The effect of a biofilm on solute diffusion in fractured porous media

At sites in fractured rock where contamination has been exposed to the rock matrix for extended periods of time, the amount of contaminant mass residing in the matrix can be considerable. Even though it may be possible to diminish concentrations by the advection of clean water through the fracture features, back diffusion from mass held in the matrix will lead to a continuing source of contamination. In such an event, the development of a biofilm (a thin film of microbial mass) on the wall of the fractures may act to limit or prevent the back diffusion process. The objective of this preliminary study is to explore the influence imparted by the presence of a biofilm on the process of matrix diffusion. The investigation was conducted using radial diffusion cells constructed from rock core in which biofilm growth was stimulated in a central reservoir. Once biofilms were developed, forward diffusion experiments were conducted in which a conservative solute migrated from the central reservoir into the intact rock sample. Diffusion experiments were performed in a total of 11 diffusion cell pairs where biofilm growth was stimulated in one member of the pair and inhibited in the other. The effect of the presence of a biofilm on tracer diffusion was determined by comparison of the diffusion curves produced by each cell pair. A semi-analytical model that accounts for the presence of a biofilm was used to investigate the effect of the biofilm on mass transfer due to changes in the effective porosity, effective diffusion coefficient, and the depth of penetration of the biofilm into the intact rock. The results show that the biofilm acted to plug the rock matrix, rather than forming a discrete layer on the reservoir surface. The reduction in effective porosity due to the biofilm ranged from 6% to 52% with the majority of the samples in the 30% to 50% range. Based on the present results, with more efficient biofilm stimulation, it is reasonable to assume that a more complete plugging of the microcrack porosity might be possible, leaving a much thicker and efficient barrier than could be achieved via a surface biofilm.     

A laboratory experiment for determining both the hydraulic and diffusive properties and the initial pore-water composition of an argillaceous rock sample: a test with the Opalinus clay (Mont Terri, Switzerland)

Argillaceous formations are thought to be suitable natural barriers to the release of radionuclides from a radioactive waste repository. However, the safety assessment of a waste repository hosted by an argillaceous rock requires knowledge of several properties of the host rock such as the hydraulic conductivity, diffusion properties and the pore water composition. This paper presents an experimental design that allows the determination of these three types of parameters on the same cylindrical rock sample. The reliability of this method was evaluated using a core sample from a well-investigated indurated argillaceous formation, the Opalinus Clay from the Mont Terri Underground Research Laboratory (URL) (Switzerland). In this test, deuterium- and oxygen-18-depleted water, bromide and caesium were injected as tracer pulses in a reservoir drilled in the centre of a cylindrical core sample. The evolution of these tracers was monitored by means of samplers included in a circulation circuit for a period of 204 days. Then, a hydraulic test (pulse-test type) was performed. Finally, the core sample was dismantled and analysed to determine tracer profiles. Diffusion parameters determined for the four tracers are consistent with those previously obtained from laboratory through-diffusion and in-situ diffusion experiments. The reconstructed initial pore-water composition (chloride and water stable-isotope concentrations) was also consistent with those previously reported. In addition, the hydraulic test led to an estimate of hydraulic conductivity in good agreement with that obtained from in-situ tests.     

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.     

A technique for estimating one-dimensional diffusion coefficients in low-permeability sedimentary rock using X-ray radiography: comparison with through-diffusion measurements

The measurement of diffusive properties of low-permeability rocks is of interest to the nuclear power industry, which is considering the option of deep geologic repositories for management of radioactive waste. We present a simple, non-destructive, constant source in-diffusion method for estimating one-dimensional pore diffusion coefficients (D(p)) in geologic materials based on X-ray radiography. Changes in X-ray absorption coefficient (Deltamicro) are used to quantify changes in relative concentration (C/C(0)) of an X-ray attenuating iodide tracer as the tracer solution diffuses through the rock pores. Estimated values of D(p) are then obtained by fitting an analytical solution to the measured concentration profiles over time. Measurements on samples before and after saturation with iodide can also be used to determine iodide-accessible porosity (phi(I)). To evaluate the radiography method, results were compared with traditional steady-state through-diffusion measurements on two rock types: shale and limestone. Values of D(p) of (4.8+/-2.5)x10(-11) m(2).s(-1) (mean+/-standard deviation) were measured for samples of Queenston Formation shale and (2.6+/-1.0)x10(-11) m(2).s(-1) for samples of Cobourg Formation limestone using the radiography method. The range of results for each rock type agree well with D(p) values of (4.6+/-2.0)x10(-11) m(2).s(-1) for shale and (3.5+/-1.8)x10(-11) m(2).s(-1) for limestone, calculated from through-diffusion experiments on adjacent rock samples. Low porosity (0.01 to 0.03) and heterogeneous distribution of porosity in the Cobourg Formation may be responsible for the slightly poorer agreement between radiography and through-diffusion results for limestones. Mean values of phi(I) for shales (0.060) and limestones (0.028) were close to mean porosity measurements made on bulk samples by the independent water loss technique (0.062 and 0.020 for shales and limestones, respectively). Radiography measurements offer the advantage of time-saving for diffusion experiments because the experiment does not require steady-state conditions and also allows for visualization of the small-scale heterogeneities in diffusive properties within rocks at the mm to cm scale.     

Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity

Matrix diffusion is an important transport process in geologic materials of low hydraulic conductivity. For predicting the fate and transport of contaminants, a detailed understanding of the diffusion processes in natural porous media is essential. In this study, diffusive tracer transport (iodide) was investigated in a variety of geologically different limestone and sandstone rocks. Porosity, structural and mineralogical composition, hydraulic conductivity, and other rock properties were determined. The effective diffusion coefficients were measured using the time-lag method. The results of the diffusion experiments indicate that there is a close relationship between total porosity and the effective diffusion coefficient of a rock (analogous to Archie's Law). Consequently, the tortousity factor can be expressed as a function of total porosity. The relationship fits best for thicker samples (> 1.0 cm) with high porosities (> 20%), because of the reduced influence of heterogeneity in larger samples. In general, these correlations appear to be a simple way to determine tortuosity and the effective diffusion coefficient from easy to determine rock porosity values.     

In situ diffusion experiment in granite: phase I

A program of in situ experiments, supported by laboratory studies, was initiated to study diffusion in sparsely fractured rock (SFR), with a goal of developing an understanding of diffusion processes within intact crystalline rock. Phase I of the in situ diffusion experiment was started in 1996, with the purpose of developing a methodology for estimating diffusion parameter values. Four in situ diffusion experiments, using a conservative iodide tracer, were performed in highly stressed SFR at a depth of 450 m in the Underground Research Laboratory (URL). The experiments, performed over a 2 year period, yielded rock permeability estimates of 2 x 10(-21) m(2) and effective diffusion coefficients varying from 2.1 x 10(-14) to 1.9 x 10(-13) m(2)/s, which were estimated using the MOTIF code. The in situ diffusion profiles reveal a characteristic "dog leg" pattern, with iodide concentrations decreasing rapidly within a centimeter of the open borehole wall. It is hypothesized that this is an artifact of local stress redistribution and creation of a zone of increased constrictivity close to the borehole wall. A comparison of estimated in situ and laboratory diffusivities and permeabilities provides evidence that the physical properties of rock samples removed from high-stress regimes change. As a result of the lessons learnt during Phase I, a Phase II in situ program has been initiated to improve our general understanding of diffusion in SFR.     

Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions

To obtain reliable diffusion parameters for diffusion testing, multiple experiments should not only be cross-checked but the internal consistency of each experiment should also be verified. In the through- and in-diffusion tests with solution reservoirs, test interpretation of different phases often makes use of simplified analytical solutions. This study explores the feasibility of steady, quasi-steady, equilibrium and transient-state analyses using simplified analytical solutions with respect to (i) valid conditions for each analytical solution, (ii) potential error, and (iii) experimental time. For increased generality, a series of numerical analyses are performed using unified dimensionless parameters and the results are all related to dimensionless reservoir volume (DRV) which includes only the sorptive parameter as an unknown. This means the above factors can be investigated on the basis of the sorption properties of the testing material and/or tracer. The main findings are that steady, quasi-steady and equilibrium-state analyses are applicable when the tracer is not highly sorptive. However, quasi-steady and equilibrium-state analyses become inefficient or impractical compared to steady state analysis when the tracer is non-sorbing and material porosity is significantly low. Systematic and comprehensive reformulation of analytical models enables the comparison of experimental times between different test methods. The applicability and potential error of each test interpretation can also be studied. These can be applied in designing, performing, and interpreting diffusion experiments by deducing DRV from the available information for the target material and tracer, combined with the results of this study.     

The effects of matrix diffusion on radionuclide migration in rock column experiments

Rock column experiments were performed to examine the effects of matrix diffusion and hydrodynamic dispersion on the migration of radionuclides at the laboratory scale. Tritiated water and chloride transportation was studied in intact mica gneiss and in altered more porous tonalite columns with narrow flow channels. The column diffusion properties were estimated prior to water flow experiments using the gas diffusion method with helium as the tracer gas. The numerical compartment model for advection and dispersion, with and without matrix diffusion, was used to interpret the tracer transport in the columns. Matrix diffusion behavior was also distinguished from dominating hydrodynamic dispersion in rock column experiments at the slowest water flow rates.     

Laboratory longitudinal diffusion tests: 2. Parameter estimation by inverse analysis

This study focuses on the verification of test interpretations for different state analyses of diffusion experiments. Part 1 of this study identified that steady, quasi-steady and equilibrium state analyses for the through- and in-diffusion tests with solution reservoirs are generally feasible where the tracer is not highly sorptive. In Part 2 we investigate parameter identifiability in transient-state analysis of reservoir concentration variation using a numerical approach. For increased generality, the analytical models, objective functions and Jacobian matrix necessary for inverse analysis of transient-state data are reformulated using unified dimensionless parameters. In these dimensionless forms, the number of unknown parameters is reduced and a single dimensionless parameter represents the sorption property. The dimensionless objective functions are evaluated for individual test methods and parameter identifiability is discussed in relation to the sorption property. The effects of multiple minima and measurement error on parameter identifiability are also investigated. The main findings are that inverse problems for inlet and outlet reservoir concentration analyses are generally unstable and well-posed, respectively. Where the tracer is sorptive, the inverse problem for the inlet reservoir concentration analysis may have multiple minima. When insufficient measurement data is collected, multiple solutions may result and this should be taken into consideration when inversely analyzing data including that of inlet reservoir concentration. Verification of test interpretation by cross-checking different state analyses is feasible where the tracer is not highly sorptive. In an actual experiment, test interpretation validity is demonstrated through consistency between theory and practice for different state analyses.     

Simultaneous estimation of effective and apparent diffusion coefficients in compacted bentonite

Effective diffusion coefficients (D(e)) are usually measured by means of "through-diffusion" experiments in which steady state is reached, and the "time-lag" methods are used to estimate the apparent diffusion coefficient (D(a)). For sorbing radionuclides (as caesium), the time needed to reach steady-state conditions is very large, and the precision in D(a) determinations is not satisfactory. In this paper, a method that allows determining simultaneously effective and apparent diffusion coefficients in compacted bentonite without reaching steady-state conditions is described. Basically, this method consists of an "in-diffusion" experiment in which the concentration profile in the bentonite sample is used to estimate D(a), and the temporal evolution of the solute concentration in the reservoir is used to estimate D(e). This method has several advantages over the typical "through-diffusion" experiments, in particular: (a) experiment duration is significantly shorter, (b) D(a) values are measured with greater precision and (c) it is not necessary to maintain a constant solute concentration in the reservoir. This new method has been used to estimate the effective and apparent diffusion coefficients for caesium in FEBEX bentonite and in order to validate it, the results have been compared with results previously obtained with standard methods. Experimental results have been satisfactorily modelled using a simple model of diffusion in porewater and the measured value of D(e)(Cs) is very similar to D(e)(HTO) in the same bentonite. There is no evidence of "surface diffusion" in FEBEX bentonite for caesium.     

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).     

Influence of the mode of matrix porosity determination on matrix diffusion calculations

The theoretical basis for matrix diffusion in fractured rocks and the methodology for the determination of diffusion coefficients in the laboratory are well established. One significant problem, however, remains in that it is difficult to quantify the degree of sample disturbance affecting the geometrical, geophysical and hydraulic properties of the rock matrix. A new technique, with in situ rock impregnation with resin, for examining the diffusion-accessible rock matrix has been developed and successfully adopted to the rock matrix behind a water-conducting fracture in host crystalline rocks at Nagra's Grimsel Test Site in Switzerland and JNC's Kamaishi In Situ Test Site in Japan. In line with the results of a large number of natural analogue and laboratory studies, the existence of an in situ interconnected pore network was substantiated. Matrix porosities determined on the laboratory samples from both the sites are 1.5-3 times higher than in situ values, irrespective of the technique applied. On the Grimsel granodiorite matrix, matrix porosity existing in situ and artefacts of stress release and physical disturbance, induced by sampling and sample preparation, were clearly distinguished, allowing in situ porosity to be quantified. Laboratory work with conventional techniques tends to overestimate the porosity of the rock matrix, hence leading to an overestimation of in situ matrix diffusion. The implications of these differences to a repository performance assessment are assessed with a couple of examples from existing assessments, and recommendations for future approaches to the examination of in situ matrix porosity are made.     

A laboratory technique for investigation of diffusion and transformation of volatile organic compounds in low permeability media

A laboratory diffusion cell technique that permits spatial and temporal estimates of porewater concentrations over short intervals suitable for estimation of effective diffusion coefficients (De) and degradation rate constants (k) of volatile organic compounds (VOCs) in saturated low permeability media is presented. The diffusion cell is a sealed cylinder containing vapour reservoirs for sampling, including a vapour reservoir source and an array of vapour-filled "mini-boreholes", which are maintained water- and sediment-free by slightly negative porewater pressures. The vapour reservoirs were sampled by Solid Phase Micro-Extraction (SPME), resulting in minimal disturbance to the experimental system. Porewater concentrations are estimated from the measured vapour concentrations. Experiments were conducted using a non-reactive medium and five VOCs with a range in partitioning properties. Calibration experiments showed that equilibrium partition coefficients could be used for calculating concentrations in the vapour reservoir source from concentrations in the SPME coating after a 1-min microextraction and that the reservoir concentration was insignificantly affected by sampling. However, equilibrium was not reached during the one-min extraction of the boreholes; the microextraction reduced the borehole vapour concentrations, leading to diffusion of VOCs from porewater into the vapour-filled borehole. Thus, empirical partitioning coefficients were required for the determination of porewater VOC concentrations. The experimental data and numerical modelling indicate masses extracted by SPME extraction are relatively small, with minimal perturbation on processes studied in diffusion experiments. This technique shows promise for laboratory investigation of diffusion and transformation processes in low permeability media.     

Diffusive flux and pore anisotropy in sedimentary rocks

Diffusion of dissolved contaminants into or from bedrock matrices can have a substantial impact on both the extent and longevity of dissolved contaminant plumes. For layered rocks, bedding orientation can have a significant impact on diffusion. A series of laboratory experiments was performed on minimally disturbed bedrock cores to measure the diffusive flux both parallel and normal to mineral bedding of four different anisotropic sedimentary rocks. Measured effective diffusion coefficients ranged from 4.9×10(-8) to 6.5×10(-7)cm(2)/s. Effective diffusion coefficients differed by as great as 10-folds when comparing diffusion normal versus parallel to bedding. Differences in the effective diffusion coefficients corresponded to differences in the "apparent" porosity in the orientation of diffusion (determined by determining the fraction of pore cross-sectional area measured using scanning electron microscopy), with the difference in apparent porosity between normal and parallel bedding orientations differing by greater than 2-folds for two of the rocks studied. Existing empirical models failed to provide accurate predictions of the effective diffusion coefficient in either bedding orientation for all four rock types studied, indicating that substantial uncertainty exists when attempting to predict diffusive flux through sedimentary rocks containing mineral bedding. A modified model based on the apparent porosity of the rocks provided a reasonable prediction of the experimental diffusion data.     

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.     

Flamelet modeling of NO formation in laminar and turbulent diffusion flames

The applicability of the laminar flamelet concept for the formation and destruction of nitric oxides in laminar and turbulent diffusion flames has been studied. In a first step, temperatures and species concentrations in an axisymmetric laminar diffusion flame have been calculated (i) by solving the detailed conservation equations and (ii) by applying the laminar flamelet concept. The main purpose of this step was the identification of differences between results from both approaches. It turned out that for highly temperature sensitive or relatively slow chemical processes, the inclusion of the full range of the prevailing scalar dissipation rates plays a major role for the calculated species concentrations. This behavior is obvious from the concept of the laminar flamelet model, where the scalar dissipation rate can be discussed in terms of the reciprocal of a residence time for attaining chemical equilibrium. In a second step, flamelet modeling of NOx formation was extended to a turbulent hydrogen diffusion flame. In both the steps, the flow fields of the flames were calculated by solving the Navier-Stokes equations in axisymmetric formulation using the SIMPLER algorithm. For the turbulent flow, Favre-averaged equations have been used and turbulence was modeled with the standard k-epsilon model including a correction term for axisymmetric systems. The averaging of the species concentrations was accomplished with presumed shape probability density functions (pdfs). The pdf of the mixture fraction was described with a beta-function whereas that of the scalar dissipation rate was assumed to be log-normal. Buoyancy effects have been taken into account. The calculated temperatures and concentrations were compared with data from different experiments.     

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.     

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.     

Diffusion of tritiated water and 22Na+ through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and 22Na(+), considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test. The experimental data were inversely modelled applying an automated Marquardt-Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D(e), and the rock capacity factor, alpha. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K(d)-values were found to be consistent with R(d)-values measured in previous batch-sorption experiments. The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption. Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.     

Use of X-ray absorption imaging to examine heterogeneous diffusion in fractured crystalline rocks

Heterogeneous diffusion in different regions of a fractured granodiorite from Japan has been observed and measured through the use of X-ray absorption imaging. These regions include gouge-filled fractures, recrystallized fracture-filling material and hydrothermally altered matrix. With the X-ray absorption imaging technique, porosity, relative concentration, and relative mass of an iodine tracer were imaged in two dimensions with a sub-millimeter pixel size. Because portions of the samples analyzed have relatively low porosity values, imaging errors can potentially impact the results. For this reason, efforts were made to better understand and quantify this error. Based on the X-ray data, pore diffusion coefficients (Dp) for the different regions were estimated assuming a single diffusion rate and a lognormal multirate distribution of Dp. Results show Dp for the gouge-filled fractures are over an order of magnitude greater than those of the recrystallized fracture-filling material, which in turn is approximately two times greater than those for the altered matrix. The recrystallized fracture-filling material was found to exhibit the greatest degree of variability. The results of these experiments also provide evidence that diffusion from advective zones in fractures through the gouge-filled fractures and recrystallized fracture-filling material could increase the pore space available for matrix diffusion. This evidence is important for understanding the performance of potential nuclear waste repositories in crystalline rocks as diffusion is thought to be an important retardation mechanism for radionuclides.