Two primary challenges in simulating hydraulic fracturing are the hydro–mechanical coupling and fracture propagation. The material point method (MPM) has advantages over conventional numerical methods by combining the advantages of particle- and mesh-based approaches in handling highly non-linear hydraulic fracturing problems. However, as MPM is primarily utilized for continuous solid simulations, therefore, to realize hydraulic fracturing simulation, a new MPM is proposed considering the discontinuous fields and seepage fields. The two-phase double-point MPM is used to simulate hydro–mechanical coupling within porous medium and fractures. Additionally, it employs the phantom-node method in conjunction with classical fracture mechanics to simulate fracture propagation, with the effect of fracture propagation on the seepage field considered by introducing an transition function. Subsequently, a comprehensive calculation process is presented. The accuracy of the proposed MPM is validated through comparison with finite element method results in two instances involving hydro–mechanical coupling and fracture propagation. Lastly, the MPM algorithm is deployed for simulating hydraulic fracturing within single and multiple fractures, followed by a detailed analysis of the hydraulic fracturing process.

中文翻译：

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多孔介质水力压裂质点法模拟方法

模拟水力压裂的两个主要挑战是水力耦合和裂缝扩展。质点法 (MPM) 结合了基于粒子和网格的方法在处理高度非线性水力压裂问题时比传统数值方法具有优势。然而，由于MPM主要用于连续固体模拟，因此，为了实现水力压裂模拟，提出了一种考虑不连续场和渗流场的新MPM。两相双点 MPM 用于模拟多孔介质和裂缝内的水力耦合。此外，采用幻像节点法结合经典断裂力学模拟裂缝扩展，通过引入过渡函数考虑裂缝扩展对渗流场的影响。随后，给出了综合计算过程。通过与涉及水力耦合和裂缝扩展的两个实例中的有限元方法结果进行比较，验证了所提出的 MPM 的准确性。最后，采用MPM算法对单裂缝和多裂缝内的水力压裂进行模拟，并对水力压裂过程进行详细分析。