基于万能网格及相场的水力压裂多尺度数值模拟方法

Energy shortage constrains our country’s economic development. As an energy source with a high amount of reserves, shale gas is attracting the attention of our country. The core technique to extract shale gas is hydraulic fracturing. Since this process has a large length scale and is not easy to be directly observed, and relevant experiments are expensive, computer simulations to predict the fracturing process are an important step in the design of the process. However, major numerical methods like the displacement discontinuity method, the traditional and extended finite element methods, and the discrete element method, all have their own limitations; it is difficult to generalize them to the case with multi-fracturing and inhomogeneous rock mass. This project will be built upon the applicant’s preliminary work and aims at developing a multi-scale finite element method for multi-fracturing based on universal meshes and phase-field models for guiding the practice of hydraulic fracturing. In particular, we will build our finite element method for fracture branching and crossing with natural fractures based on universal meshes, and adopt phase-field models as criteria for fracture branching. Considering the cost of phase-field methods, this project divides the entire calculation into two scales: extracting the general propagation and branching behaviors from a calculation for the region around the fracture tip (fine scale) and building such behaviors into a library, then applying them to the coarse-scale calculation for the evolution of the entire fracturing process. After test-runs, the coarse-scale part of the code will be implemented in a commercial software, which will benefit the scientific and industrial communities as a useful tool.

能源短缺制约着我国的经济发展。作为储量较大的能源，页岩气正引起国家的高度重视。水力压裂是开采页岩气的核心技术。由于尺度大且不方便直接观测，相关实验亦相当昂贵，利用计算模拟预测压裂过程成为工艺设计的重要环节。然而，目前主流的计算方法―位移间断法、传统及扩展有限元法和离散元法―各有其局限性，难以推广到多裂缝及岩土不均匀的情况。本项目将在申请人相关工作基础上，开发出针对页岩受水压形成多裂缝的多尺度有限元计算方法，用以指导水力压裂的实践。具体计划为利用万能网格法开发针对裂缝分叉及与天然裂缝交叉的有限元方法，同时使用相场方法作为判断裂缝分叉的准则。考虑到相场方法的成本，本项目计划把整体的计算分为两个尺度，通过对裂缝尖端附近区域的计算（小尺度）得出裂缝扩展及分叉的规律，总结成数据库并应用到大尺度计算中，模拟整个压裂过程。其中大尺度部分调试后将实现到有限元商业软件中，为科研及产业同行提供有用的工具。

能源短缺制约着我国的经济发展。作为储量较大的能源，页岩油气的开采技术已引起国家的高度重视。水力压裂是开采页岩气的核心技术。由于尺度大且不方便直接观测，相关实验亦相当昂贵，利用计算模拟预测压裂过程成为工艺设计的重要环节。本项目旨在发展相关的计算模拟方法。针对页岩受水压形成多裂缝的过程，本项目提出的多尺度有限元计算方法具体分为微观和宏观两个尺度：在微观尺度，采用断裂相场法获得裂缝扩展的规律；在宏观尺度，采用万能网格等方法为演化中的裂缝快速生成匹配网格。结合申请人的工作基础，即可模拟二维及三维压裂过程（三维限于平面裂缝）的水力压裂流固耦合问题。.断裂相场方面，项目执行期间取得的成果有：(1)通过均匀化方法得出统一的含拉压分解的本构关系及裂缝扩展的规律；(2)从图形加速器和网格自适应划分两个方面提高断裂相场法的计算效率；(3)借鉴图像识别的手段识别裂纹路径。.万能网格等宏观方法方面，项目执行期间取得的成果有：(1)提出了克服均匀和非均匀材料裂尖奇异性的映射有限元法和映射位移不连续法，均达到最优收敛率；(2)基于新的材料变分场推导了无需引入虚裂纹的弯裂纹应力强度因子计算格式；(3)发展了为二、三维分叉裂纹问题快速生成匹配网格的万能网格法，每当裂缝有所更新时，只需要微调少许结点位置即可生成匹配的网格。.受本项目资助共发表SCI论文5篇，其中包括计算力学顶级期刊International Journal for Numerical Methods in Engineering和Computer Methods in Applied Mechanics and Engineering各2篇；EI论文2篇；会议论文2篇。.