An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).     

A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.     

Bacteriophage transport through a fining-upwards sedimentary sequence: laboratory experiments and simulation

A column containing four concentric layers of progressively finer-grained glass beads (graded column) was used to study the transport of the bacteriophage T7 in water flowing parallel to layering through a fining-upwards (FU) sedimentary structure. By passing a pulse of T7, and a conservative solute tracer upwards through a column packed with a single bead size (uniform column), the capacity of each bead type to attenuate the bacteriophage was determined. Solute and bacteriophage responses were modelled using an analytical solution to the advection-dispersion equation, with first-order kinetic deposition simulating bacteriophage attenuation. Resulting deposition constants for different flow velocities indicated that filtration theory-determined values differed from experimentally determined values by less than 10%. In contrast, the responses of solute and bacteriophage tracers passing upwards through graded columns could not be reproduced with a single analytical solution. However, a flux-weighted summation of four one-dimensional advective-dispersive analytical terms approximated solute breakthrough curves. The prolonged tailing observed in the resulting curve resembled that typically generated from field-based tracer test data, reflecting the potential importance of textural heterogeneity in the transport of dissolved substances in groundwater. Moreover, bacteriophage deposition terms, determined from filtration theory, reproduced the T7 breakthrough curve once desorption and inactivation on grain surfaces were incorporated. To evaluate the effect of FU sequences on mass transport processes in more detail, bacteriophage passage through sequences resembling those sampled from a FU bed in a fluvioglacial gravel pit were carried out using an analogous approach to that employed in the laboratory. Both solute and bacteriophage breakthrough responses resembled those generated from field-based test data and in the graded column experiments. Comparisons with the results of simulations using averaged hydraulic conductivities show that simulations employing averaged parameters overestimate bacteriophage travel times and underestimate masses recovered and peak concentrations.     

Semi-analytical solution of two-dimensional sharp interface LNAPL transport models

In this paper, we present semi-analytical solutions for two-dimensional equations governing transport of Light Non-Aqueous Phase Liquids (LNAPL) in unconfined aquifers. The proposed model is based on sharp interface displacement and steady groundwater flow assumptions, where both the water–LNAPL interface and the LNAPL–air interface are represented as sharp interfaces. In the case of steady groundwater flow, these equations can be reduced to a two-dimensional nonlinear solute transport equation, with the LNAPL thickness in the free product lens being the primary unknown variable. The linearized form of this solute transport equation falls into the category of two-dimensional transport equation with time-dependent dispersion coefficients. This equation can be solved analytically for an infinite domain region. In this paper, the general form of the analytical solution for the transport equation, as well as the solutions for some specific cases are presented. To demonstrate the utility of the proposed solution, numerical results obtained for two example problems are discussed and presented comparatively with a finite-element solution and other more restrictive solutions available in the literature. Although the solutions discussed in this paper have some simplifying assumptions, such as sharp-interfaces between fluid phases, steady groundwater flow and homogeneous aquifer properties, the semi-analytical solutions presented in this study may be used effectively as bench mark solutions in evaluating LNAPL migration in the subsurface. These solutions are simple and cost effective to implement and may be used in the calibration of other more complex numerical solutions that can be found in the literature.     

Analytical solution to transport in three-dimensional heterogeneous well capture zones

Solute transport is investigated in a heterogeneous aquifer for combined natural-gradient and well flows. The heterogeneity is associated with the spatially varying hydraulic conductivity K(x, y, z), which is modelled as a log-normal stationary-random function. As such, the conductivity distribution is characterized by four parameters: the arithmetic mean K(A), the variance sigma(Y)(2) (Y=lnK), the horizontal integral scale I of the axisymmetric log-conductivity autocorrelation and the anisotropy ratio e=I(v)/I (I(v) is the vertical integral scale). The well fully penetrates an aquifer of constant thickness B and has given constant discharge QB, while the background aquifer flow is driven by an uniform mean head-gradient, - J. Therefore, for a medium of homogeneous conductivity K(A), the steady-state capture zone has a width 2L=Q/(K(A)|J|) far from the well (herein the term capture zone is used to refer both to the zone from which water is captured by a pumping well and the zone that captures fluid from an injecting well). The main aim is to determine the mean concentration as a function of time in fluid recovered by a pumping well or in a control volume of the aquifer that captures fluid from an injecting well. Relatively simple solutions to these complex problems are achieved by adopting a few assumptions: a thick aquifer B>I(v) of large horizontal extent (so that boundary effects may be neglected), weak heterogeneity sigma(Y)(2)<1, a highly anisotropic formation e<0.2 and neglect of pore-scale dispersion. Transport is analyzed to the first-order in sigma(Y)(2) in terms of the travel time of particles moving from or towards the well along the steady streamlines within the capture zone. Travel-time mean and variance to any point are computed by two quadratures for an exponential log-conductivity two-point covariance. Spreading is reflected by the variance value, which increases with sigma(Y)(2) and I/L. For illustration, the procedure is applied to two particular cases. In the first one, a well continuously injects water at constant concentration. The mean concentration as function of time for different values of the controlling parameters sigma(Y)(2) and I/L is determined within control volumes surrounding the well or in piezometers. In the second case, a solute plume, initially occupying a finite volume Omega(0), is drawn towards a pumping well. The expected solute recovery by the well as a function of time is determined in terms of the previous controlling parameters as well as the location and extent of Omega(0). The methodology is tested against a full three-dimensional simulation of a multi-well forced-gradient flow field test ([Lemke, L., W.B. II, Abriola, L., Goovaerts, P., 2004. Matching solute breakthrough with deterministic and stochastic aquifer models. Ground Water 42], SGS simulations). Although the flow and transport conditions are more complex than the ones pertinent to capture zones in uniform background flow, it was found that after proper adaptation the methodology led to results for the breakthrough curve in good agreement with a full three-dimensional simulation of flow and transport.     

Modeling hydrocarbon biodegradation in tidal aquifers with water-saturation and heat inhibition effects.

A model is developed for hydrocarbon biodegradation, which includes saturated and unsaturated flow, multi-species transport, heat transport, and bacterial growth processes. Numerical accuracy of the model was tested against analytical solutions. The model was also verified against laboratory results for a saturated-flow problem and reasonable match was obtained. Expressions are proposed for inhibition due to water content and temperature fluctuations. Bioactivities under cyclic water content variation were studied under no-flow conditions. A quantitative approach was used to reconcile some of the apparent contradictory conclusions regarding the efficiency of biodegradation of soils under wetting and drying conditions. The efficiency depends on the nature of the oxygenation process. For cases involving the presence of dissolved oxygen and the absence of O2 vapor, subjecting the soil to constant water content close to its optimal value for degradation is most efficient. However, wetting and drying can enhance degradation if O2 is only provided through aeration or direct contact between air and the medium. Also presented are the results of a typical field application of the model and a discussion of the effects of tides, saturation inhibition, and heat inhibition. Other inhibition factors, such as pH or salinity, can be easily incorporated in the formulation. The quantitative approach developed here can be used in assessing bioremediation not only in tidal aquifers but also in areas where water-table or temperature effects are of significance. The approach can be useful in the design of remediation strategies under water-flow or no-flow conditions involving water content and temperature fluctuations.     

The effect of surface-active solutes on water flow and contaminant transport in variably saturated porous media with capillary fringe effects

Organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. We used an intermediate-scale 2D flow cell (2.44 x 1.53 x 0.108 m) packed with a fine silica sand to investigate surfactant-induced flow perturbations. Surfactant solution (7% 1-butanol and dye tracer) was applied at a constant rate at a point source located on the soil surface above an unconfined synthetic aquifer with ambient groundwater flow and a capillary fringe of approximately 55 cm. A glass plate allowed for visual flow and transport observations. Thirty instrumentation stations consist of time domain reflectometry probes and tensiometers measured in-situ moisture content and pressure head, respectively. As surfactant solution was applied at the point source, a transient flow perturbation associated with the advance of the surfactant solution was observed. Above the top of the capillary fringe the advance of the surfactant solution caused a visible drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe below the point source because the air-entry pressure decreased in proportion to the decrease in surface tension caused by the surfactant. Eventually, a new capillary fringe height was established. The height of the depressed capillary fringe was proportional to height of the initial capillary fringe multiplied by the relative surface tension of the surfactant solution. The horizontal transport of surfactant in the depressed capillary fringe, driven primarily by the ambient groundwater flow, caused the propagation of a wedge-shaped drying front in the downgradient direction. Comparison of dye transport during the surfactant experiment to dye transport in an experiment without surfactant indicated that because surfactant-induced drainage decreased the storage capacity of the vadose zone, the dye breakthrough time to the water table was more than twice as fast when the contaminant solution contained surfactant. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time suggest the importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or systems, where surfactants are used for remediation of the vadose zone or unconfined aquifers.     

Analytical solutions for reactive transport under an infiltration-redistribution cycle

Transport of reactive solute in unsaturated soils under an infiltration-redistribution cycle is investigated. The study is based on the model of vertical flow and transport in the unsaturated zone proposed by Indelman et al. [J. Contam. Hydrol. 32 (1998) 77], and generalizes it by accounting for linear nonequilibrium kinetics. An exact analytical solution is derived for an irreversible desorption reaction. The transport of solute obeying linear kinetics is modeled by assuming equilibrium during the redistribution stage. The model which accounts for nonequilibrium during the infiltration and assumes equilibrium at the redistribution stage is termed partial equilibrium infiltration-redistribution model (PEIRM). It allows to derive approximate closed form solutions for transport in one-dimensional homogeneous soils. These solutions are further applied to computing the field-scale concentration by adopting the Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979) 461] column model. The effect of soil heterogeneity on the solute spread is investigated by modeling the hydraulic saturated conductivity as a random function of horizontal coordinates. The quality of the PEIRM is illustrated by calculating the critical values of the Damk?hler number which provide the achievable accuracy in estimating the solute mass in the mobile phase. The distinguishing feature of transport during the infiltration-redistribution cycle as compared to that of infiltration only is the finite depth of solute penetration. For irreversible desorption, the maximum solute penetration W/theta(r) is determined by the amount of applied water W and the residual water content theta(r). For sorption-desorption kinetics, the maximum depth of penetration z(r)(e, infinity ) also depends on the ratio between the rate of application and the column-saturated conductivity. It is shown that z(r)(e, infinity ) is bounded between the depths W/(theta(r)+K(d)) and W/theta(r) corresponding to the maximum solute penetration for equilibrium transport and for irreversible desorption, respectively. This feature of solute penetration explains the unusual phenomena of plume contraction after an initial period of spreading [Lessoff, S.C., Indelman, P., Dagan, G., 2002. Solute transport in infiltration-redistribution cycles in heterogeneous soils. In Raats, P.A.C., Smiles, D.,Warrick, A.W. (Eds), Environmental Mechanics: Water, Mass and Energy Transport in the Biosphere. American Geophysical Union, pp. 133-144]. Unlike transport under equilibrium conditions, when the solute is completely concentrated at the front, the solute under nonequilibrium conditions is spread out behind the front. Heterogeneity leads to additional spreading of the plume.     

Spatial and temporal variability of water repellency in a sandy soil contaminated with tar oil and heavy metals

Water repellency can induce preferential flow and thus affect water flow and contaminant transport at hazardous waste sites. Since the spatial patterns of water repellency are mostly unknown, it is problematic to use numerical transport models to predict leachate composition. In this study, the spatial variability of soil water repellency was studied at an industrial site contaminated with tar oil, chromium, copper and arsenic. The persistence of water repellency was assessed by the water drop penetration time (WDPT), and the degree of water repellency was quantified by the ethanol percentage (EP) test. Measurements were made at the soil surface along 3.5-12.1 m long transects at different times between March and October 2002. The spatial variability of WDPT, EP, water content, and organic matter content was quantified by variogram analyses. Both the persistence and the degree of water repellency varied seasonally, with the highest water repellency during the summer months. The correlation lengths of WDPT values ranged between 16 and 406 cm, whereas EP values showed no spatial correlation. For field-moist samples, a critical soil water threshold, below which water repellency prevails, was estimated to be 2.5-4%. For oven dry samples, the WDPT values were dependent on the water content prior to drying. The wide range of correlation lengths and the temporal dynamics of spatial repellency patterns suggest that simulations of solute leaching must consider the spatial and temporal variability of soil hydrophobic properties.     

Modelling tritium and phosphorus transport by preferential flow in structured soil

Subsurface solute transport through structured soil is studied by model interpretation of experimental breakthrough curves from tritium and phosphorus tracer tests in three intact soil monoliths. Similar geochemical conditions, with nearly neutral pH, were maintained in all the experiments. Observed transport differences for the same tracer are thus mainly due to differences in the physical transport process between the different monoliths. The modelling is based on a probabilistic Lagrangian approach that decouples physical and chemical mass transfer and transformation processes from pure and stochastic advection. Thereby, it enables explicit quantification of the physical transport process through preferential flow paths, honouring all independently available experimental information. Modelling of the tritium breakthrough curves yields a probability density function of non-reactive solute travel time that is coupled with a reaction model for linear, non-equilibrium sorption–desorption to describe the phosphorus transport. The tritium model results indicate that significant preferential flow occurs in all the experimental soil monoliths, ranging from 60–100% of the total water flow moving through only 25–40% of the total water content. In agreement with the fact that geochemical conditions were similar in all experiments, phosphorus model results yield consistent first-order kinetic parameter values for the sorption–desorption process in two of the three soil monoliths; phosphorus transport through the third monolith cannot be modelled because the apparent mean transport rate of phosphorus is anomalously rapid relative to the non-adsorptive tritium transport. The occurrence of preferential flow alters the whole shape of the phosphorus breakthrough curve, not least the peak mass flux and concentration values, and increases the transported phosphorus mass by 2–3 times relative to the estimated mass transport without preferential flow in the two modelled monoliths.     

Plant aided bioremediation in the vadose zone: model development and applications

Phytoremediation has the potential to enhance clean up of land contaminated by various pollutants. A mathematical model that includes a two-fluid phase flow model of water flow as well as a two-region soil model of contaminant reactions was developed and applied to various bioremediation scenarios in the unsaturated zone, especially to plant-aided bioremediation. To investigate model behavior and determine the main parameters and mechanisms that affect bioremediation in unplanted and planted soils, numerical simulations of theoretical scenarios were conducted before applying the model to field data. It is observed from the results that parameters affecting the contaminant concentration in the water phase, such as aqueous solubility, the octanol-water partition coefficient, and organic carbon content of the soil controlled the contaminant fate in the vadose zone. Simulation using the developed model also characterized the fate and transport of the contaminants both in planted and unplanted soils satisfactorily for field applications. Although phytoremediation has the potential for remediation of contaminated soils, results from both modeling and field studies suggested that plants may not always enhance the remediation efficiency when the soil already has a high microbial concentration, when the contaminant bioavailability is low, or when the overall reaction is mass transfer-limited. Therefore, other steps to increase contaminant bioavailability are needed in phytoremediation applications; natural purification mechanisms such as aging, volatilization, and natural bioremediation should be considered to maximize the plant effect and minimize the cost.     

Impact of varying soil structure on transport processes in different diagnostic horizons of three soil types

When soil structure varies in different soil types and the horizons of these soil types, it has a significant impact on water flow and contaminant transport in soils. This paper focuses on the effect of soil structure variations on the transport of pesticides in the soil above the water table. Transport of a pesticide (chlorotoluron) initially applied on soil columns taken from various horizons of three different soil types (Haplic Luvisol, Greyic Phaeozem and Haplic Cambisol) was studied using two scenarios of ponding infiltration. The highest infiltration rate and pesticide mobility were observed for the Bt₁ horizon of Haplic Luvisol that exhibited a well-developed prismatic structure. The lowest infiltration rate was measured for the Bw horizon of Haplic Cambisol, which had a poorly developed soil structure and a low fraction of large capillary pores and gravitational pores. Water infiltration rates were reduced during the experiments by a soil structure breakdown, swelling of clay and/or air entrapped in soil samples. The largest soil structure breakdown and infiltration decrease was observed for the Ap horizon of Haplic Luvisol due to the low aggregate stability of the initially well-aggregated soil. Single-porosity and dual-permeability (with matrix and macropore domains) flow models in HYDRUS-1D were used to estimate soil hydraulic parameters via numerical inversion using data from the first infiltration experiment. A fraction of the macropore domain in the dual-permeability model was estimated using the micro-morphological images. Final soil hydraulic parameters determined using the single-porosity and dual-permeability models were subsequently used to optimize solute transport parameters. To improve numerical inversion results, the two-site sorption model was also applied. Although structural changes observed during the experiment affected water flow and solute transport, the dual-permeability model together with the two-site sorption model proved to be able to approximate experimental data.     

Kinematic wave approximation to solute transport along preferred flow paths in soils

A routing procedure is introduced which accounts for the loss of a conservative solute tracer from preferred paths during macropore flow. Water flow is treated as a series of kinematic waves from which the tracer is lost due to mixing previously stored soil water, and an expression for solute loss is added to a previously developed model. The model parameters are estimated through experiments at three different input rates applied to a column of a macroporous forest soil.The results of seven experimental runs indicate that solute losses are consistently highest at the early stages of infiltration and drainage flow. An empirical relationship is proposed which links the frequency distribution of the flow parameter with that for solute loss from the preferred path during transient water flow and solute transport.     

Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.     

Monte Carlo analysis of field water flow comparing uni- and bimodal effective hydraulic parameters for structured soil

Soil structure critically affects the hydrological behaviour of soils. In this paper, we examined the impact of areal heterogeneity of hydraulic properties of a structured soil on soil ensemble behaviour for various soil water flow processes with different top boundary conditions (redistribution and drainage plus evaporation and infiltration). Using a numerical solution of the Richards' equation in a stochastic framework, the ensemble characteristics and flow dynamics were studied for drying and wetting processes observed during a time interval of ten days when a series of relatively intense rainfall events occurred. The effects of using unimodal and bimodal interpretative models of hydraulic properties on the ensemble hydrological behaviour of the soil were illustrated by comparing predictions to mean water contents measured over time in several sites at field scale. Although the differences between unimodal and bimodal fitting are not significant in terms of goodness of fit, the differences in process predictions are considerable with the bimodal soil simulating water content measurements much better than unimodal soil. We also investigated the relative contribution of the soil variability of each parameter on the variance of the water contents obtained as the main output of the stochastic simulations. The variability of the structural parameter, weighting the two pore space fractions in the bimodal interpretative model, has the largest contribution to water content variance. The contribution of each parameter depends only partly on the coefficient of variation, much more on the sensitivity of the model to the parameters and on the flow process being observed. We observed that the contribution of the retention parameters to uncertainty increases during drainage processes; the opposite occurs with the hydraulic conductivity parameters.     

A field experiment with variable-suction multi-compartment samplers to measure the spatio-temporal distribution of solute leaching in an agricultural soil

Solutes spread out in time and space as they move downwards from the soil surface with infiltrating water. Solute monitoring in the field is often limited to observations of resident concentrations, while flux concentrations govern the movement of solutes in soils. A recently developed multi-compartment sampler is capable of measuring fluxes at a high spatial resolution with minimal disturbance of the local pressure head field. The objective of this paper is to use this sampler to quantify the spatial and temporal variation of solute leaching below the root zone in an agricultural field under natural rainfall in winter and spring. We placed two samplers at 31 and 25 cm depth in an agricultural field, leaving the soil above undisturbed. Each sampler contained 100 separate cells of 31 × 31 mm. Water fluxes were measured every 5 min for each cell. We monitored leaching of a chloride pulse under natural rainfall by frequently extracting the collected leachate while leaving the samplers buried in situ. This experiment was followed by a dye tracer experiment. This setting yielded information that widely surpassed the information that can be provided by separate anionic and dye tracer trials, and solute transport monitoring by coring or suction cups. The detailed information provided by the samplers showed that percolation at the sampling depth started much faster (approximately 3 h after the start of rainfall) in initially wet soil (pressure head above − 65 cm) than in drier soil (more than 14 h at pressure heads below − 80 cm). At any time, 25% of the drainage passed through 5–6% of the sampled area, reflecting the effect of heterogeneity on the flow paths. The amount of solute carried by individual cells varied over four orders of magnitude. The lateral concentration differences were limited though. This suggests a convective–dispersive regime despite the short vertical travel distance. On the other hand, the dilution index indicates a slight tendency towards stochastic–convective transport at this depth. There was no evidence in the observed drainage patterns and dye stained profiles of significant disturbance of the flow field by the samplers.     

Interpretation of injection-withdrawal tracer experiments conducted between two wells in a large single fracture

Tracer experiments conducted using a flow field established by injecting water into one borehole and withdrawing water from another are often used to establish connections and investigate dispersion in fractured rock. As a result of uncertainty in the uniqueness of existing models used for interpretation, this method has not been widely used to investigate more general transport processes including matrix diffusion or advective solute exchange between mobile and immobile zones of fluid. To explore the utility of the injection-withdrawal method as a general investigative tool and with the intent to resolve the transport processes in a discrete fracture, two tracer experiments were conducted using the injection-withdrawal configuration. The experiments were conducted in a fracture which has a large aperture (>500 microm) and horizontally pervades a dolostone formation. One experiment was conducted in the direction of the hydraulic gradient and the other in the direction opposite to the natural gradient. Two tracers having significantly different values of the free-water diffusion coefficient were used. To interpret the experiments, a hybrid numerical-analytical model was developed which accounts for the arcuate shape of the flow field, advection-dispersion in the fracture, diffusion into the matrix adjacent to the fracture, and the presence of natural flow in the fracture. The model was verified by comparison to a fully analytical solution and to a well-known finite-element model. Interpretation of the tracer experiments showed that when only one tracer, advection-dispersion, and matrix diffusion are considered, non-unique results were obtained. However, by using multiple tracers and by accounting for the presence of natural flow in the fracture, unique interpretations were obtained in which a single value of matrix porosity was estimated from the results of both experiments. The estimate of porosity agrees well with independent measurements of porosity obtained from core samples. This suggests that: (i) the injection-withdrawal method is a viable tool for the investigation of general transport processes provided all relevant experimental conditions are considered and multiple conservative tracers are used; and (ii) for the conditions of the experiments conducted in this study, the dominant mechanism for exchange of solute between the fracture and surrounding medium is matrix diffusion.     

Evidence of one-dimensional scale-dependent fractional advection-dispersion

A semi-analytical inverse method and the corresponding program FADEMain for parameter estimation of the fractional advection-dispersion equation (FADE) were developed in this paper. We have analyzed Huang et al.'s [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large homogeneous and heterogeneous saturated soil columns. Trans. Porous Media 18, 283-302.] laboratory experimental data of conservative solute transport in 12.5-m long homogeneous and heterogeneous soil columns to test the non-Fickian dispersion theory of FADE. The dispersion coefficient was calculated by fitting the analytical solution of FADE to the measured data at different transport scales. We found that the dispersion coefficient increased exponentially with transport scale for the homogeneous column, whereas it increased with transport scale in a power law function for the heterogeneous column. The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. The increasing rate of dispersion coefficient versus transport distance was smaller for FADE than that for the advection-dispersion equation (ADE). Finite difference numerical approximations of the scale-dependent FADE were established to interpret the experimental results. The numerical solutions were found to be adequate for predicting scale-dependent transport in the homogeneous column, while the prediction for the heterogeneous column was less satisfactory.     

The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport

In this study, the potential effects of coupled transport phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay in Switzerland, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), are addressed. The solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters. shows that thermal osmosis is the only coupled transport mechanism that could, on its own, have a strong effect on repository performance. Based on the results from the analytical model, two-dimensional finite-difference models incorporating advection and thermal osmosis, and taking conservation of fluid mass into account, have been formulated. The results show that, under the conditions in the vicinity of the repository at the time scales of interest, and due to the constraints imposed by conservation of fluid mass, the advective component of flow will oppose and cancel the thermal-osmotic component. The overall conclusion is that coupled phenomena will only have a very minor impact on radionuclide transport in the Opalinus Clay, in terms of fluid and solute fluxes, at least under the conditions prevailing at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years).