STOCHASTIC-ANALYSIS OF SOLUTE TRANSPORT IN HETEROGENEOUS AQUIFERS SUBJECT TO SPATIALLY RANDOM RECHARGE

This paper derives and solves approximate unconditional moment equatio ns for a concentration plume in a two-dimensional spatially random tra nsmissivity field subject to spatially random recharge and non-uniform (linear trending) velocity. Closed-form expressions are derived for t he unconditional, non-stationary auto-covariances for head and velocit y, and the cross-covariances between velocity, head, recharge, and log transmissivity based on a system of coupled first-order partial diffe rential moment equations and assumed hole-type input covariance functi ons for log transmissivity and recharge. The unconditional flow relate d moment equations are incorporated into a system of solute transport moment equations, which is solved using a Galerkin finite element algo rithm. A constant positive mean recharge yields a mean velocity gradie nt, which enhances the ensemble mean plume spreading in the longitudin al direction similar to results found by Rubin and Bellin (1994) [Wate r Resour. Res., 30(4) 939-948]. Spatial variability in recharge furthe r enhances the spreading of the ensemble mean plume, especially in the lateral direction. Uncertainty in the spatial distribution of recharg e also increases the extent of the ensemble standard deviation plume, particularly in the lateral direction, and increases the coefficient o f variation of solute concentration. The uncertainty in the prediction of solute transport increases with increasing recharge variance and s patial correlation scale. (C) 1998 Elsevier Science B.V. All rights re served.