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.     

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.     

Hydraulic constraints on the performance of a groundwater denitrification wall for nitrate removal from shallow groundwater

Denitrification walls are a practical approach for decreasing non-point source pollution of surface waters. They are constructed by digging a trench perpendicular to groundwater flow and mixing the aquifer material with organic matter, such as sawdust, which acts as a carbon source to stimulate denitrification. For efficient functioning, walls need to be permeable to groundwater flow. We examined the functioning of a denitrification wall constructed in an aquifer consisting of coarse sands. Wells were monitored for changes in nitrate concentration as groundwater passed through the wall and soil samples were taken to measure microbial parameters inside the wall. Nitrate concentrations upstream of the wall ranged from 21 to 39 g N m(-3), in the wall from 0 to 2 g N m(-3) and downstream from 19 to 44 g N m(-3). An initial groundwater flow investigation using a salt tracer dilution technique showed that the flow through the wall was less than 4% of the flow occurring in the aquifer. Natural gradient tracer tests using bromide and Rhodamine-WT confirmed groundwater bypass under the wall. Hydraulic conductivity of 0.48 m day(-1) was measured inside the wall, whereas the surrounding aquifer had a hydraulic conductivity of 65.4 m day(-1). This indicated that during construction of the wall, hydraulic conductivity of the aquifer had been greatly reduced, so that most of the groundwater flowed under rather than through the wall. Denitrification rates measured in the center of the wall ranged from 0.020 to 0.13 g N m(-3) day(-1), which did not account for the rates of nitrate removal (0.16-0.29 g N m(-3) day(-1)) calculated from monitoring of groundwater nitrate concentrations. This suggested that the rate of denitrification was greater at the upstream face of the wall than in its center where it was limited by low nitrate concentrations. While denitrification walls can be an inexpensive tool for removing nitrate from groundwater, they may not be suitable in aquifers with coarse textured subsoils where simple inexpensive construction techniques result in major decreases in hydraulic conductivity.     

Combined use of field and laboratory testing to predict preferred flow paths in an heterogeneous aquifer

Elevated nitrate concentrations within a municipal water supply aquifer led to pilot testing of a field-scale, in situ denitrification technology based on carbon substrate injections. In advance of the pilot test, detailed characterization of the site was undertaken. The aquifer consisted of complex, discontinuous and interstratified silt, sand and gravel units, similar to other well studied aquifers of glaciofluvial origin, 15-40 m deep. Laboratory and field tests, including a conservative tracer test, a pumping test, a borehole flowmeter test, grain-size analysis of drill cuttings and core material, and permeameter testing performed on core samples, were performed on the most productive depth range (27-40 m), and the results were compared. The velocity profiles derived from the tracer tests served as the basis for comparison with other methods. The spatial variation in K, based on grain-size analysis, using the Hazen method, were poorly correlated with the breakthrough data. Trends in relative hydraulic conductivity (K/K(avg)) from permeameter testing compared somewhat better. However, the trends in transient drawdown with depth, measured in multilevel sampling points, corresponded particularly well with those of solute mass flux. Estimates of absolute K, based on standard pumping test analysis of the multilevel drawdown data, were inversely correlated with the tracer test data. The inverse nature of the correlation was attributed to assumptions in the transient drawdown packages that were inconsistent with the variable diffusivities encountered at the scale of the measurements. Collectively, the data showed that despite a relatively low variability in K within the aquifer under study (within a factor of 3), water and solute mass fluxes were concentrated in discrete intervals that could be targeted for later bioremediation.     

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.     

Development of a fuzzy-stochastic nonlinear model to incorporate aleatoric and epistemic uncertainty

Site uncertainties significantly influence groundwater flow and contaminant transport predictions. Aleatoric and epistemic uncertainty are both identified in site characterization and represented using proper uncertainty theories. When one theory best represents one parameter whereas a different theory may be more suitable for another parameter, the hybrid propagation of aleatoric (random) and epistemic (nonrandom) uncertainties will occur. The computational challenges of joint propagation of aleatoric and epistemic uncertainty through groundwater flow and contaminant transport models are significant. A fuzzy-stochastic nonlinear model was developed in this paper to incorporate these two types of uncertain site information and reduce the computational cost. The results show that (1) the computational cost using the nonlinear model is reduced compared with that of using the sparse grid algorithm and Monte Carlo methods; (2) the uncertainty of hydraulic conductivity (K) significantly influences the water head and solute distribution at the observation wells compared to other uncertain parameters, such as the storage coefficient and the distribution coefficient (K_d); and (3) the combination of multiple uncertain parameters substantially affects the simulation results. Neglecting site uncertainties may lead to unrealistic predictions.     

Evaluating the sensitivity of a subsurface multicomponent reactive transport model with respect to transport and reaction parameters.

The input variables for a numerical model of reactive solute transport in groundwater include both transport parameters, such as hydraulic conductivity and infiltration, and reaction parameters that describe the important chemical and biological processes in the system. These parameters are subject to uncertainty due to measurement error and due to the spatial variability of properties in the subsurface environment. This paper compares the relative effects of uncertainty in the transport and reaction parameters on the results of a solute transport model. This question is addressed by comparing the magnitudes of the local sensitivity coefficients for transport and reaction parameters. General sensitivity equations are presented for transport parameters, reaction parameters, and the initial (background) concentrations in the problem domain. Parameter sensitivity coefficients are then calculated for an example problem in which uranium(VI) hydrolysis species are transported through a two-dimensional domain with a spatially variable pattern of surface complexation sites. In this example, the reaction model includes equilibrium speciation reactions and mass transfer-limited non-electrostatic surface complexation reactions. The set of parameters to which the model is most sensitive includes the initial concentration of one of the surface sites, the formation constant (Kf) of one of the surface complexes and the hydraulic conductivity within the reactive zone. For this example problem, the sensitivity analysis demonstrates that transport and reaction parameters are equally important in terms of how their variability affects the model results.     

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

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

Effects of biofilm growth on flow and transport through a glass parallel plate fracture

The effects of biofilm growth on flow and solute transport through a sandblasted glass parallel plate fracture was investigated. The fracture was inoculated using soil microorganisms. Glucose, oxygen and other nutrients were supplied to support growth. The biomass initially formed discrete clusters attached to the glass surfaces, but over time formed a continuous biofilm. From dye tracer tests conducted during biofilm growth, it was observed that channels and low-permeability zones dominated transport. The hydraulic conductivity of the fracture showed a sigmoidal decrease with time. The hydraulic conductivity was reduced by a factor of 0.033, from 18 to 0.6 cm/s, corresponding to a 72% decrease in the hydraulic aperture, from 500 to 140 microm. In contrast, the mass balance aperture, determined from fluoride tracer tests, remained relatively constant, indicating that the impact of biomass growth on effective fracture porosity was much less than the effect on hydraulic conductivity. Analyses of pre-biofilm tracer tests revealed that both Taylor dispersion and macrodispersion were influencing transport. During biofilm growth, only macrodispersion was dominant. The macrodispersion coefficient alpha(macro) was found to increase logarithmically with hydraulic conductivity reduction.     

Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe

Rapid movement of agricultural chemicals through soil to groundwater via preferential flow pathways is one cause of water contamination. Previous studies have shown that time domain reflectometry (TDR) could be used to characterize solute transport in soil. However, previous studies have only scarcely addressed preferential flow. This study presents an extended application of TDR for determining preferential flow properties. A TDR method was tested in carefully controlled laboratory experiments using 20-cm long and 12-cm diameter undisturbed, structured soil columns. The method used a vertically installed TDR probe and a short pulse of tracer application to obtain residual mass (RM) breakthrough curves (BTC). The RM BTC obtained from TDR were used to estimate mobile/immobile model (MIM) parameters that were compared to the parameter estimates from effluent data. A conventional inverse curve fitting method (CXTFIT) was used to estimate parameters. The TDR-determined parameters were then used to generate calculated effluent BTC for comparison with observed effluent BTC for the same soil columns. Time moments of the calculated and observed BTC were calculated to quantitatively evaluate the calculated BTC. Overall, the RM BTC obtained from TDR were similar to the RM BTC obtained from effluent data. The TDR-determined parameters corresponded well to the parameters obtained from the effluent data, although they were not within the 95% confidence intervals. Correlation coefficients between the parameters obtained from TDR and from effluent data for the immobile water fraction (theta im/theta), mass exchange coefficient (alpha), and dispersion coefficient (Dm) were 0.95, 0.95, and 0.99, respectively. For three of the four soil cores, theta im/theta ranged from 0.42 to 0.82, indicating considerable preferential flow. The TDR-calculated effluent BTC also were similar to the observed effluent BTC having an average coefficient of determination of 0.94. Time moments obtained from calculated BTC were representative of those obtained from observed BTC. The vertical TDR probe method was simple and minimally destructive and provided representative preferential flow properties that enabled the characterization of solute transport in soil.     

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.     

Description of hydrogeologic heterogeneity and evaluation of radionuclide transport at an underground nuclear test

Realistic models of contaminant transport in groundwater demand detailed characterization of the spatial distribution of subsurface hydraulic properties, while at the same time programmatic constraints may limit collection of pertinent hydraulic data. Fortunately, alternate forms of data can be used to improve characterization of spatial variability. We utilize a methodology that augments sparse hydraulic information (hard data) with more widely available hydrogeologic information to generate equiprobable maps of hydrogeologic properties that incorporate patterns of connected permeable zones. Geophysical and lithologic logs are used to identify hydrogeologic categories and to condition stochastic simulations using Sequential Indicator Simulation (SIS). The resulting maps are populated with hydraulic conductivity values using field data and Sequential Gaussian Simulation (SGS). Maps of subsurface hydrogeologic heterogeneity are generated for the purpose of examining groundwater flow and transport processes at the Faultless underground nuclear test, Central Nevada Test Area (CNTA), through large-scale, three-dimensional numerical modeling. The maps provide the basis for simulation of groundwater flow, while transport of radionuclides from the nuclear cavity is modeled using particle tracking methods. Sensitivity analyses focus on model parameters that are most likely to reduce the long travel times observed in the base case. The methods employed in this study have improved our understanding of the spatial distribution of preferential flowpaths at this site and provided the critical foundation on which to build models of groundwater flow and transport. The results emphasize that the impacts of uncertainty in hydraulic and chemical parameters are dependent on the radioactive decay of specific species, with rapid decay magnifying the effects of parameters that change travel time.     

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.     

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.     

Implications of non-equilibrium transport in heterogeneous reactive barrier systems: evidence from laboratory denitrification experiments

Organic substrates in reactive barrier systems are often heterogeneous material mixtures with relatively large contrasts in hydraulic conductivity and porosity over short distances. These short-range variations in material properties imply that preferential flow paths and diffusion between regions of higher and lower hydraulic conductivity may be important for treatment efficiency. This paper presents the results of a laboratory column experiment where denitrification is investigated using a heterogeneous reactive substrate (sawdust mixed with sewage sludge). Displacement experiments with a non-reactive solute at three different flow rates are used to estimate transport parameters using a dual porosity non-equilibrium model. Parameter estimation from breakthrough curves produced relatively consistent values for the fraction of the porosity consisting of mobile water (β) and the mass transfer coefficient (α), with average values of 0.27 and 0.42 d(-1), respectively. The column system removes >95% of the influent nitrate at low and medium flow, but only 50-75% of the influent nitrate at high flow, suggesting that denitrification kinetics and diffusive mass transfer rates are limiting the degree of treatment at lower hydraulic residence times. Reactive barrier systems containing dual porosity media must therefore consider mass transfer times in their design; this is often most easily accommodated by adjusting flowpath length.     

A controlled field experiment on groundwater contamination by a multicomponent DNAPL: creation of the emplaced-source and overview of dissolved plume development

A unique field experiment has been undertaken at the CFB Borden research site to investigate the development of dissolved chlorinated solvent plumes from a residual dense non-aqueous phase liquid (DNAPL) source. The "emplaced-source" tracer test methodology involved a controlled emplacement of a block-shaped source of sand containing chlorinated solvents below the water table. The gradual dissolution of this residual DNAPL solvent source under natural aquifer conditions caused dissolved solvent plumes of trichloromethane (TCM), trichloroethene (TCE) and perchloroethene (PCE) to continuously develop down gradient. Source dissolution and 3-D plume development were successfully monitored via 173 multilevel samplers over a 475-day tracer test period prior to site remediation research being initiated. Detailed groundwater level and hydraulic conductivity data were collected. Development of plumes with concentrations spanning 1-700,000 micrograms/1 is described and key processes controlling their migration identified. Plumes were observed to be narrow due to the weakness of transverse dispersion processes and long due to advection and significant longitudinal dispersion, very limited sorptive retardation and negligible, if any, attenuation due to biodegradation or abiotic reaction. TCM was shown to be essentially conservative, TCE very nearly conservative and PCE, consistent with its greater hydrophobicity, more retarded yet having a greater mobility than observed in previous Borden field tests. The absence of biodegradation was ascribed to the prevailing aerobic conditions and lack of any additional biodegradable carbon substrates. The transient groundwater flow regime caused significant transverse lateral plume movement, plume asymmetry and was likely responsible for most of the, albeit limited, transverse horizontal plume spreading. In agreement with the widespread incidence of extensive TCE and PCE plumes throughout the industrialized world, the experiment indicates such solvent plumes are likely to be highly mobile and persistent, at least in aquifers that are aerobic and have low sorption potential (low foc content).     

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.     

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).     

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.