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Cornaton et al. [2007] introduced the concept of lifetime expectancy as a performance measure of the safety of subsurface repositories, based upon the travel time for contaminants released at a certain point in the subsurface to reach the biosphere or compliance area. The methodologies are applied to a hypothetical but realistic Canadian Shield crystalline rock environment, which is considered to be one of the most geologically stable areas on Earth. In an approximately 10\times10\times1.5 km3 hypothetical study area, up to 1000 major and intermediate fracture zones are generated from surface lineament analyses and subsurface surveys. In the study area, mean and probability density of lifetime expectancy are analyzed with realistic geologic and hydrologic shield settings in order to demonstrate the applicability of the theory and the numerical model for optimally locating a deep subsurface repository for the safe storage of spent nuclear fuel. The results demonstrate that, in general, groundwater lifetime expectancy increases with depth and it is greatest inside major matrix blocks. Various sources and aspects of uncertainty are considered, specifically geometric and hydraulic parameters of permeable fracture zones. Sensitivity analyses indicate that the existence and location of permeable fracture zones and the relationship between fracture zone permeability and depth from ground surface are the most significant factors for lifetime expectancy distribution in such a crystalline rock environment. As a consequence, it is successfully demonstrated that the concept of lifetime expectancy can be applied to siting and performance assessment studies for deep geologic repositories in crystalline fractured rock settings., Comment: 14 pages, 14 figures; Water Resources Research, Vol. 44, 2008

Long-term solutions for the disposal of toxic wastes usually involve isolation of the wastes in a deep subsurface geologic environment. In the case of spent nuclear fuel, if radionuclide leakage occurs from the engineered barrier, the geological medium represents the ultimate barrier that is relied upon to ensure safety. Consequently, an evaluation of radionuclide travel times from a repository to the biosphere is critically important in a performance assessment analysis. In this study, we develop a travel time framework based on the concept of groundwater lifetime expectancy as a safety indicator. Lifetime expectancy characterizes the time that radionuclides will spend in the subsurface after their release from the repository and prior to discharging into the biosphere. The probability density function of lifetime expectancy is computed throughout the host rock by solving the backward-in-time solute transport adjoint equation subject to a properly posed set of boundary conditions. It can then be used to define optimal repository locations. The risk associated with selected sites can be evaluated by simulating an appropriate contaminant release history. The utility of the method is illustrated by means of analytical and numerical examples, which focus on the effect of fracture networks on the uncertainty of evaluated lifetime expectancy., Comment: 11 pages, 8 figures; Water Resources Research, Vol. 44, 2008

Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion, and the equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment, and the comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas-phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporization, diffusion and biodegradation. The net effect can lead to an enrichment or depletion of the heavy isotope in the remaining organic phase depending on the compound and element considered. Finally, the isotope evolution of molecules migrating away from the source and undergoing degradation is governed by a combined degradation and diffusion isotope effect. This suggests that in the unsaturated zone, the interpretation of biodegradation based on isotope data must always be based on a model combining gas-phase diffusion and degradation., Comment: 11 pages, 6 figures

Environmental fluid circulations are very often characterized by analyzing the fate and behavior of natural and anthropogenic tracers. Among these tracers, age is taken as an ideal tracer which can yield interesting diagnoses, as for example the characterization of the mixing and renewal of water masses, of the fate and mixing of contaminants, or the calibration of hydro-dispersive parameters used by numerical models. Such diagnoses are of great interest in atmospheric and ocean circulation sciences, as well in surface and subsurface hydrology. The temporal evolution of groundwater age and its frequency distributions can display important changes as flow regimes vary due to natural change in climate and hydrologic conditions and/or human induced pressures on the resource to satisfy the water demand. Steady-state age frequency distributions can be modelled using standard numerical techniques, since the general balance equation describing age transport under steady-state flow conditions is exactly equivalent to a standard advection-dispersion equation. The time-dependent problem is however described by an extended transport operator that incorporates an additional coordinate for water age. The consequence is that numerical solutions can hardly be achieved, especially for real 3-D applications over large time periods of interest. A novel algorithm for solving the age distribution problem under time-varying flow regimes is presented and, for some specific configurations, extended to the problem of generalized component exposure time. The algorithm combines the Laplace Transform technique applied to the age (or exposure time) coordinate with standard time-marching schemes. The method is validated and illustrated using analytical and numerical solutions considering 1-D, 2-D and 3-D theoretical groundwater flow domains., Comment: 18 pages, 9 figures; Water Resources Research 2011

A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The model takes into account elastic and statistical fracture parameters, and is able to simulate real stress-dependent permeabilities from laboratory to field studies. This modeling approach gains in phenomenology in comparison to the classical ones because the permeability tensors may vary in both strength and principal directions according to effective stresses. Moreover this method allows evaluation of the fracture porosity changes, which are then translated into consolidation of the medium., Comment: 10 pages, 7 figures, submitted to Ground Water 2011

We present a methodology for determining reservoir groundwater age and transit time probability distributions in a deterministic manner, considering advective-dispersive transport in steady velocity fields. In a first step, we propose to model the statistical distribution of groundwater age at aquifer scale by means of the classical advection-dispersion equation for a conservative and nonreactive tracer, associated to proper boundary conditions. The evaluated function corresponds to the density of probability of the random variable age, age being defined as the time elapsed since the water particles entered the aquifer. An adjoint backward model is introduced to characterize the life expectancy distribution, life expectancy being the time remaining before leaving the aquifer. By convolution of these two distributions, groundwater transit time distributions, from inlet to outlet, are fully defined for the entire aquifer domain. In a second step, an accurate and efficient method is introduced to simulate the transit time distribution at discharge zones. By applying the reservoir theory to advective-dispersive aquifer systems, we demonstrate that the discharge zone transit time distribution can be evaluated if the internal age probability distribution is known. The reservoir theory also applies to internal life expectancy probabilities yielding the recharge zone life expectancy distribution. Internal groundwater volumes are finally identified with respect to age and transit time. One- and two-dimensional theoretical examples are presented to illustrate the proposed mathematical models, and make inferences on the effect of aquifer structure and macro-dispersion on the distributions of age, life expectancy and transit time., Comment: 25 pages, 11 figures

One dimensional analytical porosity-weighted solutions of the dual-porosity model are derived, providing insights on how to relate exchange and storage coefficients to the volumetric density of the high-permeability medium. It is shown that porosity-weighted storage and exchange coefficients are needed when handling highly heterogeneous systems - such as karstic aquifers - using equivalent dual-porosity models. The sensitivity of these coefficients is illustrated by means of numerical experiments with theoretical karst systems. The presented 1-D dual-porosity analytical model is used to reproduce the hydraulic responses of reference 3-D karst aquifers, modelled by a discrete single-continuum approach. Under various stress conditions, simulation results show the relations between the dual-porosity model coefficients and the structural features of the discrete single-continuum model. The calibration of the equivalent 1-D analytical dual-porosity model on reference hydraulic responses confirms the dependence of the exchange coefficient with the karstic network density. The use of the analytical model could also point out some fundamental structural properties of the karstic network that rule the shape of the hydraulic responses, such as density and connectivity., Comment: 12 pages, 8 figures

Groundwater age has become a fundamental concept in groundwater hydrology, but ages originating from isotopic analyses are still identified with a lack of clarity and using models that occasionally are unrealistic. If the effect of advection and dispersion on water ages has already been extensively identified, very few studies address the reliability of using radiometric ages as derived from isotopic data to estimate aquifer properties such as average velocities. Using simple one-dimensional and two-dimensional analytical solutions for single-site and two-sites mobile-immobile systems, we compare the radiometric ages to the mean ages (or residence times) as deduced from a direct, physically-based simulation approach (using the mean age equation), and show that the competition between isotope decay rate and dispersion coefficient can generate important discrepancies between the two types of ages. A correction for the average apparent velocity originating from apparent isotopic ages is additionally provided. The particular case of the Tritium age dating method is also addressed, and a numerical example is finally given for illustrating the analysis considering a more complex and heterogeneous aquifer system. Our results suggest that age definitions based on the radioactivity of isotopes may not be representative for the mean age of the sample or for the groundwater velocity at given locations, and may not always be suitable for constraining the calibration of hydrogeological models., Comment: 20 pages, 7 figures; Journal of Hydrology, 2011