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, dual-porosity 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 particle-tracking 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.

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