Monodisperse and polydisperse colloid transport in water-saturated fractures with various orientations: Gravity effects

Numerical experiments are conducted to examine the effects of gravity on monodisperse and polydisperse colloid transport in water-saturated fractures with uniform aperture. Dense colloids travel in water-saturated fractures by advection and diffusion while subject to the influence of gravity. Colloids are assumed to neither attach onto the fracture walls nor penetrate the rock matrix based on the assumptions that they are inert and their size is larger than the pore size of the surrounding solid matrix. Both the size distribution of a colloid plume and colloid density are shown to be significant factors impacting their transport when gravitational forces are important. A constant-spatial-step particle-tracking code simulates colloid plumes with increasing densities transporting in water-saturated fractures while accounting for three forces acting on each particle: a deterministic advective force due to the Poiseuille flow field within the fracture, a random force caused by Brownian diffusion, and the gravitational force. Integer angles of fracture orientation with respect to the horizontal ranging from ±90° are considered: three lognormally distributed colloid plumes with mean particle size of 1 μm (averaged on a volumetric basis) and standard deviation of 0.6, 1.2 and 1.8 μm are examined. Colloid plumes are assigned densities of 1.25, 1.5, 1.75 and 2.0 g/cm³. The first four spatial moments and the first two temporal moments are estimated as functions of fracture orientation angle and colloid density. Several snapshots of colloid plumes in fractures of different orientations are presented. In all cases, larger particles tend to spread over wider sections of the fracture in the flow direction, but smaller particles can travel faster or slower than larger particles depending on fracture orientation angle.     

Two-dimensional modeling of contaminant transport in porous media in the presence of colloids

It has long been known that colloids can facilitate the transport of contaminants in groundwater systems by reducing the effective retardation factor. A significant effort has been devoted to study colloid-facilitated contaminant transport during the past decade. Many of the previous studies were restricted to one-dimensional analyses and comparisons with finite-column experiments. In this work, a two-dimensional numerical model is developed and used to study the different interactions between colloids, contaminants, and porous media under homogeneous conditions. The numerical formulation of the model is based on discretizing mass balance equations and reaction equations using finite differences having a third-order, total variance-diminishing scheme for the advection terms. This scheme significantly reduces numerical dispersion and leads to greater accuracy compared to the standard central-differencing scheme. The model is tested against analytical solutions under simplified conditions as well as against experimental data, and the results are favorable. The model is used to investigate the impact of the various reaction rates and parameter values on the movement of contaminant plumes in two dimensions. The model is also used to investigate the hypothesis that colloids may increase the effective retardation factor of contaminant plumes. The analysis shows that assuming kinetic mass exchange between contaminant and colloids with constant reaction rate coefficients that are not related to the concentrations may lead to inaccurate results. These inaccurate results are exemplified in the finding that under the kinetic assumption the ratio of the initial concentration of colloids to the initial concentration of contaminant does not affect the amount of facilitation or retardation that occurs in the system. It is also found that colloids can increase the effective retardation factor for the contaminant under certain combinations of reaction rates and distribution coefficients. A quantitative empirical expression to identify whether colloids retard or facilitate the contaminant movement is presented.     

Matrix Diffusion Effects on Contaminant Migration from an Injection Well in Fractured Sandstone

Deep-well injection into fractured sandstone is an option for the disposal of contaminated mine dewatering discharge from an open pit uranium mine. As part of the assessment of potential contaminant migration from deep-well injection, the effect of matrix diffusion was evaluated. An analytical mathematical model was developed for the simulation of the radial movement of a contaminant front away from an injection point under steady flow conditions in a planar fracture with uniform properties. The model includes the effects of advection in the fracture, diffusion of contaminants from the fracture into the rock matrix, and equilibrium adsorption on the fracture surface as well as in the rock matrix. Effective diffusion coefficients obtained from laboratory experiments on 11 intact core samples varied from 3.4 × 10⁻⁸ to 3.2 × 10⁻⁷ cm²/s. Model simulations were made with diffusion coefficient values in this range and with single-fracture injection rates estimated from fracture frequencies in boreholes, and from bulk hydraulic conductivity values obtained from field tests. Because of matrix diffusion, the rate of outward movement of the front of the nonreactive contaminants from the injection well is much slower than the rate of water flow in the fractures. Simulations of the movement of contaminants that undergo adsorption indicate that even a small distribution coefficient for the rock matrix causes the contaminants to remain very close to the injection well during the one-year period. The results of the simplified model demonstrate that matrix diffusion is an important process that cannot be neglected in the assessment of a waste disposal scheme located in fractured porous rock. However, in order to make a definitive assessment of the capability of matrix diffusion and associated matrix adsorption to significantly limit the extent of contaminant migration around injection wells, it would be necessary to conduct field tests such as a preliminary or experimental injection.     

STREAM-SUBSURFACE EXCHANGE, SUSPENDED SEDIMENT TRANSPORT, AND THE COUPLED TRANSPORT OF COLLOIDS AND CONTAMINANTS IN SEDIMENT BEDS

1 INTRODUCTION Alluvial streams generally have permeable bed sediments that can admit significant pore water flows. Steady flow of surface water over bed roughness features such as sand waves or pools and riffles can then drive water flow into and out of the shallow subsurface. This is often termed hyporheic exchange, and the subsurface region where mixing between stream and ground waters occurs is the hyporheic zone (Hynes, 1983). The hyporheic zone has been shown to be a critical com…     

Shear dispersion in a fracture with porous walls

We present an analytical expression for the shear dispersion during solute transport in a coupled fracture–matrix system. The dispersion coefficient is obtained in a fracture with porous walls by taking into account an accurate boundary condition at the interface between the matrix and fracture, and the results were compared with those in a non-coupled system. The analysis presented identifies three regimes: diffusion-dominated, transition, and advection-dominated. The results showed that it is important to consider the exchange of solute between the fracture and matrix in development of the shear dispersion coefficient for the transition and advection-dominated regimes. The new dispersion coefficient is obtained by imposing the continuity of concentrations and mass fluxes along the porous walls. The resulting equivalent transport equation revealed that the effective velocity in a fracture increases while the dispersion coefficient decreases due to mass transfer between the matrix and fracture. A larger effective advection term leads to greater storage of mass in the matrix as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The findings of this study can be used for modeling of tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks.     

Semi-analytical solutions for solute transport in fractured porous media using a strip source of finite width

Transient and steady-state analytical solutions are derived to investigate solute transport in a fractured porous medium consisting of evenly spaced, parallel discrete fractures. The solutions incorporate a finite width strip source, longitudinal and transverse dispersion in the fractures, source decay, aqueous phase decay, one-dimensional diffusion into the matrix, sorption to fracture walls, and sorption within the matrix. The solutions are derived using Laplace and Fourier transforms, and inverted by interchanging the order of integration and utilizing a numerical Laplace inversion algorithm. The solutions are verified for simplified cases by comparison to solutions derived by Batu [Batu V. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type condition at the source. Wat Resour Res 1989;25(6):1125] and Sudicky and Frind [Sudicky EA, Frind EO. Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Wat Resour Res 1982;18(6):1634]. The application of the solutions to a fractured sandstone demonstrates that narrower source widths and larger values of transverse dispersivity both lead to lower downstream concentrations in the fractures and shorter steady-state plumes. The incorporation of aqueous phase decay and source concentration decay both lead to lower concentrations and shorter plumes, with even moderate amounts of decay significantly shortening the persistence of contamination.     

Mathematical modeling of colloid and virus cotransport in porous media: Application to experimental data

A conceptual mathematical model was developed to describe the simultaneous transport (cotransport) of viruses and colloids in three-dimensional, water saturated, homogeneous porous media with uniform flow. The model accounts for the migration of individual virus and colloid particles as well as viruses attached onto colloids. Viruses can be suspended in the aqueous phase, attached onto suspended colloids and the solid matrix, and attached onto colloids previously attached on the solid matrix. Colloids can be suspended in the aqueous phase or attached on the solid matrix. Viruses in all four phases (suspended in the aqueous phase, attached onto suspended colloid particles, attached on the solid matrix, and attached onto colloids previously attached on the solid matrix) may undergo inactivation with different inactivation coefficients. The governing coupled partial differential equations were solved numerically using finite difference methods, which were implemented explicitly or implicitly so that both stability and speed factors were satisfied. Furthermore, the experimental data collected by Syngouna and Chrysikopoulos [1] were satisfactorily fitted by the newly developed cotransport model.     

Plume Detachment and Recession Times in Fractured Rock

The influence of source zone concentration reduction on solute plume detachment and recession times in fractured rock was investigated using new semianalytical solutions to transient solute transport in the presence of advection, dispersion, sorption, matrix diffusion, and first-order decay. Novel aspects of these solutions are: (1) the source zone concentration behavior is simulated using a constant concentration with the option for either an instantaneous reduction to zero concentration or an exponentially decaying source zone concentration initiated at some time (t^*) after the source is introduced, and (2) different biodegradation rates in the fracture and rock matrix. These solutions were applied for sandstone bedrock and revealed that biodegradation in the matrix, not the fracture, may be the most significant attenuation mechanism and therefore may dictate remediation time scales. Also, instantaneous and complete source concentration reduction in aged plumes may not be beneficial with respect to plume response because back-diffusion can sustain plume migration for long periods of time. Moderate source zone concentration reduction has a similar impact on the rate of advance of the leading edge of the plume as aggressive concentration reduction. If the source zone concentration reduction half-life is less than the plume decay half-life, then volatile organic compound (VOC) mass sequestered in the rock matrix will ultimately dictate plume persistence and not the presence of the source zone.     

Application of generalized contaminant retardation factor to a multi‐phase system

In this study, a generalized contaminant retardation factor applicable to a multiphase system where various types of colloids exist simultaneously with contaminants is derived and incorporated into an equilibrium model which is successfully applied to experimental data for which phenanthrene was used as hydrophobic organic contaminants and dissolved organic matter (DOM) or bacteria as mobile carriers. Based on the parameter values for the experimental data regarding the association of phenanthrene with solid matrix, DOM and various bacterial isolates, numerical experiments are performed to examine the transport behaviour of hydrophobic organic contaminants in various types of the multiphase system. Numerical experiments demonstrate that the extent of contaminant transport enhancement depends on the adsorption affinity of the colloid, its concentration and its mobility, and that the importance of a third phase to contaminant transport needs to be evaluated carefully with respect to the relevance of experimental conditions applied to realistic environmental conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

Concentration rebound following in situ chemical oxidation in fractured clay

A two-dimensional, transient-flow, and transport numerical model was developed to simulate in situ chemical oxidation (ISCO) of trichloroethylene and tetrachloroethylene by potassium permanganate in fractured clay. This computer model incorporates dense, nonaqueous phase liquid dissolution, reactive aquifer material, multispecies matrix diffusion, and kinetic formulations for the oxidation reactions. A sensitivity analysis for two types of parameters, hydrogeological and engineering, including matrix porosity, matrix organic carbon, fracture aperture, potassium permanganate dosage, and hydraulic gradient, was conducted. Remediation metrics investigated were the relative rebound concentrations arising from back diffusion and percent mass destroyed. No well-defined correlation was found between the magnitude of rebound concentrations during postremedy monitoring and the amount of contaminant mass destroyed during the application. Results indicate that all investigated parameters affect ISCO remediation in some form. Results indicate that when advective transport through the fracture is dominant relative to diffusive transport into the clay matrix (large System Peclet Number), permanganate is more likely to be flushed out of the system and treatment is not optimal. If the System Peclet Number is too small, indicating that diffusion into the matrix is dominant relative to advection through the fracture, permanganate does not traverse the entire fracture, leading to postremediation concentration rebound. Optimal application of ISCO requires balancing advective transport through the fracture with diffusive transport into the clay matrix.     

Contaminant Spread and Flushing in Fractured Rocks Near Oak Ridge, Tennessee

Liquid wastes, including metals dissolved in nitric acid, were discharged into the S-3 Ponds from 1951 to 1983. During this period, contaminants in ground water spread along shallow fracture flow paths toward nearby streams. Also, a high concentration of nitrate in one well at a depth of 110 to 240 in shows that some contaminants may have moved downdip because of differences in fluid density. Neutralization of the ponds in June 1983 caused a dramatic decrease in the contaminant concentrations of Bear Creek about three months later. Since then, the contaminant concentrations of Bear Creek have decreased at a first-order exponential rate. This average rate, which is the same for both more reactive and less reactive constituents, can be interpreted to show that the contaminant reservoir consists of the unfractured rock matrix.
Flushing caused by the natural recharge and discharge of ground water is occurring at all locations, but contaminant concentrations are controlled by the relative rates of molecular diffusion from the rock matrix and advection along the fracture flow paths. Hushing has thus been most effective near the water table. If the exponential decrease in contaminant concentrations continues, water in Bear Creek will meet drinking water standards by 2012: regardless of any remedial action, contaminants will remain in the rocks for many years.     

Modelling and experimental study of coupled exchange of p,p′‐DDE and colloids in a flume simulated stream–streambed system

Stream–subsurface exchange plays a significant role in the fate and transport of contaminants in streams. It has been modelled explicitly by considering fundamental processes such as hydraulic exchange, colloid filtration, and contaminant interactions with streambed sediments and colloids. The models have been successfully applied to simulate the transport of inorganic metals and nutrients. In this study, laboratory experiments were conducted in a recirculating flume to investigate the exchange of a hydrophobic organic contaminant, p,p′‐dichloro‐diphenyl‐dichloroethane (DDE), between a stream and a quartz sand bed. A previously developed process‐based multiphase exchange model was modified by accounting for the p,p′‐DDE kinetic adsorption to and desorption from the bed sediments/colloids and was applied to interpret the experimental results. Model input parameters were obtained by conducting independent small‐scale batch experiments. Results indicate that the immobilization of p,p′‐DDE in the quartz sand bed can occur under representative natural stream conditions. The observed p,p′‐DDE exchange was successfully simulated by the process‐based model. The model sensitivity analysis results show that the exchange of p,p′‐DDE can be sensitive to either the sediment sorption/desorption parameters or colloidal parameters depending on the experimental conditions tested. For the experimental conditions employed here, the effect of colloids on contaminant transport is expected to be minimal, and the stream–subsurface exchange of p,p′‐DDE is dominated by the interaction of p,p′‐DDE with bed sediment. The work presented here contributes to a better mechanistic understanding of the complex transport process that hydrophobic organic contaminants undergo in natural streams and to the development of reliable, predictive models for the assessment of impacted streams. Copyright © 2015 John Wiley & Sons, Ltd.     

Retardation of organic contaminants in natural fractures in chalk

Transport of a conservative compound and two sorbing compounds through fractured chalk was studied using flow-through columns consisting of chalk cores with a single subvertical fracture. Two types of chalk matrix were compared, an oxidized white chalk with low organic carbon content (0.2%), and a gray chalk with a higher organic carbon content (1.3%). Initial rapid breakthrough followed by a delayed approach to a relative concentration of unity for the conservative compound (2,6–difluorobenzoic acid [DFBA]) was clear evidence for diffusion into the porous chalk matrix. Matrix diffusion of DFBA was apparently much greater in the gray chalk columns than in the white chalk columns. Breakthrough curves (BTCs) of the sorbing compounds (2,4,6–tri-bromophenol [TBP] and ametryn [AME]) were retarded in all cases as compared to the conservative compound. Sorption retardation was far greater in the gray chalk as compared with the white chalk, in good agreement with results from batch sorption experiments. BTCs for the conservative compound were relatively nonhysteretic for both white and gray chalk columns. In contrast, BTCs for the sorbing compounds were hysteretic in all cases, demonstrating that sorption was not at equilibrium before desorp-tion began. These experiments suggest that on a field scale, transport of contaminants through fractures in chalk and other fractured porous media will be attenuated by diffusion and sorption into the matrix.     

Colloid transport and distribution in the hyporheic zone

Colloids moving from the stream into the hyporheic zone may have a negative impact on aquatic ecosystems as they are potential contaminants or carriers of contaminants. Moreover, retained colloids in the hyporheic zone could not only reduce the exchange flux between the stream and streambed but also change the conditions of the bed, affecting the habitats for aquatic organisms. Previous studies focused on the exchange flux across the sediment–water interface, but the colloid transport processes and distribution of retained colloids in the streambed have received little attention. We conducted experiments within a laboratory flume to examine these processes in a streambed driven by bedform‐induced hyporheic flow. Retained colloids measured in the bed at the end of the experiments revealed colloid retention mainly in the shallow layer of hyporheic zone (0–5 cm below the interface). The results demonstrated significant effects of particle trapping and settling on the colloid transport and distribution in the streambed. Retention leads to the formation of a colloid‐filled shallow layer in the bed. Particle paths based on model simulations showed that colloid settling in pore water modifies the direction of colloid transport and allows the colloid particles to move more deeply in the bed.     

Bioremediation in Fractured Rock: 1. Modeling to Inform Design,Monitoring, and Expectations

Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.     

Effective macroscopic transport parameters between parallel plates with constant concentration boundaries

A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number.     

Discretizing the fracture-matrix interface to simulate solute transport

This article examines the required spatial discretization perpendicular to the fracture-matrix interface (FMI) for numerical simulation of solute transport in discretely fractured porous media. The discrete-fracture, finite-element model HydroGeoSphere ( Therrien et al. 2005 ) and a discrete-fracture implementation of MT3DMS ( Zheng 1990 ) were used to model solute transport in a single fracture, and the results were compared to the analytical solution of Tang et al. (1981) . To match analytical results on the relatively short timescales simulated in this study, very fine grid spacing perpendicular to the FMI of the scale of the fracture aperture is necessary if advection and/or dispersion in the fracture is high compared to diffusion in the matrix. The requirement of such extremely fine spatial discretization has not been previously reported in the literature. In cases of high matrix diffusion, matching the analytical results is achieved with larger grid spacing at the FMI. Cases where matrix diffusion is lower can employ a larger grid multiplier moving away from the FMI. The very fine spatial discretization identified in this study for cases of low matrix diffusion may limit the applicability of numerical discrete-fracture models in such cases.     

Matrix diffusion-derived plume attenuation in fractured bedrock

Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.     

Fractal travel time estimates for dispersive contaminants

Alternative fractional models of contaminant transport lead to a new travel time formula for arbitrary concentration levels. For an evolving contaminant plume in a highly heterogeneous aquifer, the new formula predicts much earlier arrival at low concentrations. Travel times of contaminant fronts and plumes are often obtained from Darcy's law calculations using estimates of average pore velocities. These estimates only provide information about the travel time of the average concentration (or peak, for contaminant pulses). Recently, it has been shown that finding the travel times of arbitrary concentration levels is a straightforward process, and equations were developed for other portions of the breakthrough curve for a nonreactive contaminant. In this paper, we generalize those equations to include alternative fractional models of contaminant transport.