低渗油气层水力压裂三维正交型裂纹扩展、交叉模拟的新型扩展有限元

Hydraulic fracturing is one of the key technique in the field of mining in low permeability oil and gas reservoirs. Due to the existence of complex fracture networks, modelling by using the existing extended finite element method (XFEM) is still challenging due to two main reasons. First, the traditional way in XFEM by using Heaviside function to treat the displacement discontinuity will become extreme cumbersome when the interaction among multiple cracks is considered. Second, although first order crack tip functions are effective in dealing with the stress singularity problem, dense local mesh is required to get satisfactory results, and when large scale hydraulic fracturing model in which the local crack behavior must also be predicted accurately is considered, the resulted computational cost may be unacceptable. In this project, the two key aspects of XFEM is enhanced to form a new method with highly solving accuracy and efficiency for the modelling of three-dimensional (3D) orthotropic crack of hydraulic fracturing. On one hand, the floating nodes are introduced to replace the Heaviside enrichment function, the location of these floating nodes are placed on the interaction points of cracks automatically to model complex geometry configuration of the cracks explicitly. On the other hand, the symplectic eigen solution of 3D crack with arbitrary crack surface traction is intended to be developed by using the symplectic approach, to construct a new symplectic analytical singular element (SASE) to replace the crack tip enrichment function of XFEM, to eliminate the necessary of local dense mesh. The new findings of this project intends to provide a new way of numerical modelling for complex 3D crack problem, and provide an effective numerical analyze tool for the study on the mechanism of formation of fracture network and the design of operation scheme of hydraulic fracturing in engineering practices.

水力压裂是低渗油气田开采中的关键技术之一。由于存在庞杂的缝网，应用现有的扩展有限元法分析面临两方面挑战。第一，应用阶跃函数处理多裂纹交叉带来的位移不连续时将变得十分复杂；第二，低阶裂纹场函数虽可处理应力奇异性问题，但需局部加密网格，这对于需兼顾局部裂纹行为的大尺度水力压裂模型而言会导致计算量不可接受。本项目拟通过对扩展有限元法中两个核心技术的改进，形成可模拟三维正交型水力压裂裂纹的高精度、高效率的方法。即，一方面通过引入浮节点来代替阶跃函数，并根据交叉裂纹的构型将浮节点自动分布在交点上，从而在几何上模拟裂纹构型；另一方面，通过使用辛方法推导出的适用于表面有任意作用力的三维裂纹辛本征解，构造一类辛解析奇异元来代替低阶裂纹场加料函数，以解决局部网格加密问题。拟取得的研究成果不仅将可能为处理复杂三维裂纹问题提供新思路，而且将可能为研究缝网形成的机理以及水力压裂方案的设计提供有效的数值分析工具。

针对低渗油气田开采中的水力压裂关键技术，通过改进现有扩展有限元法，解决了数值模拟两方面的挑战。第一，解决了应用阶跃函数处理多裂纹交叉时带来的位移不连续分析的复杂性；第二，解决了由于低阶裂纹场函数需局部加密网格的问题，从而显著缓解了大尺度水力压裂模型的计算量问题。本项目通过对扩展有限元法中两个核心技术的改进，形成了可模拟三维正交型水力压裂裂纹的高精度、高效率的方法。即，一方面通过引入浮节点来代替阶跃函数，并根据交叉裂纹的构型将浮节点自动分布在交点上，从而在几何上模拟裂纹构型；另一方面，通过使用辛方法推导出的适用于表面有任意作用力的三维裂纹辛本征解，构造了一类辛解析奇异元来代替低阶裂纹场加料函数，从而解决了局部网格加密问题。研究成果发表在高水平国际期刊上，不仅可为处理复杂三维裂纹问题提供新思路，而且为研究缝网形成的机理以及水力压裂方案的设计提供了有效的数值分析工具。

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