准脆性地层中水平井多段水压致裂的扩展有限元法模拟

Simulation of Multi-stage Fracturing of Horizontal Wells in Quasi-brittle Stratum by Extended Finite Element Method

在实际的水力压裂过程中,裂缝总是沿着垂直于最小地应力的方向扩展,地应力的分布形式和多个压裂段之间的互相影响(应力阴影效应)对于形成复杂的裂缝网络具有重要的影响。本文基于扩展有限单元法(XFEM)模拟页岩等多孔介质在水压作用下裂缝的任意扩展,由于在传统有限元法的基础上引入了扩充自由度和可以描述间断的位移阶跃函数,所以裂缝可以独立于网格扩展,而不需要重新剖分网格。通过引入一维流动假设,求解润滑方程,并考虑流体在裂缝内的流动。同时也考虑裂缝向基质中流动的滤失效应。研究实际施工中不同段间距下裂缝的扩展模式和段间距对裂缝形态的影响,结果表明,压裂段间距过小时中间的裂缝会被屏蔽;此外,裂缝会由于应力阴影效应而发生转向。

In the actual hydraulic fracturing process, the fracture always extends along a direction per- pendicular to the minimum stress. The distribution of the in-situ stress and the interaction between mul- tiple fractures （stress shadow effect） play important roles in the formation of a complex fracture net work. Based on the extended finite element method （XFEM）, in this paper, we simulate the arbitrary propagation of fractures in porous media. Since we introduce the enriched degree of freedom based on the traditional finite element method （FEM）, with which we can describe discontinuous displacement, the fracture can be propagated independent of the mesh. By introducing a one-dimensional flow assumption, we solve the lubrication equation, taking into account the flow of the fluid in the fracture. At the same time, we also consider the leak-off effect of the fracture on the matrix. We investigate the influence of the propagation pattern and stage distance on the fracture morphology under different perforation spacing in the actual construction. The results show the fracture in the middle is shielded when the stage spacing is too small. In addition, the fracture will turn due to the stress shadow effect.