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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↗

Transport of viruses through saturated and unsaturated columns packed with sand

Laboratory-scale virus transport experiments were conducted in columns packed with sand under saturated and unsaturated conditions. The viruses employed were the male-specific RNA coliphage, MS2, and the Salmonella typhimurium phage, PRD1. The mathematical model developed by Sim and Chrysikopoulos (Water Resour Res 36:173–179, 2000) that accounts for processes responsible for removal of viruses during vertical transport in one-dimensional, unsaturated porous media was used to fit the data collected from the laboratory experiments. The liquid to liquid–solid and liquid to air–liquid interface mass transfer rate coefficients were shown to increase for both bacteriophage as saturation levels were reduced. The experimental results indicate that even for unfavorable attachment conditions within a sand column (e.g., phosphate-buffered saline solution; pH = 7.5; ionic strength = 2 mM), saturation levels can affect virus transport through porous media.

Transport in Porous Media↗

Arrival times and temporal moments of breakthrough curves for an imperfectly stratified aquifer

Using concepts developed in an earlier study, a solution in Laplace transform space is obtained for transport of resident concentration in an imperfectly but yet highly stratified porous medium. The flow field, into which an instantaneous pulse of tracer is injected, is taken to be steady and mean uniform parallel to the direction of stratification. From this transform-space solution either temporal moments can be derived by taking derivatives with respect to the Laplace parameter, or the transform-space solution can be inverted numerically to obtain breakthrough curves for the mean concentration. When compared to an equivalent solution with a Fickian dispersive flux, these temporal moments indicate the extent to which transport in heterogeneous porous media deviates from classical Fickian behavior. The numerical inversion of the Laplace transform solution gives partial breakthrough curves for the mean concentration which have the appearance of conflicting with the derived moment information. A hypothesis is put forth which resolves this apparent conflict; this hypothesis is verified by adding a component of local dispersion to the governing transport equation. On the basis of the flux-averaged concentration a form for the expected probability density function for the arrival time of a tracer particle is derived; arrival time moments and an arrival time cumulative distribution function are available as a consequence. Arrival time moments, as derived from the flux-averaged concentration, do not differ significantly from the resident moments, as derived from the resident concentration.

Water Resources Research↗

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↗

A comparison of two- and three-dimensional stochastic models of regional solute movement

Recent models of solute movement in porous media that are based on a stochastic description of the porous medium properties have been dedicated primarily to a three-dimensional interpretation of solute movement. In many practical problems, however, it is more convenient and consistent with measuring techniques to consider flow and solute transport as an areal, two-dimensional phenomenon. The physics of solute movement, however, is dependent on the three-dimensional heterogeneity in the formation. A comparison of two- and three-dimensional stochastic interpretations of solute movement in a porous medium having a statistically isotropic hydraulic conductivity field is investigated. To provide an equitable comparison between the two- and three-dimensional analyses, the stochastic properties of the transmissivity are defined in terms of the stochastic properties of the hydraulic conductivity. The variance of the transmissivity is shown to be significantly reduced in comparison to that of the hydraulic conductivity, and the transmissivity is spatially correlated over larger distances. These factors influence the two-dimensional interpretations of solute movement by underestimating the longitudinal and transverse growth of the solute plume in comparison to its description as a three-dimensional phenomenon. Although this analysis is based on small perturbation approximations and the special case of a statistically isotropic hydraulic conductivity field, it casts doubt on the use of a stochastic interpretation of the transmissivity in describing regional scale movement. However, by assuming the transmissivity to be the vertical integration of the hydraulic conductivity field at a given position, the stochastic properties of the hydraulic conductivity can be estimated from the stochastic properties of the transmissivity and applied to obtain a more accurate interpretation of solute movement. ?? 1990 Kluwer Academic Publishers.

Transport in Porous Media↗

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↗

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

Open-File Report↗

Stochastic analysis of transverse dispersion in density‐coupled transport in aquifers

Spectral perturbation techniques have been used previously to derive integral expressions for dispersive mixing in concentration‐dependent transport in three‐dimensional, heterogeneous porous media, where fluid density and viscosity are functions of solute concentration. Whereas earlier work focused on evaluating longitudinal dispersivity in isotropic media and incorporating the result in a mean one‐dimensional transport model, the emphasis of this paper is on evaluation of the complete dispersion tensor, including the more general case of anisotropic media. Approximate analytic expressions for all components of the macroscopic dispersivity tensor are derived, and the tensor is shown to be asymmetric. The tensor is separated into its symmetric and antisymmetric parts, where the symmetric part is used to calculate the principal components and principal directions of dispersivity, and the antisymmetric part of the tensor is shown to modify the velocity of the solute body compared to that of the background fluid. An example set of numerical simulations incorporating the tensor illustrates the effect of density‐coupled dispersivity on a sinking plume in an aquifer. The simulations show that the effective transverse vertical spreading in a sinking plume to be significantly greater than would be predicted by a standard density‐coupled transport model that does not incorporate the coupling in the dispersivity tensor.

Water Resources Research↗

Direct comparison of kinetic and local equilibrium formulations for solute transport affected by surface reactions

Modeling transport of reacting solutes in porous media often requires a choice between models based on the local equilibrium assumption (LEA) and models involving reaction kinetics. Direct comparison of the mathematical formulations for these two types of transport models can aid in this choice. For cases of transport affected by surface reaction, such a comparison is made possible by a new derivation procedure. This procedure yields a kinetics-based formulation that is the sum of the LEA formulation and one or more kinetically influenced terms. The dimensionless form of the new kinetics-based formulation facilitates identification of critical parameter groupings which control the approach to transport behavior consistent with LEA model predictions. Results of numerical experiments demonstrate that criteria for LEA applicability can be expressed conveniently in terms of these parameter groupings. The derivation procedure is demonstrated for examples of surface reactions including first-order reversible sorption, Langmuir-type kinetics and binary, homovalent ion exchange.

Water Resources Research↗

VS2DI: Model use, calibration, and validation

VS2DI is a software package for simulating water, solute, and heat transport through soils or other porous media under conditions of variable saturation. The package contains a graphical preprocessor for constructing simulations, a postprocessor for displaying simulation results, and numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). Flow is described by the Richards equation, and solute and heat transport are described by advection-dispersion equations; the finite-difference method is used to solve these equations. Problems can be simulated in one, two, or three (assuming radial symmetry) dimensions. This article provides an overview of calibration techniques that have been used with VS2DI; included is a detailed description of calibration procedures used in simulating the interaction between groundwater and a stream fed by drainage from agricultural fields in central Indiana. Brief descriptions of VS2DI and the various types of problems that have been addressed with the software package are also presented.

Transactions of the ASABE↗

Velocity modeling of supercritical pore fluids through porous media under reservoir conditions with applications for petroleum secondary migration and carbon sequestration plumes

Computational methods to characterize secondary migration in porous media traditionally rely on fluid transport equations with assumptions of time invariance, such as flowpath modeling of buoyancy vectors, statistical percolation algorithms, capillary pressure curves, or a form of Darcy’s Law which presumes instantaneous fluid transport. However, in petroleum systems modeling, the timeframe of secondary migration from source to reservoir is important to quantify in relation to other geologic factors such as timing of petroleum generation, fault movement, and seal formation. Additionally, quantifying migration velocities enables an estimation of the distance a plume of geologically sequestered carbon dioxide travels over time, as well as the identification of low-permeability strata appropriate for long-term containment. This study introduces a method to quantify transport velocities of supercritical fluids in low-permeability lithologies for a broad range of rock and fluid properties likely encountered in the sedimentary sequence. A time-dependent form of Darcy’s Law for pressure-driven viscous flow through homogeneous isotropic porous media was used to model flow velocities within a carrier bed. Thermodynamic equations of state were used to determine thermophysical properties of supercritical pore fluids under reservoir pressures ranging from 0–200 MPa (0–29,000 psi) to constrain the momentum equations. Three case studies were examined that (1) estimated fluid flow velocities of methane within the low-permeability Upper Jurassic Haynesville Formation, (2) defined permeability-based flow units to evaluate saline formations for long-term geologic carbon sequestration, and (3) calculated the migration distance of carbon dioxide plumes at the Decatur, Illinois injection and sequestration project.

SEG-AAPG Interpretation↗

Evaluation of the applicability of the dual‐domain mass transfer model in porous media containing connected high‐conductivity channels

This paper evaluates the dual‐domain mass transfer (DDMT) model to represent transport processes when small‐scale high‐conductivity (K) preferential flow paths (PFPs) are present in a homogenous porous media matrix. The effects of PFPs upon solute transport were examined through detailed numerical experiments involving different realizations of PFP networks, PFP/matrix conductivity contrasts varying from 10:1 to 200:1, different magnitudes of effective conductivities, and a range of molecular diffusion coefficients. Results suggest that the DDMT model can reproduce both the near‐source peak and the downstream low‐concentration spreading observed in the embedded dendritic network when there are large conductivity contrasts between high‐K PFPs and the low‐K matrix. The accuracy of the DDMT model is also affected by the geometry of PFP networks and by the relative significance of the diffusion process in the network‐matrix system.

Water Resources Research↗

Comparison of transport and attachment behaviors of Cryptosporidium parvum oocysts and oocyst-sized microspheres being advected through three minerologically different granular porous media

In order to gain more information about the fate of Cryptosporidium parvum oocysts in tropical volcanic soils, the transport and attachment behaviors of oocysts and oocyst-sized polystyrene microspheres were studied in the presence of two soils. These soils were chosen because of their differing chemical and physical properties, i.e., an organic-rich (43–46% by mass) volcanic ash-derived soil from the island of Hawaii, and a red, iron (22–29% by mass), aluminum (29–45% by mass), and clay-rich (68–76% by mass) volcanic soil from the island of Oahu. A third agricultural soil, an organic- (13% by mass) and quartz-rich (40% by mass) soil from Illinois, was included for reference. In 10-cm long flow-through columns, oocysts and microspheres advecting through the red volcanic soil were almost completely (98% and 99%) immobilized. The modest breakthrough resulted from preferential flow-path structure inadvertently created by soil-particle aggregation during the re-wetting process. Although a high (99%) removal of oocysts and microsphere within the volcanic ash soil occurred initially, further examination revealed that transport was merely retarded because of highly reversible interactions with grain surfaces. Judging from the slope of the substantive and protracted tail of the breakthrough curve for the 1.8-μm microspheres, almost all (>99%) predictably would be recovered within ∼4000 pore volumes. This suggests that once contaminated, the volcanic ash soil could serve as a reservoir for subsequent contamination of groundwater, at least for pathogens of similar size or smaller. Because of the highly reversible nature of organic colloid immobilization in this soil type, C. parvum could contaminate surface water should overland flow during heavy precipitation events pick up near-surface grains to which they are attached. Surprisingly, oocyst and microsphere attachment to the reference soil from Illinois appeared to be at least as sensitive to changes in pH as was observed for the red, metal-oxide rich soil from Oahu. In contrast, colloidal attachment in the organic-rich, volcanic ash soil was relatively insensitive to changes in pH in spite of the high iron content. Given the fundamental differences in transport behavior of oocyst-sized colloids within the two volcanic soils of similar origin, agricultural practices modified to lessen C. parvum contamination of ground or surface water would necessitate taking the individual soil properties into account.

Water Research↗