A fractal analysis of radon migration in discrete fracture network model

A novel model is proposed to simulate radon migration by combining the fractal theory and the discrete fracture network (DFN) model. In the model, a power-law distribution based on fractal theory is applied to fracture length and aperture and the fracture locations and orientations are modeled with the Poisson distribution and von Mises-Fisher distribution, respectively. The model was applied to produce a computer code that can calculate the radon concentration, flux, and diffusivity of the fractured media. The key issues related to the model were analyzed and the results reveal that: (1) the threshold value of the ratio of the minimum fracture length to the maximum decreases as the fractal dimension of the fracture lengths and the relation between them follows an exponential law; (2) As the fractal dimension of the fracture lengths increases, more connected fractures are generated, resulting in a linear increase of the mean efficient radon diffusivity. (3) The dip angle is the parameter that has the greatest influence on radon migration in determining fracture orientations. (4) The radon exhalation rate increases exponentially with increasing advection velocity. (5) Models with larger fractal dimension for fracture lengths have larger representative elementary volume (REV) size and follow an exponential law.