Modeling of non-reactive solute transport in fractured clayey till during variable flow rate and time

Fractures and biopores can act as preferential flow paths in clay aquitards and may rapidly transmit contaminants into underlying aquifers. Reliable numerical models for assessment of groundwater contamination from such aquitards are needed for planning, regulatory and remediation purposes. In this investigation, high resolution preferential water-saturated flow and bromide transport data were used to evaluate the suitability of equivalent porous medium (EPM), dual porosity (DP) and discrete fracture/matrix diffusion (DFMD) numerical modeling approaches for assessment of flow and non-reactive solute transport in clayey till. The experimental data were obtained from four large undisturbed soil columns (taken from 1.5 to 3.5 m depth) in which biopores and channels along fractures controlled 96-99% of water-saturated flow. Simulating the transport data with the EPM effective porosity model (FRACTRAN in EPM mode) was not successful because calibrated effective porosity for the same column had to be varied up to 1 order of magnitude in order to simulate solute breakthrough for the applied flow rates between 11 and 49 mm/day. Attempts to simulate the same data with the DP models CXTFIT and MODFLOW/MT3D were also unsuccessful because fitted values for dispersion, mobile zone porosity, and mass transfer coefficient between mobile and immobile zones varied several orders of magnitude for the different flow rates, and because dispersion values were furthermore not physically realistic. Only the DFMD modeling approach (FRACTRAN in DFMD mode) was capable to simulate the observed changes in solute transport behavior during alternating flow rate without changing values of calibrated fracture spacing and fracture aperture to represent the macropores.     

Characterization of flow and transport processes within the unsaturated zone of Yucca Mountain, Nevada, under current and future climates

This paper presents a large-scale modeling study characterizing fluid flow and tracer transport in the unsaturated zone of Yucca Mountain, Nevada, a potential repository site for storing high-level radioactive waste. The study has been conducted using a three-dimensional numerical model, which incorporates a wide variety of field data and takes into account the coupled processes of flow and transport in the highly heterogeneous, unsaturated fractured porous rock. The modeling approach is based on a dual-continuum formulation of coupled multiphase fluid and tracer transport through fractured porous rock. Various scenarios of current and future climate conditions and their effects on the unsaturated zone are evaluated to aid in the assessment of the proposed repository's system performance using different conceptual models. These models are calibrated against field-measured data. Model-predicted flow and transport processes under current and future climates are discussed.     

A review on reactive transport model and porosity evolution in the porous media

Environmental Science and Pollution Research - This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and...     

Modeling colloid-facilitated transport of multi-species contaminants in unsaturated porous media

Colloid-facilitated transport has been recognized as a potentially important and overlooked contaminant transport process. In particular, it has been observed that conventional two phase sorption models are often unable to explain transport of highly sorbing compounds in the subsurface appropriately in the presence of colloids. In this study a one-dimensional model for colloid-facilitated transport of chemicals in unsaturated porous media is developed. The model has parts for simulating coupled flow, and colloid transport and dissolved and colloidal contaminant transport. Richards' equation is solved to model unsaturated flow, and the effect of colloid entrapment and release on porosity and hydraulic conductivity of the porous media is incorporated into the model. Both random sequential adsorption and Langmuir approaches have been implemented in the model in order to incorporate the effect of surface jamming. The concept of entrapment of colloids into the air-water interface is used for taking into account the effect of retardation caused due to existence of the air phase. A non-equilibrium sorption approach with options of linear and Langmuir sorption assumptions are implemented that can represent the competition and site saturation effects on sorption of multiple compounds both to the solid matrix and to the colloidal particles. Several demonstration calculations are performed and the conditions in which the non-equilibrium model can be approximated by an equilibrium model are also studied.     

Modelling of nonreactive tracer dipole tests in a shear zone at the Grimsel test site

The investigation of the migration of a high pH plume in a fractured shear zone is foreseen by a long-term experiment at the Grimsel rock laboratory. In order to characterise the initial conditions for the long-term experiment and to evaluate an optimal hydraulic in situ set-up, several dipole experiments with nonreacting tracers have been performed. The dipole experiments differ in geometry, pumping rates and orientation to the background water flow. Several single and double-porosity models have been applied to fit the results of these dipole tracer tests in order to extract values for some transport parameters and discriminate for certain transport processes. A two-dimensional porous medium approach was successfully used to fit tracer breakthrough curves measured for a dipole experiment. A model based on a one-dimensional dual porous medium approach was also successful, although the applied hydraulic dipole, with similar injection and extraction rates, suggests the existence of an extended two-dimensional flow field. For the two-dimensional porous medium approach, tracer breakthrough could only be fitted with a complex flow field geometry within the heterogeneous fractured shear zone. The heterogeneity was generated by heterogeneous porosity and hydraulic permeability distributions. Predictions for further dipole geometries and a sorbing tracer have been calculated by means of both models using the flow and transport parameters deduced from fits for a single dipole experiment. This allows for comparison with the measured breakthrough of sorbing tracers. The foreseen experiment with sorbing (radionuclide) tracers will help decide on the appropriate approach that should be used to describe such dipole experiments in this shear zone. Additionally, the migration and spreading of a solution with high pH has been calculated taking into account mineral dissolution and precipitation in a two-dimensional porous medium approach in order to estimate the amount and character of the mineral reactions induced by the interaction between the high pH solution and the rock.     

Nonideal transport of reactive contaminants in heterogeneous porous media: 7. distributed-domain model incorporating immiscible-liquid dissolution and rate-limited sorption/desorption

The purpose of this work is to present a distributed-domain mathematical model incorporating the primary mass-transfer processes that mediate the transport of immiscible organic liquid constituents in water-saturated, locally heterogeneous porous media. Specifically, the impact of grain/pore-scale heterogeneity on immiscible-liquid dissolution and sorption/desorption is represented in the model by describing the system as comprising a continuous distribution of mass-transfer domains. With this conceptualization, the distributions of the initial dissolution rate coefficient and the sorption/desorption rate coefficient are represented as probability density functions. Several sets of numerical experiments are conducted to examine the effects of heterogeneous dissolution and sorption/desorption on contaminant transport and elution. Four scenarios with different combinations of uniform/heterogeneous rate-limited dissolution and uniform/heterogeneous rate-limited sorption/desorption are evaluated. The results show that both heterogeneous rate-limited sorption/desorption and heterogeneous rate-limited dissolution can significantly increase the time or pore volumes required to elute immiscible-liquid constituents from a contaminated porous medium. However, sorption/desorption has minimal influence on elution behavior until essentially all of the immiscible liquid has been removed. For typical immiscible-liquid constituents that have relatively low sorption, the asymptotic elution tailing produced by heterogeneous rate-limited sorption/desorption begins at effluent concentrations that are several orders of magnitude below the initial steady-state concentrations associated with dissolution of the immiscible liquid. Conversely, the enhanced elution tailing associated with heterogeneous rate-limited dissolution begins at concentrations that are approximately one-tenth of the initial steady-state concentrations. Hence, dissolution may generally control elution behavior of immiscible-liquid constituents in cases wherein grain/pore-scale heterogeneity significantly influences both dissolution and sorption/desorption.     

Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations

This work is focused on measuring the concentration distribution of a conservative tracer in a homogeneous synthetic porous material and in heterogeneous natural sandstone using MRI techniques, and on the use of spatially resolved porosity data to define spatially variable diffusion coefficients in heterogeneous media. The measurements are made by employing SPRITE, a fast MRI method that yields quantitative, spatially-resolved tracer concentrations in porous media. Diffusion experiments involving the migration of H(2)O into D(2)O-saturated porous media are conducted. One-dimensional spatial distributions of H(2)O-tracer concentrations acquired from experiments with the homogeneous synthetic calcium silicate are fitted with the one-dimensional analytical solution of Fick's second law to confirm that the experimental method provides results that are consistent with expectations for Fickian diffusion in porous media. The MRI-measured concentration profiles match well with the solution for Fick's second law and provide a pore-water diffusion coefficient of 1.75×10(-9)m(2)s(-1). The experimental approach was then extended to evaluate diffusion in a heterogeneous natural sandstone in three dimensions. The relatively high hydraulic conductivity of the sandstone, and the contrast in fluid density between the H(2)O tracer and the D(2)O pore fluid, lead to solute transport by a combination of diffusion and density-driven advection. The MRI measurements of spatially distributed tracer concentration, combined with numerical simulations allow for the identification of the respective influences of advection and diffusion. The experimental data are interpreted with the aid of MIN3P-D - a multicomponent reactive transport code that includes the coupled processes of diffusion and density-driven advection. The model defines local diffusion coefficients as a function of spatially resolved porosity measurements. The D(e) values calculated for the heterogeneous sandstone and used to simulate diffusive and advective transport range from 5.4×10(-12) to 1.0×10(-10)m(2)s(-1). These methods have broad applicability to studies of contaminant migration in geological materials.     

Computation of the interfacial area for two-fluid porous medium systems

We develop a method to compute interfacial areas from three-dimensional digital representations of multiphase systems. We approximate the interfaces with the isosurface generated by the standard marching-cube algorithm from the discrete phase distribution. We apply this approach to two-fluid pore-scale simulations by (1) simulating a random packing of spheres that obeys the grain-size distribution and porosity of an experimental porous medium system, and (2) using a previously developed pore-morphology-based model in order to predict the phase distribution for a water-wet porous medium that undergoes primary drainage. The predicted primary drainage curve and interfacial areas are in good agreement with the experimental values reported in the literature, where interfacial areas were measured using interfacial tracers. The energy dissipation during Haines jumps is significant: thus, the mechanical work done on the system is not completely converted into surface energy, and interfacial areas may not be deduced from the primary drainage curve.     

A triple-continuum approach for modeling flow and transport processes in fractured rock

This paper presents a triple-continuum conceptual model for simulating flow and transport processes in fractured rock. Field data collected from the unsaturated zone of Yucca Mountain, a repository site of high-level nuclear waste, show a large number of small-scale fractures. The effect of these small fractures has not been considered in previous modeling investigations within the context of a continuum approach. A new triple-continuum model (consisting of matrix, small-fracture, and large-fracture continua) has been developed to investigate the effect of these small fractures. This paper derives the model formulation and discusses the basic triple-continuum behavior of flow and transport processes under different conditions, using both analytical solutions and numerical approaches. The simulation results from the site-scale model of the unsaturated zone of Yucca Mountain indicate that these small fractures may have an important effect on radionuclide transport within the mountain.     

Modeling solute diffusion in the presence of pore-scale heterogeneity: method development and an application to the Culebra dolomite member of the Rustler Formation, New Mexico, USA

Previous studies have revealed the presence of pore-scale variability in diffusivity in the Culebra (dolomite) member of the Rustler Formation, NM. In this study, eight laboratory-scale diffusion experiments on five Culebra samples were analyzed using a methodology for modeling solute diffusion through porous media in the presence of multiple matrix diffusivities, Dp. A lognormal distribution of Dp is assumed within each of the lab samples. The estimated standard deviation (sigma d) of ln(Dp) within each sample ranges from 0 to 1, with most values lying between 0.5 and 1. The variability over all samples leads to a combined sigma d in the range of 1.0-1.2, which is consistent with the distribution of independently determined formation factor measurements for similar Culebra samples. A comparison of our estimation results to other rock properties suggests that, at the lab-scale, the geometric mean of Dp increases with bulk porosity and the quantity of macroscopic features such as vugs and fractures. However, sigma d appears to be determined by variability within such macroscopic features and/or by micropore-scale heterogeneity. In addition, comparison of these experiments to those at larger spatial scales suggests that increasing sample volume results in an increase in sigma d.     

Convergent-flow tracer tests in heterogeneous media: combined experimental-numerical analysis for determination of equivalent transport parameters

In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.     

Development and Application of a Three-Dimensional Finite Element Vapor Intrusion Model

Abstract

Details of a three-dimensional finite element model of soil vapor intrusion, including the overall modeling process and the stepwise approach, are provided. The model is a quantitative modeling tool that can help guide vapor intrusion characterization efforts. It solves the soil gas continuity equation coupled with the chemical transport equation, allowing for both advective and diffusive transport. Three-dimensional pressure, velocity, and chemical concentration fields are produced from the model. Results from simulations involving common site features, such as impervious surfaces, porous foundation sub-base material, and adjacent structures are summarized herein. The results suggest that site-specific features are important to consider when characterizing vapor intrusion risks. More importantly, the results suggest that soil gas or subslab gas samples taken without proper regard for particular site features may not be suitable for evaluating vapor intrusion risks; rather, careful attention needs to be given to the many factors that affect chemical transport into and around buildings.     

Development of the FMT chemical transport simulator: Coupling aqueous density and mineral volume fraction to phase compositions

The Fracture-Matrix Transport (FMT) code couples saturated porous medium advection and diffusion with mechanistic chemical models for speciation and interphase reactions. Previous versions of FMT simulated double-porosity transport in two dimensions on the continuum from advection- to diffusion-dominated, with a user-specified velocity field to allow double-porosity transport. However, aqueous density was assumed constant, and reactive minerals were assumed to occupy negligible volume. Both of these assumptions can be considered poor for evaporite systems, where large changes in porosity and aqueous density can result from high mineral solubilities. Further development of FMT has relaxed these restrictions, allowing aqueous density to vary with phase composition, and allowing void volume to change as minerals dissolve and precipitate. This paper describes the additional mathematical complexity and code modifications required to simulate such systems. The sensitivity of advection-dominated transport to these variables is explored briefly in a one-dimensional example.     

Empirical correlations to estimate agglomerate size and deposition during injection of a polyelectrolyte-modified Fe0 nanoparticle at high particle concentration in saturated sand

Controlled emplacement of polyelectrolyte-modified nanoscale zerovalent iron (NZVI) particles at high particle concentration (1-10 g/L) is needed for effective in situ subsurface remediation using NZVI. Deep bed filtration theory cannot be used to estimate the transport and deposition of concentrated polyelectrolyte-modified NZVI dispersions (>0.03 g/L) because particles agglomerate during transport which violates a fundamental assumption of the theory. Here we develop two empirical correlations for estimating the deposition and transport of concentrated polyelectrolyte-modified NZVI dispersions in saturated porous media when NZVI agglomeration in porous media is assumed to reach steady state quickly. The first correlation determines the apparent stable agglomerate size formed during NZVI transport in porous media for a fixed hydrogeochemical condition. The second correlation estimates the attachment efficiency (sticking coefficient) of the stable agglomerates. Both correlations are described using dimensionless numbers derived from parameters affecting deposition and agglomeration in porous media. The exponents for the dimensionless numbers are determined from statistical analysis of breakthrough data for polyelectrolyte-modified NZVI dispersions collected in laboratory scale column experiments for a range of ionic strength (1, 10, and 50mM Na(+) and 0.25, 1, and 1.25 mM Ca(2+)), approach velocity (0.8 to 55 × 10(-4)m/s), average collector sizes (d(50)=99 μm, 300 μm, and 880 μm), and polyelectrolyte surface modifier properties. Attachment efficiency depended on approach velocity and was inversely related to collector size, which is contrary to that predicted from classic filtration models. High ionic strength, the presence of divalent cations, lower extended adsorbed polyelectrolyte layer thickness, decreased approach velocity, and a larger collector size promoted NZVI agglomeration and deposition and thus limited its mobility in porous media. These effects are captured quantitatively in the two correlations developed. The application and limitations of using the correlations for preliminary design of in situ NZVI emplacement strategies is discussed.     

Migration of colloids in discretely fractured porous media: effect of colloidal matrix diffusion

Numerical simulations of colloid transport in discretely fractured porous media were performed to investigate the importance of matrix diffusion of colloids as well as the filtration and remobilization of colloidal particles in both the fractures and porous matrix. To achieve this objective a finite element numerical code entitled COLDIFF was developed. The processes that COLDIFF takes into account include advective-dispersive transport of colloids, filtration and remobilization of colloidal particles in both fractures and porous matrix, and diffusive interactions of colloids between the fractures and porous matrix. Three sets of simulations were conducted to examine the importance of parameters and processes controlling colloid migration. First, a sensitivity analysis was performed using a porous block containing a single fracture to determine the relative importance of various phenomenological coefficients on colloid transport. The primary result of the analysis showed that the porosity of the matrix and the process of colloid filtration in fractures play important roles in controlling colloid migration. Second, simulations were performed to replicate and examine the results of a laboratory column study using a fractured shale saprolite. Results of this analysis showed that the filtration of colloidal particles in the porous matrix can greatly affect the tailing of colloid concentrations after the colloid source was removed. Finally, field-scale simulations were performed to examine the effect of matrix porosity, fracture filtration and fracture remobilization on long-term colloid concentration and migration distance. The field scale simulations indicated that matrix diffusion and fracture filtration can significantly reduce colloid migration distance. Results of all three analyses indicated that in environments where porosity is relatively high and colloidal particles are small enough to diffuse out of fractures, the characteristics of the porous matrix that affect colloid transport become more important than those of the fracture network. Because the properties of the fracture network tend to have greater uncertainty due to difficulties in their measurement relative to those of the porous matrix, prediction uncertainties associated with colloid transport in discretely fractured porous media may be reduced.     

Modeling the Reduction of Vapor Phase Emissions from Surface Soils Due to Soil Matrix Effects: Porosity/Tortuosity Concepts

ABSTRACT

A major route for transport of volatile organic compounds within porous media is vapor phase diffusion. The diffusion rate through a porous medium is less than that through free-air due to the decreased cross-sectional area available for gas movement and the increased path length due to pore tortuosity. Numerous empirical expressions have been published that relate the diffusion coefficient in porous media to the diffusion coefficient in free-air (unobstructed gas phase). Published measurements of relative diffusivity and air-filled porosity were combined into a database. Empirical expressions available in the literature, including the popular Millington-Quirk equation, were evaluated along with a fourth-degree polynomial expression developed by the authors to determine the best type of equation to predict relative diffusivity as a function of air-filled porosity over the domain of values for porosity ranging from 0.071 to 1 for different types of materials. Mean square deviations were used as the statistical test to compare equations. The polynomial expression developed in this project produced a significantly different effective diffusion coefficient (1.3 x 10^-6 m²/sec) compared to values of 9.2 x 10^-6 m²/sec and 3.1 x 10^-6 m²/ sec predicted by forms of the Millington-Quirk equation for a specific case.     

Spatially distributed pesticide exposure assessment in the Central Valley, California, USA

Field runoff is an important transport mechanism by which pesticides move into the hydrologic environment of intensive agricultural regions such as California's Central Valley. This study presents a spatially explicit modeling approach to extend Pesticide Root Zone Model (PRZM), a field-scale pesticide transport model, into basin level. The approach was applied to simulate chlorpyrifos use in the Central Valley during 2003-2007. The average value of loading as percent of use (LAPU) is 0.031%. Results of this study provide strong evidence that surface runoff generation and pesticide application timing are the two influencing factors on the spatial and temporal variability of chlorpyrifos sources from agricultural fields. This is one of the first studies in coupling GIS and field-scale models and providing simulations for the dynamics of pesticides over an agriculturally dominated landscape. The demonstrated modeling approach may be useful for implementations of best management practice (BMP) and total maximum daily load (TMDL).     

Modeling of flow and contaminant transport in coupled stream-aquifer systems

This paper describes an integrated approach for modeling flow and contaminant transport in hydraulically connected stream-aquifer systems. The code, FTSTREAM, extended the capabilities of the ground-water model, FTWORK, to incorporate chemical fate and transport in streams. Flow in the stream network is modeled as an unsteady, spatially varying flow, while transport modeling is based on a one-dimensional advection-dispersion equation. In addition to sorption and decay during transport in ground water, the model incorporates volatilization, settling and decay during transport in surface water. The interaction between surface water and ground water is accommodated by a leakage term and is implemented in the model using an iterative Picard-type procedure to ensure mass conservation across the interface between the two systems. The modeling approach is used to simulate contaminant transport in the Mad River, Ohio, which is hydraulically connected to a buried valley aquifer of sand and gravel outwash. The river is a receiving stream in the upstream part of the modeled area. Downstream, heavy pumping from a municipal well field causes the river to become a loosing stream. Induced infiltration from the river is responsible for a considerable portion of the well yield. The flow and transport model, developed for this study, simulates coupling between flow in the aquifer and the river. Hypothetical sources of contamination are introduced at selected locations in the upstream portion of the aquifer. The model is then used to simulate the expected transport in both the aquifer and the stream. A series of simulations elucidates the role of the river in facilitating the transport of the hypothetical contaminants in ground water and surface water. Effect of sorption, retardation and volatilization on contaminant transport is also examined for the case of the volatile organic compounds.     

Coupled effects of solution chemistry and hydrodynamics on the mobility and transport of quantum dot nanomaterials in the vadose zone

To investigate the coupled effects of solution chemistry and hydrodynamics on the mobility of quantum dot (QD) nanoparticles in the vadose zone, laboratory scale transport experiments involving single and/or sequential infiltrations of QDs in unsaturated and saturated porous media, and computations of total interaction and capillary potential energies were performed. As ionic strength increased, QD retention in the unsaturated porous media increased; however, this retention was significantly suppressed in the presence of a non-ionic surfactant in the infiltration suspensions as indicated by surfactant enhanced transport of QDs. In the vadose zone, the non-ionic surfactant limited the formation of QD aggregates, enhanced QD mobility and transport, and lowered the solution surface tension, which resulted in a decrease in capillary forces that not only led to a reduction in the removal of QDs, but also impacted the vadose zone flow processes. When chemical transport conditions were favorable (ionic strength of 5 × 10(-4)M and 5 × 10(-3)M, or ionic strengths of 5 × 10(-2)M and 0.5M with surfactant), the dominating phenomena controlling the mobility and transport of QDs in the vadose zone were meso-scale processes, where infiltration by preferential flow results in the rapid transport of QDs. When chemical transport conditions were unfavorable (ionic strength of 5 × 10(-2)M and 0.5M) the dominating phenomena controlling the mobility and transport of QDs in the vadose zone were pore-scale processes governed by gas-water interfaces (GWI) that impact the mobility of QDs. The addition of surfactant enhanced the transport of QDs both in favorable and unfavorable chemical transport conditions. The mobility and retention of QDs was controlled by interaction and capillary forces, with the latter being the most influential. GWI were found to be the dominant mechanism and site for QD removal compared with solid-water interfaces (SWI) and pore straining. Additionally, ripening phenomena were demonstrated to enhance QDs removal or retention in porous media and to be attenuated by the presence of surfactant.     

Release of colloidal particles in natural porous media by monovalent and divalent cations

We study mobilization of colloidal particles from natural porous media, such as soils and groundwater aquifers. Extensive laboratory scale column experiments of particle release from four different subsurface materials are presented. The important characteristics of the release process are (i) its non-exponential kinetics, (ii) the finite supply of colloidal particles and (iii) the strong dependence of the release kinetic on the nature of the adsorbed cations. Particle release depends most sensitively on the relative saturation of the medium with divalent cations. We propose a mathematic model, which captures all these aspects quantitatively, and can be used to describe the coupling between transport of major cations and the release of colloidal particles. The present experimental investigations as well as the developed modeling framework represent an important step towards the understanding of colloid-facilitated transport phenomena in natural porous media.