Monte Carlo study of conservative transport in heterogeneous dual-porosity media

In this study, a Monte Carlo simulation method is applied to study groundwater flow and solute transport in heterogeneous, dualporosity media. Both the hydraulic conductivity and the interregional mass diffusion rate are assumed to be spatial random variables, and their random distributions are generated through a Fast Fourier Transform (FFT) technique. A block-centered finite difference (FD) method is used to solve the flow equation. Based on the generated flow fields, a random walk particletracking algorithm is invoked to study the solute transport. The mass diffusion between the mobile and immobile water regions is simulated by a two-state, homogeneous, continuous-time Markov chain. The Monte Carlo simulation results are compared to those obtained through the first-order, Eulerian perturbation method. It is shown from the comparison that the first-order analytical method is robust for predicting mean concentration in mild heterogeneous dual-porosity media. However, large deviations are observed between the analytical and Monte Carlo results for predicting transport in moderately-highly heterogeneous media. The Monte Carlo method is also used to study the variance of the solute flux through a control plane.