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The combined influence of temporal fluctuations and spatial heterogeneity on non-reactive solute transport mechanisms in porous media can be understood by performing simulations of steady and unsteady flow and transport in heterogeneous media. The study focuses on issues such as the degree of heterogeneity, correlation length, separation of the combined effects of temporal and spatial variations, and ergodicity conditions under unsteady flow conditions. It is shown that the effect of temporal variations on solute transport is masked by the strong effect of spatial heterogeneity. There is no obvious difference in plume shape between steady and unsteady flow conditions; the first and the second spatial moments of the plume of the unsteadystate flow condition fluctuate around the steady-state flow condition with the same period of oscillations as the input signal at small storage coefficient (S≤0.001). At a relatively high standard deviation in hydraulic conductivity and a small storage coefficient, the unsteady flow condition sharpens the temporal variations in macrodispersion coefficients. The magnitude of the longitudinal macrodispersion coefficient under unsteady flow condition is almost doubled at the maximum values. However, the transverse macrodispersion coefficient fluctuates around zero. The Kubo number and Peclet number ranges are 1.2–64 and 10–250, respectively.

Temporal patterns of solute transport and transformation through the vadose zone are driven by the stochastic variability of water fluxes. This is determined by the hydrologic filtering of precipitation variability into infiltration, storage, drainage, and evapotranspiration. In this work we develop a framework for examining the role of the hydrologic filtering and, in particular, the effect of evapotranspiration in determining the travel time and delivery of sorbing, reacting solutes transported through the vadose zone by stochastic rainfall events. We describe a 1-D vertical model in which solute pulses are tracked as point loads transported to depth by a series of discrete infiltration events. Numerical solutions of this model compare well to the Richards equation–based HYDRUS model for some typical cases. We then utilize existing theory of the stochastic dynamics of soil water to derive analytical and semianalytical expressions for the probability density functions (pdf's) of solute travel time and delivery. The moments of these pdf's directly relate the mean and variance of expected travel times to the water balance and show how evapotranspiration tends to reduce (and make more uncertain) the mass of a degrading solute delivered to the base of the vadose zone. The framework suggests a classification of different modes hydrologic filtering depending on hydroclimatic and landscape controls. Results suggest that variability in travel times decreases with soil depth in wet climates but increases with soil depth in dry climates. In dry climates, rare large storms can be an important mechanism for leaching to groundwater.

In the present study, we examine non-Gaussian spreading of solutes subject to advection, dispersion and kinetic sorption (adsorption/desorption). We start considering the behavior of a single particle and apply a random walk to describe advection/dispersion plus a Markov chain to describe kinetic sorption. We show in a rigorous way that this model leads to a set of differential equations. For this combination of stochastic processes, such a derivation is new. Then, to illustrate the mechanism that leads to non-Gaussian spreading, we analyze this set of equations at first leaving out the Gaussian dispersion term (microdispersion). The set of equations now transforms to the telegrapher’s equation. Characteristic for this system is a longitudinal spreading that becomes Gaussian only in the longtime limit. We refer to this as kinetics-induced spreading. When the microdispersion process is included back again, the characteristics of the telegraph equations are still present. Now, two spreading phenomena are active, the Gaussian microdispersive spreading plus the kinetics-induced non-Gaussian spreading. In the long run, the latter becomes Gaussian as well. Another non-Gaussian feature shows itself in the 2D situation. Here, the lateral spread and the longitudinal displacement are no longer independent, as should be the case for a 2D Gaussian spreading process. In a displacing plume, this interdependence is displayed as a ‘tailing’ effect. We also analyze marginal and conditional moments, which confirm this result. With respect to effective properties (velocity and dispersion), we conclude that effective parameters can be defined properly only for large times (asymptotic times). In the two-dimensional case, it appears that the transverse spreading depends on the longitudinal coordinate. This results in ‘cigar-shaped’ contours.

The presence of numerous organic micropollutants, such as pharmaceutically active compounds (PhACs) and hormones, but also pesticides and industrial pollutants, in the sources for the drinking water supply, are a big concern for drinking water utilities. Even though not all pollutants are harmful to human health, less is known about the consumption of drinking water containing a cocktail of all these solutes. To prevent these pollutants from entering the drinking water, a solid drinking water treatment is necessary. This thesis investigates the removal of, amongst others, pharmaceuticals and hormones by nanofiltration and reverse osmosis membranes. These membranes are currently among the most advanced techniques for removal of organic micropollutants. In the thesis it is shown that even reverse osmosis membranes (the membranes with the smallest pore size) are not able to completely remove all pollutants. Combination of nanofiltration/reverse osmosis with other water treatment techniques (such as activated carbon filtration) is therefore necessary. This is no problem for the Dutch drinking water sector, since the principle of "multiple barrier treatment" is used in the Netherlands. For other countries, where the treatment plants are less advanced, the presence of pharmaceuticals and hormones may become a problem. Therefore, the policy towards pesticides, hormones and pharmaceuticals has to be changed, to prevent too many of these pollutants from entering the drinking water.