Analysis of field observations of tracer transport in a fractured till

We analyze a set of observations from a recently published, field-scale tracer test in a fractured till. These observations demonstrate a dominant, underlying non-Fickian behavior, which cannot be quantified using traditional modeling approaches. We use a continuous time random walk (CTRW) approach which thoroughly accounts for the measurements, and which is based on a physical picture of contaminant motion that is consistent with the geometric and hydraulic characterization of the fractured formation. We also incorporate convolution techniques in the CTRW theory, to consider transport between different regions containing distinct heterogeneity patterns. These results enhance the possibility that limitations in predicting non-Fickian modes of contaminant migration can be overcome.     

A stochastic multi-channel model for solute transport--analysis of tracer tests in fractured rock

Some of the basic assumptions of the advection-dispersion model (AD-model) are revisited. This model assumes a continuous mixing along the flowpath similar to Fickian diffusion. This implies that there is a constant dispersion length irrespective of observation distance. This is contrary to most field observations. The properties of an alternative model based on the assumption that individual water packages can retain their identity over long distances are investigated. The latter model is called the multi-channel model (MCh-model). Inherent in the latter model is that if the waters in the different pathways are collected and mixed, the "dispersion length" is proportional to distance. The conditions for when non-mixing between adjacent streams can be assumed are explored. The MCh- and AD-models are found to have very similar residence time distributions (RTD) for Peclet numbers larger than 3. A generalized relation between flowrate and residence time is developed, including the so-called cubic law and constant aperture assumptions. The two models extrapolate very differently when there is strong matrix interaction. The AD-model could severely underestimate the effluent concentration of a tracer pulse and overestimate the residence time. The conditions are explored for when in-filling particles in the fracture will not be equilibrated but will act as if there was seemingly a much larger flow wetted surface (FWS). It is found that for strongly sorbing tracers, relatively small particles can act in this way for systems and conditions that are typical of many tracer tests. The assumption that the tracer residence time found by cautiously injecting a small stream of traced water represents the residence time in the whole fracture is explored. It is found that the traced stream can potentially sample a much larger fraction of the fracture than the ratio between the traced flowrate and the total pumped flowrate. The MCh-model was used to simulate some recent tracer tests in what is assumed to be a single fracture at the Asp? Hard rock laboratory in Sweden. Non-sorbing tracers, HTO and Uranin were used to determine the mean residence time and its variance. Laboratory data on diffusion and sorption properties were used to "predict" the RTD of the sorbing tracers. At least 30 times larger FWS or 1000 times larger diffusion or sorption coefficients would be needed to explain the observed BTCs. Some possible reasons for such behavior are also explored.     

Analysis of a mesoscale infiltration and water seepage test in unsaturated fractured rock: Spatial variabilities and discrete fracture patterns

A mesoscale (21 m in flow distance) infiltration and seepage test was recently conducted in a deep, unsaturated fractured rock system at the crossover point of two underground tunnels. Water was released from a 3 mx4 m infiltration plot on the floor of an alcove in the upper tunnel, and seepage was collected from the ceiling of a niche in the lower tunnel. Significant temporal and (particularly) spatial variabilities were observed in both measured infiltration and seepage rates. To analyze the test results, a three-dimensional unsaturated flow model was used. A column-based scheme was developed to capture heterogeneous hydraulic properties reflected by these spatial variabilities observed. Fracture permeability and van Genuchten alpha parameter [van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892-898] were calibrated for each rock column in the upper and lower hydrogeologic units in the test bed. The calibrated fracture properties for the infiltration and seepage zone enabled a good match between simulated and measured (spatially varying) seepage rates. The numerical model was also able to capture the general trend of the highly transient seepage processes through a discrete fracture network. The calibrated properties and measured infiltration/seepage rates were further compared with mapped discrete fracture patterns at the top and bottom boundaries. The measured infiltration rates and calibrated fracture permeability of the upper unit were found to be partially controlled by the fracture patterns on the infiltration plot (as indicated by their positive correlations with fracture density). However, no correlation could be established between measured seepage rates and density of fractures mapped on the niche ceiling. This lack of correlation indicates the complexity of (preferential) unsaturated flow within the discrete fracture network. This also indicates that continuum-based modeling of unsaturated flow in fractured rock at mesoscale or a larger scale is not necessarily conditional explicitly on discrete fracture patterns.     

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

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

Flow and transport in unsaturated fractured rock: effects of multiscale heterogeneity of hydrogeologic properties

The heterogeneity of hydrogeologic properties at different scales may have different effects on flow and transport processes in a subsurface system. A model for the unsaturated zone of Yucca Mountain, Nevada, is developed to represent complex heterogeneity at two different scales: (1) layer scale corresponding to geologic layering and (2) local scale. The layer-scale hydrogeologic properties are obtained using inverse modeling, based on the available measurements collected from the Yucca Mountain site. Calibration results show a significant lateral and vertical variability in matrix and fracture properties. Hydrogeologic property distributions in a two-dimensional, vertical cross-section of the site are generated by combining the average layer-scale matrix and fracture properties with local-scale perturbations generated using a stochastic simulation method. The unsaturated water flow and conservative (nonsorbing) tracer transport through the cross-section are simulated for different sets of matrix and fracture property fields. Comparison of simulation results indicates that the local-scale heterogeneity of matrix and fracture properties has a considerable effect on unsaturated flow processes, leading to fast flow paths in fractures and the matrix. These paths shorten the travel time of a conservative tracer from the source (repository) horizon in the unsaturated zone to the water table for small fractions of total released tracer mass. As a result, the local-scale heterogeneity also has a noticeable effect on global tracer transport processes, characterized by an average breakthrough curve at the water table, especially at the early arrival time of tracer mass. However, the effect is not significant at the later time after 20% tracer mass reaches the water table. The simulation results also verify that matrix diffusion plays an important role in overall solute transport processes in the unsaturated zone at Yucca Mountain.     

A reaction-transport model for calcite precipitation and evaluation of infiltration fluxes in unsaturated fractured rock

The percolation flux in the unsaturated zone (UZ) is an important parameter addressed in site characterization and flow and transport modeling of the potential nuclear-waste repository at Yucca Mountain, NV, USA. The US Geological Survey (USGS) has documented hydrogenic calcite abundances in fractures and lithophysal cavities at Yucca Mountain to provide constraints on percolation fluxes in the UZ. The purpose of this study was to investigate the relationship between percolation flux and measured calcite abundances using reactive transport modeling. Our model considers the following essential factors affecting calcite precipitation: (1) infiltration, (2) the ambient geothermal gradient, (3) gaseous CO(2) diffusive transport and partitioning in liquid and gas phases, (4) fracture-matrix interaction for water flow and chemical constituents, and (5) water-rock interaction. Over a bounding range of 2-20 mm/year infiltration rate, the simulated calcite distributions capture the trend in calcite abundances measured in a deep borehole (WT-24) by the USGS. The calcite is found predominantly in fractures in the welded tuffs, which is also captured by the model simulations. Simulations showed that from about 2 to 6 mm/year, the amount of calcite precipitated in the welded Topopah Spring tuff is sensitive to the infiltration rate. This dependence decreases at higher infiltration rates owing to a modification of the geothermal gradient from the increased percolation flux. The model also confirms the conceptual model for higher percolation fluxes in the fractures compared to the matrix in the welded units, and the significant contribution of Ca from water-rock interaction. This study indicates that reactive transport modeling of calcite deposition can yield important constraints on the unsaturated zone infiltration-percolation flux and provide useful insight into processes such as fracture-matrix interaction as well as conditions and parameters controlling calcite deposition.     

Hydrocarbon infiltration and biodegradation in a landfarming experiment

The infiltration and biodegradation of medium molecular weight hydrocarbons were studied in field and lysimeter experiments. An initial loading rate of 4 kg m(-2) of a gas-oil cut (nC12-nC21) was applied and the weathering of hydrocarbons was monitored by gravimetry and capillary gas-chromatography. The composition and vertical distribution of biogenic hydrocarbons were studied in control plots. After 3.5 years, 94% of the fossil hydrocarbons were removed from the field and 83% from the lysimeter. Microbial degradation was active in the 30 cm upper layer of the soil. The undegraded residue was composed of cyclic alkanes and aromatics. Hydrocarbons were shown to penetrate down to 60 cm in the field and 80 cm in the lysimeter. A preferential infiltration of light hydrocarbons was noted in the lysimeter, and a selective adsorption of the heaviest compounds on the organo-mineral matrix was demonstrated in the superficial layer of the soil. The potential for leaching of unmodified hydrocarbons towards the groundwater was slight, whereas the input of total organic carbon resulting from microbial activity could account for more than 1% of the initial carbon load.     

Field-scale effective matrix diffusion coefficient for fractured rock: results from literature survey

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D_m^e, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D_m^e values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D_m^e to the lab-scale matrix diffusion coefficient, D_m, of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems.Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.     

Simulation of large particle transport near the surface under stable conditions: comparison with the Hanford tracer experiments

A plume model is presented describing the downwind transport of large particles (1–100 μm) under stable conditions. The model includes both vertical variations in wind speed and turbulence intensity as well as an algorithm for particle deposition at the surface. Model predictions compare favorably with the Hanford single and dual tracer experiments of crosswind integrated concentration (for particles: relative bias=−0.02 and 0.16, normalized mean square error=0.61 and 0.14, for the single and dual tracer experiments, respectively), whereas the US EPA's fugitive dust model consistently overestimates the observed concentrations at downwind distances beyond several hundred meters (for particles: relative bias=0.31 and 2.26, mean square error=0.42 and 1.71, respectively). For either plume model, the measured ratio of particle to gas concentration is consistently overestimated when using the deposition velocity algorithm of Sehmel and Hodgson (1978. DOE Report PNL-SA-6721, Pacific Northwest Laboratories, Richland, WA). In contrast, these same ratios are predicted with relatively little bias when using the algorithm of Kim et al. (2000. Atmospheric Environment 34 (15), 2387–2397).     

Development and testing of radionuclide transport models for fractured rock: examples from the Nagra/JNC Radionuclide Migration Programme in the Grimsel Test Site, Switzerland

The joint Swiss National Co-operative for the Disposal of Radioactive Waste (Nagra)/Japan Nuclear Cycle Development Institute (JNC) Radionuclide Migration Programme has now been on-going for over a decade in Nagra's Grimsel Test Site (GTS). The main aim of the programme has been the direct testing of radionuclide transport models in as realistic manner as possible. Although it will never be possible to fully test these models due to the large time and distance scales involved, tests of the model assumptions in scaled down but otherwise realistic conditions will contribute to developing confidence in the predictive power of the models. In this paper, the Nagra/JNC approach is highlighted with examples from a large programme of field, laboratory and natural analogue studies based around the GTS. The successes and failures are discussed as in the general approach to the thorough testing of predictive transport codes which will be used in repository performance assessment (PA). Some of the work is still on-going and this represents the first presentation of a unique set of results and conclusions.     

Using constant head step tests to determine hydraulic apertures in fractured rock

The initial step in the analysis of contaminant transport in fractured rock requires the consideration of groundwater velocity. Practical methods for estimating the average linear groundwater velocity (vˉ) in fractured rock require determination of hydraulic apertures which are commonly calculated by applying the cubic law using transmissivity (T) values and the number of hydraulically active fractures in the test interval. High-resolution, constant-head step injection testing of cored boreholes in a 100 m thick fractured dolostone aquifer was conducted using inflatable packers to isolate specific test intervals from the rest of the borehole. The steps in each test interval were gradually increased from very low to much higher injection rates. At smaller injection rates, the flow rate vs. applied pressure graph projects through the origin and indicates Darcian flow; non Darcian flow is evident at higher injection rates. Non-Darcian flow results in significantly lower calculated T values, which translates to smaller hydraulic aperture values. Further error in the calculated hydraulic aperture stems from uncertainty in the number of hydraulically active fractures in each test interval. This estimate can be inferred from borehole image and core logs, however, all of the fractures identified are not necessarily hydraulically active. This study proposes a method based on Reynolds number calculations aimed at improving confidence in the selection of the number of active fractures in each test interval.     

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.     

Analyses of locally measured bromide breakthrough curves from a natural gradient tracer experiment at Krauthausen

Solute travel time distributions were derived from breakthrough curves (BTCs) of bromide concentrations, which were measured during a large-scale tracer experiment in a quaternary fluviatile aquifer at Krauthausen. Travel time distributions to a specific point in the aquifer were derived from locally measured BTCs, using averaged absolute concentrations ?abs(x1,t), normalized concentrations ?norm(x1,t), and velocity-weighted normalized concentrations ?vw(x1,t). The travel time distributions were characterized in terms of equivalent convective-dispersive transport parameters: the equivalent solute velocity and equivalent dispersivity. Parameters were derived from BTCs using moment analyses and least-squares fits of the 1-D convection-dispersion equation (CDE). Both local and averaged BTCs showed pronounced tailing which was not well described by the 1-D CDE and which indicates the presence of macroscopic regions with low velocities in the aquifer. Therefore, dispersivities derived from CDE fits were significantly smaller than those derived from time moments. The BTCs of ?abs(x1,t) were dominated by only a few local BTCs with high concentrations and were less representative for the travel time distribution than BTCs of averaged normalized concentrations. Dispersivities derived from ?norm(x1,t) and ?vw(x1,t) were very similar. Finally, estimates of dispersivities and vertical correlation length of lnK, gamma 3, from BTCs were in agreement with a first-order estimate of the dispersivity and gamma 3 based on grain size data and flow meter measurements.     

Determination of the flow-wetted surface in fractured media

Diffusion and sorption in the rock matrix are important retardation mechanisms for radionuclide transport in fractured media. For the conditions existing in a deep repository in crystalline rock, interaction with the rock matrix is controlled by the water flowrate in the fractures and the surface area in contact with the flowing water (the so-called "flow-wetted surface" (FWS)). The flow-wetted surface may be determined from the frequency of open fractures intersecting a borehole. The choice of packer distance used in these hydraulic measurements is crucial, however, since several open fractures may be found in one packer interval. The use of a packer distance that is too large may result in a considerable underestimation of the flow-wetted surface. This is especially important in zones with a high frequency of open fractures (fracture zones) where a small packer distance is a fundamental requirement. A large volume of hydraulic data has been compiled in Sweden from measurements using quite small packer distances. Over the last decade, the most common packer distance used for the hydraulic tests has been 3 m, although some new measurements using a shorter packer distance have also been performed. In several cases, the resolution of these measurements has been less than 0.5 m. All these data have been analysed in detail. From these data, the flow-wetted surface has been calculated and compared with the flow-wetted surface estimated in earlier studies. The results show the importance of using a small packer distance for carrying out borehole transmissivity measurements.     

Simulations of physical nonequilibrium solute transport models: Application to a large-scale field experiment

Equations expressing the spatial moments of solute concentration distributions simulated by various models, in terms of model parameters, have recently been presented. Using independently obtained parameter values, these equations are used to compare simulations of physical non-equilibrium models with spatial moment data collected in a large-scale natural gradient experiment on solute transport. The physical nonequilibrium models examined postulate the existence of layered zones of immobile water through which solute is transported by a diffusion mechanism. It is found that the qualitative aspects of the measured moment behavior are simulated by the physical nonequilibrium models if the independently obtained parameters are modified somewhat on the basis of reasonable corrective assumptions. It is further demonstrated that the physical nonequilibrium models, using parameter values obtained from spatial data, can qualitatively simulate temporal behavior at individual well points in this relatively homogeneous aquifer.     

A multi-directional tracer test in the fractured Chalk aquifer of E. Yorkshire, UK

A multi-borehole radial tracer test has been conducted in the confined Chalk aquifer of E. Yorkshire, UK. Three different tracer dyes were injected into three injection boreholes and a central borehole, 25 m from the injection boreholes, was pumped at 330 m(3)/d for 8 days. The breakthrough curves show that initial breakthrough and peak times were fairly similar for all dyes but that recoveries varied markedly from 9 to 57%. The breakthrough curves show a steep rise to a peak and long tail, typical of dual porosity aquifers. The breakthrough curves were simulated using a 1D dual porosity model. Model input parameters were constrained to acceptable ranges determined from estimations of matrix porosity and diffusion coefficient, fracture spacing, initial breakthrough times and bulk transmissivity of the aquifer. The model gave equivalent hydraulic apertures for fractures in the range 363-384 microm, dispersivities of 1 to 5 m and matrix block sizes of 6 to 9 cm. Modelling suggests that matrix block size is the primary controlling parameter for solute transport in the aquifer, particularly for recovery. The observed breakthrough curves suggest results from single injection-borehole tracer tests in the Chalk may give initial breakthrough and peak times reasonably representative of the aquifer but that recovery is highly variable and sensitive to injection and abstraction borehole location. Consideration of aquifer heterogeneity suggests that high recoveries may be indicative of a high flow pathway adjacent, but not necessarily connected, to the injection and abstraction boreholes whereas low recoveries may indicate more distributed flow through many fractures of similar aperture.     

Rapid measurements and mapping of tracer gas concentrations in a large indoor space

Rapid mapping of gas concentrations in air benefits studies of atmospheric phenomena ranging from pollutant dispersion to surface layer meteorology. Here we demonstrate a technique that combines multiple-open-path tunable-diode-laser spectroscopy and computed tomography to map tracer gas concentrations with approximately 0.5 m spatial and 7 s temporal resolution. Releasing CH₄ as a tracer gas in a large (7 m×9 m×11 m high) ventilated chamber, we measured path-integrated CH₄ concentrations over a planar array of 28 “long” (2–10 m) optical paths, recording a complete sequence of measurements every 7 s during the course of hour-long experiments. Maps of CH₄ concentration were reconstructed from the long path data using a computed tomography algorithm that employed simulated annealing to search for a best fit solution. The reconstructed maps were compared with simultaneous measurements from 28 “short” (0.5 m) optical paths located in the same measurement plane. On average, the reconstructed maps capture ∼74% of the variance in the short path measurements. The accuracy of the reconstructed maps is limited, in large part, by the number of optical paths and the time required for the measurement. Straightforward enhancements to the instrumentation will allow rapid mapping of three-dimensional gas concentrations in indoor and outdoor air, with sub-second temporal resolution.     

Source function estimate by means of variational data assimilation applied to the ETEX-I tracer experiment

The ETEX data set opens new possibilities to develop data assimilation procedures in the area of long-range transport. This paper illustrates the possibilities using a variational approach, where the source term for ETEX-I was reconstructed. The MATCH model (Robertson et al., 1996) has been the basis for this attempt. The timing of the derived emission rates are in accordance with the time period for the ETEX-I release, and a cross validation, with observations beyond the selected assimilation period, shows that the source term gained holds for the entire ETEX-I experiment. A poor-man variational approach was shown to perform nearly as good as a fully variational data assimilation. The issue of quality control has not been considered in this attempt but will be an important part that has to be addressed in future work.     

Interpreting organic solute transport data from a field experiment using physical nonequilibrium models

In a field experiment, two inorganic tracers and five organic solutes were injected into an unconfined sand aquifer. Breakthrough response curves were obtained at several points downgradient of the injection zone. These response curves are analyzed using a model which assumes equilibrium sorption and two models which postulate physical nonequilibrium. The physical nonequilibrium models hypothesize the existence of zones of immobile water, which act as diffusion sources and sinks for the solutes. The physical nonequilibrium models better simulate the sharp breakthrough and extended tailing exhibited by the experimental responses than does the model assuming equilibrium sorption. The reasonableness of parameters obtained from curve-fitting the data is assessed. The two physical nonequilibrium models are compared.