Numerical Study of Spatial Behavior of Solute Particle Transport in Single Fracture with Variable Apertures

The aim of this study is to numerically analyze spatial behaviors of solute particle transport in a single fracture with spatially correlated variable apertures under application of effective normal stress conditions. The numerical results show that solute particle transport in a single fracture is strongly affected by spatial correlation length of variable apertures and applied effective normal stress. As spatial correlation length increases, mean residence time of solute particles decreases and tortuosity and Peclet number (a dimensionless number representing the relationship between the rate of advection of solute particles by the flow and the rate of diffusion of solute particles) also decreases. These results indicate that the geometry of the aperture distribution is favorable to solute particle transport when the spatial correlation length is increased. However, as effective normal stress increases, the mean residence time and tortuosity tend to increase but the Peclet number decreases. The main reason for a decreasing Peclet number is that the solute particle is transported by one or two channels with relatively higher localized flow rates owing to increase in contact areas resulting from increasing effective normal stress. Based on the numerical results of the solute particle transport produced in this study, an exponential-type correlation formula between the mean residence time and the effective normal stress is proposed