Simulation of imbibition in porous media with a tree-shaped fracture following the level-set method

Imbibition is an important mechanism for enhancing oil recovery in low-permeability reservoirs, such as shale and tight sandstone, and a tree-shaped network has been successfully used to characterize fracturing fracture. Therefore, understanding the imbibition mechanism in porous media with a tree-shaped fracture (TFPM) is important for developing low-permeability reservoirs. In this study, a simulation model for imbibition in TFPM was established based on the level-set method, and the model was verified by comparing it with an analytical solution. The influences of the fracture width, bifurcation angle, tortuosity, and water flow rate on imbibition in TFPM were then discussed. Based on the results, the following points have been established: (1) During the early stage, the imbibition in TFPM included countercurrent and a combined imbibition, and only countercurrent imbibition occurred during the later stage. (2) At a constant fracture width ratio, increasing the primary fracture width could reduce the residual oil in the TFPM, thereby improving the oil recovery factor. (3) At a fracture bifurcation angle ranging from 0° to 45°, the oil recovery factor increased as the bifurcation angle increased. (4) At a fracture tortuosity of 1.0 to 1.24, changes in tortuosity had little effect on the oil recovery factor during the early stage of imbibition, while it significantly affected the distribution of the residual oil. (5) At a water flow rate of 5 mm/s, the simulated oil recovery factor in the TFPM was highest. This investigation can provide a reference for the development of low-permeability reservoirs.