Heterogeneous rock modeling method and characteristics of multistage hydraulic fracturing based on the PHF-LSM method

The production of oil and gas can be enhanced by the multistage hydraulic fracturing. The PHF-LSM method, which is combined by the level set method (LSM) and a permeability-based hydraulic fracture (PHF) model, is introduced in this paper. LSM is used for implicitly modeling the heterogeneity of the different-scaled rock matrix, and the PHF model, which was previously used for a single point hydraulic fracture simulation, is extended for simulating multi-fracture development. The heterogeneities of the three interested rock types consist of randomly layered features in both horizontal and vertical directions, the rock matrix with irregular inclusions randomly distributed, and the property distribution of rock determined by the spatial coordinates. LSM functions are given for implicitly describing the rock matrix by introducing continuous random variables. The PHF model is used for simulating the fracture development in the proposed rock types under single point fracturing, multipoint simultaneous fracturing and multistage fracturing. Numerical simulations are performed to study the behavior of fracture propagation. The results address the characteristics of breakdown pressure, stress path, time history of pore pressure and the development of hydraulic fractures when the spacing of injection points varies from small to large range. They indicate that the proposed implicit modeling method works well with the PHF model for simulating the procedures of multipoint and multistage fracturing.