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QC 20120522

It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction., QC 20100802

The multiple scales of landscape topography produces a wide distribution of groundwater circulation cells that control the hydro-geological environments surrounding geological repositories for nuclear waste. The largest circulation cells tend to discharge water into major river reaches, large freshwater systems or the nearby Sea. We investigated numerically the release of radionuclides from repositories placed in bedrock with depths between 100 to 2,000 meters in a Swedish coastal area and found that, leakage from the deeper positions emerges primarily in the major aquatic systems. In effect, radionuclides from the deeper repositories are more rapidly transported towards the Sea by the stream system compared to leakage from more shallow repositories. The release from the shallower repositories is significantly retained in the initial stage of the transport in the (superficial) landscape because the discharge occurs in or near low-order streams with high retention characteristics. This retention and residence time for radioactivity in the landscape control radiological doses to biota and can, thus, be expected to constitute an essential part of an associated risk evaluation., QC 20120224

Quaternary deposits and topography are two geological parameters which have a great impact on transport and retardation of radionuclides from a leaking repository of high level nuclear waste in crystalline bedrock. Due to the hydraulic and sorption properties of quaternary deposits, even thin layers significantly increase the residence time of leaking radionuclides. This study also shows that the flow paths predominantly discharge in low areas of the catchments where the layers of quaternary deposits often are relatively deep. The effect of topography is depending on the relationship between the local(kilometres) topography at the repository site and the large scale(hundreds of kilometres) topography surrounding the site area. The areas studied here, are located at discharge areas of deep groundwater flow, driven by large scale topography. Therefore residence times of radionuclides significantly decrease when large scale topography is accounted for. The impact of large scale topography is particularly clear in areas of flatter local topography., QC 20120302

To be able to carry out review functions regulatory authorities must be able to make critical evaluations of proponents PA cases. In Sweden the Swedish Radiation Protection Authority (SSI) aims to have in place its own suite of performance assessment (PA) tools. These will be used to address the forthcoming PAs submitted by the Swedish Nuclear Waste Management Company (SKB)for an encapsulation plant (2006) and a geological repository for spent fuel (2008). This paper looks at the role and application of the regulator's models to important features of current modelling in SKB's latest PAs. The SSI modelling tools are applied to a mire system in which radionuclides are assumed to be released from a geological repository. Results are presented which illustrate the importance of a deeper understanding of the geosphere-biosphere interface zone than has been the case in assessments to date., QC 20120214

Hydraulics of subsurface flow filters (SSF) was studied by measurement of soil hydraulic conductivity (K) variation and performing tracer tests in two SSF filters consisting of 1-4 mm Ca rich sand (shell sand). Soil samples were carefully taken at several locations in Filter I. A tracer experiment was conducted in the undisturbed Filter II using KI. The measured K variability in Filer I was used to analyze the variations in tracer breakthrough. The spatially distribution of K was obtained by fitting a variogram to observed data and interpolation using Kriging. The tracer residence probability density function (PDF) was determined by modelling the tracer movement with a 3-D groundwater model. The observed and simulated tracer arrival was compared for cases with constant K, constant K and dispersion (D), and for spatially variable K and dispersion. The results show that groundwater models were well suited to simulate solute movement in the SSF system studied. An almost perfect fit to observed tracer PDF was obtained when variable K and dispersion was included in the model. This indicates that information on K variability and dispersion is important for studying solute movement in SSF constructed wetlands., QC 20100525

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QCR 20161214

NQC

This paper analyzes the transport of sorbing solutes by extending the advective storage path model developed for longitudinal transport of inert solutes in streams coupled with flow-induced uptake in the hyporheic zone. Independent observations of a conservative (3H) and a reactive (51Cr) tracer in both the stream water and the hyporheic zone were used to differentiate between hydraulic and sorption processes. The method of temporal moments was found to be inadequate for parameter determination, whereas fitting versus the entire tracer breakthrough curves with special emphasis on the tail indicates that the proposed model could be used to represent both conservative and reactive transport. Information on the tracer inventory of the conservative tracer in the hyporheic zone was found to be of vital importance to the evaluation of the hydraulic exchange. A model evaluation based on stream water data alone can yield predictions of a wash-out in the hyporheic zone that deviates markedly from the observed wash-out. This prohibits long-term predictions of the wash-out from the hyporheic zone as well as the evaluation of sorption properties. The sorption in the hyporheic zone was found to follow a two-step model, where the first step is instantaneous and the second kinetic. A model with a single-step sorption process could not reproduce the observed breakthrough curves. An evaluation of the relative importance of including sorption kinetics in solute stream transport models is elucidated by means of the analytical expressions for the temporal moments. The omission of the kinetics in the second sorption step in the hyporheic zone will result in relative errors in the moments of second order or higher. The error will increase with decreasing residence time in the hyporheic zone. Especially, long-term predictions of the wash-out from the hyporheic zone require consideration of the rate-limited sorption.

An approach is described for hydrological, geochemical, and ecological process modeling in assessing the migration pathways of radionuclides from a repository for radioactive waste in crystalline bedrock back to the surface environment where dose to individual humans can occur. The approach is based on the characterization residence times in geologic media of a unit pulse of Cs-135 released from the repository. Performance assessment modeling of geosphere transport processes generally focuses on the properties of the host rock (crystalline bedrock in this case). Our approach includes a detailed representation of the quaternary deposits that overlie the bedrock. Although water residence times in quaternary deposits can be short, geochemical reactions, predominantly sorption, can increase solute residence times significantly. Moreover, the quaternary deposits govern the pathways to terrestrial and aquatic ecosystems and are of utmost importance for the assessment of doses to individual humans., QC 20100525

A theoretical description of reactive solute transport in a network of stream channels is derived by convoluting unit solutions based on a physical representation of transport and topographical information of the distributions of solute load as well as pathways. The theory is applied to a generic analysis of the phosphate export in Morsa watershed due to the load from 620 individual households with a local wastewater treatment. Essential factors for the phosphate export is filtering of the water in stream-bed sediments through a distribution of hyporheic flow paths of various lengths. This generic study indicates that a significant portion of phosphate is retained in the hyporheic zones for a long time. The 90% recovery time following a hypothetical remediation action in the households is expected to be in the order of one decade., QC 20120109

In this work, we compare solute transport and hyporheic exchange in vegetated and unvegetated reaches of Sava Brook, an agricultural stream in Sweden subject to extreme variations in channel vegetation and morphology due to both natural seasonal effects and anthropogenic manipulation. A solute injection experiment was conducted in September, 2001 (late summer), at which time there was extensive in-channel vegetation in upstream reaches but none in downstream reaches due to channel excavation by farmers. Experimental results are interpreted using both the advective storage path model and the transient storage model. Results from the vegetated and excavated reaches of the stream are compared both with each other and with the results of a previous experiment conducted in April, 1998 (early spring), when the stream was not excavated but there was only minimal vegetation present in the area due to natural seasonal effects. Results from the two injection experiments are compared by using scaled parameters that appropriately include the effects of stream velocity and depth on hyporheic exchange. This analysis indicates that the variation of solute storage time in all non-excavated agricultural reaches is attributable to differences in stream flow depth, velocity, and the hydraulic conductivity of the streambed sediments. Mixing in vegetated reaches is characterized by rapid exchange and considerable lag of the mean solute peak relative to the mean channel velocity. In addition, excavation altered the stream channel geometry so as to increase the storage time of solutes and reduce the effective exchange rate. This work indicates the need to consider the effect of specific processes when analyzing hyporheic exchange using tracer-injection methods, and supports the use of model frameworks with the potential to explicitly include different formulations for various hyporheic and dead zone transport processes., QC 20100525

A transient storage model is evaluated using results from a tracer experiment, where a conservative and a reactive tracer (H-3 and Cr-51(III)) were injected simultaneously and monitored in stream water and bed sediment. About 76% of the chromium was lost from the stream water on the reach 30 km downstream of the injection point directly after the passage of the pulse in the flowing water. The bed sediment hosted the main part of the retained chromium. The time to washout 75% of the maximum solute uptake in the sediment was similar to 85 times longer for chromium than for tritium (i.e. similar to 45 days). It was possible to describe the sediment-water exchange with a diffusive flux formulation that could be evaluated using tritium breakthrough curves in the stream water or the tritium inventory breakthrough curves in the sediment. This experiment revealed further that observations of chromium concentrations in the sediment were essential for the quantifying of sorption properties, as it was not possible to catch accurately the time scale of sorption within the duration of the breakthrough curves in the stream water. There was a clear need for a rate-limited description of the sorption of chromium in the sediment. We found that a first-order kinetic description of the sorption process could acceptably describe the breakthrough curves in both the stream water and the bed sediment., QC 20100525

[1] Temporary storage of solutes in streams is often controlled by flow-induced uptake in hyporheic zones. This phenomenon accounts for the tails that are generally observed following the passage of a solute pulse, and such exchange is particularly important for the transport of reactive substances that can be subject to various biogeochemical processes in the subsurface. Advective pumping, induced by streamflow over an irregular permeable bed, leads to a distribution of pore water flow paths in the streambed and a corresponding distribution of subsurface solute residence times. This paper describes a modeling framework that couples longitudinal solute transport in streams with solute advection along a continuous distribution of hyporheic flow paths. Moment methods are used to calculate the shape of solute breakthrough curves in the stream based on various representations of hypotheic exchange, including both advective pumping and several idealized formulations. Basic hydrodynamic principles are used to derive the distribution of solute residence times due to pumping. The model provides an accurate representation of the breakthrough curves of tritium along a 30 km reach of Sava Brook in Uppland County in Sweden. Both hydrodynamic theory for pumping exchange and pore water samples obtained from the bed during the tracer experiment suggest that the residence time for solutes in the hyporheic zone is characterized by a log normal probability density function. Closed-form solutions of the central temporal moments of solute breakthrough curves in the stream reveal a significant similarity between this new model and existing models of hyporheic exchange, including the Transient Storage Model. The new model is advantageous because its fundamentally derived exchange parameters can be expressed as functions of basic hydrodynamic quantities, which allows the model results to be generalized to conditions beyond those directly observed during tracer experiments. The utility of, QC 20100525

To provide an appropriate description of the transport of a reactive substance in a stream, it is important to include a kinetic description of sorption in a transport model. In this study, first-order sorption kinetics was taken into account in both the transient storage zone and the stream water, and analytical expressions for relative error in statistical moments of the residence time PDF, resulting from disregarding sorption kinetics, were derived. The sorption rate coefficient in the water was found to influence the error in the expected value, and the error was found to approach infinity as the travel distance or sorption rate coefficient approaches zero. The sorption rate coefficient in the storage zone influences only higher-order moments. For sufficiently long distances, the error in the variance was found to be more pronounced when sorption kinetics in the storage zone was disregarded, than when sorption kinetics in the stream water was disregarded. Parameter values from a tracer experiment with 51Cr revealed that the relative error in the variance could be more than 100%, if sorption kinetics in the storage zone is disregarded.

The effective transport velocity of solutes in rivers and streams is governed by transient storage in hyporheic zones in which the longitudinal advection velocity is small relative to the main stream flow velocity. Results from a simultaneous tracer experiment using a non-reactive (tritium, 3H2O) and a sorptive tracer [chromium, 51Cr(III)] have formed the basis of a more accurate interpretation of the retention characteristics of solutes in streams than previously has been possible. By using a simultaneous injection of these two tracers, it was possible to distinguish between their different behaviours. Based on estimations of fluxes, the retained mass of chromium in the storage zones along the 30-km-long study-reach was 76% after 150 h. Independent observations in the bed sediment indicated that the loss of chromium observed in the water was mainly a result of uptake into the bed sediment. To describe the transport in the stream, a model concept including solute sorption kinetics in the bed sediment was proposed. Evaluation of parameters in the model, indicated that the uptake of chromium in the bed sediment is controlled by sorption kinetics.

As a basis for an analysis of the effect of rock heterogeneity on radionuclide migration in a single fracture, the geostatistics of the main properties governing solute transport in crystalline rock have been determined experimentally for two granitic rock types. The rock samples were collected at the Aspo Hard Rock Laboratory, Sweden and used to deduce the auto-covariance functions for the porosity, effective diffusivity and partition coefficient, k(d). and adsorption kinetics. One-dimensional analytical solutions for the mean values of the temporal moments of the residence time probability density function (PDF) show that the heterogeneity of the rock properties can have a substantial impact on the transport, A case study of the effect of heterogeneity in matrix diffusion for a single fracture could be performed by decomposing the transport problem into a one-dimensional mass transfer problem and a two-dimensional flow problem using a Lagrangian method of description. Monte Carlo simulations of the flow field indicate that the correlation length of the aperture is much longer along the trajectory paths than along an arbitrary direction. Increasing the correlation lengths and variances of the aperture and matrix diffusion increases significantly the variance of the travel time PDF., QC 20100525

A new modeling framework for internal erosion in heterogeneous stratified soils is developed by combining existing methods used to study sediment transport in canals, filtration phenomena, and stochastic processes. The framework is used to study the erosion process in sediments caused by a flow of water through a covering filter layer that deviates from geometrical filter rules. By the use of spectral analysis and Laplace transforms, mean value solutions to the transport rate and the variance about the mean are derived for a transport constraint at the upstream boundary and a constant initial transport. Increasing the heterogeneity of a defective filter layer in a canal retards the propagation of the expected bed degradation. An implication is that the heterogeneity of the riprap, in this respect prolongs the expected degradation process and the expected lifespan of the structure. The increased variance and decreased correlation length of the riprap reduces the confidence of the mean value solution. The stochastic analysis is therefore suitable as part of risk analyses of extreme events such as failure of embankment dams, for which empirical observations are rare., QC 20100525

Biogeochemical mechanisms in rivers and streams give rise to a transient storage of solute substances in hyporheic zones and hence retard the solute transport. Analytical solutions to the temporal moments of the residence times are used as the basis to compare three different transient storage models with respect to deviation in higher-order moments, model bias, and relationships between the parameters of the different models. The transient storage was formulated using either first-order mass transfer equations or a one-dimensional diffusion process in which the storage capacity of the storage zone is limited by an impermeable surface or groundwater seepage into the stream. In all three cases the mean residence time due to a solute pulse (Dirac type) at the upstream boundary increases linearly with the size ratio of the storage zone and the stream. The three models provide an identical representation up to the first three temporal moments, which implies that at least four moments must be taken into account to distinguish between the physical biases of the models and to estimate the deviation in model characteristics. By evaluating the results from three tracer experiments, limits of acceptable model bias could be estimated. Evaluation of the tracer experiments also indicated that the temporal moments can function as indicators of underlying physics. Groundwater infiltration may significantly decrease the skewness of the residence times., QC 20100525

The transport and retention of a sorbing solute in streams are affected by the transversal uptake in various hyporheic zones, each characterized by its individual turnover time. The uptake is included in a one-dimensional model for the along-stream transport on the form of first-order transfer functions by parameterizing physically derived relationships. A 51Cr(III) tracer experiment, conducted in a brook in an agricultural watershed in Sweden, provided a basis for deducing constitutive equations for three different exchange rates governing the retention of the sorbing solute in the brook. The solute exchange that occurs between the main stream channel and slowly recirculating zones, like side pockets along the stream, eddy zones behind boulders, or side pockets, is practically instantaneous and is manifested as a marked retardation of the pulse propagation in relation to the main stream velocity. The considerably slower exchange with permanent substratum, including armored bed sections, dense vegetation, or adjacent wetland, causes a reduction of the peak concentration and prolonged tails of the breakthroughs. Uptake in the alluvial sediment occurs both in particulate and dissolved phases of the solute, and is affected by the bed dynamics. The uptake in the alluvium was evaluated separately by fitting of an analytical solution of the vertical concentration profile to measured concentration profiles in the sediment. In the experimentally investigated reach, the exchange with the fine bed sediment was dominated by the dissolved phase of Cr, due to advection driven by pressure variabilities along the bed surface.

A number of biogeochemicarle actionsa nd lateral hydrodynamicm ixing affectsthe transport of solute elements in streams and rivers. The combination of the variousmechanismsg ivesr ise to an accumulationo f the solute in temporary storagez ones and aretardation of solute migration. A new model framework is proposed from which ananalyticals olutioni s derivedd escribingth e concentrationa s a function of distancea longthe stream, depth into storage zones, and time. The model includes the effects of sorptionof solutest o suspendeds olidsa nd bed sediments,a lateral exchangew ith the storagezones, first-order reactions, and dilution. The migration velocity is close to the advectionvelocityo f the streamf or a short travel distance,b ut it continuouslyd ecreasesa s thedistancei ncreasesT. he timescaleo f the processi s linearly related to a modifiedDamk6hler number; a dimensionlessfo rm of the lateral exchangec oefficient.T heanalyticals olutionh as been verified for two tracer experimentsw ith both a sorbinga nd anonreactive tracer and the Cr transport in the Vistula River, Poland. The lateral diffusioncoefficient can be tentatively evaluated from the transport of Chernobyl Cs in severalEuropeanri versa sa speciacl aseo f the interpretativme odel.T he lateralm ixingc oefficientvariesw iths treamc onditionins t heo rdero f 0.1 x 10- 6 < Ds < 10 x 10- 6 (mZ/s).