Monte Carlo Simulations of Solute Transport in Bimodal Randomly Heterogeneous Porous Media

Abstract

In this study, we consider transport of non-reactive solutes in two-dimensional bimodal randomly heterogeneous porous media. We generate a large number of realizations of the log hydraulic conductivity field by first creating binary indicator random fields of two materials and then superposing them with Gaussian random fields, thereby allowing spatial variations of log hydraulic conductivity in each material. For each realization, the steady-state flow equation is solved, a particle is released at a fixed position, and the travel time to some control planes is recorded. The particle's position in the transverse direction is also recorded. We then compute the statistics of particles from all Monte Carlo simulations. We investigate the effect of the contrast of the mean log hydraulic conductivity between two materials and the impact of the degree of heterogeneity on transport statistics. Our results show that, a unimodal distribution of Y always yields a unimodal distribution of travel time τ. However, if the distribution of Y is bimodal, the distribution of the travel time is not always bimodal. The distribution of log travel time log(τ) is bimodal only if the contrast between two materials is large while the variability of Y in each material is small. In addition, the mean travel time in a bimodal porous medium is slightly smaller than that in an equivalent unimodal porous medium. Furthermore, the transverse spreading increases as the increase of the total variability of Y , and it is larger in a bimodal porous medium than that in a corresponding equivalent unimodal porous medium.