Three-Dimensional Simulation for Radon Migration in Fractured Rock Masses: A Computational Modeling Approach

Numerical simulation of radon migration in fractured rock masses is crucial for environmental radon pollution protection, radon tracing technology and the co-exploitation of coal and uranium resources. This paper proposed a novel model based on a fractal discrete fracture network (DFN) to simulate radon migration in fractured rock masses. The paper provided a detailed method for determining the locations of three-dimensional fractures using the multiplicative cascade process. The governing equations for radon migration in fractures and the rock matrix were established and numerically solved using the finite element method. The study developed open-source software DFNRn (Discrete Fracture Network model for Radon migration), which was publicly available on GitHub. The software simulated radon migration in a fractured rock mass with a domain size of 100 m. The results demonstrate that fluid convection in fractures drives radon migration, which is dominant compared to the diffusion process. The accuracy of our proposed model was verified by comparing it with the measured data of the fractured rock. Furthermore, the study investigated the relationship between the percolation threshold of the fracture density \({P}_{32}{\prime}\) $P_{32}\prime$ and the key parameters of the DFN. The results show that \({P}_{32}{\prime}\) $P_{32}\prime$ decreased with the fractal dimension D_f (1.4 ≤ D_f ≤ 1.9) and normalization constant α (1.4 ≤ α ≤ 1.8) and is not correlated with the length exponent a (1.2 ≤ a ≤ 2.8). \({P}_{32}{\prime}\) $P_{32}\prime$ decreased with the mean orientation angle and has no correlation with the Fisher constant. The radon source term of the rock matrix has the greatest impact on radon migration in fractured rock masses compared to the radon diffusion coefficient and permeability.