Documentation of computer program VS2Dh for simulation of energy transport in variably saturated porous media: Modification of the US Geological Survey's computer program VS2DT
No abstract available.
Water-Resources Investigations Report↗
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Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions
Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.
Water Resources Research↗
Role of chemotaxis in the transport of bacteria through saturated porous media
Populations of chemotactic bacteria are able to sense and respond to chemical gradients in their surroundings and direct their migration toward increasing concentrations of chemicals that they perceive to be beneficial to their survival. It has been suggested that this phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to the chemical contaminants that they degrade. To determine the significance of chemotaxis in these processes it is necessary to quantify the magnitude of the response and compare it to other groundwater processes that affect the fate and transport of bacteria. We present a systematic approach toward quantifying the chemotactic response of bacteria in laboratory scale experiments by starting with simple, well-defined systems and gradually increasing their complexity. Swimming properties of individual cells were assessed from trajectories recorded by a tracking microscope. These properties were used to calculate motility and chemotaxis coefficients of bacterial populations in bulk aqueous media which were compared to experimental results of diffusion studies. Then effective values of motility and chemotaxis coefficients in single pores, pore networks and packed columns were analyzed. These were used to estimate the magnitude of the chemotactic response in porous media and to compare with dispersion coefficients reported in the field. This represents a compilation of many studies over a number of years. While there are certainly limitations with this approach for ultimately quantifying motility and chemotaxis in granular aquifer media, it does provide insight into what order of magnitude responses are possible and which characteristics of the bacteria and media are expected to be important.
Advances in Water Resources↗
Behavior of sensitivities in the one-dimensional advection-dispersion equation: Implications for parameter estimation and sampling design
The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one-dimensional form of the advection-dispersion equation. When parameters are estimated in regression models of one-dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) Information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance. (3) The frequency of sampling must be “in phase” with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters. (8) The time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system.
Water Resources Research↗
Hydrocarbon lakes on Titan: Distribution and interaction with a porous regolith
Synthetic Aperture Radar (SAR) images of Titan's north polar region reveal quasi‐circular to complex features which are interpreted to be liquid hydrocarbon lakes. We investigate methane transport in Titan's hydrologic cycle using the global distribution of lake features. As of May 2007, the SAR data set covers ∼22% of the surface and indicates multiple lake morphologies which are correlated across the polar region. Lakes are limited to latitudes above 55°N and vary from <10 to more than 100,000 km 2 . The size and location of lakes provide constraints on parameters associated with subsurface transport. Using porous media properties inferred from Huygens probe observations, timescales for flow into and out of observed lakes are shown to be in the tens of years, similar to seasonal cycles. Derived timescales are compared to the time between collocated SAR observations in order to consider the role of subsurface transport in Titan's hydrologic cycle.
Geophysical Research Letters↗
Simulation of the regional groundwater-flow system of the Menominee Indian Reservation, Wisconsin
A regional, two-dimensional, steady-state groundwater-flow model was developed to simulate the groundwater-flow system and groundwater/surface-water interactions within the Menominee Indian Reservation. The model was developed by the U.S. Geological Survey (USGS), in cooperation with the Menominee Indian Tribe of Wisconsin, to contribute to the fundamental understanding of the region’s hydrogeology. The objectives of the regional model were to improve understanding of the groundwater-flow system, including groundwater/surface-water interactions, and to develop a tool suitable for evaluating the effects of potential regional water-management programs. The computer code GFLOW was used because of the ease with which the model can simulate groundwater/surface-water interactions, provide a framework for simulating regional groundwater-flow systems, and be refined in a stepwise fashion to incorporate new data and simulate groundwater-flow patterns at multiple scales. Simulations made with the regional model reproduce groundwater levels and stream base flows representative of recent conditions (1970–2013) and illustrate groundwater-flow patterns with maps of (1) the simulated water table and groundwater-flow directions, (2) probabilistic areas contributing recharge to high-capacity pumped wells, and (3) estimation of the extent of infiltrated wastewater from treatment lagoons. The groundwater-flow model described in this report simulates the major hydrogeologic features of the modeled area, including surficial unconsolidated aquifers, groundwater/surface-water interactions, and groundwater withdrawals from existing high-capacity production wells. Areas contributing recharge to pumped high-capacity wells on the Menominee Indian Reservation were delineated by tracking simulated water particles from the water table to wells in combination with Monte Carlo techniques, and maps of the probability of capture for each well nest were produced. Groundwater-agebased areas contributing recharge to wells were simulated by using the calibrated set of parameters and porosity values adjusted to account for bias in simulated saturated thickness. Simulations were performed for current (2013) pumping rates. The simulations show a range in sensitivity of the simulated areas contributing recharge to wells given the parameters evaluated through the Monte Carlo analysis. The areas contributing recharge to supply wells for the villages of Zoar and Neopit are long and narrow, with a sharp gradation from high to low probability of capture. The areas contributing recharge to supply wells for Middle Village and the village of Keshena exhibit a sharp gradation from high to low probability over a relatively small area between the well and a local groundwater mound. The highest probability areas contributing recharge to the supply wells for the Villages of Onekewat and Redwing are in the immediate vicinity of the wells. These wells also have an extensive area with low probability for capturing water that is likely due to a locally low hydraulic gradient and the large degree of uncertainty associated with the lakebed resistance parameters that control interaction between groundwater and local lakes. Additional field investigations and associated local model refinements would facilitate further reductions in uncertainty associated with simulated areas contributing recharge to the wells. The likely extent of the Neopit wastewater plume was simulated by using the groundwater-flow model and Monte Carlo techniques to evaluate the sensitivity of predictive simulations to a range of model parameter values. Wastewater infiltrated from the currently operating lagoons flows predominantly south toward Tourtillotte Creek. Some of the infiltrated wastewater is simulated as having a low probability of flowing beneath Tourtillotte Creek to the nearby West Branch Wolf River. Results for the probable extent of the wastewater plume are considered to be qualitative because the method only considers advective flow and does not account for processes affecting contaminant transport in porous media. Therefore, results for the probable extent of the wastewater plume are sensitive to the number of particles used to represent flow from the lagoon and the resolution of a synthetic grid used for the analysis. Nonetheless, it is expected that the qualitative results may be of use for identifying potential downgradient areas of concern that can then be evaluated using the quantitative “area contributing recharge to wells” method or traditional contaminant-transport simulations.
Wisconsin↗
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↗
Fate and transport of bacteria injected into aquifers
Advances in our understanding of the fate and transport of bacteria introduced into aquifers, including the potential use of genetically engineered bacteria for biorestoration, are highlighted by new findings in the following areas: modeling of bacterial attachment during transport through porous media, the long-term survival of a chlorobenzoate-degrading bacterium injected into a contaminated sandy aquifer, and molecular techniques that may be used in tracking genetically engineered bacteria in groundwater environments.
Current Opinion in Biotechnology↗
Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry
A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)
Water-Resources Investigations Report↗
Use of a reactive gas transport model to determine rates of hydrocarbon biodegradation in unsaturated porous media
A mathematical model is presented that simulates the transport and reaction of any number of gaseous phase constituents (e.g. CO 2 , O 2 , N 2 , and hydrocarbons) in unsaturated porous media. The model was developed as part of a method to determine rates of hydrocarbon biodegradation associated with natural cleansing at petroleum product spill sites. The one-dimensional model can be applied to analyze data from column experiments or from field sites where gas transport in the unsaturated zone is approximately vertical. A coupled, non-Fickian constitutive relation between fluxes and concentration gradients, together with the capability of incorporating heterogeneity with respect to model parameters, results in model applicability over a wide range of experimental and field conditions. When applied in a calibration mode, the model allows for the determination of constituent production/consumption rates as a function of the spatial coordinate. Alternatively, the model can be applied in a predictive mode to obtain the distribution of constituent concentrations and fluxes on the basis of assumed values of model parameters and a biodegradation hypothesis. Data requirements for the model are illustrated by analyzing data from a column experiment designed to determine the aerobic degradation rate of toluene in sediments collected from a gasoline spill site in Galloway Township, New Jersey.
Water Resources Research↗
Nitrate transport and transformation processes in unsaturated porous media
A series of experiments was conducted on two contrasting agricultural soils to observe the influence of soil texture, preferential flow, and plants on nitrate transport and denitrification under unsaturated conditions. Calcium nitrate fertilizer was applied to the surface of four large undisturbed soil cores (30 cm diameter by 40 cm height). Two of the cores were a structured clay obtained from central Missouri and two were an unstructured fine sand obtained from central Florida. The cores were irrigated daily and maintained at a matric potential of -20 kPa, representative of soil tension in the rooting zone of irrigated agricultural fields. Volumetric water content (θ), concentration of nitrate-N in the soil solution, and nitrous oxide flux at the surface, 10, 20, and 30 cm were monitored daily. Leaching loss of surface-applied N0 3 − -N was significant in both the sand and the clay. In unplanted sand cores, almost all of the applied nitrate was leached below 30 cm within 10 days. Gaseous N loss owing to denitrification was no greater than 2% of the nitrate-N applied to the unplanted sand cores and, in general, was less than 1 %. Although leaching was somewhat retarded in the clay cores, about 60% of the applied nitrate-N was leached from the unplanted clay soil in 5–6 weeks. Under unsaturated conditions, the clay had little to no tendency to denitrify despite the greater moisture content of the clay and retarded leaching of nitrate in the clay. The planted sand cores had surprisingly large gaseous N loss owing to denitrification, as much as 17% of the nitrate-N. Results from both the clay and sand experiments show that the dynamics of nitrate transport and transformation in unsaturated soils are affected by small, localized variations in the soil moisture content profile, the gaseous diffusion coefficient of the soil, the rate at which the nitrate pulse passes through the soil, the solubility of N 2 O and N 2 and the diffusion of the gasses through the soil solution, and development of a water content profile in the soil. Limited dentrification in the clay soil was due to a limited volume of soil available for infiltration after internal catchment and the development of denitrifying conditions resulting from the presence of an extensive macropore system.
Journal of Hydrology↗
Modeling variably saturated multispecies reactive groundwater solute transport with MODFLOW-UZF and RT3D
A numerical model was developed that is capable of simulating multispecies reactive solute transport in variably saturated porous media. This model consists of a modified version of the reactive transport model RT3D (Reactive Transport in 3 Dimensions) that is linked to the Unsaturated-Zone Flow (UZF1) package and MODFLOW. Referred to as UZF-RT3D, the model is tested against published analytical benchmarks as well as other published contaminant transport models, including HYDRUS-1D, VS2DT, and SUTRA, and the coupled flow and transport modeling system of CATHY and TRAN3D. Comparisons in one-dimensional, two-dimensional, and three-dimensional variably saturated systems are explored. While several test cases are included to verify the correct implementation of variably saturated transport in UZF-RT3D, other cases are included to demonstrate the usefulness of the code in terms of model run-time and handling the reaction kinetics of multiple interacting species in variably saturated subsurface systems. As UZF1 relies on a kinematic-wave approximation for unsaturated flow that neglects the diffusive terms in Richards equation, UZF-RT3D can be used for large-scale aquifer systems for which the UZF1 formulation is reasonable, that is, capillary-pressure gradients can be neglected and soil parameters can be treated as homogeneous. Decreased model run-time and the ability to include site-specific chemical species and chemical reactions make UZF-RT3D an attractive model for efficient simulation of multispecies reactive transport in variably saturated large-scale subsurface systems.
Ground Water↗
Transport of microorganisms in the terrestrial subsurface: In situ and laboratory methods
This chapter describes and discusses laboratory and field techniques for studying microbial transport behavior in aquifer materials and model porous media. Changes in ionic strength (I) during transport studies may occur inadvertently as a result of using halides as conservative tracers and may lead to density-induced sinking of the tracer cloud. Substantive increases in I as a result of injection of high concentrations of halide tracers can also result in overestimations of microbial attachment. In order to differentiate "test" microorganisms from indigenous subsurface populations and/or from other inadvertently introduced populations, microorganisms used in laboratory or in situ transport tests are typically labeled a priori with a stable tag. Other methods of labeling microorganisms for use in in situ and column transport studies have involved the use of stable isotopes ratio mass spectrometry (IRMS). The characteristics of the conservative tracer breakthrough curve can then be used comparatively to determine some of the major transport parameters exhibited by the introduced microorganisms. Most controlled field investigations of subsurface microbial transport are conducted on limited spatial scales relative to the scales of interest to those concerned with pathogen transport to water supply wells, with microbially enhanced oil recovery from petroleum reservoirs, and with the feasibility of using introduced bacteria for aquifer restoration.
Book chapter↗
Simulating water, solute, and heat transport in the subsurface with the VS2DI software package
The software package VS2DI was developed by the U.S. Geological Survey for simulating water, solute, and heat transport in variably saturated porous media. The package consists of a graphical preprocessor to facilitate construction of a simulation, a postprocessor for visualizing simulation results, and two numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). The finite-difference method is used to solve the Richards equation for flow and the advection-dispersion equation for solute or heat transport. This study presents a brief description of the VS2DI package, an overview of the various types of problems that have been addressed with the package, and an analysis of the advantages and limitations of the package. A review of other models and modeling approaches for studying water, solute, and heat transport also is provided. ?? Soil Science Society of America. All rights reserved.
Vadose Zone Journal↗
Determination of water retention in stratified porous materials
Predicted and measured water-retention values, θ ( ψ ), were compared for repacked, stratified core samples consisting of either a sand with a stone-bearing layer or a sand with a clay loam layer in various spatial orientations. Stratified core samples were packed in submersible pressure outflow cells, then water-retention measurements were performed between matric potentials, ψ , of 0 to -100 kPa. Predictions of θ ( ψ ) were based on a simple volume-averaging model using estimates of the relative fraction and θ ( ψ ) values of each textural component within a stratified sample. In general, predicted θ ( ψ ) curves resembled measured curves well, except at higher saturations in a sample consisting of a clay loam layer over a sand layer. In this case, the model averaged the air-entry of both materials, while the air-entry of the sample was controlled by the clay loam in contact with the cell's air-pressure inlet. In situ, avenues for air-entry generally exist around clay layers, so that the model should adequately predict air-entry for stratified formations regardless of spatial orientation of fine versus coarse layers. Agreement between measured and predicted volumetric water contents, θ , was variable though encouraging, with mean differences between measured and predicted θ values in the range of 10%. Differences in θ of this magnitude are expected due to variability in pore structure between samples, and do not indicate inherent problems with the volume averaging model. This suggets that explicit modeling of stratified formations through detailed characterization of the stratigraphy has the potential of yielding accurate θ ( ψ ) values. However, hydraulic-equilibration times were distinctly different for each variation in spatial orientation of textural layering, indicating that transient behavior during drainage in stratified formations is highly sensitive to the stratigraphic sequence of textural components, as well as the volume fraction of each textural component in a formation. This indicates that prolonged residence times of water, nutrients, and pollutants are likely within finer-textured layers, when ψ conditions have resulted in drainage of underlying coarser-textured strata.
Transport in Porous Media↗
Applying dispersive changes to Lagrangian particles in groundwater transport models
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.
Transport in Porous Media↗
Effects of clay dispersion on aquifer storage and recovery in coastal aquifers
Cyclic injection, storage, and withdrawal of freshwater in brackish aquifers is a form of aquifer storage and recovery (ASR) that can beneficially supplement water supplies in coastal areas. A 1970s field experiment in Norfolk, Virginia, showed that clay dispersion in the unconsolidated sedimentary aquifer occurred because of cation exchange on clay minerals as freshwater displaced brackish formation water. Migration of interstitial clay particles clogged pores, reduced permeability, and decreased recovery efficiency, but a calcium preflush was found to reduce clay dispersion and lead to a higher recovery efficiency. Column experiments were performed in this study to quantify the relations between permeability changes and clay mineralogy, clay content, and initial water salinity. The results of these experiments indicate that dispersion of montmorillonite clay is a primary contributor to formation damage. The reduction in permeability by clay dispersion may be expressed as a linear function of chloride content. Incorporating these simple functions into a radial, cross-sectional, variable-density, ground-water flow and transport model yielded a satisfactory simulation of the Norfolk field test - and represented an improvement over the model that ignored changes in permeability. This type of model offers a useful planning and design tool for ASR operations in coastal clastic aquifer systems.
Transport in Porous Media↗
Chemical reactions simulated by ground-water-quality models
Recent literature concerning the modeling of chemical reactions during transport in ground water is examined with emphasis on sorption reactions. The theory of transport and reactions in porous media has been well documented. Numerous equations have been developed from this theory, to provide both continuous and sequential or multistep models, with the water phase considered for both mobile and immobile phases. Chemical reactions can be either equilibrium or non-equilibrium, and can be quantified in linear or non-linear mathematical forms. Non-equilibrium reactions can be separated into kinetic and diffusional rate-limiting mechanisms. Solutions to the equations are available by either analytical expressions or numerical techniques. Saturated and unsaturated batch, column, and field studies are discussed with one-dimensional, laboratory-column experiments predominating. A summary table is presented that references the various kinds of models studied and their applications in predicting chemical concentrations in ground waters.
Water Resources Bulletin↗