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Results for “Transport in Porous Media”

Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

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At least 55 records · Page 3Linked to original sources
USGS1977

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↗
USGS2003

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↗
USGS2010

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↗
USGS2012

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↗
USGS2022

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↗
USGS1996

Experimental investigation and modeling of uranium (VI) transport under variable chemical conditions

The transport of adsorbing and complexing metal ions in porous media was investigated with a series of batch and column experiments and with reactive solute transport modeling. Pulses of solutions containing U(VI) were pumped through columns filled with quartz grains, and the breakthrough of U(VI) was studied as a function of variable solution composition ( p H, total U(VI) concentration, total fluoride concentration, and p H-buffering capacity). Decreasing p H and the formation of nonadsorbing aqueous complexes with fluoride increased U(VI) mobility. A transport simulation with surface complexation model (SCM) parameters estimated from batch experiments was able to predict U(VI) retardation in the column experiments within 30%. SCM parameters were also estimated directly from transport data, using the results of three column experiments collected at different p H and U(VI) pulse concentrations. SCM formulations of varying complexity (multiple surface types and reaction stoichiometries) were tested to examine the trade-off between model simplicity and goodness of fit to breakthrough. A two-site model (weak- and strong-binding sites) with three surface complexation reactions fit these transport data well. With this reaction set the model was able to predict (1) the effects of fluoride complexation on U(VI) retardation at two different p H values and (2) the effects of temporal variability of p H on U(VI) transport caused by low p H buffering. The results illustrate the utility of the SCM approach in modeling the transport of adsorbing inorganic solutes under variable chemical conditions.

Water Resources Research↗
USGS2002

Transport of suspended solids from a karstic to an alluvial aquifer: The role of the karst/alluvium interface

This study focuses on the coupled transport of dissolved constituents and particulates, from their infiltration on a karst plateau to their discharge from a karst spring and their arrival at a well in an alluvial plain. Particulate markers were identified and the transport of solids was characterised in situ in porous and karstic media, based on particle size analyses, SEM, and traces. Transport from the sinkhole to the spring appeared to be dominated by flow through karst: particulate transport was apparently conservative between the two sites, and there was little difference in the overall character of the particle size distribution of the particulates infiltrating the sinkhole and of those discharging from the spring. Qualitatively, the mineralogy of the infiltrating and discharging material was similar, although at the spring an autochthonous contribution from the aquifer was noted (chalk particles eroded from the parent rock by weathering). In contrast, transport between the spring and the well appears to be affected by the overlying alluvium: particles in the water from the well, showed evidence of considerable size-sorting. Additionally, SEM images of the well samples showed the presence of particles originating from the overlying alluvial system; these particles were not found in samples from the sinkhole or the spring. The differences between the particulates discharging from the spring and the well indicate that the water pumped from the alluvial plain is coming from the karst aquifer via the very transmissive, complex geologic interface between the underlying chalk formation and the gravel at the base of the overlying alluvial system. ?? 2002 Elsevier Science B.V. All rights reserved.

Journal of Hydrology↗
USGS1999

Stochastic analysis of virus transport in aquifers

A large-scale model of virus transport in aquifers is derived using spectral perturbation analysis. The effects of spatial variability in aquifer hydraulic conductivity and virus transport (attachment, detachment, and inactivation) parameters on large-scale virus transport are evaluated. A stochastic mean model of virus transport is developed by linking a simple system of local-scale free-virus transport and attached-virus conservation equations from the current literature with a random-field representation of aquifer and virus transport properties. The resultant mean equations for free and attached viruses are found to differ considerably from the local-scale equations on which they are based and include effects such as a free-virus effective velocity that is a function of aquifer heterogeneity as well as virus transport parameters. Stochastic mean free-virus breakthrough curves are compared with local model output in order to observe the effects of spatial variability on mean one-dimensional virus transport in three-dimensionally heterogeneous porous media. Significant findings from this theoretical analysis include the following: (1) Stochastic model breakthrough occurs earlier than local model breakthrough, and this effect is most pronounced for the least conductive aquifers studied. (2) A high degree of aquifer heterogeneity can lead to virus breakthrough actually preceding that of a conservative tracer. (3) As the mean hydraulic conductivity is increased, the mean model shows less sensitivity to the variance of the natural-logarithm hydraulic conductivity and mean virus diameter. (4) Incorporation of a heterogeneous colloid filtration term results in higher predicted concentrations than a simple first-order adsorption term for a given mean attachment rate. (5) Incorporation of aquifer heterogeneity leads to a greater range of virus diameters for which significant breakthrough occurs. (6) The mean model is more sensitive to the inactivation rate of viruses associated with solid surfaces than to the inactivation rate of viruses in solution.

Water Resources Research↗
USGS2008

Comment on “Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations” by L. Moreno et al.

Moreno et al. [1988] (hereinafter referred to as MT) used a particle-tracking scheme to investigate the physics of solute movement in a variable-aperture planar fracture. The spatially heterogeneous fluid velocity was assumed to be the only mechanism of solute movement; local or pore scale dispersion and molecular diffusion were assumed to be negligible. The particle-tracking scheme used by MT consisted of routing particles from node to node in a finite difference grid. In this scheme, the direction of an individual particle is randomly selected and the probability associated with the particle movement in a given direction is proportional to the fluid flux in that direction. The same method was used by Desbarats [1990] to investigate advective transport in aquifers composed of two porous media of different hydraulic conductivities.

Water Resources Research↗
USGS1977

The use of Galerkin finite-element methods to solve mass-transport equations

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Water-Resources Investigations Report↗
USGS1983

Front-tracking model for convective transport in flowing ground water

A finite-difference numerical model that simulates the convective transport of water or tracer particles through porous media is described. It can be applied to one- or two-dimensional problems involving either steady-state or transient flow. The model tracks representative water or tracer particles, initially located along specified lines, as they move in response to the groundwater velocity filed. Aquifer properties may be both anisotropic and nonhomogeneous. Included in the report is a listing of the program along with input formats and test problem results. The front-tracking model provides a useful first approximation determining the movement of solutes in an aquifer, particularly in cases when dispersion and dilution is of minor consideration. (USGS)

Water-Resources Investigations Report↗
USGS2018

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.

Hydrological Processes↗
USGS2021

Co-transport of biogenic nano-hydroxyapatite and Pb(II) in saturated sand columns: Controlling factors and stochastic modeling

Biogenic nano-hydroxyapatite (bio-nHAP) has recently gained great interest in many domains, especially in the remediation of heavy metal-contaminated soil, due to its high reactivity, low cost, and eco-friendly nature. The co-transport and reaction of bio-nHAP with Pb(II) in saturated porous media, however, are not well understood. This work investigated the effects of ionic strength (IS), ionic composition (IC), dissolved organic matter (DOM), and flow velocity on transport-reaction dynamics of Pb(II) and bio-nHAP by combining column breakthrough experiments and model simulations. Results showed that the mobility of Pb(II) was significantly enhanced with increasing IS/IC but less affected by flow velocity during the transport-reaction process of bio-nHAP and Pb(II) in the saturated sand column; while the transport of bio-nHAP was restricted by increasing IS/IC but facilitated by increasing velocity. IC, IS, and velocity only slightly affected the reaction kinetics between Pb(II) and bio-nHAP, likely due to the fast reaction rate between Pb(II) and bio-nHAP and precipitation of pyromorphite. The transport dynamics of bio-nHAP and Pb(II) were significantly changed by DOM, and this effect depended strongly on the type of DOM with different molecular weights. Breakthrough curves of Pb(II) and bio-nHAP exhibited apparent “anomalous”, sub-diffusive transport behaviors, which could be well quantified by a novel tempered fractional derivative bimolecular reaction equation (T-FBRE). Our findings highlighted the accurate simulation of the co-transport and reaction of bio-nHAP with Pb(II) using T-FBRE and had a great benefit for risk assessment and remediation strategy development for Pb(II) contaminated soil.

Chemosphere↗
USGS2002

Effect of growth conditions and staining procedure upon the subsurface transport and attachment behaviors of a groundwater protist

The transport and attachment behaviors of Spumella guttula (Kent), a nanoflagellate (protist) found in contaminated and uncontaminated aquifer sediments in Cape Cod, Mass., were assessed in flowthrough and static columns and in a field injection-and-recovery transport experiment involving an array of multilevel samplers. Transport of S. guttula harvested from low-nutrient (10 mg of dissolved organic carbon per liter), slightly acidic, granular (porous) growth media was compared to earlier observations involving nanoflagellates grown in a traditional high-nutrient liquid broth. In contrast to the highly retarded (retardation factor of ∼3) subsurface transport previously reported for S. guttula , the peak concentration of porous-medium-grown S. guttula traveled concomitantly with that of a conservative (bromide) tracer. About one-third of the porous-medium-grown nanoflagellates added to the aquifer were transported at least 2.8 m downgradient, compared to only ∼2% of the broth-grown nanoflagellates. Flowthrough column studies revealed that a vital (hydroethidine [HE]) staining procedure resulted in considerably less attachment (more transport) of S. guttula in aquifer sediments than did a staining-and-fixation procedure involving 4′,6′-diamidino-2-phenylindole (DAPI) and glutaraldehyde. The calculated collision efficiency (∼10 −2 for porous-medium-grown, DAPI-stained nanoflagellates) was comparable to that observed earlier for the indigenous community of unattached groundwater bacteria that serve as prey. The attachment of HE-labeled S. guttula onto aquifer sediment grains was independent of pH (over the range from pH 3 to 9) suggesting a primary attachment mechanism that may be fundamentally different from that of their prey bacteria, which exhibit sharp decreases in fractional attachment with increasing pH. The high degree of mobility of S. guttula in the aquifer sediments has important ecological implications for the protistan community within the temporally changing plume of organic contaminants in the Cape Cod aquifer.

Applied and Environmental Microbiology↗
USGS2018

The dual‐domain porosity apparatus: Characterizing dual porosity at the sediment/water interface

The characterization of pore-space connectivity in porous media at the sediment/water interface is critical to understanding contaminant transport and reactive biogeochemical processes in zones of groundwater and surface-water exchange. Previous in situ studies of dual-domain (i.e., mobile/less-mobile porosity) studies have been limited to solute tracer injections at scales of meters to 100s of meters and subsequent numerical model parameterization using fluid concentration histories. Pairing fine-scale (e.g., sub-meter) geoelectrical measurements with fluid tracer data over time alleviates dependence on flowpath-scale experiments, enabling spatially targeted characterization of shallow sediment/water interface media where biogeochemical reactivity is often high. The Dual-Domain Porosity Apparatus is a field-tested device capable of variable rate-controlled downward flow experiments. The Dual-Domain Porosity Apparatus facilitates meter-scale inference of dual-domain parameters, i.e., mobile/less-mobile exchange rate coefficient and the ratio of less mobile to mobile porosity. The Dual-Domain Porosity Apparatus experimental procedure uses water electrical conductivity as a conservative tracer of differential loading and flushing of pore spaces within the region of measurement. Variable injection rates permit the direct quantification of the flow-dependence of dual-domain parameters, which has been theorized for decades but remains challenging to assess using existing experimental methodologies.

Groundwater↗
USGS1990

Reevaluation of large-scale dispersivities for a waste chloride plume: Effects of transient flow

This paper investigates the effects of transient groundwater flow on dispersion of a waste chloride plume in the basaltic aquifer beneath the Idaho (USA) National Engineering Laboratory. In an early application of numerical modeling techniques to the two-dimensional simulation of field-scale plumes, previous investigators identified longitudinal and transverse dispersivities using an independently calibrated steady-state flow model and matching contours of observed and simulated concentrations. The unusual result of calibrated transverse dispersivity (140 m) being significantly larger than longitudinal dispersivity (90 m) has been attributed to spatial heterogeneity, the fractured nature of the aquifer, and to the use of a two-dimensional model. New calibrations of the solute-transport model are performed on point concentration observations using a flow model incorporating transient recharge conditions that cause significant fluctuations in velocity. Under transient flow conditions, lowest calibration errors are achieved with significantly larger dispersivities than previously hypothesized, and with the longitudinal component larger than the transverse component. Unfortunately, the sensitivity of the model calibration error to dispersivity is low. Incorporating transient flow in this two-dimensional porous-media model does not significantly improve our understanding of the processes controlling chloride transport at this site.

Conference Paper↗
USGS2004

Extent of reaction in open systems with multiple heterogeneous reactions

The familiar batch concept of extent of reaction is reexamined for systems of reactions occurring in open systems. Because species concentrations change as a result of transport processes as well as reactions in open systems, the extent of reaction has been less useful in practice in these applications. It is shown that by defining the extent of the equivalent batch reaction and a second contribution to the extent of reaction due to the transport processes, it is possible to treat the description of the dynamics of flow through porous media accompanied by many chemical reactions in a uniform, concise manner. This approach tends to isolate the reaction terms among themselves and away from the model partial differential equations, thereby enabling treatment of large problems involving both equilibrium and kinetically controlled reactions. Implications on the number of coupled partial differential equations necessary to be solved and on numerical algorithms for solving such problems are discussed. Examples provided illustrate the theory applied to solute transport in groundwater flow.

American Institute of Chemical Engineers↗
USGS2010

A solute flux approach to transport in heterogeneous formations: 2. Uncertainty analysis

Uncertainty in the mass flux for advection dominated solute movement in heterogeneous porous media is investigated using the Lagrangian framework developed in paper 1 by Dagan et al. (this issue). Expressions for the covariance of the mass flux and cumulative mass flux are derived as functions of the injection volume and sampling area size relative to the scale of heterogeneity. The result is illustrated for solute advection in three types of heterogeneous porous media: stratified formations, two‐ and three‐dimensional porous media; small perturbation approximation is used for the two‐ and three‐dimensional cases. Variances of the mass flux and cumulative mass flux are evaluated as functions of the injection volume (area) scale versus log‐hydraulic conductivity integral scale. The greatest decrease in coefficient of variation (CV) of the mass flux is for the source scale 1–5 times the hydraulic conductivity integral scale; further increase in the source size decreases CV comparatively less. The variance of the cumulative mass flux (or total discharge) indicates that for the source size of 20 hydraulic conductivity integral scales, the transport conditions are almost ergodic. The present results also indicate that the cumulative mass flux is a relatively robust quantity for describing field‐scale solute transport.

Water Resources Research↗