Anders Wörman

Effect of flow-induced exchange in hyporheic zones on longitudinal transport of solutes in streams and rivers

[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 o ...

Exact three‐dimensional spectral solution to surface‐groundwater interactions with arbitrary surface topography

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. Her ...

Analytical solution and timescale for transport of reacting solutes in rivers and streams

A number of biogeochemical reactions and lateral hydrodynamic mixing affects the transport of solute elements in streams and rivers. The combination of the various mechanisms gives rise to an accumulation of the solute in temporary storage zones and a retardation of solute migration. A new model framework is proposed from which an analytical solution is derived describing the concentration as a function of distance along the stream, depth into storage zones, and time. The model includes the effects of sorption of solutes to suspended solids and bed sediments, a lateral exchange with the storage zones, first-order reactions, and dilution. The migration velocity is close to the advection velocity of the stream for a short travel distance, but it continuously decreases as the distance increases. The timescale of the process is linearly related to a modified Damkohler number; a dimensionless form of the lateral exchange coefficient. The analytical solution has been verified for two tracer experiments with both a sorbing and a nonreactive tracer and the Cr transport in the Vistula River, Poland. The lateral diffusion coefficient can be tentatively evaluated from the transport of Chernobyl Cs in several European rivers as a special case of the interpretative model. The lateral mixing coefficient varies with stream conditions in the order of 0.1 × 10−6 < Ds < 10 × 10−6 (m2/s).

Hyporheic exchange of reactive and conservative solutes in streams—tracer methodology and model interpretation

A transient storage model is evaluated using results from a tracer experiment, where a conservative and a reactive tracer ( 3 H and 51 Cr(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 ,85 times longer for chromium than for tritium (i.e. , 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. q 2003 Elsevier Science B.V. All rights reserved.

Retention of conservative and sorptive solutes in streams - simultaneous tracer experiments

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.

Heterogeneous matrix diffusion in crystalline rock — implications for geosphere retardation of migrating radionuclides

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 Aspö Hard Rock Laboratory, Sweden and used to deduce the auto-covariance functions for the porosity, effective diffusivity and partition coefficient, kd, 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.

Effect of Sorption Kinetics on the Transport of Solutes in Streams

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.

Influence of Hyporheic Exchange on Solute Transport in a Highly Hydropower-Regulated River

Understanding of the processes affecting solute transport in flowing water is important for the possibility to predict the evolution with time of polluted stream systems. This thesis presents tracer experiment methodology and model developments for solute transport in streams, with special focus on retention processes and their effect on solute stream transport. Results are presented from a tracer experiment in the Sava Stream, Uppland County, Sweden, where both a conservative (3H as tritiated water) and a reactive (51Cr as trivalent chromium ion) tracer were injected simultaneously. The time and length scales of the experiment were prolonged compared to previous studies, which allowed for new critical tests of different model concepts. It was found that the hyporheic exchange greatly affected the solute transport of both tracers. However, the retention of chromium was significantly more pronounced. About 76% of the injected chromium was lost from the stream water phase directly after the passage of the pulse 30 km downstream of the injection point. The inventory of chromium in the sediments indicated that the main part was retrieved in the hyporheic zone. Both a diffusive and an advective hyporheic exchange model were developed and evaluated versus independent observations in the stream water and hyporheic zone. Analytical expressions for the central temporal moments of the breakthrough curve and semi-analytical solutions for the solute concentration in the Laplace domain were derived. Both models were found useful in representing the observations.For the transport of the reactive solute, it was found essential to consider a kinetic sorption on to particulate matter in the hyporheic zone. The time needed for a wash-out of 75% of the maximum uptake in the hyporheic zone was found to be ~85 times longer for the reactive solute, compared to the conservative solute. Neglecting the sorption kinetics in the transport model yielded significant errors in the central temporal moments, which implied an incorrect description of the wash-out process from the hyporheic zone. Independent observations in the stream water and hyporheic zone as well as choice of evaluation method are essential for a correct interpretation of the processes.A first attempt was also made to link model parameters such as the residence time in the hyporheic zone with measurable parameters of the stream. Such a relationship offers the possibility to generalize results for other streams and stream conditions. A generic study of the transport of an inert solute in the Lule River, Sweden, using this kind of relationship, indicated that the hyporheic exchange can have a large practical implication.

A Study of K Variability and Its Effect on Solute Transport in Subsurface-Flow Sand Filters by Measurement and Modelling

Abstract 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.

Analysis of Radionuclide Migration in Rock Fractures with Heterogeneous Matrix Diffusion

Two transport models for radionuclide migration in rock fractures, one with an infinite and one with a limited diffusion depth in the rock matrix, have been compared. The limited diffusion depth has a significant effect on the transport of radionuclides in fractured rocks. Further, the effect of the uncertainty in heterogeneous diffusion depth on the solute transport was studied together with other main rock property parameters. Closed-form solutions of the mean values of the temporal moments of a travel-time probability density function (PDF) were derived by using the spectral method. Auto-covariance functions of rock property parameters were estimated experimentally to obtain the solutions. The variance of the residence-time PDF increases with increasing variance and correlation length of the diffusion depth.