SIMULATION OF GROUNDWATER AGE USING BACKWARD TRAVEL TIME DISTRIBUTIONS OF SORBING SOLUTES

A volume of groundwater that is sampled at a well contains a collection of water molecules that recharged the aquifer at different times. Knowledge of the distribution of these groundwater ages can be used to assess the potential for future degradation of water quality. Assuming ergodicity, this distribution of groundwater ages is equivalent to a backward travel time probability density function (PDF) between the well and the land surface. For a contaminant or water particle sampled at the well, a backward travel time PDF represents the random travel time from an upgradient point of interest (e.g., the land surface) to the well. For sorbing solutes, the travel time PDF accounts for both the transit time of the particle in the aqueous phase and the time during which it was immobilized in the sorbed phase. The backward travel time PDF can be calculated efficiently by solving the adjoint of a forward transport equation. We present the method for calculating travel time PDFs of sorbing solutes and demonstrate their utility in determining groundwater age.