Stochastic numerical method for analysis of solute transport in fractured porous media

Many of the earlier studies analyzed the spatial moments for the solute in the fractured media by assuming constant medium properties, such as, fracture aperture, diffusion coefficient, matrix porosity and fracture sorption, etc. However, these medium properties often exhibit random variations in space. Therefore, we developed stochastic two dimensional numerical models for the solute transport through fractured rock, treating the matrix diffusion coefficient as a stochastic process and evaluated the effect of the variance of log diffusion and integral scale on mean travel distance, spreading behavior and effective dispersion coefficient for the solute in the fracture. Subsequently, the analysis is done to study the effect of varying coefficient of variation of aperture, matrix porosity, fracture sorption, and decay rate coefficient on spatial moments for the solute in the fracture. It is shown that the higher value of integral scale ratio increases the mean travel distance and decreases the spreading behavior of the solute in the fracture. This phenomenon occurs due to the stochastic process of diffusion. The study indicates that the behavior of spatial moments for the solute in the fracture is affected due to random variability of diffusion, porosity, and aperture and sorption coefficient.

► Diffusion, sorption, aperture and decay rate are considered as stochastic process.
► Effect of integral scale ratio and coefficient of variation on spatial moments.
► Effect of aperture, porosity, sorption and decay rate on spatial moments.