A Method for Conducting Simultaneous Convergent Tracer Tests in Multilayered Aquifers

Forced gradient tracer tests between two boreholes can be used to study contaminant transport processes at the small field scale or investigate the transport properties of an aquifer. Full depth tests, in which tracer samples are collected just from the discharge of the abstraction borehole, often give rise to breakthrough curves with multiple peaks that are usually attributed to different flow paths through the aquifer that can rarely be identified from the test results alone. Tests in selected levels of the aquifer, such as those between packer‐isolated sections of the boreholes, are time consuming, expensive; and the identification of major transport pathways is not guaranteed. We present a method for simultaneously conducting multiple tracer tests covering the full depth of the boreholes, in which tracer sampling and monitoring is carried out by a novel multilevel sampling system allowing high frequency and cumulative sampling options. The method is applied to a tracer test using fluorescein conducted in the multilayered sandstone aquifer beneath the city of Birmingham, UK, producing six well‐defined tracer breakthrough curves.     

A spreadsheet program for two-well tracer test data analysis

Two-well tracer tests are often conducted to investigate subsurface solute transport in the field. Analyzing breakthrough curves in extraction and monitoring wells using numerical methods is nontrivial due to highly nonuniform flow conditions. We extended approximate analytical solutions for the advection-dispersion equation for an injection-extraction well doublet in a homogeneous confined aquifer under steady-state flow conditions for equal injection and extraction rates with no transverse dispersion and negligible ambient flow, and implemented the solutions in Microsoft Excel using Visual Basic for Application (VBA). Functions were implemented to calculate concentrations in extraction and monitoring wells at any location due to a step or pulse injection. Type curves for a step injection were compared with those calculated by numerically integrating the solution for a pulse injection. The results from the two approaches are similar when the dispersivity is small. As the dispersivity increases, the latter was found to be more accurate but requires more computing time. The code was verified by comparing the results with published-type curves and applied to analyze data from the literature. The method can be used as a first approximation for two-well tracer test design and data analysis, and to check accuracy of numerical solutions. The code and example files are publicly available.     

Estimating Reaction Rate Coefficients Within a Travel‐Time Modeling Framework

A generalized, efficient, and practical approach based on the travel‐time modeling framework is developed to estimate in situ reaction rate coefficients for groundwater remediation in heterogeneous aquifers. The required information for this approach can be obtained by conducting tracer tests with injection of a mixture of conservative and reactive tracers and measurements of both breakthrough curves (BTCs). The conservative BTC is used to infer the travel‐time distribution from the injection point to the observation point. For advection‐dominant reactive transport with well‐mixed reactive species and a constant travel‐time distribution, the reactive BTC is obtained by integrating the solutions to advective‐reactive transport over the entire travel‐time distribution, and then is used in optimization to determine the in situ reaction rate coefficients. By directly working on the conservative and reactive BTCs, this approach avoids costly aquifer characterization and improves the estimation for transport in heterogeneous aquifers which may not be sufficiently described by traditional mechanistic transport models with constant transport parameters. Simplified schemes are proposed for reactive transport with zero‐, first‐, nth‐order, and Michaelis‐Menten reactions. The proposed approach is validated by a reactive transport case in a two‐dimensional synthetic heterogeneous aquifer and a field‐scale bioremediation experiment conducted at Oak Ridge, Tennessee. The field application indicates that ethanol degradation for U(VI)‐bioremediation is better approximated by zero‐order reaction kinetics than first‐order reaction kinetics.     

Influence of injection conditions on field tracer experiments

Calibration of ground water transport models is often performed using results of field tracer experiments. However, little attention is usually paid to the influence, on resulting breakthrough curves, of injection conditions and well-aquifer interactions, more particularly of the influence of the possible trapping of the tracer in the injection wellbore. Recently, a new mathematical and numerical approach has been developed to model injection conditions and well-aquifer interactions in a very accurate way. Using an analytical solution derived from this model, a detailed analysis is made of the evolution of the tracer input function in the aquifer. By varying injection conditions from one simulation to another, synthetic breakthrough curves are generated with the SUFT3D ground water flow and transport finite-element simulator. These tests show clearly that the shape of the breakthrough curves can be dramatically affected by injection conditions. Using generated breakthrough curves as "actual" field results, a calibration of hydrodispersive parameters is performed, neglecting the influence of injection conditions. This shows that neglecting the influence of actual injection conditions can lead to (1) errors on fitted parameters and (2) misleading identification of the active transport processes. Conclusions and guidelines are drawn in terms of proposed methodologies for better controlling the tracer injection in the field, in order to minimize risk of misinterpretation of results.     

The Horizontal Reactive Media Treatment Well (HRX Well®) for Passive In‐Situ Remediation

A new in‐situ remediation concept termed a Horizontal Reactive Media Treatment Well (HRX Well®) is presented that utilizes horizontal wells filled with reactive media to passively treat contaminated groundwater in‐situ. The approach involves the use of large‐diameter directionally drilled horizontal wells filled with granular reactive media generally installed parallel to the direction of groundwater flow. The design leverages natural “flow‐focusing” behavior induced by the high in‐well hydraulic conductivity of the reactive media relative to the aquifer hydraulic conductivity to passively capture and treat proportionally large volumes of groundwater within the well. Clean groundwater then exits the horizontal well along its downgradient sections. Many different types of solid granular reactive media are already available (e.g., zero valent iron, activated carbon, ion exchange resins, zeolite, apatite, chitin); therefore, this concept could be used to address a wide range of contaminants. Three‐dimensional flow and transport simulations were completed to assess the general hydraulic performance, capture zones, residence times, effects of aquifer heterogeneity, and treatment effectiveness of the concept. The results demonstrate that capture and treatment widths of up to tens of feet can be achieved for many aquifer settings, and that reductions in downgradient concentrations and contaminant mass flux are nearly immediate. For a representative example, the predicted treatment zone width for the HRX Well is approximately 27 to 44 feet, and contaminant concentrations immediately downgradient of the HRX Well decreased an order of magnitude within 10 days. A series of laboratory‐scale physical tests (i.e., tank tests) were completed that further demonstrate the concept and confirm model prediction performance. For example, the breakthrough time, peak concentration and total mass recovery of methylene blue (reactive tracer) was about 2, 35, and 20 times (respectively) less than chloride (conservative tracer) at the outlet of the tank‐scale HRX Well.     

A two‐dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water

Groundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Discontinuous Steady‐State Analytical Solutions of the Boussinesq Equation and Their Numerical Representation by Modflow

Known analytical solutions of groundwater flow equations are routinely used for verification of computer codes. However, these analytical solutions (e.g., the Dupuit solution for the steady‐state unconfined unidirectional flow in a uniform aquifer with a flat bottom) represent smooth and continuous water table configurations, simulating which does not pose any significant problems for the numerical groundwater flow models, like MODFLOW. One of the most challenging numerical cases for MODFLOW arises from drying‐rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. Numerical solutions of groundwater flow equations cannot be rigorously verified for such cases due to the lack of corresponding exact analytical solutions. Analytical solutions of the steady‐state Boussinesq equation, associated with the discontinuous water table configurations over a stairway impervious base, are presented in this article. Conditions resulting in such configurations are analyzed and discussed. These solutions appear to be well suited for testing and verification of computer codes. Numerical solutions, obtained by the latest versions of MODFLOW (MODFLOW‐2005 and MODFLOW‐NWT), are compared with the presented discontinuous analytical solutions. It is shown that standard MODFLOW‐2005 code (as well as MODFLOW‐2000 and older versions) has significant convergence problems simulating such cases. The problems manifest themselves either in a total convergence failure or erroneous results. Alternatively, MODFLOW‐NWT, providing a good match to the presented discontinuous analytical solutions, appears to be a more reliable and appropriate code for simulating abrupt changes in water table elevations.     

Analytical model for fully three‐dimensional radial dispersion in a finite‐thickness aquifer

Analytical solutions for contaminant transport in a non‐uniform flow filed are very difficult and relatively rare in subsurface hydrology. The difficulty is because of the fact that velocity vector in the non‐uniform flow field is space‐dependent rather than constant. In this study, an analytical model is presented for describing the three‐dimensional contaminant transport from an area source in a radial flow field which is a simplest case of the non‐uniform flow. The development of the analytical model is achieved by coupling the power series technique, the Laplace transform and the two finite Fourier cosine transform. The developed analytical model is examined by comparing with the Laplace transform finite difference (LTFD) solution. Excellent agreements between the developed analytical model and the numerical model certificate the accuracy of the developed model. The developed model can evaluate solution for Peclet number up to 100. Moreover, the mathematical behaviours of the developed solution are also studied. More specifically, a hypothetical convergent flow tracer test is considered as an illustrative example to demonstrate the three‐dimensional concentration distribution in a radial flow field. The developed model can serve as benchmark to check the more comprehensive three‐dimensional numerical solutions describing non‐uniform flow contaminant transport. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.     

Determination of the conduit structure in a karst aquifer based on tracer data—Lurbach system,Austria

A structure model was used to analyse solute‐transport parameter estimates based on tracer breakthrough curves. In the model system, groundwater flow is envisioned to be organised in a complex conduit network providing a variety of short circuits with relative small carrying capacities along different erosion levels. The discharge through the fully filled conduits is limited owing to void geometries and turbulent flow; thus, a hierarchic overflow system evolves where conduits are (re‐)activated or dried up depending on the flow condition. Exemplified on the Lurbach–Tanneben karst aquifer, the applicability of the model approach was tested. Information derived from multi‐tracer experiments performed at different volumetric flow rates enabled to develop a structural model of the karst network, under constraint of the geomorphological and hydrological evolution of the site. Depending on the flow rate, groundwater is divided into up to eight flow paths. The spatial hierarchy of flow paths controls the sequence of flow path activation. Conduits of the topmost level are strongly influenced by reversible alteration processes. Sedimentation or blocking causes an overflow of water to the next higher conduit. Flow path specific dissolutional denudation rates were estimated using the temporal development of the partial discharge. Copyright © 2012 John Wiley & Sons, Ltd.     

Heat Tracing in a Fractured Aquifer with Injection of Hot and Cold Water

Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.     

Contaminant transport in one‐dimensional single fractured media: semi‐analytical solution for three‐member decay chain with pulse and Heaviside input sources

A semi‐analytical solution of the one‐dimensional transport for considering a three‐member decay chain in a single fracture with pulse and Heaviside input sources has been studied using the Laplace transform and its numerical inversion. The results reveal that breakthrough curves of dimensionless concentration for the decay chain of Np‐237, U‐233, and Th‐229 in the fracture can be well demonstrated in the temporal and spatial domains. The conditions with and without retardation effects are also compared. During the preliminary screening phase the solutions are suitable for performance assessment on radioactive waste disposal sites under a one‐dimensional single fracture condition. Copyright © 2007 John Wiley & Sons, Ltd.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer

A two‐dimensional semi‐analytical solution to analyse stream–aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two‐dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non‐dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one‐dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water‐level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water‐level variations due to stream and tidal boundaries are sensitive to specific yield. Copyright © 2006 John Wiley & Sons, Ltd.     

Process-based interpretation of tracer tests in carbonate aquifers

A tracer test in a carbonate aquifer is analyzed using the method of moments and two analytical advection-dispersion models (ADMs) as well as a numerical model. The numerical model is a coupled continuum-pipe flow and transport model that accounts for two different flow components in karstified carbonate aquifers, i.e., rapid and often turbulent conduit flow and Darcian flow in the fissured porous rock. All techniques employed provide reasonable fits to the tracer breakthrough curve (TBC) measured at a spring. The resulting parameter estimates are compared to investigate how each conceptual model of flow and transport processes that forms the basis of the analyses affects the interpretation of the tracer test. Numerical modeling results suggest that the method of moments and the analytical ADMs tend to overestimate the conduit volume because part of the water discharged at the spring is wrongly attributed to the conduit system if flow in the fissured porous rock is ignored. In addition, numerical modeling suggests that mixing of the two flow components accounts for part of the dispersion apparent in the measured TBC, while the remaining part can be attributed to Taylor dispersion. These processes, however, cannot reasonably explain the tail of the TBC. Instead, retention in immobile-fluid regions as included in a nonequilibrium ADM provides a possible explanation.     

Contaminant transport in fractured chalk: laboratory and field experiments

Laboratory experiments were performed on chalk samples from Denmark and Israel to determine diffusion and distribution coefficients. Batch tests were used to define sorption isotherms for naphthalene and o-xylene. Linear sorption isotherms were observed and described with Henry-isotherms. Because of the high purity and low contents of clay minerals and organic carbon, Danish and white Israeli chalk generally have low retardation capacities. Contrarily, gray Israeli chalk, with organic carbon fractions as high as 1.092%, remarkably retards organic contaminants. The K(OC) concept is not applicable to predicting distribution coefficients based on the organic carbon content in the chalk samples. Effective diffusivities of o-xylene, naphthalene, and several artificial tracers were determined using through-diffusion experiments. Based on measured diffusion coefficients and available literature values, a chalk specific exponent of 2.36 for Archie's law was derived, allowing a satisfactory estimate of relative diffusivities in chalk. A field-scale tracer test with uranine and lithium was performed in the Negev desert (Israel) to examine the transferability of diffusivities determined on small rock samples in the laboratory. Due to low recovery rates of the tracer, a modified single fissure dispersion model was used for inverse modeling of the breakthrough curves. Resulting diffusivities deviate insignificantly from the laboratory values, which are considered to be representative for the investigated part of the aquifer and applicable in transport models.     

A Tracer Test to Characterize Treatment of TCE in a Permeable Reactive Barrier

A tracer test was conducted to characterize the flow of groundwater across a permeable reactive barrier constructed with plant mulch (a biowall) at the OU‐1 site on Altus Air Force Base, Oklahoma. This biowall is intended to intercept and treat groundwater contaminated by trichloroethylene (TCE) in a shallow aquifer. The biowall is 139‐m long, 7.3‐m deep, and 0.5‐m wide. Bromide was injected from an upgradient well into the groundwater as a conservative tracer, and was subsequently observed breaking through in monitoring wells within and downgradient of the biowall. The bromide breakthrough data demonstrate that groundwater entering the biowall migrated across it, following the slope of the local groundwater surface. The average seepage velocity of groundwater was approximately 0.06 m/d. On the basis of the Darcy velocity of groundwater and geometry of the biowall, the average residence time of groundwater in the biowall was estimated at 10 d. Assuming all TCE removal occurred in the biowall, the reduction in TCE concentrations in groundwater across the biowall corresponds to a first‐order attenuation rate constant in the range of 0.38 to 0.15 per d. As an independent estimate of the degradation rate constant, STANMOD software was used to fit curves through data on the breakthrough of bromide and TCE in selected wells downgradient of the injection wells. Best fits to the data required a first‐order degradation rate constant for TCE removal in the range of 0.13 to 0.17 per d. The approach used in this study provides an objective evaluation of the remedial performance of the biowall that can provide a basis for design of other biowalls that are intended to remediate TCE‐contaminated groundwater.     

Rainfall infiltration‐derived submarine groundwater discharge from multi‐layered aquifer system terminating at the coastline

This article investigates the quantity of submarine groundwater discharge (SGD) from a coastal multi‐layered aquifer system in response to constant rainfall infiltration. The system comprises an unconfined aquifer, a leaky confined aquifer and an aquitard between them and terminates at the coastline. An approximate analytical solution is derived based on the following assumptions: (i) flow is horizontal in the aquifers and vertical in the aquitard, and (ii) flow in the unconfined aquifer is described by nonlinear Boussinesq equation. The analytical solution is compared with numerical solutions of the strictly two‐dimensional nonlinear model to validate the model assumptions used for the analytical solution. The SGD from the leaky confined aquifer increases with the inland rainfall infiltration recharge and the specific leakage of aquitard. The maximum SGD ranges from 1·87 to 10·37 m³ per day per meter of shoreline when rainfall infiltration ranges from 18·2 to 182 mm/year and the specific leakage of aquitard varies from 10^?9 to 10^?1 l/day. Copyright © 2011 John Wiley & Sons, Ltd.