Effects of pore volume-transmissivity correlation on transport phenomena

The relevant velocity that describes transport phenomena in a porous medium is the pore velocity. For this reason, one needs not only to describe the variability of transmissivity, which fully determines the Darcy velocity field for given source terms and boundary conditions, but also any variability of the pore volume. We demonstrate that hydraulically equivalent media with exactly the same transmissivity field can produce dramatic differences in the displacement of a solute if they have different pore volume distributions. In particular, we demonstrate that correlation between pore volume and transmissivity leads to a much smoother and more homogeneous solute distribution. This was observed in a laboratory experiment performed in artificial fractures made of two plexiglass plates into which a space-dependent aperture distribution was milled. Using visualization by a light transmission technique, we observe that the solute behaviour is much smoother and more regular after the fractures are filled with glass powder, which plays the role of a homogeneous fault gouge material. This is due to a perfect correlation between pore volume and transmissivity that causes pore velocity to be not directly dependent on the transmissivity, but only indirectly through the hydraulic gradient, which is a much smoother function due to the diffusive behaviour of the flow equation acting as a filter. This smoothing property of the pore volume-transmissivity correlation is also supported by numerical simulations of tracer tests in a dipole flow field. Three different conceptual models are used: an empty fracture, a rough-walled fracture filled with a homogeneous material and a parallel-plate fracture with a heterogeneous fault gouge. All three models are hydraulically equivalent, yet they have a different pore volume distribution. Even if piezometric heads and specific flow rates are exactly the same at any point of the domain, the transport process differs dramatically. These differences make it important to discriminate in situ among different conceptual models in order to simulate correctly the transport phenomena. For this reason, we study the solute breakthrough and recovery curves at the extraction wells. Our numerical case studies show that discrimination on the basis of such data might be impossible except under very favourable conditions, i.e. the integral scale of the transmissivity field has to be known and small compared to the dipole size. If the latter conditions are satisfied, discrimination between the rough-walled fracture filled with a homogeneous material and the other two models becomes possible, whereas the parallel-plate fracture with a heterogeneous fault gouge and the empty fracture still show identifiability problems. The latter may be solved by inspection of aperture and pressure testing.     

Water-soluble gases as partitioning tracers to investigate the pore volume-transmissivity correlation in a fracture

Hydraulically equivalent fractures may show striking differences when a gas-migration experiment is performed because of the different correlations between transmissivity, pore volume and entry pressure. We numerically simulate gas migration between injection and extraction boreholes in a parallel plate fracture with a heterogeneous fault gouge, in a rough-walled fracture filled with homogeneous material, and in a rough-walled empty fracture. The parallel plate model and the empty model clearly show the existence of preferential paths; for high variance of the transmissivity field, gas flow takes place only in few discrete channels separated by water-saturated regions. In contrast, in the fracture filled with homogeneous fault gouge, the gas saturation is continuous and more uniformly distributed. It appears a fundamental issue to be able to discriminate in situ among conceptual models that can yield such a different gas-saturation distribution. As in practice, the saturation distribution cannot be directly observed, tracer experiments are performed to characterize a fracture. For these reasons, we simulate the transport of tracers, which are added to the gas phase as soon as quasi-steady saturation distribution and extraction rate are achieved, and we compare the breakthrough curves obtained assuming different models. Our numerical simulations suggest that discrimination among the models on the basis of single-tracer tests is unlikely. A better tool to investigate fracture properties is provided by a gas-tracer test, in which a cocktail of gases with different water solubility is employed. These gases behave as partitioning tracers and allow us to estimate the gas saturation in the fracture. Indeed, by comparison of the residence-time distributions of different gases, we are able to compute a streamline effective saturation, which is an excellent estimate of fracture saturation. In addition, the streamline effective saturation curve contains information that is useful to identify the conceptual model that more likely applies to the fracture.     

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

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

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.     

Solute transport in crystalline rocks at Aspö--I: geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted Asp? Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175]. The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments. While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours-days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption K(d)s are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.     

Modelling of nonreactive tracer dipole tests in a shear zone at the Grimsel test site

The investigation of the migration of a high pH plume in a fractured shear zone is foreseen by a long-term experiment at the Grimsel rock laboratory. In order to characterise the initial conditions for the long-term experiment and to evaluate an optimal hydraulic in situ set-up, several dipole experiments with nonreacting tracers have been performed. The dipole experiments differ in geometry, pumping rates and orientation to the background water flow. Several single and double-porosity models have been applied to fit the results of these dipole tracer tests in order to extract values for some transport parameters and discriminate for certain transport processes. A two-dimensional porous medium approach was successfully used to fit tracer breakthrough curves measured for a dipole experiment. A model based on a one-dimensional dual porous medium approach was also successful, although the applied hydraulic dipole, with similar injection and extraction rates, suggests the existence of an extended two-dimensional flow field. For the two-dimensional porous medium approach, tracer breakthrough could only be fitted with a complex flow field geometry within the heterogeneous fractured shear zone. The heterogeneity was generated by heterogeneous porosity and hydraulic permeability distributions. Predictions for further dipole geometries and a sorbing tracer have been calculated by means of both models using the flow and transport parameters deduced from fits for a single dipole experiment. This allows for comparison with the measured breakthrough of sorbing tracers. The foreseen experiment with sorbing (radionuclide) tracers will help decide on the appropriate approach that should be used to describe such dipole experiments in this shear zone. Additionally, the migration and spreading of a solution with high pH has been calculated taking into account mineral dissolution and precipitation in a two-dimensional porous medium approach in order to estimate the amount and character of the mineral reactions induced by the interaction between the high pH solution and the rock.     

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.     

Solute transport in crystalline rocks at Äspö — I: Geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted Äspö Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175].The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments.While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours–days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption K_ds are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.     

A comparison of hydraulic and transport parameters measured in low-permeability fractured media

Data from 90 tracer experiments performed in low-permeability fractured media have been studied to explore correlations among parameters controlling flow and transport. The original data had been interpreted by different authors using different models, which prevents direct comparison of their estimated parameters. In order to produce comparable parameters, the data have been reexamined using simple models (homogeneous domain, steady-state flow regime, single porosity). Specifically, hydraulic conductivity has been derived as the ratio of water flux to head gradient and apparent porosity as the ratio of water velocity to water flux; the former estimated from both first and peak arrival times. Hydraulic conductivity and porosity correlate along a straight line of slope 1:3 in log scale. While the regression is too noisy to be of predictive use, it lends some support to the use of a generalized cubic law. The fact that correlation for first arrival time porosity (0.77) is larger than for peak arrival porosity (0.62) suggests that first arrival is controlled by the same flow paths as hydraulic conductivity. Apparent porosity derived from peak arrival time is found to grow with travel time along a line of 0.55 slope (again log scale). The correlation coefficient ranges between 0.73 and 0.80 (depending on the data set) for hard rocks. The fact that this correlation is maintained when varying the flow rate at a given site leads us to suggest that it is caused by diffusion mechanisms. This conclusion is further supported by the increase of apparent porosity with the matrix porosity of the rock on which the experiments were performed.     

Fluorescent dye imaging of the volume sampled by single well forced-gradient tracer tests evaluated in a laboratory-scale aquifer physical model

This study presents a new method to visualise forced-gradient tracer tests in 2-D using a laboratory-scale aquifer physical model. Experiments were designed to investigate the volume of aquifer sampled in vertical dipole flow tracer tests (DFTT) and push-pull tests (PPT), using a miniature monitoring well and straddle packer arrangement equipped with solute injection and recovery chambers. These tests have previously been used to estimate bulk aquifer hydraulic and transport properties for the evaluation of natural attenuation and other remediation approaches. Experiments were performed in a silica glass bead-filled box, using a fluorescent tracer (fluorescein) to deduce conservative solute transport paths. Digital images of fluorescein transport were captured under ultraviolet light and processed to analyse tracer plume geometry and obtain point-concentration breakthrough histories. Inorganic anion mixtures were also used to obtain conventional tracer breakthrough histories. Concentration data from the conservative tracer breakthrough curves was compared with the digital images and a well characterised numerical model. The results show that the peak tracer breakthrough response in dipole flow tracer tests samples a zone of aquifer close to the well screen, while the sampling volume of push-pull tests is limited by the length of the straddle packers used. The effective sampling volume of these single well forced-gradient tests in isotropic conditions can be estimated with simple equations. The experimental approach offers the opportunity to evaluate under controlled conditions the theoretical basis, design and performance of DFTTs and PPTs in porous media in relation to measured flow and transport properties.     

Single-well reactive tracer test and stable isotope analysis for determination of microbial activity in a fast hydrocarbon-contaminated aquifer

Single-well reactive tracer tests, such as the push-pull test are useful tools for characterising in-situ bioattenuation processes in contaminated aquifers. However, the analytical models that are used to interpret push-pull data may be over-simplified, and potentially overlook important processes responsible for the frequent discrepancy between predicted and observed results obtained from push-pull tests. In this study, the limitations underlying the push-pull test methodology were investigated and were supported with results from a push-pull test conducted in a sulphate-reducing aquifer contaminated by crude oil. Poor (<7%) mass recovery was achieved when the push-pull test was performed in a fast-flowing aquifer, preventing a quantifiable reaction rate to be determined. Breakthrough curve data were unexplainable using simplified analytical models, but exhibited trends analogous with tests conducted by others, when >20% mass recoveries were achieved. Push-pull test data collected from sulphate-reducing aquifers indicate that the assumption of a well-mixed batch reactor system is incorrect and that reaction rates obtained from push-pull tests in such systems may be affected by the extraction regime implemented. Evidence of microbial respiration of the reactive tracer was provided by stable sulphur isotope analysis, from which an isotope fractionation factor of +9.9 +/- 8.1 per thousand was estimated. The stable isotope data support the argument that reaction rates calculated using push-pull tests are not uniformly distributed in space and time and are likely to be influenced by heterogeneities in the flow field.     

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.     

Solute transport in crystalline rocks at Aspö--II: blind predictions,inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish Asp? Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing 22Na(+), 85Sr(2+), 47Ca(2+)and more strongly sorbing 86Rb(+), 133Ba(2+), 137Cs(+). Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity. The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations. After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2-15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted K(d) values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25-60, but agree within a factor of 3-5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning K(d)s is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.     

Push-pull partitioning tracer tests using radon-222 to quantify non-aqueous phase liquid contamination

Naturally occurring radon in groundwater can be used as an in situ partitioning tracer for locating and quantifying non-aqueous phase liquid (NAPL) contamination in the subsurface. When combined with the single-well, push-pull test, this methodology has the potential to provide a low-cost alternative to inter-well partitioning tracer tests. During a push-pull test, a known volume of test solution (radon-free water containing a conservative tracer) is first injected ("pushed") into a well; flow is then reversed and the test solution/groundwater mixture is extracted ("pulled") from the same well. In the presence of NAPL radon transport is retarded relative to the conservative tracer. Assuming linear equilibrium partitioning, retardation factors for radon can be used to estimate NAPL saturations. The utility of this methodology was evaluated in laboratory and field settings. Laboratory push-pull tests were conducted in both non-contaminated and trichloroethene NAPL (TCE)-contaminated sediment. The methodology was then applied in wells located in non-contaminated and light non-aqueous phase liquid (LNAPL)-contaminated portions of an aquifer at a former petroleum refinery. The method of temporal moments and an approximate analytical solution to the governing transport equations were used to interpret breakthrough curves and estimate radon retardation factors; estimated retardation factors were then used to calculate TCE saturations. Numerical simulations were used to further investigate the behavior of the breakthrough curves. The laboratory and field push-pull tests demonstrated that radon retardation does occur in the presence of TCE and LNAPL and that radon retardation can be used to calculate TCE saturations. Laboratory injection-phase test results in TCE-contaminated sediment yielded radon retardation factors ranging from 1.1 to 1.5, resulting in calculated TCE saturations ranging from 0.2 to 0.9%. Laboratory extraction-phase test results in the same sediment yielded a radon retardation factor of 5.0, with a calculated TCE saturation of 6.5%. Numerical simulation breakthrough curves provided reasonably good matches to the approximate analytical solution breakthrough curves. However, non-equilibrium radon partitioning and heterogeneous TCE distributions may affect the retardation factors and TCE saturation estimates.     

Evidence of one-dimensional scale-dependent fractional advection-dispersion

A semi-analytical inverse method and the corresponding program FADEMain for parameter estimation of the fractional advection-dispersion equation (FADE) were developed in this paper. We have analyzed Huang et al.'s [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large homogeneous and heterogeneous saturated soil columns. Trans. Porous Media 18, 283-302.] laboratory experimental data of conservative solute transport in 12.5-m long homogeneous and heterogeneous soil columns to test the non-Fickian dispersion theory of FADE. The dispersion coefficient was calculated by fitting the analytical solution of FADE to the measured data at different transport scales. We found that the dispersion coefficient increased exponentially with transport scale for the homogeneous column, whereas it increased with transport scale in a power law function for the heterogeneous column. The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. The increasing rate of dispersion coefficient versus transport distance was smaller for FADE than that for the advection-dispersion equation (ADE). Finite difference numerical approximations of the scale-dependent FADE were established to interpret the experimental results. The numerical solutions were found to be adequate for predicting scale-dependent transport in the homogeneous column, while the prediction for the heterogeneous column was less satisfactory.     

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.     

Consistent interpretation of the results of through-, out-diffusion and tracer profile analysis for trace anion diffusion in compacted montmorillonite

Literature data for anion diffusion in compacted swelling clays contain systematic inconsistencies when the results of through-diffusion tests are compared with those of out-diffusion or tracer profile analysis. In the present work we investigated whether these inconsistencies can be explained by taking into account heterogeneities in the compacted samples; in particular increased porosities at the clay boundaries. Based on the combined results of out-diffusion, tracer profile analysis and the spatial distribution of the electrolyte anion in the clay, we conclude that the inconsistencies can indeed be resolved by taking into account a heterogeneous distribution of the total and the anion-accessible porosity. This, by definition, leads to a position dependence of the effective diffusion coefficient. Neglecting these effects results in a rather subordinate systematic error in the determination of effective diffusion coefficients of anions from through-diffusion tests with clay thicknesses in the centimetre range. However, stronger errors in terms of absolute values and conceptual interpretation may be introduced in out-diffusion tests and profile analyses of the diffused tracer. We recommend that anion diffusion tests should be accompanied by measurements of the total and anion-accessible porosity as a function of position in the direction of diffusion.     

Macrodispersion by diverging radial flows in randomly heterogeneous porous media

Radial flow takes place in a heterogeneous porous formation where the transmissivity T is modelled as a stationary random space function (RSF). The steady flow is driven by a given rate, and the mean velocity is radial. A pulse-like of a tracer is injected in the porous formation, and the thin plume spreads due to the fluctuations of the velocity which results a RSF as well. Transport is characterized by the mean front, and by the second spatial moment of the plume. We are primarily interested in tracer macrodispersion modelling. With the neglect of pore-scale dispersion, macrodispersion coefficients are computed at the second order of approximation, without neglecting the head-gradient fluctuations. Although transport is non-ergodic at the source, it is shown that ergodicity is achieved at small distances from the source. This is due to the fact that close to the source local velocities are quite large, and therefore solute particles become uncorrelated very soon. Under ergodic conditions, we compare macrodispersion mechanism in radial flows with that occurring in mean uniform flows. At short distances the spreading effect is highly enhanced by the large variability of the flow field, whereas at large distances transport exhibits a lesser dispersion due to the reduction of velocities. This supports the explanation provided by Indelman and Dagan (1999) to justify why the macrodispersivity is found smaller than that pertaining to mean uniform flows. The model is tested against a tracer transport experiment (Fernàndez-Garcia et al., 2004) by comparing the theoretical and experimental breakthrough curves. The accordance with real data, that is achieved without any fitting to concentration values, strengthens the capability of the proposed model to grasp the main features of such an experiment, the approximations as well as experimental uncertainties notwithstanding.     

Importance of considering intraborehole flow in solute transport modeling under highly dynamic flow conditions

Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions.