Adjoint Simulation of Solute Age to Evaluate the Persistence of Groundwater Well Contamination

The solute age of a groundwater sample quantifies the amount of time since the solute has entered the aquifer. A groundwater sample contains a mixture of solute particles that recharged the aquifer at different times; thus the groundwater sample contains a distribution of solute ages. For tracers, solute age is equivalent to groundwater age, which quantifies the amount of time since groundwater has recharged the aquifer. For sorbing solutes, however, solute age is higher than groundwater age. One application of solute age is to quantify the persistence of contamination at a groundwater well. If a well is contaminated and the source of contamination is removed, the well will remain contaminated until all of the residual contamination has passed the aquifer. This persistence of contamination can be quantified by the solute age distribution. We present an adjoint approach for calculating solute age. In the adjoint approach, information is propagated upgradient and backward in time, from the well to the source of contamination. The solute age distribution can be obtained with one adjoint simulation. We demonstrate the use of the solute age distribution in evaluating the persistence of groundwater well contamination.