolution rates indicated by the model show that this mechanism can produce significant increases in porosity and permeability over time spans on the order of tens of thousands of years. Given the comparatively long span of geologic time, this process may be largely responsible for porosity and permeability development observed in those carbonate rocks through which a freshwater-saltwater mixing zone had at one time migrated.

Water Resources Research↗
USGS2010

Accounting for intracell flow in models with emphasis on water table recharge and stream-aquifer interaction: 2. A procedure

Intercepted intracell flow, especially if cell includes water table recharge and a stream ((sink), can result in significant model error if not accounted for. A procedure utilizing net flow per cell ( F n ) that accounts for intercepted intracell flow can be used for both steady state and transient simulations. Germane to the procedure is the determination of the ratio of area of influence of the interior sink to the area of the cell ( A i / A c ). A i is the area in which water table recharge has the potential to be intercepted by the sink. Determining A i / A c requires either a detailed water table map or observation of stream conditions within the cell. A proportioning parameter M , which is equal to 1 or slightly less and is a function of cell geometry, is used to determine how much of the water that has potential for interception is intercepted by the sink within the cell. Also germane to the procedure is the determination of the flow across the streambed ( F s ), which is not directly a function of cell size, due to difference in head between the water level in the stream and the potentiometric surface of the aquifer underlying the streambed. The use of F n for steady state simulations allows simulation of water levels without utilizing head-dependent or constant head boundary conditions which tend to constrain the model-calculated water levels, an undesirable result if a comparison of measured and calculated water levels is being made. Transient simulations of streams usually utilize a head-dependent boundary condition and a leakance value to model a stream. Leakance values for each model cell can be determined from a steady state simulation, which used the net flow per cell procedure. For transient simulation, F n would not include F s . Also, for transient simulation it is necessary to check F n at different time intervals because M and A i / A c are not constant and change with time. The procedure was used successfully in two different models of the aquifer system in the Ozarks. The use of F n was essential to the two model studies because most model cells in both models contained water table recharge and multiple sinks.

Water Resources Research↗
USGS2010

A random spatial network model based on elementary postulates

A model for generating random spatial networks that is based on elementary postulates comparable to those of the random topology model is proposed. In contrast to the random topology model, this model ascribes a unique spatial specification to generated drainage networks, a distinguishing property of some network growth models. The simplicity of the postulates creates an opportunity for potential analytic investigations of the probabilistic structure of the drainage networks, while the spatial specification enables analyses of spatially dependent network properties. In the random topology model all drainage networks, conditioned on magnitude (number of first-order streams), are equally likely, whereas in this model all spanning trees of a grid, conditioned on area and drainage density, are equally likely. As a result, link lengths in the generated networks are not independent, as usually assumed in the random topology model. For a preliminary model evaluation, scale-dependent network characteristics, such as geometric diameter and link length properties, and topologic characteristics, such as bifurcation ratio, are computed for sets of drainage networks generated on square and rectangular grids. Statistics of the bifurcation and length ratios fall within the range of values reported for natural drainage networks, but geometric diameters tend to be relatively longer than those for natural networks.

Water Resources Research↗
USGS2010

The relationship of catchment topography and soil hydraulic characteristics to lake alkalinity in the northeastern United States

We undertook the task of determining whether base flow alkalinity of surface waters in the northeastern United States is related to indices of soil contact time and flow path partitioning that are derived from topographic and soils information. The influence of topography and soils on catchment hydrology has been incorporated previously in the variable source area model TOPMODEL as the relative frequency distribution of ln ( a/Kb tan B ), where ln is the Naperian logarithm, “ a ” is the area drained per unit contour, K is the saturated hydraulic conductivity, b is the soil depth, and tan B is the slope. Using digital elevation and soil survey data, we calculated the ln ( a/Kb tan B ) distribution for 145 catchments. Indices of flow path partitioning and soil contact time were derived from the ln ( a/Kb tan B ) distributions and compared to measurements of alkalinity in lakes to which the catchments drain. We found that alkalinity was, in general, positively correlated with the index of soil contact time, whereas the correlation between alkalinity and the flow path partitioning index was weak at best. A portion of the correlation between the soil contact time index and alkalinity was attributable to covariation with soil base saturation and cation exchange capacity, while another portion was found to be independent of these factors. Although our results indicate that catchments with long soil contact time indices are most likely to produce high alkalinity base flow, a sensitivity analysis of TOPMODEL suggests that surface waters of these same watersheds may be susceptible to alkalinity depressions during storm events, due to the role of flow paths.

Water Resources Research↗
USGS2010

Solute advection in stratified formations

Advection‐dominated solute movement in stratified formations is investigated using a Lagrangian interpretation of particle motion. A probability density function (pdf) for particle position quantifies the expected depth‐integrated resident concentration. A pdf for particle arrival time quantifies the expected depth‐integrated rate of mass arrival, from which the flux‐averaged concentration can be defined. The difference between the flux‐averaged and resident concentrations is shown to be significant for the variability in the hydraulic conductivity that is commonly encountered in field applications. The influence of porosity variations on the advection‐dominated solute movement in stratified porous media is shown to be notable only for large variability in the effective porosity.

Water Resources Research↗
USGS2010

Water content dependence of trapped air in two soils

An improved air pycnometer method was used to examine the water content dependence of trapped-air volumes in two repacked, nonswelling soils. Trapped-air volumes were determined at a series of hydrostatic equilibrium stages which were attained during water pressure-controlled wetting and drying cycles over a range of 0 to −10 kPa for a sand and 0 to −20 kPa for a loam. Small pressure perturbations, between 0.2 and 0.6 kPa, were used in the air pycnometer method. Volumes of trapped air obtained at each hydrostatic equilibrium stage were independent of perturbation level and remained relatively constant over the time required to make repeated determinations. In contrast with most of the results obtained in previous studies, which often showed irregular relations, in this study the volume fraction of trapped air was found to be a regular, monotonically increasing (though possibly hysteretic) function of water content. For the soils studied, the function definitely exceeded zero only at water contents greater than 70% of saturation. However, during the initial drying from complete water saturation, the volume fraction of trapped air was virtually zero. Air trapping influenced the water retention curves significantly only at water contents higher than about 60% of saturation. Except at zero water pressure, however, not all of the differences between the initial and the other drying retention curves were accounted for by observed differences in trapped-air volumes. Air trapping was not required for the onset of hysteresis in the water retention relation for the cases studied, i.e., when drying-to-wetting reversals were imposed at about 27% and 40% of saturation for the sand and loam soils, respectively.

Water Resources Research↗
USGS2010

Air permeability and trapped-air content in two soils

To improve understanding of hysteretic air permeability relations, a need exists for data on the water content dependence of air permeability, matric pressure, and air trapping (especially for wetting-drying cycles). To obtain these data, a special instrument was designed. The instrument is a combination of a gas permeameter (for air permeability determination), a suction plate apparatus (for retentivity curve determination), and an air pycnometer (for trapped-air-volume determination). This design allowed values of air permeability, matric pressure, and air trapping to be codetermined, i.e., determined at the same values of water content using the same sample and the same inflow-outflow boundaries. Such data were obtained for two nonswelling soils. The validity of the air permeability determinations was repeatedly confirmed by rigorous tests of Darcy's law. During initial drying from complete water saturation, supplementary measurements were made to assess the magnitude of gas slip. The extended Darcy equation accurately described the measured flux gradient relations for each condition of absolute gas pressure tested. Air permeability functions exhibited zero-permeability regions at high water contents as well as an abruptly appearing hysteresis at low water contents. Measurements in the zero-permeability regions revealed that the total amount of air in general exceeded the amount of trapped air. This indicates that the medium' s air space is partitioned into three measurable domains: through-flowing air, locally accessible air (i.e., air accessible from only one flow boundary), and trapped air. During repeated wetting and drying, the disappearance and reappearance of air permeability coincided closely with the reappearance and disappearance, respectively, of trapped air. The observed relation between critical features of the air permeability functions and those of the air-trapping functions suggest that water-based blockages play a significant role in the disruption of gas-phase connectivity and in preventing air flow, and must be considered in any effectual model of air permeability relations.

Water Resources Research↗
USGS2010

Multiobjective sampling design for parameter estimation and model discrimination in groundwater solute transport

Sampling design for site characterization studies of solute transport in porous media is formulated as a multiobjective problem. Optimal design of a sampling network is a sequential process in which the next phase of sampling is designed on the basis of all available physical knowledge of the system. Three objectives are considered: model discrimination, parameter estimation, and cost minimization. For the first two objectives, physically based measures of the value of information obtained from a set of observations are specified. In model discrimination, value of information of an observation point is measured in terms of the difference in solute concentration predicted by hypothesized models of transport. Points of greatest difference in predictions can contribute the most information to the discriminatory power of a sampling design. Sensitivity of solute concentration to a change in a parameter contributes information on the relative variance of a parameter estimate. Inclusion of points in a sampling design with high sensitivities to parameters tends to reduce variance in parameter estimates. Cost minimization accounts for both the capital cost of well installation and the operating costs of collection and analysis of field samples. Sensitivities, discrimination information, and well installation and sampling costs are used to form coefficients in the multiobjective problem in which the decision variables are binary (zero/one), each corresponding to the selection of an observation point in time and space. The solution to the multiobjective problem is a noninferior set of designs. To gain insight into effective design strategies, a one-dimensional solute transport problem is hypothesized. Then, an approximation of the noninferior set is found by enumerating 120 designs and evaluating objective functions for each of the designs. Trade-offs between pairs of objectives are demonstrated among the models. The value of an objective function for a given design is shown to correspond to the ability of a design to actually meet an objective.

Water Resources Research↗
USGS2010

Particle velocity interpolation in block-centered finite difference groundwater flow models

A block-centered, finite difference model of two-dimensional groundwater flow yields velocity values at the midpoints of interfaces between adjacent blocks. Method of characteristics, random walk and particle-tracking models of solute transport require velocities at arbitrary particle locations within the finite difference grid. Particle path lines and travel times are sensitive to the spatial interpolation scheme employed, particularly in heterogeneous aquifers. This paper briefly reviews linear and bilinear interpolation of velocity and introduces a new interpolation scheme. Linear interpolation of velocity is consistent with the numerical solution of the flow equation and preserves discontinuities in velocity caused by abrupt (blocky) changes in transmissivity or hydraulic conductivity. However, linear interpolation yields discontinuous and somewhat unrealistic velocities in homogeneous aquifers. Bilinear interpolation of velocity yields continuous and realistic velocities in homogeneous and smoothly heterogeneous aquifers but does not preserve discontinuities in velocity at abrupt transmissivity boundaries. The new scheme uses potentiometric head gradients and offers improved accuracy for nonuniform flow in heterogeneous aquifers with abrupt changes in transmissivity. The new scheme is equivalent to bilinear interpolation in homogeneous media and is equivalent to linear interpolation where gradients are uniform. Selecting the best interpolation scheme depends, in part, on the conceptualization of aquifer heterogeneity, that is, whether changes in transmissivity occur abruptly or smoothly.

Water Resources Research↗
USGS2010

Characterization of transport in an acidic and metal-rich mountain stream based on a lithium tracer injection and simulations of transient storage

Physical parameters characterizing solute transport in the Snake River (an acidic and metal-rich mountain stream near Montezuma, Colorado) were variable along a 5.2-km study reach. Stream cross-sectional area and volumetric inflow each varied by a factor of 3. Because of transient storage, the residence time of injected tracers in the Snake River was longer than would be calculated by consideration of convective travel time alone. Distributed inflows along the stream were a significant source of in-stream chemical variations. These transport characteristics of the Snake River were established on the basis of the assumption of lithium as an ideally conservative tracer and use of simulations of advection, dispersion, and transient storage. Evaluations of the validity of this combined tracer and simulation approach lend confidence to the estimation of the physical transport parameters, but further development is warranted for methods of onsite transport experimentation in hydrologically complex, chemically reactive environments.

Water Resources Research↗
USGS2010

Application of the Stefan-Maxwell Equations to determine limitations of Fick's law when modeling organic vapor transport in sand columns

The organic component of the vapor phase of a porous medium contaminated by an immiscible organic liquid can be significant enough to violate the condition of a dilute species diffusing in a bulk phase assumed by Fick's law. The Stefan-Maxwell equations provide a more comprehensive model for quantifying steady state transport for a vapor phase composed of arbitrary proportions of its constituents. The application of both types of models to the analysis of column experiments demonstrates that use of a Fickian-based transport model can lead to significant overestimates of soil tortuosity constants. Further, the physical displacement of naturally occurring gases (e.g., O 2 ), predicted by the Stefan-Maxwell model but not by application of Fick's Law, can be attributed improperly to a sink term such as microbial degradation in a Fickian-based transport model.

Water Resources Research↗
USGS2010

A multilayered sharp interface model of coupled freshwater and saltwater flow in coastal systems: Model development and application

A quasi three-dimensional, finite difference model, that simulates freshwater and saltwater flow separated by a sharp interface, has been developed to study layered coastal aquifer systems. The model allows for regional simulation of coastal groundwater conditions, including the effects of saltwater dynamics on the freshwater system. Vertically integrated freshwater and saltwater flow equations incorporating the interface boundary condition are solved within each aquifer. Leakage through confining layers is calculated by Darcy's law, accounting for density differences across the layer. The locations of the interface tip and toe, within grid blocks, are tracked by linearly extrapolating the position of the interface. The model has been verified using available analytical solutions and experimental results. Application of the model to the Soquel-Aptos basin, Santa Cruz County, California, illustrates the use of the quasi three-dimensional, sharp interface approach for the examination of freshwater-saltwater dynamics in regional systems. Simulation suggests that the interface, today, is still responding to long-term Pleistocene sea level fluctuations and has not achieved equilibrium with present day sea level conditions.

Water Resources Research↗
USGS2010

An efficient deterministic-probabilistic approach to modeling regional groundwater flow: 1. Theory

An efficient probabilistic model is developed and cascaded with a deterministic model for predicting water table elevations in regional aquifers. The objective is to quantify model uncertainty where precise estimates of water table elevations may be required. The probabilistic model is based on the two-point probability method which only requires prior knowledge of uncertain variables mean and coefficient of variation. The two-point estimate method is theoretically developed and compared with the Monte Carlo simulation method. The results of comparisons using hypothetical determinisitic problems indicate that the two-point estimate method is only generally valid for linear problems where the coefficients of variation of uncertain parameters (for example, storage coefficient and hydraulic conductivity) is small. The two-point estimate method may be applied to slightly nonlinear problems with good results, provided coefficients of variation are small. In such cases, the two-point estimate method is much more efficient than the Monte Carlo method provided the number of uncertain variables is less than eight.

Water Resources Research↗
USGS2010

An efficient deterministic-probabilistic approach to modeling regional groundwater flow: 2. Application to Owens Valley, California

The applicability of a deterministic-probabilistic model for predicting water tables in southern Owens Valley, California, is evaluated. The model is based on a two-layer deterministic model that is cascaded with a two-point probability model. To reduce the potentially large number of uncertain variables in the deterministic model, lumping of uncertain variables was evaluated by sensitivity analysis to reduce the total number of uncertain variables to three variables: hydraulic conductivity, storage coefficient or specific yield, and source-sink function. Results demonstrate that lumping of uncertain parameters reduces computational effort while providing sufficient precision for the case studied. Simulated spatial coefficients of variation for water table temporal position in most of the basin is small, which suggests that deterministic models can predict water tables in these areas with good precision. However, in several important areas where pumping occurs or the geology is complex, the simulated spatial coefficients of variation are over estimated by the two-point probability method.

California↗
USGS2010

Comparison of Darcian flow in corresponding flat and folded surfaces

F olds of aquifers are rarely accounted for in models of groundwater flow. To account for aquifer folds in groundwater flow models, the equation describing Darcian flow in a general surface is derived. The equation is used to calculate steady state hydraulic head distributions for corresponding folded and flat surfaces. Each flat surface has the same hydraulic conductivity distribution and boundary condition as the corresponding folded surface. The folded surfaces have folds similar to the folds of selected aquifers and have folds that have much larger changes in slope. The largest difference in hydraulic head caused by all folding is only about 0.5% of the largest difference in hydraulic head across each surface. Because of the smaller areal extent and the fact that the effect of a sequence of folds is not cumulative, the minor folds do not generate substantially larger hydraulic head differences than the major folds.

Water Resources Research↗
USGS2010

Response of the water level in a well to Earth tides and atmospheric loading under unconfined conditions

The response of the water level in a well to Earth tides and atmospheric loading under unconfined conditions can be explained if the water level is controlled by the aquifer response averaged over the saturated depth of the well. Because vertical averaging tends to diminish the influence of the water table, the response is qualitatively similar to the response of a well under partially confined conditions. When the influence of well bore storage can be ignored, the response to Earth tides is strongly governed by a dimensionless aquifer frequency Q ′ u . The response to atmospheric loading is strongly governed by two dimensionless vertical fluid flow parameters: a dimensionless unsaturated zone frequency, R , and a dimensionless aquifer frequency Q u . The differences between Q ′ u and Q u are generally small for aquifers which are highly sensitive to Earth tides. When Q ′ u and Q u are large, the response of the well to Earth tides and atmospheric loading approaches the static response of the aquifer under confined conditions. At small values of Q ′ u and Q u , well response to Earth tides and atmospheric loading is strongly influenced by water table drainage. When R is large relative to Q u , the response to atmospheric loading is strongly influenced by attenuation and phase shift of the pneumatic pressure signal in the unsaturated zone. The presence of partial penetration retards phase advance in well response to Earth tides and atmospheric loading. When the theoretical response of a phreatic well to Earth tides and atmospheric loading is fit to the well response inferred from cross-spectral estimation, it is possible to obtain estimates of the pneumatic diffusivity of the unsaturated zone and the vertical hydraulic conductivity of the aquifer.

Water Resources Research↗
USGS2010

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

Water Resources Research↗
USGS2010

Solute transport with multisegment, equilibrium-controlled reactions: A feed forward simulation method

The feed forward method (FF method) is one of the ways of formulating operational equations which simulate transport of solutes influenced by equilibrium-controlled reaction networks. The FF method provides increased solution efficiency by adapting its formulations to some of the network's fundamental features. In this study the FF method is further developed by adapting and testing it for a variety of network conditions. Classes of homogeneous, classical heterogeneous, and ion exchange network segments are studied. Networks may contain only a single class of segments or they may involve two or three segment classes. The FF method is found applicable to all the cases tested. In only one of these cases, for the more complex configurations of network segments, the FF method does not attain all of its objectives. A systematic, stepwise approach to method development is employed. It reveals, for certain subnetworks, an a priori inadmissibility, irrespective of the method used, and, for some other networks, an a priori irrelevance to transport dynamics. It also demonstrates that when certain subnetworks, belonging to different segment classes, form a single network, synergism (or antagonism) may occasionally arise and decrease (or increase) the difficulty of solving the transport problem.

Water Resources Research↗