Propagation model of multi-stage hydraulic fracturing for horizontal wells on shale gas reservoirs

Multi-stage hydraulic fracturing of horizontal wells is a key technique used for exploiting shale gas reservoirs at present. Moreover, it has become a commercially successful technique. The application of this technique has changed the fracturing area effectively. Due to the lack of the knowledge about the initiation and extension of the fracture branches, the hydraulic fracturing design is rough. The application of the minimum action principle makes the Lagrangian function satisfy the Hamiltonian integral condition, and the Lagrangian function is composed of the fluid pressure energy, fluid kinetic energy, elastic energy, rock surface energy and frictional loss energy. The virtual number and virtual length models of fracture are established, which can describe the complexity of fractures. The single factor analysis on the virtual number model and the growth rate model of fracures show that the Young’s modulus and Fanning’s friction coefficient have a significant effect on the number of fractures, and the net pressure and Fenning friction coefficient have a significant effect on the growth rate of fractures. The field study in Weiyuan-Changning block show that the virtual number of fractures in W1 well is higher than that of N1 well, and the reservoir volume of W1 well is better than that of N1 well, and the complexity of W1 well is better. The virtual number of fractures can reflect the actual complexity, which provides theoretical guidance for completion engineers to improve the design and analysis accuracy of shale gas reservoir fracturing.