A Fractal Model For Relative Permeability In Shale With Tree-Like Branching Fracture Network

The gas–liquid two-phase flow is often caused by pressure difference and seepage, and there are also various fracture channels in shale. The multiphase flow characteristics in the shale matrix are affected by the fracture network, and the multiphase flow characteristics in the fracture network are also affected by the shale matrix. Relative permeability is an important parameter characterizing the multiscale macroscopic multiphase flow characteristics in shale. However, there are a few studies on the influences of matrix and fracture networks on the relative permeability in shale. This study establishes a fractal model for relative permeability in shale with tree-like fracture network and investigates the influences of shale matrix and fracture parameters on the relative permeability by using the proposed model. The reliability of the model is verified by comparing the results obtained by the model with those obtained by existing models. The results indicate that the fractal dimension of the pore size in shale matrix, the ratio of capillary pore size, along with the geometric parameters (length ratio, diameter ratio, number of bifurcation and fractal dimension of the pore size) in fracture have a significant impact on the relative permeability in shale with tree-like branching fracture network. The effect is more significant at high saturation. This study has important application prospects for the accurate evaluation of multiphase flow characteristics in shale reservoirs.