Modeling the Hydraulic Fracturing Processes in Shale Formations Using a Meshless Method

Complex bedding properties and in situ stress conditions of shale formation lead to complex hydraulic fracturing morphologies. However, due to the limitations of traditional numerical methods, the simulation of hydraulic fracturing in shale formation still needs further development. Based on this, the liquid–solid interaction modes and the SPH governing equations considering liquid–solid interaction force have been introduced. The smoothing kernel function in the traditional SPH method is improved by introducing the fracture mark ξ, which can realize the simulation of rock hydraulic fracturing processes. The stress boundary of the SPH method is applied by stress mapping of “stress particles”, and the feasibility and correctness of the method are verified by two numerical examples. Then, the simulation of hydraulic fracturing processes of bedding shale formations are carried out. With the increase of horizontal stress ratio, the total number of damaged particles decreases, but the initiation and extension pressure increase gradually. The initiation stress of small bedding dip angles (θ 45°). The hydraulic fracture propagation range at low horizontal stress ratio is wider and the fracture is along the direction of maximum principal stress, while the hydraulic fracture propagation range at high horizontal stress ratio is limited to the perforation. The hydraulic fracture will propagate through the bedding with small dip angles. However, when the bedding dip angle is larger, the hydraulic fracture will propagate along the bedding direction.