| Stochastic analyses and Monte Carlo simulations for non-ergodic transport of a non-reactive solute plume in a heterogeneous aquifer were conducted in three different cases: (1) a statistically isotropic three-dimensional aquifer under uniform mean flow; (2) a statistically anisotropic three-dimensional aquifer under uniform mean flow; (3) a statistically isotropic two-dimensional aquifer with nonuniform mean velocity.; The hydraulic conductivity, K(x), was modeled as a random field which is assumed to be log-normally distributed using an isotropic or an anisotropic exponential covariance function. The simulation model was validated with an excellent comparison of the simulated variograms with the theoretical model of the log K field, small balance errors, and a large number of Monte Carlo runs. For each cases, the ensemble averages of the dimensionless second spatial moments of a solute plume, &angl0;S'ijt' ,l'&angr0; (i, j = 1, 2, 3) and the plume centroid variances, R'ijt' ,l' ), of 1600 Monte Carlo runs were simulated for three degrees of heterogeneity, s2Y = 0.1, 0.25, and 0.5 where s2Y is the variance of log hydraulic conductivity, and a line or a square source of three different lengths along y- and/or z-axis. The simulation results were compared with theoretical ones to assess that the first-order theoretical results.; Several conclusions can be drawn from this study: (1) at least 800 Monte Carlo runs are needed to stabilize the simulated moments even for the mildly heterogeneous aquifers of s2Y ≤ 0.5; (2) the ergodic condition is far from reaching for a source with the initial dimension of several integral scales of log K field; (3) the physical spreading of a solute plume and the uncertainty of its center increase as an aquifer becomes more heterogeneous; (4) the larger the initial source, the larger its spreading and the smaller the uncertainty of its center; (5) the first-order theory predicts well the longitudinal moments but it underestimates transverse moments significantly, especially in a more heterogeneous aquifer. |
