  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.
