Groundwater age, life expectancy and transit time distributions in advective–dispersive systems: 1. Generalized reservoir theory

摘要

We present a methodology for determining reservoir groundwater age andtransit time probability distributions in a deterministic manner, consideringadvective-dispersive transport in steady velocity fields. In a first step, wepropose to model the statistical distribution of groundwater age at aquiferscale by means of the classical advection-dispersion equation for aconservative and nonreactive tracer, associated to proper boundary conditions.The evaluated function corresponds to the density of probability of the randomvariable age, age being defined as the time elapsed since the water particlesentered the aquifer. An adjoint backward model is introduced to characterizethe life expectancy distribution, life expectancy being the time remainingbefore leaving the aquifer. By convolution of these two distributions,groundwater transit time distributions, from inlet to outlet, are fully definedfor the entire aquifer domain. In a second step, an accurate and efficientmethod is introduced to simulate the transit time distribution at dischargezones. By applying the reservoir theory to advective-dispersive aquifersystems, we demonstrate that the discharge zone transit time distribution canbe evaluated if the internal age probability distribution is known. Thereservoir theory also applies to internal life expectancy probabilitiesyielding the recharge zone life expectancy distribution. Internal groundwatervolumes are finally identified with respect to age and transit time. One- andtwo-dimensional theoretical examples are presented to illustrate the proposedmathematical models, and make inferences on the effect of aquifer structure andmacro-dispersion on the distributions of age, life expectancy and transit time.