Stochastic analysis of solute transport in heterogeneous aquifers subject to spatially random recharge

Abstract

This paper derives and solves approximate unconditional moment equations for a concentration plume in a two-dimensional spatially random transmissivity field subject to spatially random recharge and non-uniform (linear trending) velocity. Closed-form expressions are derived for the unconditional, non-stationary auto-covariances for head and velocity, and the cross-covariances between velocity, head, recharge, and log transmissivity based on a system of coupled first-order partial differential moment equations and assumed hole-type input covariance functions for log transmissivity and recharge. The unconditional flow related moment equations are incorporated into a system of solute transport moment equations, which is solved using a Galerkin finite element algorithm. A constant positive mean recharge yields a mean velocity gradient, which enhances the ensemble mean plume spreading in the longitudinal direction similar to results found by Rubin and Bellin (1994) [Water Resour. Res., 30(4) 939–948]. Spatial variability in recharge further enhances the spreading of the ensemble mean plume, especially in the lateral direction. Uncertainty in the spatial distribution of recharge also increases the extent of the ensemble standard deviation plume, particularly in the lateral direction, and increases the coefficient of variation of solute concentration. The uncertainty in the prediction of solute transport increases with increasing recharge variance and spatial correlation scale.