水力压裂过程的扩展有限元数值模拟方法

EXTENDED FINITE ELEMENT MODELING OF HYDRAULIC FRACTURE PROPAGATION

建立了基于扩展有限元法的水力压裂数值模拟方法,使水力裂缝独立于网格存在,无需预设裂缝扩展方位。在扩展有限元计算框架下,将裂缝面处理为求解域内边界,将缝内水压力转化为相关单元等效节点力;运用考虑缝内水压力作用的相互积分法来数值求解缝尖应力强度因子;采用最大能量释放率准则确定裂缝是否继续扩展及扩展方位;最终编制了计算机程序。利用该方法数值模拟了单条水力裂缝在恒定水压力作用下作非平面扩展,所得结果分别与室内试验和解析模型相对比。结果表明,数值结果与室内试验和解析解吻合较好,缝尖应力强度因子最大相对误差不高于0.45%,验证了该方法的可行性和准确性。

This paper proposed a numerical scheme to simulate the hydraulic fracture propagation in a frame by an extended finite element method, in which a crack representation is explicit and independent of the mesh grid. The crack faces are treated as internal boundaries, which are opened and supported by hydraulic pressure. An integral scheme is presented to an equal the hydraulic pressure as nodal forces. The interactive integral method is used to calculate the stress intensity factor with the consideration of hydraulic pressure on crack faces. The maximum energy release criterion is selected to determine the propagation condition and crack direction. The corresponding code was prepared and used to simulate the non-planar propagation of a single hydraulic fracture with a constant hydraulic pressure. The numerical results are compared with the lab test and the analytical model. The results show that the numerical results of mode I have an excellent agreement with analytical results, in which the maximum relative error is below 0.45%.