Stochastic modeling of discrete fracture network considering spatial pattern and variability of fracture distribution

The distribution of fractures has a crucial influence on the connectivity of fractures. The discrete fracture network (DFN) model integrating the spatial variability of fracture distribution is of great significance for describing flow and solute transport behaviors in fractures. This study proposes a framework for simulating discrete fracture networks considering the spatial pattern and variability of fracture distributions. Three main types of fracture distributions were summarized, including fracture distributions with spatial continuous variation characteristics, spatial trend variation characteristics, and spatial division characteristics. The kriging interpolation and spatial trend function or spatial distribution function were used to generate the spatial distribution of the facture quantity, and then the Monte Carlo method was employed to establish the DFN model based on the spatial distribution of the facture quantity. Two DFN cases with different fracture distribution types were designed to evaluate the rationality of the DFN model built with the proposed method. The results show that the root mean square error (RMSE) of the fracture quantification distribution of the DFN model is greatly reduced compared with that of the DFN model built with the traditional Monte Carlo method, and the RMSE of the hydraulic head distribution is also greatly reduced. The application of these cases illustrates that the proposed discrete fracture network stochastic simulation integrating the spatial variability of fracture distribution can better approximate the real distribution of fracture quantity.