Application of ERT,Saline Tracer and Numerical Studies to Delineate Preferential Paths in Fractured Granites

Accurate quantification of in situ heterogeneity and flow processes through fractured geologic media remains elusive for hydrogeologists due to the complexity in fracture characterization and its multiscale behavior. In this research, we demonstrated the efficacy of tracer-electrical resistivity tomography (ERT) experiments combined with numerical simulations to characterize heterogeneity and delineate preferential flow paths in a fractured granite aquifer. A series of natural gradient saline tracer experiments were conducted from a depth window of 18 to 22 m in an injection well (IW) located inside the Indian Institute of Technology Hyderabad campus. Tracer migration was monitored in a time-lapse mode using two cross-sectional surface ERT profiles placed in the direction of flow gradient. ERT data quality was improved by considering stacking, reciprocal measurements, resolution indicators, and geophysical logs. Dynamic changes in subsurface electrical properties inferred via resistivity anomalies were used to highlight preferential flow paths of the study area. Temporal changes in electrical resistivity and tracer concentration were monitored along the vertical in an observation well located at 48 m to the east of the IW. ERT-derived tracer breakthrough curves were in agreement with geochemical sample measurements. Fracture geometry and hydraulic properties derived from ERT and pumping tests were further used to evaluate two mathematical conceptualizations that are relevant to fractured aquifers. Results of numerical analysis conclude that dual continuum model that combines matrix and fracture systems through a flow exchange term has outperformed equivalent continuum model in reproducing tracer concentrations at the monitoring wells (evident by a decrease in RMSE from 199 to 65 mg/L). A sensitivity analysis on model simulations conclude that spatial variability in hydraulic conductivity, local-scale dispersion, and flow exchange at fracture-matrix interface have a profound effect on model simulations.     

Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.     

A stochastic interpretation of the tailing effect in solute transport

 The advection-dispersion equation (ADE) is inadequate for describing tails in solute breakthrough curves. Re-examination of solute breakthrough curves from one-dimensional experiments in porous media and channel flow literature shows a consistent discrepancy compared with solutions to the ADE. The leading tail of breakthrough curves is sharper, and the trailing tail is longer and smoother, than best fitting, least-squares ADE solutions. A random particle simulation exercise shows that the ADE may firstly be erroneous because of the assumption of time steps over which random solute movements are considered independent. Definition of such time steps hinges upon the slowest random movements, such as those predominantly by molecular diffusion. A second potential source of error is the highly skewed nature of the inverse distribution of underlying, micro-scale velocities, which causes slow convergence to normality under the central limit theorem.     

A 3D ERT study of solute transport in a large experimental tank

A high resolution, cross-borehole, 3D electrical resistivity tomography (ERT) study of solute transport was conducted in a large experimental tank. ERT voxels comprising the time sequence of electrical images were converted into a 3D array of ERT estimated fluid conductivity breakthrough curves and compared with direct measurements of fluid conductivity breakthrough made in wells. The 3D ERT images of solute transport behaviour were also compared with predictions based on a 3D finite-element, coupled flow and transport model, accounting for gravity induced flow caused by concentration differences.The tank (dimensions 185×245×186 cm) was filled with medium sand, with a gravel channel and a fine sand layer installed. This heterogeneous system was designed to complicate solute transport behaviour relative to a homogeneous sand tank, and to thus provide a challenging but insightful analysis of the ability of 3D ERT to resolve transport phenomena. Four ERT arrays and 20 piezometers were installed during filling. A NaCl tracer (conductivity 1.34 S/m) was injected and intensively monitored with 3D ERT and direct sampling of fluid chemistry in piezometers.We converted the bulk conductivity estimate for 250 voxels in the ERT imaged volume into ERT estimated voxel fluid conductivity by assuming that matrix conduction in the tank is negligible. In general, the ERT voxel response is in reasonable agreement with the shape of fluid conductivity breakthrough observed in six wells in which direct measurements of fluid conductivity were made. However, discrepancies occur, particularly at early times, which we attribute to differences between the scale of the image voxels and the fluid conductivity measurement, measurement errors mapped into the electrical inversion and artificial image roughness resulting from the inversion.ERT images revealed the 3D tracer distribution at 15 times after tracer injection. The general pattern and timing of solute breakthrough observed with ERT agreed with that predicted from the flow/transport modelling. However, the ERT images indicate a vertical component of tracer transport and preferential flow paths in the medium sand. We attribute this to transient vertical gradients established during tracer injection, and heterogeneity caused by sorting of the sand resulting from the filling procedure. In this study, ERT provided a unique dataset of 250 voxel breakthrough curves in 1.04 m³. The use of 3D ERT to generate an array of densely sampled estimated fluid conductivity breakthrough curves is a potentially powerful tool for quantifying solute transport processes.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

The Effect of Hydraulic Gradient and Pattern of Conduit Systems on Tracing Tests: Bench-Scale Modeling

Tracer breakthrough curves provide valuable information about the traced media, especially in inherently heterogeneous karst aquifers. In order to study the effect of variations in hydraulic gradient and conduit systems on breakthrough curves, a bench scale karst model was constructed. The bench scale karst model contains both matrix and a conduit. Eight tracing tests were conducted under a wide range of hydraulic gradients from 1 to greater than 5 for branchwork and network-conduit systems. Sampling points at varying distances from the injection point were utilized. Results demonstrate that mean tracer velocities, tracer mass recovery and linear rising slope of the breakthrough curves were directly controlled by hydraulic gradient. As hydraulic gradient increased, both one half the time for peak concentration and one fifth the time for peak concentration decreased. The results demonstrate the variations in one half the time for peak concentration and one fifth the time for peak concentration of the descending limb for different sampling points under differing hydraulic gradients are mainly controlled by the interactions of advection with dispersion. The results are discussed from three perspectives: different conduit systems, different hydraulic-gradient conditions, and different sampling points. The research confirmed the undeniable role of hydrogeological setting (i.e., hydraulic gradient and conduit system) on the shape of the breakthrough curve. The extracted parameters (mobile-fluid velocity, tracer-mass recovery, linear rising limb, one half the time for peak concentration, and one fifth the time for peak concentration) allow for differentiating hydrogeological settings and enhance interpretations the tracing tests in karst aquifers.     

FracKfinder: A MATLAB Toolbox for Computing Three-Dimensional Hydraulic Conductivity Tensors for Fractured Porous Media

Fractures in porous media have been documented extensively. However, they are often omitted from groundwater flow and mass transport models due to a lack of data on fracture hydraulic properties and the computational burden of simulating fractures explicitly in large model domains. We present a MATLAB toolbox, FracKfinder, that automates HydroGeoSphere (HGS), a variably saturated, control volume finite-element model, to simulate an ensemble of discrete fracture network (DFN) flow experiments on a single cubic model mesh containing a stochastically generated fracture network. Because DFN simulations in HGS can simulate flow in both a porous media and a fracture domain, this toolbox computes tensors for both the matrix and fractures of a porous medium. Each model in the ensemble represents a different orientation of the hydraulic gradient, thus minimizing the likelihood that a single hydraulic gradient orientation will dominate the tensor computation. Linear regression on matrices containing the computed three-dimensional hydraulic conductivity (K) values from each rotation of the hydraulic gradient is used to compute the K tensors. This approach shows that the hydraulic behavior of fracture networks can be simulated where fracture hydraulic data are limited. Simulation of a bromide tracer experiment using K tensors computed with FracKfinder in HGS demonstrates good agreement with a previous large-column, laboratory study. The toolbox provides a potential pathway to upscale groundwater flow and mass transport processes in fractured media to larger scales.     

Are Visible Fractures Accurate Predictors of Flow and Mass Transport in Fractured Till?

Tracer experiments conducted in the laboratory on undisturbed core samples (<7.3-cm-diameter) have been a standard method for estimating hydraulic and transport properties of fractured till since the 1980s. This study assesses the relationship between visible fractures on the top and bottom of core samples and the resulting hydraulic and mass transport properties of the core. We hypothesized that more visible fractures would indicate the presence of a well-connected fracture network, leading to greater hydraulic conductivity (K) values and earlier chemical breakthrough times. To test this hypothesis, water flow and bromide (Br-) tracer experiments were performed on 10, 16-cm diameter, 16-cm-tall samples of fractured Dows Formation till from central Iowa. Visually identifiable fractures were present on the top and bottom of every sample. Results indicate that the visual identification of fractures does not predict a connected fracture network, as some samples produced breakthrough curves showing rapid first arrival times and shapes characteristic of solute transport in a fractured medium, while others appeared similar to an unfractured medium. No correlation was found between the number of visible fractures and K (Pearson's r = 0.25), or Br- first arrival time (r = −0.33), but a strong negative correlation between K and first arrival time (r = −0.92). Results indicate that the sample volume was not large enough to reliably contain a connected fracture network. Thus, testing large volumes of till at the field scale coupled with fracture-flow modeling likely represents the best approach for estimating hydraulic and mass transport properties for fractured till.     

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin,France)

A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.     

Macropores as preferential flow paths in meander bends

Macropores are subsurface connected void spaces caused by processes such as fracture of soils, micro‐erosion, and fauna burrows. They are common near streams (e.g. hyporheic and riparian zones) and may act as preferential flow paths between surface and groundwaters, affecting hydrologic and biogeochemical processes. We tested the hydrologic function of macropores by constructing an artificial macropore within the saturated zone of a meander bend (open macropore, ‘OM’) and later filling its upstream end (partially filled macropore, ‘PFM’). For each treatment, we injected saline tracer at an upgradient monitoring well within the meander and monitored downgradient hydraulics and tracer transport. Pressure transducers in monitoring wells indicated hydraulic gradients within the meander were 32% higher perpendicular to and 6% higher parallel to the macropore for the OM than for the PFM. Additionally, hydraulic conductivities measured via falling head tests were 29 to 550 times higher along the macropore than in nearby sediment. We used electrical conductivity probes in wells and electrical resistivity imaging to track solute transport. Transport velocities through the meander were on average 9 and 21% higher (per temporal moment analysis and observed tracer peak, respectively) for the OM than for the PFM. Furthermore, temporal moments of tracer breakthrough analysis indicated downgradient longitudinal dispersion and breakthrough tracer curve tailing were on average 234% and 182% higher for the OM, respectively. This suggests the OM enabled solute transport at overall shorter timescales than the matrix but also increased tailing. Our results demonstrate the importance of macropores to meander bend hydrology and solute transport. Copyright © 2012 John Wiley & Sons, Ltd.     

Interpreting Variations in Groundwater Flows from Repeated Distributed Thermal Perturbation Tests

To better understand the groundwater resources of southern Nye County, Nevada, a multipart distributed thermal perturbation sensing (DTPS) test was performed on a complex of three wells. These wells penetrate an alluvial aquifer that drains the Nevada National Security Site, and characterizing the hydraulic properties and flow paths of the regional groundwater flow system has proven very difficult. The well complex comprised one pumping well and two observation wells, both located 18 m from the pumping well. Using fiber‐optic cables and line heaters, DTPS tests were performed under both stressed and unstressed conditions. Each test injects heat into the water column over a period of one to two days, and observes the rising temperature during heat injection and falling temperatures after heating ceases. Aquifer thermal properties are inferred from temperature patterns in the cased section of the wells, and fluxes through the 30‐m screened section are estimated based on a model that incorporates conductive and advective heat fluxes. Vertical variations in flux are examined on a scale of tens of cm. The actively flowing zones of the aquifer change between the stressed and unstressed test, and anisotropy in the aquifer permeability is apparent from the changing fluxes between tests. The fluxes inferred from the DTPS tests are compared to solute tracer tests previously performed on the same site. The DTPS‐based fluxes are consistent with the fastest solute transport observed in the tracer test, but appear to overestimate the mean flux through the system.     

New combined log and tracer test interpretation method for identifying transfers in fissured aquifers

Tracer tests represent the most appropriate approach for assessing hydrodispersive parameters such as transversal and longitudinal dispersivities or kinematic porosity on an aquifer scale. They are generally carried out by injecting a tracer in a borehole and measuring its concentration over time in neighboring boreholes by extracted volume sampling or downhole measurements. Logging is one of the most suitable methods for evaluating fissured reservoirs. But short circuits between fractures with different hydraulic potential through boreholes induce mixing phenomena that cannot be avoided without packers. This mixing can shift the breakthrough curves deduced from the logs for each producing fracture and distort determination of their location.
The method proposed in this paper aims at measuring the flow rate and the solute breakthrough for hydraulically active fractures, in open boreholes. It involves estimating a velocity profile along the borehole column by the analysis of two successive logs: a shift function according to depth is thus determined by comparison between log portions on each successive one. The velocity gradients reflect the inward or outward flow rates produced by each fracture. On the basis of these flow rates, it is possible to determine the mixing effects inside the borehole and then to plot unbiased breakthrough curves for each producing fracture.
This method was applied at a granitic site in the eastern Pyrenees. In spite of some questionable limitations, the results showed that the method seems adapted to situations with many fractures. The precise hydraulic pattern which is obtained at the borehole scale is discussed in terms of a dual porosity model. Furthermore, interpretation of the breakthrough curves for fractures corrected for mixing effects revealed that Peclet numbers are strongly underestimated if this phenomenon is not considered.     

Tracer mass recovery in fractured aquifers estimated from multiple well tests

Forced-gradient tracer tests in fractured aquifers often report low mass recoveries. In fractured aquifers, fractures intersected by one borehole may not be intersected by another. As a result (1) injected tracer can follow pathways away from the withdrawal well causing low mass recovery and (2) recovered water can follow pathways not connected to the injection well causing significant tracer dilution. These two effects occur along with other forms of apparent mass loss. If the strength of the connection between wells and the amount of dilution can be predicted ahead of time, tracer tests can be designed to optimize mass recovery and dilution. A technique is developed to use hydraulic tests in fractured aquifers to calculate the conductance (strength of connection) between well pairs and to predict mass recovery and amount of dilution during forced gradient tracer tests. Flow is considered to take place through conduits, which connect the wells to each other and to distant sources or sinks. Mass recovery is related to the proportion of flow leaving the injection well and arriving at the withdrawal well, and dilution is related to the proportion of the flow from the withdrawal well that is derived from the injection well. The technique can be used to choose well pairs for tracer tests, what injection and withdrawal rates to use, and which direction to establish the hydraulic gradient to maximize mass recovery and/or minimize dilution. The method is applied to several tracer tests in fractured aquifers in the Clare Valley, South Australia.     

Discretizing the fracture-matrix interface to simulate solute transport

This article examines the required spatial discretization perpendicular to the fracture-matrix interface (FMI) for numerical simulation of solute transport in discretely fractured porous media. The discrete-fracture, finite-element model HydroGeoSphere ( Therrien et al. 2005 ) and a discrete-fracture implementation of MT3DMS ( Zheng 1990 ) were used to model solute transport in a single fracture, and the results were compared to the analytical solution of Tang et al. (1981) . To match analytical results on the relatively short timescales simulated in this study, very fine grid spacing perpendicular to the FMI of the scale of the fracture aperture is necessary if advection and/or dispersion in the fracture is high compared to diffusion in the matrix. The requirement of such extremely fine spatial discretization has not been previously reported in the literature. In cases of high matrix diffusion, matching the analytical results is achieved with larger grid spacing at the FMI. Cases where matrix diffusion is lower can employ a larger grid multiplier moving away from the FMI. The very fine spatial discretization identified in this study for cases of low matrix diffusion may limit the applicability of numerical discrete-fracture models in such cases.     

Two-dimensional power series solution for non-axisymmetrical transport in a radially convergent tracer test with scale-dependent dispersion

It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power series solution and the numerical solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at any observation point.     

Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison of approaches for predicting solute transport: sandbox experiments

The main purpose of this paper was to compare three approaches for predicting solute transport. The approaches include: (1) an effective parameter/macrodispersion approach (Gelhar and Axness 1983); (2) a heterogeneous approach using ordinary kriging based on core samples; and (3) a heterogeneous approach based on hydraulic tomography. We conducted our comparison in a heterogeneous sandbox aquifer. The aquifer was first characterized by taking 48 core samples to obtain local-scale hydraulic conductivity (K). The spatial statistics of these K values were then used to calculate the effective parameters. These K values and their statistics were also used for kriging to obtain a heterogeneous K field. In parallel, we performed a hydraulic tomography survey using hydraulic tests conducted in a dipole fashion with the drawdown data analyzed using the sequential successive linear estimator code (Yeh and Liu 2000) to obtain a K distribution (or K tomogram). The effective parameters and the heterogeneous K fields from kriging and hydraulic tomography were used in forward simulations of a dipole conservative tracer test. The simulated and observed breakthrough curves and their temporal moments were compared. Results show an improvement in predictions of drawdown behavior and tracer transport when the K tomogram from hydraulic tomography was used. This suggests that the high-resolution prediction of solute transport is possible without collecting a large number of small-scale samples to estimate flow and transport properties that are costly to obtain at the field scale.     

Tracer tests in fractured rocks with a new fluorescent dye—pyrene-1,3,6,8-tetra sulphonic acid (PTS) / Tests de traçage en roches fracturées avec un nouveau produit fluorescent—l'acide pyrène 1.3.6.8 tétra sulfonique (PTS)

Abstract

Two multi-tracer tests were performed in fissured rocks accessible in underground laboratories to examine a new fluorescent dye: pyrene-1,3,6,8-tetra sulphonic acid (PTS). The first test was carried out at the Lindau Rock Laboratory (LRL), Germany, in a highly permeable ore dike, and the second, at the Grimsel Test Site (GTS), Switzerland, in a heterogeneous granite fault zone (AU 126). At the LRL new tracer was injected together with uranine in a convergent flow field (monopole test), and slightly different tracer breakthrough curves were observed according to different diffusion coefficients of both tracers. The matrix porosity calculated with the aid of the one-dimensional (1-D) single-fissure dispersion model (SFDM) agrees well with that found in earlier tracer tests and with measurements performed on core samples. At the GTS, the PTS tracer was applied together with pyranine in two-well injection–withdrawal (dipole) tests. Both tracers yielded identical tracer concentration curves, which confirm their conservative behaviour. Mathematical simulations performed with the aid of a 3-D numerical model (FRAC3DVS) yielded equally good fits for different sets of parameters, independent of whether matrix porosity was included or neglected. That lack of unique solution and the difficulty in observing the influence of matrix diffusion result from a wide distribution of the transit times of particular streamlines, which is characteristic for injection–withdrawal tests. However, both tracer tests clearly indicated that the new tracer (PTS) behaves conservatively at high pH values and can be successfully used for groundwater labelling.     

A Dye Tracer Approach for Quantifying Fluid and Solute Flux Across the Sediment–Water Interface

We propose a dye tracer method to characterize fluid and solute fluxes across the sediment-water interface. Zones of groundwater discharge within the streambed are first identified, and small volume slugs of 0.5 to 1 mL fluorescein dye are released at known subsurface depths. Fluorescein dye allows for visual identification of interface breakthrough locations and times, and dye concentrations at the point of discharge are recorded over time by a fluorometer to generate high resolution breakthrough curves. Groundwater velocities and dispersivities at the demonstration site are estimated by numerically fitting dye breakthroughs to the classical advection-dispersion equation, although the methodology is not limited to a specific transport model. Breakthroughs across the stream-sediment interface at the demonstration site are nonlinear with tracer release depth, and velocity estimates from breakthrough analysis are significantly more reliable than visual dye (time to first dye expression) and Darcy methods which tend to overestimate and underestimate groundwater velocity, respectively. The use of permanent injection points within the streambed and demonstrated reproducibility of dye breakthroughs allow for study of fluid and solute fluxes under seasonally varying hydrologic conditions. The proposed approach also provides a framework for field study of nonconservative, reactive solutes and allows for the determination of characteristic residence times at various depths in the streambed to better understand chemical and nutrient transformations.     

Shear dispersion in a fracture with porous walls

We present an analytical expression for the shear dispersion during solute transport in a coupled fracture–matrix system. The dispersion coefficient is obtained in a fracture with porous walls by taking into account an accurate boundary condition at the interface between the matrix and fracture, and the results were compared with those in a non-coupled system. The analysis presented identifies three regimes: diffusion-dominated, transition, and advection-dominated. The results showed that it is important to consider the exchange of solute between the fracture and matrix in development of the shear dispersion coefficient for the transition and advection-dominated regimes. The new dispersion coefficient is obtained by imposing the continuity of concentrations and mass fluxes along the porous walls. The resulting equivalent transport equation revealed that the effective velocity in a fracture increases while the dispersion coefficient decreases due to mass transfer between the matrix and fracture. A larger effective advection term leads to greater storage of mass in the matrix as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The findings of this study can be used for modeling of tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks.