考虑支撑剂输运的三维水力压裂并行扩展有限元方法研究

Hydraulic fracturing is one of the key measures for shale gas development. Proppant transport has a significant influence on the conductivity of fracture network. However, it still lacks effective hydraulic fracturing models considering proppant transport in both academia and engineering community. Moreover, existing models are difficult to meet the growing engineering application requirements because they are mostly based on plane strain assumption and short of research on large-scale parallel computing algorithms. In this research project, a three-dimensional solid-fluid-proppant coupling model and corresponding solution algorithms will be established by fully taking advantage of the extended finite element method (XFEM) and overcoming the deficiencies of the finite element method (FEM) induced by massive remeshing, and then the model will be adopted to study the evolution mechanism of fracture network in reservoir. In order to clarify the mechanism of proppant transport and allocation within L-shaped, T-shaped and cross-shaped junction fractures, a proppant transport model will be established on the basis of experimental study. Aiming at hydraulic fracturing simulation with more than ten million degrees of freedom and improving the simulation efficiency, a dual adaptive partitioning scheme together with an optimized pre-conditioner of sparse linear systems will be developed based on the principle of load balancing. Based on the above study, a hybrid MPI/OpenMP parallel simulation system for three-dimensional hydraulic fracturing in consideration of proppant transport will be established, which provides the theoretical basis and technical support for quantitative fracturing design and scientific evaluation of fracturing treatment.

水力压裂是页岩气开发的核心增产措施之一，其中支撑剂的输运对压裂缝网的导流能力有着重要影响，然而学术界和工程界一直缺少有效的考虑支撑剂输运的压裂模型。此外，现有压裂模型多基于平面应变假设，且缺乏大规模并行计算优化算法研究，难以满足日益增长的工程应用需求。本项目充分发挥扩展有限元法的优势，克服有限元法需要大量网格重构的不足，构建三维“固体-流体-支撑剂”耦合模型及其求解算法，揭示储层压裂缝网演化规律；结合实验，建立L型、T型和十字型交叉裂缝支撑剂输运模型，阐明支撑剂分配的力学机理；依据负载均衡原则，提出双重自适应区域剖分算法，探索稀疏线性系统的最优预条件子，实现千万以上自由度的求解规模，提高压裂仿真的求解效率。基于上述研究，项目将形成考虑支撑剂输运的三维水力压裂MPI/OpenMP混合并行仿真系统，为压裂参数定量化设计和压裂效果科学预测提供理论依据和技术支撑。

水力压裂技术是页岩气等非常规能源开采的核心增产措施。压裂过程中，支撑剂随着压裂液进入水力裂缝并保持裂缝张开，为页岩气的抽采提供有效的裂缝网络。本项目基于扩展有限元方法，建立了真三维流固耦合模型，给出了逐个单元共轭梯度求解器及其预处理器。基于显式裂缝面描述算法、Schöllmann裂缝扩展准则以及Taubin光滑算法，构建了任意复杂裂缝网络的扩展演化模型。提出了基于裂缝面两侧高斯积分点数目的增强节点选择判据，从而有效解决了刚度矩阵条件数高、线性方程组收敛性差的问题。导出了压剪型天然裂缝增强自由度罚函数表达式，避免了大量天然裂缝的接触迭代，有效降低了整体计算量。构建了三维空间L型、T型和十字型交叉裂缝支撑剂运移力学模型，借助有限差分算法建立了支撑剂分配模型，并实现了“固体-流体-支撑剂”耦合仿真，揭示了储层压裂缝网演化规律。在动态区域剖分算法的基础上，借助MPI/OpenMP实现了大规模并行计算，通过优化数据结构大幅降低了内存占用。本项目建立的考虑支撑剂输运的三维水力压裂并行扩展有限元数值计算模型，为工程尺度大规模水力压裂仿真提供了有效工具。在本项目的资助下，共出版专著1部，发表SCI论文5篇，取得软件著作权1项。