Modeling tracer diffusion in fractured and unfractured, unsaturated, porous media

A proposed tracer diffusion test for the Exploratory Shaft Facility at Yucca Mountain, NV, is modeled. For the proposed test, a solution containing conservative tracers will be introduced into a borehole in the geologic medium of interest. The tracers will diffuse and advect from the saturated source region into the unsaturated matrix in the surrounding tuff. After some time, the borehole is to be overcored, and tracer concentrations in the fluid will be measured in the core as a function of distance from emplacement. The data will be used to evaluate diffusive behavior and to derive effective diffusion coefficients for the tracers in the specific tuff. Numerical simulations are used to study the effects of effective diffusion coefficient, porosity, saturation, and fracturing on tracer transport. Results are reported for numerical simulations of tests in the Topopah Spring Member and the Tuff of Calico Hills, which have significantly different porosities and saturations. The simulations make the following predictions: The spread of tracer during the test will be sensitive to the effective diffusion coefficient of the tracer. Tracer will diffuse farther in the Topopah Spring Member than in the Tuff of Calico Hills because of the former's lower porosity and saturation. Tracer transport by advection into the Topopah Spring Member will be greater than that into the Tuff of Calico Hills because of capillary effects. While advection will be a significant mechanism for tracer penetration into the Topopah Spring tuff, it will be less significant for tracer penetration into the Calico Hills tuff. The proximity of a single vertical fracture to the source region determines its effects on tracer transport, especially if the fracture diverts fluid flowing from the source region into the matrix.     

Field tracer-transport tests in unsaturated fractured tuff.

This paper presents the results of a field investigation in the unsaturated, fractured welded tuff within the Exploratory Studies Facility (ESF) at Yucca Mountain, NV. This investigation included a series of tests during which tracer-laced water was released into a high-permeability zone within a horizontal injection borehole. The tracer concentration was monitored in the seepage collected in an excavated slot about 1.6 m below the borehole. Results showed significant variability in the hydrologic response of fractures and the matrix. Analyses of the breakthrough curves suggest that flow and transport pathways are dynamic, rather than fixed, and related to liquid-release rates. Under high release rates, fractures acted as the predominant flow pathways, with limited fracture-matrix interaction. Under low release rates, fracture flow was comparatively less dominant, with a noticeable contribution from matrix flow. Observations of tracer concentrations rebounding in seepage water, following an interruption of flow, provided evidence of mass exchange between the fast-flowing fractures and slow- or non-flowing regions. The tests also showed the applicability of fluorinated benzoate tracers in situations where multiple tracers of similar physical properties are warranted.     

Modeling field-scale multiple tracer injection at a low-level waste disposal site in fractured rocks: effect of multiscale heterogeneity and source term uncertainty on conceptual understanding of mass transfer processes

Multiple factors may affect the scale-up of laboratory multi-tracer injection into structured porous media to the field. Under transient flow conditions and with multiscale heterogeneities in the field, previous attempts to scale-up laboratory experiments have not answered definitely the questions about the governing mechanisms and the spatial extent of the influence of small-scale mass transfer processes such as matrix diffusion. The objective of this research is to investigate the effects of multiscale heterogeneity, mechanistic and site model conceptualization, and source term density effect on elucidating and interpreting tracer movement in the field. Tracer release and monitoring information previously obtained in a field campaign of multiple, conservative tracer injection under natural hydraulic gradients at a low-level waste disposal site in eastern Tennessee, United States, is used for the research. A suite of two-pore-domain, or fracture-matrix, groundwater flow and transport models are calibrated and used to conduct model parameter and prediction uncertainty analyses. These efforts are facilitated by a novel nested Latin-hypercube sampling technique. Our results verify, at field scale, a multiple-pore-domain, multiscale mechanistic conceptual model that was used previously to interpret only laboratory observations. The results also suggest that, integrated over the entire field site, mass flux rates attributable to small-scale mass transfer are comparable to that of field-scale solute transport. The uncertainty analyses show that fracture spacing is the most important model parameter and model prediction uncertainty is relatively higher at the interface between the preferred flow path and its parent bedrock. The comparisons of site conceptual models indicate that the effect of matrix diffusion may be confined to the immediate neighborhood of the preferential flow path. Finally, because the relatively large amount of tracer needed for field studies, it is likely that source term density effect may exaggerate or obscure the effect of matrix diffusion on the movement of tracers from the preferred flow path into the bedrock.     

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.     

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.     

KAPPA-G,A Non-Gaussian Plume Dispersion Model: Description and Evaluation Against Tracer Measurements

This paper presents a mixed methodology for the simulation of atmospheric disperson phenomena in which vertical diffusion is computed using an analytical solution of the K-theory equation, while horizontal diffusion is simulated by the Gaussian formula. This new formulation, while maintaining a simple analytical form for the concentration field, incorporates the effects of power-law vertical profiles of both wind speed and eddy diffusivity. The performance of this approach, which has been implemented into a full computer package (KAPPA-G), is evaluated by comparison with data from SF₆ tracer experiments.     

Influence of hydrological and geochemical processes on the transport of chelated metals and chromate in fractured shale bedrock

Field-scale processes governing the transport of chelated radionuclides in groundwater remain conceptually unclear for highly structured, heterogeneous environments. The objectives of this research were to provide an improved understanding and predictive capability of the hydrological and geochemical mechanisms that control the transport behavior of chelated radionuclides and metals in anoxic subsurface environments that are complicated by fracture flow and matrix diffusion. Our approach involved a long-term, steady-state natural gradient field experiment where nonreactive Br- and reactive 57Co(II)EDTA2- 109CdEDTA2-, and 51Cr(VI) were injected into a fracture zone of a contaminated fractured shale bedrock. The spatial and temporal distribution of the tracer and solutes was monitored for 500 days using an array of groundwater sampling wells instrumented within the fast-flowing fracture regime and a slower flowing matrix regime. The tracers were preferentially transported along strike-parallel fractures coupled with the slow diffusion of significant tracer mass into the bedrock matrix. The chelated radionuclides and metals were significantly retarded by the solid phase with the mechanisms of retardation largely due to redox reactions and sorption coupled with mineral-induced chelate-radionuclide dissociation. The formation of significant Fe(III)EDTA byproduct that accompanied the dissociation of the radionuclide-chelate complexes was believed to be the result of surface interactions with biotite which was the only Fe(III)-bearing mineral phase present in these Fe-reducing environments. These results counter current conceptual models that suggest chelated contaminants move conservatively through Fe-reducing environments since they are devoid of Fe-oxyhydroxides that are known to aggressively compete for chelates in oxic regimes. Modeling results further demonstrated that chelate-radionuclide dissociation reactions were most prevalent along fractures where accelerated weathering processes are expected to expose more primary minerals than the surrounding rock matrix. The findings of this study suggest that physical retardation mechanisms (i.e. diffusion) are dominant within the matrix regime, whereas geochemical retardation mechanisms are dominant within the fracture regime.     

Experimental determination of sorption in fractured flow systems

Fracture "skins" are alteration zones on fracture surfaces created by a variety of biological, chemical, and physical processes. Skins increase surface area, where sorption occurs, compared to the unaltered rock matrix. This study examines the sorption of organic solutes on altered fracture surfaces in an experimental fracture-flow apparatus. Fracture skins containing abundant metal oxides, clays, and organic material from the Breathitt Formation (Kentucky, USA) were collected in a manner such that skin surface integrity was maintained. The samples were reassembled in the lab in a flow-through apparatus that simulated approximately 2.7 m of a linear fracture "conduit." A dual-tracer injection scheme was utilized with the sorbing or reactive tracer compared to a non-reactive tracer (chloride) injected simultaneously. Sorption was assessed from the ratio of the first temporal moments of the breakthrough curves and from the loss of reactive tracer mass and evaluated as a function of flow velocity and solute type. The breakthrough curves suggest dual-flow regimes in the fracture with both sorbing and non-sorbing flow fields. Significant sorption occurs for the reactive components, and sorption increased with decreasing flow rate and decreasing compound solubility. Based on moment analysis, however, there was little retardation of the center of solute mass. These data suggest that non-equilibrium sorption processes dominate and that slow desorption and boundary layer diffusion cause extensive tailing in the breakthrough curves.     

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).     

Mass removal of chlorinated ethenes from rough-walled fractures using permanganate

In situ chemical oxidation (ISCO) employing permanganate is an emerging technology that has been successful at enhancing mass removal from DNAPL source zones in unconsolidated media at the pilot-scale. The focus of this study was to evaluate the applicability of flushing a permanganate solution across two single vertical fractures in a laboratory environment to remove free phase DNAPL. The fracture experiments were designed to represent a portion of a larger fractured aquifer system impacted by a near-surface DNAPL spill over a shallow fractured rock aquifer. Each fracture was characterized by hydraulic and tracer tests, and the aperture field for one of the fractures was mapped using a co-ordinate measurement machine. Following DNAPL emplacement, a series of water and permanganate flushes were performed. To support observations from the fracture experiments, a set of batch experiments was conducted. The data from both fracture experiments showed that the post-oxidation effluent concentration was not impacted by the oxidant flush; however, changes in the aperture distribution, flow field, and flow rate were observed. These changes resulted in a significant decrease to the mass loading from the fractures, and were attributed to the build-up of oxidation by-products (manganese oxides and carbon dioxide) within the fracture which was corroborated by the batch experiment data and visual examination of the walls of one fracture. These results provide insight into the potential impact that a permanganate solution and oxidation by-products can have on the aperture distribution within a fracture and on DNAPL mass transfer rates. A permanganate flush or injection completed within a fractured rock aquifer may lead to the development of an insoluble product adjacent to the DNAPL which results in the reduction or complete elimination of advective regions near the DNAPL and reduces mass transfer rates. This outcome would have significant implications on the plume generating potential of the remaining DNAPL.     

Tracer transport model at Japan meteorological agency and its application to the ETEX data

This paper describes the JMA tracer transport model and its sensitivity to model physics and initial conditions by using the ETEX data. Compared with observations, the model overestimates ground-level concentration in the early stage within about one day from the emission, possibly due to underestimation of vertical diffusion. In the early stage, the enhanced vertical diffusion effectively transports the tracer upward and decreases the ground-level concentration, while in the later stage, it enhances downward transports from the upper layer and increases the ground-level concentration. A conceptual model is given for understanding the vertical transport due to vertical diffusion. The horizontal diffusion introduced to the model has preferable impacts on forecasts especially in the early stage. Finally, we discuss the predictability of this model based on sensitivity to initial conditions of emission time and height.     

Quantifying the physical and chemical mass transfer processes for the fate and transport of Co(II)EDTA in a partially-weathered limestone-shale saprolite

The objective of the research is to quantify the relative contributions of physical and chemical mass transfer to the movement of Co(II/III)EDTA (chelates of Cobalt and Ethylene Diamine Tetraacetic Acid or EDTA) through a limestone-shale saprolite soil. Saprolite is a collective term referring to partially-weathered bedrock. It exists extensively in the subsurface. Because the parent bedding structures are maintained during the weathering process, saprolite soils are characterized by intensive fractures and secondary deposits of minerals such as Al-, Fe- and Mn-oxides on the fracture surfaces. Movement of reactive species through the soils may be influenced by diffusion into the rock matrix, a physical mass transfer (PMT) process, and interfacial chemical reactions, a chemical mass transfer (CMT) process. The PMT and CMT processes are phenomenologically similar but mechanistically different. In this research, previous laboratory observations from a Br and Co(II)EDTA tracer injection into an undisturbed saprolite soil column were used. Mechanistic reactive transport models were formulated to quantify the PMT and CMT processes. The PMT process was independently characterized by using the non-reactive tracer Br. Model parameters thus obtained were subsequently used as constraints to quantify the CMT processes involving Co(II)EDTA and its oxidation product Co(III)EDTA. Our calculations indicated that the PMT rates of the less reactive Co(III)EDTA were comparable with their theoretical CMT rates. In contrast, for the more reactive species Co(II)EDTA, CMT rates are higher than PMT rates. Evaluations of alternative CMT process models further confirmed one of our hypotheses on the basis of previous experimental understandings. The hypothesis suggested that competition from Fe-oxide for Co(II)EDTA may account for the majority of the decrease of Co(III)EDTA effluent concentrations that resulted in the separation of total Co and Co(III)EDTA breakthrough curves. Because Co(III)EDTA is more mobile than Co(II)EDTA in the subsurface, the results of this research suggest independent quantifications of CoEDTA PMT and CMT processes if laboratory results are to be interpreted correctly and scaled up for field and predictive uses.     

An evaluation of contaminant migration patterns at two waste disposal sites on fractured porous media in terms of the equivalent porous medium (EPM) model

Contamination has occurred many non-indurated and bedrock systems wherein the groundwater flows almost exclusively through a network of connected, open fractures. The matrix surrounding the fractures often possesses porosity which allows contaminant diffusion into the matrix. If the diffusion rates are fast relative to the fracture groundwater velocity, transport effects may be predicted by considering the system to be an equivalent porous medium (EPM). The rapidity with which fracture/immobile-matrix equilibrium is established will be determined in part by the: fracture aperture (2b); interfracture spacing (2B); porosity in the immobile matrix (θ_im); and the matrix diffusion coefficient (D′). Two systems which are characterized by very different values of the above parameters have been studied by our laboratories. At Alkali Lake, Oregon, the EPM approach describes contaminant transport well. At Bayview Park, Ontario, the EPM approach is not appropriate. Several features of the two sites are compared to illustrate the different nature of these two sites. These features include: (1) natural characteristics of the groundwater systems; (2) contaminant distributions; (3) observed transport; and (4) computed fracture/immobile-matrix diffusion times.     

Matrix diffusion coefficients in volcanic rocks at the Nevada test site: influence of matrix porosity, matrix permeability, and fracture coating minerals

Diffusion cell experiments were conducted to measure nonsorbing solute matrix diffusion coefficients in forty-seven different volcanic rock matrix samples from eight different locations (with multiple depth intervals represented at several locations) at the Nevada Test Site. The solutes used in the experiments included bromide, iodide, pentafluorobenzoate (PFBA), and tritiated water ((3)HHO). The porosity and saturated permeability of most of the diffusion cell samples were measured to evaluate the correlation of these two variables with tracer matrix diffusion coefficients divided by the free-water diffusion coefficient (D(m)/D*). To investigate the influence of fracture coating minerals on matrix diffusion, ten of the diffusion cells represented paired samples from the same depth interval in which one sample contained a fracture surface with mineral coatings and the other sample consisted of only pure matrix. The log of (D(m)/D*) was found to be positively correlated with both the matrix porosity and the log of matrix permeability. A multiple linear regression analysis indicated that both parameters contributed significantly to the regression at the 95% confidence level. However, the log of the matrix diffusion coefficient was more highly-correlated with the log of matrix permeability than with matrix porosity, which suggests that matrix diffusion coefficients, like matrix permeabilities, have a greater dependence on the interconnectedness of matrix porosity than on the matrix porosity itself. The regression equation for the volcanic rocks was found to provide satisfactory predictions of log(D(m)/D*) for other types of rocks with similar ranges of matrix porosity and permeability as the volcanic rocks, but it did a poorer job predicting log(D(m)/D*) for rocks with lower porosities and/or permeabilities. The presence of mineral coatings on fracture walls did not appear to have a significant effect on matrix diffusion in the ten paired diffusion cell experiments.     

Observations of winds above and below a forest canopy located near a clearing

Measurements of wind movements have been made within and above a forest canopy located near a 0.5 km² clearing. They showed the existence of complex wind systems characterized by strong horizontal jets of air and large vertical velocities beneath the canopy during unstable atmospheric conditions. Under stable situations wind flows seemed to be less complex with both horizontal and vertical winds being greater above the canopy than below.     

Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

Prediction of some in situ tracer tests with sorbing tracers using independent data

Some recent converging tracer tests with sorbing tracers at the Asp? Hard Rock Laboratory in Sweden, the TRUE tests, have been predicted using only laboratory data and hydraulic data from borehole measurements. No model parameters were adjusted to obtain a better fit with the experiments. The independent data were fracture frequency and transmissivity data obtained in the field and laboratory data on sorption and matrix diffusion. Transmissivity measurements in five boreholes in the rock volume containing the region surrounding the injection and collection points show that there is a high frequency of water conducting fractures. Of 162 packed off sections with 0.5 m packer distances, 112 were found to have a transmissivity above the detection limit. The specific flow-wetted surface (FWS) of the rock mass could be estimated from these data. The transmissivities were found to be reasonably well described by a lognormal distribution. Laboratory data on diffusion and sorption properties together with the hydraulic data were used to "predict" the residence time distribution (RTD) of the sorbing tracers. The results were compared with the experimental breakthrough curves. In these experiments, the water residence time is very small compared to the residence time of the sorbing tracers due to their diffusion and sorption within the rock matrix. We thus could neglect the influence of the water residence time in our predictions. Therefore, no information on water residence times or on "dispersion" was needed. The dispersion of the sorbing tracers is caused by the different sorbing tracer residence times in different pathways. The sorbing tracer residence time is determined by the ratio of flowrate to the flow-wetted surface in the different pathways and not by the water residence time. Assuming a three-dimensional flow pattern and using the observed fracture frequency and flowrate distribution, breakthrough curves for three strongly sorbing tracers were predicted. Only the laboratory data, the transmissivity measurements and the pumping flowrate were used in the predictions. No information on the water residence time as obtained by the nonsorbing tracers was used. The predictions were surprisingly accurate.     

Field investigation into unsaturated flow and transport in a fault: model analyses

Results of a fault test performed in the unsaturated zone of Yucca Mountain, Nevada, were analyzed using a three-dimensional numerical model. The fault was explicitly represented as a discrete feature and the surrounding rock was treated as a dual-continuum (fracture-matrix) system. Model calibration against seepage and water-travel-velocity data suggests that lithophysal cavities connected to fractures can considerably enhance the effective fracture porosity and therefore retard water flow in fractures. Comparisons between simulation results and tracer concentration data also indicate that matrix diffusion is an important mechanism for solute transport in unsaturated fractured rock. We found that an increased fault-matrix and fracture-matrix interface areas were needed to match the observed tracer data, which is consistent with previous studies. The study results suggest that the current site-scale model for the unsaturated zone of Yucca Mountain may underestimate radionuclide transport time within the unsaturated zone, because an increased fracture-matrix interface area and the increased effective fracture porosity arising from lithophysal cavities are not considered in the current site-scale model.     

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

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

Simulation and analysis of solute transport in 2D fracture/pipe networks: the SOLFRAC program

The Time Domain Random Walk (TDRW) method has been recently developed by Delay and Bodin [Delay, F. and Bodin, J., 2001. Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks. Geophys. Res. Lett., 28(21): 4051-4054.] and Bodin et al. [Bodin, J., Porel, G. and Delay, F., 2003c. Simulation of solute transport in discrete fracture networks using the time domain random walk method. Earth Planet. Sci. Lett., 6566: 1-8.] for simulating solute transport in discrete fracture networks. It is assumed that the fracture network can reasonably be represented by a network of interconnected one-dimensional pipes (i.e. flow channels). Processes accounted for are: (1) advection and hydrodynamic dispersion in the channels, (2) matrix diffusion, (3) diffusion into stagnant zones within the fracture planes, (4) sorption reactions onto the fracture walls and in the matrix, (5) linear decay, and (6) mass sharing at fracture intersections. The TDRW method is handy and very efficient in terms of computation costs since it allows for the one-step calculation of the particle residence time in each bond of the network. This method has been programmed in C++, and efforts have been made to develop an efficient and user-friendly software, called SOLFRAC. This program is freely downloadable at the URL (labo.univ-poitiers.fr/hydrasa/intranet/telechargement.htm). It calculates solute transport into 2D pipe networks, while considering different types of injections and different concepts of local dispersion within each flow channel. Post-simulation analyses are also available, such as the mean velocity or the macroscopic dispersion at the scale of the entire network. The program may be used to evaluate how a given transport mechanism influences the macroscopic transport behaviour of fracture networks. It may also be used, as is the case, e.g., with analytical solutions, to interpret laboratory or field tracer test experiments performed in single fractures.