European Geosciences Union General Assembly

p. 1

Presentation's date: 2019-04-09

Abstract:

Evidence shows that probability density distributions of hydrogeological properties, such as the hydraulic conduc-tivity in aquifers, tend to be non-Gaussian. In these distributions, the spatial increments of the log-conductivity Ybetween two locations separated by a distance s present distributions with peaks that grow sharper and tails thatbecome heavier as the lag s decreases. Recently, the Generalized Sub-Gaussian (GSG) model has been introduced.This model captures the main features that characterize the behavior of non-Gaussian variables. Here, we presentthe results of a numerical study to evaluate the implications on solute transport of GSG log-conductivity fields.The spatial and temporal evolution of a solute plume in a three-dimensional saturated column is compared forGSG log-conductivity distributions with differing degrees of “non-Gaussianity”, i.e. of departure from the Gaus-sian behavior. The results show that, after a few integral scales, the evolution of the second spatial moment of theconcentrations in a GSG field coincides with that associated with a Gaussian field with a lower log-conductivityvariance. Although the evolution of higher-order moments of solute plumes in GSG fields differs from what canbe found in Gaussian settings, these differences become small after the solute travels across a few integral scales.Hence, these discrepancies might be extremely hard to detect so that it would be difficult to differentiate betweenGaussian and non-Gaussian fields by relying on these types of observations. Moreover, local-scale dispersion canalso affect transport, its contribution being intimately intertwined with that of Y heterogeneity. Another signatureof the GSG conductivity field is the emergence of power-law tailing of solute breakthrough curves where it wouldnot be expected in the presence of Gaussian log-conductivities. We found that GSG fields, due to their higher de-gree of spatial disorder, tend to enhance the stretching of an initially regular interface between two solutions whencompared to Gaussian fields. This can be relevant in the context of reactive transport scenarios, as it may yieldenhanced rates of mixing and reaction.]]>

Journal of hydrology

Vol. 494, num. 28, p. 107-115

DOI: 10.1016/j.jhydrol.2013.04.040

Date of publication: 2013-06

Abstract:

We addressed the value of hydrogeological information on the assessment of the risk that an operating pumping well is polluted. The work considered a heterogeneous aquifer and focused on the statistical characterization of the contaminant mass fraction from a diffused source recovered at the well and the solute arrival times. We explored the role of the key length scales that characterize and control the well capture region and its probabilistic delineation with respect to the contaminant source location and size. The impact of augmenting the data-base of hydraulic information on the reduction of uncertainty associated with the environmental scenario analyzed was then investigated. It was found that obtaining a robust characterization of the target Environmental Performance Metrics (EPMs) depends on the length scale considered. For the sampling scheme considered, the importance of conditioning on the probability distributions of solute mass fraction and travel times is strongly affected by the location of the contaminant source within the probabilistic well catchment. With reference to the characterization of the travel time distribution associated with the recovery of a given mass fraction, the worth of augmenting the hydraulic parameter data-sets tends to decrease with decreasing solute residence time within the well catchment.]]>

European Geosciences Union General Assembly

p. 1

Presentation's date: 2013-04-07

American Geophysical Union Fall Meeting

p. 1454-

Presentation's date: 2012-12-03

IAHR International Groundwater Symposium

p. 10

Presentation's date: 2012-11

European Geosciences Union General Assembly

p. 1

Presentation's date: 2011-04-03

American Geophysical Union Fall Meeting

p. 1

Presentation's date: 2010-12-13

Water resources research

Vol. 46, num. W12510, p. 1-7

DOI: 10.1029/2010WR009539

Date of publication: 2010-12-02

Mathematical geosciences

Vol. 41, num. 3, p. 323-351

DOI: 10.1007/s11004-008-9204-2

Date of publication: 2009-03

Abstract:

This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.]]>

European Geosciences Union General Assembly

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European Geosciences Union General Assembly

p. 1

European Geosciences Union General Assembly

p. 1

Advances in water resources

Vol. 31, num. 10, p. 1364-1376

DOI: 10.1016/j.advwatres.2008.07.001

Date of publication: 2008-10

Abstract:

Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so that the system can locally equilibrate. In general, a multicomponent reactive transport problem is described through a system of coupled non-linear partial differential equations. Under instantaneous chemical equilibrium, a complex geochemical problem can be highly simplified by fully defining the system in terms of conservative quantities, termed master species or components, and the space–time distribution of reaction rates. We investigate the parameters controlling reaction rates in a heterogeneous aquifer at short distances from the source. Hydraulic conductivity at this scale is modeled as a random process with highly anisotropic correlation structure. In the limit for very large horizontal integral scales, the medium can be considered as stratified. Upon modeling transport by means of an ADE (Advection Dispersion Equation), we derive closed-form analytical solutions for statistical moments of reaction rates for the particular case of negligible transverse dispersion. This allows obtaining an expression for an effective hydraulic conductivity, , as a representative parameter describing the mean behavior of the reactive system. The resulting is significantly smaller than the effective conductivity representative of the flow problem. Finally, we analyze numerically the effect of accounting for transverse local dispersion. We show that transverse dispersion causes no variation in the distribution of (ensemble) moments of local reaction rates at very short travel times, while it becomes the dominant effect for intermediate to large travel times.]]>

Journal of contaminant hydrology

Vol. 101, num. 1-4, p. 1-13

DOI: 10.1016/j.jconhyd.2008.07.004

Date of publication: 2008-10

Abstract:

We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity (K) and porosity (¿), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.]]>

Mathematical geosciences

Vol. 41, num. 3, p. 323-351

DOI: 10.1007/s11004-008-9204-2

Date of publication: 2008

Sixth International Conference on Calibration and Reliability in Groundwater Modelling

VI European Conference for Geostatistics for Environmental Applications,

p. 127-151