Variability in the displacement of solute particles in heterogeneous confined aquifers

In this work, the variability of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is quantified by the variance of the displacement of a solute particle. In the traditional stochastic approach to solute transport at the regional scale, the variability of solute displacement is attributed to the variability of the transmissivity fields. In this work, however, variability in solute displacement is attributed to variability in hydraulic conductivity and aquifer thickness fields. A general stochastic methodology for deriving the variance of the displacement of a solute particle based on the convection velocity of solute particles, developed from the relationship between the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation, is given. Assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes, a closed-form expression for the solute displacement variance in the mean flow direction is obtained for the case of advection-dominated solute transport. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances.