Transport of a non-volatile contaminant in unsaturated porous media in the presence of colloids

Stable colloidal particles can travel long distances in subsurface environments and carry particle-reactive contaminants with them to locations further than predicted by the conventional advective-dispersive transport equation. When such carriers exist in a saturated porous medium, the system can be idealized as consisting of three phases: an aqueous phase, a carrier phase, and a stationary solid matrix phase. However, when colloids are present in an unsaturated porous medium, the system representation should include one more phase, i.e. the air phase. In the work reported, a mathematical model was developed to describe the transport and fate of the colloidal particles and a non-volatile contaminant in unsaturated porous media. The model is based on mass balance equations in a four-phase porous medium. Colloid mass transfer mechanisms among aqueous, solid matrix, and air phases, and contaminant mass transfer between aqueous and colloid phases are represented by kinetic expressions. Governing equations are non-dimensionalized and solved to investigate colloid and contaminant transport in an unsaturated porous medium. A sensitivity analysis of the transport model was utilized to assess the effects of several parameters on model behavior. The colloid transport model matches successfully with experimental data of Wan and Wilson. The presence of air-water interface retards the colloid transport significantly counterbalancing the facilitating effect of colloids. However, the retardation of contaminant transport by colloids is highly dependent on the properties of the contaminant and the colloidal surface.     

Preliminary 3-D site-scale studies of radioactive colloid transport in the unsaturated zone at Yucca Mountain,Nevada

The U.S. Department of Energy (DOE) is actively investigating the technical feasibility of permanent disposal of high-level nuclear waste in a repository to be situated in the unsaturated zone (UZ) at Yucca Mountain (YM), Nevada. In this study we investigate, by means of numerical simulation, the transport of radioactive colloids under ambient conditions from the potential repository horizon to the water table. The site hydrology and the effects of the spatial distribution of hydraulic and transport properties in the Yucca Mountain subsurface are considered. The study of migration and retardation of colloids accounts for the complex processes in the unsaturated zone of Yucca Mountain, and includes advection, diffusion, hydrodynamic dispersion, kinetic colloid filtration, colloid straining, and radioactive decay. The results of the study indicate that the most important factors affecting colloid transport are the subsurface geology and site hydrology, i.e., the presence of faults (they dominate and control transport), fractures (the main migration pathways), and the relative distribution of zeolitic and vitric tuffs. The transport of colloids is strongly influenced by their size (as it affects diffusion into the matrix, straining at hydrogeologic unit interfaces, and transport velocity) and by the parameters of the kinetic-filtration model used for the simulations. Arrival times at the water table decrease with an increasing colloid size because of smaller diffusion, increased straining, and higher transport velocities. The importance of diffusion as a retardation mechanism increases with a decreasing colloid size, but appears to be minimal in large colloids.     

A novel two-dimensional model for colloid transport in physically and geochemically heterogeneous porous media

A two-dimensional model for colloid transport in geochemically and physically heterogeneous porous media is presented. The model considers patchwise geochemical heterogeneity, which is suitable to describe the chemical variability of many surficial aquifers with ferric oxyhydroxide-coated porous matrix, as well as spatial variability of hydraulic conductivity, which results in heterogeneous flow field. The model is comprised of a transient fluid flow equation, a transient colloid transport equation, and an equation for the dynamics of colloid deposition and release. Numerical simulations were carried out with the model to investigate the colloid transport behavior in layered and randomly heterogeneous porous media. Results demonstrate that physical and geochemical heterogeneities markedly affect the colloid transport behavior. Layered physical or geochemical heterogeneity can result in distinct preferential flow paths of colloidal particles. Furthermore, the combined effect of layered physical and geochemical heterogeneity may result in enhanced or reduced preferential flow of colloids. Random distribution of physical heterogeneity (hydraulic conductivity) results in a random flow field and an irregularly distributed colloid concentration profile in the porous medium. Contrary to random physical heterogeneity, the effect of random patchwise geochemical heterogeneity on colloid transport behavior is not significant. It is mostly the mean value of geochemical heterogeneity rather than its distribution that governs the colloid transport behavior.     

Colloid and suspended particle migration experiments in a granite fracture

To determine the mobility of colloids (0.001–0.45 μm) and suspended particles (> 0.45 μm) in granite fractures, laboratory particle-migration and conservative tracer studies have been carried out in a natural fracture within a large granite block, with overall dimensions of 83×90×60 cm. Flow fields within this horizontal fracture were controlled through a set of 9 boreholes drilled orthogonally to the fracture. Laboratory experiments were performed using a range of average water velocities which contained values low enough to closely approximate the natural flow velocities of < 2 m yr⁻¹ in plutonic rocks of the Canadian Shield. The particles used had diameters between 0.02 and 22 μm, and included latex spheres, glass spheres and colloidal silica. Migration experiments were carried out with a filtered groundwater, ionic strength of 0.01 mol kg⁻¹, obtained from a granite fracture within the Whiteshell Research Area of Manitoba. Flushing experiments showed that suspended particles as large as 40 μm could be mobilized from the fracture surface. The mobility of suspended particles was significantly less than that of colloids. However, within the size range of colloids used in these studies (0.022–0.090 μm), colloid size did not affect colloid migration. Although, in general, colloids eluted ahead of the conservative tracer, colloid mobility was significantly reduced when the average groundwater velocity dropped below between 32 and 240 m yr⁻¹. Colloid transport was found to be very sensitive to flow path and flow direction.     

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.     

Field-scale colloid migration experiments in a granite fracture

An understanding of particle migration in fractured rock, required to assess the potential for colloid-facilitated transport of radionuclides, can best be evaluated when the results of laboratory experiments are demonstrated in the field. Field-scale migration experiments with silica colloids were carried out at AECL's Underground Research Laboratory (URL), located in southern Manitoba, to develop the methodology for large-scale migration experiments and to determine whether colloid transport is possible over distances up to 17 m. In addition, these experiments were designed to evaluate the effects of flow rate and flow path geometry, and to determine whether colloid tracers could be used to provide additional information on subsurface transport to that provided by conservative tracers alone. The colloid migration studies were carried out as part of AECL's Transport Properties in Highly Fractured Rock Experiment, the objective of which was to develop and demonstrate methods for evaluating the solute transport characteristics of zones of highly fractured rock. The experiments were carried out within fracture zone 2 as two-well recirculating, two-well non-recirculating, and convergent flow tests, using injection rates of 5 and 10 1 min⁻¹. Silica colloids with a 20 nm size were used because they are potentially mobile due to their stability, small size and negative surface charge. The shapes of elution profiles for colloids and conservative tracers were similar, demonstrating that colloids can migrate over distances of 17 m. The local region of drawdown towards the URL shaft affected colloid migration and, to a lesser extent, conservative tracer migration within the flow field established by the two-well tracer tests. These results indicate that stable colloids, with sizes as small as 20 nm, have different migration properties from dissolved conservative tracers. - 1997 Atomic Energy of Canada.     

Colloid transport in a geochemically heterogeneous porous medium: aquifer tank experiment and modeling

To examine colloid transport in geochemically heterogeneous porous media at a scale comparable to field experiments, we monitored the migration of silica-coated zirconia colloids in a two-dimensional layered porous media containing sand coated to three different extents by ferric oxyhydroxides. Transport of the colloids was measured over 1.65 m and 95 days. Colloid transport was modeled by an advection-dispersion-deposition equation incorporating geochemical heterogeneity and colloid deposition dynamics (blocking). Geochemical heterogeneity was represented as favorable (ferric oxyhydroxide-coated) and unfavorable (uncoated sand) deposition surface areas. Blocking was modeled as random sequential adsorption (RSA). Release of deposited colloids was negligible. The time to colloid breakthrough after the onset of blocking increased with increasing ferric oxyhydroxide-coated surface area. As the ferric oxyhydroxide surface area increased, the concentration of colloids in the breakthrough decreased. Model-fits to the experimental data were made by inverse solutions to determine the fraction of surface area favorable for deposition and the deposition rate coefficients for the favorable (ferric oxyhydroxide-coated) and unfavorable sites. The favorable deposition rate coefficient was also calculated by colloid filtration theory. The model described the time to colloid breakthrough and the blocking effect reasonably well and estimated the favorable surface area fraction very well for the two layers with more than 1% ferric oxyhydroxide coating. If mica edges in the uncoated sand were considered as favorable surface area in addition to the ferric oxyhydroxide coatings, the model predicted the favorable surface area fraction accurately for the layer with less than 1% ferric oxyhydroxide coating.     

Anomalous transport of colloids and solutes in a shear zone

Transport experiments with colloids and radionuclides in a shear zone were conducted during the Colloid and Radionuclide Retardation experiment (CRR) at Nagra's Grimsel Test Site. Breakthrough curves of bentonite colloids and uranine, a non-sorbing solute, were measured in an asymmetric dipole flow field. The colloid breakthrough is earlier than that of uranine. Both breakthrough curves show anomalously long late time tails and the slope of the late time tails for the colloids is slightly higher. Anomalous late time tails are commonly associated with matrix diffusion processes; the diffusive interaction of solutes transported in open channels with the adjacent porous rock matrix or zones of stagnant water. The breakthrough curves for different colloid size classes are very similar and show no signs of fractionation due to their (size-dependent) diffusivity. It is proposed that tailing of the colloids is mainly caused by the structure of the flow field and that for the colloid transport, matrix diffusion is of minor importance. This has consequences for the interpretation of the uranine breakthrough. Comparisons of experimental results with numerical studies and with the evaluation of the colloid breakthrough with continuous time random theory imply that the tailing in the conservative solute breakthrough in this shear zone is not only caused by matrix diffusion. Part of the tailing can be attributed to advective transport in fracture networks and advection in low velocity regions. Models based on the advection-dispersion equation and matrix diffusion do not properly describe the temporal and spatial evolution of colloid and solute transport in such systems with a consistent set of parameters.     

Migration of a water pulse through fractured porous media

Contaminant transport from waste-disposal sites is strongly affected by the presence of fractures and the degree of fracture matrix interaction. Characterization of potential contaminant plumes at such sites is difficult, both experimentally and numerically. Simulations of water flow through fractured rock were performed to examine the penetration depth of a large pulse of water entering such a system. Construction water traced with lithium bromide was released during the excavation of a tunnel at Yucca Mountain, Nevada, which is located in an unsaturated fractured tuff formation. Modeling of construction-water migration is qualitatively compared with bromide-to-chloride ratio (Br/Cl) data for pore-water salts extracted from drillcores. The influences of local heterogeneities in the fracture network and variations in hydrogeologic parameters were examined by sensitivity analyses and Monte Carlo simulations. The simulation results are qualitatively consistent with the observed Br/Cl signals, although these data may only indicate a minimum penetration depth, and water may have migrated farther through the fracture network.     

Colloid migration in symmetrical non-uniform fractures: particle tracking in three dimensions

A three-dimensional model for the migration of colloids in a saturated fracture is presented, which considers the motion of colloids as a result of advection and diffusion, as well as colloid-surface interactions at the fracture walls. This model is successfully incorporated into a three-dimensional particle tracking algorithm that tracks particles within a continuum and allows consideration of the migration of colloids in symmetrical, three-dimensional, non-uniform fractures. The framework is general enough to incorporate non-local interactions that provide colloid motion relative to the fluid. The algorithm is verified against classical Taylor dispersion, and its generalization to a sorbing phase, in a uniform fracture and shows excellent agreement with theory. A simple, non-uniform fracture that has an analytically tractable velocity field is also considered, and both quantitative and qualitative comparisons are made with the uniform fracture case. The modelling of more complex fracture geometries is also discussed and a particular case is implemented within the particle tracking framework.     

Strontium migration in a crystalline medium: effects of the presence of bentonite colloids

The effects of bentonite colloids on strontium migration in fractured crystalline medium were investigated. We analyzed first the transport behaviour of bentonite colloids alone at different flow rates; then we compared the transport behaviour of strontium as solute and of strontium previously adsorbed onto stable bentonite colloids at a water velocity of approximately 7.1·10(-6)m/s-224m/yr. Experiments with bentonite colloids alone showed that - at the lowest water flow rate used in our experiments (7.1·10(-6)m/s) - approximately 70% of the initially injected colloids were retained in the fracture. Nevertheless, the mobile colloidal fraction, moved through the fracture without retardation, at any flow rate. Bentonite colloids deposited over the fracture surface were identified during post-mortem analyses. The breakthrough curve of strontium as a solute, presented a retardation factor, R(f)~6, in agreement with its sorption onto the granite fracture surface. The breakthrough curve of strontium in the presence of bentonite colloids was much more complex, suggesting additional contributions of colloids to strontium transport. A very small fraction of strontium adsorbed on mobile colloids moved un-retarded (R(f)=1) and this fraction was much lower than the expected, considering the quantity of strontium initially adsorbed onto colloids (90%). This behaviour suggests the hypothesis of strontium sorption reversibility from colloids. On the other hand, bentonite colloids retained within the granite fracture played a major role, contributing to a slower strontium transport in comparison with strontium as a solute. This was shown by a clear peak in the breakthrough curve corresponding to a retardation factor of approximately 20.     

Transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic interactions

Transport of reactive colloids in groundwater may enhance the transport of contaminants in groundwater. Often, the interpretation of results of transport experiments is not a simple task as both reactions of colloids with the solid matrix and reactions of contaminants with the solid matrix and mobile and immobile colloids may be time dependent and nonlinear. Further colloid transport properties may differ from solute transport properties. In this paper, a one-dimensional model for coupled and contaminant in a porous medium (COLTRAP) is presented together with simulation results. Calculated breakthrough curves (BTC's) during contamination and decontamination show systematically the effect of nonlinear and kinetic interactions on contaminant transport in the presence of reactive colloids, and the effect of colloid transport properties that differ from solute transport properties. It is shown that in case of linear kinetic reactions, the rate of exchange of mobile and immobile colloids have a large impact on the shape of BTC's even if the solid matrix is saturated with respect to colloids. BTC's during the contamination and decontamination phase have identical shapes in this case. Moreover, the slow reactions of contaminants and colloids may lead to unretarded breakthrough of contaminants. Independent of reaction rates, nonlinear reactions lead to BTC's that are steeper during contamination than in the linear case. A characteristic aspect of nonlinear sorption is that shapes of BTC's differ during the contamination and decontamination phase. It has been observed that shapes of some of the simulated adsorption and desorption curves are similar as shapes found in experiments reported in literature. This stresses the importance of incorporating both kinetics and nonlinearity in models for coupled colloid and contaminant transport and the capability of COLTRAP to interpret experimental results. Finally, to figure out whether nonlinear processes play a role, it is very important to consider both contamination and decontamination in transport experiments.     

Particle transport in unsaturated fractured chalk under arid conditions

A series of field and laboratory experiments were conducted to study the mechanisms of particle detachment and transport from fractures in vadose chalk. Experiments of intermittent flow events along fracture surfaces were carried out in the laboratory. In the field, water was percolated from land surface via a discrete fracture into a compartmental sampler installed inside a horizontal corehole located I m below the surface. The mass, size distribution, and composition of the particles drained from the fracture voids were examined along with flow rates and salt dissolution. Two boreholes penetrating the underlying saturated zone were sampled and analyzed for colloidal concentration and composition. Most of the particle and solute release at the drained effluents occurred during the first several hours of flow, but erratic pulses of particles were still observed after long periods of time. Most of the detached particles had a mean diameter of >2 microm, while the mobile colloidal phase in the groundwater had a mean diameter of approximately 1 microm. Mineralogical composition of the groundwater colloids and the particles detached from the upper vadose fracture were similar. Laboratory observations demonstrated the importance of the existence of a coating layer, made of weathered particles and salts, on particle detachment. The results of this study suggest that: (1) particle detachment causes flow-rate variability in the unsaturated fracture; (2) the mechanisms of particle detachment and salt dissolution within the fracture are linked: and (3) although most of the detached particles are large and likely to accumulate inside fractures, some colloidal particles also eroded from the fracture void and are likely to be transported to the groundwater.     

Colloid facilitated transport of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) to the groundwater at Ma Da Area, Vietnam

PCDD/Fs are hydrophobic organic substances and strongly sorbing to soil particles. Once adsorbed to soil particles they are believed to be virtually immobile. However, research in the last decades confirmed that strong sorbing contaminants may reach the groundwater via colloid-facilitated transport. This pathway has not been investigated before in Vietnam. Ma Da area, 100 km north of Ho Chi Minh City, was repeatedly sprayed during the Vietnam War (1962–1971) with herbicides like Agent Orange containing, beside others, the teratogenic contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). 11 surface soil samples and 12 water samples were collected in Ma Da area for analysis of PCDD/Fs in solids. Soil TCDD concentrations ranged from 1–41 ppt with a mean of 8.8 ppt and a mean I-TEQ of 9.7 ppt. Two surface water samples showed colloid bound TCDD (7 and 19 ppt). Groundwater samples showed elevated colloid bound PCDD concentrations (mean 770 ng/kg), mainly octachlorodibenzo-p-dioxin. Groundwater colloids separated by filtration did not show any TCDD. The results support that TCDD/Fs can be relocated from the top soil to the groundwater by colloidal pathway. They did not provide evidence that the dioxins bound to groundwater colloids are leftovers from the Second Indochinese War. However, this study reinforces that the colloidal transport pathway has to be included investigating the relocation of strong sorbing organic contaminants.     

Numerical analysis of water and solute transport in variably-saturated fractured clayey till

This study numerically investigates the influence of initial water content and rain intensities on the preferential migration of two fluorescent tracers, Acid Yellow 7 (AY7) and Sulforhodamine B (SB), through variably-saturated fractured clayey till. The simulations are based on the numerical model HydroGeoSphere, which solves 3D variably-saturated flow and solute transport in discretely-fractured porous media. Using detailed knowledge of the matrix, fracture, and biopore properties, the numerical model is calibrated and validated against experimental high-resolution tracer images/data collected under dry and wet soil conditions and for three different rain events. The model could reproduce reasonably well the observed preferential migration of AY7 and SB through the fractured till, although it did not capture the exact depth of migration and the negligible impact of the dead-end biopores in a near-saturated matrix. A sensitivity analysis suggests fast flow mechanisms and dynamic surface coating in the biopores, and the presence of a plough pan in the till.     

Analysis of colloid and tracer breakthrough curves

We consider the dispersion and elution of colloids and dissolved nonsorbing tracers within saturated heterogeneous porous media. Since flow path geometry in natural systems is often ill-characterized macroscopic (mean) flow rates and dispersion tensors are utilized in order to account for the sub-model scale microscopic fluctuations in media structure (and the consequent hydrodynamic profile). Even for tracer migration and dispersal this issue is far from settled.Here we consider how colloid and tracer migration phenomena can be treated consistently. Theoretical calculations for model flow geometries yield two quantitative predictions for the transport of free (not yet captured) colloids with reference to a non-sorbing dissolved tracer within the same medium: the average migration velocity of the free colloids is higher than that of the tracer; and that the ratio of the equivalent hydrodynamic dispersion rates of colloids and tracer is dependent only upon properties of the colloids and the porous medium, it is independent of pathlengths and fluid flux, once length scales are large enough.The first of these is well known, since even in simple flow paths free colloids must stay more centre stream. The second, if validated suggests how solute and colloid dispersion may be dealt with consistently in macroscopic migration models. This is crucial since dispersion is usually ill-characterized and unaddressed by the experimental literature. In this paper we present evidence based upon an existing Drigg field injection test for the validity of these predictions.We show that starting from experimental data the fitted dispersion rates of both colloids and non-sorbing tracers increase with the measured elution rates (obeying slightly different rules for tracers and colloids); and that the ratio of colloid and nonsorbing tracer elution rates, and the ratio of colloid and nonsorbing tracer dispersion rates may be dependent upon properties of the colloids and the medium (not the flow regime).It is important to realize that even for unretarded species, an earlier peak in the breakthrough curve does not necessarily correspond to a faster mean elution rate, or vice versa. But rather that a colloid may elute faster but disperse less than an equivalent tracer. Hence its peak may be retarded compared to that of the tracer, even assuming no retardation. Hence one must consider a combination of mean elution rate and mean dispersion rate, and not rely on “peak times” to corroborate chromatographic effects. The importance of this lies in the fact that these processes are not independent and yet upscale differently. Thus realistic estimates of effective colloid dispersion rates should be upscaled in a way consistent with that adopted for tracers within the same system.     

Colloid-facilitated transport of radionuclides through fractured media

The sorption of radionuclides on natural colloids may significantly modify their transport behaviour through fractured media, since radionuclides bound to colloids may not be subject to the important retardation mechanisms of matrix diffusion and sorption onto pore surfaces. This paper reports on theoretical and experimental work aimed at assessing the relevance of colloid-facilitated transport to repository safety analyses, with specific reference to the Swiss case. Transport models are presented, developed in conjunction with field- and laboratory-based studies of deep groundwater in the crystalline basement of northern Switzerland, in which colloid size distributions, compositions and sorption properties have been measured. Various potential mechanisms giving rise to both reversible and irreversible sorption are discussed. In the first case, a simple approach is examined which is based on previously reported models of colloid transport and assumes reversible, linear sorption on colloids, for which experimental data have been obtained. It is shown that transport of radionuclides would not, in general, be significantly enhanced because of this process. A more recently developed and more complex model is then described incorporating irreversible sorption, in which case the transport of radionuclides tends to be strongly dependent on the extent of colloid-fracture wall interaction.     

Laboratory migration experiments with radionuclides and natural colloids in a granite fracture

Natural colloids in groundwater could facilitate radionuclide transport, provided the colloids are mobile, are present in sufficient concentrations and can adsorb radionuclides. This paper describes the results of a laboratory migration study carried out with combinations of radionuclides and natural colloids within a fracture in a large granite block to experimentally determine the impact of colloids on radionuclide transport. The 85Sr used in this study is an example of a moderately sorbing radionuclide, while the 241Am is typical of a strongly sorbed radionuclide with very low solubility. The natural colloids used in this study were isolated from granite groundwater from Atomic Energy of Canada (AECL) Underground Research Laboratory (URL), and consisted of mostly 1-10 nm organic colloids, along with lesser amounts of 10-450 nm colloids (organics and aluminosilicates). The measured coefficients for radionuclide sorption onto these colloids were between 3 x 10(2) and 1 x 10(3) ml/g for 85Sr, and between 7 x 10(4) and 7 x 10(5) mg/l for 241Am. The 85Sr sorption on the natural colloids appeared to be reversible. Migration experiments in the granite block were carried out by establishing a flow field between two boreholes (out of a total of nine) intersecting a main horizontal fracture. These experiments showed that dissolved 85Sr behaved as a moderately sorbing tracer, while dissolved 241Am was completely adsorbed by the fracture surfaces and showed no evidence of transport. However, when natural colloids were injected together with dissolved 241Am, a small amount of 241Am transport was observed, demonstrating the ability of natural colloids to facilitate the transport of radionuclides with low solubility. Natural colloids had only a minor effect on the transport of 85Sr. In a separate experiment to test the effect of higher colloid concentrations on 85Sr migration, synthetic colloids were produced from Avonlea bentonite. The introduction of a relatively high concentration of bentonite colloids actually reduced 85Sr transport because, compared to natural colloids, the bentonite colloids were less mobile and they sorbed 85Sr more strongly.     

Variable-density groundwater flow and solute transport in heterogeneous porous media: approaches, resolutions and future challenges

In certain hydrogeological situations, fluid density variations occur because of changes in the solute or colloidal concentration, temperature, and pressure of the groundwater. These include seawater intrusion, high-level radioactive waste disposal, groundwater contamination, and geothermal energy production. When the density of the invading fluid is greater than that of the ambient one, density-driven free convection can lead to transport of heat and solutes over larger spatial scales and significantly shorter time scales than compared with diffusion alone. Beginning with the work of Lord Rayleigh in 1916, thermal and solute instabilities in homogeneous media have been studied in detail for almost a century. Recently, these theoretical and experimental studies have been applied in the study of groundwater phenomena, where the assumptions of homogeneity and isotropy rarely, if ever, apply. The critical role that heterogeneity plays in the onset as well as the growth and/or decay of convective motion is discussed by way of a review of pertinent literature and numerical simulations performed using a variable-density flow and solute transport numerical code. Different styles of heterogeneity are considered and range from continuously "trending" heterogeneity (sinusoidal and stochastic permeability distributions) to discretely fractured geologic media. Results indicate that both the onset of instabilities and their subsequent growth and decay are intimately related to the structure and variance of the permeability field. While disordered heterogeneity tends to dissipate convection through dispersive mixing, an ordered heterogeneity (e.g., sets of vertical fractures) allows instabilities to propagate at modest combinations of fracture aperture and separation distances. Despite a clearer understanding of the processes that control the onset and propagation of instabilities, resultant plume patterns and their migration rates and pathways do not appear amenable to prediction at present. The classical Rayleigh number used to predict the occurrence of instabilities fails, in most cases, when heterogeneous conditions prevail. The incorporation of key characteristics of the heterogeneous permeability field into relevant stability criteria and numerical models remains a challenge for future research.     

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).