Anton Leijnse

A non-linear theory of high-concentration-gradient dispersion in porous media.

Abstract The application of Ficks law to describe hydrodynamic dispersion in porous media is based on the assumption of a linear dependance of a solute dispersive mass flux on its concentration gradient. Both theoretical and experimental studies have shown that the Fickian description of dispersion is not valid when large concentration variations in the porous medium are encountered. However, an appropriate alternative is still lacking. In this work, based on a theoretical derivation of the Fickian dispersion equation, a non-linear theory of dispersion is suggested. In the non-linear theory, in addition to the longitudinal and transversal dispersivities, a new parameter is introduced. Miscible displacement experiments are carried out in order to investigate the effects of large variations in salt mass fraction and to assess the validity of the new theory. Low-concentration liquid is displaced upwards in a vertical column by a high-concentration liquid. Thus, only hydrodynamically stable flow regimes are considered. The experiments are simulated by means of both classical Ficks law and the new non-linear theory. It is found that low-concentration-gradient experiments can be simulated satisfactorily using the Fickian-type dispersion equation. However, calculated breakthrough curves for high-concentration-gradient experiments deviate substantially from the measured curves. It appears that a satisfactory fit to high-concentration-gradient data can be obtained only if the value of longitudinal dispersivity is reduced by a factor of three. Using the non-linear theory, however, it is possible to simulate both low- and high-concentration-gradient experiments with a unique set of parameter values.

Transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic interactions

Transport of reactive colloids in groundwater may enhance the transport of contaminants in groundwater. Often, the interpretation of results of transport experiments is not a simple task as both reactions of colloids with the solid matrix and reactions of contaminants with the solid matrix and mobile and immobile colloids may be time dependent and nonlinear. Further colloid transport properties may differ from solute transport properties. In this paper, a one-dimensional model for coupled colloid and contaminant transport in a porous medium (COLTRAP) is presented together with simulation results. Calculated breakthrough curves (BTCs) during contamination and decontamination show systematically the effect of nonlinear and kinetic interactions on contaminant transport in the presence of reactive colloids, and the effect of colloid transport properties that differ from solute transport properties. It is shown that in case of linear kinetic reactions, the rate of exchange of mobile and immobile colloids have a large impact on the shape of BTCs even if the solid matrix is saturated with respect to colloids. BTCs during the contamination and decontamination phase have identical shapes in this case. Moreover, the slow reactions of contaminants and colloids may lead to unretarded breakthrough of contaminants. Independent of reaction rates, nonlinear reactions lead to BTCs that are steeper during contamination than in the linear case. A characteristic aspect of nonlinear sorption is that shapes of BTCs differ during the contamination and decontamination phase. It has been observed that shapes of some of the simulated adsorption and desorption curves are similar as shapes found in experiments reported in literature. This stresses the importance of incorporating both kinetics and nonlinearity in models for coupled colloid and contaminant transport and the capability of COLTRAP to interpret experimental results. Finally, to figure out whether nonlinear processes play a role, it is very important to consider both contamination and decontamination in transport experiments.

Assessment of the effect of kinetics on colloid facilitated radionuclide transport in porous media

Abstract Binding of radionuclides to natural colloids can significantly alter their transport behaviour in porous media. Dependent on the interaction between radionuclides, colloids and the solid matrix, radionuclide transport may be enhanced or retarded as a result of the presence of colloids. Often, equilibrium models are used to describe interactions between radionuclides, colloids and the solid matrix. However, experimental results indicate that kinetic processes may be important. In this paper, a model for coupled colloid and radionuclide transport in porous media is presented. Kinetic relationships are incorporated for the interaction between radionuclides, colloids and solid matrix. With this transport model, column experiments have been simulated, and modelling results are compared with experimental data reported in literature. It appears that kinetic interaction relationships are required to adequately model the experimental data.

Modeling transport of a mixture of natural organic molecules: Effects of dynamic competitive sorption from particle to aquifer scale

Natural organic matter (NOM) can act as a carder for contaminants. Therefore it is of great importance to understand its adsorption/desorption and transport behavior. NOM is a mixture of molecules varying from simple small molecules like citric acid to complicated large molecules like humic acid. To simulate sorption and transport of NOM in aquifer material, we used a previously developed model (NOMADS) describing the dynamic competitive sorption of NOM fractions. We calibrated NOMADS using independent batch adsorption data and incorporated it in a transport code. Sorption and transport of NOM in laboratory column experiments and a field experiment were well simulated using the calibrated model, indicating that the process descriptions used are valid over a wide range of temporal and spatial scales and mass-to-volume ratios. Simulation results provided insights into the influence of pore water velocity and NOM concentration history on the shape of breakthrough curves of NOM fractions. The heterogeneity of NOM appears to be essential to understanding its adsorption and transport behavior.

Upscaling of tracer transport including convection and Brownian motion using a 3D network model

We present a rigorous Lagrangian-Eulerian numerical approach for up-scaling transport in porous media from the Brownian motion of tracer particles to the core scale. The porous medium is assumed to be a surrogate of variously sized non-deformable Taylors cylindrical tubes in 3D Euclidian space (i.e., a 3D pore network), where flow of incompressible fluid is assumed to obey the Hagen-Poiseuille law. In the Lagrangian-Eulerian framework, Brownian tracer particles are allowed to describe three-dimensional random leaps in a velocity field described by the parabolic law. This algorithm was verified by reproducing Taylors classical experiments. The most intriguing problem in such a network is that the dispersion function at the intersection of tubes is discontinuous. This poses the problem in tracking the particles from the exit of one tube to the entrance of another. This problem has been tackled with the help of transition probabilities that are based on the Sorbie-Clifford conjecture [8]. Simulations have been carried out with two different intratube velocity profiles (parabolic and non-parabolic) and two different nodal jump conditions, i.e., with and without taking diffusion into account. The relation between the longitudinal dispersion ( D L ) and the characteristic Peclet Number (Pe l ) obtained in this work is very close to theoretical and experimental evidence. The results show that the velocity profile changes the relation qualitatively, whereas incorporation of diffusion in the nodal jump algorithm only leads to some quantitative differences.

Modeling Uranium Transport in Koongarra, Australia: The Effect of a Moving Weathering Zone

Natural analogues are an important source of long-term data and may be viewed as naturally occurring experiments that often include processes, phenomena, and scenarios that are important to nuclear waste disposal safety assessment studies. The Koongarra uranium deposit in the Alligator Rivers region of Australia is one of the best-studied natural analogue sites. The deposit has been subjected to chemical weathering over several million years, during which many climatological, hydrological, and geological changes have taken place, resulting in the mobilization and spreading of uranium. Secondary uranium mineralization and dispersed uranium are present from the surface down to the base of the weathering zone, some 25 m deep. In this work, a simple uranium transport model is presented and sensitivity analyses are conducted for key model parameters. Analyses of field and laboratory data show that three layers can be distinguished in the Koongarra area: (1) a top layer that is fully weathered, (2) an intermediate layer that is partially weathered (the weathering zone), and (3) a lower layer that is unweathered. The weathering zone has been moving downward as the weathering process proceeds. Groundwater velocities are found to be largest in the weathering zone. Transport of uranium is believed to take place primarily in this zone. It appears that changes in the direction of groundwater flow have not had a significant effect on the uranium dispersion pattern. The solid-phase uranium data show that the uranium concentration does not significantly change with depth within the fully weathered zone. This implies that uranium transport has stopped in these layers. A two-dimensional vertically integrated model for transport of uranium in the weathering zone has been developed. Simulations with a velocity field constant in time and space have been carried out, taking into account the downward movement of this zone and the dissolution of uranium in the orebody. The latter has been modelled by a nonequilibrium relationship. In these simulations, pseudo-steady state uranium distributions are computed. The main conclusion drawn from this study is that the movement of the weathering zone and the nonequilibrium dissolution of uranium in the orebody play an important role in the transport of uranium. Despite the fact that the model is a gross simplification of what has actually happened in the past two million years, a reasonable fit of calculated and observed uranium distributions was obtained with acceptable values for the model parameters.

Fresh Water Lens Persistence and Root Zone Salinization Hazard Under Temperate Climate

In low lying deltaic areas in temperate climates, groundwater can be brackish to saline at shallow depth, even with a yearly rainfall excess. For primary production in horticulture, agriculture, and terrestrial nature areas, the fresh water availability may be restricted to so-called fresh water lenses: relatively thin pockets of fresh groundwater floating on top of saline groundwater. The persistence of such fresh water lenses, as well as the quantity and quality of surface water is expected to be under pressure due to climate change, as summer droughts may intensify in North-West Europe. Better understanding through modelling of these fresh water resources may help anticipate the impact of salinity on primary production. We use a simple model to determine in which circumstances fresh water lenses may disappear during summer droughts, as that could give rise to enhanced root zone salinity. With a more involved combination of expert judgement and numerical simulations, it is possible to give an appraisal of the hazard that fresh water lenses disappear for the Dutch coastal regions. For such situations, we derive an analytical tool for anticipating the resulting salinization of the root zone, which agrees well with numerical simulations. The provided tools give a basis to quantify which lenses are in hazard of disappearing periodically, as well as an impression in which coastal areas this hazard is largest. Accordingly, these results and the followed procedure may assist water management decisions and prioritization strategies leading to a secure/robust fresh water supply on a national to regional scale.

Saltwater Upconing Due to Cyclic Pumping by Horizontal Wells in Freshwater Lenses.

This article deals with the quantification of saltwater upconing below horizontal wells in freshwater lenses using analytical solutions as a computationally fast alternative to numerical simulations. Comparisons between analytical calculations and numerical simulations are presented regarding three aspects: (1) cyclic pumping; (2) dispersion; and (3) finite horizontal wells in a finite domain (a freshwater lens). Various hydrogeological conditions and pumping regimes within a dry half year are considered. The results show that the influence of elastic and phreatic storage (which are not taken into account in the analytical solutions) on the upconing of the interface is minimal. Furthermore, the analytical calculations based on the interface approach compare well with numerical simulations as long as the dimensionless interface upconing is below 1/3, which is in line with previous studies on steady pumping. Superimposing an analytical solution for mixing by dispersion below the well over an analytical solution based on the interface approach is appropriate in case the vertical flow velocity around the interface is nearly constant but should not be used for estimating the salinity of the pumped groundwater. The analytical calculations of interface upconing below a finite horizontal well compare well with the numerical simulations in case the distance between the horizontal well and the initial interface does not vary significantly along the well and in case the natural fluctuation of the freshwater lens is small. In order to maintain a low level of salinity in the well during a dry half year, the dimensionless analytically calculated interface upconing should stay below 0.25.