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Abstract: The salinity of groundwater increases with depth in the Canadian Shield (up to 1.3kg/L of density). The existence of brine can be critically important for the safe geologic disposal of radioactive wastes, as dense brine can significantly retard the upward migration of radionuclides released from repositories. Static and flushing conditions of the deep brine are analyzed using a U-tube analogy model. Velocity reduction due to the presence of dense brine is derived under flushing conditions. A set of illustrative numerical simulations in a two-dimensional cross section is presented to demonstrate that dense brine can significantly influence regional groundwater flow patterns in a shield environment. It is implied from the results that (1) the existence of Shield brine can be an indicator of a hydrogeologically stable environment, (2) activities near ground surface may not perturb the stable groundwater environment in the deep brine region, and thus, (3) the deep brine region can be considered as a candidate geologic site for the safe disposal of waste. In addition to brine, other issues associated with long-term waste disposal, such as geological, glacial and seismic events, may need to be considered for the safe storage of spent nuclear fuel in a shield environment. [Copyright &y& Elsevier]

Abstract: In general, the accuracy of numerical simulations is determined by spatial and temporal discretization levels. In fractured porous media, the time step size is a key factor in controlling the solution accuracy for a given spatial discretization. If the time step size is restricted by the relatively rapid responses in the fracture domain to maintain an acceptable level of accuracy in the entire simulation domain, the matrix tends to be temporally over-discretized. Implicit sub-time stepping applies smaller sub-time steps only to the sub-domain where the accuracy requirements are less tolerant and is most suitable for problems where the response is high in only a small portion of the domain, such as within and near the fractures in fractured porous media. It is demonstrated with illustrative examples that implicit sub-time stepping can significantly improve the simulation efficiency with minimal loss in accuracy when simulating flow and transport in fractured porous media. The methodology is successfully applied to density-dependent flow and transport simulations in a Canadian Shield environment, where the flow and transport is dominated by discrete, highly conductive fracture zones. [Copyright &y& Elsevier]

Although high performance computers and advanced numerical methods have made the application of fully-integrated surface and subsurface flow and transport models such as HydroGeoSphere common place, run times for large complex basin models can still be on the order of days to weeks, thus, limiting the usefulness of traditional workhorse algorithms for uncertainty quantification (UQ) such as Latin Hypercube simulation (LHS) or Monte Carlo simulation (MCS), which generally require thousands of simulations to achieve an acceptable level of accuracy. In this paper we investigate non-intrusive polynomial chaos for uncertainty quantification, which in contrast to random sampling methods (e.g., LHS and MCS), represents a model response of interest as a weighted sum of polynomials over the random inputs. Once a chaos expansion has been constructed, approximating the mean, covariance, probability density function, cumulative distribution function, and other common statistics as well as local and global sensitivity measures is straightforward and computationally inexpensive, thus making PCE an attractive UQ method for hydrologic models with long run times. Our polynomial chaos implementation was validated through comparison with analytical solutions as well as solutions obtained via LHS for simple numerical problems. It was then used to quantify parametric uncertainty in a series of numerical problems with increasing complexity, including a two-dimensional fully-saturated, steady flow and transient transport problem with six uncertain parameters and one quantity of interest; a one-dimensional variably-saturated column test involving transient flow and transport, four uncertain parameters, and two quantities of interest at 101 spatial locations and five different times each (1010 total); and a three-dimensional fully-integrated surface and subsurface flow and transport problem for a small test catchment involving seven uncertain parameters and three quantities of interest at 241 different times each. Numerical experiments show that polynomial chaos is an effective and robust method for quantifying uncertainty in fully-integrated hydrologic simulations, which provides a rich set of features and is computationally efficient. Our approach has the potential for significant speedup over existing sampling based methods when the number of uncertain model parameters is modest ( ≤ 20). To our knowledge, this is the first implementation of the algorithm in a comprehensive, fully-integrated, physically-based three-dimensional hydrosystem model. [ABSTRACT FROM AUTHOR]