Analysis of a vertical dipole tracer test in highly fractured rock

The results of a vertical dipole tracer experiment performed in highly fractured rocks of the Clare Valley, South Australia, are presented. The injection and withdrawal piezometers were both screened over 3 m and were separated by 6 m (midpoint to midpoint). Due to the long screen length, several fracture sets were intersected, some of which do not connect the two piezometers. Dissolved helium and bromide were injected into the dipole flow field for 75 minutes, followed by an additional 510 minutes of flushing. The breakthrough of helium was retarded relative to bromide, as was expected due to the greater aqueous diffusion coefficient of helium. Also, only -25% of the total mass injected of both tracers was recovered. Modeling of the tracer transport was accomplished using an analytical one-dimensional flow and transport model for flow through a fracture with diffusion into the matrix. The assumptions made include: streamlines connecting the injection and withdrawal point can be modeled as a dipole of equal strength, flow along each streamline is one dimensional, and there is a constant Peclet number for each streamline. In contrast to many other field tracer studies performed in fractured rock, the actual travel length between piezometers was not known. Modeling was accomplished by fitting the characteristics of the tracer breakthrough curves (BTCs), such as arrival times of the peak concentration and the center of mass. The important steps were to determine the fracture aperture (240 microm) based on the parameters that influence the rate of matrix diffusion (this controls the arrival time of the peak concentration); estimating the travel distance (11 m) by fitting the time of arrival of the centers of mass of the tracers; and estimating fracture dispersivity (0.5 m) by fitting the times that the inflection points occurred on the front and back limbs of the BTCs. This method works even though there was dilution in the withdrawal well, the amount of which can be estimated by determining the value that the modeled concentrations need to be reduced to fit the data (approximately 50%). The use of two tracers with different diffusion coefficients was not necessary, but it provides important checks in the modeling process because the apparent retardation between the two tracers is evidence of matrix diffusion and the BTCs of both tracers need to be accurately modeled by the best fit parameters.     

Density contrast effects on tracer dispersion in variable aperture fractures

We investigate the development of preferential flow paths and anomalous dispersion resulting from weak density contrasts in the course of tracer experiments in a tortuous natural fracture. The processes are first documented by the non-invasive measurement of the fracture aperture and of the time-resolved distribution of the tracer using Positron Emission Projection Imaging. Then, numerical simulations of the three-dimensional tracer transport in the fracture are performed to explore the parameters that control the development and the persistence of the tracer localization, as a function of the density contrast between the tracer and the resident solution. Results reveal that density contrasts representative of what could be expected in borehole and laboratory tracer tests can induce irreversible localization along preferential channels. As density contrast increases, the correlation between velocity and aperture distributions vanishes whereas (i) velocity field increasingly correlates with the fracture median plan elevation and (ii) the longitudinal dispersion coefficient increases. The anomalous velocity distribution may persist well after the injection stops due to the occurrence of tracer trapped zone.     

Energetics of gas-driven limnic and volcanic eruptions

This paper lays the foundation for the rigorous treatment of the energetics of gas exsolution from a gas-containing liquid, which powers gas-driven volcanic and limnic eruptions. Various exsolution processes (reversible or irreversible, slow or rapid) are discussed, and the maximum amount of kinetic energy derivable from a reversible gas exsolution process is obtained. The concept of dynamic irreversibility is proposed for discussing the kinetic energy available from irreversible gas exsolution processes. The changes of thermodynamic properties during gas exsolution processes are derived. Density–pressure relations for gas–liquid mixtures are presented, including empirical relations for irreversible gas exsolution. The energetics of gas-driven eruptions through both fluid and rigid media, including the role of buoyancy and the role of magma chamber expansion work, are investigated. For reversible processes, the energetics can be used to discuss the dynamics of gas-driven eruptions, leading to maximum erupting velocities and maximum eruptible fractions. For irreversible processes, empirical relations and parameters must be employed. The exit velocities of the Lake Nyos eruption and the 18 May 1980 eruption of Mount St. Helens are modeled by incorporating possible irreversibility.     

Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state

Under steady-state conditions, the degradation of contaminant plumes introduced continuously into an aquifer is controlled by transverse dispersion when the other reacting compound is provided from ambient groundwater. Given that the reaction is instantaneous and longitudinal dispersion can be neglected, the length of the plume is inversely proportional to the transverse dispersion coefficient. In typical scenarios of natural attenuation, however, the considered reaction is biotic and kinetic. The standard model of bioreactive transport relies on double-Monod kinetics and pseudo first-order biomass decay. Under these conditions, a fraction of the injected mass flux remains beyond the length of the plume determined for the instantaneous reaction. We present an analytical framework to derive the steady-state concentration distributions of the dissolved compounds and the biomass from the concentration distribution of a conservative compound, assuming double-Monod kinetics and two different models describing biomass decay. The first biomass-decay model assumes a constant first-order decay coefficient, while the second assumes that the decay coefficient depends upon the electron-acceptor concentration. We apply the method to the case of a line-injection in two-dimensional uniform flow. In general, the bioreactive concentration distributions are similar to the distributions computed for an instantaneous reaction. The similarity is greater when the biomass decay coefficient is assumed to depend on the electron-acceptor concentration rather than being constant.     

Investigating peat hydrological properties using field and laboratory methods: application to the Lanoraie peatland complex (southern Quebec,Canada)

Flow dynamics within a peatland are governed by hydraulic parameters such as hydraulic conductivity, dispersivity and specific yield, as well as by anisotropy and heterogeneity. The aim of this study is to investigate hydraulic parameters variability in peat through the use of different field and laboratory methods. An experimental site located in the Lanoraie peatland complex (southern Quebec, Canada) was used to test the different approaches. Slug and bail tests were performed in piezometer standpipes to investigate catotelm hydraulic conductivity. Combined Darcy tests and tracer experiments were conducted on cubic samples using the modified cube method (MCM) to assess catotelm hydraulic conductivity, anisotropy and dispersivity. A new laboratory method is proposed for assessing acrotelm hydraulic conductivity and gravity drainage using a laboratory experimental tank. Most of slug tests' recovery curves were characteristic of compressible media, and important variability was observed depending on the initial head difference. The Darcy experiments on cubic samples provided reproducible results, and anisotropy (K_h > K_v) was observed for most of samples. All tracer experiments displayed asymmetrical breakthrough curves, suggesting the presence of retardation and/or dual porosity. Hydraulic conductivity estimates performed using the experimental tank showed K variations over a factor of 44 within the upper 40 cm of the acrotelm. The results demonstrate that the intrinsic variability associated with the different field and laboratory methods is small compared with the spatial variability of hydraulic parameters. It is suggested that a comprehensive assessment of peat hydrological properties can be obtained through the combined use of complementary field and laboratory investigations. Copyright © 2007 John Wiley & Sons, Ltd.     

Mathematical modeling and practical verification of groundwater and contaminant transport in a chosen natural aquifer

The paper addresses the 2D mathematical equation of conservative contaminant transport in an aquifer for chosen contaminants. The contaminants (chlorides and sulfates) are subject to instantaneous reversible part of sorption process. The term of instantaneous reversible sorption in the presented equation has been described by the non-linear Freundlich adsorption isotherm, widely applied in practice in relation to static processes (for local equilibrium). The numerical solution (using the finite difference method) has been based on the previously calculated values of longitudinal and transverse dispersion coefficients and the non-linear adsorption parameters for the chosen contaminants. Based on this model, the values of chloride and sulfate concentration isolines have been calculated and compared with the measured maximal concentrations in the chosen natural aquifer (installed piezometers). Additionally, the values of chloride concentrations have been calculated taking into account the influence of radioactive decay term, using the numerical value of the firstorder decay rate constant for an adopted theoretical radionuclide.     

Herbicide contamination and the potential impact to seagrass meadows in Hervey Bay, Queensland, Australia

Low concentrations of herbicides (up to 70 ng l(-1)), chiefly diuron (up to 50 ng l(-1)) were detected in surface waters associated with inter-tidal seagrass meadows of Zostera muelleri in Hervey Bay, south-east Queensland, Australia. Diuron and atrazine (up to 1.1 ng g(-1) dry weight of sediment) were detected in the sediments of these seagrass meadows. Concentration of the herbicides diuron, simazine and atrazine increased in surface waters associated with seagrass meadows during moderate river flow events indicating herbicides were washed from the catchment to the marine environment. Maximum herbicide concentration (sum of eight herbicides) in the Mary River during a moderate river flow event was 4260 ng l(-1). No photosynthetic stress was detected in seagrass in this study during low river flow. However, with moderate river flow events, nearshore seagrasses are at risk of being exposed to concentrations of herbicides that are known to inhibit photosynthesis.     

EXPERIMENTAL STUDY ON EQUILIBRIUM CONCENTRATION OF DEBRIS FLOWS

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A comparative modeling study of a dual tracer experiment in a large lysimeter under atmospheric conditions

In this paper, five model approaches with different physical and mathematical concepts varying in their model complexity and requirements were applied to identify the transport processes in the unsaturated zone. The applicability of these model approaches were compared and evaluated investigating two tracer breakthrough curves (bromide, deuterium) in a cropped, free-draining lysimeter experiment under natural atmospheric boundary conditions. The data set consisted of time series of water balance, depth resolved water contents, pressure heads and resident concentrations measured during 800 days. The tracer transport parameters were determined using a simple stochastic (stream tube model), three lumped parameter (constant water content model, multi-flow dispersion model, variable flow dispersion model) and a transient model approach. All of them were able to fit the tracer breakthrough curves. The identified transport parameters of each model approach were compared. Despite the differing physical and mathematical concepts the resulting parameters (mean water contents, mean water flux, dispersivities) of the five model approaches were all in the same range. The results indicate that the flow processes are also describable assuming steady state conditions. Homogeneous matrix flow is dominant and a small pore volume with enhanced flow velocities near saturation was identified with variable saturation flow and transport approach. The multi-flow dispersion model also identified preferential flow and additionally suggested a third less mobile flow component. Due to high fitting accuracy and parameter similarity all model approaches indicated reliable results.     

Characterization of a multilayer aquifer using open well dilution tests

An approach to characterization of multilayer aquifer systems using open well borehole dilution is described. The approach involves measuring observation well flow velocities while a nearby extraction well is pumped by introducing a saline tracer into observation wells and collecting dilution vs. depth profiles. Inspection of tracer profile evolution allows discrete permeable layers within the aquifer to be identified. Dilution profiles for well sections between permeable layers are then converted into vertical borehole flow velocities and their evolution, using an analytic solution to the advection-dispersion equation applied to borehole flow. The dilution approach is potentially able to measure much smaller flow velocities that would be detectable using flowmeters. Vertical flow velocity data from the observation wells are then matched to those generated using a hydraulic model of the aquifer system, "shorted" by the observation wells, to yield the hydraulic properties of the constituent layers. Observation well flow monitoring of pumping tests represents a cost-effective alternative or preliminary approach to pump testing each layer of a multilayer aquifer system separately using straddle packers or screened wells and requires no prior knowledge of permeable layer depths and thicknesses. The modification described here, of using tracer dilution rather than flowmeter logging to obtain well flow velocities, allows the approach to be extended to greater well separations, thus characterizing a larger volume of the aquifer. An example of the application of this approach to a multilayer Chalk Aquifer in Yorkshire, Northeast England, is presented.     

Tracer Method to Determine Residence Time in a Permeable Reactive Barrier

A method is presented to evaluate ground water residence time in a zero‐valent iron (ZVI) permeable reactive barrier (PRB) using radon‐222 (²²²Rn) as a radioactive tracer. Residence time is a useful indicator of PRB hydraulic performance, with application to estimating the volumetric rate of ground water flow through a PRB, identifying flow heterogeneity, and characterizing flow conditions over time as a PRB matures. The tracer method relies on monitoring the decay of naturally occurring aqueous ²²²Rn as ground water flows through a PRB. Application of the method at a PRB site near Monticello, Utah, shows that after 8 years of operation, residence times in the ZVI range from 80 to 486 h and correlate well with chemical parameters (pH, Ca, SO₄, and Fe) that indicate the relative residence time. Residence times in this case study are determined directly from the first‐order decay equation because we show no significant emanation of ²²²Rn within the PRB and no measurable loss of ²²²Rn other than by radioactive decay.     

Exponential data fitting applied to infiltration, hydrograph separation, and variogram fitting

Most lumped rainfall-runoff models separate the interflow and groundwater components from the measured runoff hydrograph in an attempt to model these as hydrologic reservoir units. Similarly, rainfall losses due to infiltration as well as other abstractions are separated from the measured rainfall hyetograph, which are then used as inputs to the various hydrologic reservoir units. This data pre-processing is necessary in order to use the linear unit hydrograph theory, as well as for maintaining a hydrologic budget between the surface and subsurface flow processes. Since infiltration determines the shape of the runoff hydrograph, it must be estimated as accurately as possible. When measured infiltration data is available, Horton’s exponential infiltration model is preferable due to its simplicity. However, estimating the parameters from Horton’s model constitutes a nonlinear least squares fitting problem. Hence, an iterative procedure that requires initialization is subject to convergence. In a similar context, the separation of direct runoff, interflow, and baseflow from the total hydrograph is typically done in an ad hoc manner. However, many practitioners use exponential models in a rather “layer peeling” fashion to perform this separation. In essence, this also constitutes an exponential data fitting problem. Likewise, certain variogram functions can be fitted using exponential data fitting techniques. In this paper we show that fitting a Hortonian model to experimental data, as well as performing hydrograph separation, and total hydrograph and variogram fitting can all be formulated as a system identification problem using Hankel-based realization algorithms. The main advantage is that the parameters can be estimated in a noniterative fashion, using robust numerical linear algebra techniques. As such, the system identification algorithms overcome the problem of convergence inherent in iterative techniques. In addition, the algorithms are robust to noise in the data since they optimally separate the signal and noise subspaces from the observed noisy data. The algorithms are tested with real data from field experiments performed in Surinam, as well as with real hydrograph data from a watershed in Louisiana. The system identification techniques presented herein can also be used with any other type of exponential data such as exponential decays from nuclear experiments, tracer studies, and compartmental analysis studies.     

Numerical analysis of bacterial transport in saturated porous media

A mathematical model to describe bacterial transport in saturated porous media is presented. Reversible/irreversible attachment and growth/decay terms were incorporated into the transport model. Additionally, the changes of porosity and permeability due to bacterial deposition and/or growth were accounted for in the model. The predictive model was used to fit the column experimental data from the literature, and the fitting result showed a good match with the data. Based on the parameter values determined from the literature experimental data, numerical experiments were performed to examine bacterial sorption and/or growth during bacterial transport through saturated porous media. In addition, sensitivity analysis was performed to investigate the impact of key model parameters for bacterial transport on the permeability and porosity of porous media. The model results show that the permeability and porosity of porous media could be altered due to bacterial deposition and growth on the solid matrix. However, variation of permeability due to bacterial growth was trivial compared with natural permeability variation. Copyright © 2005 John Wiley & Sons, Ltd.     

Deriving formulas for an unsteady virtual velocity of bedload tracers

In a flume experiment with steady flow conditions, H. A. Einstein recognised the transport of bedload particles as consisting of steps of rolling, sliding, or saltation with intermittent rest periods, and introduced the concept of an average, ‘virtual’ transport velocity. This virtual velocity then has also been derived from tracer studies in the field by dividing the travelled distance of a tracer by the duration of competent flow. As a consequence, the virtual velocity in the field is represented by one single value only, despite the unsteady flow variables. Tracer measurements in a river have not been yet used to express transport velocity as a direct function of these actual variables, and insights from tracer measurements into the processes of sediment transport remain limited. In particular, the unsteady conditions for bedload in the field have impeded the derivation of sediment transport characteristics as determined from laboratory experiments, as well as the transfer of laboratory insights to a field setting. We introduce a method of data regression for the derivation of an ‘unsteady’ virtual velocity from repeated surveys of tracer positions. The regression program called graVel (provided as supplementary material) relates the integral of an excess flow variable term to measured travel distances, yielding the most probable threshold value for entrainment and the coefficient of linear and non‐linear formulas. An extended regression allows additional fitting of the exponent in non‐linear formulas. Application to published tracer data from the Mameyes River, Puerto Rico, shows that the unsteady virtual velocity is more likely governed by non‐linear relations to excess Shields stress, similar to bedload transport, than by relations linking the particle velocity linearly to excess shear velocity. Partial agreements with non‐dimensional results derived from the larger, non‐wadeable Mur River encourage the establishment of a generalised formula for the unsteady virtual velocity. Copyright © 2017 John Wiley & Sons, Ltd.     

Unsaturated Zone Flow Processes and Aquifer Response Time in the Chalk Aquifer,Brighton, South East England

The Chalk aquifer is one of the main sources of water in South East England. The unsaturated zone in the aquifer plays an important role controlling the time and magnitude of recharge and is major pathway for contaminant transport to the water table. A range of previous work has addressed flow processes in the Chalk unsaturated zone, but physical understanding is still incomplete. Here we present the results of a study on flow mechanism in the Chalk unsaturated zone using a combination of statistical analysis and novel laboratory methods. The study was undertaken at three sites (North Heath Barn [NHB], Pyecombe East [PE], and Preston Park [PP]) on the Chalk of the Brighton block, South East England. Daily and hourly time series data of groundwater level and rainfall were correlated. The results show that a slower groundwater level response to rainfall occurs during dry seasons (summer and autumn) when the amount of effective rainfall is less than 4 mm/day, with a thicker and drier unsaturated zone. A faster response occurs during wet seasons (winter and spring) when the daily effective rainfall exceeds 4 mm/day with a thinner and wetter unsaturated zone. Periods of very rapid response (within 15 h) were observed during wet seasons at NHB and PE sites, with unsaturated hydraulic conductivity (K_u) inferred to reach 839 mm/day. A slower response was observed at an urbanized site (PP) as a result of reduction in direct recharge due to reduced infiltration, due to presences of impermeable infrastructure covering the area around PP borehole. Laboratory measurements of K_u of the Chalk matrix using a geotechnical centrifuge show variation from 4.27 to 0.07 mm/day, according to the level of saturation. Thus, the rapid responses cannot be linked to matrix flow only but indicate the contribution of fracture and karstic flow processes in conducting water.     

Response to the slug injection of a tracer—a large-scale experiment in a natural river / Réponse à l'injection impulsionnelle d'un traceur—expérience à grande échelle en rivière naturelle

Abstract

A unique, large-scale tracer test performed along a 90-km reach of a natural river is presented. This method was crucial for evaluating the impact of a retention reservoir on protected areas of the river downstream, and to assess the threats due to potentially catastrophic releases of toxic substances into that river. The response to the slug injection of a soluble tracer is assumed to imitate the characteristics of a soluble pollutant, so an understanding of how tracers mix and disperse in a stream is essential to understanding the processes of pollution transport. The procedure applied during this experiment consisted of the instantaneous injection of a known quantity of Rhodamine WT into the stream and the determination of the temporal variation in concentration of the tracer at sites as it moved downstream. The results were analysed from the perspective of a transient storage model. Relevant model parameters were evaluated by fitting the computed breakthrough curves to the observed ones on a reach-by-reach basis.     

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.     

Escherichia coli strains harvested from springs in Kampala,Uganda: cell characterization and transport in saturated porous media

We hypothesized that the transport of Escherichia coli strains harvested from springs could be characterized by a similar set of cell characteristics and transport parameters. The hypothesis was tested by sampling springs throughout the Lubigi catchment in Kampala, Uganda. Chemo‐physical parameters in addition to total coliform concentrations were determined. Furthermore, E. coli strains were harvested, and cell properties determined. Column experiments in saturated quartz columns of 7 cm height were conducted to determine transport parameters of selected E. coli strains. Using a two‐site non‐equilibrium sorption model, transport was modelled by fitting breakthrough data in HYDRUS 1D. Results indicated faecal contamination of the springs with high concentrations of total coliforms, chloride and nitrate. Furthermore, the maximum relative E. coli concentrations (C/C₀)_max in the column experiments were high. Compared with our previous work on E. coli strains, collected from a pasture and from zoo animals, attachment was low. Modelling revealed that both equilibrium and kinetic sorption were not important under conditions employed in the experiments. These observations are explained by the way in which the strains were harvested: from termination points of flow lines (springs). Such strains may possess characteristics that might have influenced their transport in the subsurface leading to their low attachment efficiency and possibly contributing to the lack of influence of equilibrium and kinetic sorption characteristics. There was no significant correlation between cell properties and transport parameters. Furthermore, 58% of the tested strains were of the O21:H7 serotype, and all definable serotypes identified were associated with diseases. We speculate that this serotype may possess characteristics that allow preferential transport through the aquifers of the area. We demonstrated that bacteria harvested from termination points of flow lines compared with those obtained from pollution sources, which have not undergone transport yet, present a good option for the assessment of bacteria transport characteristics in aquifers. Copyright © 2013 John Wiley & Sons, Ltd.     

Relationships between hydraulic parameters in a small stream under varying flow and seasonal conditions

Twenty conservative tracer injections were carried out in the same reach of a small woodland stream in order to determine how variation in discharge and leaf accumulation affect stream hydraulic parameters. The injections were made at various discharge rates ranging from 2·6 to 40 l/s. Five of the injections were made during late autumn, when there were large accumulations of leaves in the stream. Estimates of hydraulic parameters were made by fitting a transient storage solute transport model to conservative tracer concentration profiles. Velocity increased almost linearly with increasing discharge, indicating a decline in the Darcy friction factor. Dispersion also increased with increasing discharge, especially for the lower flow injections. The relative size of the storage zone was small (∽0·1). There was no definable relationship between discharge and the relative storage zone size, but the rates of exchange between the storage zone and the main channel increased markedly with increasing discharge. The presence of large accumulations of leaves had a clear effect on the hydraulic characteristics of the stream, producing much higher friction factors, larger storage zone sizes and lower velocity than would have been predicted by discharge alone. Copyright © 1999 John Wiley & Sons, Ltd.     

BIOB: A mathematical model for the biodegradation of low solubility hydrocarbons

Modeling oil biodegradation is an important step in predicting the long term fate of oil on beaches. Unfortunately, existing models do not account mechanistically for environmental factors, such as pore water nutrient concentration, affecting oil biodegradation, rather in an empirical way. We present herein a numerical model, BIOB, to simulate the biodegradation of insoluble attached hydrocarbon. The model was used to simulate an experimental oil spill on a sand beach. The biodegradation kinetic parameters were estimated by fitting the model to the experimental data of alkanes and aromatics. It was found that parameter values are comparable to their counterparts for the biodegradation of dissolved organic matter. The biodegradation of aromatics was highly affected by the decay of aromatic biomass, probably due to its low growth rate. Numerical simulations revealed that the biodegradation rate increases by 3–4 folds when the nutrient concentration is increased from 0.2 to 2.0 mg N/L.