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At least 1,063 records · Page 59Linked to original sources
USGS2010

Convergent radial dispersion: A Laplace transform solution for aquifer tracer testing

A Laplace transform solution was obtained for the injection of a tracer in a well situated in a homogeneous aquifer where steady, horizontal, radially convergent flow has been established due to pumping at a second well. The standard advection-dispersion equation for mass transfer was used as the controlling equation. For boundary conditions, mass balances that account for mixing of the tracer with the fluid residing in the injection and pumped wells were used. The derived solution, which can be adapted for either resident or flux-averaged concentration, is of practical use only for the pumped well. This problem is of interest because it is easily applied to field determination of aquifer dispersivity and effective porosity. Breakthrough curves were obtained by numerical inversion of the Laplace transform solution. It was found that tracer mixing with fluid in the pumped and injection wells, especially in low-porosity aquifers, may have a significant influence on the shape of the tracer breakthrough curves.

Water Resources Research↗
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: 1. Problems and concepts

Intracell flow is important in modeling cells that contain both sources and sinks. Special attention is needed if recharge through the water table is a source. One method of modeling multiple sources and sinks is to determine the net recharge per cell. For example, for a model cell containing both a sink and recharge through the water table, the amount of recharge should be reduced by the ratio of the area of influence of the sink within the cell to the area of the cell. The reduction is the intercepted portion of the recharge. In a multilayer model this amount is further reduced by a proportion factor, which is a function of the depth of the flow lines from the water table boundary to the internal sink. A gaining section of a stream is a typical sink. The aquifer contribution to a gaining stream can be conceptualized as having two parts; the first part is the intercepted lateral flow from the water table and the second is the flow across the streambed due to differences in head between the water level in the stream and the aquifer below. The amount intercepted is a function of the geometry of the cell, but the amount due to difference in head across the stream bed is largely independent of cell geometry. A discharging well can intercept recharge through the water table within a model cell. The net recharge to the cell would be reduced in proportion to the area of influence of the well within the cell. The area of influence generally changes with time. Thus the amount of intercepted recharge and net recharge may not be constant with time. During periods when the well is not discharging there will be no intercepted recharge even though the area of influence from previous pumping may still exist. The reduction of net recharge per cell due to internal interception of flow will result in a model-calculated mass balance less than the prototype. Additionally the “effective transmissivity” along the intercell flow paths may be altered when flow paths are occupied by intercepted recharge.

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 channel dynamics model for real-time flood forecasting

A new channel dynamics scheme (alternative system predictor in real time (ASPIRE)), designed specifically for real-time river flow forecasting, is introduced to reduce uncertainty in the forecast. ASPIRE is a storage routing model that limits the influence of catchment model forecast errors to the downstream station closest to the catchment. Comparisons with the Muskingum routing scheme in field tests suggest that the ASPIRE scheme can provide more accurate forecasts, probably because discharge observations are used to a maximum advantage and routing reaches (and model errors in each reach) are uncoupled. Using ASPIRE in conjunction with the Kalman filter did not improve forecast accuracy relative to a deterministic updating procedure. Theoretical analysis suggests that this is due to a large process noise to measurement noise ratio.

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

Assessing the validity of the channel model of fracture aperture under field conditions

I n recent investigations of fluid and solute movement in discrete fractures, spatial heterogeneity of the fracture aperture has been conceptualized as a series of noninterconnecting constant aperture flow paths, or channels. Two methods of estimating the distribution of the aperture sizes are presented using information from a single-hole pumping test and a radially converging tracer test. The first method uses the transmissivity of the fracture and mean arrival time of the tracer, while the second method uses the mean and variance of the solute arrival time. If the fracture can be conceptualized as a series of nonintersecting flow paths of constant aperture, the two methods should yield identical estimates for the parameters of the distribution. The validity of the channel model can be assessed by comparing the parameters of the distribution that are estimated by the two methods. This technique was demonstrated using hydraulic and tracer tests conducted in a discrete, areally extensive, horizontal fracture in the Silurian dolomite in the northeastern Illinois. A lognormal and a truncated gamma distribution were used to describe the distribution of constant aperture flow paths. The lognormal distribution could not reproduce the abrupt rising limb and maximum rate of mass arrival that characterized the tracer tests. The gamma distribution more accurately predicted the shape of the breakthrough curves; however, the two methods of estimating the parameters of the distribution provided significantly different estimates of the variances of the aperture sizes. The mean aperture as estimated by the two methods was similar. The difference in the variance of the aperture as estimated by the two methods indicates that alternative conceptual models of aperture heterogeneity are required to more accurately describe both fluid and solute movement in this field situation.

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

Dune migration in a steep, coarse-bedded stream

During 1986 and 1987, migrating bed forms composed of coarse sand and fine gravel ( d 50 =1.8 to 9.1 mm) were documented in the North Fork Toutle River at Kid Valley, Washington, at flow velocities ranging from 1.6 to 3.4 m s −1 and depths of 0.8 to 2.2 m. The bed forms (predominantly lower regime dunes) were studied with a sonic depth sounder transducer suspended in the river at a stationary point. Twelve temporal depth-sounding records were collected during storm runoff and nearly steady, average streamflow, with record durations ranging from 37 to 261 min. Waveform height was defined by dune front heights, which ranged from 12 to 70 cm. A weak correlation between flow depth and the standard deviation of bed elevation was noted. Dune front counts and spectral analyses of the temporal records showed that dune crests passed the observation point every 2 to 5 min. Dunes were often superposed on larger bed forms with wave periods between 10 and 30 min. Gradual changes in waveform height and periodicity occurred over several hours during storm runoff. The processes of dune growth and decay were both time-dependent and affected by changes in streamflow. Rates of migration for typical dunes were estimated to be 3 cm s −1 , and dune wavelengths were estimated to be 6 to 7 m.

Washington↗
USGS2010

Estimating constituent loads

Several recent articles have called attention to the problem of retransformation bias, which can arise when log linear regression models are used to estimate sediment or other constituent loads. In some cases the bias can lead to underestimation of constituent loads by as much as 50%, and several procedures have been suggested for reducing or eliminating it. However, some of the procedures recommended for reducing the bias can actually increase it. This paper compares the bias and variance of three procedures that can be used with log linear regression models: the traditional rating curve estimator, a modified rating curve method, and a minimum variance unbiased estimator (MVUE). Analytical derivations of the bias and efficiency of all three estimators are presented. It is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates. However, other conditions exist where they have substantial bias and a large mean square error. These conditions commonly occur when sample sizes are small, or when loads are estimated during high-flow conditions. The MVUE, however, is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct. Since an efficient unbiased estimator is available, there seems to be no reason to employ biased estimators.

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

Circular convection during subsurface injection of liquid waste, St. Petersburg, Florida

I njection of liquid waste into a highly transmissive, saltwater-bearing, fractured dolomite underlying the city of St. Petersburg, Florida, provided an opportunity to study density-dependent flow associated with two miscible and density-different liquids. The injection zone was 98 m thick with a radial hydraulic conductivity of 762 m/d and a vertical hydraulic conductivity of 152 m/d. Mean chloride concentrations of the injectant during two tests of 91 and 366 days duration were 180 and 170 mg/L, respectively, whereas chloride concentration of native salt water ranged from 19,000 to 20,000 mg/L. During the 366-day test, chloride concentration in water from a well open to the upper part of the injection zone 223 m from the injection well approximately stabilized at about 4000 mg/L. Relatively constant chloride concentrations in water from this observation well at a level significantly greater than the injectant concentration suggested the hypothesis that circular convection with saltwater flow added chloride ions to the injection zone flow sampled at the observation well. In order to assess the acceptability of the circular convection hypothesis, information was required about the velocity field during injection. Mass transport model simulations were used to provide this information, after determining that the fractured injection zone could be treated as an equivalent porous medium with a single porosity. The mass transport model was calibrated using the 91-day test data from two observation wells 223 m from the injection well. The model was then run without parameter changes to simulate the 366-day test. Mass fractions of injectant computed for four observation wells during the 366-day test compared favorably with observed mass fractions. Observed mass fractions were calculated as a function of chloride concentration and density. Comparisons between model-computed mass fraction and velocity fields in a radial section showed circular convection, with salt water flowing toward the injection well in the lower part of the injection zone. The salt water then mixed with the injectant, and the mixture flowed away from the injection well in the upper part of the injection zone. On the basis of the model results and the assumed reasonableness of treating the injection zone as an equivalent porous medium with a single porosity, the hypothesis of circular convection with saltwater flow during subsurface injection of liquid waste into a highly transmissive saltwater-bearing fractured dolomite was judged acceptable.

Florida↗
USGS2010

Speciation and equilibrium relations of soluble aluminum in a headwater stream at base flow and during rain events

In a small watershed in the Shenandoah National Park, Virginia, the short-term dynamics of soluble aluminum in stream water sampled during rain events differed significantly from stream water sampled during base flow conditions. Three fractions of dissolved aluminum were measured. The inorganic monomeric fraction made up approximately two thirds of the total reactive aluminum at base flow, followed by the acid-soluble and organic monomeric fractions, respectively. Equilibrium modeling showed that hydroxide complexes were the most abundant form of inorganic monomeric aluminum followed by fluoride, free aluminum ion, and sulfate. The activity of inorganic monomeric aluminum at base flow appears to be in equilibrium with an Al(OH) 3 phase with solubility intermediate between microcrystalline gibbsite and natural gibbsite. During two rain events, the concentration of all three aluminum fractions increased significantly. Available chemical evidence indicates that acidic soil water was the primary source of dissolved aluminum. As flow increased, the Al(OH) 3 saturation index in the stream water increased significantly. The primary cause of the transient increase in the Al(OH) 3 saturation index appears to have been the neutralization of excess H + added by soil water through reaction with stream water HCO 3 − at a more rapid rate than excess inorganic monomeric aluminum could be removed from solution by hydroxide mineral precipitation. A soil water/stream water mixing model was developed based on measured changes of stream water alkalinity, silica concentration, and charge imbalance during the rain events. Model results indicate that a small amount of soil water (3–11%) was present in the stream at peak stage.

Virginia↗
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

Interpretation of oscillatory water levels in observation wells during aquifer tests in fractured rock

Oscillatory water levels in observation wells have commonly been recorded at the beginning of aquifer tests in highly transmissive fractured formations. In this paper, oscillatory water levels are predicted by the equations coupling the fluid movement in the observation well and the fluid movement in the surrounding formation. The equivalent-porous medium and dual-porosity models of fractured rock are two models considered in this analysis; however, other conceptual models of fractured media can also be coupled with the model presented here for fluid movement in the observation well. Type curves for the response of water levels in observation wells due to pumping in another well are generated by numerical inversion of the Laplace transform solution to the governing equations. Overdamped conditions, where inertial effects are insignificant, and underdamped conditions, where oscillations arise, are predicted by the solution to the governing equations. By matching water level measurements with the appropriate type curve, a conceptual model of the formation can be identified, and aquifer properties can be estimated. This analysis is applied in the interpretation of an aquifer test conducted in a fractured dolomite in northeastern Illinois. If the early time oscillations are ignored, the measured water levels can be explained by an equivalent-porous medium model. By analyzing the early time oscillations, however, the formation is shown to respond as a dual-porosity medium with a storativity of the fracture porosity that is an order of magnitude smaller than the storativity estimated from the equivalent-porous medium model.

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

Kinetically influenced terms for solute transport affected by heterogeneous and homogeneous classical reactions

Simulation of transport affected by heterogeneous or homogeneous reversible reactions requires a choice between local equilibrium-based and kinetics-based models. The error associated with the use of equilibrium-based models is equivalent to the error of neglecting certain mathematical terms in the governing kinetics-based transport equations. Identification and evaluation of these kinetically influenced terms can therefore aid in the development of criteria for applicability of local equilibrium- based transport models. This paper extends a four-step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions (solution phase complex formation or oxidation-reduction) and/or precipitation-dissolution reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation-dissolution reaction are used to demonstrate the nature of departures from equilibrium-controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes.

Water Resources Research↗