Numerical models of groundwater flow and solute transport in three-dimensional heterogeneous aquifers

This numerical modeling study is a part of numerical implementation and verification of the stochastic theories of groundwater solute transport (Kavvas and Karakas, 1996). The conditional simulation techniques were applied to generate synthetic hydraulic conductivity random fields for two- or three-dimensional heterogeneous aquifers. With the preconditioning spatial configurations, the computational efforts required for the very large number of computational nodes reduce significantly for the random field generation. The hydraulic conductivity random field generator was then integrated with MODFLOW (McDonald and Harbaugh, 1988). This expanded and modified version of MODFLOW was used to study velocity covariance structures and mean velocity in heterogeneous aquifers. The time integrals of the covariance function of the pore flow velocity and the cross-covariance tensor of pore flow velocity with its gradient were calculated for the macro-dispersion tensor and convection-correction vector, respectively, for steady, spatially stationary flow based on the stochastic theories (Kavvas and Karakas, 1996).; The deterministic partial differential equation for the time-space evolution of the mean solute concentration, derived by Kavvas and Karakas (1996), has a form similar to the convection-dispersion equation. Consequently, the three-dimensional numerical mass transport model MT3D (Zheng, 1990) was adopted and modified for predicting the mean solute concentration. To verify the mean solute transport obtained by the predictive PDE, the hydraulic conductivity random field generator, the groundwater flow model (MODFLOW), and the mass transport model (MT3D) were integrated into one numerical model, which enables one to perform Monte Carlo analysis of solute transport in heterogeneous aquifers.; The application results of the stochastic theory for the case of transport by steady spatially-stationary flow in a highly heterogeneous aquifer are quite encouraging. Numerical results show that the time-space evolution of mean solute concentration in the two- and three- dimensional heterogeneous aquifers, as predicted by the predictive PDE of Kavvas and Karakas (1996), agrees with that obtained by Monte Carlo simulations. The stochastic theory predicts the shape and overall location of the solute plume very well in a heterogeneous aquifer where log hydraulic conductivity variance is 1.2. Also, the observed asymmetry of the plume with respect to its core center is accounted for by the new convection-correction term in the equation. As demonstrated by an application example, the new convection-correction term can account for (i) the asymmetry of the solute plume with respect to the solute core center, and (ii) for the delayed position of the plume core center, as seen from a comparison of Monte Carlo simulations to predictions by the standard convective-dispersive form of the conservation equations.