María Pool

Effects of tidal fluctuations and spatial heterogeneity on mixing and spreading in spatially heterogeneous coastal aquifers

We study the combined effect of heterogeneity in the hydraulic conductivity field and tidal oscillations on the three-dimensional dynamics of seawater intrusion in coastal aquifers. We focus on the quantification of its impact on solute mixing and spreading of the freshwater–seawater interface. Three-dimensional Monte Carlo realizations of log-normally distributed permeability fields were performed, and for each realization, numerical variable density flow and solute transport simulations were conducted. Mixing is characterized by the spatial moments of concentration. The enhanced solute mixing is quantified by an effective dispersion coefficient. The simulations show that heterogeneity produces an inland movement of the toe location along with a significant widening of the transition zone, which is linearly proportional to the product of the arithmetic mean of the correlation lengths in the three spatial dimensions (λa) and the permeability field variance ( σlnk2). We find that once tidal oscillations are included, as the degree of heterogeneity increases, the combined effect of heterogeneity and tidal oscillations on mixing and spreading of the interface reduces. This is explained by the fact that an increase in the log-permeability variance induces an increase in both the effective permeability and the spatial connectivity, which implies a more uniform hydraulic response to tidal forcing and, as a result, the degree of mixing decreases. This study also identifies that the mixing behavior induced by tidal oscillations in heterogeneous coastal aquifers is controlled by the effective tidal mixing number ( ntme) which depends on the amplitude, the period, the storativity, and the effective horizontal permeability.

Effects of tidal fluctuations on mixing and spreading in coastal aquifers: Homogeneous case

While the hydraulics of tidally dominated groundwater systems have been studied extensively, tidally induced solute spreading in the fresh-saltwater transition zone of coastal aquifers remains largely unexplored. Here we systematically quantify tidal impacts on solute mixing and spreading in seawater intrusion problems for an idealized homogeneous system. Mixing is characterized by the spatial moments of the solute concentration distribution and quantified by an effective dispersion coefficient. Parametric analysis reveals that the key dimensionless parameter controlling the tidal mixing behavior is the tidal mixing number ( ntm) which depends on the tidal amplitude, the period and the hydraulic diffusivity. We find that for ntm≤600, tides lead to a significant impact on the shape and location of the interface. The maximum effect on transverse and longitudinal dispersion occurs for large values of storativity, a hydrogeologic parameter that has been previously understated in terms of its significance. Large storativity implies a nonuniform hydraulic response to the tidal forcing, such that the resulting nonuniform time-dependent velocity field enhances mixing. As a result, the interface spreads mainly at the bottom of the aquifer, where the saline end of the mixing zone migrates seaward, whereas the spatial extent of low salt concentrations migrates landward. These insights critically underpin quantitative guidance on the inclusion and exclusion of tidal effects in the analysis of seawater intrusion.

Transient forcing effects on mixing of two fluids for a stable stratification

Mixing and dispersion in coastal aquifers are strongly influenced by periodic temporal flow fluctuations on multiple time-scales ranging from days (tides), seasons (pumping and recharge) to glacial cycles (regression and transgressions). Transient forcing effects lead to a complex space- ant time-dependent flow response which induces enhanced spreading and mixing of dissolved substances. We study effective mixing and solute transport in temporally fluctuating one-dimensional flow for a stable stratification of two fluids of different density using detailed numerical simulation as well as accurate column experiments. We quantify the observed transport behaviors and interface evolution by a time-averaged model that is obtained from a two-scale expansion of the full transport problem, and derive explicit expressions for the center of mass and width of the mixing zone between the two fluids. We find that the magnitude of transient-driven mixing is mainly controlled by the hydraulic diffusivity, the period and the initial interface location. At an initial time regime, mixing can be characterized by an effective dispersion coefficient and both the interface position and width evolve linearly in time. At larger times, the spatial variability of the flow velocity leads to a deceleration of the interface and a compression of its width, which is manifested by a subdiffusive evolution of its width as t1/2. This article is protected by copyright. All rights reserved.

Effects of Heterogeneity, Connectivity, and Density Variations on Mixing and Chemical Reactions Under Temporally Fluctuating Flow Conditions and the Formation of Reaction Patterns

14 Solute mixing, spreading and fast chemical reactions in aquifers are strongly influenced by 15 spatial variability of the hydraulic properties, temporal flow fluctuations and fluid density 16 differences. We study the coupling of heterogeneity, transient forcing and density-driven 17 flow on mixing and chemical reactions between two fluids of different density under a sta18 ble stratification. We consider the reaction of the fast dissolution of calcite. We find that 19 temporal fluctuations and heterogeneity cause strong local enhancement of the mixing and 20 reaction rates and this impact increases with the degree of connectivity of hydraulic con21 ductivity. The global mixing and reactivity, however, are on the order of or smaller than 22 their homogeneous counterparts due to heterogeneity-induced fluid segregation. The local 23 maxima of the mixing and reaction rates are found to be located around strongly stretched 24 regions corresponding to high velocity zones where dispersive mass transfer mechanisms 25 are increased by dispersion. We also find that density variations compress the interface, 26 which in turn emphasizes local maxima in mixing and reaction rates. Numerical results 27 provide evidence that the stretching of the interface induced by spatial heterogeneity and 28 transient effects coupled with density variations leads to the formation of complex pat29 terns of reactive hotspots, zones of enhanced reaction efficiency, and that its distribution 30 is directly linked to the deformation properties and topology of the flow field. These re31 sults provide new insights into the role of spatial and temporal variability on the mixing 32 and reaction efficiency as well as the formation of reactive geochemical patterns in actual 33 environmental systems. 34

Correction to “Vertical average for modeling seawater intrusion”

[1] In the paper “Vertical average for modeling seawater intrusion” by M. Pool et al. (Water Resources Research, 47, W11506, doi:10.1029/2011WR010447, 2011), equations (3), (4), (6), (7), (14), (16), (17), (A1), (A2), (A4), (A6), (A8), (A9), and (A11) have typographical errors. The vector products should be r instead of r . Moreover, in equation (14), the last w was omitted from the second line of the equation. In Figure 3 caption, typographical errors have been noted, as u nw|x=L and u nws should be u nw|x=L and u nws, respectively. The corrections are as follows.