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).     

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.     

Through-electromigration: a new method of investigating pore connectivity and obtaining formation factors

The retardation of radionuclides and other contaminants in fractured crystalline rock is strongly associated with the diffusive properties of the rock matrix. At present, the scientific community is divided concerning the question of long-range pore connectivity in intrusive igneous rock. This paper presents a fast new method, called the through-electromigration method, of obtaining formation factors and investigating pore connectivity. The method involves the migration of an ionic tracer through a rock sample with an electrical potential gradient as the main driving force. The method is analogous to the through-diffusion method but the experimental time is reduced by orders of magnitude. This enables investigations of pore connectivity, as measurements can be made on longer samples. In a preliminary investigation, the new method is compared to the traditional through-diffusion method as well as to rock resistivity methods. The diffusive properties of nine granitic rock samples from Laxemar in Sweden, ranging from 15 to 121 mm in length, have been investigated and the results are compared.     

Applied tracer tests in fractured rock: Can we predict natural gradient solute transport more accurately than fracture and matrix parameters?

Applied tracer tests provide a means to estimate aquifer parameters in fractured rock. The traditional approach to analysing these tests has been using a single fracture model to find the parameter values that generate the best fit to the measured breakthrough curve. In many cases, the ultimate aim is to predict solute transport under the natural gradient. Usually, no confidence limits are placed on parameter values and the impact of parameter errors on predictions of solute transport is not discussed. The assumption inherent in this approach is that the parameters determined under forced conditions will enable prediction of solute transport under the natural gradient. This paper considers the parameter and prediction uncertainty that might arise from analysis of breakthrough curves obtained from forced gradient applied tracer tests. By adding noise to an exact solution for transport in a single fracture in a porous matrix we create multiple realisations of an initial breakthrough curve. A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values. The suite of parameters is then used to make predictions of solute transport under lower hydraulic gradients and the uncertainty of estimated parameters and subsequent predictions of solute transport is compared. The results of this study show that predictions of breakthrough curve characteristics (first inflection point time, peak arrival time and peak concentration) for groundwater flow speeds with orders of magnitude smaller than that at which a test is conducted can sometimes be determined even more accurately than the fracture and matrix parameters.     

Field-scale colloid migration experiments in a granite fracture

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

An axisymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples

Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an axisymmetric diffusion experiment coupled with tracer profiling may be a promising approach to estimate of diffusion anisotropy of sedimentary rocks.     

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

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

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.     

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.     

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.     

Electrokinetic ion transport through unsaturated soil: 1. Theory, model development, and testing

An electromigration transport model for non-reactive ion transport in unsaturated soil was developed and tested against laboratory experiments. This model assumed the electric potential field was constant with respect to time, an assumption valid for highly buffered soil, or when the electrode electrolysis reactions are neutralized. The model also assumed constant moisture contents and temperature with respect to time, and that electroosmotic and hydraulic transport of water through the soil was negligible. A functional relationship between ionic mobility and the electrolyte concentration was estimated using the chemical activity coefficient. Tortuosity was calculated from a mathematical relationship fitted to the electrical conductivity of the bulk pore water and soil moisture data. The functional relationship between ionic mobility, pore-water concentration, and tortuosity as a function of moisture content allowed the model to predict ion transport in heterogeneous unsaturated soils. The model was tested against laboratory measurements assessing anionic electromigration as a function of moisture content. In the test cell, a strip of soil was spiked with red dye No 40 and monitored for a 24-h period while a 10-mA current was maintained between the electrodes. Electromigration velocities predicted by the electromigration transport model were in agreement with laboratory experimental results. Both laboratory-measured and model-predicted dye migration results indicated a maximum transport velocity at moisture contents less than saturation due to competing effects between current density and tortuosity as moisture content decreases.     

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.     

Formation factor logging by electrical methods. Comparison of formation factor logs obtained in situ and in the laboratory

In this paper, a new in situ method for obtaining the formation factor, which is essential for the matrix diffusion, is described and tested in intrusive igneous rock. The method is based on electrical resistivity measurements in rock where the pore water and rock resistivities are essential parameters. The method is based on electromigration instead of diffusion as in traditional diffusion experiments. In previous works, quantitative formation factors of rock have been obtained by electrical methods in the laboratory. Here, a similar approach is used in situ. An in situ logging campaign was performed by SKB during 2000 in the 1700-m-deep borehole KLX02 in Laxemar, Sweden. The rock resistivity was measured with the slimhole Dual Laterolog from Antares. The groundwater resistivity was measured with the Difference Flow Meter from Posiva. A formation factor log was obtained with the maximum vertical resolution of 10 cm. In order to validate the log, 100 rock samples were taken from the bore core, and a formation factor log was obtained by using electrical methods in the laboratory. Both direct current (DC) and alternating current (AC) were used. The measurements on the core confirmed that the in situ log was quantitative, but with a possible systematic error. The in situ formation factors were on average about 1/3 to 1/5 of the laboratory formation factors, depending on depth.     

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

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

Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.     

Theory for reactive solute transport through clay membrane barriers

The theoretical development for one-dimensional, coupled migration of solutes with different ionic mobilities through clay soils that behave as ion-restrictive membranes, referred to as clay membrane barriers (CMBs), is presented. The transport formulation is based on principles of irreversible thermodynamics and accounts explicitly for coupling effects of hyperfiltration (ultrafiltration) and chemico-osmotic counter-advection associated with clay membrane behavior in the absence of electrical current. Since, by definition, no solute can enter a "perfect" or "ideal" membrane, the concept of an implicit coupling effect, such that the effective salt-diffusion coefficient, Ds* approaches zero as the chemico-osmotic efficiency coefficient, omega approaches unity is introduced. The theoretical development also illustrates that, even in the absence of membrane behavior, traditional advective-dispersive transport theory based on a constant value of Ds* for the solutes may not be appropriate for simulating transient transport in reactive (ion exchanging) systems. This potential limitation is illustrated through simulations for solute mass flux involving the migration of a binary salt solution (KCl) through a clay barrier with exchange sites saturated with a single exchangeable cation (e.g., Na+) that enters the pore solution upon ion exchange with the salt cation (K+).     

Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater

Analytical solutions are widely used as screening tools for estimating the potential for contaminant transport in groundwater, or for interpreting tracer tests or groundwater quality data. A solution for three-dimensional solute migration from a plane-source source that is frequently used in practice is the approximate solution of Domenico [J. Hydrol. 91 (1987) 49-58]. A more rigorous solution to the same problem was provided by Sagar [ASCE, J. Hydraul. Div. 108, no. HY1 (1982) 47-62]. A comprehensive and unambiguous comparison between these two solutions is provided using dimensionless analysis. The solutions are first cast in terms of dimensionless parameters and then used to provide type curves covering a wide range of dimensionless parameter values. Results show that while discrepancies between the two solutions are relatively negligible along the plume centreline (for flow regimes dominated by advection and mechanical dispersion), large concentration differences can be observed as lateral distance from the centreline increases, especially in the presence of solute decay.     

Degradation of deicing chemicals affects the natural redox system in airfield soils

During winter operations at airports, large amounts of organic deicing chemicals (DIC) accumulate beside the runways and infiltrate into the soil during spring. To study the transport and degradation of DIC in the unsaturated zone, eight undisturbed soil cores were retrieved at Oslo airport, Norway, and installed as lysimeters at a nearby field site. Before snowmelt in 2010 and 2011, snow amended with a mix of the DICs propylene glycol (PG) and formate as well as bromide as conservative tracer was applied. Water samples were collected and analyzed until summer 2012. Water flow and solute transport varied considerably among the lysimeters but also temporally between 2010 and 2011. High infiltration rates during snowmelt resulted in the discharge of up to 51 and 82 % PG in 2010 and 2011, respectively. The discharge of formate remained comparatively low, indicating its favored degradation even at freezing temperatures compared with PG. Manganese (Mn) and iron (Fe) were observed in the drainage in autumn owing to the anaerobic degradation of residual PG during summer. Our findings suggest that upper boundary conditions, i.e., snow cover and infiltration rate, and the extent of preferential flowpaths, control water flow and solute transport of bromide and PG during snowmelt. PG may therefore locally reach deeper soil regions where it may pose a risk for groundwater. In the long term, the use of DIC furthermore causes the depletion of potential electron acceptors and the transport of considerable amounts of Fe and Mn. To avoid an overload of the unsaturated zone with DIC and to maintain the natural redox system, the development of suitable remediation techniques is required.     

Predictive modelling of dispersion controlled reactive plumes at the laboratory-scale

A model-based interpretation of laboratory-scale experimental data is presented. Hydrolysis experiments carried out using thin glass tanks filled with glass beads to construct a hypothetical and inert, homogeneous porous medium were analysed using a 2D numerical model. A new empirical formula, based upon results for non-reactive (tracer) experiments is used to calculate transversal dispersivity values for a range of grain sizes and any flow velocities. Combined with effective diffusion coefficients calculated from Stokes-Einstein type equations, plume lengths arising from mixing between two solutes can be predicted accurately using numerical modelling techniques. Moreover, pH and ion concentration profiles lateral to the direction of flow of the mixing species can be determined at any given point downstream, without the need for result fitting. In our case, this approach does not lead to overpredictions of lateral mixing, as previously reported when using parameters derived from non-reactive tracer experiments to describe reactive solute transport. The theory is based on the assumption of medium homogeneity.     

The effects of scale and spatial heterogeneities on diffusion in volcanic breccias and basalts: Amchitka Island, Alaska

Knowledge of the factors that influence the diffusion of contaminants, such as the diffusivity and the connected porosity, is crucial to modeling the long-term fate and transport of contaminants in subsurface systems with small or negligible advective flow, such as in fractured crystalline rock. Fractured rock is naturally heterogeneous, and hence, understanding the diffusivity of a molecule through this material (or the formation factor of the medium) becomes a complex problem, with critical concerns about the scale of laboratory measurements and about the spatial variability of these measurements relative to the scale needed for fate and transport modeling. This study employed both electrical and tracer-based laboratory methods to investigate the effects of scale and pore system connectivity on the diffusivity for volcanic matrix rock derived from the study site, a former underground nuclear test site at Amchitka Island, Alaska. The results of these investigations indicate a relatively well-connected pore system with scale effects generally limited to approximately 6 cm lengths and well-correlated to observed heterogeneous features. An important conclusion resulting from this study, however, is that there is a potential for the estimated diffusivity to be misrepresented by an order of magnitude if multiple samples or longer sample lengths are not used. Given the relatively large number of measurements resulting from these investigations, an analysis of the probability density function (PDF) of the diffusivity was possible. The PDF of the diffusivity was shown to generally follow a normal distribution for individual geologic layers. However, when all of the geologic layers are considered together, the distribution of the subsurface as a whole was shown to follow a lognormal distribution due to the order of magnitude differences amongst the layers. An understanding of these distributions is essential for future stochastic modeling efforts.